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CHAPTER 2

FRACTURE MECHANICS IN DESIGN AND SERVICE

The ultimate goal in the field of applied solid mechanics is to be able to design structures

or components that are capable of safely withstanding static or dynamic service loads for a

certain period of time. The design rules are based on current understanding of how

materials fail, which is derived from extensive observations of failure mechanisms,

together with theoretical models that have been developed to describe these mechanisms

of failure. In general, the various failure mechanisms may be classified into the two broad

fields, as deformation and fracture.

2.1 DESIGN PHILOSOPfflES

For many applications, it is sufficient to determine the maximum static or dynamic stress

that the material can withstand, and then design the structure to ensure that the stresses

remain below acceptable limits. This involves fairly routine constitutive modeling and

numerical or analytical solution of appropriate boundary value problems. More critical

applications require some kind of defect tolerance analysis. In these cases, the material or

structure is considered to contain flaws, and one must decide whether to replace the part;

or leave it in service under a more tolerable loading for a certain period of time. This kind

of decision is usually made using the disciplines of fracture mechanics. In general, one

may distinguish three different design philosophies as follows:

Safe Life: The component is considered to be free of defects after fabrication and is

designed to remain defect-free during service and withstand the maximum static or

dynamic working stresses for a certain period of time. If flaws, cracks, or similar damages

are visited during service, the component should be discarded immediately.

Fail Safe: The component is designed to withstand the maximum static or dynamic

working stresses for a certain period of time in such a way that its probable failure would

not be catastrophic. For example a pressure vessel designed to work under the leak before-

burst (LBB) condition should show leakage as a result of crack propagation. The aim is to

prevent catastrophic failure by detecting the crack at its early stages of growth and also

reducing the internal pressure.

Damage Tolerance: The component is designed to withstand the maximum static or

dynamic working stresses for a certain period of time even in presence of flaws, cracks, or

similar damages of certain geometry and size.

2.2 INTRODUCTION TO FRACTURE MECHANICS

Fracture mechanics is primarily concerned with the strength of the cracked bodies or

structural elements. It deals with the analysis, prediction and prevention of structural

failures due to flaws or cracks. Cracks may exist in structural component due to various

processes of fabrication and the limitations of the techniques used to inspect the finished

components for cracks or flaws. Cracks may also form and grow due to the fluctuating

stresses, strain histories, service temperature and the surface condition, in which the

component functions. The growth of the crack may be enhanced considerably [1], if the

component is exposed to corrosive environment. Accidental damages could also be a

source of cracking. Engineering materials such as metals and alloys generally contain a

variety of defects, which act as stress raisers on microscale. Examples of such defects are

pores or voids, slag particles, inclusions, brittle particles, etc. the stress concentration

effect of these defects induce cracking under the stresses experienced in service. Hence,

for all practical purposes cracks on microscale in the structural components are an inherent

problem and failure results in service generally as a consequence of these cracks [2]. The

failure of the structural components because of such inherent cracks has resulted in the

evolution of the ' Fail-Safe' or 'Crack Tolerant' design philosophy.

Fracture will always have a wide-ranging importance to a man. An attempt to illustrate

this importance is shown in Figure 2.1. The first illustration is a stone hand-axe dating

from the Palaeolithic era. However, man and his hominid ancestors had been fashioning

stone for more than a million years when it was made. Once man built large expensive

structures, he had to ensure that they did not fracture and collapse [3]. Fracture mechanics

is basically about scaling. Leonardo da Vinci (1452-1519) was the first to record an

understanding the scaling of fracture and the second illustration in Figure 2.1 comes from

one of his notebooks and illustrates his strength tests on iron wires. Galileo Galilei (1638)

writing in his "Dialogues Concerning Two New Sciences" was the first to give the correct

scaling laws for bars under tension and bending. His illustration for a discussion of the

fracture of beams is shown Figure 2.1. Size effect is very important in fracture and Galileo

saw that this effect placed a limit on the size of structures, both man-made and natural,

which makes it impossible to build ships, palaces, or temples of enormous size in such a

way that all their oars, yards, beams, iron bolts, etc. will hold together; nor can nature

produce trees of extraordinary size because their branches would break down under their

own weight.

