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ANNA UNIV FAQs.

UNIT 3

Fracture mechanics is the field ofmechanics concerned with the study of the

propagation of cracks in materials. It uses methods of analytical solid mechanics to

calculate the driving force on a crack and those of experimental solid mechanics to

characterize the material's resistance to fracture.

In modern materials science, fracture mechanics is an important tool in improving

the mechanical performance of materials and components. It appliesthe physics ofstress andstrain, in particular the theories ofelasticity and plasticity, to

the microscopic crystallographic defects found in real materials in order to predict

the macroscopic mechanical failure of bodies.Fractography is widely used with

fracture mechanics to understand the causes of failures and also verify the

theoretical failure predictions with real life failures.

An edge crack (flaw) of length a in a material.

LINEAR ELASTIC FRACTURE MECHANICS (LEFM THEORY) (16m)

Griffith's criterion

Fracture mechanics was developed during World War I by English aeronautical

engineer, A. A. Griffith, to explain the failure of brittle materials.[1]

Griffith's work was

motivated by two contradictory facts:

The stress needed to fracture bulk glass is around 100 MPa (15,000 psi). The theoretical stress needed for breaking atomic bonds is approximately

10,000 MPa (1,500,000 psi).
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A theory was needed to reconcile these conflicting observations. Also, experiments

on glass fibers that Griffith himself conducted suggested that the fracture stress

increases as the fiber diameter decreases. Hence the uniaxial tensile strength, which

had been used extensively to predict material failure before Griffith, could not be a

specimen-independent material property. Griffith suggested that the low fracturestrength observed in experiments, as well as the size-dependence of strength, was

due to the presence of microscopic flaws in the bulk material.

To verify the flaw hypothesis, Griffith introduced an artificial flaw in his experimental

specimens. The artificial flaw was in the form of a surface crack which was much

larger than other flaws in a specimen. The experiments showed that the product of

the square root of the flaw length (a) and the stress at fracture (f) was nearly

constant, which is expressed by the equation:

An explanation of this relation in terms of linear elasticity theory is problematic.

Linear elasticity theory predicts that stress (and hence the strain) at the tip of a sharp

flaw in a linear elastic material is infinite. To avoid that problem, Griffith developed

a thermodynamic approach to explain the relation that he observed.

The growth of a crack requires the creation of two new surfaces and hence an

increase in the surface energy. Griffith found an expression for the constant Cin

terms of the surface energy of the crack by solving the elasticity problem of a finitecrack in an elastic plate. Briefly, the approach was:

Compute the potential energy stored in a perfect specimen under an uniaxial tensile

load.

Fix the boundary so that the applied load does no work and then introduce a crack

into the specimen. The crack relaxes the stress and hence reduces the elastic

energy near the crack faces. On the other hand, the crack increases the total surface

energy of the specimen.

Compute the change in the free energy (surface energy elastic energy) as a

function of the crack length. Failure occurs when the free energy attains a peak value

at a critical crack length, beyond which the free energy decreases by increasing the

crack length, i.e. by causing fracture. Using this procedure, Griffith found that
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where Eis the Young's modulus of the material and is the surface energy density of

the material. Assuming E= 62 GPa and = 1 J/m2gives excellent agreement of

Griffith's predicted fracture stress with experimental results for glass.

Irwin's modification

The plastic zone around a crack tip in a ductile material.

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 () predicted by Griffith's theory is

usually unrealistically high. A group working under G. R. Irwin[3]

at the U.S. Naval

Research Laboratory (NRL) during World War II realized that plasticity must play asignificant role in the fracture of ductile materials.

In ductile materials (and even in materials that appear to be brittle[4]

), a plastic zone

develops at the tip of the crack. As the applied loadincreases, the plastic zone

increases in size until the crack grows and the material behind the crack tip unloads.

The plastic loading and unloading cycle near the crack tip leads to

the dissipation ofenergy 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 tobrittle 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 thethermodynamic driving force for fracture.

the dissipated energy which includes plastic dissipation and the surfaceenergy (and any other dissipative forces that may be at work). The dissipated

energy provides the thermodynamic resistance to fracture. Then the totalenergy dissipated is
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G= 2 +Gp

where is the surface energy and Gp is the plastic dissipation (and dissipation from

other sources) per unit area of crack growth.

The modified version of Griffith's energy criterion can then be written as

For brittle materials such as glass, the surface energy term dominates

and . For ductile materials such as steel, the plastic dissipation

term dominates and . For polymers close to the glasstransition temperature, we have intermediate values of .

