FATIGUE DR. AL EMRAN ISMAIL.

FATIGUE DR. AL EMRAN ISMAIL

INTRODUCTION Fatigue in materials subjected to repeated cyclic loading can be defined as a progressive failure due to crack initiation (stage I), crack growth (stage II), and crack propagation (stage III) or instability stage. For instance, crack initiation of crack-free solids may be characterized by fatigue crack nuclei due to dislocation motion, which generates slip bands at the surface having slip steps in the order of 0.1m in height or slip may occur at matrix-inclusion interfaces.

INTRODUCTION These steps produce surface intrusions and extrusions as schematically indicate below for stages I and II. These intrusions caused by reversed slip due to load reversal are the source for crack initiation, which may consume most of the solid life before crack growth. This crack initiation may occur along the slip direction due to a local maximum shear stress.

INTRODUCTION After the consumption of many cycles, the crack may change in direction when the maximum principal normal stress (in the vicinity of the crack tip) governs crack growth. In this stage II some materials show striations and beach marks as common surface features of fatigue fracture.

INTRODUCTION In general, fatigue is a form of failure caused by fluctuating or cyclic loads over a short or prolong period of time. Therefore, fatigue is a time-dependent failure mechanism related to microstructural features. The fluctuating loading condition is not a continuous failure process as opposed to cyclic loading. The former is manifested in bridges, aircrafts and machine components, while the latter requires a continuous constant or variable stress amplitude until fracture occurs.

INTRODUCTION It is also important for the reader to know that fatigue failure or fracture can occur at a maximum stress below the static yield strength of a particular material. Obviously, temperature effects must be considered in fatigue failure characterization. From an engineering point of view, predicting fatigue life is major a requirement.

MECHANICAL FATIGUE FAILURE
Car drive line component.

9.5 mm long brass chain link from weight driven clock.

Cracking in aircraft jet engine nacelle.

CYCLIC STRESS HISTORY The common stress parameters extracted from the constant amplitude (symmetrical) curves are the mean stress, m alternating stress, a the stress ratio, R and the stress amplitude, As.

CYCLIC STRESS HISTORY These stress parameters can be varied while conducting fatigue tests for characterizing materials having specific geometries, weldments or microstructural features. In fact, varying stress ratio is the most common parameter in determining the fatigue behavior of crack-free and cracked specimens. For crack-free specimens, the number of cycles to initiate a fatigue crack is known as the fatigue-crack initiation life, Ni which can have a very large magnitude representing most of the usual life of a component.

CYCLIC STRESS HISTORY The remaining fatigue life, Nf is related to stable fatigue crack growth till the crack reaches a critical length and consequently, crack propagation occurs very rapidly without any warning. As a result, a component can have a fatigue life defined by the total number of cycles, N = Ni + Nf consumed during testing or service. Conversely, a pre-existing crack reduces fatigue life because Ni = 0 and N = Nf .

CYCLIC STRESS HISTORY Despite that fatigue represents a cumulative damage in structural components, it is the fluctuating or cyclic local stresses and strains imparted by an external or nominal loading mode that are the primary factors for localized crack initiation and growth. Therefore, fatigue life can be prolonged if the nominal fluctuating or cyclic stress level is reduced or eliminated, the microstructure is homogeneous, dimensional changes are not severe enough or if the environment is not significantly corrosive.

CYCLIC STRESS HISTORY For crack-free or notched specimens, the usual characterization of fatigue behavior is through a stress-cycle curve, commonly known as a S-N diagram. Figure below shows two S-N curves for different materials. How to construct the S-N curves

CYCLIC STRESS HISTORY

FATIGUE TEST Conventionally, results are presented as S/N curves. These are plots of alternating Stress versus Number of cycles to failure, with an appropriate curve fitted through the individual data points. Sometimes, stress range is used; care is needed when using data to check which convention has been used.

FATIGUE TEST Failure is usually defined as the separation of a specimen into two parts, but other definitions are sometimes used. For example, loss of a specified amount of stiffness or the appearance of a crack of a specified size.

FATIGUE TEST S/N curves are sometimes called Wöhler curves after August Wohler (see Section 2.2.2). The number of cycles to failure is sometimes called the life or the endurance. It is usually plotted on a logarithmic scale, but the alternating stress may be plotted on either a linear or a logarithmic scale.

Plain fatigue specimen for testing in four point rotating bending.
FATIGUE TEST Plain fatigue specimen for testing in four point rotating bending.