o o o o o 1/1 f») -^

o

10*

Years Past"*

10-' 10^ 10 10^

Years Future Present

•n*j? >> a js s *" e "^ SiS'O »-« S a. ^ a > Jt ^ js -C P. •^>^>

Is 'S ^̂ « o g o §

Figure 2.1 The Fracture Perspective

Iron, and from the 1860s, steel saw increasing structural use in the 19^^ century and

fracture was a problem. David Kirkaldy opened his Testing and Experimental works in

1865 and his testing mark is illustrated in Figure 2.1. He published a comprehensive

account of his experiments and discussed some of the fracture problems with steel, the

new structural material. However, the most prophetic pronouncement about the brittle

fracture problems with steel that were to come, occurred in 1861 in a leading article of

"The Engineer" that is worth quoting: "Effects of percussion and frost upon iron... We

need hardly say that this is one of the most important subjects that engineers of the present

day are called upon to investigate. The lives of many persons, and the property of many

more, will be saved if the truth of the matter be discovered-lost if it be not".

Apart from the pioneering work, the understanding of fracture waited until the last century

of the second Millennium. Even then it took until well into the second half of this century

until a rational approach was used by engineers and taught in engineering schools. The

author vividly remembers being taught the five theories of strength as an undergraduate in

the early 1950s without any real explanation. A major spur to the development of fracture

theory from 1940 onwards was the brittle fracture of large welded structures such as

bridges, ships and oil storage containers. This period is illustrated in Figure 2.1 by a

photograph of the Schenectady that broke in two while lying in the fitting-out dock in

January 1943. One of the most successful applications of linear elastic fracture mechanics

(LEFM) is to the reliability assessment of aircraft. A picture of the ill-fated Comet is

shown in Figure 2.1. A fast fracture initiated from a fatigue crack that grew from an astro-

navigation window and caused the loss of two aircraft in 1953 and 1954. One of the first

10

applications of LEFM was an explanation of this fast fracture. The next picture in Figure

2.1 is the Boeing 737 that lost a top section of the fuselage over Hawaii in 1988 and yet it

still managed to land safely. The cause of this fatigue failure was multisite fatigue, which

is still managed to land safely. The final picture in Figure 2.1 is a schematic illustration of

a microelectronic package to indicate that many of current fracture interests are outside

traditional engineering. What problems will the future bring? It does not take much

imagination to realize that there will be more and more applications of fracture mechanics

to tiny functional devices that need structural integrity. Structural problems will not go

away, but most will be able to be solved with present techniques provided the problems

are remembered. Alan Wells once remarked that the same fracture problem reappears

every thirty years, the length of time for a new generation of engineers that have not

experienced the problem.

The collapse of the Titanic ship and the WTC are the two extreme failures caused due to

the change in the service temperatures [4,5], which made the material to undergo rapid

fracture. It has been shown that an interrelation exists between material, design,

fabrication, service condition and loading as well as maintenance. Fractures cannot be

eliminated in structures by merely using materials with improved notch toughness. The

designer still has the fundamental responsibility for the overall safety and reliability of the

structure. Hence a thorough study of object failed is necessary before giving any reasons

for failure.

2.3 BASIC CRITERION IN FRACTURE MECHANICS

A material fractures when enough stress and work are applied on the atomic level to break

the attractive forces (bonds) between atoms. Fracture mechanics tries to evaluate the

structural integrity of components containing any defects in atomic bonds, and specify

whether they are capable of continued, safe operation. When cracks are identified in

structures or components during service, they must be evaluated to determine suitability

for continued operation. The basic criterion in any fracture mechanics analysis is to avoid

unexpected failure. To do so, the crack driving force must be kept less than the material

resistance to cracking, as illustrated in the figure 2.2.

