FAILURE MECHANISMIn

Ductile & Brittle Material

FRACTURE. DEFINATION: Simple fracture is the separation of a body into two or

more pieces in response to an imposed stress that is static (i.e., constant or slowly changing with time)

A fracture is the separation of an object or material into two or more pieces under the action of stress.

The fracture of a solid usually occurs due to the development of certain

displacement discontinuity surfaces within the solid.

If a displacement develops perpendicular to the surface of displacement, it is called a normal tensile crack or simply a crack; if a displacement develops tangentially to the surface of displacement, it is called a shear crack, slip band, or dislocation.

Fracture strength or breaking strength is the stress when a specimen fails or fractures.

Types of Fracture 1 Ductile fracture 2 Brittle fracture

Fracture Mechanism Fracture mechanics is the field of mechanics concerned with

the study of the propagation of cracks in materials. In modern materials science, fracture mechanics is an

important tool in improving the mechanical performance of mechanical components. It applies the physics of stress & strain, in particular the theories of elasticity & plasticity, to the microscopic crystallographic defects found in real materials in order to predict the macroscopic mechanical failure of bodies.

Ductile Fracture When a ductile material has a gradually increasing

tensile stress, it behaves elastically up to a limiting stress & then plastic deformation occurs. As stress is increased, the cross sectional area of the material is reduced & a necked region is produced. With a ductile material, there is a considerable amount of plastic deformation before failure occurs in the material, there is a considerable amount of plastic deformation before failure occurs in the necked region

Steps in Ductile Fracture

Necking.Small Cavities Formation.Formation of Crack.Cup & Cone Fracture

NECKING Necking, in engineering or

materials science, is a mode of tensile deformation where relatively large amounts of strain localize disproportionately in a small region of the material.

With elastic strain the material becomes plastically deformed & neck formation process starts

Deformation of material depends upon material purity

Necking

Force Applied (F)

Small cavities forming. Within the neck, small cavities or voids are

formed. These develop as a result of the stress causing small particle of impurities or other discontinuities in the material to either fracture or separate from metal matrix. More such nuclei are available to trigger the development of these cavities, the less the material will extend before fracture & less ductile the material

As purity of material increases, ductility of the material also increases.

Small cavities forming.

Force Applied (F)

Formation of Crack

Small cavities, or micro voids, form in the interior of the cross section enlarge, come together, & coalesce to form an elliptical crack, which has its long axis perpendicular to the stress direction. The crack continues to grow in a direction parallel to its major axis by this micro void coalescence process.

Force Applied (F)

Formation of crack perpendicular to force applied

Cup & Cone Fracture Finally, fracture ensues by the rapid

propagation of a crack around the outer perimeter of the neck by shear deformation at an angle of about 45 degree with the tensile axis this is the angle at which the shear stress is a maximum.

Sometimes a fracture having this characteristic surface contour is termed a cup-and-cone fracture because one of the mating surfaces is in the form of a cup, the other like a cone.

In this type of fractured specimen the central interior region of the surface has an irregular & fibrous appearance, which is indicative of plastic deformation.

Cup

Cone

cup-and-cone fracture

Brittle Fracture Brittle fracture takes place without any appreciable

deformation, & by rapid crack propagation. The direction of crack motion is very nearly perpendicular to the direction of the applied tensile stress & yields a relatively flat fracture surface

When gradual tensile load is applied on material in tensile test, at the end of elastic limit, without any prior indication material breaks. This type of fracture is called as Brittle Fracture

Factors affecting Fracture

Factors affecting the fracture of a material includes.

1. Stress Concentration.(Notch Sensitivity) 2. The speed with which the load is

applied. 3. The temperature. 4. Thermal shock loading.

Stress Concentration (Notch Sensitivity) Notch sensitivity is defined as, ‘A reduction in properties due to

the presence of stress concentration’. Any kind of irregularities produces stress concentration in material, such as

1. Crack. 2. A grain boundary. 3. An internal corner of engineering plant. If you want to break a small piece of material, one way is to

make a small notch in the surface of the material & then apply a force. The presence of a notch or any sudden change in section of a piece of material, can very significantly change the stress at which occurs. The notch or sudden change in section produced in the metal, is called as stress concentration. They disturb the normal stress distribution & produce local concentration of stress. The effect of various factors on increase in stress are as follow,

An increase in stress - Increases depth of notch - Reduces radius of tip

- Increases change in section

Stress Concentration in Brittle Material A crack in a brittle material will have quite a pointed

tip & hence a small radius. Such crack thus produces a large increase in stress at its tip, one way of arresting the progress of such a crack is to drill a hole at the end of the crack to increase its radius & so to reduce the stress concentration. In brittle material, fracture will occur if the stress concentration exceeds, i.e. decrease in the strength of material.