FATIGUE TEST Schematic diagram of Wohler’s rotating cantilever bending fatigue testing machine.

Plain fatigue specimen for testing in direct stress.
FATIGUE TEST Plain fatigue specimen for testing in direct stress.

FATIGUE TEST Schematic Fatigue S-N Curves

FATIGUE PREVENTIONS Metal fatigue is a significant engineering problem because it can occur due to repeated or cyclic stresses below the static yield strength, unexpected and catastrophic failure of a vital structural part may occur and rack initiation may start at discontinuities in highly stressed regions of the component. Fatigue failure may be due to discontinuities such as inadequate design, improper maintenance and so forth.

FATIGUE PREVENTIONS Fatigue failure can be prevented by:
Avoiding sharp surfaces caused by punching, stamping, shearing and the like Preventing the development of surface discontinuities during processing. Reducing or eliminating tensile residual stresses caused by manufacturing Avoiding misuse and abuse

FATIGUE PREVENTIONS Avoiding assembling errors, improper maintenance, manufacturing defects, design errors Using proper material and heat treatment procedures Using inert environments whenever possible Furthermore, normally the nominal stresses in most structures are elastic or below the static yield strength of the base material. In pertinent cases, the strain-life can be determined instead of the stress-life (S-N) in high low cycle fatigue schemes.

FATIGUE ANALYSIS Fatigue analysis can be divided generally into:
Stress-Life Approach Strain-Life Approach What is the main differences between these two approaches? Where these approaches to be used?

STRESS-LIFE APPROACH STRESS-LIFE DIAGRAMS S-N Curve for 1045 Steel

STRESS-LIFE APPROACH S-N Curve for 2024-T4 Aluminum
STRESS-LIFE DIAGRAMS S-N Curve for 2024-T4 Aluminum

STRESS-LIFE APPROACH STRESS-LIFE DIAGRAMS The stress-life approach ignores true stress-strain behavior and treats all strains as elastic. This may be significant since the initiation of fatigue cracks is caused by plastic deformation. The simplifying assumptions of the S-N approach are valid only if the plastic strains are small. At long lives most steels have only a small component of cyclic strain which is plastic and the S- N approach is valid.

STRESS-LIFE APPROACH S-N test are usually presented on a log-log plot.
STRESS-LIFE DIAGRAMS S-N test are usually presented on a log-log plot. BCC steels have an endurance or fatigue limit, Se. Below this limit, the material has an infinite life. The endurance limit is due to interstitial elements which pin dislocations. This presents the slip mechanisms that leads to the formation of microcracks. The endurance limit is affected by: 1) Periodic overloads, 2) Corrosive environments & 3) High temperatures.

STRESS-LIFE APPROACH STRESS-LIFE DIAGRAMS There are certain general empirical relationship between the fatigue properties of steel and the less expensively obtained monotonic tension and hardness properties. When the S-N curves for several steel alloys are plotted in nondimensional form using the ultimate strength, they tend to follow the same curve.

STRESS-LIFE APPROACH STRESS-LIFE DIAGRAMS

STRESS-LIFE APPROACH STRESS-LIFE DIAGRAMS The ratio of endurance limit to ultimate strength is shown below. Most steels with an ultimate strength below 200ksi have a fatigue ratio of 0.5. This ratio can be ranged from 0.35 to 0.6. Steels with an ultimate strength over 200ksi often have carbide inclusion formed during the tempering of martensite. These nonmetallic inclusion serve as crack initiation points which effectively reduce the endurance limit.

STRESS-LIFE APPROACH STRESS-LIFE DIAGRAMS
Relation Between Rotating Bending Endurance Limit and Tensile Strength of Wrought Steel

STRESS-LIFE APPROACH STRESS-LIFE DIAGRAMS The relationship between hardness and ultimate strength: Su (ksi)  0.5 x BHN (Brinell hardness number). The relationship between endurance limit related to hardness for steel: Se (ksi)  0.25 x BHN (for BHN ≤ 400) and Se  100 ksi (for BHN > 400). The endurance limit related to ultimate strength: Se  0.5 x Su (for Su ≤ 200 ksi)

STRESS-LIFE APPROACH STRESS-LIFE DIAGRAMS

STRESS-LIFE APPROACH STRESS-LIFE DIAGRAMS The alternating stress level corresponding to a life of 1000 cycles, S1000 can be estimated as 0.9 times the ultimate strength. The line connecting this point and the endurance limit is the estimate used for the S-N design line if no actual fatigue data are available for the material. In place of the graphical approach shown above, a power relationship can be used to estimate the S-N curve for steel: S = 10CNb (for 103 < N < 106)

STRESS-LIFE APPROACH STRESS-LIFE DIAGRAMS The exponents , C and b of the S-N curve are determined using two defined points shown in Figure above.

