Atlas of Fatigue Curves Copyright © 1986 ASM International® H.E. Boyer, Author All rights reserved www.asminternational.org 1 Fatigue Testing ence of reversed stresses that exceed the flow Introduction stress, followed by development of cracks at per­ Fatigue is the progressive, localized, perma­ sistent slip bands or at grain boundaries. nent structural change that occurs in materials subjected to fluctuating stresses and strains that Prediction of Fatigue life may result in cracks or fracture after a sufficient The fatigue life of any specimen or structure is number of fluctuations. Fatigue fractures are the number of stress (strain) cycles required to caused by the simultaneous action of cyclic cause failure. This number is a function of many stress, tensile stress and plastic strain. If any one variables, including stress level, stress state, cy­ of these three is not present, fatigue cracking will clic wave form, fatigue environment, and the not initiate and propagate. The cyclic stress metallurgical condition of the material. Small starts the crack; the tensile stress produces crack changes in the specimen or test conditions can growth (propagation). Although compressive significantly affect fatigue behavior, making ana­ stress will not cause fatigue, compression load lytical prediction of fatigue life difficult. There­ may do so. fore, the designer may rely on experience with The process of fatigue consists of three stages: similar components in service rather than on • Initial fatigue damage leading to crack nu­ laboratory evaluation of mechanical test speci­ cleation and crack initiation mens. Laboratory tests, however, are essential in • Progressive cyclic growth of a crack (crack understanding fatigue behavior, and current propagation) until the remaining uncracked studies with fracture mechanics test specimens cross section of a part becomes too weak to are beginning to provide satisfactory design sustain the loads imposed criteria. • Final, sudden fracture of the remaining Laboratory fatigue tests can be classified as cross section crack initiation or crack propagation. In crack initiation testing, specimens or parts are sub­ Fatigue cracking normally results from cyclic jected to the number of stress cycles required for stresses that are well below the static yield a fatigue crack to initiate and to subsequently strength of the material. (In low-cycle fatigue, grow large enough to produce failure. however, or if the material has an appreciable In crack propagation testing, fracture mechan­ work-hardening rate, the stresses also may be ics methods are used to determine the crack above the static yield strength.) growth rates of preexisting cracks under cyclic Fatigue cracks initiate and propagate in re­ loading. Fatigue crack propagation may be gions where the strain is most severe. Because caused by cyclic stresses in a benign environ­ most engineering materials contain defects and ment, or by the combined effects of cyclic stresses thus regions of stress concentration that intensify and an aggressive environment (corrosion fa­ strain, most fatigue cracks initiate and grow tigue). from structural defects. Under the action of cy­ clic loading, a plastic zone (or region of deforma­ tion) develops at the defect tip. This zone of high Fatigue Crack Initiation deformation becomes an initiation site for a fa­ Most laboratory fatigue testing is done either tigue crack. The crack propagates under the ap­ with axial loading, or in bending, thus producing plied stress through the material until complete only tensile and compressive stresses. The stress fracture results. On the microscopic scale, the usually is cycled either between a maximum and most important feature of the fatigue process is a minimum tensile stress, or between a maximum nucleation of one or more cracks under the influ- tensile stress and a maximum compressive stress. 2 Fatigue Testing 1100 The latter is considered a negative tensile stress, 1 150 is given an algebraic minus sign, and therefore is 1000 2340 ~teel known as the minimum stress. o"i:, 48 HAC The stress ratio is the algebraic ratio of two 900 (unnoto;hed)- "-"' 'b.. 125 ·~ specified stress values in a stress cycle. Two :;: BOO "F attgue---:- - T--: tmtt s, "" commonly used stress ratios are the ratio, A, of --' VJ" VJ" the alternating stress amplitude to the mean 700 234~lsteel ~ 100 ID 48 HAC _ ID stress (A= S"/ S ml and the ratio, R, of the min­ "C 600 '\.. "C '),. (notched) -~ imum stress to the maximum stress (R = Smin/ ~ 500 "' 75 c. ~- . ,__ .. c. Smax). E Fattgue It mit, s, t-• E If the stresses are fully reversed, the stress ratio 400 "'00 1 "'00 R becomes -I; if the stresses are partially re­ 00 Aluminum alloy 50 00 ~ 300 --,; 1?. versed, Rbecomes a negative number less than 1. iii ~7075-TS iii 200 If the stress is cycled between a maximum stress 25 and no load, the stress ratio R becomes zero. If 100 ~ Stress ratio (R) = - 1 the stress is cycled between two tensile stresses, 0 - 0 the stress ratio R becomes a positive number less 10 6 107 10' than 1. A stress ratio R of 1 indicates no variation in stress, making the test a sustained-load creep Number of cycles to fracture, N test rather than a fatigue test. Fig. 2 Typical S-N curves for constant Applied stresses are described by three pa­ amplitude and sinusoidal loading rameters. The mean stress, S m• is the algebraic average of the maximum and minimum stresses ing plot of the data is an S-N curve. Three typical in one cycle, Sm= (Smax+ Smin)/2. In the com­ S-N curves are shown in Fig. 2. pletely reversed cycle test, the mean stress is zero. The number of cycles of stress that a metal can The range of stress, S, is the algebraic difference endure before failure increases with decreasing between the maximum and minimum stresses in stress. For some engineering materials such as one cycle, Sr = S max- S min· The stress amplitude, steel (see Fig. 2) and titanium, the S-N curve be­ S" is one half the range of stress, S" = S ,/ 2 = comes horizontal at a certain limiting stress. (Sm.,- Sm;.)/2. Below this limiting stress, known as the fatigue During a fatigue test, the stress cycle usually is limit or endurance limit, the material can endure maintained constant so that the applied stress an infinite number of cycles without failure. conditions can be written Sm ± S a• where Sm is the Fatigue Limit and Fatigue Strength. The hor­ static or mean stress, and Sa is the alternating izontal portion of an S-N curve represents the stress, which is equal to half the stress range. maximum stress that the metal can withstand for Nomenclature to describe test parameters in­ an infinitely large number of cycles with 50% volved in cyclic stress testing are shown in Fig. 1. probability of failure and is known as the fatigue (endurance) limit, Sp Most nonferrous metals do not exhibit a fatigue limit. Instead, their S-N curves continue to drop at a slow rate at high numbers of cycles, as shown by the curve for aluminum alloy 7075-T6 in Fig. 2. For these types of metals, fatigue strength rather than fatigue limit is reported, which is the stress to which the metal can be subjected for a specified number of cycles. Because there is no Fig. 1 Nomenclature to describe test standard number of cycles, each table offatigue parameters involved in cyclic stress testing strengths must specify the number of cycles for which the strengths are reported. The fatigue 8 S-N Curves. The results of fatigue crack initia­ strength of nonferrous metals at I 00 million ( 10 ) 8 tion tests usually are plotted as maximum stress, or 500 million (5 X 10 ) cycles is erroneously minimum stress, or stress amplitude to number called the fatigue limit. of cycles, N, to failure using a logarithmic scale Low-Cycle Fatigue. For the low-cycle fatigue for the number of cycles. Stress is plotted on region (N < 104 cycles) tests are conducted with either a linear or a logarithmic scale. The result- controlled cycles of elastic plus plastic strain, Introduction 3 rather than with controlled load or stress cycles. Under controlled strain testing, fatigue life be­ havior is represented by a log-log plot of the total strain range, .6.e 1 versus the number of cycles to ~ 10 -l 1-----l-~" fiihue (Fig. 3). c The total strain range is separated into elastic ~ and plastic components. For many metals and alloys, the elastic strain range, A<, is equal to the stress range divided by the modulus of elasticity. The plastic strain range, A< P' is the difference be­ tween the total strain range and the elastic strain range. Stress-Concentration Factor. Stress is concen­ trated in a metal by structural discontinuities, Cycles to failure such as notches, holes, or scratches, which act as stress raisers. The stress-concentration factor, Fig. 3 Typical plot of strain range versus cycles-to-failure for low-cycle fatigue , K 1 is the ratio of the area test stress in the region oft he notch (or other stress concentrators) to the cling of notched specimens that have been pre­ corresponding nominal stress. For determina­ cracked in fatigue. Crack length is measured as a , tion of K 1 the greatest stress in the region of the function of elapsed cycles, and these data are notch is calculated from the theory of elasticity, subjected to numerical analysis to establish the or equivalent values are derived experimentally. rate of crack growth, da/ dN The fatigue notch factor, Kp is the ratio of the Crack growth rates are expressed as a function fatigue strength of a smooth (unnotched) speci­ of the crack tip stress-intensity factor range, AK.