High Temperature Materials

VelTech Dr.RR & Dr.SR Technical University

AE2354 - High Temperature Materials

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UNIT – I

HIGH TEMPERATURE MATERIALS

1. CREEP :

Creep may be defied as the slow and progressive deformation of a material with time

under a constant stress at a temperature approximately above 0.4 Tm, i.e.., the recrystallisation

temperature of the material (Where Tm is the melting point of the metal or alloy in degrees Kelvin).

Creep is function of temperature and time. Creep deformation is plastic in nature and occurs even

though the acting stress is below the yield stress of the material. The rate of creep is very small

but at higher temperatures it becomes very significant.

Certain metals such as lead and tin which have low melting temperatures creep at room

temperature.

Creep behaviour is very much important when studying the behaviour of materials that are

used in high temperature applications. For example steam plants, gas turbines, nuclear reactor,

body of space crafts, tungsten filaments used in electric bulbs and radiator shields in furnaces are

mede of molybdenum.

Creep strength of a metal is usually defined by the limiting stress below which creep is so

slow that it will not result in fracture within any finite length of time. Similarly Creep rupture

strength or rupture strength of a material is the highest stress that a material can with stand for a

given time without rupture.

Creep limit may be defined as the maximum stress that will cause creep to occur at a rate

not exceeding the specified deformation at a given temperature. In general the creep rate is higher

and time to fracture shorter with increasing temperature and load.

Creep curve

The creep is tested for a material by subjecting the specimen at constant tensile stress at

constant temperature and measuring the extent of strain or deformation with respect to time. (The

creep test is similar to a tension test but under the influence of temperature). A typical creep

curve is shown in figure.



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Figure

The curve shows three stages of elongation.

I. (a) Initial instantaneous elongation after the application of load.

(b) Primary of Transient creep.

II. Secondary or viscous or steady state creep.

III. Tertiary creep or accelerated creep.

Instantaneous elongation : This a stage that is initially observed. With the first application of

load an instantaneous elastic strain occurs. If the initial load applied is higher then there is some

plastic strain, in such a case the instantaneous elongation is elastic strain + plastic strain.

Primary creep or Transient creep : At the beginning of primary creep there is strain hardening

effect (i.e., The material resists deformation and becomes hard due to its own elongation ) and the

deformation is slow at a decreasing rate.

For low melting temperature metals, primary creep is the predominant creep process.

Secondary creep or steady state creep : In this region the creep is constant and the creep rate is

constant. The reason for this steady state is due to an equilibrium between the strain hardening

effect and the annealing effect.

Since creep occurs at an elevated temperature the annealing effect occurs to and the

material tends increase in strain causes the material to resist further deformation hence there is a

balance between the strain hardening effect and the annealing effect which results is a steady state

creep. The constant creep rate of the secondary stage is usually assumed to be the material’s

minimum rate and is called as minimum creep rate (MCR).



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Tertiary creep or accelerated creep : This is the final stage of creep before fracture. The creep

occurs rapidly because of a decreases in cross-sectional area and necking of the specimen occurs,

the true stress increases rapidly. During this stage there is progressive damage to the

intercrystalline regions by the formation of voids and sivere oxidation of the metal (note :

oxidation occurs because the material is tested for creep at elevated temperature). The material is

unable to strain harden and finally fractures. Du ring tertiary creep there are changes to the

microstructure, grain coarsening and recrystallisation, these factors are also responsible for the

acceleration of the creep.

Creep fracture :

At high temperatures grains show more strength than grain boundaries and at low

temperatures grain boundaries are stronger than the grains. The temperature at which the

strength of grains equal the grain boundaries is called equicohesive temperature. The crack

always initiates and propagates through weak portion and hence below equicohesive

temperature. Creep is a high temperature process and hence fractures always occurs by

intergranular mode.

Figure:

Creep Variables

Creep resistant materials are used at high temperatures. They are capable of withstanding

such temperatures without undergoing creep upto a certain limit.

The following are the factors that influence the creep property of a material.

(i) Higher creep resistance is observed with metals having high melting point. Creep

becomes significant above 0.4 Tm . Metals such as iron, cobalt, molybdenum, tungsten

that have high melting temperature are used in high temperature services.

(ii) A coarsed grained metal has high creep resistance than a fine gained metal. At creep

temperatures the grain boundaries become quasi – viscous. The coarse grained

materials have less total grain boundary and hence it. Developes less quasi - viscous



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Single crystals have excellent creep resistance because they have no grain boundary.

(iii) Dispersion hardening improves creep resistance.

(iv) Metals having higher oxidation and scaling resistance have more creep strength.

(v) For steels, increase in carbon content increases creep resistance.

(vi) Aluminium, when added to steal acts as deoxidizer, this makes the steel to resist creep.

(vii) Creep resistance is increased by adding alloying elements such as; W, Mo, V, Cr, Ti, Nb

and Co, these elements form carbides with the iron present in steel. The presence of

carbides increase the resistance to soften at elevated temperatures thus resisting creep.

2. Materials for elevated temperature use :

A material suitable for high-temperature service should possess a high melting point and

modulus of elasticity, and low diffusivity. In addition, such materials must possess a

combination of superior creep strength, thermal fatigue resistance, and oxidation and hot

corrosion resistance. As a result, alloy development has focused primarily on nickel-and cobalt-

based superalloys, with earlier iron-based alloys being replaced because of their relatively low

melting point and high diffusivity. These high-temperature alloys have been produced by several

methods including casting, mechanical forming, powder mechanical alloying.

For the case of nickel-based superalloys, constituent elements are introduced to enhance

solid solution properties, as precipitate and carbide formers, and as grain boundary and free

surface stabilizers. Tungsten (W), molybdenum (Mo), and titanium (Ti) are very effective solid

solution strengtheners : W and Mo also serve to lower the diffusion coefficient of the alloy. (There

is a general inverse relation between the melting point and alloy diffusivity). Though the

incremental influence of chromium (Cr) on solid solution strengthening is small (i.e., dT/dc is

low), the overall solid solution strengthening potential of Cr in nickel (Ni) alloys is large since

large amounts of Cr can be dissolver in the Ni matrix. Cobalt (Co) provides relatively little solid

solution strengthening but serves to enhance the stability of the submicron-size Ni3(AI,X)

()precipitates within the nickel solid solution () matrix (Figure(a)). Within the phase, X

corresponds to the presence of Ti, niobium (Nb),or tantalum (Ta). The difficulty of dislocation

motion through the ordered particles in these alloys is responsible for their high creep strength

at elevated temperatures. Of particular note, the phase exhibits unusual behavior in that

strength increases by three to sixfold with increasing temperature from ambient to approximately

700oC.70-72



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FIGURE :Electron micrographs revealing Ni3AI precipitates () in a nickel solid solution ( )

matrix. Matrix. (a) Cubic from in MAR M-200. (b) Rafted morphology in Ni-14.3 Mo-6Ta-5.8AI

(Alloy 143). Tensite stress axis is in vertical direction and parallel to [001] direction. Creep

tested with 210 MPa at 1040C. (Courtesy E. Thompson).

Also noteworthy is the fact that precipitates in single-crystal alloys tend to coarsen under

stress at 1000C and form thin parallel platelike arrays that are oriented normal to the applied

stress axis. Recent studies have confirmed that alloy creep resistance is enhance by the

development of this ‚rafted‛ microstructure, it is believed that the absence of dislocation climb

around the particles, due to their lenticular shape, forces dislocations to cut across the ordered

phase. As note in Section 4.4.2, this dislocation path enhances the alloy’s resistance to plastic

flow.

The presence of carbides along grain boundaries in polycrystalline alloys serves to restrict

grain- boundary sliding and migration. Carbide formers such as W, Mo, Nb, Ta, Ti, Cr, and

vanadium (V) lead to the formation of M7C3,M23C6, M6C, and MC, with MC carbides being most

stable (e.g., TiC). When Cr levels are relatively high, Cr23C6 particles are formed.

Surface stabilizer include Cr, Al, boron (B), zirconium (Zr), and hafnium (Hf). The presence

of Cr in solid solution allows for the formation of Cr2O3, which reduces the rate of oxidation and

hot corrosion, Aluminum contributes to improved oxidation resistance and resistance to oxide

spalling. Finally, B, Zr, and Hf are added to impart improved hot strength , hot ductility, and

rupture life.75Cobalt-based alloys derive their strength from a combination of solid solution

hardening and carbide dispersion strengthening. The mechanical properties of representative

nickel-based and cobalt-based alloys are given in Table 5.3; references 63 to 68 provide additional

information concerning these materials.

Recent efforts to improve the high-temperature performance of superalloys have tended

more toward optimizing component design and making use of advance processing techniques

rather than tinkering with alloy chemistry.76 For example, when inlet guide vanes and first-stage



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turbine blades of the gas turbine engine are air cooled via internal channels, the gas turbine inlet

temperature can be increased markedly with a concomitant improvement in engine operating

efficiency. Several processing techniques have been developed and applied to the manufacture of

gas turbine components.

TABLE : Mechanical Properties of Selected Superalloys :

Date correspond to 816oC (1500oF).

Directionally solidified.

Extrapolated values.

Data courtesy Inco Alloys Inc.

One such technique involves the directional solidification of conventional superalloys to

produce either highly elongated grain boundaries or single-crystal components (Figure). Helical

molds are used to cast single-crystal turbine blades; multiple grains form initially and grow into

the helical section of the mold. The faster growing (100) –oriented grains then crowd out other

grains until a single (100) grain is left to fill the mold cavity.77-79 Current sophisticated mold

designs now allow for the simultaneous growth of two turbine blades form the same single

crystal.79 The alignment of airfoils (turbine blades) along the (100) axis parallel to the centrifugal

stress direction allows for a 40% reduction is the elastic modulus and associated lower plastic

strain range during thermal fatigue cycling; a 6- to 10- fold improvement in thermal fatigue

resistance is thus achieved. Since grain boundaries are eliminated, their influence on grain-

boundary sliding, cavitation, and cracking is obviated.77,78 furthermore, it is no longer necessary to

add such elements as hafnium, boron, carbon, and zirconium for the purpose of improving grain-

boundary hot strength and ductility.80 without these elements, the incipient melting temperature

of the alloy is in creased by approximately 120oC and the alloy chemistry simplified. The

development of cast superalloys turbine blades is shown in Figure (a) ; the relative ranking of the

rupture lifetime for equiaxed and columnar polycrystalline alloys is compared with that of

single-crystal alloys in Figure b. By applying unidirectional solidification to alloys of eutectic



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composition, it has been possible to produce eutectic composite alloys possessing properties

superior to those found in conventional superalloys (figure). A number of these alloys contain a

/ matrix that is reinforced with high-strength whiskers of a third phase; these strong

filamentary particles are oriented.

FIGURE: conventional and directional solidification used to prepare gas turbine blades with

equiaxed, columnar, and single-crystal morphologies. (F.L.VerSnyder and E.R. Thompson,

Alloys for the 80’s, R.Q. Bar, Ed., Climax Molybdenum Co., 1980, p.69 : with permission.)

(a) (b)

Figure: (a) Development of turbine blade temperature capability.

(b) Comparative high temperature strength and corrosion resistance of equiaxed, columnar,

and single-crystal superalloys.79 (Reprinted with permission from Journal of Metals, 39(7),

11(1987), a publication of the Metallurgical Society, Warrendale, PA. 15086.)



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Figure : 1000-hr strength as a function of temperature in eutectic superalloys and conventional

directionally solidified single-crystal and oxide-dispersion-strengthened superalloys. In situ

(eutectic) composites reveal generally superior stress rupture behavior. (From Lemkey81,

reprinted by permission of the publisher from F.D. Lemkey, Proceeding, MRS Conference, CISC

IV, Vol. 12, F.D. Lemkey, H.E. Cline, and M. McLean, Eds., copyright by Elsevier science

Publishing Co., Inc., Amsterdam, (c ) 1982.) parallel to the maximum stress direction. A though

the properties of these alloys are very good, the allowable solidification rates for their

manufacture are much lower than those permissible in the manufacture of directionally solidified

columnar or single-crystal microstructures. One is then faced with a trade-off between the

superior properties of eutectic composites and their higher manufacturing costs.

Another new fabrication technique involves forging under superplastic conditions. In this

process, the material is first hot extruded just below the solvus temperature, which causes the

material to undergo spontaneous recrystallisation. Since the precipitates in the nickel solid

solution matrix tend to restrict grain diameter remains relatively stable in the size range of 1 to5

m . The part is then forged isothermally at a strain rate that enables the material to deform

superplastically (recall Section). At this point, the superplastically formed component is solution

treated to increases the grain size for the purpose of enhancing creep strength . The material is

then quenched and aged to optimize the / microstructure and the associated set of mechanical

properties. One major advantage of superplastic forging is its ability to produce a part closer to

its final dimensions. One major advantage of superplastic forging is its ability to produce a part

closer to its final dimensions, thereby reducing final machining costs.

Superalloys can also be fabricated from powders produced by vacuum spray atomization

of liquid or by solid-state mechanical alloying techniques (recall Sect4.5). Powders may then be

placed in a container that is a geometrically larger version on the final component shape. The can

is then heated under vaccum and hydrostatically compressed to yield a fully dense component



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with dimensions close to the design values. The microstructure of hot isostatically pressed (HIP)

Astroloy superalloys is shown in Figure.5.33a. Note the persistence of the necklace of prior

particle boundary borides, carbides, and oxides that surround the atomized powder particles.

Hot isostatic pressing is also being used to heal defects in conventionally cast parts and to heal

certain defects in parts that experience creep damage in service.

With significant additions of formers, such as AI and Ti, mechanically alloyed oxide-

dispersion-strengthened (MA/ODS) products possess attractive strength levels over a broad

temperature range.84-85 Two such alloys are Ma6000 and Alloy 51, which contain approximately 55

v/o and 75 v/o , respectively (figure 5.33b).84-85 The 1000-hr rupture strength (normalized with

respect to density) of these alloys and others is shown in figure.5.34 as a function of temperature.

As expected, directionally solidified (DS MAR-M200) and single-crystal (PWA 1480) cast alloys

are superior to the two mechanically alloyed products at temperatures up to 900oC with the

relative rankings being reversed above this temperature. At high temperatures near the solvus

temperature, the particles that dominate the precipitation hardening process tend to coarsen

and/or go back into solution. The superiority of MA materials relative to that of directionally

solidified and single-crystal cast alloys at temperatures in excess of 900oC is due to the oxide-

dispersion-strengthening influence of the Y2O3 particles that remain in the microstructure and do

not coarsen to any significant degree.

Recent attention has focused on the unusual creep rate and rupture-life stress dependence

of ODS alloys. Whereas most pure metals and associated solid solutions reveal a 4 5

dependence of (recall Equation 5-15 and 5-20), the steady-state creep rate in ODS alloys exhibits

a stress dependency of 20 or more.70.87.86 furthermore, the apparent activation energy for the creep

process is found to be two three times.

FIGURE : Transmission electron micrographs of P/M nicket-based alloys.



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(a) Macrostructure of HIP’d Astroloy superalloys. Note persistent necklaces of prior particle

boundary borides, carbides, and oxides. (Reprinted with permission from J.S. Crompton and

R.w. Hertzberg, J.Mater Sci., 21,3445 (1986), Chapmen & Hall Pub.)

(b) Microstructure of MA 6000 showing precipitates (large light areas) and Y2O3 dispersoids

(small dark regions). (Photo courtesy W. Hoffelener from w. Hoffelener and R.F. singer ,

Metallurgical Transactions 16A, 393(1985).

FIGURE : Comparison of 1000-rupture strength (density corrected) in directionally solidified and

oxide-dispersion-strengthened nickel-based superalloys. Note superior properties of ODS alloys

at temperatures above 900oC .(Reprinted with permission from S.K.Kang and R.C. Benn,

Metallurgical Transactions, 16A, 1285 (1985).)

Greater than the activation energy for self-diffusion. Tien and coworkers have suggested that

these apparent difference in creep response can be rationalized by considering creep to be

dominated by an effective stress rather than the applied stress; the effective stress is defined as

the applied stress minus a back stress that reflects dislocation interactions with Y2O3 dispersion

strengthening particles. When the applied stress level is replaced by the effective stress value in

Equation.5-20, the stress dependency of s and apparent activation energy for creep are found to

be similar to those values corresponding to pure metals (i.e.,n4-5 and Hc HSD).

In corresponding fashion, the rupture life of ODS alloys can reveal a very strong applied

stress dependency and an upward slope change with increasing rupture lifetime, opposite to that

observed in many other alloy (e.g.recall Figure 5.3). Figure 5.35 reveals that MA6000 and Alloy 51

exhibit two regions of behavior; Region I corresponds to high stress levels and intermediate

temperatures and is dominated by the precipitates, At higher temperatures, lower stress levels

and longer times (Region II), stress rupture is dominated by the Y2O3 dispersoid phases. Note

that ODS alloy MA754, which contains no phase, does not exhibit Region I behavior;

conversely, cast alloy IN939, which contains no dispersion strengthening phase, exhibits no



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Region II behavior. Recent studies have sougth to clarify the nature of the dislocation dispersoid

particle interation so as to better understand the unique phenomenological behavior of ODS

alloys.

In another recent thrust, researchers have focused attention of the development of a gas

turbine engine using ceramic components. Since ceramics often possess higher melting points

and moduli of elasticity and lower diffusivities than metal systems, they offer considerable

potential in such applications. Unfortunately, ceramics suffer from low ductility and brittle

behavior in tension (see Table 10.8). This serious problem must be resolved before the ceramic

engine can become a reality. Progress toward this end is being made as discussed in Section

10.4.3.

Finally, fiber-reinforced superalloys are receiving increased attention as candidate materials

for structural used at elevated temperatures. Tungsten fibers hold promise as

FIGURE : Stress rupture response of MA/ODS cast nickel superalloys..84 (From R.C. Benn and

s.K.Kang, superalloys 1984, American Society for Metals, Metals Park, OH, 1984, with

permission.)

A suitable reinforcement for superalloys in that they possess superior high-temperature strength

and creep resistance.88 In addition, a good interface is developed between the superalloy matrix

and the tungsten fibers without excessive surface reactions that degrade W-fiber mechanical

properties. Preliminary studies have shown that operation temperatures of fiber-reinforced

superalloys may be increased by 175oC over that of unreinforced superalloys.

Whatever the alloy or process used to fabricate superalloy parts, the high-temperature

environments that are experienced demand that careful attention be given to the suppression of

oxidation and corrosion damage. To this end, coatings such as MCrAl/Y (where M = Ni, Co, and

Fe) may be placed on the component’s exterior surface; surface coatings with such compositions



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promote the formation and retention of Al2O3, which serves as an effective barrier to the diffusion

of oxygen into the component interior. Unfortunately, these coatings tend to spall away during

thermal cycling and must be stabilized. Other ceramics (e.g., ZrO2) may serve as thermal barrier

coatings (approximately 0.25 mm thick) that can reduce superalloy turbine blade surface

temperatures by as much as 125-2500C. Here, too the tendency for spallation due to thermally

induced strains must be suppressed.

3. TEMPERATURE-STRESS-STRAIN-RELATION

Since the creep life and total elongation of a material depends strongly on the magnitude of the

steady-state creep rate s (Equation 5-1 and 5-5), much effort has been given to the identification of

those variables that strongly affect s. As mentioned in Section 5.1, the external variables,

temperature and stress, exert a strong influence along with a number of material variables. Hence

the steady-state creep rate may be given by

1 2( , , , , )s f T m m

Where T = absolute temperature

= applied tensile stress

= creep strain

1m = various intrinsic lattice properties, such as the elastic modulus G and the crystal

structure

2m = Various metallurgical factors, such as grain and sub grain size, stacking fault energy,

and thermo mechanical history

It is important to recognize that 2m also depends on T, ,and . For example, subgrain

diameter decreases markedly with increasing stress. Consequently, there exists a subtle but

important problems of separating the effect of the major test variables on the structure from the

deformation process itself that controls the creep rate. Dorn, Sherby, and coworkers10-13 suggested

that where 0.5hT for the steady-state condition, the structure could be defined by relating the

creep strain to a parameter

( )f

Where = te-H/RT described as the temperature-compensated time parameter

t = time

H = activation energy for the rate-controlling process

T = absolute temperature

R = gas constant



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The activation energy H, shown schematically in Figure. Represents the energy barrier to

be overcome so that an atom might move from A to the lower energy location at B. Upon

differentiating Equation with respect to time, one finds .