Stress intensity factor (8m)

Another significant achievement of Irwin and his colleagues was to find a method of

calculating the amount of energy available for fracture in terms of the asymptotic

stress and displacement fields around a crack front in a linear elastic solid .[3]

This

asymptotic expression for the stress field around a crack tip is

where ij are the Cauchy stresses, ris the distance from the crack tip, is the angle

with respect to the plane of the crack, and fij are functions that are independent of

the crack geometry and loading conditions. Irwin called the quantity Kthestress

intensity factor. Since the quantityfij is dimensionless, the stress intensity factor can

be expressed in units of .

\When a rigid line inclusion is considered, a similar asymptotic expression for the

stress fields is obtained.

Strain energy release(8m with derivation)

Irwin was the first to observe that if the size of the plastic zone around a crack is

small compared to the size of the crack, the energy required to grow the crack will

not be critically dependent on the state of stress at the crack tip .[2]

In other words, a

purely elastic solution may be used to calculate the amount of energy available forfracture.
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The energy release rate for crack growth or strain energy release rate may then be

calculated as the change in elastic strain energy per unit area of crack growth, i.e.,

where U is the elastic energy of the system and a is the crack length. Either the

load P or the displacement u can be kept fixed while evaluating the above

expressions.

Irwin showed that for a mode I crack (opening mode) the strain energy release rate

and the stress intensity factor are related by:

where Eis the Young's modulus,is Poisson's ratio, and KI is the stress intensity

factor in mode I. Irwin also showed that the strain energy release rate of a planar

crack in a linear elastic body can be expressed in terms of the mode I, mode II (sliding

mode), and mode III (tearing mode) stress intensity factors for the most general

loading conditions.

Next, Irwin adopted the additional assumption that the size and shape of the energy

dissipation zone remains approximately constant during brittle fracture. This

assumption suggests that the energy needed to create a unit fracture surface is a

constant that depends only on the material. This new material property was given

the namefracture toughnessand designated GIc. Today, it is the critical stress

intensity factorKIc which is accepted as the defining property in linear elastic fracture

mechanics.

Limitations

But a problem arose for the NRL researchers because naval materials, e.g., ship-plate

steel, are not perfectly elastic but undergo significant plastic deformation at the tip

of a crack. One basic assumption in Irwin's linear elastic fracture mechanics is that

the size of the plastic zone is small compared to the crack length. However, this

assumption is quite restrictive for certain types of failure in structural steels though

such steels can be prone to brittle fracture, which has led to a number of

catastrophic failures.
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Linear-elastic fracture mechanics is of limited practical use for structural steels for

another more practical reason. Fracture toughness testing is very expensive and

engineers believe that sufficient information for selection of steels can be obtained

from the simpler and cheaper Charpy impact test.[citation needed]

Elasticplastic fracture mechanics(EPF THEORY) (8m)

Most engineering materials show some nonlinear elastic and inelastic behavior under

operating conditions that involve large loads.[citation needed]

In such materials the

assumptions of linear elastic fracture mechanics may not hold, that is,

the plastic zone at a crack tip may have a size of the same order of magnitude

as the crack size

the size and shape of the plastic zone may change as the applied load is

increased and also as the crack length increases.

Therefore a more general theory of crack growth is needed for elastic-plastic

materials that can account for:

the local conditions for initial crack growth which include the nucleation,

growth, and coalescence of voids or decohesion at a crack tip.

a global energy balance criterion for further crack growth and unstable

fracture.

R-curve

An early attempt in the direction of elastic-plastic fracture mechanics

was Irwin'scrack extension resistance curve or R-curve. This curve acknowledges the

fact that the resistance to fracture increases with growing crack size in elastic-plastic

materials. The R-curve is a plot of the total energy dissipation rate as a function of

the crack size and can be used to examine the processes of slow stable crack growth

and unstable fracture. However, the R-curve was not widely used in applications until

the early 1970s. The main reasons appear to be that the R-curve depends on the

geometry of the specimen and the crack driving force may be difficult to calculate.[2]

J-integral

In the mid-1960s James R. Rice (then at Brown University) and G. P. Cherepanov

independently developed a new toughness measure to describe the case where

there is sufficient crack-tip deformation that the part no longer obeys the linear-

elastic approximation. Rice's analysis, which assumes non-linear elastic (or

monotonic deformation theory plastic) deformation ahead of the crack tip, is

designated the J integral.[5]

This analysis is limited to situations where plastic

deformation at the crack tip does not extend to the furthest edge of the loaded part.It also demands that the assumed non-linear elastic behavior of the material is a
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reasonable approximation in shape and magnitude to the real material's load

response. The elastic-plastic failure parameter is designated JIc and is conventionally

converted to KIc using Equation (3.1) of the Appendix to this article. Also note that

the J integral approach reduces to the Griffith theory for linear-elastic behavior.

