CHAPTER 2 : FRACTURE BEHAVIOUR

Griffith’s theory of brittle fracture • Griffith proposed ideas that did have a great influence on the thinking

about the fracture of metals.• He proposed that a brittle material contains a population of fine cracks

which produces a stress concentration of sufficient magnitude so that the theoretical cohesive strength is reached in localized regions at a nominal stress which is below the theoretical value.

• When one crack starts spreads into a brittle fracture , it produces an increase in the surface area of the sides of the crack.

• This requires energy to overcome the cohesive force of the atoms , or when expressed in another way , it requires an increase in the surface energy.

• The source of the increased surface energy is the elastic strain energy which is released as the crack spreads.

• Griffith established the following criterion for the propagation of a crack.

• “A crack will propagate when the decrease in elastic strain energy is at least equal to the energy required to create the new surface.”

• This criterion can be used to determine the magnitude of the tensile stress which will just cause a crack of a certain size to propagate as a brittle fracture.

• The elastic strain energy required per unite of the plate thickness is equal to :

• Ue=-((c^2)(^2))/E• Where =Tensile stress acting normal to the crack

of length 2a• A negative sign is used because growth of the

crack releases elastic strain energy.

Stress Intensity Factor• The stress intensity factor ,”K” , is

used in fracture mechanics to predict the stress state ("stress intensity") near the tip of a crack caused by a remote load or stresses.

• The magnitude of ”K” depends on sample geometry, the size and location of the crack, and the magnitude and the distribution of loads on the material.

• The stress intensity factor for the crack as show in the following figure is given as :

K=(a)

• For a general case the stress intensity factor is written by the following formula :

• K=(a)• Where is a parameter that depends on the specimen and crack

geometry.

Fracture toughness• Fracture toughness is a property which

describes the ability of a material containing a crack to resist fracture , and is one of the most important properties of any material for virtually all design applications.

• The linear-elastic fracture toughness of a material is determined from the Stress intensity factor (K) at which a thin crack in the material begins to grow.

• The Fracture toughness is entirely a material property like Ultimate stress of a material , and hence the fracture toughness is independent of the crack length , geometry , or loading system and depends only on the nature of the material.

• They are generally represented as “Kic”.

Ductile-to-Brittle Transition• The ductile to brittle transition is a very

important engineering phenomenon which causes the “ductile to brittle” transition in fracture behavior , which commonly occurs with decrease in temperate as in the case of steel and the other bcc materials as well.

• The temperature that governs the transition of the fracture from ductile to brittle is known as the transition temperature.

• Key features :– High frictional resistance would always lead to

a brittle fracture . – When the surface energy is large then the

brittle fracture is suppressed.

As seen in the following diagram , (a) Brittle fracture (b) Ductile fracture(c) Completely Ductile fracture

Creep• “Creep” is referred to the progressive

deformation of the material at a constant stress.

• A plot of the strain of the material upon applying a constant load and a constant temperature , against the time gives you the “creep curve” as shown.

• The rate at which the strain changes with respect to time is called as the Creep rate.

• During the initial load the creep rate decreases with time then essentially reaches a steady state in which the creep rate changes little with time, and finally the creep rate increases rapidly with time until fracture occurs.

• There are 3 stages to the creep curve . • Primary creep :In this stage that the creep

rate gradually decreases with time , and the above occurs as a consequence of the creep resistance due to the material deformation under the load .

• Secondary creep :In this stage , the creep rate is almost nearly a constant .The above is possible due to the balancing effects of strain hardening and recovery acting as competing processes.

• Tertiary creep :In this stage, occurs in constant load creep tests carried out at high temperatures ,at high stresses. This occurs as a consequence of the “necking” of the metal before it undergoes the fracture .

• The third stage is often associated with metallurgical changes recrystallization etc.

Deformation mechanism maps• A deformation mechanism map is a way

of representing the dominant deformation mechanism in a material loaded under a given set of conditions and thereby its likely failure mode. Deformation mechanism maps consist of some kind of stress plotted against some kind of temperature axis.

• The various types of deformations or creeps are mentioned in the map , each separated by boundaries or lines.

• An example is as shown in the diagram on the right hand side .

