Microestructura DeFZ y Grain Growth

8/14/2019 Microestructura DeFZ y Grain Growth

1/17

Weld Metal Microstructure in Low Alloy Steels

3.1 Introduction

The weld metal microstructure is formed under highly nonequilibrium

conditions and differ distinctly from those experienced during casting,

thermomechanical processing, and heat treatment. For low alloy steels, the weld

microstructure evolution starts from the solidification with epitaxial growth of columnar

delta-ferrite () from the hot grain-structure of the parent plate at the fusion surface. ,!

The final weld metal microstructure is determined by the combination of alloy chemical

composition and the cooling rates experienced.

3.1.1 Classification of Weld Metal Microstructure

"alculation of microstructure needs a detailed description of each phase. For a

meaningful classification of the different features in a microstructure, the various phases

and microconstituents should be identified by using a system of nomenclature that is

both widely accepted and well understood. #n wrought steels, this need has been

satisfied to a large degree by the $ube scheme,%in which various ferrites are classified

according to their morphologies. Four well defined ferrite morphologies recogni&ed by

$ube% and later extended by 'aronson are grain boundary allotriomorphs,

*idmansttaten side plates or laths, intragranular idiomorphs, and intragranular plates.

the ma+or components in the weld metal of low alloy steels include

allotriomorphic ferrite (), *idmanstatten ferrite (w), and acicular ferrite(a). There

may also some microphases composed of martensite (), retained austensite () or

degenerate pearlite (). #t can be noted that this classification of ferrite is consistent with

the morphological classification proposed by $ube,% although the notations are

somewhat different. 'cicular ferrite does not figure in the $ube scheme because it is

rarely observed in wrought steels. Fig. ./ shows the typical morphologies of the ma+or

microstructural components in the weld metal as well as typical phases in the 0'1 of

low alloy steels.

/./ 'llotriomorphic Ferrite ()


2/17


3/17

9icrophases in this content means the transformation structures resulting from

carbon enriched retained austenite in low alloy steels. #t might include martensite,

retained austenite, bainite or degenerate pearlite.

(a) (b)

Fig 5./ (a) 9a+or microstructural components in the weld metal of low alloy steels: The

term ;F, *F, 'F, and F refer to grain boundary ferrite (allotriomorphic ferrite),

*idmansatten ferrite, acicular ferrite (intragranular plates), and polygonal ferrite

(idiomorphic ferrite), respectively. (b) 9a+or microstructural components in the 0'1 of

low alloy steels: The term =, and 9 refer to upper banite, lower banite, and

martensite, respectively./?

3.3 Microstructural Evolution In The Weld Metal

The microstructural evolution in the weld metal of low alloy steel is

schematically shown in Fig. 6 (adapted from =hadeshia5). The final weld metal

microstructure is dominantly determined by the austenite decomposition process within

the temperature range %?? - @?? ". $uring cooling of the weld metal, allotriomorphic

ferrite is the first phase to form from the decomposition of austenite in low alloy steels.

#t nucleates at the austenite grain boundaries and grows by a diffusional mechanism.

's the temperature decreases, diffusion becomes sluggish and displacive

transformation is 4inetically favored. 't relatively low undercoolings, plates of*idmanstatten ferrite forms by a displacive mechanism. 't further undercoolings,


4/17

bainite nucleates by the same mechanism as *idmanstatten ferrite and grows in the

form of sheaves of small platelets. 'cicular ferrite nucleates intragranularly at

inclusions and is assumed to grow by the same mechanism as bainite in the present

model./-, @The morphology of acicular ferrite differs from that of conventional bainite

because the former nucleates intragranularly at inclusions and within large austenite

grains, while the latter nucleates initially at austenite grain boundaries and grows by the

repeated formation of subunits to generate the classical sheaf morphology.


5/17

0.1 1 10 100

Time (s)

0

400

800

1200

1600

Temperature(oC)

(a) (b) (c)

(d)

(e)

(f)

Ms

Liquid

Coolingcurve

Fig.6 7chematic of microstructure evolution in the weld metal of low alloy steels. (a)

inclusion formation: (b) liquid metal solidification to ferrite: (c) single austenite

region: (d) allotriomorphic ferrite: (e) *idmanstatten side plate: (f) acicular ferrite8

bainite. (adapted from 0. A. $. 0. =hadeshia5)


6/17

rain rowth

'ssuming that grain growth is diffusion controlled, driven by grain boundary

energy, and requires no nucleation, then the extent of transformation depends on the

integrated number of diffusive +umps during the weld thermal cycle. The austenitegrain growth in the 0'1 can be calculated by a 4inetic equation as

g g 4 e dt

B

CT t6?6

/?