/( ) H RTZ f e

Which describes the strain-rate-temperature relation for a given stable structure and

applied stress. When the rate process is given by the minimums creep rate .

s and its logarithm

plotted against 1/T, a series of parallel straight lines for different stress levels is predicted from

Equation (Figure). The slope of theses lines, H/2.3R, then defines the activation energy for the

controlling creep process. The fact that the is stress lines were straight in figure suggests that

only one process had controlled creep in the TiO2 single crystals throughout the stress and

temperature range examined. Were different mechanisms to control the creep rate at different

temperatures, the log .

s vs. 1/T plots would be nonlinear. When multiple creep mechanisms are

present and act in a concurrent and dependent manner, the slowest mechanism would control .

s . The overall strain rate would take the form

. . . . .

1 2 3

1 1 1 1 1...

T n

Where .

T = overall creep rate .

1,2,3,....,n = creep rates associated with n mechanisms

For the simple case where only two mechanisms act interdependently

. .

1 2. .

1 2

T

Conversely, if the n mechanisms were to act independently of one another, the fastes one

would control. For this case, .

T would be given by

. . . . .

1 2 3 ...T n



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Figure: Diagram revealing significance of activation energy required in moving an atom form

A to B.

To determine the activation energy for creep over a small temperature interval, where the

controlling mechanism would not be expected to be expected to vary, researchers often make use

of the temperature differential creep test method. After a given amount of strain at temperature

T1, the temperature is changed abruptly to T2, which may be slightly above or below T1. The

difference in the steady-state creep rate associated with T1 and T2 is then recorded (figure). If the

stress is held constant and the assumption made that the small change in temperature does not

change the alloy

Figure. Log steady-state creep rate versus reciprocal of absolute temperature for rutile (TiO2.)

at various stress levels. (From W.M.Hirthe and J.O. Brittain;14reprinted with permission from

the American Ceramic society, Copy right ( C ) 1963).



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Figure. Incremental step test involving slight change in test temperature to produce change n

steady-state creep rate in aluminum. ( From J.e. Dorn, Creep and Recovery, reprinted with

permission from American Society for Metals, Metals Park, OH, copyright (c ) 1957).

Structure, then Z is assumed constant. From Equation the activation energy for creep may

then be calculated by

. .

1 2

2 1

/

1/ 1/c

RInH

T T

Where CH = activation energy for creep

. .

1 2 = creep rates at T1 and T2, respectively

This value of CH should correspond to the activation energy determined by a data

analysis like that shown in Figure, as long as the same mechanism controls the creep process over

the expanded temperature range in the latter instance. As shown in Figure, this not always the

case. The activation energy for creep in aluminum is seen to increase with increasing temperature

up to Th 0.5, whereupon CH remains



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FIGURE. Variation of apparent activation energy for creep in aluminum as a function of

temperature. (From O.D. Sherby, J.L. Lytton, and J.E. Dorn,13 reprinted with permission from

Sherby and Pergamon Press, Elmsford, NY, 1957).

Constant up to the melting point. Similar results have been found in other metals. It would

appear that different processes were rate controlling over the test temperature range.

furthermore, it should be recognized that CH may represent some average activation energy

reflecting the integrated effect of several mechanisms operating simultaneously and

interdependently (see Section ).

Dorn, Garofalo, and Weertman have compiled a considerable body of data to demonstrate

that at hT , CH is most often equal in magnitude to sDH , the activation energy for self-

diffusion Figure; this fact strongly suggests the latter to be the creep rate-controlling process in

this temperature regime. While the approximate equality between CH and SDH seems to hold

for many metals and ceramics at temperatures equal to and greater than half the melting point,

some exceptions do exist, particularly for the case of intermetallic and nonmetallic compounds.

It is found that small departures from stoichioometry of theses compounds have a pronounced

effect on CH , which in turn affects the creep rate. For example , a reduction in oxygen content

in rutile from TiO2 to TiO1.99 causes a reduction in CH from about 280 to 120 kJ/mol(67-29

kcal/mol)* with an associated 100-fold increase in .

s14 for the more general case, however, the

creep process is found to be controlled by the diffusivity of the material

/SDH RToD D e

Where D = diffusivity, cm2/s

D0 = diffusivity constant 1 cm2/S

SDH = activation energy, J/mol

R = gas constant, J/K

T = absolute temperature, K



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FIGURE. Correlation between activation energy for self-diffusion and creep in numerous

metals and ceramics. (From J. Weertman,16 reprinted with permission from American society

for Metals, Metals Park, OH, copyright (c ) 1968.

( ) /o mk V T ToD D e

0K = dependent on the crystal structure and equal to 14 for BCC lattice, 17 for FCC and HCP

lattices, and 21 for diamond-cubic lattice

V = valence of the material

mT = absolute melting temperature

The constants 0K are estimates associated with an assumed diffusivity constant 1cm2/s.

By combining Equation.5-13 and 5-14

0( )SD mH RT K V

We see that activation energy for self-diffusion increases (corresponding to a reduction D)

with increasing melting point, valence, packing density, and degree of convalency. Consequently,

although refractory metals with high melting points, such as tungsten, molybdenum, and

chromium, seem to hold promise as candidates for high-temperature service, their performance in

high-temperature application is adversely affected by their open BCC lattice, which enhances

diffusion rates. From Equation. Ceramics are identified as the best high-temperature materials

because of their high melting point and the covalent bonding that often exists.



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It is important to recognize that creep rates for all materials cannot be normalized on the

basis of D alone because other test variables affect the creep process in different materials. For

example, Barrett and coworkers19 noted the important influence of elastic modulus on the creep

rate and on determination of the true activation energy for creep. A semi-empirical relationship

with the form

.n

s kTA

DGb G

Has been proposed1 to account for other factors where

.

= steady-state creep rate

K = Boltzman’s constant


D = diffusivity

G = Shear modulus

B = Burgers vector

= applied stress

A,n = material constants

By combining Equation. 5-8 and 5.13 , the steady-state creep rate at different temperatures

can be normalized with respect to D to produce a single curve, as shown in Figure. This is an

important finding since it allows one to conveniently portray a great deal of data for a given

material. For example, we see from a reexamination of Figure. That at the allotropic

transformation temperature, the creep rate in -ion (FCC lattice) is found to be approximately 200

time slower than that experienced by -iron (BCC lattice).6 This substantial difference is traced

directly to the 350-fold lower diffusivity in the close-packed FCC lattice in -ion. Similar findings

were reviewed by Sherby andBurke17 for the allotropic transformation from HCP to BCC in

thallium. Therefore, it is appropriate to briefly consider those factors that strongly inflorescence

magnitude of D. Sherby andsimnad18 reported an empirical correlation showing D to be a

function f the type of lattice, the valence, and the absolute melting point of the material.

Here again we see that creep is assumed to be diffusion controlled. Even after normalizing

creep data with Equation, a three-decade scatter band still exists for the various metals shown in

Figure. While some of this difference might be attributable to actual test scatter or relatively

imprecise high-temperature measurements of D and G, other as yet unaccounted for variables

most likely will account for the remaining inexactness. For example, there appears to be a trend

toward higher creep rates in FCC metals and alloys possessing high stacking fault energy (SFE).

Whether the SFE variable should be incorporated into either A or n id the subject of current

discussion.20-22 The role of substructure on A and n must also be identified more precisely.

One important factor in Equation. Is the stress dependency of the steady-state creep rate.



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FIGURE. Creep data in aluminum. (a) Stress versus steady-state creep rate .

s divided by the

diffusion coefficient. (From O.D. Sherby and P.M. Burke;17 reprinted with permission from

Sherby and Pergamon Press, Elmsford,Ny, 1968).

It is now generally recognized that .

s varies directly with at low stresses and

temperatures near the melting point. At intermediate to high stresses and at tompet atures above

0.5Tm, where the thermally activated creep process is dominated by the activation energy for self-

diffusion, .

s 4-5 (so-called power law creep). It should be noted that this stress dependency

holds for pure metals and their solid solutions. Much stronger stress dependencies of .

s and ts

have been reported in oxide-dispersion-strengthened superalloys (see Section). At very high

stress levels .

s e . Garofalo23 showed that power law and exponential creep resented limiting

cases for a general empirical relationship

.

s (sinh )n

Equation . reduces to power law creep when <0.8, but approximates exponential creep

when < 1.2. An explanation for the changing stress dependence of .

s in several operative

deformation mechanisms is discussed in the next section.



20

FIGURE. Creep data in metals. (a) Data for FCC metals; materials with high-stacking lault

energy then to have higher steady-state creep rates. (b) Data for BCC metals. (From A.K.

Mukherjee, J.E. Bird, and J.E. Dorn1; copyright American society for Metals, Metals Park, OH,

( c) 1969).

4. Creep laws, Factors Affecting Creep, Mechanism of Creep.

Primary, secondary and tertiary creep curves follow different creep laws for various materials.

The variation of creep strain cr with time t may be expressed as below.

Andrade’s law of transient creep for metals and some plasties expresses creep strains as,

ncr Ct

where C is constant, and n is power index constant whose value is 1/3. Logarithmic law of

transient creep for glass and rubber expresses creep strain as,

1

log 1cr c

tK

t



21

Where K is a constant and t1 is any arbitrarily choosen time.

Hyperbolic law of transient creep for concrete expresses creep strain as,

cr

t

n t

Where is a constant, and n is creep-time constant.

Secondary creep law may be stated by

1cr crv t

Where 1 is creep intercept (see Figure) and crv is viscous or minimum creep rate.

Minimum creep rate increases with increasing stress and is given by

ncrv A (n>1)

Where A and n are constants.

Example: During a creep test on pure aluminium at 280oC under steady stress of 6.85 MPa, the

following data were recorded.

Plot strain-time curve, and show the extents of primary, secondary and tertiary stages on it.

Determine (a) minimum creep rate, (b) the creep intercept, and (c) transient creep law.

Solution : The strain-time cries shown in Figure. Primary and secondary creep stages are market

or it. It does not have tertiary creep stage.

Time t

(min)

Stain

(mm’mm)

Time t

(min)

Strain

(mm/mm)

0 0 24 0.094

1 0.020 32 0.109

2 0.029 40 0.122

4 0.041 48 0.136

8 0.057 60 0.156

16 0.078 72 0.176



22

(a) The minimum creep rate is found by taking slope of the viscous part of the curves. It is

shown in above figure and is obtained as

12

0.85714

crv mm/mm

(b) the creep intercept marked in above figure is found to be

1 = 0.055 mm/mm

(c) As the material is the question is a metal (pure A1), we shall use Equation. Taking log on

both sides of this equation.

log log logcr C n t

Considering the data for t= min and t = 4 min, the Equation. (I may be written as

log 0.02 = log C + n log 1

log 0.041 = log C + n log 4

Solution of Equation. (ii) and (iii) yields

n = 0.51

Now substitution of this value n other of Equation (ii)and (iii) gives

C = 0.02

Hence transient law is obtained as

0.510.02 cr t



23

Factors Affecting Creep :

It has already been pointed-out that the load (hence stress) and tempera ture influence the

creep behaviour of a material. So we obtain different curve profiles as shown in figure . There

separate curves marked A, Band C for the same material are shown. If the temperature is

Figure. Effect of changing temperature at constant stress and changing stress at constant

temper

Constant, the curves A, B and C are obtained at stresses 1 2 3 3 2 1 ( )and

respectively. Similarly if the stress is kept constant, the curves A, B and C are noticed at

temperatures 1, 2 3 3 2 1 and ( )T T T T T T . Although a single diagram is shown to explain two effects,

but it does not mean that the same curves are inter-replace abed in the two cases of = constant

and T = constant.

It may be concluded that the effect of increasing stress and temperature is to speed-up the

rate or creep At higher stress or at higher temperature. The total strain is large and creep fracture

occurs in lesser time . The duration of three creep stages also very. Consequently viscous stage It

is prolonged in curved reduced in curve B and messing in curve C .

Mechanism of Creep :

Occurrence

1. Vacancy diffusion

2. Edge dislocation climb-up or climb-down.

3. Grain boundary sliding

4. Screw dislocations cross-slip

5. Elastic aftereffect.



24

Figure. Mechanism of creep (a) vacancy diffusion (b) dislocation climb-up or climb-down, and

(c ) grain boundary sliding.

Creep Resistant Materials :

Machine and structural parts functioning at higher temperatures must be creep resistant.

Pressure vessels and heat exchangers in oil refinery and chemical industries operate at elevated

temperatures. Heat engines need to operate at higher operating temperatures to achieve

enhanced thermal efficiency. This necessitates the creep resistant materials to have high melting

points. Some of the probable materials may be as

follows :

1. Refractories,

2. Tungsten bases alloys,

3. Nickel based alloys and nickel superalloys,

4. Cobalt based alloys

5. Steel based alloys,

6. Monocrystal titanium, and

7. Thoria (ThO2



25

Of these the Refractories are brittle and cannot take purposeful tensile load. Tungsten and

titanium are costly metals. Tungsten is also heavy. Nickel based alloys, cobalt based alloys and

steel based alloys are suitable for use from different view-points.

Nickel using Thoria by dispersion hardening method is a very good creep resistant

material. It can maintain its strength upto a temperature of about 0.9 Tm. some of the latest

materials as given below are also useful.

1. Silicon nitride (Si3N4) for piston rings and cylinder heads.

2. Sialons (alloys of Si3N4 and Al2O3) for gas turbine blades upto 1300oC

Finer grained materials having small crystals are undesirable for use as creep resistant materials.



26

UNIT – II

1. HARDENING (CONVENTIONAL HARDENING) :

By Hardening process a new hard & brittle structure called Martensite is formed.

Hardening can be explained y drawing the appropriate cooling curve in the TTT diagram.

Every steel/alloy steel used in heavy engineering industry must undergo hardening. This

may be understood from the following example. The needle that we use to stitch clothes is

actually a highly flexible steel wire, it is only after the hardening process that it obtains the

necessary hardness and does not bend.

Purpose of hardening (i) develop high hardness (ii) Improve mechanical properties

(strength, elasticity, ductility and toughness) (iii) Improve wear resistance. Consider the

following cooling curve drawn on a TTT diagram for a hypoeutectiod steel.



27

Figure. Heat treatment cycle for conventional hardening process

It is obvious that the surface and the centre of the specimen will have slight different cooling

curves, which depends on the cross section of the specimen, both the curves must come under

the same region in order to have the same structure on the surface and the core.

Hardening process :

The steel is heated to the austenitic temperature above A3 for hypoeutectoid steel and above

A31 for hypereutectoid steel (see figure (b) and kept in that region (soaking for the complete

transformation of the structure to austenite. It is then drastically cooled to room temperature

(Note : It is not cooled below room temperature). And much of the austenite will transform to a

new needle like or have like or acicular structure called Martensite. The cooling (quenching) may

be performed by using a salt bath (molten KCN or NaCN, salt) or oil bath or brine solution.

The mechanism by which Martensite is formed has already been explained in section

figure.

It is important to note that even the drastic cooling is not sufficient to convert the entire

austenite to Martensite, hence some unstable austenite remains even after cooling as shown in

figure. This austenite is called retained austenite.



28

Figure. Scheme showing the formation of martensitic structure

The transformation that takes place for a hypoeutectoid steel is :

(FCC structure) slowcooling (bcc structure ) + Fe3C

Drastic cooling (quenching)

M (BCT Body Centered Tretragonal structure).

In most steels, the amount of Martensite that forms is a function of the temperature of

which the austenite is cooled and not a function of time.

Figure: Representation of percentage of Martensite formed as a function of temperature

The martensitic transformation occurs with out a change in composition, it occurs by a

process of shear and is not caused by diffusion of carbon.

The hardness of Martensite depends on the carbon percentage present. It increases rapidly

with increases in carbon content. The maximum value reached is around 64 Rc (Rockwell

hardness on ‘C’ scale) at about 0.6% carbon.



29

Figure:

Martensitic structure is extremely hard and brittle and the steel becomes too brittle to be

used in engineering applications. Martensite is said to be in a metastable phase.

The steel as quenched (i.e., after quenching and without further heat treatment process)

may even crack at room temperature, such is the unstability and thermal stresses created within

the martensitic structure, and further heat treatment is required to remove these stresses and

avoid cracking (called quench cracks)

The steel is reheated to reduce its brittleness, without much loss of hardness. This heat

treatment process is called Tempering.

It may be observed in Figure that not all the austenite converts to Martensite after

quenching. Some of the austenite remains and is called as retained austenite.

During tempering the steel is reheated to a lower temperature above the Ms (Martensite

start formation) temperature see figure and is cooled to room temperature for a transformation to

complete.

Depending on the tempering temperature some small percentage of retained austenite and

a soft structure which is generally called tempered Martensite (the detailed structre will be

explained in unit) is obtained. The formation of the soft structure lowers the hardness. In the

case of alloy steel such as high speed. steel the hardness actually increased due to tempering and

then drops. In this the retained austenite converts to Martensite there by increasing the

hardness(this is called secondary hardening) and there is also the formation of complex carbides

with the alloying elements present in steel. The Martensite already present becomes tempered

Martensite. Two to three tempering may be required in order to completely transform the



30

retained austenite to Martensite. Each tempering stage must be followed by cooling to room

temperature as the transformation from retained austenite to Marten site takes place after cooling

below Marten site transformation temperature.

Figure Effect of tempering temperature on hardness

The following figure explains a typical heat treatment cycle for high speed steel. Preheating

is required in order to avoid stress cracks that may be formed if the steel is directly heated to the

austenitic temperature form room temperature. The heating time and temperature depends on

the cross section of the component heat treated.

Figure. Time/temperature sequence chart for heat treating high speed steels (HSS)



31

Note on retained austenite :

Austenite to Martensite transformation depends on temperature. The transformation is

never completed to 100% Martensite.

The amount of retained austenite varies from surface of the component to centre. It is less

at or near the surface and more in the centre. This is because the surface cools first and then the

centre. The amount of retained austenite also depends of the quenching temperature. Drastic low

temperature quenching results in the formation of more percentage of Martensite. Retained

austenite has certain advantages;

(i) Austenite reduces the tendency of cracking during hardening and hence about 10%

retained austenite is desirable.

(ii) If the retained austenite is more say 30-40% the steel can be easily cold worked to some

extent without cracking.

Retained austenite has certain disadvantages ;

(i) Austernite is a soft unstable phase and the presence of retained austenite reduces the

hardness of hardened steel.

(ii) Small amount of retained austenite does not decrease the hardness much, but it may

increases the brittleness of steel. This is because of the fact that the austenite may get

transformed to Martensite if the material is subjected to plastic deformation. This

deformation (strain) induces transformation of austenite to Martensite and increases stress

and as a result of which the mechanical properties decreases.

(iii) The retained austenite may slowly transform to bainite even at room temperature. This

liner expansion may be 0.0001 cu/cm for every 0.3% retained austenite by volume and may

cause increase in dimensions especially in sensitive gauges and tools.

Thus tempering eliminates the presence of retained austenite to some extent. Repeated

tempering (atleast two ) transforms more retained austenite to Martensite. Each tempering stage

must be followed by cooling to room temperate see figure.

An effective way of eliminating retained austenite is sub zero treatment, where the steel

component is cooled to very low temperatures, substances such as acetone and dry ice (-100oF) or

liquefied gases such as nitrogen (-321oF), oxygen (-297oF) or helium (-4530F) may be used as

quenching medium. After subzero treatment the steel is quenched to room temperature in

conventional quenching mediums (air, oil, water). (It is beyond the scope of this book to deal with

sub zero treatment in detail). It is also possible to eliminate austenite by plastic deformation above

Ms Temperature. The phenomenon is called induced martensitic transformation. This method is

suitable for steels with large amount of retained austenite.



32

Calculation for the time required to Harden :

It is useful to calculate the length of time required for hardening. Newton’s law of heating

is a means of calculating the hardening time. The rate of heating of metals which are good

conductors is limited to the transfer of heat from the surroundings i.e., furnace atmosphere to the

surface of the metal piece being heat treated and not by internal resistance to heat flow in the

metal piece being heated. Temperature difference within the piece are small when compared to

those between surface and surroundings. For the purpose of describing the rate of heating it is

assumed that the metal piece obtains uniform temperature throughout the piece.