Material

Environment - Temperature -Radiation

Loading rate

Fatigue

11

Applied stress

Crack size

Geometry <rf crack body

Loading rate/cycles

Figure 2.2 Basic Criterion in Fracture Mechanics

The crack driving force and the material resistance depend on the fracture mechanics

regime. Under a given state of stresses, the flaw size at which the crack driving force

equals the material resistance is called the critical flaw size. In general, a safety factor is

considered to the material resistance with regard to the crack driving force to find out the

permissible flaw size for a component. This method is called "damage tolerance". Damage

tolerance permits subcritical flaws to stay in a structure. Normally, an allowable flaw size

would be defined by dividing the critical size by a safety factor. The structure would then

be allowed to operate until the flaw grew to the maximum allowable size. Fracture

analysis can be done using either energy and/or stress intensity approach. These

approaches are the same in certain circumstances.

2.3.1 Progressive Crack Extension

Progressive forward motion of the leading edge of a crack, the crack front, occurs when

the stresses, deformations, and advance openings in and near the fracture process zone

reach critical conditions relative to local fracturing. Development and joining of the

advance openings are the mechanisms of progressive fracturing usually observed. Because

of the stress and strain intensifications near the crack front, a gross section tensile stress

below that necessary for general yielding may be large enough to cause forward motion of

the crack.

2.3.2 Fracture Process Zone

Adjacent to the crack front lies a region that contains the advance separations and

deformations directly associated with local separation mechanisms. This region is termed

as the fracture process zone. Outside of a boundary line enclosing the fracture process

12

zone, it is convenient to assume that the rules of continuum mechanics apply in a

straightforward manner.

2.3.3 Analysis Model of A Crack

A simplified model of a crack used in elastic stress analysis is called the analysis model of

a crack. In stress free body, the crack has two smooth surfaces that are coincident and join

within the body along a smooth curve called the crack front. In two dimensional

representations the crack front is called crack tip.

2.3.4 The Energy Approach

The energy approach states that, the crack extension occurs when the energy available for

the crack growth is sufficient to overcome the resistance of the material. Resistance of

material may include surface-energy, plastic work or any type of energy dissipation

associated with a propagating work. Griffith proposed energy criterion, but Irwin is

responsible for present version.

2.3.5 The Stress Intensity Factor Approach

According to this approach stress state at the tip of a crack is proportional to the stress

intensity factor, K. Likewise, fracture occurs at critical stress intensity, Kc,which is an

alternate measure of fracture toughness. Fracture mechanics may be classified into; brittle

fracture (CleavageJ, which requires little energy, and ductile fracture, which requires much

energy. In brittle fracture, basically no permanent deformations occur and therefore the

broken parts usually may be refitted together to the original dimensions. Conversely, in

ductile fracture considerable plastic deformation happens before rupture, and as a result it

is unlikely to refit the damaged parts.

2.4 FRACTURE MECHANICS BRANCHES

Material behavior defines different branch of fracture. The concepts of early fracture

mechanics, prior to 1960, are applicable only to materials that obey Hooke's law.

Although corrections for small-scale plasticity were proposed as early as 1948, these

analyses are restricted to structures whose global behavior is linear elastic. Since 1960,

fracture mechanics theories have been developed to account for nonlinear material

behaviors (i.e. plasticity, viscoplasticity, and viscoelasticity) as well as dynamic effects. In

general, fracture mechanics can be categorized as.

13

1. Linear Elastic Fracture Mechanics (LEFM)

2. Nonlinear Fracture Mechanics (EPFM)

-i.LJ. Crock

T'TT

a,.UL, Crock

T"r"r

rS^i

(a) (b) (c)

Figure 2.3 Yielding at the Crack Tip, a) LEFM Localized yielding at the crack tip, b)

EPFM Net section yielding, c) Limit load Entire section yielding

2.4.1 Linear Elastic Fracture Mechanics (LEFM)

Linear elastic fracture mechanics is a technological approach to fracturing based entirely

on linear elastic theory. It provides an analytical procedure that relates the stress field in

the vicinity of a crack tip to other parameters, such as the nominal stress applied to the

structure and the size, shape, and orientation of the crack. Thus it permits representation of

the material fracture properties, often in terms of a single parameter. LEFM is based on the

application of the theory of elasticity to bodies containing cracks or defects with the

assumption of small deformations and a linear relationship between stresses and strains.

