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FatigueB.E MYD

Muhammad Ali Siddiqui

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Introduction to Fatigue It has been known since

1830 metal or a component is subjected to a repetitive or fluctuation stresses it fails at a stress much lower than tensile or yield strength for a static load.

Failure occurs under condition of dynamic and fluctuation loading are

called Fatigue. Fatigue has become

progressively more prevalent (common) as technology has developed a greater amount of equipment's and structure, such as automobiles, aircraft, compressor, pumps, turbines, bridges etc.

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It is often stated that fatigue accounts 90% of all service failure due to mechanical causes and it will occur after lengthy period of repeated stress or strain cycle.

Furthermore it is catastrophic and insidious (dangerous), occurring very suddenly and without warning.

Fatigue failure is brittle-appearing in nature, with no dross plastic deformation associated with failure.

Fatigue usually occurs at a point of stress concentration such as sharp corner or notch or at a metallurgical stress concentration like an inclusion.

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Factors causes fatigue failure Three factors are necessary to

cause fatigue failure.

1. A maximum tensile stress of sufficient high value.

2. A large enough variation or fluctuation in the applied stress.

3. A sufficient large number of cycles of the applied stress.

Other host Variables/Factors are:

• stress concentration, corrosion, temperature, overload, metallurgical structure, residual stresses and combined stresses which tend to alter the conditions of fatigue.

• Since we have not yet gained a complete understanding of what causes fatigue in metal.

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Stress Cycle (Cyclic stresses)

• The applied stress may axial (tension, compression), flexure (bending) or torsion (twisting) in nature.

• In general three different fluctuation stress-time modes are possible.

1. Completely Reversed Stress cycle: 2. Repeated Stress Cycle:3. Irregular or random stress cycle

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1. Completely Reversed Stress cycle:

Where in the amplitude is symmetrical about a mean zero stress level, for example, alternating from a maximum tensile stress (σmax) to a minimum compressive stress (σmin) of equal magnitude; this is referred to as a reversed stress cycle.

This is an idealized situation which is proposed by an R.R.Moore rotating-beam fatigue machine (which is approached in service by a rotating shaft operating at constant speed without overload).

σa = Alternating or variable or stress amplitude,

σr = Range of the stress, is the algebraic difference between the maximum and minimum stress in cycle

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2. Repeated Stress Cycle

The maxima and minima are asymmetrical relative to the zero stress level. (σmax and σmin

stress are not equal)

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3. Irregular or random stress cycle

Finally, the stress level may vary randomly in amplitude and frequency. (complicated stress cycle such as in aircraft wings etc)

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The Fatigue Testing and S-N Curve

• *ASTM Standard

E 466, ‘‘Standard Practice for Conducting Constant Amplitude Axial Fatigue Tests of Metallic Materials,’’

E 468, ‘‘Standard Practice for Presentation of Constant Amplitude Fatigue Test Results for Metallic Materials.’’

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As with other mechanical characteristics, the fatigue properties of materials can be determined from laboratory simulation tests.

A test apparatus should be designed to duplicate as nearly as possible the service stress conditions (stress level, time frequency, stress pattern, etc.).

A schematic diagram of a rotating-bending test apparatus, commonly used for fatigue testing, is shown in Figure;

The compression and tensile stresses are imposed on the specimen as it is simultaneously bent and rotated.

The basic method of presenting engineering fatigue data is by means of the S – N curve (a plot of stress amplitude σa, S versus the logarithm of the number of cycles to failure)

The value of stress may be σmax, σmin, Most determination of the fatigue

properties of material have been made in complete reverse bending mode, where the mean stress σm, is zero

σm = (σmax + σmin ) / 2 = 0

Different Fatigue Machines

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Procedure A series of tests are commenced by subjecting a specimen to the

stress cycling at relatively large maximum stress amplitude, usually on the order of two thirds of the static tensile strength; the number of cycles to failure is counted.

This procedure is repeated on other specimens at progressively decreasing maximum stress amplitudes. (Approx 8 to 12 specimen)

This test stress is decreased for each succeeding specimen until one or two specimens do not fail in the specified number of cycles, which is usually at least 107 cycles. (as shown in figure)

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Endurance limit or Fatigue limit, Fatigue strength and Fatigue life

Two distinct types of S–N behavior are observed, which are represented schematically in Figure 9.25(ferrous and non ferrous).