The rate of heat absorption can be represented as :

P P

dTQ V C

dt

Where PV = Volume density = mass

PC = Specificheat

dT

dt = rate of change of temperature with time

The rate of heat transfer from the surrounding to the surface (by convection and radiation )

can be represented by :

Q = h A ( Tf – T )

Where h = heat transfer coefficient

A = Total surface area

Tf = furnace temperature

T = Temperature to which the piece is being heated

Q = V P Cp dT

dt

Also

Q = h A(Tf - T)

Equating these two expressions we get :

P

dT Q

dt V C

( )f

P

hA T TdT

dt V C

( )P

f

dtc V C

dT hA T T

( )

P

f

V C dTdt

hA T T



33

0

)

fT

P

fT

V C dTt

hA T T

To – Initial temperature of the piece when it is placed in the furnace

Tf – Furnace temperature

02.3

logfP

f

T TV Ct

hA T T

The value 0f

f

T T

T T

is direct by proportional to the volume to total surface area ratio (V/A).

this ration depends on the size and shape of the part.

2. Strain (work) Hardening

Stain hardening (also referred to as work hardening or cold working) dates back to the Bronze

Age and is perhaps the first widely used strengthening mechanism for metals. Artisans

hammered and bent metals to desired shapes and achieved superior strength in the process.

Typical cold-worked commercial products that find used today include cold-drawn piano wire

and cold-rolled sheet metal. Strain hardening results from a dramatic increases in the number of

dislocation-dislocation interactions and which reduces dislocation mobility. As a result, larger

stresses must be applied in order that additional deformation deformation may take place. It is

interesting to note that the strength of a metal approaches extremely high levels when there are

either no dislocations present (recall Equation) or when the number of dislocation is extremely

high ( 10 210 / cm

); low strength levels correspond to the presence of moderate numbers of

dislocation ( 103 – 105/cm2) (Figure).

To characterize more clearly the strain – hardening behavior of metal crystals, it is helpful

to examine the stress-strain response of single crystals. From Figure. the

FIGURE : Strength of metal crystals as a function of dislocation density.



34

Resolved shear stress- shear strain curve is seen to contain several distinct regions: an initial

region of elastic response where the resolved shear stress is less than T CRSS; stage I, a region of

easy glide; Stage II, a region of linear hardening; and Stage III, a region of dynamic recovery or

parabolic hardening. The latter three regions involve different aspects of the plastic deformation

process for a given crystal. It is known that the extent of Stages I, II, and depends on such factors

as the test temperature, crystal purity, initial dislocation density, and initial crystal orientation.12 It

should be noted that Stage III Closely resembles the stress-strain response of the polycrystals form

of the same material.

FIGURE : Shear stress-strain curve for single crystal revealing elastic behavior when T<Tcrss and

Stage I,II,III plastic response when T > Tcrss. ,I II III measure the strain hardening rate in each

region.

A number of theories of theories have been proposed to explain the strain-hardening

process in crystals, including the reason for the dramatic changes in strain-hardening rate

associated with the three stages of plastic deformation. An extensive literature3 has developed

regarding these theories, al of which have focused on some of the dislocation interaction

mechanisms described in the previous chapter. Seeger4 and Friedel,5 for example, argued that

rapid strain hardening in Stage II resulted from extensive formation of dislocation pileups at

strong obstacles such as Cottrell-Lomer locks.6.7 The latter represents a sessile (nonmobile )

dislocation that impedes the motion of other dislocation on their respective slip planes. An

example of such a barrier is given by

The 011 110and dislocations, which move along their slip planes, (111) and (11 1 ),

respectively, join to produce the sessile dislocation 110, which cannot move along either plane.

Note that this dislocation reaction is permissible since the total elastic energy is reduced (recall

Equation). Mott8 proposed that heavily jogged dislocation produced by dislocation-dislocation

interactions(see Section) would be more resistant to movement, there by enhancing the hardening

rate. Unfortunately, a certain degree of confusion has arisen in this field because of the varying

importance of certain dislocation interactions in different alloy crystals. One wonders then why

the three distinct stages of deformation are so reproducible from one material to another and why



35

the work hardening coefficient II associated with Stage II deformation is almost universally

constant at G/300. For these reasons the ‚mesh length‛ theory of strain hardening proposed by

Kuhlmann-Wilsdorf 9,10 is appealing pedagogically, since it does not depend on any specific

dislocations model that might be appropriate for one material but not for another. Her theory

may be summarized as follows: In stage I a heterogeneous distribution of low-density dislocation

exists in the crystal. Since these dislocations can move along their slip planes with little

interference from other dislocations, the strain hardening rate I is low. The easy glide region

(Stage I) is considered to end when a fairly uniform dislocation distribution of moderate density

is developed but not necessarily in lockstep with the onset of conjugate slip where a marked

increase in dislocation – dislocation interactions would be expected. At this point Kuhlmann-

Wilsdorf theorizes the existence of a quasi-uniform dislocation density array with clusters of

dislocations surrounding cells of relatively low dislocation density figure. It is believed that such

cell structures represent a minimum energy and, hence, preferred dislocation configuration

within the crystal. Studies have shown that high stacking fault energy metals (e.g., aluminum)

exhibit cell walls that are narrower and cell interiors that are more dislocation-free than lower

stacking fault energy metals (e.g., coper) figure. (In very low stacking fault energy metals (e.g.,

Cu-7% Al) the crystal substructure is characterized by dislocation planar arrays, consistent with

the tendency for these materials to exhibit restricted cross slip.

The stress necessary for further plastic deformation is then seen to depend on the mean

free dislocation length l in a manner similar to that necessary for the activation of a Frank-Read

source where

Gb

Tl



36

Figure. Dislocation substructures in metals : (a)aluminium; (b) copper; (c) copper-7%

aluminium. (d) Variation in dislocation cell size with percentage reduction of area in

polycrystalline niobium steel alloy.



37

Since the dislocation density is proportional to 1/ l 2, Equation may be written in the form

Gb

Where = dislocation density

T= incremental shear stress necessary to overcome dislocation barriers

The relationship has been verified experimentally for an impressive number of materials

and represents a necessary requirement for any strain hardening theory. With increasing plastic

deformation, increases resulting in a decrease in the mean free dislocation length l . From

equation, the stress necessary for further deformation then increases. Kuhlmann-Wilsdorf

suggests9 that there is a continued reduction in cell size and an associated increase in flow stress

throughout the linear hardening region. In other words, the character of the dislocation

distribution remains unchanged, only the scale of the distribution changes (see region AB in

figure). With further deformation, the number of free dislocations within the cell interior

decreases to the point where glide dislocations can move relatively unimpeded from one cell wall

to another. Since the formation of new cell walls (and hence a reduction in l ) is believed to

depend on such interations, a point would be reached where the cell size l would stabilize or at

best decrease slowly with further deformation. According to Kuhlmann-Wilsdorf,10 this condition

signals the onset of Stage III and a lower strain hardening rate, since lwould not decrease.

Recently Bassin and Klassen provided experimental confirmation that Stage III behaviour

corresponds to strain levels where l remains constant (see region BC in figure). Of particular

note, the data reported in figure are measurements taken from a polycrystalline niobium steel

alloy; as such, the mesh length theory of strain hardening is applicable for both single crystal and

polycrystalline commercial alloys.

Stacking fault energy is considered to be important to the onset of Stage III. Seeger4 has

argued that Stage III begins when dislocations can cross-slip around their barriers, a view initially

supported by kuhlmann-Wilsdorf. From Seeger’s point of view, Stage III would occur sooner for

high stacking fault energy materials since cross-slip would be activated at a lower stress.

Conversely, a low stacking fault energy material, such as brass, would require a larger stress

necessary to force the widely separated partial dislocations to recombine a larger stress necessary

to force the widely separated partial dislocations to recombine and hence cross-slip. More

recently, Kuhlman-wils dorf10,11 suggested that the mesh length theory could also explain the

sensitivity of TIII to stacking fault energy by proposing that enhanced cross-slip associated with a

high cvalue of stacking fault energy would accelerate the dislocation rearrangement process.

Consequently, l would become stabilized at a lower stress level. Setting aside for the moment the

question of the correctness of the seeger versus Kuhlmann. Wilsdorf interperetations,

interpretains, is is sufficient for us to note that both theories account for the inverse dependence of

TIII on stacking fault energy.



38

In discussing the deformation structure of metals, it is important to keep in mind the

temperature of the operation. In is know that the highly oriented grain structure in a wrought

product, which has a very high dislocation density (1011to1013 dislocations/cm2), remains stable

only when the combination of stored strain energy (related to the dislocation substructure) is

below a certain level. If not, the microstructure becomes unstable and new strain-free equiaxed

grains are formed by combined recovery, recrystallisation, and grain growth processes. These

new grains will have a much lower dislocation density (in the range of 104 to 106

dislocations/cm2). When mechanical deformation at a given temperature causes the

microstructure to recrystallize spontaneously, the material is said to have been hot worked. If the

microstructure were stable at that temperature, the metal experienced cold working. The

temperature at which metals undergo hot working varies widely from one alloy to another but is

generally found to occur at about one-third the absolute melting temperature. Accordingly, lead

is hot worked at room temperature, while tungsten may be cold worked at 15000C.

Before concluding the discussion of single-crystal stress-strain curves, it is appropriate to

consider whether one can relate qualitative and quantitative aspects of the stress-strain Response

of single-crystal and polycrystalline specimens of the same material. For one thing, the early

stages of single-crystal deformation would not be expected in a polycrystalline sample because of

the large number of slip systems that would operate (especially near grain boundary regions) and

interact with one another. Consequently, the tensile stress-strain responses of the polycrystalline

sample is found to be similar only to the Stage III single-crystal shear stress-strain plot. A number

of attempts have been made to relate these two stress-strain curves. From Equation.

1

cos cosM

A

where M = 1/(coscos)

Assuming the individual grains in a polycrystalline aggregate to be randomly oriented, M

would very with each grain such that some average orientation factor Mwould have to be

defined. Since there are 384 combination of the five necessary slip systems to accomplish an

arbitrary shape change, M is not easy to compute. From section 3.1, Taylor14 determined the

preferred combination to be the one for which the sum of the glide shears west minimized. As a

result it may be shown15 that

M

By combining Equation 1 and 2 it is seen that

2d d

Md d



39

For the case of 111 110 slip in FCC metals and 110 111 slip in BCC metals, Taylor14

and Groves and Kelly16 showed M equal to 3.07. Subsequently. Chin et al.17.18 analyzed the more

difficult case of 110 111 + 112 111 + 123 111 slip in BCC crystals and found M = 2.75. In

either case, one can see from Equation. That the strain-hardening rate of a polycrystalline material

is many times greater than its single-crystal counterpart.

3 Rupture life of Creep

The Larson-Miller parameter is, perhaps, most widely used. Larson and Miller57correctly

surmised creep to be thermally activated with the creep rate described by an Arrhenius-type

expression of the form /H RTr Ae

Where r = creep process rate

H = activation energy for the creep process


R = gas constant

A = constant

Equation 5-24 also can be written as

H

InrRT

After rearranging and multiplying by T, Equation becomes / ( )H R T InA Inr

Since r (l/t) (also suggested by Equation), Equation can be written as

/1' H RTA e

t

Therefore,

'H

Int InART

And after rearranging Equation, multiplying by T, and converting Int to logt / ( )H R T Iogt

Which represents the most widely used form of the Larson-Miller relation. Assuming

H to be independent of applied stress and temperature(not always true as demonstrated earlier)

the material is thought to exhibit a particular Larson-Miller parameter ( log )T c t for a given

applied stress. That is to say, the rupture life of a sample at a given stress level will very with test

temperature in such a way that the Larson-Miller parameter ( log )T c t remains unchanged. For

example, if the test temperature for a particular material with c = 20 were increased from 8000C to

10000C, the rupture life would decrease from an arbitrary value of 100hr at 8000C to 0.035 hr at



40

10000C. The value of this parametric relation is shown by examining the creep rupture data in

Figure, which are the very same data used in Figure. The normalization potential of the Larson-

Miller parameter for this material is immediately obvious. Furthermore, long-time rupture life

for a given material can be estimated by extrapolating high-temperature, short rupture life

response toward the more time-consuming low-tem-perature, long rupture life regime. It is

generally found that such extrapolations to longer time conditions are reasonably accurate at

higher stress levels because a smaller degree of uncertainty is associated with this portion of the

Larson-Miller plot. In-

FIGURE: Larson-Miller plot showing s-590 iron-based alloy data presented in Fjigure5.3.

Creased extrapolation error is found at lower stress levels where experimental scatter is

greater. A comparison between predicted and experimentally determined rupture lives will be

considered later in this section.

The magnitude of C for each material may be determined from a minimum of two sets of

time and temperature data. Again, assuming /H R to be invariant and rearranging Equation.

2 2 1 1

1 2

log logT t T tC

T T



41

It is also possible to determine C graphically based on a rearrangement of Equation

Where

tanlog

cons tt C

T

When experimental creep rupture data are plotted as shown in Figure, the intersection of

the different stress curves at 1/T = 0defines the value of C. It is important to note that not all creep

rupture data given the same trends found in Figure. For example, isostress line may be parallel,

as shown in Figure, for the case of rutile 2( )TiO and other ceramics and metals. Representative

values of C for selected materials57 are given in Table. For convenience, the constant is sometimes

not determined experimentally but instead assumed equal to 20. Note that the magnitude of the

material constant C does not depend on the temperature scale but only on units of time. (Since

practically all data reported in the literature given both the material constant C and the rupture

life in more convenient units of hours rather than in seconds-the recommended SI unit for time-

test results in this section will be described in units of hours.)

In addition to being used for the extrapolation of data, the Larson-Muller parameter also

serves as a figure of merit against which the elevated temperature response of

FIGURE: Convergence of isostress lines in plot of logtR versus 1/T to determine magnitude of

constant C in Larson-Miller parameter.

Table: Material Constants for Selected Alloys57



42

Different materials may be compared(e.g., in the case of alloy development studies). For

example, when the curves for two materials with the same constant C are coincident, the

materials obviously possess the same creep rupture behavior(Figure a). The same conclusion

does not follow, however, when the coincident curves result for materials with different values of

C(Figure b). when A BC C , material A would be the stronger of the two. (For the same

parameter P, and at the same lest temperature, logARt for alloy A would have to greater than

logBRt since

B AC C .) A direct comparison of material behavior is evident when C is the same but

the parametric curves are distinct from one another(Figure c). Here alloy A is clearly the superior

material. While such alloy comparisons for specified condition of stress and temperature are

possible using the Larson-Miller parameter(and other parameters as well), it should be

understood that such paramet4ers provide little insight into the mechanisms responsible for the

creep response in a particular time-temperature regime. This is done more successfully by

examining deformation maps.

The Sherby-Dorn (SD) parameter /R = t H RTe (where t = tR) described in equation has been

used to compare creep rupture data for different alloys much in the same manner as the Larson-

Miller (LM) parameter. Reasonably good results have been obtained with this parameter in

correlating high-temperature data of relatively pure metals. The reader should recognize that if

the Sherby-Dorn parameter does apply for a given material, then when is constant, a plot of the

logarithm of rupture life against 1/T should yield a series of straight lines corresponding to

different stress levels.

Figure: Parametric comparison of alloy behaviour. (a) Alloy A = Alloy B; (b) and (c) Alloy A

superior to Alloy B.



43

Figure: Correlation of stress rupture data using temperature-compensated time parameter /

R = t H RTe for pure aluminium. (From J.E. Dorn, Creep and Recovery reprinted with

permission from American Society for Metals Park, OH, copy right © 1957.)

This is contrary to the response predicted by the Larson-Miller parameter, where the

isostress lines coverage when 1/T = 0. The choice of the LM or SD parameters to evaluate a

material’s creep rupture response would obviously depend on whether the isostress lines

converge to a common point or are parallel. In fact, the choice of a particular parameter (recall

that over 30 exist) to correlate creep data for a specific alloy is a very tricky matter. Some

parameters seem to provide better correlations than others for one material but one another. This

may be readily seen by considering Goldhoff’s tabulated results for 19 different alloys. Shown

here are root-mean-square (RMS) values reflecting the accuracy of the LM, SD, and other

parameters in predicting creep rupture life. The RMS value is defined as

1/ 22

log actual time to rupture-log predicted time to rupture RMS=

number of long-time data points



44

TABLE: Comparative RMS Values Reflecting Accuracy of Different Time-Temperature

Parameters

Note that form some metals, either the LM or SD parameter represented the best time

temperature parameter (TTP) of the four examined by Goldhoff and predicted actual test results

most correctly. Alternatively, these two parameters provided poor correlations when compared

to other parameters for different materials; the use of the LM or SD parameters in evaluating

these alloys led to significant error in the prediction of actual rupture life.

This inconsistency with which a particular TTP predicts actual creep rupture life for

different alloys represents a severe shortcoming of the parametric approach to creep design.

These deficiencies may be traced in part to some of the assumptions underlying each parameters.

For example, the LM and SD parameters are based on the assumption that the activation energy

the creep process is not a function of stress and temperature. Clearly, the test results shown in

figure and the extended discussion in Section discredit this supposition. (Recall, however, than

when T 0.5Tm, the activation energy for creep is essentially constant and equivalent to the

activation energy for self-diffusion.) Furthermore, none of the TTP make provision for

metallurgical instabilities.



45

4. The Monkman-Grant relationship ?

The need to extrapolate the result of accelerated creep tests has been met by the

development of several methods. We discuss one of these in some detail in Section 2.6. A simpler

approach is the Monkman-Grant relationship, which states that for a given material in a certain

range of stress and strain (Monkman and Grant. 1956).

min 1C t = Constant

where

min ( , )C f T is the minimum steady-state creep rate

1 ( , )t g T Is the time to fracture.

and the constant characterized the material.

Using the Monkman –Grant relationship, minC and 1t can be determined at a convenient

stress and temperature, minC can be determined at the operating stress and temperature and hence

t1 for operating conditions may be calculated. The relationship (2.2) often holds true (Figure (a) )

but in some cases it needs to be adapted to the form

min 1( ) tan 1C t cons t

For the IN 597 alloys in Figure 2.8(b) it is clear that the use of the Monkman Grant

relationship in the form of equation (2.2) would lead to an overestimation of the creep rupture life

at low stresses. Therefore. The Monkman Grant relationship cannot be used with confidence

unless the value for the alloy III question has been determined. There are also cases (e.g. Benn

1984 ) in which the actual creep rate at low stresses is lower and the ruptures life is hugher than

crlrapolation from higher stresses would suggest.



46

UNIT – III

1. FRACTURE :

The separation of a solid body into two or more parts under the action of stresses is called

‚Fracture‛ . Fracture of a material by cracking may occur in many ways. They are :

1. slow application of external loads (tension).

2. Rapid application of external load (Impact).

3. Repeated cyclic loading (Fatigue).

4. time and temperature dependent failure under a constant load (creep).

The fracture processes occur due to crack initiation, and crack propagation (i.e., groth of

crack ) after which it finally breaks.

Ideal fracture stress :

If an increasing tensile stress is applied on an ideal material (i.e., groth of crack ) then the

binding atoms in the material will fail as soon as the stress reaches a critical value known as ideal

fracture stress. The fracture occurs on a plane perpendicular to the direction of tensile stress.

Types of fracture

The application of stress to any material results in an elastic and/or plastic strain and if the

stress is increased progressively, fracture will ultimately occur. The fracture may be classified as;

1. Ductile fracture. (occurs in polycrystal ductile materials)

2. Brittle fracture. (occurs in single crystal and polycrystal brittle materials)

3. Shearing fracture. (occurs in single crystal ductile materials)

In ductile fracture there is extensive plastic deformation. Ductile fracture takes plase at

some stress above the shear strength of the material so that plastic flow takes place before it

fractures. Such a crack is said to be stable.

In brittle fracture the cracks may spread very rapidly with very little plastic deformations,

such a crack is said to be unstable. Brittle fracture occurs in materials such as cast iron, glass and

concrete. Fracture of this type is also termed as ‚cleavage fracture‛.



47

Ductile fracture is preferred over brittle fracture for two main reasons

(i) Brittle fracture occurs suddenly and without any warning.

(ii) In the case of ductile fracture there is always plastic deformation and the material yields

for some time before it fractures and hence suitable preventive measures can be taken.

1. Ductile fracture

There are two types of ductile fracture, as shown in figure (a) and fig (b). In both the types

plastic deformation occurs before fracture, due to progressive deformation when necking begins.

The completely ductile material necks till the end of fracture where there is 100% reduction in

area. Such type of fracture is found in very soft polycrystalline materials such as lead and pure

gold at room temperature. The figure shows the appearance of a completely ductile material.