Fatigue • Fatigue is the progressive and localized structural damage that occurs when

a material is subjected to cyclic loading. • The nominal maximum stress values are less than the ultimate tensile

values.• Fatigue results in a brittle-appearing fracture, with no gross deformation at

fracture.• On macroscopic scales , the fatigue surface is normal to the direction of the

principle tensile stress.• The fatigue failure is usually recognized with the presence of both smooth

hand rough regions.• The smooth regions occur as a consequence of the rubbing action as the

crack propagated and the rough regions occur as a consequence of ductile failure when the cross section is no longer able to carry the load.

• Failure usually occurs at points of stress concentration such as sharp corners or notches .

There are three basic factors for the fatigue failure :-• Maximum tensile stress of sufficiently high value • A large variation or fluctuation in the applied

stress and • A sufficiently large number of cycles of the

applied stress.• In addition there are host of other variables like

corrosion , temperature , overload , stress concentration , metallurgical structure.

• STRESS CYCLE :-• A stress cycle is defined as a change in the force

distribution being applied upon the material at regular intervals .

• They can be of many types such as reverse (a) , repeated (b), irregular or random stress cycles (c) as well .

• The types are as shown in the figure .

High-cycle fatigue

• High cycle fatigue of the material is that failure that occurs when the number of cycles that the material undergoes in very high that is in the order of 10,000 cycles etc.

• The following are the key features necessary for the high cycle fatigue.

- Stress below yield strength - Macroscopically brittle - May be very long life

S-N Curves• In high-cycle fatigue

situations, materials performance is commonly characterized by an S-N curve, also known as a Wöhler curve . This is a graph of the magnitude of a cyclic stress (S) against the logarithmic scale of cycles to failure (N).

Mechanism involved

• There are three steps to the High cycle fatigue . • Local yielding at a defect or in a stress

concentration (filet root, scratch, bend, hole)• Dislocation pile up/ saturation• Crack formation• Crack propagation

Low cycle fatigue

• When fatigue occurs within lesser number of cycles with stresses greater that yielding strength is called as the low fatigue failure .

• The features are as follows :-• Stress exceeds yield strength• Very few cycles to failure• Lots of plastic deformation

Mechanism involved

• There are 4 steps again:• Sharp Crack – closed• Stress opens crack• Tip of crack blunts• Crack closure/

sharpening• Repeat

Fracture of non metallic materials • In brittle fracture, no apparent

plastic deformation takes place before fracture.

• In brittle crystalline materials, fracture can occur by cleavage as the result of tensile stress acting normal to crystallographic planes with low bonding (cleavage planes).

• In amorphous solids, by contrast, the lack of a crystalline structure results in a special type of fracture, with cracks proceeding normal to the applied tension.

Failure Analysis• Failure analysis is process of obtaining information (as much as possible )

from the “failed” part itself along with the investigation of the conditions at the time of failure .

• A component is said to have failed is the “unacceptable” deformation or fracture, which is a relative term. (The term varies depending upon the product description)

• The failure analysis has its fundamental use in the “Reliability” of the product being manufactured that determines his popularity and the extent to which customer satisfaction is achieved by the same .

• There various types of failures that occur , some of them are as follows : – Fracture – Fatigue– Creep

Source of failure • Failure causes are defects in design, process, quality, or part application, which are the

underlying cause of a failure or which initiate a process which leads to failure. Where failure depends on the user of the product or process, then human error must be considered.

• They include corrosion, welding of contacts due to an abnormal electrical current, return spring fatigue failure, unintended command failure, dust accumulation and blockage of mechanism, etc.

• The real root causes found in most cases be traced back to some kind of human error, e.g. design failure, operational errors.

• Some types of mechanical failure mechanisms are: excessive deflection, ductile fracture, brittle fracture, impact, creep, relaxation, thermal shock, wear, corrosion, stress corrosion cracking, and various types of fatigue.

• Each produces a different type of fracture surface, and other indicators near the fracture surface(s).

• The way the product is loaded, and the loading history are also important factors which determine the outcome. Of critical importance is design geometry because stress concentrations can magnify the applied load locally to very high levels, and from which cracks usually grow.

Procedure to Failure analysis • They are of many steps :- Initial observation :• Make a detailed visual study of the actual component that failed.• Record all details by photographs • Interpretation must be made of deformation markings, fracture appearance,

deterioration etc. Background data :• Collect all data concerned with specifications and drawings, component design,

fabrication, repairs, maintenance and service use. Laboratory studies:• Verify the chemical composition of the material within specified limits.• Other tests such as NDT(Non –destructive tests) , heat treatment are carried out. Synthesis of Failure : • Study all the positives and negatives of the situation and indicate a solution to

the problem of failure.

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