Stress Concentration in Ductile Material

In ductile material, strain permit adjustments to be localized with a reduction of the stress concentration. Notch sensitivity cannot have any relation unless we have specific knowledge of the behavior obtained experimentally of different classes of materials.

E.g. Good ductility in tension does not necessarily mean low notch sensitivity. There is no adequate correlation between yield or tensile strengths & fatigue notch sensitivity.

Speed at which load is applied.

A sudden application of load or impact loading may lead to fracture where the same stress is applied more slowly, it would not break. With a very high rate of application of stress there may be in sufficient time for plastic deformation of a material to occur & so what, under normal condition a material behaves ductile through it were brittle.

The Charpy & Izod tests give a measure of a behavior of notched sample of material where subject to a sudden impact load. The results are expressed in terms of the energy needed to break a standard size test piece. The smaller the energy needed, the easier it is for failure. Low energy associated with material is termed brittle. Ductile materials needs higher energies for fracture.

Thermal shocks The temperature of material

can effect its behavior when subject to stress many materials which are ductile at a higher temperature are brittle at lower temperature

The temperature Pouring hot water in cold glass, can

cause the glass to crack. This is the cause of thermal shock loading. The layer of glass in contact with the hot water trying to expand but is restrained by the colder outer layer of the glass. These layers are not heating up quickly because of poor thermal conductivity of glass. Result is the setting up of stress which can be sufficiently high to cause of brittle glass

Fracture toughness Defects & cracks are present in all engineering

materials. They may be introduced during solidification or heat treatment stages of the material. The fracture resisting capacity of machine component or engineering structures must be evaluated in the presence of cracks. The fracture resistance of a material in the presence of a crack or discontinuities is known as its fracture toughness.

From Griffith type of approach, the fracture toughness is defined by the critical value of parameter ‘Gc’. ‘Gc’ gives the value of the strain energy release per unit area of the crack surface, when unstable crack extension (lead to fracture) take place. For an elastic crack of length ‘2c’,

Ductility TransitionOne of the primary functions of Charpy & Izod tests is to determine whether or not a material experiences a ductile-to-brittle transition with decreasing temperature &, if so, the range of temperatures over which it occurs. The ductile-to-brittle transition is related to the temperature dependence of the measured impact energy absorption. This transition is represented for a steel by curve A in Fig At higher temperatures the CVN energy is relatively large, in correlation with a ductile mode of fracture. As the temperature is lowered, the impact energy drops suddenly over a relatively narrow temperature range, below which the energy has a constant but small value; that is, the mode of fracture is brittle. Alternatively, appearance of the failure surface is indicative of the nature of fracture & may be used in transition temperature determinations. For ductile fracture this surface appears fibrous or dull (or of shear character), as in the steel specimen of Fig that was tested at 79 degree Celsius. Conversely, totally brittle surfaces have a granular (shiny) texture (or cleavage character) (the -59 degree Celsius Specimen, Figure 8.14). Over the ductile-to-brittle transition, features of both types will exist (in Figure 8.14, displayed by specimens tested at & ). Frequently, the percent shear fracture is plotted as a function of temperature—curve B in Fig

Ductile - Brittle transition in steel.

-200 -100 0 100 300200

100

80

40

60

20

AUSTENITE (FCC)

Factors Affecting on Ductile Brittle Transition Temperature:

Following factors affect Ductile – Brittle transition temperature. Transition temperature increases - When grain size of material increases. - When alloying elements are added in the material. - When impurities in metal increases. - When percentage of carbon in steel increases. Common BCC (body centered cubic type of atomic structure) metals become brittle at low

temperature or at extremely high rates of strain. Many FCC ( face centered cubic ) metals, on the other hand, remain ductile even at very low temperatures. Polycrystalline HCP ( hexagonal closed packing ) metals are brittle, as there are not enough slip systems to maintain grain boundary integrity.

Griffith's Theory of Brittle Fracture

Fracture mechanics was developed during World War I by English aeronautical engineer, A. A. Griffith, to explain the failure of brittle materials.