STRESS-LIFE APPROACH STRESS-LIFE DIAGRAMS The equation giving life in terms of an alternating stress is: N = 10-C/bS1/b (for 103 < N < 106). When the estimates for S1000 and Se are made: S1000  0.9Su and Se  0.5Su. The S-N curve is defined as: S = 1.62SuN Similar empirical relationships for materials other than steel are not as clearly defined.

STRESS-LIFE APPROACH Certain points about the S-N curve:
STRESS-LIFE DIAGRAMS Certain points about the S-N curve: The empirical relationship outlined in this section are only estimates. Depending on the level of certainty required in the fatigue analysis, actual test data may be necessary. The most useful concept of the S-N methods is the endurance limit which is used in infinite life or safe stress designs. In general, the S-N approach should not be used to estimate lives below 1000 cycles.

STRESS-LIFE APPROACH MEAN STRESS EFFECTS

STRESS-LIFE APPROACH Terminology for Alternating Stress
MEAN STRESS EFFECTS Terminology for Alternating Stress

STRESS-LIFE APPROACH MEAN STRESS EFFECTS

STRESS-LIFE APPROACH MEAN STRESS EFFECTS The results of a fatigue test using nonzero mean stress are plotted on a Haigh diagram (alternating stress versus mean stress) with lines of constant life.

STRESS-LIFE APPROACH MEAN STRESS EFFECTS This diagram is sometimes incorrectly called the modified Goodman diagram.

STRESS-LIFE APPROACH MEAN STRESS EFFECTS Since the tests required to generate a Haigh diagram can be expensive. Several empirical relationship have been developed to generate the line defining the infinite- life design region. These methods use various curves to connect the endurance limit on the alternating stress axis to either the yield strength, Sy, ultimate strength, Su or true fracture stress, f on the mean stress axis.

STRESS-LIFE APPROACH MEAN STRESS EFFECTS
Comparison of a mean stress equations: Soderberg Goodman Gerber Morrow

STRESS-LIFE APPROACH The following generalization can be made:
MEAN STRESS EFFECTS The following generalization can be made: The Soderberg method is very conservative and seldom used. Actual test data tend to fall between the Goodman and Gerber curves. For hard steel (brittle, Su  f), the Morrow and Goodman line are essentially the same. For ductile steel (Su < f), the Morrow line predicts less sensitivity to mean stress.

STRESS-LIFE APPROACH MEAN STRESS EFFECTS For most fatigue design situations (R < 1), small mean stress in relation to alternating stress), There is little difference in the theories. In the range where the theories show a large difference (R  1), There is little experimental data. In this region the yield criterion may bet design limits. Note: For finite-life calculations the endurance limit in any of the equations can be replaced with a fully reversed alternating stress level corresponding to that finite-life value.

FACTORS THAT AFFECTING FATIGUE STRENGTH
STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH For many years the emphasis of most fatigue testing was to gain an empirical understanding of the effect of various factors on the baseline S-N curves for ferrous alloys in the intermediate to long life range. The variable investigated include: Size Type of loading Surface finish Surface treatments Temperature Environment

FACTORS THAT AFFECTING FATIGUE STRENGTH
STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH The results of these tests have been quantified as modification factors which are applied to the baseline S-N data: Se = S’eCsizeCloadCsirf.fin…….. These modification factors are empirical models and may give limited insight into the underlying physical processes. Great care must be taken when extrapolating theses empirical modification factors.

FACTORS THAT AFFECTING FATIGUE STRENGTH (SIZE EFFECTS)
STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SIZE EFFECTS)

STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SIZE EFFECTS) There are many empirical fits to the size effect data: where d is the diameter of the component. A large component will have a less steep stress gradient and hence a larger volume of material subjected to this high stress. There will be a greater probability of initiating a fatigue crack in large components.

STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SIZE EFFECTS) Stress Gradient for Large and Small Components

FACTORS THAT AFFECTING FATIGUE STRENGTH (LOADING EFFECTS)
STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (LOADING EFFECTS) Since the axial specimen has no gradient, it has a greater volume of material subjected to the high stress. The ratio of endurance limits for a material found using axial and rotating bending tests ranges from 0.6 to 0.9. These tests data may include some error due to eccentricity in axial loading. A conservative estimate: Se(axial)0.70Se(bending)

FACTORS THAT AFFECTING FATIGUE STRENGTH (LOADING EFFECTS)
STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (LOADING EFFECTS) The ratio of endurance limit found using torsion and rotating bending tests ranges from 0.5 to 0.6. A theoretical value of has been explained using the von Mises failure criterion. A reasonable estimate: e(torsion) = 0.577Se(bending)

FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE FINISH)
STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE FINISH) The scratches, pits and machining marks on the surface of a material add stress concentration. Surface finish factors for steel parts

STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE FINISH) Surface finish factor versus surface roughness and strength for steel parts

STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE FINISH) Some important points about the surface finish effect: The condition of the surface is more important for higher strength steels. The residual surface stress caused by a machining operation can be important. At shorter lives, where crack propagation dominates, the condition of surface finish has less effect on the fatigue life. Localized surface irregularities such as stamping marks can serve as very effective stress concentration and should not be ignored.

FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE TREATMENT)
STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE TREATMENT) Fatigue cracks almost always initiate at a free surface. Any surface treatment can have a significant effect on fatigue life. Consider the un-notched beam subjected to a varying bending moment. Assuming that the beam is elastic-perfectly plastic.

STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE TREATMENT) Residual stress in un-notched beam in bending

STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE TREATMENT) Residual stress in notched member under axial loading

STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE TREATMENT) Endurance limit of plate with hole under axial loading

STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE TREATMENT) In the following discussion on surface treatments are: Since fatigue is a surface phenomenon, the residual stress at the surface of the material is critical. Compressive residual stresses are beneficial and tensile stresses are detrimental to fatigue life. Residual stress are not always permanent and various factors such as high temperatures and overloads may cause stress relaxation.

FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE TREATMENT - PLATING)
STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE TREATMENT - PLATING) Chrome and nickel plating of steels can cause up to 60% reduction in endurance limits. This is due primarily to the high residual tensile stresses generated by the plating process. The following process operation can help alleviate the residual tensile stress problem: Nitride the part before plating. Shot peen the part before or after plating. Bake or anneal the part after plating.

STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE TREATMENT - PLATING) Effect of chrome plating on S-N curve of 4140 steel.

STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE TREATMENT - PLATING) Effect of nickel plating on S-N curve of steel (Su = 63 ksi).

STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE TREATMENT - PLATING) Effect of shot peening on S-N curve of nickel plated steel.

STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE TREATMENT - PLATING) There are many factors involved with a plating (Cr and Ni) which can affect fatigue life are: There is a greater reduction of fatigue strength as the yield strength of the material being plated increases. The fatigue strength reduction is greater as the thickness of the plating increases. The fatigue strength reduction due to plating is greater at longer lives. When fatigue occurs in a corrosive environment, the extra corrosion resistance offered by plating can be more than offset the reduction in fatigue strength.

STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE TREATMENT - PLATING) Effect on nitriding on endurance limit

FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE TREATMENT - THERMAL)
STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE TREATMENT - THERMAL) Diffusion processes such as carburizing and nitriding are very beneficial for fatigue strength. These processes have the combined effect of producing a higher strength material on the surface as well as causing volumetric changes which produce residual compressive surface stresses. Flame and induction hardening cause a phase transformation which in turn causes a volumetric expansion. If these processes are localized to the surface, they produce a compressive residual stress which is beneficial for fatigue strength.

STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE TREATMENT - THERMAL) Hot rolling and forging can cause surface decarburizing. The loss of carbon atoms from the surface material causes it to have a lower strength and may also produce residual tensile stresses.

STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE TREATMENT - THERMAL) Effect of decarburization on endurance limit

STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE TREATMENT - THERMAL) Effect of forging on the endurance limit of steels

STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE TREATMENT - THERMAL) Effect of grinding on S-N curve of steel

STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE TREATMENT - MECHANICAL) There are several methods used to cold work the surface of a component to produce a residual compressive stress. The two most important are cold rolling and shot peening. Along with producing compressive residual stresses, these methods also work-harden the surface material. The great improvement in fatigue life is due primarily to the residual compressive stresses.

STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE TREATMENT - MECHANICAL) Cold rolling involves pressing steel rollers to the surface of a component. This method is used on large parts and can produce a deep residual stress layer. Shot peening is one of the most important methods of producing a residual compressive stress. This procedure involves blasting the surface of a component with high velocity steel or glass beads. This puts the core of the material in residual tension and the skin in residual compression.

STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE TREATMENT - MECHANICAL) Effects of cold rolling on S-N curve of steel

STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE TREATMENT - MECHANICAL) S-N curve of carburized gears in peened and unpeened conditions

STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE TREATMENT - MECHANICAL) Effect of shot peening on endurance limit of high strength steel

STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE TREATMENT - MECHANICAL) Some important points about cold working for residual compressive stresses are: Cold rolling and shot peening have their greatest effect at long lives. At very short lives, there is almost no improvement in the fatigue strength. At shorter lives the stress levels are high enough to cause yielding which eliminates residual stresses. The residual stresses can be relaxed or faded out by high temperatures and overstressing (5500F for steel and 2500F for aluminum)

STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE TREATMENT - MECHANICAL) Steel with yield strength below 80ksi are seldom cold rolled or shot peened. This is due to their low yield points and quite easy to introduce plastic strains that wipe out residual stresses. A surface residual compressive stress has the greatest effect on fatigue life when it is applied to an area of the component where there is a stress gradient primarily around notches. It is possible to overpeen a surface. There is usually an optimum level for peening of a component and more peening will actually begin to decrease fatigue strength.

STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE TREATMENT - ENVIRONMENT) When fatigue loading takes place in a corrosive environment the resulting detrimental effects are more significant than would be predicted by considering fatigue and corrosion separately. The interaction of fatigue and corrosion which is called corrosion-fatigue. A corrosive environment attacks the surface of a metal and produces an oxide film. At the same time corrosion causes localized pitting of the surface and these pits serve as stress concentrations.

STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE TREATMENT - ENVIRONMENT) Effect of various environments on the S-N curve of steel.

STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE TREATMENT - ENVIRONMENT) Influence of tensile strength and chemical composition on corrosion-fatigue strength of steels

STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE TREATMENT - ENVIRONMENT) Fatigue strength of steels in corrosive environment.

STRESS-LIFE APPROACH FACTORS THAT AFFECTING FATIGUE STRENGTH (SURFACE TREATMENT - ENVIRONMENT) Effect of various surface treatment on the corrosion fatigue of mild steel.

STRAIN-LIFE APPROACH INTRODUCTION The strain-life method is based on the observation that in many components the response of the material in critical locations is strain or deformation dependent. When load levels are low, stresses and strains are linearly related. Consequently, in this range, load-controlled and strain- controlled are equivalent. At high load levels, in the low cycle fatigue regime, the cyclic stress-strain response and the material behaviors are best modeled under strain-controlled conditions. At long lives where plastic strain is negligible and stress and strain are easily related, both methods are essentially the same.

STRAIN-LIFE APPROACH INTRODUCTION Although most engineering structures and components are designed such that the nominal loads remain elastic, stress concentration often cause plastic strains to develop in the vicinity of notches. Due to the constraint imposed by the elastically stressed material surrounding the plastic zone, deformation at the notch root is considered strain-controlled. The strain-life method assumes that smooth specimens tested under strain-controlled can simulate fatigue damage at the notch root.

STRAIN-LIFE APPROACH INTRODUCTION
The laboratory specimen models an equally stressed volume of material at the notch root.

STRAIN-LIFE APPROACH INTRODUCTION Fatigue life predictions may be made using the strain- life approach with the following: Material properties obtained from smooth specimen strain-controlled laboratory fatigue data. Stress-strain history at the critical locations. Technique for identifying damage events (cyclic counting). Methods to incorporate mean stress effects. Damage summation technique (Miner’s rule)

MONOTONIC STRESS AND STRAIN BEHAVIOUR
STRAIN-LIFE APPROACH MONOTONIC STRESS AND STRAIN BEHAVIOUR

MONOTONIC STRESS AND STRAIN BEHAVIOUR
STRAIN-LIFE APPROACH MONOTONIC STRESS AND STRAIN BEHAVIOUR Comparison of engineering and true stress-strain.

STRESS-STRAIN RELATIONSHIPS – LINEAR ELASTIC STRAIN
STRAIN-LIFE APPROACH STRESS-STRAIN RELATIONSHIPS – LINEAR ELASTIC STRAIN

STRESS-STRAIN RELATIONSHIPS – LINEAR ELASTIC STRAIN
STRAIN-LIFE APPROACH STRESS-STRAIN RELATIONSHIPS – LINEAR ELASTIC STRAIN For most metals a log-log plot of true stress versus true strain is modeled as a straight line can be represented as: Where K is the strength coefficient and n is the strain hardening exponent.