One of the underlying principles of LEFM is that unstable fracture occurs, when the sfress

intensity factor at the crack tip reaches a critical value, the fracture toughness of the

material is in question. Knowing the critical sfress intensity factor, a designer can either

determine flaw sizes that possibly may be tolerated at a given sfress level or find the

design sfress level, which may safely be used for a crack that may or may not be present in

a component.

2.4.2 Elastic-Plastic Fracture Mechanics (EPFM)

Linear Elastic Fracture Mechanics (LEFM) is, despite its denotation, valid also when

plastic deformation occurs. However, this plastic deformation has to be confined to a small

region ahead of the crack tip. In many materials and for many combinations of loading and

geometry, these conditions are not fiilfiUed. This calls for models, which can deal with

larger plastic zones. Elastic Plastic Fracture Mechanics (EPFM) deals with such models.

Elastic plastic fracture mechanics analysis is an extension of the linear elastic analysis. As

14

already mentioned low to medium strength structural materials used in the section for

large complex structures are of insufficient thickness to maintain plane strain conditions

under slow loading conditions at normal service temperatures [6, 7]. LEFM predicts

infinite stress at the crack tip, so that obviously there must be an inner core where the

elastic solution breaks down. This factor was early recognized by Irwin who, by simple

equilibrium arguments, estimated the size of the plastic zone (dp) at a crack tip in a

material with particular yield strength.

There is a regime where the plastic zone does have a significant effect on the outside stress

field. In this regime, Irwin showed that LEFM could still be used, provided that an

effective crack length equal to dp/2 was added to the actual length. However, as the

plastic zone becomes large LEFM breaks down and plastic deformation has to be

considered in detail. The beauty of LEFM is that it is a one-parameter model that only

depends upon the state of stress and not its history.

2.5 MODES OF CRACK TIP DEFORMATION

Failure of structural members is caused by the propagation of cracks, especially in fatigue.

Therefore an understanding of the magnitude and distribution of the stress field in the

vicinity of the crack front is essential to determine the safety and reliability of structures.

Because fracture mechanics is based on a stress analysis, a quantitative evaluation of the

safety and reliability of a structure is possible [8]. It is convenient to define three types of

relative movements of two crack surfaces. Before analyzing to a variety of crack

problems, it is important to know that there are three modes of cracking as illustrated in

figure 4. These displacement modes represent the local deformation in an infinitesimal

element containing a crack form.

Made 1 Mode 3

Figure 2.4 Examples for the three basic modes of fracture

15

Mode-I - Opening Mode: Where the crack surfaces separate symmetrically with respect

to the plane occupied by the crack prior to the deformation (results from normal stresses

perpendicular to the crack plane). Mode I loading is normal to the crack plane, and tends

to open the crack. The crack surfaces tend to separate symmetrically with respect to the

crack plane.

Mode-II - Sliding Mode: Where the crack surfaces glide over one another in opposite

directions but in the same plane (results from in-plane shear). Mode n corresponds to in-

plane shear loading and tends to slide one crack face with respect to the other (shearing

mode). The stress is parallel to the crack growth direction.

Mode-HI - Tearing Mode: Where the crack surfaces are displaced in the crack plane and

parallel to the crack front (results from out-of-plane shear). Mode HI corresponds to out-

of-plane shear, or tearing.

A cracked body can be loaded in any of these modes, or a combination of two or three

modes. Each mode of loading produces the singularity at the crack tip. In a mixed mode

problem (more than one mode is present), due to the principle of linear superposition, the

individual contributions to the stress component are additive. This module can find the

stress and displacement fields for Mode-I, Mode-II, Mode-Ill, and mixed mode loadings.

Note that Mode-Ill loading is the same in both plane stress and plane strain loadings.

Figure 2.4 shows the example for the three modes of fracture.