According to Griffith, there are micro cracks in the metal that causes local concentration of stress to values high enough to propagate the crack & eventually to fracture of metal.

In Griffith theory, an energy method is employed to estimate the stress necessary to cause a crack to propagate

Griffith’s work was motivated by two contradictory facts: (a) The stress needed to fracture bulk glass is around 100 Mpa. (An

amorphous metal also known metallic glass or glassy metal) (b) The theoretical stress needed for breaking atomic bond is

approximately 10,000 Mpa.

Assumption to Griffith’s Consider lens ( elliptical ) shaped crack of length ‘2c’. Material of 1 unit thickness. Crack run from the front to back face. Longitudinal tensile stress ( ) sigma is applied The crack tends to increase its length in transverse

direction. If crack spreads, the surface area of crack increases,

while the elastic strain energy stored in the material decreases, because strains cannot be continuous across the cracked region.

( ) is surface energy per unit area of the material. No energy (elastic) is stored in cylindrical volume around

crack. Elastic energy is released when crack is introduced.

Griffith was of the opinion that, “ A crack will propagate ( travel) when decrease in elastic strain energy is at least equal to the energy required to create a new crack.

The surface energy associated with a flat crack of length 2c & unit thickness is 4C ,, ( where = surface energy/unit area of crack surface)

Taking into consideration this plastic deformation of the surface of the crack requiring energy ‘p’ per unit area, the total energy required to create crack is,

U = 4C( +p) This energy is supplied by the elastic strain

energy released by formation of crackTotal energy per unit volume (Ue) when crack

introduced is, Ue = [( /4)*(2C)2 *(t)]* [1/2* * e*2] t= unit thickness = 1; 2C = length of crack; E=

Young’s Modulus; = stress applied; e= strain in material.

We know that, e= /E.

Ue = [( /4)*(2C)2 *(t)]* [1/2* * e*2] Ue = C2 2 .

E

An existing crack will propagate with change in elastic strain energy w.r.t C.

Griffiths theory in its original form is applicable to a perfectly crystal.

Orowan’s Modification Griffith's theory provides excellent agreement with experimental data for brittle

materials such as glass. For ductile materials such as steel, though the relation still holds, the surface energy (γ) predicted by Griffith's theory is usually unrealistically high. A group working under G. R. Irwin at the U.S. Naval Research Laboratory (NRL) during WW II realized that plasticity must play a significant role in the fracture of ductile materials.

In ductile materials (& even in materials that appear to be brittle), a plastic zone develops at the tip of the crack. As the applied load increases, the plastic zone increases in size until the crack grows & the material behind the crack tip unloads. The plastic loading & unloading cycle near the crack tip leads to the dissipation of energy as heat. Hence, a dissipative term has to be added to the energy balance relation devised by Griffith for brittle materials. In physical terms, additional energy is needed for crack growth in ductile materials when compared to brittle materials.

Irwin's strategy was to partition the energy into two parts: the stored elastic strain energy which is released as a crack grows. This is the

thermodynamic driving force for fracture. the dissipated energy which includes plastic dissipation & the surface energy (&

any other dissipative forces that may be at work). The dissipated energy provides the thermodynamic resistance to fracture. Then the total energy dissipated is

where γ is the surface energy & Gp is the plastic dissipation (& dissipation from

other sources) per unit area of crack growth. The modified version of Griffith's energy criterion can then be written as

Critical stress & crack propagation velocity

C=

Fatigue Failure. Fatigue is a form of failure that occurs in structures subjected

to dynamic & fluctuating stresses (e.g., bridges, aircraft, & machine components). Under these circumstances it is possible for failure to occur at a stress level considerably lower than the tensile or yield strength for a static load. The term “fatigue” is used because this type of failure normally occurs after a lengthy period of repeated stress or strain cycling. Fatigue is important inasmuch as it is the single largest cause of failure in metals, estimated to comprise approximately 90% of all metallic failures; polymers & ceramics (except for glasses) are also susceptible to this type of failure. Furthermore, fatigue is catastrophic & insidious, occurring very suddenly & without warning. Fatigue failure is brittle like in nature even in normally ductile metals, in that there is very little, if any, gross plastic deformation associated with failure. The process occurs by the initiation & propagation of cracks, & ordinarily the fracture surface is perpendicular to the direction of an applied tensile stress.