Figure: Ductile fracture

The other type of ductile fracture that occurs for most polycrystalline ductile materials is

popularly caked the called the cup and cone fracture. The various stage of a cup and cone fracture

is shown in fig.

In the cup and cone ductile failure the fracture propagates in the following stages (a)

Necking begins at the point of plastic deformation due to the triaxial stress. (b) Small nuclei or

cavities or voids form in the interior of the cross section due to the tri-axial stress induced in that

region. (c) As deformation continues the voids enlarge due to the triaxial stress, and coalesce to

form a central elliptical crack which has its long axis perpendicular to the direction of stress. (d)

The crack continuoes to grow in a direction parallel to its major axis until it approaches the surface

of the specimen. (e) Finally fracture results by the rapid propagation of the crack around the outer

perimeter of the neck, this occurs in a direction approximately 45o to the tensile axis. The angle 45o

is the angle at which shear stress is maximum. This fracture is known as cup and cone fracture.

Since one half of the surface appears as cup and the other half like a cone.



48

Figure: Stage in the cup and cone fracture

(a) initial necking (b) formation of nuclei (c) formation of crack (d) crack propagration (e) final

fracture at an angle of 45o with respect to the tensile axis.

The fractured surface has a fibrous appearance. The fibrous appearance is due to the

presence of hard elongated fibre lke phase in a soft matrix. For example, wrought iron contains

elongated hard inclusion in a ferrite matrix and low carbon steel contains pearlite bands in a

ferrite matrix. Due to presence of the fibrous bands the material that has fractured shows a

fibrous appearance. The fig. shows the fibrous appearance in a ductile material.

Figure: Fibrous fracture

2. Brittle fracture :

The word brittle signifies minimum plastic deformation.

Brittle fracture occurs with minimum plastic deformation and without necking. Once the

crack sets in, it propagates rapidly and fractures.



49

The direction of crack is nearly perpendicular to the direction of applied tensile stress and

the surface produced is relatively flat. Brittle fracture mechanism for single crystals and

polycrystals are the same.

Figure:

Brittle fracture occurs by repeated breaking of atomic bonds along specific

crystallographies planes, such a process of breaking is called cleavage as illustrated in Figure.

Clevaging is like splitting a plane with a sharp wedge. (similar to cutting wood with a

wedge shaped axe)

Figure Clevaging

Brittle fracture can also occur along the grain boundaries, this type of fractures is called

intergranular fracture. The tendency for a material to brittle fracture may be due to the following

reasons.



50

(i) Decreasing temperature. (ii) Increasing strain rate. (iii) Triaxial stress conditions

that is usually produced by a notch.

A brittle fracture shows granular, shiny and a smooth appearance.

Difference between Ductile and brittle fracture :

Figure.

Ductile fracture Brittle fracture

1. Ductile fracture is the one which is

accompanied with large plastic

deformation and is a result of intense

localized plastic deformation adjacent

to crack.

2. slow rate of crack propagation.

3. failure is due to shear stress developed

at 45 o

4. surface obtained at the fracture is

fibrous and accompanied with the

formation of slip planes.

5. It is characterized by the formation of

cup and cone.

1. Brittle fracture is the one which has

the movement of crack with a

negligible plastic deformation

adjacent to crack.

2. Rapid rate of crock propagation.

3. Failure is due to direct axial stress.

4. Surface obtained at the fracture is

shining and accompanied with hills

and valleys. (downs).

5. It is characterized by separation at a

normal to the tensile stress.



51

Figure:

6. It occurs when the material is in plastic

condition.

7. The tendency of ductile fracture is

increased by dislocation and other

defects in metals.

8. Example of materials that undergo

ductile fracture are mild steel and brass.

Materials such as lead and gold

completely ductile.

Figure

6. It occurs when the material is in

elastic condition.

7. The tendency of brittle fracture is

increased by decreasing temperature ,

increasing strain rate and

workhardening.

8. Examples of materials that are

perfectly brittle are oxide glass,

crystalline ceramics such as AI2 O3

and Si O2. Metals such as cast iron are

brittle in nature.

It is also possible to explain the difference between ductile and brittle fracture with the

following example.



52

Figure Behaviour of materials in stress

In case (i). The material is stressed below is elastic limit, when the stress is removed it

returns to its original stage, i.e., when the stress in removed there is no strain on the material.

In case (ii) Such as a ductile material when it is subjected to a greater stress is undergoes

elastic and plastic deformation. The material recovers slightly but not fully, this is because, it has

aliped and the plastic deformation remains.

In case (iii) The materials does not strain to cause plastic deformation but instead it splits

into two along the cleavage plane, this type of failure is typical for brittle materials.

3. Shearing fracture :

This is a type of ductile fracture but occurs without necking / reduction in cross-section at

the region of failure. This type of failure occurs in single crystal ductile materials.

The shearing fracture is by slip on successive basal planes until finally the crystal separates

by shear. This type of failure mainly occurs in single crystal HCP structure metals.



53

Figure Shearing fracture

GRIFFITH THEORY :

In the early 1920’s British physist A.A Griffith developed an approach to predict failure by

fracture on an analytic basic.

Experiment have shown that the tensile stress required to break all the atomic bonds

simultaneously across a perfect cross-section of a solid is in the order off E/6 (E-Young’s modulus

of the solid). But most brittle materials fracture at a much lower stress in the order of E/500 to

E/1000 this is because the crack in brittle materials propagate at low stress levels and cause

fracture.

According to Griffith, the energy required for fracture of brittle materials is not uniformly

distributed over the volume of a material but there are regions of energy concentration produced

by minute faults and cracks in the material. If a flaw (defect in the material appears as a narrow

elliptical hole in a brittle material subjected to a tensile stress, the maximum stress acting at the

end of the elliptical hole is given by

1/ 2

max 2c

r

Where m - maximum stress

C - half length of the crack

R - radius of curvature at the ends of the major axis

- applied stress



54

Figure Model for Griffith fracture theory

As the crack begins to propagate propagate elastic strain energy is released and this elastic

strain energy per unit volume is given by,

2

2 2

2E

E

U Area WithE

cU

E

Where E – youngs modulus

When the crack propagates the surface area of the crack increases and the elastic strain

energy in the material decreases

If is the surface energy per unit area of the material then the surface energy for the crack

with length 2c and unit width is equal to;

(2 ) 2 4EU c c

We multiply by 2 because there are two faces. The total energy for the crack formation is

given by ;

2

4c

U cE

The - ve sign in the above equation indicates that elastic energy stored in the material is

relased as the crack forms. According to Griffith, a crack will propagate spontaneously and

produce brittle fracture when 0dU

dc



55

2 2

4 0dU d c

cdc dc E

2 E

c

the stress ( ) is the critical stress applied to a brittle material to cause the pre-existing crack in the

material to propagate spontaneous with a decreases in energy before finally causing fracture,

hence we can write equation as;

2 E

c

griffith equation

Where ( c )is the critical fracture stress. The critical fracture stress is inversely

proportional to the square of root of the crack length c. For the crack to propagate according to

Griffith condition, there must be a crack tip with sufficient stress concentration, highly brittle

materials such as silicate glass fail according to Griffith conditions since in such a material the

cracks are sharp with a high stress concentration at the tip.

In materials with less brittle nature the crack propagation is more difficult to occur since

there is not sufficient stress concentration at the crock tip.

More energy is required to rupture the interatomic bonds at the tip of the crack. There is

also some plastic deformation that always occurs hence more work is required to cause fracture,

a s a result of which the Griffiths equation can not be applied to such materials and needs to be

modified. It may be observed in the Griffith equation that it has only parameters related to

surface energy of the crack faces and there is consideration for plastic deformation.

Griffith equation can only be applied for perfectly brittle materials that do not deform

plastically examples of such materials are oxide glasses, most cystalline ceramics such as AI2 O3

and SiO2 . Hoverer many structural components are fabricated from metals with under go atleast

some plastic deformation prior to fracture. Thus Griffith’s theory in its original form does not

apply to metals and can not be used for many engineering applications.

Two decades later Orowan modified the equation after observing sharp cracks in metals

where ductility is significant.

224 0

c

E



56

Orowan hypothesized that a quantity called the effective surface energy should replace the

true surface energy. In Griffith equation the effective surface every ,e is the sum of the true

surface every s and the energy dissipated during plastic deformation around the crack grows

P .

That is :

e s P

P is much greater than

s P

Thus Orowan modified Griffiths equation as ;

2 eE

c

modified Griffith Orowans equation.

FARACTURE TOUGHNESS :

Fracture always begins at some point where there is stress concentration. The region of

this stress concentration may be near a rivet hole, keyway of a shaft, along scratch marks or any

defect in the metal itself. In each of these case the stress is concentrated in that region because the

load is unable to uniformly distribute itself across the full area. This is shown schematically in the

Figure for an elliptical hole.

Note : It is assumed that the half crack length ‚c‛ is less than 10% of the total plate width.

Figure:



57

The stress intensity is greatest at the tip. The intensity increases proportional to the

nominal stress C f which is the stress necessary to cause sudden failure and the square root of

the crack length c.

c fK c

Where CK is the stress intensity factor and it depends on the nature of the material. With more

greater stress of if the crack is much sharper, the stress intensity becomes sufficient to cause

failure spontaneously, this threshold stress intensity is a property of the material and is called the

critical stress-intensity factor 1cK or fracture toughness of the material.

At fracture, 1c cK K this means that there is a critical value of the stress intensity factor at

which fracture will take place.

MINERS LAW :

The effect of fatigue are cumulative and it is difficult to predict the fatigue life of a

component that works under varying conditions of stress. For example an aircraft in a strong

weather causes a reduction in fatigue life and when the same aircraft in normal weather

conditions show lesser fatigue life. Hence it is important to calculate the fatigue life by finite

endurance limit.

Figure. Variation of stresses in an aircraft operation

According to Miner’s law the total life of a part can be estimated by adding up the

percentage of life consumed by each over stress cycle. If n1 cycles in a cyclic loading leads to

failure after N1 cycles then 1

1

n

N is the proportion of damage that has occurred. If the stress

amplitude change to n2 cycles and at that amplitude failure occurs after N2 cycles then 2

1

n

N is a

measure of the proportion of damage caused during that period. According to Miner’s law the

component will fail when the sum of all the cyclic ration‛ equals to unity.



58

31 2 4

1 2 3 4

1 or ... 1n

N

nn n n

N N N N

Miner law is also called as Fatigue Miner’s rule or cumulative damage rule

BAUSCHINGER EFFECT :

According Bauschinger under cyclic stress (fatigue) the proportionality limit (Yield

strength) of the material does not remain constant but varies according to the direction of stress.

During plastic deformation, the yield strength of the metal increases in the direction of

plastic flow when loaded beyond the elastic limit. But the plastic deformation would start at a

lower yield stress if the stress is applied in the direction opposite to the initial direction. This is

due to the fact that under the reverse load the residual stresses caused by initial deformation

increases the stresses. This phenomenon is called as Bauschinger effect of elastic hysteresis.

Figure:

Consider the figure (a). The points A and B on the curve represents the yield stresses of the

metal when it is loaded in tension and compression respectively. The yield stresses at A and B

will be equal in magnitude and opposite in sign.

Supposing if the tensile load is gradually applied at higher stresses than the yield stress

(i.e,. stressed beyond elastic limit) we obtain the curve Of (Figure(b).

The point F is at a higher stress than the yield point A. Now if the load is gradually

removed then the curve will follow the path FE instead of FO. This means that the metal has

developed a permanent strain OE. If the metal is reloaded in a direction opposite to the original

slip direction (i.e compressive load is applied gradually), the plastic flow begins at D.



59

The compressive stress at D is low than the original value of compressive yield stress at F.

This decrease in compressive yield stress after the tensile loading of the metal is know as

Bauschinger effect.

Similarly if the metal is loaded initially in compression, the Bauschinger effect will be

observed when the metal is reloaded in tension at point G. Thus the reduction in compressive or

tensile stress is due to the presence of residual stress even after the removal of load. These

residual stress cause the dislocation to move more easily in a direction opposite to the original

direction even at low stresses, also when the slip direction is reversed, dislocations of opposite

signs may be created which attract and cause slip easier. The total result is the softening of the

metal. Hence the plastic flow begins at a lower stress and failure by fatigue occur by repeated

cyclic loading.

BLUE BRITTLENESS :

When a material is tested at elevated temperature thy yield point is not well defined and

the slope of the plastic reform of the curve becomes steep and some times serrated (figure)

The specimen rapidly reaches a high stress value and failure occurs at low elongation (less

strain). This phenomenon is blue brittleness.

It is observed in iron at about 200oC – 300oC. The reason for blue brittleness is that at these

temperatures, there is sudden breaking of dislocation causing a pattern of yield points an the

stress strain curve.

Figure



60

ORANGE PEEL EFFECT :

This occurs in coarse grained metals in which individual grains deform independently, this

causes a rough surface, and is called orange peel.

These marks occur on many metals during stretching at low temperatures. The orange peel

can be completely removed by refining the grains by heat treatment such as annealing.

2. Cleavage Fracture?

The process of cleavage involves transcrystalline fracture along specific crystallographic

planes and is usually associated with low-energy fracture. This mechanism is observed in BCC,

HCP, and ionic and covalently bonded crystals, but occurs in FCC metals only when they are

subjected to severe environmental conditions. Cleavage facets are typically flat, although they

may reflect a parallel plateau and ledge morphology. Often cleavage steps appear as ‚river

patterns‛ wherein fine steps are seen to merge progressively into larger ones. It is generally

believed that the ‚flow‛ of the ‚river pattern‛ is the direction of microscopic crack propagation

(from right to left). The sudden appearance of the ‚river pattern‛ in figure was probably brought

on by the movement of a cleavage crack across a high-angle grain boundary, where the splintering

of the crack plane represents an accommodation process as the advancing crack reoriented in

search of cleavage planes in the new grain. It is also possible that the cleave crack traversed a low-

angle twist boundary, where the splintering of the crack plane represents cleavage planes in the

new grain. It is also possible that the cleavage crack traversed a low-angle twist boundary, and

the cleavage steps were produced by the intersection of the cleavage crack with screw

dislocations.

In some materials, such as ferritic steel alloys, the temperature and strain-rate regime

necessary for cleavage formation is similar to that required to activate deformation twinning. Fine

scale height elevations (so called tongues) seen in figure, provide proof of deformation twinning

during or immediately preceding failure. In BCC iron, etch pit studies have verified that these

fracture surfaces consist of {100} cleavage facets and {112} tongues, the latter representing failure

along twin matrix interfaces.

Little information may be obtained from cleavage facets for use in failure analyses.

However, one may learn something about the phase responsible for failure by noting the shape of

the facet and comparing it to the morphology of different phases in the alloy.



61

Figure: Cleavage fracture in a low-carbon steel. Note parallel plateau and ledge morphology

and river patterns reflecting crack propagation along many parallel cleavage planes: (a) TEM;

(b) SEM.

Figure: Cleavage facets revealing fine-sclae height elevations caused by localized deflection of

the cleavage crack along twin-matrix interfaces: (a) TEM; (b) SEM.

Furthermore, in materials that undergo a fracture mechanism transition (e.g., void

coalescence to cleavage failure), it is possible to relate the presence of the cleavage mechanism to a

general set of external conditions. In most mild steel alloys (which undergo the above fracture

mechanism transition), the observation of cleavage indicates that the component was subjected to

some combination of low-temperature, high-strain-rate, and/or a high tensile triaxial stress

condition.

3. Micro void coalescence.

Micro void coalescence (MVC), observed in most metallic alloys and many engineering

plastics, takes place by the nucleation of micro voids, followed by their growth and eventual

coalescence. These mechanically, induced microspores should not be confused with preexistence

microsporosity sometimes present as a result of casting or powder sintering procedures. The

initiation stage has largely been attributed to either particle cracking or interfacial failure between

an inclusion or precipitate particle and the surrounding matrix. Accordingly, the spacing



62

between adjacent microvoids is closely related tot eh distance between inclusions. Where a given

material contains more than one type of inclusion, associated with a bimodal size distribution,

micro voids with different sizes are often found on the fracture surface. The criteria for void

nucleation are complex and depend on several factors, including inclusion size, stress and strain

levels, local deformation modes, and alloy purity. Earlier computations have shown that most of

the fracture energy associated with MVC is consumed during growth of the micro voids. At least

two growth mechanism have been identified: (1) plastic flow of the matrix that surrounds the

nucleation site, and (2) plastic flow enhanced by decohesion of small particles in the matrix. The

final step of MVC that leads to leads to final failure involves the coalescence of countless

microvoids into large cracks. Often, this process occurs by the necking down of material

ligaments located between adjacent microvoids, thereby leading to the impingement of the

adjacent microvoids. Coalescence may also proceed by linking together large microvoids with

many smaller voids that form within strain-localized intense shear bands (see figure).

The fracture surface appearance of microvoids depends on the state of stress. Under simple

uniaxial loading conditions, the microvoids will tend to form in association with fractured

particles and/or interfaces and grow out in a plane generally normal to the stress axis. (This

occurs in the fibrous zone of the cup-cone failure shown in section). The resulting micron-sized

‚equiaxed dimples‛ are generally spherical, as shown in figure. Since the growth and coalescence

of these voids involves a plastic deformation process, it is to be expected that total fracture energy

should be related in some fashion to the size of these dimples. In fact, it has been shown in

laboratory experiments that fracture energy does increase with increasing depth and width of the

observed dimples.

When failure is influenced by shear stresses, the voids that nucleate in the manner cited

above grow and subsequently coalesce along planes of maximum shear stress. Consequently,

those voids tends to be elongated and result in the formation of parabolic depressions on the

fracture surface, as shown in figure (such voids are found in the shear walls of the cup-cone

failure). If one were to compare the orientation of these ‚elongated dimples‛ from matching

fracture faces, one would find that the voids are elongated in the direction of the shear stresses

and point in opposite directions on the two matching surfaces.

Finally, when the stress state is one of combined tension and bending, the resulting tearing

process produces ‚elongated dimples‛, which can appear on gross planes normal to the direction

of loading. The basic difference between these ‚elongated dimples‛ and those produced by shear

is that the tear dimples point in the same direction on both halves of the fracture surface. It is

important to note that these dimples point back toward the crack origin. Consequently, when

viewing a replica that contains impressions of tear dimples, the dimples may be used to direct the

viewer to the crack origin. A schematic diagram illustrating the effect of stress state on

microvoids morphology is presented in figure.



63

It may be desirable to determine the chemical composition of the particle responsible for

the initiation of the voids. By selected area diffraction in the TEM of particles extracted from

replicas or by X-ray detector instrumentation in the SEM, it often is possible to identify the

composition of particles responsible for microvoid initiation.

Figure: Micro void coalescence under tensile loading, which leads to “equiaxed dimple”

morphology: (a) TEM fractograph shows “dimples” as mounds; (b) SEM fractograph shows

“dimples” as true depressions.

Figure: Microvoid coalescence under shear loading, which leads to “elongated dimple”

morphology : (a) TEM fractograph shows “dimples” as raised parabolas; (b) SEM fractograph

shows “dimples” as true elongated troughs.



64

Figure: Diagram illustrating the effect of three stress state on microvoid morphology: (a) tensile

stresses produce equiaxed microvoids; (b) pure shear stresses generate microvoids elongated in

the shearing direction (voids point in opposite directions, on the two fracture surfaces); (c)

tearing associated with nonuniform stress, which produces elongated dimples on both fracture

surfaces that point back to crack origin.

With this information, it may be possible to select a different heat treating procedure and/or

select an alloy of higher purity so as to suppress the void formation initiation process.

4) VOID GROWTH

In this section, we describe the approaches that result in expression for void volume

fraction and tertiary creep strain resulting from void growth. As noted, this growth can take place

by boundary-diffusion control (spherical voids), surface-diffusion control (wedge-shaped voids).

Or power-law creep. We consider only one mechanism-boundary-diffusion control-in detail,

although results for the other mechanisms are given. The Cocks and Ashby reference can be

consulted for details relative to these other mechanisms.

The flux of matter from the void surface/grain boundary junction to a boundary position

intermediate between two voids is given by since surface diffusions us rapid vis-a-vis boundary

diffusion, the chemical-potential driving force is dissipated along the grain boundary and not the

void periphery.