=

( )

(./)

where g is the grain si&e after time t, g?is the initial grain si&e, 4/is a 4inetic constant, B

is the activation energy for grain growth, T(t) is the temperature varying with time, and

C is the gas constant. The term in the brac4et of equation (/) is called the 24inetic

strength3 of the cycle, the extent of which reflects the total number of diffusive +umps

which ta4e place during the cycle. The quantity of 24inetic strength3 is shown as the

shadow area in Fig. 6. =ased on the concept of 24inetic strength3, the grain growth

equation can be simplified as

PRT

Q

ekgg

= /6

?

6

(.6)

where is a characteristic time constant for the thermal cycle, Tp is the pea4

temperatureof the thermal cycle, is a variable determined by B and Tpand expressed

as/

Q

RTP

6=

(for thic4 plate) (../)

= 6CT

B

-

(for thin plate)

(..6)

The 4inetic constant 4/ in equations (./) and (.6), which contains uncertain

4inetic factors, can be eliminated by using experimental data.


7/17

(.5), the grain si&e for a specified weld thermal cycle can be calculated by the

following equation

=

PP

TTR

Q

e

gg

gg//

DD6

?

6D

6

?

6D

(.@)

Equation (.@) establishes a relationship between grain si&e g and the thermal

cycle characteri&ed by variables Tp and , which allows grain si&e in the 0'1 to be

drawn in a Tpand space.

3.!.1.! "reci#itate dissolution and coarsening

3.!.1.!.A "reci#itate dissolution$epending on the pea4 temperature and duration of the thermal cycle, carbides

and nitrides in the 0'1 of low alloy steels may dissolve or coarsen. #n this algorithm,

the precipitate particles are assumed roughly spherical and each precipitate is assumed

to be associated with a volume of surrounding matrix of radius l. The volume fraction

available for dissolution considering impingement of the diffusion fields in the

algorithm is calculated by ohnson and 9ehl66and 'vrami6type equation

( )

f e

$t

l=

/

6

8

(.)

where f is the volume fraction available for dissolution, t is the time, and $ is the

diffusion coefficient of the element of the precipitate which diffuses most slowly.

7tarting from equation (.), the dissolution of the precipitates during a weld thermal

cycle can be calculated based on the concept of 24inetic strength3 as described in the

above section. The volume fraction available for the dissolution of a precipitate during a

weld thermal cycle in the algorithm is derived and expressed as

f e

B

C T T- -=

/

6 / / 6

D D Dexp

8

(.!)

where B6 is the activation energy for diffusion of the atoms of the precipitate which

diffuse most slowly, is a characteristic time constant for the thermal cycle, is a

variable determined by B6and Tp (the pea4 temperature of the thermal cycle) in the

same relation as that described in equations (../) and (..6), and are the values

of and corresponding to the complete dissolution at a temperature TD.


8/17

3.!.1.!.$ "reci#itate coarsening

For precipitates remain undissolved, they will coarsen during the subsequent

cooling procedure. The change of the precipitate radius (p-p ?) can be related with

coarsening time t at a constant temperature T by the standard equation65,6@

- -

4 t

T e

B

CT 6?

=

(.%)

where p is the radius of precipitate at time t, p?is the initial radius of the precipitate, 46

contains constants which depends on matrix composition, and B is the activation

energy for diffusion between precipitates. #ntegrating equation (.%) over the thermal

cycle and using the method of section 6././, the radius of the precipitate can be related

with its cycle characteri&ed by a and t as following

p p

p p

T

T e

-

-

B

C T T- -.

?.

.?.

/ /.

=

D D D

DD

(.)

where is a variable determined by Band Tp (the pea4 temperature of the thermal

cycle) in the same relation as that described in equations (../) and (..6), pD is the

average precipitate radius, which is produced by a thermal cycle characteri&ed by a

thermal variables TpDand D.