SIGNIFICANCE OF CYCLIC STRESS

Cyclic stress distribution of forces (a stress) that changes over time in a repetitive fashion. When cyclic stresses are applied to a material, even though the stresses do not cause plastic deformation, the material may fail due to fatigue. Fatigue failure is typically modeled by decomposing cyclic stresses into mean & alternating components. Mean stress is the time average of the principal stress. The definition of alternating stress varies between different sources. It is either defined as the difference between the minimum & the maximum stress, or the difference between the mean & maximum stress. Engineers try to design mechanisms whose parts are subjected to a single type (bending, axial, or torsional) of cyclic stress.

Mechanism of fatigueFatigue Mechanics.

It can be developed in four stages. 1. Crack nucleation; 2. Stage I crack-growth; 3. Ultimate failure.

The figure shows mechanism of fatigue failure in three stages. The crack propagates slowly from the source, the fracture surface rub together due to pulsating nature of the stress & so the surface become burnished. Fatigue failure in metals is very easy to identify. The fatigue cracks are not result of brittle fracture but of plastic slip.

Crack Nucleation: Fatigue failure begins with formation of a small crack, generally at some point on the external surface

Crack Growth: The crack formed on surface is then develops slowly into the material in a direction roughly perpendicular to the main tensile axis. Ultimately the cross-sectional area of the member will have been so reduced that it can no longer withstand the applied load & ordinary tensile fracture will result .

Fracture: A fatigue crack ‘front’ advances a small amount during each stress cycle & each increment of advance is shown on the fracture surface as a minute ripple line. These ripple lines radiate out from the origin of fracture as a series of approximately concentric arcs. These individual ripples are visible only by very high-powered metallographic methods. Few ripples much larger than the rest & shows the general path which the crack has followed

Theories of fatigue failureA number of theories (or mechanism) proposed for

fatigue failure are as follow:

Orowan’s theoryWood’s theoryCottrell & hull theoryMott theory

Orowan’s theoryThe metal is considered to contain

small, weak regions, which may be areas of favorable orientation for slip or areas of high stress concentration due to metallurgical notches such as inclusions. If the loading or the stress is such that the total plastic strain in the weak region exceeds the critical value, a crack is formed.

Mott theory Mott suggested a model involving

the cross slip of screw dislocations & as a result a column of metal is extruded from the surface & a cavity is left behind in the interior of the crystal which is source of fatigue crack & ultimately the fatigue fracture occurs

Wood’s theory: wood interprets microscopic observation of slip

produced by fatigue as indicated that slip bands are the result of a systematic build-up of fine slip movement, corresponding movements of the order of 10^-5 to 10^-4 cm, which are observed for static slip bands. According to wood, the back & fort fine slip movement of fatigue could build up notches or ridges at the surface as shown in figure.

These notches act as stress raisers & this way starts a fatigue crack which ultimately leads to fatigue fracture.

Cottrell & Hull Theory: a model involving the interaction of

edge dislocation on slip systems was suggested by Cottrell & Hull. Two different slip systems when work with different directions & planes of slip produce slip step at surface, thereby forming intrusions & extrusions as shown in figure

Fatigue crack starts from intrusions at the surface.

Fatigue testing The method of testing the metal for fatigue was developed by

Wohler. The figure shows a typical experimental set up for Wohler’s setup. The specimen is in the form of a cantilever & loaded at one end through ball bearing. It is rotated by means of a high speed motor to which a counter is attached to count the number of rotations. At any instant, the upper surface of the specimen is under tension & lower surface is under compression, with the neutral axis. In one rotation, the specimen undergoes two cyclic fluctuations of stress. The number of cycles to cause failure will vary with the applied stress. Higher the stress, lower will be the cycles to cause failure. Similarly, if the stress is lowered, more number of cycles will be required to cause failure.

Test data presentation & statistical evaluation In the statistical analysis of fatigue data, it is essential to test more number of specimens. It is

necessary to think in terms of the probability of a specimen attaining a certain life at a given stress or probability of failure at a given stress in the vicinity of the fatigue limit. The basic method for expressing fatigue data should be a 3 dimensional surface representing the relationship between stress, number of cycles to failure & probability of failure. Figure shows 2 dimensional plot at constant stress. Based on this, curves of constant probability of failure are drawn. Thus, at sigma1 there is 1% of the specimens would be expected to fail at N1 cycles, 50% at N2 cycles etc. the figure indicates decrease in fatigue life with increasing stress.