As these plots indicate, the higher the magnitude of the stress, the smaller the number of cycles the material is capable of sustaining before failure.

For some ferrous (iron base) and titanium alloys, the S–N curve (Figure 9.25a) becomes horizontal at higher N values; or, there is a limiting stress level, called the fatigue limit (also sometimes the endurance limit), below which fatigue failure will not occur.

This fatigue limit represents the largest value of fluctuating stress that will not cause failure for essentially an infinite number of cycles.

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For many steels, fatigue limits range between 35 and 60% of the tensile strength.

Most nonferrous alloys (e.g., aluminum, copper, magnesium) do not have a fatigue limit, in that the S–N curve continues its downward trend at increasingly greater N values (Figure 9.25b).

Thus, fatigue will ultimately occur regardless of the magnitude of the stress.

For these materials, the fatigue response is specified as fatigue strength, which is defined as the stress level at which failure will occur for some specified number of cycles (e.g., 107 cycles).

The determination of fatigue strength is also demonstrated in Figure 9.25b.

Another important parameter that characterizes a material’s fatigue behavior is fatigue life Nf. It is the number of cycles to cause failure at a specified stress level, as taken from the S–N plot (Figure 9.25b).

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Low - cycle and high-cycle fatigueThe fatigue behaviors represented in Figures 9.25a and 9.25b may be classified into two domains. 1) Low-cycle fatigue: One is associated with relatively high loads

that produce not only elastic strain but also some plastic strain during each cycle.

Consequently, fatigue lives are relatively short; this domain is termed low-cycle fatigue and occurs at less than about 104 to 105 cycles. (N < 104 to 105 cycles)

2) High-cycle fatigue: For lower stress levels wherein

deformations are totally elastic, longer lives result.

This is called high-cycle fatigue in as much as relatively large numbers of cycles are required to produce fatigue failure.

High-cycle fatigue is associated with fatigue lives greater than about 104 to 105 cycles. (N > 104 to 105 cycles)

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Statistical Nature of Fatigue• In determining the “fatigue limit” it should be recognized that

the specimen has its own fatigue limit of a material.

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• The figure blow shows Summary of S-N curves, each based on 10 specimens, drawn from the same bar of steel

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• Unfortunately, there always exists considerable scatter in fatigue data as shown in figure above, that is, a variation in the measured N value for a number of specimens tested at the same stress level.

• This may lead to significant design uncertainties when fatigue life and/or fatigue limit (or strength) are being considered.

• The scatter in results is a consequence of the fatigue sensitivity to a number of test and material parameters that are impossible to control precisely.

• These parameters include specimen fabrication and surface preparation, metallurgical variables, specimen alignment in the apparatus, mean stress, and test frequency.

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• Several statistical techniques have been developed to specify fatigue life and fatigue limit in terms of probabilities.

Example1:• A distribution

of fatigue life at constant stress is illustrated schematically in the figure 12-4.

• Curves of constant probability (P) of failure are drawn

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• Thus at stress σ1, 1 percent (P = 0.01) of the specimens would be expected to fail at N1 …50 percent (P= 0.50) at N2 and so on.

• The figure indicates a decreasing scatter in fatigue life with increasing stress level.

• The statistical distribution function which describes the distribution of fatigue life at constant stress is not accurately known, for this would require the testing of over 1,000 identical specimens under identical condition at constant stress.

• It is now recognized that the “fatigue limit” is really a “statistical quantity” which requires special techniques for an accurate determination.

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• Example 2: One convenient way of representing data treated in this manner is with a series of constant probability curves, several of which are plotted in Figure 9.26.

• The P value associated with each curve represents the probability of failure. For example, at a stress of 200 MPa (30,000 psi),

• We would expect 1% of the specimens to fail at about 106 cycles and 50% to fail at about 2x107 cycles, and so on.

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• It should be remembered that S–N curves represented in the literature are normally average values, unless noted otherwise.

• Fatigue S–N curves similar to those shown in Figure 9.25 represent ‘‘best fit’’ curves which have been drawn through average-value data points.

• It is a little unsettling to realize that approximately one half of the specimens tested actually failed at stress levels lying nearly 25% below the curve (as determined on the basis of statistical treatments).

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Effect of Mean Stress on Fatigue

• Much of the fatigue data in the literature have been determined for conditions of completely reserved cycles of stress, σm = 0.