2.6 CRACK TIP CHARACTERIZATION PARAMETERS

There are many parameters by which the magnitude of the stress field in the neighborhood

of a crack tip is characterized [9]. These parameters manly concentrate on the initiation,

growth and propagation of the crack in the loaded member. The main parameters are,

2.6.1 Stress Intensity Factor

The stress intensity factor is the magnitude of the crack tip stress field for a particular

mode in a homogeneous linear elastic material. Usually denoted by Ki. If Ki is known for

the geometry of interest, then the entire stress distribution at the crack tip can be

computed. This constant Ki is called as SIF. This completely characterizes the crack tip

conditions in a linear elastic material, if it is assumed that the material fails locally at some

critical combination of stress and strain, then it fallows that the fracture must occur at a

critical SIF Kic. Thus Kic is an alternate measure of the fracture toughness.

16

2.6.2 Crack Extension Force

The crack extension force G is the loss of stress field energy at the crack tip per unit of

new separation area during a virtual increment of forward crack extension. The material is

assumed to be elastic. The calculation of G depends on the infinitesimal and virtual

increment of new separation area and can be applied to either a stationary or running

crack. For each of the three modes and assuming linear elastic analysis, K̂ is proportional

to G through a proportionality factor, which is usually known. For the dynamic stress field

of a running crack, the proportionality factor is additionally influenced by the crack speed.

2.6.3 J-Integral

The J characterization factor has the same definition as G relative to the elastic stress-

strain behavior of the basic analysis. J-Integral method is conventionally used as a fracture

parameter for characterization of elastic-plastic behavior of engineering materials. J-

Integral method is mainly used for characterization of a crack tip in the presence of large

scale yielding. For applications, crack tip is assumed stationary; strains are assumed to

increase monotonically with time during loading. Also the stress field energy density is

considered to be same by assuming reversible stress-strain behavior. Specimens of

different initial crack lengths are loaded. Carefully xy recordings of load verses

displacement are made. The area between two adjacent crack size-loading curves, up to

some fixed value of load point displacement is assumed to Jbda. In its simplest form, the

material resistance in this regime is measured by the elastic-plastic fracture toughness

(Jic). Because of the ductile nature of materials in the EPFM regime, there may also be

considerable stable crack extension of the material even when the applied Ji reaches the Jic

value.

2.6.4 Crack Tip Opening Displacement (CTOD)

Wells, in 1961, discovered that the test samples, which were too tough to be characterized

by LEFM had a blunting of the crack tip. The crack tip opening displacement, CTOD,

measures the pre-fracture deformation at the tip of a sharp crack under conditions of

inelastic behavior, and the degree of blunting increased in proportion to the toughness and

was thus proposed as a fracture toughness measure. CTOD is estimated by measuring the

displacement at the crack tip, and assuming rigid specimens rotating around a hinge point.

The crack tip opening displacement 8 is the value of J divided by a judgment estimate of

the effective yield strength controlling plastic strains near the fracture process zone. This

model presumes ideally plastic materials, but can be enhanced by dividing the deformation

17

into elastic and plastic parts. This is easily done by the use of a load-displacement plot for

the experiment.

2.6.5 Commonly Used Relations

Because of the wide familiarity with measurements of fracture toughness in terms of K,

determination of fracture toughness in terms of G, J and 6 are frequently converted to

equivalent K values using the relations,

^ - = G = J=CTS (2.1)

E^ '

Where Ei is identical with E for plane stress and identical with E/(1 - V̂ ) for plane strain.

2.6.6 Tearing Modulus

The parameter, tearing modulus is used to characterize the crack growth resistance.

Material instability parameter tearing modulus, T is given by

daSo^

T = ( " 1 i " ) ^)A^\

( «

X . (2.2)

2.7 FRACTURE TOUGHNESS

A general tendency of decreasing toughness while increasing strength, made urgent the

need for improved quantitative assessments of both these properties [10]. It also gave rise

to a new approach in appreciating factors of importance in the satisfactory application of

materials. The most significant single feature was the realization that it is no longer

sensible to consider flawless materials. Even if it were possible to guarantee the

manufacture of such materials in the first place, it would still be near impossible to ensure

that their surfaces were maintained free from damage. The present approach, which has

gained increasing recognition over the past few years, is to assume that all materials may

contain flaws of some magnitude. The realistic assessment of their fracture toughness then

depends on their fracture behavior with flaws of particular size.