Muller-stock tested 200 steel specimens at a single stress & found that the frequency distribution of N followed the Gaussian, or normal distribution if the fatigue life was expressed as logN. For engineering purposes it is sufficiently accurate to assume a logarithmic normal distribution of fatigue life at constant life in the region of the probability of failure of P=0.10 to P=0.90. however, it is frequently important to be able to predict the fatigue life corresponding to a probability of failure of 1% or less

S-N Curve & its interpretation The basic method of presenting

engineering fatigue data is by means of the S-N curve, a plot of stress ‘S’ against the number of cycles to failure ‘N’. A log scale is used for ‘N’. The value of stress that is plotted can be alternating stress, maximum stress, or minimum stress. Most determinations of the fatigue properties of materials have been made in completed reverse bending, where the mean stress is 0. figure gives typical S-N curves from rotating beam tests.

Figure shows that, the number of cycles of stress which metal can endure before failure increases with decreasing stress. Fatigue tests at low stresses are usually carried out for 10^7 cycles & sometimes to 5*10^7 cycles of nonferrous metals. For a few important engineering materials such as steel & titanium, the S-N curve becomes horizontal at a certain limiting stress. Below this limiting stress, which is called the fatigue limit or endurance limit, the material can endure an infinite number of cycles without failure.Most non ferrous metals, like aluminium, magnesium & copper alloys, have an S-N curve which slopes gradually downward with increasing number of cycles. These materials do not have a true fatigue limit because the S-N curve never becomes horizontal. In in such cases it is common practice to characterize the fatigue properties of material by giving the fatigue strength at an arbitrary number of cycles, e.g. 10^8 cycles.

Influence of Important factor on Fatigue

Fatigue strength is seriously reduced by following factors:

Notch effect Surface effect Corrosion fatigue Thermal fatigue Pre-stressing

Notch effect: fatigue strength of material is reduced by presence of notch in the material. In machine element it contains fillets, keyways, screw threads and holes. Fatigue cracks in structure parts usually starts at such geometrical irregularities.

the effect of fatigue is generally studied by specimens containing a ‘V’ notch or a circular notch. The effect of notches on fatigue strength is determined by comparing the S-N curves of notched and unnotched specimens.

Thermal fatigue: Fatigue failure can be produced by fluctuating thermal

stress under conditions where no stress are produced by mechanical causes. Thermal stress result when the change in dimensions of a member as the result of a temperature change. For the simple case of a bar with fixed end supports, the thermal stress developed by a temperature change ‘ T’ is

= * E* T, where , = linear thermal coefficient of expansion. E = elastic modulus. if failure occurs by one application of thermal stress, the condition is called

thermal shock. However, if failure occurs after repeated application of thermal stress, of a lower magnitude, it is called thermal fatigue. It exist at high temperature. Austenitic stainless steel is sensitive to this phenomenon because of its low thermal conductivity and high thermal expansion.

Surface effect: all fatigue failures start at the surface. The factors which affect on the surface of a fatigue specimen are roughly divided into 3 categories:

(a) Surface roughness (b) Changes in surface properties (c) Surface residual stress (a) Surface roughness: Smoothly polished specimen in which the fine

scratches are oriented parallel with the direction of the principle tensile stress, give the highest values in fatigue tests. Such polished specimen are usually used in laboratory fatigue tests and are known as ‘par bars’.

(b) Change in surface properties: Fatigue failure is dependent on the surface conditions. Decarburization of the surface of heat-treated steel reduces fatigue performance. Carburizing and nitriding makes steel surface stronger and harder, which improves fatigue properties. The fatigue performance is improved when notched fatigue specimens are nitrided. Electroplating of surface generally decreases the fatigue limit of steel.

(c) Surface residual stress: Residual stresses are stresses that exist in a part independent of any external force. Nearly every manufacturing operation will result in residual stresses in varying degrees. Residual stresses are beneficial when they are opposite to the applied load. Since cracks are propagated only by tensile stress. Surface residual compressive stress would be most desirable. Heat treating processes produce compressive residual stresses are such as nitriding, flame hardening, induction hardening and carburizing.

Figure shows that mirror polished specimen gives more fatigue strength & fatigue strength reduces with increase in surface roughness.