3.!.1.3 Calculation of #hase volu%e fractions

The volume fractions of the various phases (ferrite8pearlite, bainite, and

martensite) are determined by the time necessary cooling from %?? to @?? o" (t) and

the carbon equivalent of the steel ("eq). #n this algorithm, the volume fractions of

various phases are related with t based on the data of #naga4i and 7e4iguchi6 who

established continuous cooling transformation (""T) diagrams for a wide range of

structural steels. Two specific cooling times are ta4en in the algorithm to give a @?G

martensite8@?G bainite structure, t/86m, and a @?G bainite8@?G ferrite or pearlite

structure, t/86b, as shown in Fig. . The influence of the alloying elements on these

critical cooling times can be related to the carbon equivalent of the steel (" eq) by

empirical equations such as that recommended by the #nternational #nstitute of

*elding6!

" "

9n "r 9o H "u Ii

eq = + +

+ +

+

+

G

G G G G G G

@ /@ (./?)


9/17

Then the critical cooling times are calculated as by the following equations 6

log . .8t Cm

eq/ 6 % !( /@6= (.//./)

log . .8t "b

eq/ 6 % %5 ? !5= (.//.6)

where thas units of seconds and "eqis measured in weight percent.

The ohnson-9ehl equation66 is used to calculate the volume fractions of various

phases. #n their algorithm, the volume fraction of ferrite and pearlite are not

distinguished and expressed by the same equation

H efp

t

t

n

=

/

? / 6

.8

(./6./)

where Hfp is the volume fraction of ferrite8pearlite after a time t (characteri&ing the

cooling part of the weld thermal cycle), t/86 is the time required for half the

transformation to occur, n is a value depending on the nucleation sites (it ta4es the

value for random nucleation, 6 for nucleation on grain edges, and / for nucleation on

grain corners). The volume fractions of bainite and martensite formed from the

untranformed austenite during subsequent cooling can calculated and expressed as

H em

t

t m

=

?

/ 6

6

.

8

(./6.6)

H e Hb

t

t

m

b

=

?

/ 6

6

.

8

(./6.)

where Hband Hmare the volume fractions of bainite and martensite, respectively.

The effect of prior austenite grain si&e on the transformation 4inetics are

considered in the algorithm by modifying the critical transformation times t/86, t/86b

and t/86m. 'ssuming that the transformation time for a given grain si&e g?is t/86

?, it is

easy to understand that the volume fraction of ferrite8pearlite which forms within time

t for a different grain si&e g can be expressed by following equation (./) as

H efp

g t

g t

n

=

/

? ?

/ 6?

.

8

(./)

This equation shows that as the grains grow, the amount of ferrite8pearlite which

can form during a given quench decreases, and the volume fractions of bainite and

martensite consequently increase. The equations for calculation of the volume fractions

of bainite and martensite can be similarly modified by considering effects of grain si&e


10/17

on the corresponding transformation times, t/86m and t/86

b. The corrected

transformation times will be

( ) tg

g tm m/ 6

?/ 6

?

8 8=(./5./)

( ) tg

g tb b/ 6

?/ 6

?

8 8=(./5.6)

where (t/86m)? and (t/86

b)?are the transformation times for martensite and bainite at

given grain si&e g?.

3.!.1.& Co%%ents on the algorith%

The advantage of the algorithm is that microstructural diagrams can be

established, from which the austenite grain si&e, the extent of the dissolution of the

precipitates, and the amount of martensite in the 0'1 can be directly read. Two types of

0'1 microstructural diagrams can be developed by using the methods described above.

Jne is based on axes of log heat input and pea4 temperature, as shown in Fig. .5(a),

and the other on both linear and logarithmic scales of heat input and distance below the

center line of the weld, as shown in Fig. .5(b). The former is useful for obtaining an

overall picture of the effect of various welding processes on microstructure: the latter

provides a more physical picture of an actual weld. The results have been correlated

with actual welding experiments.

0owever, as ac4nowledged by the authors themselves, the least certain part of

the procedure is the calculation of the volume fractions of microstructural constituents.

Iot only the differences between some competitive products such as ferrite8pearlite are

not separated, but also ferrites formed by different phase transformation mechanisms

such as allotriomorphic and *idmanstatten ferrites are not distinguished. #n addition,

the transformation rates for ferrite8pearlite, bainite, and martensite are approximated by

using empirical formula based on the carbon equivalent index, which is somewhat

crude.