BB

DJ

kT x



65

In equation DB is the boundary-diffusion coefficient (m2/s), is the atomic volume

(m3/atom), kT has its usual meaning (dimensions of energy , e.g., joules (J)), and ∆ is the change

in chemical potential (, dimensions of Nm/atom) which is dissipated over the distance ∆x .

We note that JB has dimensions of [number (of atoms)]/(m2s). Taking the diffusion distance as half

the intervoid spacing, l, we have

BB

DJ

kTl

Multiplying JB by the area available for diffusion (proportional rhB , where B is the grain-

boundary thickness) give the number of atoms per second leaving the void volume. And

multiplying this term in turn by the atomic volume gives the rate of increase in void volume due

to atoms departing it. Calling this rate of change in volume dv/dt, we have

( / )

B BB B n

n

D gD rdv

dt dTl kT l r

The above expression is not exact; it does not consider geometrical details, for example.

However, the physics of void growth is essentially described by equation. Further, knowing dv/dt

permits us to obtain expressions for the instantaneous values of the void radium and voided

grain-boundary area ( hf , the ‚damage:, the void radius and damage are related through 2 2/h hf r l ). Beyond that we can calculate the tertiary strain rate and strain resulting from void

growth. This strain arises from two effects. One is the strain directly associated with void growth.

This strain arises is a result of the plating of material on the grain boundaries; this causes the

grains to elongate, i.e., to produce a creep strain. Performing the necessary (any labored)

‚arithmetic,‛ the following expressions are obtained for the damage and tertiary strain rate for

boundary-diffusion-controlled void growth.

3 1/ 2

1

ln(1/ )n B B

h h

df D

dt kTl f f

2

1 2

1 (1/ )B B

t

n

D

n f kTl d

Equation stipulates only the tertiary creep rate (t). The total creep rate is obtained by

adding to it the steady-state creep rate. Note that the expression for t contains the grain size, d.

This is because the tertiary extension must be divided by an appropriate gage length. Since the

growing voids are separated by the grain diameter along the tensile axis, the grain size is the

appropriate gage length.



66

A similar analysis applies to surface-diffusion-controlled void growth, with but two

alterations. One is geometrical. The analysis assumes that the void grows laterally only,

neglecting any extension of the void dimension, r0, along the gage length. In addition, the analysis

considers the effect of the surface energy, s, which acts to restrict the formation fo wedge-shaped

voids. Because of the latter considerations, it is found that the damage and tertiary creep rates

depend more strongly on stress for surface-diffusion-controlled void growth than for boundary-

diffusion-controlled void growth. Results of the analysis for the growth of ‚wedge-like‛ voids

lead to the following expressions for the damage and tertiary strain rates;

1/ 2 3

3 2

1/ 2 2

0.71

91

h h S S

sh

h S St

h s

df f D

dt kTldf

f D

f kTld

In equation DS is the surface-diffusion coefficient and S is the effective thickness over

which surface diffusion occurs. The other terms have their previous meanings.

Voids can grow by power-law creep, too. As indicated in figure, for power-law creep the

strain rate in the voided region is increased by the factor (1 – fh)-m in comparison to that in material

within the grains. The higher strain rate in the boundary regions causes the voids to dilate and

grow, and this leads to an increase in damage and to tertiary creep. Analysis shows that the

damage and strain rates are given by

'

0 0

'1/ 2'

0 0

10.6 (1 ) (1 )

1.21 1

m

mhh h

m

mhth

dff f

dt

ff

d

In equations new terms, 0 and 0 are introduced. These are linked to the steady-state

power-law creep rate (ss) through ss = 0 (/0)-m’, and can be coached in terms of the analysis of

e.g., table). However, for the present purposes it is easier to consider the terms 0 and 0 as a

normalized strain rate and a normalized stress such that when the applied stress is equal to 0 , the

material’s steady-state creep rate is 0.

Transgranular creep fracture – which is controlled by power-law creep-can be handled in

the same way used here to describe power-law creep ICF. Induced, an expression, the same as

that equations holds for the damage rate for TCF. However, because voids are present throughout

the material during TCF – and not restricted to grain boundaries – the TCF tertiary creep strain



67

greater. The proper correction is made by multiplying equation by the ration d/l to obtain the

expression for the TCF tertiary creep strain rate.

What is one to make of, or to do with, the above equations? First, some of their physics.

We see that the damage and tertiary creep rates depend on material parameters (e.g., diffusion

coefficient, surface energy, etc.,), the instantaneous value of the damage, and the applied stress.

The dominant void-growth mechanism, therefore depends on these factors. And, since the

damage rate depends differently on stress growth mechanisms at different stress levels.

Boundary-diffusion-controlled void growth should dominate at low stress levels, for it depends

only linearly on the stress. At somewhat higher stresses, surface-diffusion control-for which the

damage rate varies with the cube of the stress-should supersede boundary-diffusion control. This

is in agreement with experimental observations that ‚w‛ cavities are found at higher stress levels

that are ‚r‛ cavities. Finally, at even higher stress levels, power-law creep should control because

the damage rate for it depends on the stress to the m’ power (m’ is usually greater than three for

power-law creep). Had we knowledge of the pertinent parameters in the damage rate equations

and the pertinent scale to the voids (particularly their spacing, 2/l) equations, and would permit us

to estimate fracture times. How to go about conducting such an estimate is discussed in the next

section.

EXAMPLE PROBLEM

Compare grain-boundary- and surface-diffusion-controlled void growth in the following

way. For equal volumetric void growth in the following way. For equal volumetric void growth

rates, determine the ratio of the damage accumulation rate (dfh/dt) for the two mechanism.

Solution. The damage is the voided area ratio in the unit cell pillbox of figures. The radius

of the pill box is l: the radius of the void is rh. Thus, the damage is given by 2 2/h hf r l in both

cases and the damage rate is

2

2h h hdf r dr

dt l dt

The volume rate of change of a spherical void (volume = 34 / 3hr ) is d /dt = 24 ( / )h hr dr dt .

For the penny-shaped void (volume = 202 hr r ), d /dt 4rhr0 (drh / dt). Expressing the damage rate

in terms of the volume mass transfer rate, we have

2h

20

1( control) =

2 r

1( control) =

2 r

h

h

df dvboundary diffusion

dt l dt

df dvsurface diffusion

dt l dt



68

Thus, for equal values of dv/dt, the damage rate for surface-diffusion control is greater by

the factor rh/r0. This means for equivalent mass transfer, damage accumulation is greater when the

voids are penny-shaped.

iii. DOMINANT VOID-GROWTH MODES. In this section, we restrict our discussion to

ICF; extrapolation of the approach to TCF can be easily done. In analyzing creep fracture, we

must first determine – for diffusion-controlled void growth-whether voids grow by boundary-

diffusion control (spherical voids) or surface-diffusion control (penny-shaped voids). This is done

by comparing the respective damage rate equations and determining which is less. (Recalls that

the diffusion processes are series processes). The assessment depends on the instantaneous value

of the damage and further presumes the proper ancillary data are available. Following this, we

determine whether the damage rate for power-law creep is greater than that for the dominant

diffusion-control mechanism; this depends on the stress level as well as the instantaneous damage

value. We then reasonably take the damage rate as that of the mechanism having the higher

damage rate. This assumption neglects ‚coupling‛ of mechanism, and is not always a good

assumption. See Cocks and Ashby for application. However, our assumption makes discussion

of the already complicated physics of void growth a little less hairy.

Determination of the dominant void-growth mechanism is conveniently done graphically;

examples are shown in figure (a) and fig(b). Figure a plots nor malized damage rate (i.e., the

damage rate divided by 0 ) vs.normalized stress (the stress divided by 0 ). Here we have

assumed that boundary diffusion controls diffusional void growth so that the voids are spherical.

The graph is also constructued for specific values of the microstructural parameters (d and l) and

thermophysical parameters (e.g., the diffusion coefficient). The graph also pertains to a specified

value of fh; 0.01 in this instance. Note that in fig.a there is a transition nin the dominant void-

growth mechanism with increasing stress. Boundary diffusion controls the damage rate at low

stress levels and power-law creep does so at high stress levels. This transition is the creep-fracture

analog to the like transition in creep deformation mode when the dominant creep mechanism

changes from diffusional to power-law creep (Fig) with increasing stress. T the total damage rate

is that resulting from both processes and is represented by the solid line in fig. a resulting from

both processes and is represented by the solid line in fig.a. Over a reasonable stress range, the

total damge rate can be taken as that resulting the dominant mechanism.

Just as increases in stress cause a transition in the controlling mode of damge accumulation,

a similar transition is effected by increases in fh. This is illustrated in Fig(b), in which boundary-

diffusion and power-law creep damge rates are plotted vs. fh at a constant stress (material

properties are the same as in fig. a and in fig(b) we have taken =0). For 25 10 ,hf damage

accumulation is controlled by boundary diffusion; when fh is greater than this value, power-law

creep controls damage accumulation. The solid line in fig (b) represents the total damge rate. As

before, it is approximately the sum of the individual rates.



69

The intersection of the two curves of fig(b) represents a transition in void-growth

mechanism with damge accumulation. That is, voids initially grow by boundary diffusion until a

transition value of fh (designated 2; 5 10tf in fig.(b) is realized. The later stages of void growth

are controlled by power-law creep. A similar discussion of the transition from surface-diffusion-

controlled to power-law-creep-controlled damage accumulation can be carried out. It is left as an

exercise.

We can also have transitions from boundary-diffusion-controlled void growth to surface-

diffusion-controlled growth. However, since these processes operate in series, rather than

parallel, it is the lesser of their rates that determines damage accumulation.



70

Figure: (a) Damage rate as a function of stress for void growth controlled by grain-boundary

diffusion and by power-law creep. The rates of the individual mechanism and are shown by

the dotted lines. The solid line represents a more detailed development that considers

coupling of the mechanisms and represents the total damage rate; it can be approximated as the

sum of the individual rates. For low stresses 0( 0.4 ), damage rate is controlled by

diffusional void growth; at high stresses 0( 3.0 ). power-law creep void growth determines

the damage rate. The stress at which the dominant void-growth mode changes is slightly

greater than 0. (Note: The curves are drawn for a specific material, as reflected in the value of

m’ and for specific values of diffusion coefficient, etc., and for a fixed damage). (b) Damage

rate as a function of damage for void growth controlled by grain-boundary diffusion and by

power-law creep. Again, the dotted lines represent Equations. The solid line represents the

damage rate due to both mechanisms. Boundary diffusion controls damage rate when the

damage is low and power-law creep controls it when fh is high. The transition in dominant

void-growth mode takes place at fh = ft. The curves are drawn for the same material properties

as in (a) and for a stress 0 . (Reprinted from A.C.f. Cocks and M.F. Ashby, Prog.Matls. Sc.,

27, 189, Copyright 1982, with permission from Elsevier Science).

While the damage rates for the two mechanisms depend on the instantaneous damage in

different ways, the important kinetic variable that differentiates the mechanisms is the diffusion

coefficient. To a first approximation, for example, we would expect that if DB > Ds, penny-shapped

cracks would form, surface diffusion would control void growth, and the damage rate is

expressed by Equation. Since DB and Ds vary differently with temperature, the transition from

boundary-diffusions from one or the other of the diffusion-controlled growth mechanisms to

power-law creep control is also temperature sensitive. The complexities associated with

temperature and stress-induced transitions in void-growth mechanisms can be reduced by

representing them in the form of a void-growth map.

Void-growth maps have the same axes m/ and T/TE as fracture mechanism maps;

indeed, they can be considered a refinement of fracture maps. Void-growth maps constructed fro

the metal Cu are shown in fig (a) and (b). The lower dotted lines in these diagrams represent the

sintering limit; applied stress levels less than this lead to void shrinkage and not growth. The

solid line separating the two diffusion-controlled void-growth regions is the approximate locus for

which Ds = DB. The transitions from surface-diffusion control (at higher temperatures) to power-

law creep control are obtained from plots similar to those of fig.(a). The stress at which the

transitions occur is temperature sensitive, as can be seen in this diagram. The upper boundary

line at high stress levels in figs, corresponds to void-growth maps are constructed fro a specific

value of fh; thus, each map is a ‚snapshot‛ in time and Figs.(a) and (b) are different because they

have been constructed for different damage higher) than does fig (a). In addition, the maps are

constructed for a specific value of inter void spacing (=24 m for the maps of Figs).



71

As shown in figs, contours of constant damage rate can be drawn on void-growth maps

and this increases their utility. As in deformation-and fracture-mechanisms maps, the boundaries

between various regions in a void-growth map are diffuse. For void-growth maps this reflects

both the uncertainty in the data used to construct them and the ‚coupling‛ effects associated with

void growth.

Although void-growth maps are conceptually useful for determining the controlling

damage accumulation mechanism, they have limitations. For example, they are ‚permissive‛

maps. As noted, they are constructed for a specific fh cavities of the specified amount were

present. As an illustration, copper dynamically recrystallizes and undergoes rupture fracture over

much of the temperature-stress regime occupied by ‚power-low creep growth‛ in fig. In this case,

while the maps tell us the rate and mechanism of goid growth if voids are present, as a result of

dynamic recrystallization they are not. We also see that the boundaries of the map ‚sweep

downward‛ as fh increases (compare fig(b) 1 210 . 10 .h hf toFig a f This is a manifestation of

the kinds of transitionshown in fig.b. i.e., power-law creep dominates void growth at higher

values of fh. The sintering limit also decreases as void volume (more precisely, void size)

increases. For the maps of fig, which are constructed for a constant void spacing, the limit

decreases by a factor of 1

210 as fh increases from 10-2 to 10-1. This is expected because the limit

scales with 1 ,hr and since 2 ,h hf r the sintering limit varies as

1/ 2.hf



72

Figure: Void-growth mechanism maps appropriate to cu with l=12 m, and for a damage of (a)

10-2 and (b) 10-1. The boundary lines separating the regions are loci of equivalent damage rate

due to two mechanisms. Within the power-law creep region, damage rate due to this process is

greater than that due to the controlling diffusion process. Likewise, when (either of the)

diffusional damage rates is greater than that due to power-law creep, a diffusion-controlled

growth region is shown in the diagram. The shaded regions indicted stress-temperature

combinations for which coupled growth must be considered. The lower broken line represents

the sintering limit; at stresses less than this, voids shrink rather than grow. Contours of

constant damage rate are also shown in the diagrams. (From A.C.F. Cocks and M.F. Ashby,

Prog. Matls. Sc., 27, 189, Copyright 1982, with permission from Elsevier Science).

(iv) Time and strains to fracture

Equation permit (in principle) determination of creep-fracture strains and fracture times. It

is assumed that voids nucleate at some time, tn, and with some initial void volume fraction, fh0.

The dominant damage accumulation mechanism for these initial conditions is identified, and the

damage rate is integrated until a value of damage is attained at which a transition in the

controlling damage mechanism takes place (e.g., from diffusion control to power-law creep

control, fig.b). Then the damage rate is further integrated from the transition damage value, ft,

until the critical damage value (reasonably approximated as 0.25) is attained. Doing this permits a

fracture time to be calculated. It is the sum of the void nucleation. Likewise, the tertiary creep

strain is the sum of the strains occurring during the two different damage accumulation modes.

The creep-fracture strain is obtained by adding to it the steady-state creep strain accumulated over

the fracture time. Details of the procedures can be found in the Cocks and Ashby reference.

The procedure appears straightforward enough. And it is-in principle! Now we repeat

why its practical implementation is difficult. First, we do not know the void nucleation time. If

voids nucleate early during creep deformation,‛ we can approximate the creep-fracture time as

that time associated with void growth until the critical damage value is reached. If cavities

nucleate late during creep deformation, the fracture time just arrived at is a conservative estimate

of the material life time. We must also estimate a value of the as-nucleated damage. (One can

probably reasonably bracket initial damage values. Then the uncertainty in the fracture time is

that time needed for the damage to increase between its initial bracketed values). More serious,

though, is that the initial void spacing must also be stipulated to realistically employ the damage-

rate equations. Our present state of understanding of void nucleation does not permit us to do

this. (although here, too, we can likely realistically bracket this spacing). Finally, the ancillary

data to effectively use the damage-rate and tertiary-creep-strain rate equations are, for the most

part, missing. Surface energies can be guessed at within a factor of two or so, but grain-boundary

and surface diffusivities are seldom known to precision. So we are left with the distasteful

situation where a physically appealing model cannot be employed in engineering design because



73

we have too many unknowns to contend with. Let’s hope that this will not always be the

situation.

Before leaving fracture-mechanism and void-growth maps, some final comments are in

order. We have treated high-and low-temperature fracture as if they were entirely separable, but

they are not. Let us reconsider fig c, the fracture map of Mg. This map implies that low-

temperature Mode I fracture is supplanted by ICF at a critical (stress-dependent) temperature.

There is a temperature range, however, over which the transition from Model I low-temperature

fracture to ICF in Mg is gradual. During this transition, preexisting cracks in Mg still propagate as

a result of the stress intensification at their tips. But, because creep deformation takes place at the

crack tip, the propensity fro rapid crack advance is lessened relative to what it is at low

temperature. On the other hand, the stress intensification associated with the crack cn enhance the

growth of voids somewhat removed from the crack. Ice serves as a good example here. We think

of ordinary low-temperature (i.e., temperatures slightly below 0oC) fracture of ice as brittle.

However, we are familiar with fracture of ice at high stresses. At lower stress levels, crack

advance in ice involves aspects of both low-temperature fracture mechanics and diffusion. In fact,

a new field of fracture mechanics describes this type of ‚combined‛ fracture, not only in ice but in

other materials that behave similarly.

5. Fracture maps for different alloys and oxides?

Nickel

Figure a fracture mechanism map for nickel, is typical of fracture maps for many FCC

metals and alloys. It shows four mechanism fields, at high stresses and low temperatures, the

metal fails by ductile fracture; that is, by the formation of a fibrous ‚cup‛, surrounded by a shear

lip or ‚cone‛ forming in the necked regime of the tensile specimen. As the temperature is raised,

the metal starts to creep and, in the range of temperature and stress indicated in the figure, it fails

by a transgranular creep fracture. The fracture mechanism is identical with that of ductile

fracture, but the dominant mode of plasticity causing this growth and linkage has changed; it is

power law creep, not glide plasticity. The boundary between these two fields simply shows

where power-law creep becomes the dominant mode of flow. Below this transgranular creep-

fracture field lies as a field of intergranular creep fracture. Specimens stressed in this regime fail

because creep cavities or wedge cracks nucleate and grow on grain boundaries (often those

carrying the largest normal traction) until they link, reducing the cross section of the specimen

until plasticity causes the remaining ligaments to fail. Such samples show little or no necking and

may fail after very small strains. The transition is a gradual one with the shaded band. A mixed

mode of fracture-part transgranular, part intergranular-is observed. As the temperature is raised

further, strain-induced grain growth and dynamic recrystallisation accompany the creep test. The

result is a broad transition to rupture seeking to a point or chisel edge.



74

Figure illustrates all these mechanisms observed in nickel tested in four fields. The transition

from power-law creep-controlled fracture to diffusion controlled fracture is shown in the map.

However, the regime of wedge cracking is separated by a dotted line from the regime of creep

cavitation, and both these submechanisms are observed in the intergranular creep fracture field.

Fracture mechanism maps for copper and silver the very similar, if not identical, to that for nickel.

Nickel-Base Alloys

Nickel-base alloys are used over a wider range of temperature than any other alloys, from

eryogenic temperatures (-0.02 TM) to over 1000 C (0.74 C TM). In this section, we examine how,

over this broad temperature large, the fracture mechanisms of nickel are influenced, first by a

solid solution along, by solid solution and precipitation hardening, and by a stable oxide

dispersion.

Figure shows a map for Monel, a solid solution of nickel and copper. The four basic fracture

mechanism, seen in the map, are comparable to close observed in pure nickel. There are,

however, several differences. The creep-rupture data are so consistent that we could draw the

contours of constant time-to-failure. The other difference is that the field boundaries are shifted

to higher stresses and dynamic recrystallisation is shifted to higher temperature. The fracture

mechanism map for Nichrome is very similar to the map for Monel.

The above observations are more vivid in tagonet X-750, where the effect of solid solution

strengthening, along with precipitation strengthening, is seen by the shrinkage of transgranular

creep fracture and rupture fields. The higher stresses observed in this alloy may also suggest that

the ductility may be the major concern in the intergranular creep-fracture field. A map for

Nimonic-80A looks very similar to figure.