Corrosion fatigue : the simultaneous action of cyclic stress and chemical attack is known as corrosion fatigue. Corrosion attack without superimposed stress often produces pitting of metal surfaces. The pits acts as notches and produce a reduction in fatigue strength. When corrosion and fatigue occur simultaneously, the chemical attack greatly accelerates the rate at which fatigue cracks propagate. Material which shows a definite fatigue limit when tested in air at room temperature shows no indication of a fatigue limit when the test is carried out in a corrosive environment. When fatigue test is carried out in air not affected by the speed of testing, over a range from about 10 to 200 Hz, when test is carried out in corrosive environment there is a definite dependence on testing speed. Since corrosive attack is a time-dependent phenomenon, the higher the testing speed, the smaller the damage due to corrosion. In usual method, corrosion-fatigue test is carried out by continuously subjecting specimen in combined influences of corrosion and cyclic stress until failure occurs. A number of method are available for minimizing corrosion-fatigue damage. In general material is protected from corrosive environment by metallic and non-metallic coating is successful method. Nitriding is effective in minimizing corrosion fatigue.

Pre- stressing: Pre-stressing is the process of loading an engineering component under controlled conditions to a cyclic stress for a fixed number of cycles prior to any possibility of fatigue failure. When magnitude of pre-stressing is lower than thew operating stress level then it is known as under-stressing.

Under controlled conditions when the magnitude of the stress is higher than operating stress level the condition is called overstressing. The number of pre-stressing cycles is always lesser than the number of cycles needed to cause fatigue failure. Pre-stressing is desirable under conditions of under-stressing. An understressed components always exhibits best fatigue resistance.

For an over-stressed component the failure resistance is lesser compared to a components that has been pre-stresses. Thus under stressing cause significant improvement in fatigue behavior by strengthening the weak regions and enhancing their dynamic response to operating stress.

Creep Materials are often placed in service at

elevated temperatures and exposed to static mechanical stresses (e.g., turbine rotors in jet engines and steam generators that experience centrifugal stresses, and high-pressure steam lines). Deformation under such circumstances is termed creep

Creep is slow plastic deformation of metal under constant stresses at constant temperature for prolonged period

Defined as the time-dependent and permanent deformation of materials when subjected to a constant load or stress, creep is normally an undesirable phenomenon and is often the limiting factor in the lifetime of a part.

Effect of temperature on mechanical behavior of materials When temperature of material increases, the mobility of atoms increases

rapidly, which changes mechanical properties of material. High temperature will also result in greater mobility of dislocation by the mechanism of dislocation climb. The equilibrium concentration of vacancies increase and new deformation may form at high . In some metals, the slip system changes or additional slip system are introduced with increasing temperature. At high temperature, cold-worked metals will recrystallize and undergo grain coarsening while age hardening alloys may overage by prolonged exposure at high temperature and loose strength.

Successful use of metals at high temperature involves a number of problems. But modern technology demand better high temperature strength and oxidation resistance.

Creep testing The specimen to be tested is placed in the electric furnace where it is

heated to a given temperature. The usual method of creep testing consist of subjecting the specimen at constant tensile stress at constant temperature and measuring the extent of deformation or strain with the time. The typical creep testing machine is shown in figure even though, it appears to be simple, it requires considerable laboratory equipment, great care and precision in performance. The time of each test may be matter of hour, weeks, months or even years. Creep is also determined in compression, shear and bending.

The data is presented by plotting creep curve as deformation verses time at constant temperature and stress. The test specimen may be circular, square or rectangular in cross-section. Either a continuous record of deformation with time or sufficient number of deformation readings with time should be taken over the entire period of test. The strain is measured by strain gauge. The strain generally lies between 0.1% to 1% and the period of testing does not exceed 10,000 hours. If creep is continued until fracture occurs, the test is called as ‘creep-rupture’ test. It determines the time necessary for fracture of the test piece

Data presentation and analysis It is frequently important to be able to expolate creep or stress-rupture data into

regions where data are not available. Therefore, common methods of plotting creep data are based on plots which yield reasonable straight line. Figure shows the common method of presenting the influence of stress on the state or minimum creep rate.

Note that a log-log plot is used, so that extrapolation of one log-cycle represents a tenfold change. A change in slope of the line will sometimes occur. It has been shown that the value of the minimum creep rate depends on the length of time the creep test has been carried out. It has been shown for long-time creep test(t> 10,000 hours) that the creep strength based on ‘1%’ creep strain is essentially equal to creep strength based on true minimum creep rate.

