Fatigue - ASM International

Name ///sr-nova/Dclabs wip/Metallurgy/5224 243-264.pdf/Chap 14/2/6/2008 9:57AM Plate # 0 2008 ASM International. All Rights Reserved.Elements of Metallurgy and Engineering Alloys (#05224G)pg 243www.asminternational.orgCHAPTER 14FatigueFATIGUE FAILURES OCCUR due to theapplication of fluctuating stresses that are muchlower than the stress required to cause failureduring a single application of stress. It has beenestimated that fatigue contributes to approximately 90% of all mechanical service failures.Fatigue is a problem that can affect any part orcomponent that moves. Automobiles on roads,aircraft wings and fuselages, ships at sea, nuclear reactors, jet engines, and land-based turbines are all subject to fatigue failures. Fatiguewas initially recognized as a problem in the early1800s when investigators in Europe observedthat bridge and railroad components werecracking when subjected to repeated loading. Asthe century progressed and the use of metalsexpanded with the increasing use of machines,more and more failures of components subjectedto repeated loads were recorded. Today, structural fatigue has assumed an even greaterimportance as a result of the ever-increasing useof high-strength materials and the desire forhigher performance from these materials.of the data in the literature is for fully reversedbending with no mean stress applied on top of it.Another common stress cycle is the repeatedstress cycle, in which there is a mean stress (sm)applied on top of the maximum and minimum14.1 Stress CyclesThere are three basic factors necessary tocause fatigue: (1) a maximum tensile stress ofsufficiently high value, (2) a large enough variation or fluctuation in the applied stress, and (3)a sufficiently large number of cycles of theapplied stress. There are many types of fluctuating stresses. Several of the more commontypes encountered are shown in Fig. 14.1. Afully reversed stress cycle, shown in the topgraph of Fig. 14.1, where the maximum andminimum stresses are equal, is commonly usedin testing. This is the type of stress produced, forexample, by the R.R. Moore rotating-beamfatigue machine shown in Fig. 14.2, which issimilar to what a shaft may encounter duringservice. Since this was the original type ofmachine used to generate fatigue data, quite a bitFig. 14.1Typical loading cycles

Name ///sr-nova/Dclabs wip/Metallurgy/5224 243-264.pdf/Chap 14/2/6/2008 9:57AM Plate # 0 2008 ASM International. All Rights Reserved.Elements of Metallurgy and Engineering Alloys (#05224G)pg 244www.asminternational.org244 / Elements of Metallurgy and Engineering Alloysstresses. The middle graph in Fig. 14.1 shows thecondition where both stresses (cyclic and applied) are tensile (greater than zero), but it is alsopossible to test with both stresses in compression. In addition, the maximum and minimumstresses in the cycle do not necessarily have to beequal in value. The last type of loading cycle isthe random or irregular stress cycle, in which thepart is subjected to random loads during service,as shown in the bottom graph of Fig. 14.1.Although a majority of the fatigue data in theliterature is for fully reversed bending, there arealso axial test machines (Fig. 14.3) that arecapable of tension and compression loading inboth the high- and low-cycle fatigue ranges.These modern test frames are closed-loopservohydraulically controlled and can be programmed with almost any desired fatigue spectrum.A fluctuating stress is made up of two components: a mean or steady stress, sm, and analternating or variable stress, sa. The stressrange, sr, is the difference between the maximum and minimum stress in a cycle:sr smax 7smin(Eq 14.1)The alternating stress is one-half the stressrange:sa sr smax 7smin 22(Eq 14.2)The mean stress is the algebraic average of themaximum and minimum stress in the cycle:sm smax smin2Fig. 14.2(Eq 14.3)Two ratios frequently used in presentingfatigue data are:Stress ratioAmplitude ratioR sminsmaxA (Eq 14.4)sa17R sm 1 R(Eq 14.5)14.2 High-Cycle FatigueHigh-cycle fatigue involves a large number ofcycles (N4105 cycles) and an elasticallyapplied stress. High-cycle fatigue tests areusually carried out for 107 cycles and sometimes5 · 108 cycles for nonferrous metals. Althoughthe applied stress is low enough to be elastic,plastic deformation can take place at the cracktip. High-cycle fatigue data are usually presented as a plot of stress, S, versus the number ofcycles to failure, N. A log scale is used for thenumber of cycles. The value of stress, S, can bethe maximum stress, smax, the minimum stress,smin, or the stress amplitude, sa. The S-N relationship is usually determined for a specifiedvalue of the mean stress, sm, or one of the tworatios, R or A.The fatigue life is the number of cycles tofailure at a specified stress level, while the fatigue strength (also referred to as the endurancelimit) is the stress below which failure does notoccur. As the applied stress level is decreased,the number of cycles to failure increases.Normally, the fatigue strength increases as thestatic tensile strength increases. For example,Schematic of R.R. Moore reversed-bending fatigue machine. Source: Ref 1