75

Figure: Optical scanning electron micrographs characterizing the four fields of the map for

nickel



76

Figure: A map for Monel-400, roughly a 70:30 Ni-Cu solid solution. It shows the same fields as

figure displaced to higher stresses. Contours of constant time-to-fracture are shown.

Finally, a stable oxide dispersion can completely suppress dynamic recrystallisation in

nickel. As a result the rupture field may disappear from the fracture map for DS-Nickel.

Advanced superalloy technology now permits preparation of dispersion-strengthened

superalloys which find application in intermediate and high temperature operations in gas

turbines.

Figure: A map for Inconel X-750. (The materials data references are R18, R19.)

Aluminium and Its Alloys

Aluminium differs from most other FCC metals in two respects. First, when aluminium is

pure enough, intergranular fracture is displaced to very low stresses or suppressed entirely. The

reason for this may be that the metal wets the inclusions it contains, making nucleation of grain

boundary cavities difficult, or that the stresses within pure aluminium, which is very soft, are

low-perhaps too low to nucleate grain-boundary cavities. The second difference is that

aluminium does not show dynamic recrystallisation. In spite of this, however, the regime of

rupture appears also on the map for aluminium.



77

Figure: A map for nickel containing about 2 vol% of finely dispersal (DS-Nickel). The strengthens

the nickel and <<<..

This section describes maps for high-purity (99.9%) aluminium (figure) for commercial

grade (99.9%) aluminium figure, and for creep resistant aluminium alloy RR58. They show in a

more pronounced and the same progression (the effect of solid solution and precipitation)

observed in nickel alloy. Intergranular creep fracture is not observed in the purest aluminum but

impuities and alloying loise the overall strees level and cause the intergtanular fracture field to

expand that a tlenunttes the creep tegune. The result is used the for the heavles alloyed RRSS is

unlike that for crop the overall stress level and cause the intergranular fracture field to expand

until it dominates the creep regime. The result is not the for the



78

Figure: A map for high purity (99.9%) aluminum. No interoperate also the tribute field has

been observed, and rupture (in fine – grain found specimens) is observed only above 0.6 Tst

Bead and its deluxe differs:

Bead like aluminium differs from the more typical FCC metals nickel coppet and sitys in

that tends to fail by rupture over a wiber tenge of stress and tempenature. Rupture in nicked is

associated with sottening caused by dynames for restallration, and in all but the puress single

erystals, it is obsessed only above 0.65 Tst . Rupture in lead, however, is common at toain

temperature.



79

Figure: A map for commercial 2S grade (99 + %) aluminum. Intergranular fracture appears.

(Ref R26, R27, R31 – R 33)

Most of the previousls published tests on lead and its dilute alloys were swlisted has the beste to

imptove cable shcathing. The data were obtained be can the best tests on tubes having relatively

thin walls or to thin she agun, were always them. Because of this number is in the speion was

generally small (<100), and the consolation pears in the neck of a larger cylindrical specimen was

absent. Both ause the general strees level (and particular the hydrostatic ten the sample to be

lower than that in a fine grain cylindrical specimen, reason, the tube and sheet fail by rupture,

under conditions which be – grain cylindrical specimens to show a transgranular ductile



80

Figure: A map for Hiduminum RR 58. Intergranular fracture has become more prominent,

following the progression shown by the nickel – base alloys

Two for this, maps for lead show a widely and associated with the boundary of the rupture

field. The right be band refers to cylindrical specimens with many grains in the cross the left edge

refers to the sheet with a few grains in the section intergranular creep failures are reported in both

materials at low stress and long fracture lives (> 108 s in pure Pb and > 107 s in lead – antimony

alloy)

Iridium and Rhodium:

Maps for FCC metals and alloys shown in the previous sections do not contain fields for

cleavage failures. At least two FCC metals, iridium and rhodium, show intrinsic cleavage,

meaning that these failure mechanisms operate even when the material is very pure. The fracture

maps for iridium and rhodium are similar to those for refractory metals, which are described in

section.



81

Figure: A map lot pure of soft lead the size of the rupture field depends on purity, grain size,

and specimen shape. The limits shown here are ten cost the grain she and for time grain round

ten sile bars. (Ref R27, R38 R 41)



82

UNIT – IV

OXIDATION AND HOT CORROSION

1. OXDATION

Introduction :

With the increasing use of alloys at high temperatures the problem of oxidation has become

increasingly important.

Oxidation is a type of corrosion, a reaction of metals and alloys with oxygen at high

temperatures, usually in the absence of moisture.

It differ from the rusting of iron that occurs in the presence of moisture.

Oxidation is a diffusion process and usually continued oxidation proceeds by the diffusion

of metal ions and electrons through the oxide layer.

The resistance to oxidation of any metal at elevated temperatures is dependent on the

nature of the oxide scale formed.

If the scale is loose and porous, the oxidation will continue until ultimately the complete

section of metal is oxidized.

And, if the oxide scale is adherent and non-porous, the thin film first formed will act as a

protection to the underlying metal.

Kinds of oxides Formed on the Metal Surfaces :

1. Unstable Oxides : If the oxide’s dissociation pressure is less than the applied partial

pressure of oxygen, the oxide is unstable, as in the case of gold oxide and oxidation does not

occur.

2. Volatile Oxides : The oxide may be volatile, as in the case of molybdenum oxide, and

oxidation occurs at a constant, relatively high rate.

3. Oxide Layers : One or more oxides may form porous of nonporous layer(s) at the metal

surface.

This Kind (i.e., oxide layers) of oxidation is the most common and various aspects of its behaviour

are discussed below.



83

3. (a) Oxide Films and Scales :

Surface oxide layers are known as films when they are less than 3000oA thick the are called

scales when their thickness exceeds this value and is more easily measured.

Non-porous oxide films serve as thin protective films (as in aluminium ) and decrease the

rate of additional oxidation.

An example of film formation is seen is steel heat-treatment, i.e., the formation of temper

colours during the heating of steels in the range 450oF to 600oF.

Protective oxide films are usually typical ionic crystals. Their growth may occur by,

(a) Outward diffusion of metal ions and electrons figure (a).

(b) Migration of oxygen ions toward the metal – oxide interfa

(c) ce and concomitant outward movement of electrons figure (b).

(d) Combination of (a) and (b) or by a counter-current movement of metal ions and electrons

outward and oxygen ions inward figure (c).

Figure: Mechanism of oxide film growth.

Oxide films may exhibit ionic of electronic conductivity.

From the above mechanism of the growth of oxide films, it may be concluded that

oxidation resistance of metals may be improved by alloying them with suitable elements

such as chromium or aluminum which form thermally stable and protective oxide films.

The oxidation of some metals can be controlled by the diffusion of ionic defects such as

interstitials and vacancies, through an oxide layer.

Figure shows how the addition of chromium creates additional cation vacancies thereby

increasing the oxidation rate.



84

Figure:

3. (b) Internal oxidation :

Under certain conditions, oxidation of an alloying element my occur below the surface of

the base metal. Such internal oxidation requires following conditions :

1. Alloying element should have more affinity for oxygen than does the base metal.

2. Oxygen must diffuse rapidly in base metal as compared with the diffusion of the

alloying element.

3. Scaling of the base metal should not be too rapid to destroy the surface region in

which internal oxidation is talking place.

Internal oxide layers create problems and these layers are difficult to remove by the usual

cleaning methods.

In some cases internal oxidation may be usefully employed as a method of surface

hardening.

CORROSION (AND OXIDATION) CONTROL :

Introduction :

The types of corrosion are many and the conditions under which corrosion takes place are

extremely varied. For this reason, many ways have been found out to control and prevent

the corrosion of metals and alloys.

Broadly the methods to control corrosion base upon :

(a) Proper design of structures (i.e., Design against corrosion ).

(b) Control of corrosion mechanism.

(c) Insulation of the material from the corrosive environment.



85

Different techniques of corrosion control are :

1. Design against corrosion.

2. Use of high purity metals.

3. Use of alloy additions.

4. Use of special heat-treatments.

5. Cathodic protection.

6. Use of inhibitors.

7. Environment control.

8. Use of protective surface coatings.

1. Design against corrosion :

Proper design should permit least contact between the structure and the corroding agent.

Joints should be such that the liquid does not get a chance to enter and be retained.

The use of dissimilar – metal contacts should be avoided where the presence of an electrolyte

may result in galvanic corrosion.

If two different metals have to be used, they should be as close as possibility of each other in

the galvanic series.

If this is not possible, they (i.e., metals) should be separated (i.e., insulated) by rubber or

plastic to reduce the possibility of galvanic corrosion, Figure.

Figure: Practice of insulating to avoid galvanic corrosion

The anodic material should have as large an area as possible, whereas the Cathodic material

should be of much smaller area.

Crevices, recesses, pockets and sharp corners should be avoided.

Structure should be stress free and possess good surface finish.

Welded joints, rather than brazed, soldered or bolted joints, may be used in order to avoid

crevices, etc.

A proper design should avoid conditions that may subject some area of the structure to cold



86

working in service.

All equipments should be kept clean and free from sediments.

Lastly, a proper design should select corrosion resistant materials for the fabrication of

structures.

2. Use of high purity metals :

The corrosion resistance of a given metal may be improved by increasing its purity.

In most cases, the use of high purity metals tends to reduce pitting corrosion : for example,

pure, pure aluminium suffers much less from pitting corrosion as compared to aluminium

alloys. Impurities in metals reduce corrosion resistance.

However, pure metals possess low strength as compared to their alloys.

3. Use of alloy additions (Corrosion-resistant alloys)

It is common to increase both strength and corrosion resistance by the use of suitable alloying

elements.

For example :

1. Small amounts of phosphorous and copper improve the resistance of structural

steels to atmospheric corrosion

2. About 10% aluminium renders iron extremely resistant to high temperature

oxidation (but also makes it brittle).

3. Intergranular corrosion in stainless steels may be avoided either by reducing carbon

to a low value ( below 0.03%) or by the addition of titanium or columbium.

4. Use of heat-treatments :

Heat-treatment that leads to homogenization of solid solutions, especially in cast alloys that

are subject to coring, tends to improve corrosion resistance.

Stress-relief treatments following cold working are widely used to improve the resistance of

alloys susceptible to stress corrosion.

5. Cathodic protection :

Cathodic protection is the most effective method of corrosion control; in fact, it is the only

one capable of completely preventing corrosion.



87

This is accomplished by placing a metal that is higher in the electropotential series(e.g.,

zinc) in contact with metal (e.g., steel) to be protected.

In this manner, the inserted metal (Zn, Al or Mg), the anode, which should not form a

functional part of the structure, will establish a potential with the metal to be protected and will

prevent corrosion. Of course, from time to time it is necessary to replace the other (less active)

metal. This protecting metal (e.g., Zn) is known as sacrificial anode.

An example of Cathodic protection is Galvanized iron, in which zinc coating itself gets

consumed under working conditions but protects iron from being corroded.

Structures most frequently protected by this method (i.e., cathodically) are underground

pipelines, hulls of ship and boilers. For protection of underground pipe, anodes are buried

some 2 to 3 metres from the pipe. The depth of the hole should be sufficient to locate the

anode in permanently moist soil.

Individual anodes are connected to a collector wire which in turn is brazed to the pipe line.

The currect discharges from the anode to the soil, collects on the pipeline and returns to the anode

through the connecting wire.

To protect ship hulls cathodically, Zinc or Magnesium anodes are fastened to the rudder

and to the hull itself in the region around the propeller.

For Cathodic protection of domestic and industrial water heaters and elevated water

storage tank, Magnesium anodes have been widely employed.

Care should be exercised in Cathodic protection that polarization* does not occur, which

would counteract the expected benefits.

Moreover, the anode area should be small as compared with cathode area to secure

expected protection against corrosion.

6. Use of inhibitors :

Inhibitors are (chemical) compounds added to an electrolyte which protectively coat the

anode or cathode and stop corrosion.

Inhibitors are added to the antifreeze mixtures used in automobile radiators.

Oxidizing agents when added to the corrosive solution will produce oxide films on

aluminium, chromium and manganese.

Anodic and Cathodic inhibitors.



88

(i) Anodic inhibitors suppress the anodic reaction or metal dissolution. Examples of

anodic inhibitors are oxidizing substances such as phosphates, etc., used for the

protection of iron and steel.

(ii) Cathodic inhibitors either prevent the evolution of hydrogen or oxygen absorption at

the cathodic areas. Examples of cathodic inhibitors are calcium bicarbonates in hard

water, Magnesium, Nickel and Zinc salts, etc

Inorganic and organic inhibitors.

Inorganic inhibitors such as chromates and nitrates, phosphates, silicates and hydroxides,

etc., are generally protective in neutral and alkaline solutions but they offer little or no protection

in the presence of acids, acid brines, reducing conditions and microbiological action.

For such conditions polar organic compounds and colloidal organic materials are mostly

used as inhibitors.

The inhibitive action of organic compounds is the result of physical absorption and

chemisorption of molecules at the metal surface.

Examples of organic inhibitors are various amines, mercaptans, heterocyclic nitrogen

compounds, substituted ureas and thioureas, sulphides, and heavy metal soaps.

7. Environment control :

One method of corrosion prevention is to modify the environment. This may involve

removing the corrosive constituent (e.g.,use of vacuum instead of a corrosive atmosphere )

or by using inhibitors (as explained above).

A slight decrease in the temperature of the corroding medium may cause a pronounced

decrease in the amount of corrosion.

Corrosion rate can usually be lowered by reducing velocity of corroding medium.

Changes in the chemical composition of the corroding medium (by introducing inhibitors

or otherwise, e.g., by removing the dissolved oxygen from the corroding medium such a

water) may have a great effect on corrosion behaviour.

Protective atmosphere such as an inert gas like helium, hydrogen and the mixture of

hydrogen and nitrogen produced by dissociation ammonia (NH3) have been successfully

employed to stop high temperature (oxidation) corrosion of ferrous metals and alloys.

An example of a gaseous controlled atmosphere, employed to prevent both high

temperature oxidation of steel and change in its surface carbon –dioxide.



89

Purified and dehumidified atmosphere around the structure decidedly reduces corrosion.

Use of protective Surface Coatings :

Protective surface coatings include

Salt (phosphate films) and oxide (Anodising on A1) films.

Metallic coatings (Zn, Cu, Cr, etc.)

Organic coatings (paints)

Ceramic (vitreous enamel) coatings.

2. Corrosion may be defined as : Destruction of material by

Chemical, electrochemical or metallurgical interaction between the environment and material,

or

Dissolution of material in the environment.

This includes the destruction of metals in all types of atmospheres and liquids and at any

temperature.

Generally, corrosion is a slow process but it is persistent in character.

There are no metals which will withstand corrosive attack in all environments. Any metal

will corrode under certain conditions and, then, will either get destroyed or rendered

useless (Figure)

Mechanical strength is reduced and the section ultimately fails if extensive corrosion occurs.

When the corrosion is localized, sever pitting may occur, and if a hole is produced, particularly in

a vessel containing a liquid, the result may be disastrous.

The importance of corrosion in metallurgy is indicated by the use of paints, enamels and

porcelain on metal structures, by the growing use of rustless steels, by the widespread use

of zinc, Nickel and chromium coating and by the immense tonnage of metals scrapped each

year as a result of the ravages of corrosion, where these and other preventives have not

been applied or have not sufficed.

Corrosion and its prevention is a problem of great importance to the engineering industry.



90

Figure Corrosion on an admiralty bras disc after rotation is sew water

Almost all corrosion involves electrochemical action of some kind. Corrosion of a metal by a

liquid or a gas, both involve the loss of electrons by the metal atoms-known as oxidation-and

gain of electrons by other atoms-reduction.

Thus oxidation is a type of corrosion that involves the reaction of metals with oxygen at high

temperatures, usually in the absence of moisture. (Rusting of iron does not belong to this

particular category).

Oxidation involves absorption of oxygen by a metal to form an oxide. In general, oxidation

process may be slow, as in atmospheric corrosion, or fast, as in combustion.

FACTORS INFLUENCING CORROSION :

1. Difference in electrical potential of dissimilar metals when coupled together and

immersed in an electrolyte.

2. This potential is due to the chemical nature of the anodic and cathodic regions.

3. The potential difference on different areas of the surfaces of a metal may be due to

the microstructure and composition of the metal.

4. For example the standard electrode potentials (at 25oC) in volts for Al, Cu and Au

are – 1.67, 0.345 and 1.68 respectively.



91

5. Factors influencing corrosion rate are

Agitation that brings fresh corroding solution into contact with metal as in case of an

admiralty-brass disc rotating in sea water (Figure).

Residual stresses.

Voids, inclusions and dissolved gases.

Concentration and temperature of corrodant.

Existence of stray electric currents.

Surface films.

Presence of other ions in the solution.

Applied stresses.

Presence of impurities (e.g., dust, dirt, foreign matter, etc.)

Gases absorbed on the metal surface.

TYPES OF CORROSION

It is customary to classify the multitude of possible corrosion reactions into a few broad types

such as

1. Direct corrosion.

2. Electrochemical and galvanic corrosion (Room Temperature).

3. Liquid-Metal corrosion(High Temperature).

4. Corrosion of a metal by a gas.

5. special corrosion types.

Direct Corrosion :

It is essentially an ordinary chemical attack by a corrosive solution on a metal.

Acid picking used to clean steel surfaces is another example of direct corrosion

Fe + 2H+ Fe++ + H2 (gas).

The reaction describes the direct attack of iron by hydrogen ions in the (e.g., 5-10%H2So4)

acid pickling of steel.

In acid solution, the metal surface dissolves uniformly and can be measured in milligrams

per square decimeter per day (mdd).

The direct corroded surface has an etched appearance and may look clean as though it were

ground or it may look darkened by the appearance of the non-metallic compounds which are



92

formed.

The rate of direct corrosion tends to be relatively high as compared with that of other

corrosion mechanisms.

Direct corrosion may be controlled by suitable addition (of an inhibiting chemical ) to the

corroding medium to cause to for a protective layer of the corrosion reaction product to alter

the process by which corrosion occurs.

Electrochemical Corrosion :

Probably the most serious corrosion takes the form of chemical reaction in conjunction with

electrolysis.

The factors governing electrochemical corrosion are :

1. Existing potential difference, between a metal and its surrounding medium or

between difference parts of the same metal (owing to difference in microstructure or

composition ).

2. The presence of an electrolyte. An electrolyte is any solution that contains ions. Ions

are electrically charged atoms (or groups of atoms).

3. Electrolyte can be plain water, salt water, or acid or alkaline solutions of any

concentration.

4. The completion of a closed circuit; because corrosion requires a flow of electricity

between certain areas of a metal surface, through an electrolyte.

To complete the electric circuit, there must be (two electrodes) an anode and a cathode

which may be two different kinds of metals(e.g., Fe and Cu) or they may be different areas on the

same piece of metal.

The connection between the anode and the cathode may be by a metallic bridge, but in

corrosion, it is usually achieved simply by contact. Electricity flows because of the potential

difference between one metal (i.e., anode).

The maintenance of current through the circuit. Current flow may stop if hydrogen

evolved in the electrolytic circuit tends to concentrate on the cathode surface and thus forms an

insulation layer that slows down or stops the electro-chemical action. This is known as cathodic

polarization.

If this hydrogen layer gets broken down or swept away by some other reaction at the

surface or by virtue of convection currents in the electrolyte, the initial conditions will be resorted,

current will begin to flow and corrosion will start once again.



93

Figure shows the action of hydrochloric acid solution on a piece of iron.

Numerous tiny anode and cathode areas get for met on the surface of iron, owing to surface

imperfections, localized stresses, grain orientations, inclusions in the metal or perhaps due to

variations in the environment.

Figure Electrochemical corrosion

At the anode, positive charged iron atoms detach themselves from the solid surface and

enter the solution (electrolyte) as positive ions; while the negative charges (electrons ) that are

released pass round the external circuit to cathode, thus constituting the current.

Fe Fe++ + 2 electrons (or 2e)

Iron passes and thus dissolves into solution, whereas there free electrons on reaching the

cathode, meet and neutralize some positively charged hydrogen ions which have arrived at the

(cathode) surface through the elrctrolyte. In losing their charge, the positive hydrogen ions

become neutral atoms and these atoms combine to form (molecular ) hydrogen gas

2H+ + 2e H2 (forms bubble at the cathode surface )

The amount of metal (iron) which dissolves in the electrolyte is proportional to the number

of electrons flowing, which in turn is dependent upon the potential and resistance of the metal.