!.!. Algorith%s 'y (ir)aldy and Watt1*+1,

' computer algorithm originally developed by Air4aldy et al./-6/for predicting

the hardenability of low alloy steels was adapted by *att et al.

/!,/%

to calculate themicrostructural development in the 0'1. This algorithm simulates the 4inetics of the


11/17

decomposition of austenite to its various daughter products. The required inputs for this

algorithm are the eutectoid temperature ('e/), the solidus temperature of the (+)/

phase boundary ('e), the ferrite solubility temperature as a function of carbon (F7), the

bainite start temperature (=7), and the martensite start temperature (97). #n thealgorithm, these inputs are empirically calculated from the composition of the alloy as

equations (./@./)K(./@.@) and are listed in Table ./. The prior austenite grain si&e in

the 0'1 is calculated by the grain growth equations proposed by 'shby and

Easterling,/@,/as discussed section .6././.

' set of equations were developed in this algorithm to model each of the

daughter products from austenite decomposition process. These equations assume that a

single continuous function can describe both nucleation and subsequent growth for each

of the daughter phases. The general reaction rate for each reaction can be expressed

as/!,/%

( ) ( )dL

dt = ; T L L

m p= , /(./)

where L is the volume fraction of the daughter product, = is an effective rate coefficient

which depends on T, the temperature, and ;, the austenite grain si&e. The semi-

empirical coefficients, m and p, are set to less than one to assure convergence in a form

that is derived from a point nucleation and impingement growth model.6% The rate

coefficient includes the effect of grain si&e on the density of nucleation sites. #t also

includes the amount of austenite supercooling, and the effect of alloying elements and

temperature on diffusion. =ased on the general reaction rate equation, the reaction rates

for various products are determined by considering the corresponding phase

transformation characteristics. These reaction rate equations are expressed as equations

(./!./)K(./!.) in the algorithm and are listed in Table .6.

#n the rate equations listed in Table 6, it is important to use the precise definition

of L. #f one simply defines L as the volume fraction of ferrite then it is possible to use

equation (/!./) alone to form more than the equilibrium amount of ferrite in the

intercritical temperature region. This and the relative change in the thermodynamics

driving force for the reaction are corrected in the algorithm by proposing a phantom

reaction which go to completion. The phantom reaction product is LFM LLFEwhere

LFEis the equilibrium fraction of ferrite given by the lever law at that temperature. Thus

in equation (/!./), L is set to be L M LF8LFE. #f some of the austenite has previously

transformed to ferrite at the onset of pearlite formation, then the amount of


12/17

untransformed austenite will be (/-LFE). 's the result, L is set to be L M Lp8(/-LFE) in

equation (/!.6) for pearlite formation. #f pearlite exists before the bainite start

temperature is crossed, it is assumed that the existing pearlite-austenite interface

continues to transform, but now yielding to bainite. Thus L in equation (/!.) is

originally Lp. #f no pearlite exists, then

Table ./ "alculation of the temperatures for various phase transformation.

'e/(") M !6 - /?.! 9n - /. Ii N 6 7i N /. "r N 6? 's N .5 * (./@./)

'e " " Ii 7i H 9o *

9n "r "u - 'l 's Ti

/6 6? /@ 6 55 ! /?5 /@ //

? // 6? !?? 5?? /6? 5??

( ) . . . .

..................

= + + + + + + + +

(./@.6)

F7(") M /6 - %5%" (./@.)

=7(") M @ - @%" - @9n -!@7i - /@Ii - 5"r - 5/ 9o (./@.5)

97(") M @/ - 5!5" -9n -/!Ii - /!"r - 6/ 9o (./@.@)

D The compositions in the table are in wtG.

Table .6 Cate equations for formation of various phase products.

Ceaction Cate equation "omment

Ferrite

formation

dL

dt

T L L

"J9 CT)

; L L

=

6 /

6 ???