Cohesive zone models

When a significant region around a crack tip has undergone plastic deformation,

other approaches can be used to determine the possibility of further crack extension

and the direction of crack growth and branching. A simple technique that is easily

incorporated into numerical calculations is the cohesive zone model method which is

based on concepts proposed independently by Barenblatt[6]

and Dugdale[7]

in the

early 1960s. The relationship between the Dugale-Barenblatt models and Griffith's

theory was first discussed by Willis in 1967.[8]

The equivalence of the two approaches

in the context of brittle fracture was shown by Rice in 1968.[5]Interest in cohesivezone modeling of fracture has been reignited since 2000 following the pioneering

work on dynamic fracture by Xu and Needleman[9]

, and Camacho and Ortiz.[10]

Fully plastic failure

If the material is so tough that the yielded region ahead of the crack extends to the

far edge of the specimen before fracture, the crack is no longer an effective

stress concentrator. Instead, the presence of the crack merely serves to reduce the

load-bearing area. In this regime the failure stress is conventionally assumed to be

the average of the yield and ultimate strengths of the material.

Engineering applications

The following information is needed for a fracture mechanics prediction of failure:

Applied load Residual stress Size and shape of the part Size, shape, location, and orientation of the crack

Usually not all of this information is available and conservative assumptions have to

be made.

Occasionally post-mortem fracture-mechanics analyses are carried out. In the

absence of an extreme overload, the causes are either insufficient toughness (K Ic) or

an excessively large crack that was not detected during routine inspection.
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Appendix: mathematical relations(LEFM THEORY contd.)

Griffith's criterion

For the simple case of a thin rectangular plate with a crack perpendicular to the load

Griffiths theory becomes:

(1.1)

where G is the strain energy release rate, is the applied stress, a is half the crack

length, and Eis theYoungs modulus. The strain energy release rate can otherwise be

understood as: the rate at which energy is absorbed by growth of the crack.

However, we also have that:

(1.2)

IfGGc, this is the criterion for which the crack will begin to propagate.

Irwin's modifications

Eventually a modification of Griffiths solids theory emerged from this work; a termcalled stress intensity replaced strain energy release rate and a term called fracture

toughness replaced surface weakness energy. Both of these terms are simply related

to the energy terms that Griffith used:

(2.1)

and

(for plane stress) (2.2)

(for plane strain) (2.3)
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where KI is the stress intensity,Kc the fracture toughness, and is Poissons ratio. It is

important to recognize the fact that fracture parameter Kc has different values when

measured under plane stress and plane strain

Fracture occurs when K1>=Kc. For the special case of plane strain

deformation, Kc becomes KIc and is considered a material property. The subscript I

arises because of the different ways of loading a material to enable a crack to

propagate. It refers to so-called "mode I" loading as opposed to mode II or III:

The three fracture modes. (16m with eqns)

There are three ways of applying a force to enable a crack to propagate:

Mode I crack Opening mode (a tensile stress normal to the plane of the

crack)

Mode II crack Sliding mode (a shear stress acting parallel to the plane of the

crack and perpendicular to the crack front)

Mode III crack Tearing mode (a shear stress acting parallel to the plane of

the crack and parallel to the crack front)

We must note that the expression for KI in equation 2.1 will be different for

geometries other than the center-cracked infinite plate, as discussed in the article on

the stress intensity factor. Consequently, it is necessary to introduce a dimensionlesscorrection factor,Y, in order to characterize the geometry. We thus have:

(2.4)

where Yis a function of the crack length and width of sheet given by:

(2.5)
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for a sheet of finite width Wcontaining a through-thickness crack of length 2a, or

(2.6)

for a sheet of finite width Wcontaining a through-thickness edge crack of length a

Elasticity and plasticity

Since engineers became accustomed to using KIc to characterise fracture toughness,

a relation has been used to reduceJIc to it:

where E

*

= Efor plane stress and for planestrain (3.1)

The remainder of the mathematics employed in this approach is interesting, but is

probably better summarised in external pages due to its complex nature.

Fracture toughness (8m with effect of thickness on FT)

In materials science, fracture toughness is a property which describes the ability of amaterial containing a crack to resist fracture, and is one of the most important

properties of any material for virtually all design applications. The fracture toughness

of a material is determined from the stress intensity factor (K) at which a thin crack in

the material begins to grow. It is denoted KIc and has the units of .

The subscript Ic denotes mode I crack opening under a normal tensile stress

perpendicular to the crack, since the material can be made deep enough to stand

shear (mode II) or tear (mode III).