STRAIN-LIFE APPROACH STRAIN-LIFE CURVES Basquin observed that stress-life (S-N) data could be plotted linearly on a log-log scale.

STRAIN-LIFE APPROACH STRAIN-LIFE CURVES Coffin and Manson found that plastic strain-life (p- N) data could be linearized on log-log and plastic strain can be related by a power law:

STRAIN-LIFE APPROACH STRAIN-LIFE CURVES

DETERMINATION OF FATIGUE PROPERTIES
STRAIN-LIFE APPROACH DETERMINATION OF FATIGUE PROPERTIES The strain-life equation requires four empirical constants. Several points must be considered in attempting to obtain these constants from fatigue tests: Not all materials may be represented by the four parameters strain-life equations (Al & Ti). The fatigue constants may represent a curve fit to a limited number of data points. The values of these constant may be changed if more data points are included in the curve fit.

STRAIN-LIFE APPROACH DETERMINATION OF FATIGUE PROPERTIES The fatigue constants are determined from a set of data points over a given range. Gross error may occur when extrapolating fatigue life estimates outside this range. The use of power law relationship is strictly a matter of mathematical convenience and it not on a physical phenomenon.

STRAIN-LIFE APPROACH DETERMINATION OF FATIGUE PROPERTIES The following properties may be related: Fatigue properties may be approximated from monotonic properties. The following approximate methods may also be used:

STRAIN-LIFE APPROACH DETERMINATION OF FATIGUE PROPERTIES Fatigue strength coefficient, ’f (A fairly good approximation): ’f = f. For steel with hardness below 500 BHN: ’f = Su + 50 ksi. Fatigue strength exponent, b ( b varies from – to – 0.12 for most metals with an average of – ). Fatigue ductility coefficient, ’f (A fairly good approximation): ’f = f.

STRAIN-LIFE APPROACH DETERMINATION OF FATIGUE PROPERTIES Fatigue ductility exponent, c. It is not well defined as the other parameters. A rule of thumb must be followed rather than an empirical equation: Coffin found c to be about – 0.5, Manson found c to be about – 0.6 & Morrow found that c varied between – 0.6 and – 0.7. Fairly ductile metals (f  1) have average values of c = For strong metal (f  0.5), a value of c = 0.5 is probably more reasonable.

STRAIN-LIFE APPROACH MEAN STRESS EFFECT Cyclic fatigue properties of a material are obtained from completely reversed, constant amplitude strain- controlled tests. Components seldom experience this type of loading, as some mean stress or mean strain us usually present. The effect of mean strain is, for the most part, negligible on the fatigue life of a component. Mean stresses, on the other hand, may have significant effect on the fatigue life. Mean stress effects are seen predominantly at longer lives.

STRAIN-LIFE APPROACH MEAN STRESS EFFECT
Effect of mean stress on strain-life curve

STRAIN-LIFE APPROACH MEAN STRESS EFFECT At high strain amplitudes (0.5& to 1% or above), where plastic strains are significant, mean stress relaxation occurs and the mean stress tends towards zero.

STRAIN-LIFE APPROACH MEAN STRESS EFFECT

STRAIN-LIFE APPROACH MEAN STRESS EFFECT Modifications to the strain-life equation have been made to account for mean stress effects. Morrow suggested that the mean stress effect could be taken into account by modifying the elastic term:

STRAIN-LIFE APPROACH MEAN STRESS EFFECT The strain-life equation accounting for mean stresses:

STRAIN-LIFE APPROACH MEAN STRESS EFFECT

STRAIN-LIFE APPROACH MEAN STRESS EFFECT The predictions made with this equation are consistent with the observations that mean stress effects are significant at low values of plastic strain where the elastic strain dominates. It is reflected the trend that mean stresses have little effect at shorter lives, where plastic strains are large.

STRAIN-LIFE APPROACH MEAN STRESS EFFECT Manson & Halford modified both the elastic and plastic term of the strain-life equation to maintain the independence of the elastic-plastic strain ratio from mean stress: This equation tends to predict too much mean stress effect at short lives or where plastic strains dominate. At high plastic strains, mean stress relaxation occurs.

STRAIN-LIFE APPROACH MEAN STRESS EFFECT Smith, Watson & Topper (SWT) have proposed another equation to account for mean stress effect for completely reversed loading:

STRAIN-LIFE APPROACH MEAN STRESS EFFECT
Mean stress correction for independence of elastic/plastic strain ratio from mean stress

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