Creep curve A creep curve is a plot between the total creep or strain and the time

for the entire duration of test.(a) Primary creep: the primary or transient creep is a decreasing creep

rate because of the work hardening process resulting from deformation(b) Secondary creep: during the secondary or steady state creep(i.e.

minimum creep rate), the deformation continues at an approximately constant rate. During this process, a balance exist between the rate of work hardening and rate of softening because of recovery or recrystallization. The steady state creep may be essentially viscous or plastic in character, depending upon the stress level and temperature.

© Tertiary Creep: if the stress is sufficiently high and temperature is also high, there is a tertiary stage in which the creep rate accelerates until fracture occurs. In this stage there is void formation and extensive crack formation occurs

Mechanism of creep failure Creep is a deformation process in which three main

features to be involved are:(1) The normal movement of dislocation along slip planes.(2) Process ‘dislocation climb’ which is responsible for

rapid creep at temperatures above .5 tm.(3) Slipping at grain boundaries. The following mechanism are known to be responsible

for creep in crystalline materials.(a) Dislocation climb.(b) Vacancy diffusion.(c) Grain boundary sliding.

Dislocation climb: In the primary stages of creep, dislocation move quickly at first but soon becomes pilled up at various barriers. At temperature in excess of 0.5 tm, thermal activation is sufficient to promote a process known as ‘dislocation climb’. It is shown in figure this would bring into use new slip planes and so reduce the rate of work hardening.

In addition to plastic deformation by dislocation movement, deformation by a form of slip at grain boundaries also occurs during the secondary stage of creep. These movements possibly leads to the formation of ‘vacant sites’, that is lattice position from which atoms are missing and this in turn makes possible ‘ dislocation climb’.

In the tertiary stage of creep micro-cracks are initiated at grain boundaries due to the movement of dislocations. In some cases, there is migration of vacant site, as a result necking and consequent rapid failure follows.

Vacancy diffusion: the diffusion of vacancies control creep rate. In this mechanism, grain boundary acts as a source and sink for vacancies. The mechanism depends on the migration of vacancies from one side of a grain to another. Referring to figure a grain ABCD is under stress ‘p’, the atoms moved from faces ‘BC’ and ‘AD’, along the path shown and the grain creeps in the direction of stress

Movement of atoms creating vacancies on face ‘AB’ & ‘DC’ and destroying them on the other faces.

Grain boundary: the sliding of neighboring grains with respect to the boundary that separates them. Figure shows that, grain boundaries lose their strength at lower temperature than the grains themselves. This effect arises from non crystalline structure of the grain boundary

Analysis of classical creep curve Andrade’s work on analysis of classical creep curve is focused on topic

of creep. He considered that the constant stress creep curve represents the superposition of two separate creep processes which occur after the sudden strain which results from applying the load. The first component of the creep curve is a ‘transient creep’ with a creep rate decreasing with time. Added to this is a constant-rate ‘viscous-creep’ component figure shows Andrade's analysis of the classical creep curve.

Andrade found that the creep curve could be represented by the following empirical equation.e = e0 [1+ t^(1/3)] e^(kt)

Where, e= strain, t= time, & k = constant, e0 = instantaneous strain.

Creep resistance materials: creep resistant material are required for structural and machine components used at elevated temperatures. They should be capable of withstanding these temperatures without undergoing creep beyond the specified limit, which may cause dimensional changes beyond permissible limit used in the design.

The following are the requirements of a creep resistance material.

(1) It should have high melting point because, the creep becomes significant above 0.4 tm (tm=melting point). If the melting point is high, material can be used at higher temperature, e.g. iron, nickel, cobalt.

(2) It should have coarse grained structure. The grain boundary region becomes quasi-viscous at creep temperature . Since in coarse grained materials grain boundary area is less, so that less amount of quasi-viscous region is formed with a less tendency to flow, reducing the creep deformation.

(3) It should be precipitation hardenable. It should have fine insoluble precipitates at the operating temperature. If coherent precipitates are present, maximum creep resistance is obtained e.g. in nickel base and iron-nickel-base superalloy coherent precipitates of Ni3 (Al, Ti) is formed.

(4) Dispersion hardening improves creep resistance.(5) It should have high oxidation resistance i.e. the oxide film should

follow either a logarithmic or a cubic law of growth.