Fracture toughness is a quantitative way of expressing a material's resistance

to brittle fracture when a crack is present. If a material has much fracture toughness

it will probably undergo ductile fracture. Brittle fracture is very characteristic of

materials with less fracture toughness.[1]

Fracture mechanics, which leads to the concept of fracture toughness, was broadly

based on the work ofA. A. Griffith who, among other things, studied the behavior of

cracks in brittle materials.
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A related concept is thework of fracture(wof) which is directly proportional

to , where Eis the Young's modulus of the material.[2]

Note that, in SI

units, wofis given in J/m2.

Fatigue life(16m phases of fatigue life)

ASTM definesfatigue life, Nf, as the number of stress cycles of a specified character

that a specimen sustains before failure of a specified nature occurs.[1]

One method to predict fatigue life of materials is the Uniform Material Law

(UML).[2]

UML was developed for fatigue life prediction

ofaluminumand titanium alloys by the end of 20th century and extended to high-

strength steels.[3]

and cast iron.[4]

Characteristics of fatigue

In metals and alloys, the process starts with dislocation movements, eventually

forming persistent slip bands that nucleate short cracks.

Fatigue is a stochastic process, often showing considerable scatter even incontrolled environments.

The greater the applied stress range, the shorter the life. Fatigue life scatter tends to increase for longer fatigue lives. Damage is cumulative. Materials do not recover when rested.

Fatigue life is influenced by a variety of factors, such as temperature, surface finish,

microstructure, presence ofoxidizing or inert chemicals, residual stresses, contact

(fretting), etc.

Some materials (e.g., some steel and titanium alloys) exhibit a theoretical fatigue

limit below which continued loading does not lead to structural failure.

In recent years, researchers (see, for example, the work of Bathias, Murakami, andStanzl-Tschegg) have found that failures occur below the theoretical fatigue limit at

very high fatigue lives (109

to 1010

cycles). An ultrasonic resonance technique is used

in these experiments with frequencies around 1020 kHz.[citation needed]

High cycle fatigue strength (about 103

to 108

cycles) can be described by stress-based

parameters. A load-controlled servo-hydraulic test rig is commonly used in these

tests, with frequencies of around 2050 Hz. Other sorts of machineslike resonant

magnetic machinescan also be used, achieving frequencies up to 250 Hz.
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Low cycle fatigue (typically less than 103

cycles) is associated with widespread

plasticity in metals; thus, a strain-based parameter should be used for fatigue life

prediction in metals and alloys. Testing is conducted with constant strain amplitudes

typically at 0.015 Hz.

Fatigue and fracture mechanics

The account above is purely empirical and, though it allows life prediction and design

assurance, life improvement or design optimisation can be enhanced using fracture

mechanics. It can be developed in four stages.

i. Crack nucleation;ii. Stage I crack-growth;

iii.

Stage II crack-growth; andiv. Ultimate ductile failure.

Factors that affect fatigue-life

Cyclic stress state: Depending on the complexity of the geometry and the loading,

one or more properties of the stress state need to be considered, such as stress

amplitude, mean stress, biaxiality, in-phase or out-of-phase shear stress, and load

sequence,

Geometry: Notches and variation in cross section throughout a part lead to stress

concentrations where fatigue cracks initiate.

Surface quality. Surface roughness cause microscopic stress concentrations that

lower the fatigue strength. Compressive residual stresses can be introduced in the

surface by e.g. shot peening to increase fatigue life. Such techniques for producing

surface stress are often referred to aspeening, whatever the mechanism used to

produce the stress. Low plasticity burnishing, laser peening, and ultrasonic impact

treatment can also produce this surface compressive stress and can increase thefatigue life of the component. This improvement is normally observed only for high-

cycle fatigue.

Material Type: Fatigue life, as well as the behavior during cyclic loading, varies

widely for different materials, e.g. composites and polymers differ markedly from

metals.

Residual stresses: Welding, cutting, casting, and other manufacturing processes

involving heat or deformation can produce high levels of tensile residual stress,

which decreases the fatigue strength.
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Size and distribution of internal defects: Casting defects such as gas porosity, non-

metallic inclusions and shrinkage voids can significantly reduce fatigue strength.

Direction of loading: For non-isotropic materials, fatigue strength depends on

the direction of the principal stress.

Grain size: For most metals, smaller grains yield longer fatigue lives, however, the

presence of surface defects or scratches will have a greater influence than in a coarse

grained alloy.

Environment: Environmental conditions can cause erosion, corrosion, or gas-phase

embrittlement, which all affect fatigue life. Corrosion fatigue is a problem

encountered in many aggressive environments.

Temperature: Extreme high or low temperatures can decrease fatigue strength.