18

Fracture toughness is a measure of the ability of a material to resist the growth of a pre

existing crack or flaw. This parameter is used extensively to design fracture safe

structures. Fracture mechanics is the science, which relates the strength of a fractured

structure to the material's fracture toughness, and to the crack size, shape, location, and

sharpness. Test methods, which measure a material's fracture toughness [11.12], are

necessary for safe design and for accurate failure analysis. The fracture toughness (Kjc) of

a material is characterized by the energy per unit area, which is required to create new

crack surfaces, and thereby propagate a crack through the material. This value is known as

the critical stress intensity factor, and is determined at the time of crack extension.

Fracture toughness is the resistance to the propagation of a crack. This propagation is often

thought to be unstable, resulting in a complete separation of the component into two or

more pieces. Actually, the fracture event can be stable or unstable, with unstable crack

extension, often associated with a brittle fracture event, the fracture occurs at a well

defined point and the fracture characterization can be given by a single value of the

fracture parameter [13]. With stable fracture, often associated with a ductile fracture

process, the fracture is an ongoing process that cannot be readily described by a point.

This fracture process is characterized by a crack growth resistance curve or /?-curve.

2.8 FRACTURE BEHAVIOR OF COATED MATERIALS

The applications of materials in harsh environments or with stringent performance

requirements call for advanced materials as well as technologies to improve the

performance of existing materials. Of the latter category, coating technologies are among

the most prominent and promising technologies that are being developed. Many problems

arising out of recent developments in technology are being successfully resolved by

adopting various methods of protection of materials used in construction. Protective

coating of different types, and for different purposes, are being used on an increasingly

wider scale in atomic power stations, gas turbine sets, aviation, rocket building, chemical

technology and in many other fields of modem technology. The problems of forming

protective coatings, study of their properties, and investigation of complex physico-

chemical processes [14], occurring under a variety of interactions between the substance

and the surrounding medium are attracting the attention of a wide range of specialists. The

development of protective coatings, based on a firm scientific footing, including their

production on an industrial scale enables to solve two important problems namely.

19

• Improvement in the properties of existing alloys and construction materials by

producing heat-resistant, strengthened, plasticized and other coatings.

• Widening the scope of application of refractory metals and their alloys by

developing anticorrosion and high temperature coatings.

Industrial finishing is an integral and important part of most manufacturing process.

Protective treatments and coatings are used to enhance resistance to corrosion and

abrasion, modify physical and mechanical properties of the surface or enhance the surface

finish to improve artistic appearance and sales appeal. When a coating is applied to

specimen, the coating becomes an extension of it. In only certain instances are the strains

transmitted to the coating represent a three-dimensional extension of the specimen; and it

is loaded by means of shear and normal tractions at the interface. These tractions must

vary, so that the displacement fields of the coating and specimen are identical at the

interface (as dictated by perfect bonding). Thus, in the most general case, the average

strain in the coating does not equal the strain at the interface [14], a strain gradient exists

through the thickness of the coating, and the coating reinforces the specimen. These three

thickness effects tend to vanish, as the coating thickness approaches zero. The basic

question concerns the extent of the error introduced by these thickness effects in the

application of the coating to different classes of stress analysis problems. This question is

complex and has been the subject of controversy during the past decade. Certain aspects

still must be solved; however, progress has been made in understanding many of the

factors contributing to the thickness effects of photo elastic coatings and in providing

corrections to account for those effects. A common characteristic of many coatings is that

they are more brittle than the substrate to which they are applied. When a substrate coated

with more brittle coating is stressed, the first form of failure will be a crack in the coating.

This crack will typically initiate and propagate rapidly through the entire thickness of

coating. When the crack reaches the coating/substrate interface, it can continue into the

substrate and cause complete structural failure. Thus the fracture behavior of coated

materials is entirely different from that of the uncoated materials.