/ 6 6 / 6 ( )8 ( ) 8 8( )

exp( , 8

(/!./)

T M 'e- T:

"J9 M @.G9n N

/.5@GIi N !.!G"r N

655G 9o

earlite

formation

dL

dt

T $L L

"r 9o Ii

; L L

=

+ + +

6 /

/ ! @ 56 5G

/ 6 6 / 6 ( )8 ( )8 8( )

. . (G G G )

(/!.6)

T M 'e/- T:

$ is the effective

diffusion coefficient

for carbon modified

by considering the

presence of other

alloying elements.

=ainite

formation

dL

dt

T e L L)

" "r 9o f L,

; CT L L

=

+ + +

6 /

6 5 /? /G %G /G /?

/ 6 6 6! ??? 6 / 6

5

( )8 , 8 ( ) 8 8(

( . . . ) (

(/!.)

T M =7 - T:

f(L,"i) is a coefficient

determined by L and

the content of alloying

elements

D L is the existing daughter product volume fraction , dL8dt is the units of volume

fraction per second: ; is the '7T9 grain si&e number of austenite.


13/17

because the bainite reaction is sluggish, L is simply the fraction of bainite formed and it

continues to transform until the remaining austenite is consumed or the martensite start

temperature is reached.

The form of the austenite decomposition equations in this algorithm has its basis

in the theory of reaction 4inetics. The empirical factors used in the equations have been

accumulated over 6?? different steel compositions to produce a good fit to their TTT

and ""T diagrams. The algorithm has been combined with a finite element heat transfer

model to predict the 0'1 microstructure.6The predicted microstructure was found

comparable with the experimental results. 0owever, li4e the algorithm developed by

Easterling et al., no distinguish has been made between allotriomorphic ferrite and

*idmanstatten ferrite in this algorithm. #n addition, the reaction 4inetic arguments on

which the algorithm are based are not universally accepted.?,/ #n particular, the

assumption that the nucleation and subsequent growth can be treated as a single

continuous function may not be valid.

6. 9odel by =hadeshia and co-wor4ers/-

The two algorithms described above are only used for prediction of the

microstructural development in the 0'1. This is mainly because many of the empirical

constants in their algorithms were obtained by 2mechanically3 fitting the experimental

data (e.g. experimentally determined TTT and ""T diagrams) into the classical 4inetic

equations. These experimental TTT and ""T diagrams were normally established under

the condition that the chemical composition within the prior austenite is homogeneous.

Therefore, the algorithms stemming from using these data will not be suitable for

prediction of microstructural development in the weld metal, in which there exists

significant solute segregation in the prior austenite due to nonequilibrium solidification.

=ased on thermodynamics and phase transformation 4inetics, =hadeshia et al /-

developed a comprehensive model for the decomposition of austenite in the weld metal

of low alloy steels. #n this model, the phase transformation mechanisms for the various

microconstituents, the multicomponent phase diagram, and non-equilibrium cooling

conditions have been systematically considered in predicting the microstructural

development in the weld metal. The transformation start temperatures for a time-

temperature-transformation diagram in low alloy steel can be calculated from this

model. The volume fractions of various microstructural constituents are calculated


14/17

based on their corresponding phase transformation mechanisms. #n the present research,

the model developed by =hadeshia et al-5will be coupled with the cooling rates from

our $ heat transfer and fluid flow model to model the microstructural evolution in the

weld metal of low alloy steels.

/. 0. A. $. 0. =hadeshia and >. -E. 7vensson in Mathematical Modeling of Weld

Phenomena, ed. by 0. "er+a4 and A.E. Easterling, p. /?, #nstitute of 9aterials

(/)..


15/17

6. 0. A. $. 0. =hadeshia in ORecent Trends in Welding Science and Technology, ed.

by 7. '. $avid and . 9. Hite4, p. /%, '79 #ITECI'T#JI'>, 9aterials ar4,

J0 (/?).

. 0. A. $. 0. =hadeshia, >. -E. 7vensson, and =. ;retoft Acta metall., 33, /6!/

(/%@).

5. 0. A. $. 0. =hadeshiaProgress in Materials Science, !-, 6/ (/%@).

@. 0. A. $. 0. =hadeshiaainite in Steels, #nstitute of 9aterials (/6).

. *. F. 7avage, ". $. >undin, and '. 0. 'aronson Weld. !., &&, /!@ (/@).

!. ;. . $avies and . ;. ;arland"nt. Metall#rgical Re$., !, % (/!@).