Design against fatigue

Dependable design against fatigue-failure requires thorough education and

supervised experience in structural engineering, mechanical engineering,

or materials science. There are three principal approaches to life assurance for

mechanical parts that display increasing degrees of sophistication:

Design to keep stress below threshold of fatigue limit (infinite lifetimeconcept);

Design (conservatively) for a fixed life after which the user is instructed toreplace the part with a new one (a so-called lifedpart, finite lifetime concept,

or "safe-life" design practice);

Instruct the user to inspect the part periodically for cracks and to replace the part

once a crack exceeds a critical length. This approach usually uses the technologies

ofnondestructive testing and requires an accurate prediction of the rate of crack-

growth between inspections. This is often referred to as damage tolerant design or

"retirement-for-cause".

Stopping fatigue

Fatigue cracks that have begun to propagate can sometimes be stopped

by drilling holes, called drill stops, in the path of the fatigue crack.[12]

This is not

recommended as a general practice because the hole represents a stress

concentration factor which depends on the size of the hole and geometry, though

the hole is typically less of a stress concentration than the removed tip of the crack.
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The possibility remains of a new crack starting in the side of the hole. It is always far

better to replace the cracked part entirely.

Material change

Changes in the materials used in parts can also improve fatigue life. For example,

parts can be made from better fatigue rated metals. Complete replacement and

redesign of parts can also reduce if not eliminate fatigue problems. Thus helicopter

rotor blades and propellers in metal are being replaced by composite equivalents.

They are not only lighter, but also much more resistant to fatigue. They are more

expensive, but the extra cost is amply repaid by their greater integrity, since loss of a

rotor blade usually leads to total loss of the aircraft. A similar argument has been

made for replacement of metal fuselages, wings and tails of aircraft.

Stress intensity factor (16m and for various geometries)

Polar coordinates at the crack tip.

The stress intensity factor, K, is used

in fracture mechanics to predict

the stressstate ("stress intensity")

near the tip of a crack caused by a

remote load or residual stresses.[1]

It

is a theoretical construct usually

applied to a homogeneous,

linearelastic material and is useful for

providing a failure criterion

for brittle materials. The concept can also be applied to materials that exhibit small-

scale yieldingat a crack tip.

The magnitude ofKdepends on sample geometry, the size and location of the crack,

and the magnitude and the modal distribution of loads on the material.

Linear elastic theory predicts that the stress distribution (ij) near the crack tip,

inpolar coordinates (r,) with origin at the crack tip, has the form[2]

where Kis the stress intensity factor (with units of stress length1/2

) andfijis a

dimensionless quantity that depends on the load and geometry. This relation breaks

down very close to the tip (small r) because as rgoes to 0, the stress ijgoes toPlastic distortion typically occurs at high stresses and the linear elastic solution is no
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longer applicable close to the crack tip. However, if the crack-tip plastic zone is small,

it can be assumed that the stress distribution near the crack is still given by the above

relation.

Stress intensity factors for various modes

Mode I, Mode II, and Mode III crack loading.

Three linearly independent cracking modes are used in fracture mechanics. These

load types are categorized as Mode I, II, or III as shown in the figure. Mode I, shown

to the right, is an opening (tensile) mode where the crack surfaces move directly

apart. Mode II is a sliding (in-plane shear) mode where the crack surfaces slide over

one another in a direction perpendicular to the leading edge of the crack. Mode III is

a tearing (antiplane shear) mode where the crack surfaces move relative to oneanother and parallel to the leading edge of the crack. Mode I is the most common

load type encountered in engineering design.

Different subscripts are used to designate the stress intensity factor for the three

different modes. The stress intensity factor for mode I is designated KIand applied to

the crack opening mode. The mode II stress intensity factor, KII, applies to the crack

sliding mode and the mode III stress intensity factor, KIII, applies to the tearing mode.

These factors are formally defined as[3]
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Relationship to energy release rate and J-integral (energy relese rate derivation

16m)

The strain energy release rate (G) for a crack under mode I loading is related to the

stress intensity factor by

where Eis the Young's modulus and is the Poisson's ratio of the material. The

material is assumed to be an isotropic, homogeneous, and linear elastic. Plane

strain has been assumed and the crack has been assumed to extend along the

direction of the initial crack. For plane stress conditions, the above relation simplifies

to

For pure mode II loading, we have similar relations

For pure mode III loading,

where is the shear modulus. For general loading in plane strain, the relationship

between the strain energy and the stress intensity factors for the three modes is

A similar relation is obtained for plane stress by adding the contributions for the

three modes.