Name ///sr-nova/Dclabs wip/Metallurgy/5224 243-264.pdf/Chap 14/ 2008 ASM International. All Rights Reserved.Elements of Metallurgy and Engineering Alloys (#05224G)2/6/2008 9:57AM Plate # 0pg 245www.asminternational.orgChapter 14: Fatigue / 245high-strength steels heat treated to over1400 MPa (200 ksi) yield strengths have muchhigher fatigue strengths than aluminum alloyswith 480 MPa (70 ksi) yield strengths. A comparison of the S-N curves for steel and aluminumis shown in Fig. 14.4. Note that steel not only hasa higher fatigue strength than aluminum, but italso has an endurance limit. Below a certainstress level, the steel alloy will never fail dueto cyclic loading alone. On the other hand,aluminum does not have a true endurance limit.It will always fail if tested to a sufficient numberof cycles. Therefore, the fatigue strength ofaluminum is usually reported as the stress level itcan survive at a large total number of cycles,usually 5 · 108 cycles. It should be noted thatthere is a considerable amount of scatter infatigue test results. It is therefore important totest a sufficient number of specimens to obtainstatistically meaningful results.For a large number of steels, there is a directcorrelation between tensile strength and fatiguestrength; higher-tensile-strength steels havehigher endurance limits. The endurance limit isnormally in the range of 0.35 to 0.60 of thetensile strength. This relationship holds upto a hardness of approximately 40 HRC( 1200 MPa, or 180 ksi tensile strength), andthen the scatter becomes too great to be reliable(Fig. 14.5). This does not necessarily mean it iswise to use as high a strength steel as possibleto maximize fatigue life because, as the tensilestrength increases, the fracture toughness decreases and the environmental sensitivityincreases. The endurance limit of high-strengthsteels is extremely sensitive to surfacecondition, residual-stress state, and the presenceof inclusions that act as stress concentrations.Fatigue cracking can occur quite early in theservice life of the component by the formation ofa small crack, generally at some point on theexternal surface. The crack then propagatesslowly through the material in a directionroughly perpendicular to the main tensile axis(Fig. 14.6). Ultimately, the cross-sectional areaof the member is reduced to the point that it canno longer carry the load, and the member fails intension. The fracture surface of a fatigued highstrength part is shown in Fig. 14.7. The portionof the fracture surface due to fatigue crackgrowth and the portion finally cracked due tooverload are clearly evident.As previously mentioned, much of the fatiguedata in the literature has been determined forcompletely reversed bending with sm 0. However, the effects of mean stress are important,Alignment fixtureLoad cellHeating coilAssemblyTop gripHeat shieldSpecimenExtensometerBottom gripFig. 14.3Modern fatigue test frame

Name ///sr-nova/Dclabs wip/Metallurgy/5224 243-264.pdf/Chap 14/2/6/2008 9:57AM Plate # 0 2008 ASM International. All Rights Reserved.Elements of Metallurgy and Engineering Alloys (#05224G)pg 246www.asminternational.org246 / Elements of Metallurgy and Engineering Alloysand an increase in mean stress will always causea reduction in the fatigue life (Fig. 14.8). Anumber of mathematical models have beendeveloped that allow the effects of mean stresson stress amplitude to be predicted from fullyreversed-bending data. Goodman developed alinear model, while Gerber used a parabolicmodel (Fig. 14.9). Test data for ductile metalsEnduranceLimit1045 Steel60400300No EnduranceLimit200402024-T6 Al205001000103104105106107108Stress Amplitude (MPa)Stress Amplitude (ksi)800109 1010Number of CyclesFig. 14.4Comparison of steel and aluminum fatigue behavior. Source: Ref 2usually fall closer to the Gerber parabolic curve;however, because of the scatter in fatigue dataand the fact that notched data fall closer to theGoodman line, the more conservative Goodmanrelationship is often used in practice. If thecomponent design is based on yield rather thanultimate strength, as most are, then the evenmore conservative Soderberg relationship canbe used. Mathematically, the three relationshipscan be expressed by: x smsa se 17su(Eq 14.6)where x 1 for the Goodman line, x 2 for theGerber curve, su sy for the Soderberg curve,and se is the fatigue limit for completelyreversed bending.14.3 Low-Cycle FatigueDuring cyclic loading within the elasticregime, stress and strain are directly relatedthrough the elastic modulus. However, for cyclic140130900All test results fromone laboratoryAll specimens 0 to 2micro-in. finish1201107001009060080Quenched and tempered 8640405343409262705006020Fig. 14.5253035504045Rockwell C hardnessEndurance limit versus hardness for steels. Source: Ref 355606570400Fatigue limit, (MPa)Fatigue limit, (ksi)800

Name ///sr-nova/Dclabs wip/Metallurgy/5224 243-264.pdf/Chap 14/2/6/2008 9:57AM Plate # 0 2008 ASM International. All Rights Reserved.Elements of Metallurgy and Engineering Alloys (#05224G)pg 247www.asminternational.orgChapter 14: Fatigue / 247loading that produces plastic strains, the responses are more complex and form a hysteresisloop (Fig. 14.10). From point O up to point A,the component is in tension. On unloading,the strain response of the specimen followsthe curve from A to D. At D, the componentis under no stress. As the component is subjectedto compressive stress, the strain responsefollows the curve from D to B. Releasing thecompressive stress from B and reapplyingtensile stress, the component stress-strain condition returns to point A along the curve defined by B, C, and A. Points A and B represent thecyclic stress and strain limits. The total strain,NucleationDe, consists of both elastic and plastic components:De Dee Depwhere Dee is the elastic strain and Dee Ds/E,and Dep is the plastic strain and Dep is the widthof the loop at its center, that is, the distance CDin Fig. 14.10. The area of the hysteresis loop isequal to the work done or the energy loss percycle.In cyclic strain-controlled fatigue, the strainamplitude is held constant during cycling.Since plastic deformation is not completelyCrack GrowthFig. 14.6Typical propagation of a fatigue crack. Source: Ref 4Fig. 14.7Fatigue crack growth in a high-strength steel part(Eq 14.7)Final Failure