%. ". '. $ube, 0. #. 'aronson, and C. F. 9ehlRe$. Met., //, 6?/ (/@%).

. 0. #. 'aronson in%ecom&osition of A#stenite 'y %iff#sional Processes, ed. by H. F.

1ac4ay and 0. #. 'aronson, p. %!, *iley, Iew Por4 (/6).

/?. Jystein ;rongMetall#rgical Modelling of Welding, p. xx, #nstitute of 9aterials

(/5).

//. 9'"

/6. J. ;rong and $. A. 9atloc4"nt. Met. Re$., 31, 6! (/%).

/. $. . 'bson and C. . argeter"nt. Met. Re$., 31, /5/ (/%).

/5. 0. A. $. 0. =hadeshia inPhase Transformation(), ed. by ;. *. >orrimer, p. ?,

#nstitute of 9etals, >ondon (/%%).

/@. 'shby and A. E. EasterlingActa metall., 3, / (/%6).

/. . ". #on, A. E. Easterling, and 9. F. 'shbyActa metall., 3!, /5 (/%5).

/!. $. F. *att, >. "oon, 9. =ibby, . ;olda4, and ". 0enwood Acta metall., 30, ?6

(/%%).

/%. >. "oon and $. F. *att in Comter Modeling of *a'rication Processes and

Constit#ti$e eha$io#r of Materials, ed. by . Too, p. 5!, "'I9ET, Jttawa (/%!).

/. . 7. Air4aldy and $. Henugopalan inPhase Transformations in *erro#s Alloys, ed. by

'. C. 9arder and . #. ;oldenstein, p. /6@, 'm. #nst. 9in. Engrs, hiladephia, '

(/%5).

6?. . 7. Air4aldy and C. ". 7harma Scri&ta metall., 10, // (/%6).

6/. . 7. Air4aldyMetall. Trans., &, 66! (/!).

66. *. '. ohnson and C. F. 9ehl Trans. Am. "nst. Min. +ngrs, 130, 5/ (/).

6. 9. 'vrami!. Chem Phys., -, /!! (/5/).

65. #. 9. >ifshit& and H.H. 7lyo&ov . hys. "hem.,1-, @ (//).

6@. ". 9. *agner 1. Electrochem., 0/, @%/(//).


16/17

6. 9. #naga4i and 0. 7e4iguchi Trans. atn. Res. "nst. Metals, apan, !, /?6

(/?).

6!. #nternational #nstitute of *elding $oc. ##78##*-%6-!/, 2;uide to the

*eldability of "-9n 7teels and "-9n 9icroalloyed 7teels3 (/!/).

6%. . *. "ahnActa metall., &, @!6 (/@).

6. ". 0enwood, 9. =ibby, . ;olda4, and $. F. *attActa metall., 30, ?6 (/%%).

?. 9. =. Auban, C. ayaraman, E. =. 0awbolt, and . A. =rimacombe Metall. Trans.,

1*A, /5 (/%).

/. E. =. 0awbolt, =. "hau and . A. =rimacombeMetall. Trans., 1&A, /%? (/%).

6. A. ". CussellActa metall., 10, !/ (/%).

. A. ". CussellActa metall., 1*, //6 (/).

5. 0. A. $. 0. =hadeshia%oc#ment of -Weld Microstr#ct#re Program, $epartment of

9at. 7ci and 9etallurgy,


17/17

@?. E. '. 9et&bower, ;. 7panos, C. *. Fonda, and C. '. Handermeer/ Science and

Technology of Welding and !oining, !, xx (/!).

@/. . *. "hristian and $. H. Edmonds "nt. Conf. 2n Phase Transformations in

*erro#s Alloys, ed. by '. C. 9arder and . #. ;oldenstein, p. 6, 'm. #nst. 9in.

Engrs, hiladephia, ' (/%5).

@6. A. E. Easterling in ORecent Trends in Welding Science and Technology, ed. by

7. '. $avid and . 9. Hite4, p. /!!, '79 #ITECI'T#JI'>, 9aterials ar4, J0

(/?).

@. 7. '. $avid and 7. 7. =abu in OMathematical Modelling of Weld Phenomena,

ed. by 0. "er+a4 and 0. A. $. 0. =hadeshia, p. /?, #nstitute of 9aterials (/!).

Documents

Microestructura DeFZ y Grain Growth