The above relations can also be used to connect the J integral to the stress intensity

factor because
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Critical stress intensity factor

The stress intensity factor, K, is a parameter that amplifies the magnitude of the

applied stress that includes the geometrical parameter Y(load type). Stress intensity

in any mode situation is directly proportional to the applied load on the material. If a

very sharp crack can be made in a material, the minimum value of KI can be

empirically determined, which is the critical value of stress intensity required to

propagate the crack. This critical value determined for mode I loading in plane

strain is referred to as the critical fracture toughness (KIc) of the material. KIc has units

of stress times the root of a distance. The units ofKIc imply that the fracture stress of

the material must be reached over some critical distance in order for KIc to be

reached and crack propagation to occur. The Mode I critical stress intensity factor,KIc,

is the most often used engineering design parameter in fracture mechanics and

hence must be understood if we are to design fracture tolerant materials used in

bridges, buildings, aircraft, or even bells. Polishing cannot detect a crack. Typically, ifa crack can be seen it is very close to the critical stress state predicted by the stress

intensity factor.

Gcriterion

The G-criterion is a fracture criterion that relates the critical stress intensity factor (or

fracture toughness) to the stress intensity factors for the three modes. This failure

criterion is written as[4]

where KIc is the mode I fracture toughness, E' = E/ (1

2) for plane strain and E' = Efor plane stress. The critical stress intensity factor

forplane stress is often written as Kc.

Surface energy quantifies the disruption of intermolecular bonds that occur when a

surface is created. In the physics ofsolids, surfaces must be intrinsically less

energetically favorable than the bulk of a material, otherwise there would be a

driving force for surfaces to be created, removing the bulk of the material(see sublimation). The surface energy may therefore be defined as the excess energy

at the surface of a material compared to the bulk.

potential energy is the energy stored in a body or in a system due to its position in

a force field or due to its configuration.[1]

The SI unit of measure for energy and work

is the Joule(symbol J).
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Critical energy release rate

The energy release per unit increase crack area, G, is computed; if the energy

release rate is lower than the critical energy release rate (G < Gc ) the crack is stable.

Conversely, if G> Gc, the crack propagates.

In the case when the energy release rate is equal to the critical energy release rate

(G=Gc), a metastable equilibrium is obtained.

LEVEL CROSSING COUNTING unit2 (8m)

The results of the level crossing count are shown in Figure G.1. There are practically

restrictions on the level crossing counts which are often specified to eliminate small

amplitude variations. By this way, small amplitude variations can give rise to a largenumber of counts. This can be accomplished by making no counts at the reference

load and to specify that only one count be made between successive crossings of a

secondary level associated with each level above the reference load, or a secondary

higher level associated with each level below the reference load. Figure G.1(b)

illustrates this method. The most damaging cycle count for fatigue analysis is derived

from the level crossing count by first constructing the largest possible cycle, followed

by the second largest, etc., until all level crossings are used. Reversal points are

assumed to occur halfway between levels. This process is shown in Figure G.1(c).Once this most damaging cycle count is obtained, the cycles could be applied in any

desired order, and this order could have a secondary effect on the amount of

damage

PEAK COUNTING (8m)

Peak counting identifies the occurrence of a relative maximum or minimum load

value. Peaks above the reference load level are counted, and valleys below the

reference load level are counted. This illustrates in Figure G.2(a). Results for peaks

and valleys are reported separately. A variation of this method is to count all peaksand valleys without regard to the reference load. To eliminate small amplitude


19/27

loadings, mean crossing peak counting is often used. Instead of counting all peaks

and valleys, only the largest peak or valley between two successive mean crossings is

counted as can be seen in Figure G.2(b).

Shot peening unit 5(8m)

Shot peening is a cold working process used to

produce a compressive residual stress layer and

modify mechanical properties ofmetals. It entails

impacting a surface with shot (round metallic, glass,

or ceramic particles) with force sufficient to create

plastic deformation.[1]

It is similar tosandblasting,

except that it operates by the mechanism

ofplasticity rather than abrasion: each particle functions as a ball-peen hammer. In

practice, this means that less material is removed by the process, and less dust

created.

Details

Peening a surface spreads it plastically, causing changes in the mechanical propertiesof the surface. Shot peening is often called for in aircraft repairs to relieve tensile

stresses built up in the grinding process and replace them with beneficial

compressive stresses. Depending on the part geometry, part material, shot material,

shot quality, shot intensity, shot coverage, shot peening can increase fatigue life up

to 1000%.

Plastic deformation induces a residual compressive stress in a peened surface, along

with tensile stress in the interior. Surface compressive stresses confer resistance to
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metal fatigue and to some forms of stress corrosion.[1]

The tensile stresses deep in

the part are not as problematic as tensile stresses on the surface because cracks are

less likely to start in the interior.