The (corrosion process) continues, till, in some cases where the evolution of the hydrogen

gas at the cathode is very slow and the accumulation of a layer of hydrogen on the cathode is very

slow and the accumulation of layer of hydrogen on the cathode surface slows down the

electrochemical reaction. This is called Cathodic polarization. However, oxygen dissolved in the

electrolyte can react with accumulated hydrogen to form water and thus permitting corrosion to

proceed. The effective concentration of oxygen in water adjacent to cathode depends upon

degree of aeration, temperature, degree of agitation (motion), presence of dissolved salts, etc.



94

4. Corrosion of Metal by a Liquid : Galvanic Cells :

- Galvanic corrosion is the mechanism of nearly all corrosion of metals by liquids, in which anode

metal is made to dissolve or corrode continuously.

Galvanic corrosion occurs when two dissimilar metals are in electrical contact with each

other and are exposed to electrolyte.

A less noble metal such as Zn will dissolve and form the anode, whereas the more noble

metal such as Cu will act as the cathode(figure)

Figure Galvanic corrosion Zn and Cu form the two electrodes and their potential are referred to as electrode

potentials. The combination of electrodes and electrolyte is called a galvanic cell.

Depending upon the nature of the corrosive environment, the cathodic reaction may involve

hydrogen evolution or oxygen adsorption.*

As the two electrodes are joined by a conductor, the electronic current flows prom the anode

(Zn) through conductor to the cathode (Cu.) At the anode some of the excess electrons are

removed, permitting more (anode) metal atoms to be oxidized and go into solution. At the

cathode more electrons are added that are intercepted by the positive ions deposited there.

The Corrosion current flows at the expense of anode metal, which is corroded

continuously, whereas the cathode metal is protected from the attack.

Electrochemical Corrosion versus Galvanic corrosion :

So far as corrosion is concerned, the galvanic series is more valuable than the

electrochemical series, but even small environmental changes tend to shift the potential in either

direction.



95

The open circuit potential difference between the anodic and cathodic areas determines the

direction of the flow of the galvanic current.

The polarization characteristics of the electrodes determine the magnitude of the galvanic

current. However, the driving force of corrosion remains the free energy change of the overall

corrosion reaction.

The Electrochemical series The Galvanic series (sea Water )

Electrode reaction Standard Electrode

Potential Eo,Volts, 25o c

Magnesium< Corroded

end (anodic or least moble)

Li = Li+ e - 3.05 Zine

Mg = Mg++ 2e - 2.34 Aluminium 2s

Mn = Mn++ 2e -1.05 Cadmium

Fe = Fe++ 2e -0.440 Steel or Iron

2

1

2H = H+ e 0.000 Lead

Cu = Cu++ 2e 0.345 Tin

Ag = Ag+ e 0.800 Nickel(active)

Au = Au+ e 1.680 Brasses

Copper

Silver

Platinum<<Protected end

(cathodic or most noble )

Liquid – Metal Corrosion :

Whereas electrochemical and galvanic corrosions take place at or near room temperature,

the liquid-metal corrosion discussed under occurs at high temperatures.

Usually the driving force for this form of corrosion as is the tendency of the solid to

dissolve in the liquid up to the solubility limit at the given temperature.

A serious damage by liquid – metal attack occurs in heat exchangers carrying liquid-metal

(Bi and Na) Coolants. As the solid container (e.g., copper tubing ) approaches equilibrium with

the liquid-metal coolant in the hot zone of the heat exchanger, a portion of the solid goes into

solution in the liquid.



96

As the liquid (containing this solid) moves to a cooler part of the heat exchanger, the solid

tends to deposit on the walls of the exchanger tubes.

This way the hot zone of the heat exchanger is continuously corroded and the cold zone becomes

plugged with the deposited corrosion products.

Corrosion of Metal by a Gas :

In this type of corrosion, the gas molecules are absorbed on the surface of metal and they react

with surface atoms of metal.

Most metals (M) react with air, oxygen or other gases to produce corrosion products.

2

2 2 3

2

y + ;

24 + 3O 2

2 + C1 2 1.

x yxM O M O For example

Fe Fe O

Na NaC

The products of corrosion always form a layer of film on the metal surface (figure (a) )

If the volume of corrosion product is greater than that of the metal consumed in the reaction,

the layer must be compressed to fit the surface on which it is formed; and the result is a

nonporous (Protective) shield over the metal surface. In case, volume of

Figure:



97

Corrosion product is lesser than that of the metal consumed, the result is a porous film that

offers little or no protection against further corrosion; because porous layer will allow the

corroding gas to come in direct contact with metal.

When a nonporous, adhering layer is formed, corrosion can proceed only by diffusion, an

electrolytic action in which the corrosion film behaves as a galvanic cell.

Since diffusion is an important factor in metal-gas corrosion, the corrosion rate increases

rapidly at high temperatures. The oxidation of iron and steel in air is an outstanding example

of high temperature corrosion. This principle reaction is

2Fe++ + O2----2FeO

The surface layer of film grows with time in following fashions (Figure(b)), namely

(i) Linear (in case of porous films),

(ii) Parabolic (in case of nonporous adherent film),and

(iii) Logarithmic.

These three modes are know as Laws of Oxidation.

(i) Iron 900 oC, impure calcium at 500oc and titanium between 650-350oc obey the Linear

law.

(ii) The parabolic Law is found in iron 200oC and copper at 800oC.

(iii) The Logarithmic Law is found in iron 200o C, zinc 4010oC and aluminium at room

temperature.

As the oxide layer thickens (10-100 oA) Interference colours are produced.

Oxides have a higher thermal emissivity than the underlying metal.

The coefficient of friction is reduced by the formation of an oxide layer.

If the oxide penetrates into the metal, i.e., the oxygen ions diffuse into the metal, the

mechanical properties are lowered due to the presence of the brittle oxide constituent.

Specific Corrosion Types :

Some specific, industrially important corrosion types are :

1. Uniform corrosion : when the entire surface of the metal is attacked to the same degree, it

is known as uniform corrosion. One type of uniform corrosion may be the uniform

dezincification that proceeds through a brass water pipe.



98

Dezincification does not necessarily means that only zinc is removed; this term is now

applied to any condition of corrosion is which a specific element is removed for an alloy.

Dezincification is associated with galvanic action.

Mostly, the uniform corrosion is unusual in metals, since they (i.e, metals) are rarely so

homogeneous that the surface will be evenly corroded.

2. Atmosplferic corrosion

Atmospheric corrosion is very frequent on ferrous materials.

Humid atmosphere is mainly responsible for this type of corrosion.

Atmospheric corrosion generally follows oxygen absorption mechanism.

A layer of corrosion products forms; cracks in this layer expose fresh metal to corrosive

atmosphere.

3. Pitting corrosion :

It is a non-uniform corrosion that results from inhomogeneities in metal due to

inclusions, coring and distorted zones which set up difference of potential at localized

spots to cause deep isolated hole or pits.

Pitting corrosion results from electrochemical reaction.

Pitting of the metal occurs when there is a break in the protecting layer; for example when

the chromium plate(film) in a steel auto bumper breaks, the point of film breakage

becomes anode while the surrounding unbroken film works as a cathode and thus the

pitting of the exposed steel begins.

4. Intergranular corrosion :

It is a no –uniform corrosion.

From the solid solution, when a phase precipitates at the grain boundaries, the material in

the vicinity of the grain boundary becomes depleted of the dissolved element, thus

creating a potential difference between the grain boundaries and rest of the alloy.

When this situation exists and the alloy is placed in contact with a corrosive agent, attack

begins at the surface in the region of this grain boundary material and then penetrates into the

body of the alloy, following the boundaries.

Intergranular corrosion is detrimental to the strength of the alloy.

Microscopic examination can reveal clearly the intergranular corrosion.

18/8 stainless steel, aluminium alloys and copper alloys are susceptible to this type of

corrosion.



99

5. Stress corrosion :

In cold worked stressed metals, the pile-up of dislocations at grain boundaries and other

points increases the energy in those regions so that they become sufficiently anodic to the rest

of the structure (under certain environments).

Therefore, corrosion takes place in these regions of high energy and the stresses locket up

(in the metal), give rise to the formation of cracks which grow progressively with the

continuance of corrosion. The cracks may be transgranular(i.e., in the grain) or intergranular

(i.e., along the grain boundaries) or a combination of both.

It has been observed that most commercial alloys (such as those of aluminium, brasses,

stainless steels and low carbon steels) are susceptible to stress-corrosion cracking when subjected

to high tensile stresses and exposed to certain specific corrosive environments. Pure metals are

relatively immune to stress corrosion cracking.

For instance, aluminium alloys and low carbon steels stress corrode in sea water.

Well known example of stress corrosion are season cracking the occurs in brasses,

especially in the presence of moisture and traces of ammonia, and caustic embrittlement of steel

exposed to solutions containing NaOH.

An effective control against stress corrosion is the elimination of tensile stresses from the

component part.

6. Corrosion fatigue :

Corrosion fatigue is the combined action of corrosion and repeated loading (stresses) and this

is much more serious than the sum of these two factors acting individually.

The influence of corrosion of fatigue strength is expressed by the Damage Ratio (D.R.) which

is

Corrosion fatigue strength

. . =

DRNormal fatigue strength

D.R. with salt water as a corroding medium is

0.2 for carbon steels,

0.5 for stainless steels, and

0.4 for aluminium alloys.



100

The mechanism of corrosion fatigue is something as follows :

The action of the corrosive medium will tend to be concentrated at any surface flaw or

irregularity and behaves as a focal point for the initiation of a fatigue crack.

Once a crack has been formed, it will spread rapidly as a result of the corrosive action

combined with alternating loading which tends to break any passivating film that may form on

the surface.

Corrosion fatigue may be minimized by

treatment of the corroding medium,

nitriding of steels.

7. Fretting corrosion:

Fretting corrosion is allied to corrosion fatigue and occurs particularly where close fitting

machine parts are subjected to vibrational stresses.

In steel, fretting corrosion appears as patches of finely divided ferric oxide (Fe2O3).

Fretting corrosion is common at surfaces of clamped or press fits, splines, keyways, etc.

Fretting corrosion ruing bearings, destroys dimension and reduced fatigue strength.

Fretting corrosion is a mechanical-chemical phenomenon. The oscillating sliding motion

under pressure continually removes protective surface films, leaving the surface exposed. Thus

exposed surface under the action of vibration stresses and (corrosive) atmosphere tends to

corrode.

Fretting corrosion may be minimized by :

Avoiding vibrations.

Sealing the area with rubber cement to exclude atmospheres.

Raising hardness of mating surfaces.

Nitriding, chromium plating or hardening.

Introducing compressive stresses in the surface by shot peening or surface rolling.

8. Erosion corrosion (or Impingement corrosion) :

o This type of corrosion refers to the combined effects of

1. Mechanical abrasion of the metal surface caused by the impingement of entrained air

bubbles, abrasive particles suspended in the liquid or turbulent flow of liquids, and



101

2. Chemical corrosion, on a metallic surface.

Erosion corrosion is caused by the breakdown of the protective film at the spot of

impingement, which contributes, to the formation of differential cells at such areas and causes

localized pitting at the anodic points of the cells.

The place from where the scale has been broken, forms anode whereas the unbroken

protective layer (e.g., oxide film) surrounding that place (of removed layer) acts as cathode.

This type of corrosion is encountered in

pump mechanisms,

Turbines,

Condenser tubes and pipings, and

Tubes carrying sea water.

9. Cavitation corrosion :

The flow of fluids around solid bodies often produces rapidly changing pressures under

which bubbles or cavities form and collapse in swift succession.

Cavities collapsing near a solid surface exert a pounding action (impact) on the surface like

that of many small hammer blows. These gradually remove particles of the metal surface,

eventually forming deep pits, depressions and pock-marks(which is result of cavitation

corrosion).

When corroding liquid (electrolyte) comes in contact with these pits, the effect is further

accelerated.

Materials such as cast iron, bronze and steel casting and steel plates are susceptible to

cavitation damage.

Examples of cavitation- corrosion damage are found in marine propellers, pumps and valves

where sea water acts as the electrolyte.

Cavitation corrosion may be minimized by the use of

High strength, corrosion resistant metals such as Cr- Ni stainless steels.

A protective coating (metallic or nonmetallic).

10. Crevice corrosion:

Crevice corrosion implies accelerated attack at the junction of two metals exposed to a

corrosive environment.



102

Corrosion is more likely to occur in crevices that retain ( Corrosive ) solutions and take

longer to dry out.

Corrosion also occurs at crevices completely immersed in solution.

Accelerated attack can occur because of a differential in oxygen concentration (figure )

Oxygen has relatively easy access to the outside of the joint, which is cathodic. The main

metal in the joint

Figure Crevice corrosion.

Is relatively anodic. The deposit of insoluble corrosion product around the anodic centre

tends to more completely exclude oxygen, resulting in a low oxygen concentration area and

increased electrical potential.

If the action continues, an irregular pit forms in the centre. Crevice corrosion occurs in the

area having low oxygen concentration.

11. Microbiological corrosion

Microbiological corrosion is caused by the metabolic activity of various micro– roganisms.

The micro-organisms can develop in an environment with or without oxygen and can be

classified as either aerobic or anaerobic micro-roganisms.

The more important micro-organisms responsible for most corrosion failures are

(a) Sulphate reducing bacteria that are responsible for the anaerobic corrosion of iron and steel.

(b) Sulphur bacteria yields sulphuric acid that attacks the iron.

(c) Iron and Manganese bacteria.

(d) Micro-organisms such as bacteria fungi, algae etc. capable of forming Microbiological films

on an iron surface.



103

UNIT – V

1. Solid solution strengthening.

When the shear stress fields associated with both edge and screw dislocations are resolved

into their normal stress components (figure) ,note that the absolute magnitude of the shear stress

is equal to the normal stress; of importance, however, is the fact that the sign of the normal stress

is reversed along the 450 directions. It follows that the shear stress field surrounding a screw

dislocation is distortional (i.e., stretched in one direction and compressed in the other), whereas

the edge dislocation contains both distortional and dilatational components.

The potential interaction between an edge or screw dislocation with a solute atom depends

on the stress field associated with the solute atom. For example, if an atom of chromium were to

substitute for an atom of FCC nickel or BCC iron, the host lattices would experience a symmetrical

(hydrostatic) misfit stress associated with difference in size between solute and solvent atoms.29

Lattice distortion would be felt equally in all direction, with the strengthening contribution being

proportional to the magnitude of the misfit such that

da

dc

where a = lattice parameter

c = solute concentration

The hydrostatic stress field of a substitution solute atom interacts with the hydrostatic

stress field associated with edge dislocations but not with the distortional stress field surrounding

screw dislocations in the lattice. The level of hardening also depends on how much the local

modulus G of the crystal was altered as a function of solute content (i.e., G-1(dG/dc).

Figure. Resolution of shear stress field into normal stress components.



104

A much greater solute atom-dislocation interaction occurs when the stress field associated

with the solute atom interacts with both edge and screw dislocations. The stress fields associated

with the four lattice defects shown in Figure. satisfy this requirement in that they are

nonsymmetrical and, as such, will interact with the nonsymmetrical stress components of both

edge and screw dislocations. The defect type shown in Figure . identifies one of the octahedral

interstitial sites within the BCC iron lattice where carbon and / or nitrogen atoms are located. The

size of this octahedral interstitial site along any edge in the BCC lattice (or its equivalent location

in the middle of each cube face) is not symmetrical and provides insufficient room for carbon and

nitrogen atoms in the 100 direction30; this arises from the fact that the site size is 0.38 and 1.56 o

A .

In the 100 and 110 directions, respectively, whereas the diameter of the carbon atom is 1.54 o

A .

Theoretical considerations as well as experimental findings have shown that steel alloys strength

increases rapidly at small carbon concentrations with a relationship of the from c . Such alloy

strengthening is of great commercial interest to the steel industry. The insufficient amount of

space available for the carbon atom in the BCC lattice also accounts for the very limited solid

solubility of carbon in BCC iron (approximately 0.02%)

Figure: Nonsymmetrical strees fields in crystals. (a) octahedral interstitial site in BCC crystal

100 anisotropy ; (b) divalent ion – vacancy pair 11 0 anisotropy ; (c) interstitial pair in FCC

crystal 100 anisotropy (d) vacancy disk 111 anisotropy



105

Figure: Alloy strength dependence on solute content. Greater strengthening associated with

non symmetrical defect site. (Reprinted with permission from K.M. Ralls, T.H. Courtney and J.

Wulff, Introduction to Materials Science and Engineering, Wiley, New York (1976)

And leads to the development of a body – centered – tetragonal lattice in high carbon

Martensite rather than the body – centered – cubic crystal form for pure iron. It should be noted

that the octahedral interstitial site in FCC iron is symmetrical and provides space for an atom

whose diameter is as great as 1.02 A. since the extent of lattice distortion in the FCC lattice is

much less than that found in the BCC form, the strengthening contribution of carbon in FCC iron

(i.e., austenite) is low. (At the same time, the solubility limit of carbon in FCC iron is in excess of

2% - more than 100 times greater than that associated with carbon in the BCC ferrite phase). To

summarize, the strengthening potential for carbon in FCC iron is much less than that for carbon in

BCC iron since the strain field surrounding the interstitial atom site is symmetrical in the FCC

lattice; solute atom interaction with screw dislocations is then much weaker than for the

placement of carbon atoms in the non symmetrical interstitial site in the BCC lattice.

Other non symmetrical defects are shown in figure. The substitution of a divalent ion in a

monovalent crystal requires that two monovalent ions be replaced by a single divalent ion; this is

necessary to maintain charge balance. The divalent ion and the associated vacancy have an

affinity for one another which establishes a nonsymmetrical stress field in the 110 direction

figure. Interstitial atom pairs such as those resulting from irradiation damage in an FCC crystal

produce a stress field in the 100 direction. Finally, the collapsed vacancy disk in an FCC lattice

produces a dislocation loop with asymmetry in the 111 direction.

From the above discussion, it is seen that the relative strengthening potential for a given

solute atom is determined by the nature of the stress field associated with the solute atom. When

the stress field is symmetrical, the solute atom interacts only with the edge dislocation and solid



106

solution strengthening is limited. Example of such symmetrical defects are shown in table. In

sharp contrast, when the stress field.

TABLE: Dislocation-solute Interaction Potential

Surrounding the solute atom is nonsymmetrical in character, the solute atom interacts

strongly with both edge and screw dislocations; in this instance, the magnitude of solid solution

strengthening is much greater (table). Note that the degree of solid solution strengthening

depends on whether the solute atom possesses a symmetrical or nonsymmetrical stress field and

not whether it is of the substitutional or interstitial type. Examples of solid solution strengthening

in both symmetrical (Pd or Pt in Cu) and asymmetrical distortional stress fields (C in Fe and N in

Nb) are shown in figure. Finally, it is interesting to note that the addition of a given amount of

solute atoms to the host metal may, in some instances, lead to solid solution hardening at one

temperature and solftening at another. It has been suggested that this contrasting response is due

to complex temperature-dependent interactions of screw dislocations with Peierls and solute

misfit strain fields.

2. Precipitation hardening?

Microstructural Characteristics

When the solute concentration in an alloy exceeds the limits of solubility for the matrix

phase, equilibrium conditions dictate the nucleation and growth of second phase particles,

provided that suitable thermal conditions are present. From the figure.



107

Figure: Portion of equilibrium phase diagram showing alloy composition X and associated

solvus temperature Tr.

Which shows a portion of an equilibrium phase diagram, wee that for an alloy of

composition X, a single phase is predicted at temperatures above Ts whereas two phases, and

, are stable below the solvus line. When such an alloy is heated into the single-phase field (called

a solution treatment) and then rapidly quenched, the resulting microstructure contains only

supersaturated solid solution even though the phase diagram predicts a two-phase mixture; the

absence of the phase is attributed to insufficient atomic diffusion. If this alloy is heated to an

intermediate temperature (called the aging temperature) below the solvus temperature,

diffusional processes are enhanced and result in the precipitation of particles either within

grains or at their respective grain boundaries.

The onset of precipitation depends strongly on the aging temperature itself. At

temperature approaching the solvus temperature, there is little driving force for the precipitation

process, even though diffusion kinetics are rapid. Alternatively, precipitation of the second phase

proceeds slowly at temperatures well below Ts despite the large driving force for nucleation of the

second phase; in this instance, diffusional processes are restricted. An optimal temperature for

rapid precipitation is then identified at an intermediate temperature corresponding to an ideal

combination of particle nucleation and growth rates.