• However there are several possible methods of determining an S-N diagram for a situation where the mean stress is not equal to zero, σm ≠ 0

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• The following figure shows the most common method of presenting the data.

• In figure (a): the maximum stress is plotted against log N for constant values of the stress ratio R = σmin/ σmax.

• The is achieved by applying a series of stress cycle with decreasing maximum stress and adjusting the minimum stress in each case so that it is a constant fraction of the maximum stress.

• The case of completely reversed stress is given at R = -1.0.

• Note that as R becomes more positive, which is equivalent to increasing the mean stress; the measured fatigue limit becomes grater.

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Mechanism of Fatigue Failure

• The process of fatigue failure is characterized by three distinct steps:

(1)Crack initiation, wherein a small crack forms at some point of high stress concentration;

(2)Crack propagation, during which this crack advances incrementally with each stress cycle; and

(3)Final failure, which occurs very rapidly once the advancing crack has reached a critical size.

• The fatigue life Nf , the total number of cycles to failure, therefore can be taken as the sum of the number of cycles for crack initiation Ni and crack propagation Np

Nf = Ni + Np

• The contribution of the final failure step to the total fatigue life is insignificant since it occurs so rapidly.

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• Relative proportions to the total life of Ni and Np depend on the particular material and test conditions.

• At low stress levels (i.e., for high-cycle fatigue), a large fraction of the fatigue life is utilized in crack initiation. With increasing stress level, Ni decreases and the cracks form more rapidly.

• Thus, for high stress levels (i.e, for low-cycle fatigue ), the propagation step predominates (i.e., Np > Ni).

• Cracks associated with fatigue failure almost always initiate (or nucleate) on the surface of a component at some point of stress concentration.

• Crack nucleation sites include surface scratches, sharp fillets, keyways, threads, dents, and the like.

• In addition, cyclic loading can produce microscopic surface discontinuities resulting from dislocation slip steps which may also act as stress raisers, and therefore as crack initiation sites.

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• Once a stable crack has nucleated, it then initially propagates very slowly and, in polycrystalline metals, along crystallographic planes of high shear stress; this is sometimes termed stage I propagation (Figure 9.28).

• This stage may constitute (make) a large or small fraction of the total fatigue life depending on stress level and the nature of the test specimen; high stresses and the presence of notches favor a short lived stage I.

• In polycrystalline metals, cracks normally extend through several grains during this propagation stage. The fatigue surface that is formed during stage I propagation has a flat and featureless appearance.

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• Eventually (finally), a second propagation stage (stage II) takes over, wherein the crack extension rate increases dramatically.

• Furthermore, at this point there is also change in propagation direction to one that is roughly perpendicular to the applied tensile stress (see Figure 9.28).

• During this stage of propagation, crack growth proceeds by a repetitive plastic blunting and sharpening process at the crack tip, a mechanism illustrated in Figure 9.29.

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• At the beginning of the stress cycle (zero or maximum compressive load), the crack tip has the shape of a sharp double-notch (Figure 9.29a).

• As the tensile stress is applied (Figure 9.29b), localized deformation occurs at each of these tip notches along slip planes that are oriented at 45o angles relative to the plane of the crack.

• With increased crack widening, the tip advances by continued shear deformation and the assumption of a blunted (dull rounded) configuration (Figure 9.29c).

• During compression, the directions of shear deformation at the crack tip are reversed (Figure 9.29d) until, at the culmination (peak) of the cycle, a new sharp double-notch tip has formed (Figure 9.29e).

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• Thus, the crack tip has advanced a one-notch distance during the course of a complete cycle.

• This process is repeated with each subsequent cycle until eventually some critical crack dimension is achieved that precipitates the final failure step and catastrophic failure results.

• The region of a fracture surface that formed during stage II propagation may be characterized by two types of markings termed beachmarks and striations.

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Figure: Fatigue fracture surface. (a) At low magnifications, the beach mark pattern indicates fatigue as the fracture mechanism. The arrows show the direction of growth of the crack front, whose origin is at the bottom of the photograph. (Image (a) is from C.C. Cottell, ‘‘Fatigue Failures with Special Reference to Fracture Characteristics,’’ Failure Analysis: The British Engine Technical Reports, American Society for Metals, 1981, p. 318.) (b) At very high magnifications, closely spaced striations formed during fatigue are observed (x 1000)

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(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.