Intensityis a key parameter of the shot peening process. A continuous compressivelystressed surface of the workpiece has been shown to be produced at less than 50%

coverage but falls as 100% is approached. Optimizing coverage level for the process

being performed is important for producing the desired surface effect.[2]

Process and equipment

Popular methods for propelling shot media include air blast systems and centrifugal

blast wheels. In the air blast systems, media is introduced by various methods into

the path of high pressure air and accelerated through a nozzle directed at the part tobe peened. The centrifugal blast wheel consists of a high speed paddle wheel. Shot

media is introduced in the center of the spinning wheel and propelled by the

centrifugal force by the spinning paddles towards the part by adjusting the media

entrance location, effectively timing the release of the media. Other methods include

ultrasonic peening, wet peening, and laser peening (which does not use media).

Stress Amplitude (2m)

One-half the range of fluctuating stress developed in a specimen in a fatigue test.Stress amplitude often is used to construct an S-N diagram.

Mean Stress(2m)

Algebraic difference between maximum and minimum stress in one cycle of

fluctuating loading, as in a fatigue test. Tensile stress is considered positive and

compressive stress negative.

Stress Ratio (2m)

Ratio of minimum stress to maximum stress in one cycle of loading in a fatigue test.

Tensile stresses are considered positive and compressive stresses negative.

Stress Range(2m)Difference in operating stresses at minimum and maximum loads
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Castings unit 5(processing failures)

Several factors effect the quality of metal castings. Some of these factors are listed

below:

Coefficients of thermal conductivity Thermal expansion and contraction, Chemistry Precision of molds and dies Shrinkage allowances Dryness of molds Casting design Method of pouring liquid metal Design of gates and risers

Imperfections in castings may not be of concern for many types of service. They are

commonly referred to as casting defects sincecastings are not perfect. This is

unfortunate as imperfections beyond engineering design specifications should be

considered defects, while imperfections within engineering design specifications

should not be considered defects.

Some casting imperfections may have no effect on the function or service life of

castings. Many imperfections are easily corrected by blast cleaning or

grinding. Other imperfections may be acceptable in some locations.

It is not uncommon for engineers to zone a casting drawing. Depending on the

criticality of the location or zone the same imperfection would be judged acceptable

in one location while unacceptable in another location.

Casting Discontinuities

Some common casting deficiencies are:

Inclusions Porosity (blow holes, pinholes) Cold Cracking Hot Cracking Cold Shuts Surface irregularities Distortion


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Improper compositionCasting failures can be due to various causes. Some castings fail due to design

deficiencies, while other castings fail due to casting deficiencies.

Casting Failure Analysis

Casting failures can be due to various causes. Improper loading or environment may

contribute to the cause of failure. Casting imperfections may or may not contribute

to the cause of failure. Some imperfections may be commonly occurring

discontinuities or anomalies that are normally expected to be present in

castings. Other imperfections are casting defects that result in failure of the

casting. Failure analysis can determine the cause of the casting failure and

determine if a casting imperfections was the primary or contributing cause of failure.

Common Causes of Failure

Misuse or Abuse Assembly errors Manufacturing defects Improper maintenance Fastener failure Design errors Improper material Improper heat treatments Unforeseen operating conditions Inadequate quality assurance Inadequate environmental protection/control Casting discontinuities

Stress Ratio

The most commonly used stress ratio is R, the ratio of the minimum stress to the

maximum stress (Smin/Smax).

If the stresses are fully reversed, then R = -1. If the stresses are partially reversed, R = a negative number less than 1. If the stress is cycled between a maximum stress and no load, R = zero. If the stress is cycled between two tensile stresses, R = a positive number less

than 1.
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Variations in the stress ratios can significantly affect fatigue life. The presence of a

mean stress component has a substantial effect on fatigue failure. When a tensile

mean stress is added to the alternating stresses, a component will fail at lower

alternating stress than it does under a fully reversed stress.

Preventing Fatigue Failure

The most effective method of improving fatigue performance is improvements in

design:

Eliminate or reduce stress raisers by streamlining the part Avoid sharp surface tears resulting from punching, stamping, shearing, or

other processes

Prevent the development of surface discontinuities during processing.

Reduce or eliminate tensile residual stresses caused by manufacturing. Improve the details of fabrication and fastening procedures

In metalworking,rolling is a metal forming process in which metal stock is passed

through a pair of rolls. Rolling is classified according to the temperature of the metal

rolled. If the temperature of the metal is above its recrystallization temperature,

then the process is termed as hot rolling. If the temperature of the metal is below its

recrystallization temperature, the process is termed ascold rolling. In terms of usage,

hot rolling processes more tonnage than any other manufacturing process and cold

rolling processes the most tonnage out of all cold working processes.[1][2]

There are many types of rolling processes, including flat rolling,foil rolling, ring

rolling, roll bending, roll forming,profile rolling, and controlled rolling.