The development of the two-phase mixture can most generally be described as taking place

in three stages. After an incubation period, clusters of solute atoms form and second-phase

particles nucleate and begin to grow either homogeneously within the host grains or

heterogeneously along host grain-boundary sites. During the second stage of aging, particle

nucleation continues along with the growth of existing precipitates; these processes continue until

the equilibrium volume fraction of the second phase has been reached. In the third and final stage

of aging, these second-phase particles coarsen, with larger particles growing at the expense of



108

smaller ones. This process, referred as Ostwald ripening, is diffusion-driven so as to reduce the

total amount of interfacial area between the two phases.

For reasons to be addressed shortly, the precipitation of second phase particles throughout

the matrix increases the difficulty of dislocation motion through the lattice. (Conversely, little

strengthening has been attributed to the presence of grain-boundary precipitates.) Typically, the

hardness and strength of the alloy increases initially with time (and particle size) but may then

decrease with further aging. The strength and sense of the strength-time slope ( / )d dt depends on

four major factors: the volume fraction, distribution, the nature of the precipitate, and the nature

of the interphase boundary. Surely, were all things to remain constant, the resistance to

dislocation motion through the lattice would be expected to increase with increasing volume

fraction of the dislocation barrier (i.e., the precipitate). Accordingly, the first two stages of aging

generally contribute to increased strengthening with time and/or particle dimension (ie., position

( / )d dt . On the other hand, Ostwald ripening, corresponding to long aging times and/or the

growth of large second-phase particles, leads to negative ( / )d dt conditions (see curves B and C in

figure).

Figure: Precipitation rate is maximized at intermediate aging temperature.

Whether the dislocation cuts through or avoids the precipitate depends on the structure of

the second phase and the nature of the particle-matrix interface. The interface between the two

phases may be coherent, which implies good registry between the two lattices. A dislocation

moving through one phase would then be expected to pass readily from the matrix lattice into that

of the precipitate. Such a coherent interface possesses a low surface energy. At the same time,

however, lattice misfit (related to the difference in lattice parameters between the two phases)

leads to the development of elastic strain fields surrounding the coherent phase boundary.

Researchers have found that the shape of the precipitate particles depends on the degree of misfit.

For example, when the misfit strain is small, spherical particles are formed such as in the case of

the Al-Li binary alloy. When such particles grow in size and/or when a large misfit is developed,



109

cuboidal particles are formed the microstructure reveals aligned cubes or rodlike particles. As

these small coherent precipitates grow with time, their interfaces may become semicoherent, with

the increased lattice misfit between the two phases being accommodated by the development of

interface dislocations, which bring the two lattices back into registry.

Figure: (a) Aging curves in 6061-T4 aluminium alloy. (From J.E. Hatch, Ed., Aluminium

Properties and Physical Metallurgy, ASM, Metals Park, OH, 1984, p.178; with permission.) (b)

Schematic representation of aging process at low (A), high (B), and intermediate (C)

temperatures.

Figure: Precipitate morphology dependence on degree of lattice misfit. (a) Low misfit spherical

particles in Al-Li alloy. (Courtesy S. Baumann). (b) Moderate misfit cuboidal particles in Ni-Al

alloy. Both are sheared by dislocations.

At this stage, misfit energy decreases markedly, whereas surface energy increases to a

significant degree. Finally, in the latter stages of aging associated with the development of coarse

particles, the interface between the two phases may break down completed and become inherent;

the surface energy associated with this interphase boundary is then increased whereas its strain

field is essentially eliminated.



110

3. Grain boundary strengthening.

The presence of grain boundaries has an additional effect on the deformation behavior of a

material by serving as an effective barrier to the movement of glide dislocations. From the work

of Petch and Hall, the yield strength of a polycrystalline material could be given

1/ 2ys i yk d

Where ys = yield strength of polycrystalline sample

i = overall resistance of lattice to dislocation movement

ky =‚locking parameter,‛ which measures relative hardening contribution of grain

boundaries.

d = grain size

The derivation of equation can be traced to the work of Eshelby et al. The number of

dislocation that can occupy a distance L between the dislocation source and the grain boundary in

given by

idnGb

Where n = number of dislocation in the pileup

= constant

s = average resolved shear stress in the slip plane

d = grain diameter

G = shear modulus

b = burgers vector

The stress acting on the lead dislocation is found to be n times greater than c. When this

local stress exceeds a critical value c the blocked dislocation are able to glide past the grain

boundary. Hence

2s

c s

dn

Gb

Since the resolved shear stress c = is equal to the applied stress less the frictional stress I

associated with intrinsic lattice resistance to dislocation motion, equation may be written as

2( )i

c

d

Gb



111

After rearranging,

1/ 2i ik d

Which is the shear stress form of equation. the petch-Hall relation also characterizes alloy

yield strength in terms of other microstructural parameters such as the peralite lamellae spacing

and Martensite packet size. It is readily seen that grain refinement techniques (e.g., normalizing

alloy steels) provide additional barriers to dislocation movement and enhance the yield strength.

As will be shown in, improved toughness also results from grain refinement

Conrad has demonstrated clearly that i may be separated into two components: ST which

is not temperature sensitive but structure sensitive where dislocation-dislocation, dislocation-

precipitate, and dislocation-solute atom interactions are important; and T , which is strongly

temperature sensitive and related to the Peierls stress. The yield strength of a material may then

be given by

1/ 2ys T ST yk d

Note that the overall yield strength of a material depends on both short-and long-range

stress field interactions with moving dislocations.

The universal of the Petch-Hall relation to characterize the behavior of metal alloys should

be viewed with caution since other equation can sometimes better describe the observed strength-

microstructural size relation. In addition, extrapolation of equation to extremely small grain sizes

leads to the prediction of unrealistic yield strength levels that approach theoretical levels. Finally,

there is growing consensus that grain boundary-induced dislocation pileups may not be

responsible for the yield-strength-microstructural size relation described above. Instead, recent

thought focuses on the important role of the grain boundary as a source for dislocations, with the

yield strength being given by.

i Gb

Short-range

order Peierls

stress effects

(<10 A

)

Long-range order

dislocation stress

field effects (100-

1000 A

)

Very long-range

structural size

effects (>104 A

)



112

Li theorized that dislocations were generated at grain-boundary ledges and noted that the

dislocation density was inversely proportional to the grain size. Consequently, equation has the

same form as equation.

4. LEAD, NICKEL AND ITS ALLOYS.

Introduction:

Lead is the oldest of the commonly used metals and the softest of the heavy metals. When it is

cast or cut, it is lustrous silvery colour to begin with. After standing for a time, however, the

surface turns a dull bluish grey due to oxidation. Lead is poisonous and should not be

brought into contact with food,. Lead has a F.C.C. crystal structure.

Properties of Lead:

(1) It has a low melting point of 3270C and density is 11.34 kg/dm3.

(2) It is very resistant to corrosion, against most acids, but not against aqua regia (HCI-

HNo3mixture).

(3) It is poisonous.

(4) Its strength, hardness and elasticity are low, e.g., tensile strength 15 N/mm2, extensibility up to

60%.

(5) It has low resistance to deformation but high formability, cold forming is preferred.

(6) Lead can be easily soldered, welded and cast. It can be spread over other metal surfaces.

In addition lead has :

(7) Heavy weight

(8) High density

(9) Softness

(10) Malleability

(11) Lubricating properties

(12) High coefficient of expansion

(13) Low electrical conductivity

Uses and applications of lead :

1. Manufacture of storage batteries.

2. As an alloying element to improve the machinability of bronzes, brasses and free machining

steels.

3. Tank linings for corrosion protection.

4. Pipe and drainage fittings.

5. Bearing metals.



113

6. Lead compounds in paints.

7. Lead sheathing of electric cable

8. Low melting solders.

9. Terne plate(lead-tin coated steel), etc.

10. Radiation protection (from x-rays)

Available Forms

Lead is available commercially in the following forms :

(i) sheet and foil (down to 0.0125 mm)

(ii) Extrusions

(iii) Castings

(iv) Laminations

(v) Powder

(vi) Shot

(vii) Wool

(viii) Lead alloys

Lead alloys:

Lead alloys containing 8% to 10% pb are used as bearing (antifriction) metals, in cable

sheaths, accumulation plates, etc.

Antimony makes the alloy hard.

Lead compounds include red lead and white lead.

Lead glass (lead crystal glass) refracts light strongly.

Alloy Composittion in % Uses

Lg Pb Sb 12

(Bearing hard lead)

Pb (Sb)

Pb Sb As

Sb 10.5-13

Cu 0.3-1.15

Ni 0-0.3

As 0-1.5

Rest lead

Sb 0.2-0.3

Rest lead

Sb 2.0-3.8

As 1.2-1.7

Rest lead

In mechanical engineering,

Easily soldered to steel, for

Lining bearings.

Drain pipes

Buckshot



114

NICKEL AND ITS ALLOY:

Introduction:

The element nickel (alongwith the elements Fe and Co) constitute the transition group in

the fourth series of the periodic table.

It has an atomic number of 28, an atomic weight of 58,71, density 8.908 g/cu cm at 200C and

melting point of 14530C.

The normal crystallographic system of nickel is F.C.C. at all temperatures.

The usual commercial grade of wrought nickel (‘A’ nickel) nominally contains 99.0% nickel

+ upto 0.4% cobalt, which traditionally are combined and reported as 99.4% nickel.

Commercially pure nickel is almost as hard as a low-carbon steel. Nickel work-hardens

rapidly when cold worked.

With suitable modifications in temperatures, tools, pressures, rates etc., wrought nickel is

amenable to most of the fabrication processes used for mild steel. It can be forged, rolled,

bent, extruded, sheared, punched, spun, deep drawn, machined, ground, polished and

buffed.

Properties:

Nickel:

(1) is a hard lustrous white metal.

(2) Possesses good corrosion and oxidation resistance.

(3) Has high tensile strength and can be easily formed hot or cold.

(4) Can take up high polish.

(5) Can be fabricated using processes similar for mild steel.

(6) Is ferromagnetic at ordinary and low temperatures but becomes paramagnetic at elevated

temperatures.

- Melting point <<<.. 1453OC

- Density, gm/cu cm, at 200C <<.8.908

- Coef. Of Thermal expansion 10-6/0 C (25 to 1000C) <<..13.3

- Tensile strength <<.65000 to 115000 psi (From hot rolled (4565 to 8075 kg/cu2) to cold

drawn)

- Mod. Of ?Elasticity <<<<.30 106pasi (2.11 106 kg/cm2)

- Hardness RB <<<<<40 to 100 (depending upon whether Ni is hot rolled, annealed or cold

drawn )

- Resistance to corrosion; resistance to hot concentrated caustic soda, chlorine and fluoring

gases at temperatures up to 1000 F (5380C)



115

Use:

(i) For corrosion protection of iron and steel parts and Zn-base die castings used in the

automotive field.

(ii) In the chemical, soap, caustic and allied industries for the construction of evaporators, tanks,

jacketed kettles, heating coils, tubular condensers and many other processing equipments.

(iii) As an alloying element in both ferrous and non-ferrous alloys. Nickel is a strong austenite

stabilizer and with chromium is used to form the important AISI 300 series of non-

magnetic austenitic stainless steels.

(iv) As a coating for parts subjected to corrosion and wear. There-for the second important use

of nickel is in electroplating.

(v) In the incandescent lamp and radio industries.

(vi) In electronic (Vacuum electronic tubes) and low-current electrical applications.

(vii) As permanent magnets.

(viii) As anodes in low-power tubes and in photocells.

(ix) As thermocouple material.

Nickel alloys:

Various nickel alloys are:

(a) Nickel-Iron alloys

(b) Nickel-Copper alloys

(c) Nickel-Copper-Zinc alloys

(d) Nickel-Chromium alloys

(e) Nickel-Molybdenum alloys

(f) Super alloys

(a) Nickel-Iron alloys:

Nickel and iron form a series of alloys with thermal-expansion and magnetic characteristics

of commercial importance.

Invar is the Trademark for an iron-nickel alloy containing 40-50% nickel and is

characterized by an extremely low coefficient of thermal expansion. Invar is used for

making precision instruments, measuring tapes, weights etc.

The addition of 12% chromium, in lieu of some of the iron, produces and alloy (Elinvar)

with an invariable modulus of elasticity over a considerable temperature range as well as a

fairly low coefficient of expansion.



116

(b) Nickel-Copper alloys :

(i) the major nickel-based alloy with copper is Monel which nominally contains 66% Ni, 31.5%

Cu, 1.35% Fe, 0.90% Mn, plus residuals.

Properties :

Monel has a brighter appearance than nicke, is stronger and tougher than mild steel, has

excellent resistance to atmospheric and sea- water corrosion and generally is more resistant than

nickel to acid, less resistant to alkalies and equally resistant to salts.

Use :

Monel is used in architectural and marine applications where appearance and corrosion

resistance is important and in specialized equipment used by the food, pharmaceutical, paper, oil

and chemical industries.

Several variations of monel have been produced to obtain an additional characteristic.

These include :

An age-hardenable grade (K Monel),

A free machining grade (R Monel),

A hard-casting grade (H Monel),

An age-hardenable casting grade (S Monel), etc.

Constantan, another alloy of nickel and copper contains 45% Ni and 55% Cu.

Properties :

Highest electrical resistivity,

Lowest temperature coefficient of resistance, and

Highest thermal emf against platinum of any of the copper-nickel alloys.

Use :

Electrical resistors

Thermocouples

Wheatstone bridges, etc.



117

(c) Ni-Cu-Zn alloys (Nickel-Silver) :

Nickel-copper-zinc alloys though known as nickel-silver, do not contain silver, and in

actuality they are brasses with sufficient nickel added to give a silvery white colour,

improved corrosion resistance and high strength.

These alloys are used as low cost substitutes for silver in tableware and jewellery, usually

with a silver or gold electroplate on the surface.

Nickel silvers are also construction materials for many musical, drafting and scientific

instruments and are also used for marine and architectural applications.

(d) Nickel-Chromium alloys :

Nickel-Chromium alloys with or without iron, form a series of corrosion and heat-resistant

materials.

In this group the 80% Ni, 14% Cr, 6% Fe alloy (Inconel) with many modifications resists

progressive oxidation below 10930C and is used in applications such as furnace chambers,

salt pots, aircraft exhaust manifolds, and high-temperature springs.

It was originally developed for use in the milk industry as a corrosion-resistant alloy and

now is much used in many chemical industries because of its excellent corrosion resistance.

The 80% Ni, 20% Cr alloy (chromel A, Nichrome V, Topher A) and the 60% Ni, 16% Cr,

24% Fe alloy (Nichrome, chromel C, Topher C) form the bulk of materials used for heater

elements.

The 90% Ni, 10% Cr (Chromel) alloy in combination with alumel is much used as a

dependable base-metal thermocouple.

(e) Nickel-Molybdenum alloys :

Nickel-Molybdenum alloys such as Hastelloy A, Hastelloy C and Hastelloy D possess very

good resistance to corrosion.

Type of

Alloy

% composition Properties and Uses

Ni Mo Fe Cr W

Hastelloy A 57 20 20 - - High strength and ductility. Can be

forged enrolled. Resists attack of

acids. Used in chemical industry for

equipments such as storage tanks

and for material handling and

transportation.

Hastelloy C 54 17 5 15 4 Can be cast and machined. Resistant

to HNO3, free chlorine and acid



118

solutions of salts such as cupric and

ferric. Used in chemical industry for

pumps, valves, spray nozzles etc.

(f) Super alloys :

The superalloys have superlative combinations of properties.

These materials are classified according to the predominant metal in the alloy, which may

be cobalt, nickel or iron. Other alloying elements include the refractory metals (Nb, Mo, W,

Ta), chromium and titanium.

Super alloys are atleast five time as strong as steels routinely used for making bridges and

large buildings. They can withstand enormous strains and exhibit remarkable resistance to

metal fatigue. They possess high impact strength and superior strength-to-mass ration.

They are probably the toughest materials ever produced.

Superalloys are used in aircraft turbine components, which must withstand exposure to

severely oxidizing environments and high temperatures for reasonable time periods.

Mechanical integrity under these conditions is critical; in this regard, density is an

important consideration because centrifugal stresses are diminished in rotating members

when the density is reduced.

In addition to turbine applications, these alloys are utilized in nuclear reactors and

petrochemical equipment.

Nominal Composition of Some Typical Superalloys, %

Alloy Ni Cr Fe Co Mo Cb W Al Ti B Zr C

Iron-Bases

16-25-6 25 16 Rest - 6 - - - - - 0.06

19-9-DL 9 19 Rest - 1.3 0.4 1.2 - 0.3 - - 0.30

A-286 26 15 Rest - 1.3 - - 0.2 2.0 0.003 - 0.06

High cobalt

s-816 20 20 3.5 Rest 4 4 4 - - - - 0.38

HS-151 - 20 - Rest - - 12.7 - - 0.05 - 0.50

J-1650 26 19 - Rest - - 12 - 4 0.02 - 0.2&Ta-

2

Nickel-Base

Nimonic

alloy 75

18 20 Low - - - - - 0.4 - - 0.12

Inconel

alloy 722

74 15 7 - - - - 0.6 2.4 - - 0.04



119

Udimet 700 53 15 1

max

19 5.2 - - 4.3 3.5 0.1

max

- 0.12

Nimonic

alloy 115

57 15 - 15 .5 - - 4 5 - - 0.18

N.B. : Many of the superalloys can be heat- treated, forge, hot worked, formed, machined, welded

and brazed.

5. COBALT AND ITS ALLOYS:

Introduction:

Cobalt is a silvery-white metal with al faint bluish tinge, closely resembling nickel in

appearance and mechanical properties.

Its chemical properties resemble, in part, those of both nickel and iron.

Below 4210C, cobalt is H.C.P.; above, it is F.C.C. structure.

Cobalt alloys – Composition and Properties.

A few cobalt containing alloys are as follows:

% Composition Application

Cr 19-27, Ni 0-15, M 0-5.5 High temperature alloy

Rest Cobalt

Cr26-33, W5-14, C1-2.5, Rest Cobalt Hard facing alloys (satellites)

Cr 30-32, Mo 1.3-3.5, C0.05-2, Rest Cobalt Wear resistant alloys

Co49-50, V0.2, Rest Fe High permeability

Ni28-29, Co17-18, Fe Glass-metal seals Kovar (w*)

Co64, Cr30, Mo 5 Dental prosthesis and

osteosynthesis

vitallium (C+).

The desirable high-temperature properties of the first alloy-high stress rupture, creep, thermal

shock resistance and resistance to carburization- may be the result of the allotropic change of

cobalt from a close-packed hexagonal at room temperature to a face-centered cubic lattice at

high temperatures.

The stellite alloys are immune to all ordinary corroding media and are highly resistant to many

corrosive acids and chemicals, satellites combine high reflectivity, permanence of finish and

resistance to abrasion.

Cobalt’s high curie temperature (11210c) imparts high damping characteristics useful for alloys

subjected to vibration, such as in high pressure, high-temperature steam turbines.



120

The interesting engineering property of cobalt-containing permanent, soft and const and

permeability magnets are a result of the electronic configuration of the metal and its high curie

temperature.

In cutting alloys and high speed steel, cobalt seems to contribute to low coefficients of friction

and to maintaining red hardness.

The Co-Cr-base alloys for dental and surgical application are not attached by the body fluids

and hence do not set up an electromotive force in the body to cause irritation of the tissue;

thus the Vitallium alloys are also used as bone replacements. They are ductile enough to

permit anchoring of dentures on neighboring teeth.

Cobalt reduces the hardenability of steel. When dissolved in ferrite, cobalt provides resistance

to softening at elevated temperatures.

Cobalt alloys can be

(i) Cast.

(ii) Forged, extruded, rolled, swaged and drawn.

(iii) Welded and brazed.

(iv) Shaped by powder metallurgy.

Cobalt alloys are commercially available in following forms :

Ingot Wire Sheet Anode Powder

Bar Tubing Foil Casting Rod

Plate Forging, etc.

Application :

1. High temperature alloys.

2. Permanent magnets.

3. Hardfacing purposes.

4. Searchlight reflectors

5. Components of jet aircraft engines such as gas turbines, superchargers, turbojet nozzles and

vanes etc.

6. Nuclear reactors.

7. Wear resistant components in nuclear submarines.

8. Dies and cutting tools.

9. Rocked and motor cases for the space age.

Documents

High Temperature Materials