Figure : Schematic representation of a fatigue fracture surface in a steel shaft, showing the initiation region, the propagation of fatigue crack (with beam markings), and catastrophic rupture when the crack length exceeds a critical value at the applied stress

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Fatigue Failure Analysis of a CrankshaftExample

A crankshaft in a diesel engine fails. Examination of the crankshaft reveals no plastic deformation. The fracture surface is smooth. In addition, several other cracks appear at other locations in the crankshaft. What type of failure mechanism would you expect?

Solution

Since the crankshaft is a rotating part, the surface experiences cyclical loading. We should immediately suspect fatigue. The absence of plastic deformation supports our suspicion. Furthermore, the presence of other cracks is consistent with fatigue; the other cracks didn’t have time to grow to the size that produced catastrophic failure. Examination of the fracture surface will probably reveal beach marks or fatigue striations.

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Example 6.12Automobile Axle Failure AnalysisAn engineer investigating the cause of an automobileaccident finds that the right rear wheel has broken of at theaxle. The axle is bent. The fracture surface reveals aChevron pattern pointing toward the surface of the axle.Suggest a possible cause for the fracture.Example 6.12 SOLUTION 

The Chevron pattern indicates that the wheel wassubjected to an intense impact blow, which wastransmitted to the axle, causing failure.

Further examination of the fracture surface,microstructure, composition, and properties may verifythat the axle was manufactured properly.

                                                                                                                                                                                                        

Example

Automobile Axle Failure Analysis. An engineer investigating the cause of an automobile accident finds that the right rear wheel has broken of at the axle. The axle is bent. The fracture surface reveals a Chevron pattern pointing toward the surface of the axle. Suggest a possible cause for the fracture.

Solution

• The Chevron pattern indicates that the wheel was subjected to an intense impact blow, which was transmitted to the axle, causing failure.

• Further examination of the fracture surface, microstructure, composition, and properties may verify that the axle was manufactured properly.

Automobile Axle Failure Analysis

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Factors that affect fatigue-life

1. 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,

2. Geometry: Notches and variation in cross section throughout a part lead to stress concentrations where fatigue cracks initiate.

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3. 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 as peening, 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 the fatigue life of the component. This improvement is normally observed only for high-cycle fatigue.

4. 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.

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5. 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.

6. Size and distribution of internal defects: Casting defects such as gas porosity, non-metallic inclusions and shrinkage voids can significantly reduce fatigue strength.

7. Direction of loading: For non-isotropic materials, fatigue strength depends on the direction of the principal stress.

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8. 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.

9. 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.

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

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Crack Growth Rate

• In many cases, a component may not be in danger of failure even a crack is present.

• To estimate when failure occur; rate of crack propagation become important.

• Following figure shows the crack growth rate v/s range of the stress intensity factor ΔK, which characterizes crack geometry and stress amplitude.

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Figure : Crack growth rate versus stress-intensity factor range for a high-strength steel.

For this steel, C = 1.62 1012 and n = 3.2 for the units shown.

Crac

k Gr

owth

rate

(m/c

ycle

s)Crack Growth Rate

Crack growth rate given by: Eq:01

= 2

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• Below Threshold ΔK= crack does not grow

• For some what higher stress-intensities, crack grow slowly.

• And still higher intensities a crack grow at a rate of given by Eq:01

• When ΔK is still higher, crack grow in a rapid and unstable manner until fracture occurs.

Crack Growth Rate

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• Knowledge of crack growth rate is of assistance in designing component and in nondestructive evaluation to determine if a crack poses imminent danger to the structure.

• One approach to this problem is to estimate the number of cycle required before failure occurs. By rearranging Equation 01 and substituting for and integrate this b/w the initial size of the crack and the crack size required for fracture to occur, we find that.

•ai = initial Flaw size

•ac = flaw size required to fracture.

•C and n = are empirical constant depends upon the material.

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Design of a Fatigue-Resistant Plate

Example:

A high-strength steel plate (Figure 6.52), which has a plane strain fracture toughness of 80 MPa , is alternately loaded in tension to 500 MPa and in compression to 60 MPa. The plate is to survive for 10 years, with the stress being applied at a frequency of once every 5 minutes. Design a manufacturing and testing procedure that assures that the component will serve as intended.

m

For High strength steel, C = 1.62 1012 and n = 3.2 for the units shown.

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SOLUTION

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The End