High-cycle fatigue

Historically, most attention has focused on situations that require more than

104

cycles to failure where stress is low and deformation primarily elastic.
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The S-N curve (unit 2 high fatigue cycle) (16m)

In high-cycle fatigue situations, materials performance is commonly characterized by

an S-N curve, also known as aWhlercurve . This is a graph of the magnitude of a

cyclic stress (S) against the logarithmic scale of cycles to failure (N).

S-N curves are derived from tests on samples of the material to be characterized

(often called coupons) where a regular sinusoidal stress is applied by a testing

machine which also counts the number of cycles to failure. This process is sometimes

known as coupon testing. Each coupon test generates a point on the plot though in

some cases there is a runoutwhere the time to failure exceeds that available for the

test (see censoring). Analysis of fatigue data requires techniques from statistics,

especially survival analysis and linear regression.

Probabilistic nature of fatigue

As coupons sampled from a homogeneous frame will manifest variation in their

number of cycles to failure, the S-N curve should more properly be an S-N-P

curve capturing the probability of failure after a given number of cycles of a certain

stress. Probability distributions that are common in data analysis and in design

against fatigue include the lognormal distribution, extreme value

distribution, BirnbaumSaunders distribution, and Weibull distribution.

Combine the individual contributions using an algorithm such as Miner's rule.

Miner's rule

In 1945, M. A. Miner popularised a rule that had first been proposed by A.

Palmgren in 1924. The rule, variously called Miner's rule or thePalmgren-Miner linear

damage hypothesis, states that where there are kdifferent stress magnitudes in a

spectrum, Si(1 ik), each contributing ni(Si) cycles, then ifNi(Si) is the number of

cycles to failure of a constant stress reversal Si, failure occurs when:

C is experimentally found to be between 0.7 and 2.2. Usually for design purposes, C

is assumed to be 1.This can be thought of as assessing what proportion of life is

consumed by stress reversal at each magnitude then forming a linear combination of

their aggregate.
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Though Miner's rule is a useful approximation in many circumstances, it has several

major limitations:

It fails to recognise the probabilistic nature of fatigue and there is no simpleway to relate life predicted by the rule with the characteristics of a probabilitydistribution. Industry analysts often use design curves, adjusted to account for

scatter, to calculateNi(Si).

There is sometimes an effect in the order in which the reversals occur. Insome circumstances, cycles of low stress followed by high stress cause more

damage than would be predicted by the rule. It does not consider the effect of

overload or high stress which may result in a compressive residual stress. High

stress followed by low stress may have less damage due to the presence of

compressive residual stress.

Paris' Relationship

In Fracture mechanics, Anderson, Gomez and Paris derived relationships for the

stage II crack growth with cycles N, in terms of the cyclical component K of

the Stress Intensity Factor K[9]

where a is the crack length and m is typically in the range 3 to 5 (for metals).

This relationship was later modified (by Forman, 1967[10]

) to make better allowance

for the mean stress, by introducing a factor depending on (1-R) where R = min

stress/max stress, in the denominator.
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Dislocations Theory (8m)

Dislocations introduce imperfection into the structure and therefore these could

explain how real materials exhibit lower yield stress value than those observed in

theory.Produce imperfection in crystal structures

Lower the yield stress from theoretical values.

Produce plastic deformation (strain hardening).

Effects mechanical properties of materials

Burgers vector is the most characteristic feature of a dislocation, which defines the

magnitude and the direction of slip.

Screw Burgers vector is || to the dislocation line.

Edge Burgers vector is perpendicluar to the dislocation line.

Macroscopic deformation produced by glide of

(a) edge dislocation and (b) screw dislocation.

Both shear stress and final deformation are identical for both situations.

Note: Most dislocations found in crystalline materials are probably neither pure edge

or pure screw but mixed

Dislocations in single crystals are straight lines. But in general, dislocations appear in

curves or loops, which in three dimensions form and interlocking dislocation

network.

Dislocation loop lying in a slip plane.

Any small segments of the dislocation can be resolved into edge and screw

components. Ex: pure screw at point A and pure edge at point B where along most of its length

contains mixed edge and screw. But with the same Burgers vector

Dislocation dissociation occurs when the strength of

dislocation is more than unity. The system becomes

unstable

dislocation therefore dissociate into twodislocation.

Note: Dislocation of unit strength is a dislocation with a

Burgers vector equal to one lattice spacing.The dissociation reaction b1=b2 + b3 will occur


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when b12

> b22

+ b32.

A dislocation of unit strength has a minimum energy when its Burgers vector is

parallel to a direction of closest atomic packing.

In close-packed lattices, dislocations with strength less than unity are possible. _

therefore crystals always slip in the close-packed direction.

anna univ faqs f&;f

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