2.9 FRACTURE BEHAVIOR OF HEAT TREATED MATERIALS

Heat treatment of metals and alloys is one of the many wonderful processes discovered by

man to mould materials to desired properties for making implements in his ascent to

modem civilization. Heat treatment of steels alone covers a very wide range of processes.

20

It is used in a variety of ways ranging from stress relieving of parts for reducing

fabrication stresses and full annealing for softening steels for easy shaping to hardening

and tempering for developing high strength and toughness. Even in this hardening process,

which involves phase transformations, there are several refinements and tempering

treatments to develop a series of combinations of strength and toughness in steels for

different engineering applications. Again heat treatment is a process by which micro-

structural refinement is achieved. There are a variety of surface heat treatments to convert

chemically and physically surface material ranging in thickness from a few microns to

substantial depths of the cross sections in order to impart enhanced hardness and wear

resistance properties.

Effectively, heat treatment is designed to alter the mode of occurrence of the soluble

alloying elements, particularly copper, magnesium, silicon and zinc, which can combine

with one and other to form intermetallic compounds. Heat treatment of aluminum is done

through precipitation hardening or ageing, and also by quenching. Solution heat treatment

takes these relatively hard constituents into solid solution, thereby softening the alloy:

quenching retains the constituents in solid solution at room temperature, so that the alloy is

still soft but unstable. The hard constituents gradually precipitate out in a more uniform

pattern than they formed in the original un heat treated alloy, thereby improving the alloy's

mechanical properties. Rates of precipitation vary from alloy to alloy so that the stable

condition represented by complete precipitation may take anything from a few days to

several years to achieve unless artificial ageing is used. Even with alloys which achieve

relatively stable properties by natural ageing it is possible to obtain higher strengths by

artificial ageing following solution treatment. In some alloys an additional increase in

strength is possible by controlled cold-working of the alloy immediately after quenching

from the solution heat treatment temperature. Because of the complex interactions that

take place during the processes of the heat-treatment, different alloys have different

characteristics that require careful selection and control of the heating operations and

specific combinations of temperature and time-at-temperature if the required properties are

to be achieved in the heat-treated product.

The crack behavior of heat treated materials is different from that of normal material.

Usually the cracks are developed in a component due to stresses produced during the

structural transformation [15], with its accompanying increase in volume. Many heat

treating processes will soften the material and also the scale formation is another problem

21

of heat treated materials. The fracture toughness of the heat treated materials depends

mainly on the type of the heat treatment and the temperature of the heat treatment.

2.10 THE TRANSITION TEMPERATURE

If the test temperature is varied from high to low, then a metal such as mild steel, which

exhibits the property of brittle fracture, will have a range of test temperature in which the

mechanism of fracture changes from shear to cleavage [13]. This is known as the

transition temperature. One is to take the temperature at which impact specimen fractures

with a half-brittle and half-ductile fracture surface. A second way of defining the transition

temperature uses the energy criterion. The temperature at which the energy absorbed falls

to one-half the difference between that needed to fracture a completely ductile specimen

and that needed to fracture a completely brittle specimen.

hi

C

12 u a

Temperature (in ^C) Temperature (in ^C)

(a) (b)

Figure 2.5 Brittle - Ductile Energy versus Temperature

Figure 2.6 (a) and (b), shows the typical transition curves in which plastic deformation or

energy to fracture is plotted against test temperature. The first diagram shows what is

known as bimodal behavior in which there are two distinct branches, one at high energy

and temperature and the other at low energy and temperature joined by a narrow region of

scattered points at upper and lower energy values. The second diagram shows continuous

behavior where there is a gradual fall from high to low energy with decrease in

22

temperature. In general, there is no single specific criterion for defining a transition

temperature; various definitions are used,

• Fracture Transition Plastic (FTP) is the temperature above which the fracture is

100% fibrous/shear (0% cleavage/ductile). This is the most conservatoire estimate.

• Nil Ductility Temperature (NDT) is the temperature below which the fracture is

100% cleavage/shear.

• Fracture Appearance Transition Temperature (FATT) is the temperature at which

the fracture surface is 50- 50% cleavage and fibrous. This can alternatively be

based upon the mean of the upper and lower shelf energies.