20 Budynas-Nisbett:Shigley's ll.Failure Prevention 6.Fatigue Failure Resulting ©The McGraw-Hfl Mechanical Engineering from Variable Loading Companies,2008 Design,Eighth Edition Fatigue Failure Resulting from Variable Loading Chapter Outline 6-1 Introduction to Fatigue in Metals 258 6-2 Approach to Fatigue Failure in Analysis and Design 264 6-3 Fatigue-Life Methods 265 6-4 The Stress-Life Method 265 6-5 The Strain-Life Method 268 6-6 The Linear-Elastic Fracture Mechanics Method 270 6-7 The Endurance Limit 274 6-8 Fatigue Strength 275 6-9 Endurance Limit Modifying Factors 278 6-10 Stress Concentration and Notch Sensitivity 287 6-11 Characterizing Fluctuating Stresses 292 6-12 Fatigue Failure Criteria for Fluctuating Stress 295 6-13 Torsional Fatigue Strength under Fluctuating Stresses 309 6-14 Combinations of Loading Modes 309 6-15 Varying,Fluctuating Stresses;Cumulative Fatigue Damage 313 6-16 Surface Fatigue Strength 319 6-17 Stochastic Analysis 322 6-18 Road Maps and Important Design Equations for the Stress-Life Method 336 257
Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition II. Failure Prevention 6. Fatigue Failure Resulting from Variable Loading 260 © The McGraw−Hill Companies, 2008 6Fatigue Failure Resulting from Variable Loading Chapter Outline 6–1 Introduction to Fatigue in Metals 258 6–2 Approach to Fatigue Failure in Analysis and Design 264 6–3 Fatigue-Life Methods 265 6–4 The Stress-Life Method 265 6–5 The Strain-Life Method 268 6–6 The Linear-Elastic Fracture Mechanics Method 270 6–7 The Endurance Limit 274 6–8 Fatigue Strength 275 6–9 Endurance Limit Modifying Factors 278 6–10 Stress Concentration and Notch Sensitivity 287 6–11 Characterizing Fluctuating Stresses 292 6–12 Fatigue Failure Criteria for Fluctuating Stress 295 6–13 Torsional Fatigue Strength under Fluctuating Stresses 309 6–14 Combinations of Loading Modes 309 6–15 Varying, Fluctuating Stresses; Cumulative Fatigue Damage 313 6–16 Surface Fatigue Strength 319 6–17 Stochastic Analysis 322 6–18 Road Maps and Important Design Equations for the Stress-Life Method 336 257
Budynas-Nisbett:Shigley's ll.Failure Prevention 6.Fatigue Failure Resulting T©The McGraw-Hill 261 Mechanical Engineering from Variable Loading Companies,2008 Design,Eighth Edition 258 Mechanical Engineering Design In Chap.5 we considered the analysis and design of parts subjected to static loading. The behavior of machine parts is entirely different when they are subjected to time- varying loading.In this chapter we shall examine how parts fail under variable loading and how to proportion them to successfully resist such conditions. 6-1 Introduction to Fatigue in Metals In most testing of those properties of materials that relate to the stress-strain diagram, the load is applied gradually,to give sufficient time for the strain to fully develop. Furthermore,the specimen is tested to destruction,and so the stresses are applied only once.Testing of this kind is applicable,to what are known as static conditions;such conditions closely approximate the actual conditions to which many structural and machine members are subjected. The condition frequently arises,however,in which the stresses vary with time or they fluctuate between different levels.For example,a particular fiber on the surface of a rotating shaft subjected to the action of bending loads undergoes both tension and com- pression for each revolution of the shaft.If the shaft is part of an electric motor rotating at 1725 rev/min,the fiber is stressed in tension and compression 1725 times each minute. If,in addition,the shaft is also axially loaded (as it would be,for example.by a helical or worm gear),an axial component of stress is superposed upon the bending component. In this case,some stress is always present in any one fiber,but now the level of stress is fluctuating.These and other kinds of loading occurring in machine members produce stresses that are called variable,repeated,alternating,or fluctuating stresses. Often,machine members are found to have failed under the action of repeated or fluctuating stresses;yet the most careful analysis reveals that the actual maximum stresses were well below the ultimate strength of the material,and quite frequently even below the yield strength.The most distinguishing characteristic of these failures is that the stresses have been repeated a very large number of times.Hence the failure is called a fatigue failure. When machine parts fail statically,they usually develop a very large deflection, because the stress has exceeded the yield strength,and the part is replaced before fracture actually occurs.Thus many static failures give visible warning in advance.But a fatigue failure gives no warning!It is sudden and total,and hence dangerous.It is relatively sim- ple to design against a static failure,because our knowledge is comprehensive.Fatigue is a much more complicated phenomenon,only partially understood,and the engineer seek- ing competence must acquire as much knowledge of the subject as possible. A fatigue failure has an appearance similar to a brittle fracture,as the fracture sur- faces are flat and perpendicular to the stress axis with the absence of necking.The frac- ture features of a fatigue failure,however,are quite different from a static brittle fracture arising from three stages of development.Stage is the initiation of one or more micro- cracks due to cyclic plastic deformation followed by crystallographic propagation extending from two to five grains about the origin.Stage I cracks are not normally dis- cernible to the naked eye.Stage /progresses from microcracks to macrocracks forming parallel plateau-like fracture surfaces separated by longitudinal ridges.The plateaus are generally smooth and normal to the direction of maximum tensile stress.These surfaces can be wavy dark and light bands referred to as beach marks or clamshell marks,as seen in Fig.6-1.During cyclic loading,these cracked surfaces open and close,rubbing together,and the beach mark appearance depends on the changes in the level or fre- quency of loading and the corrosive nature of the environment.Stage l//occurs during the final stress cycle when the remaining material cannot support the loads,resulting in
Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition II. Failure Prevention 6. Fatigue Failure Resulting from Variable Loading © The McGraw−Hill 261 Companies, 2008 258 Mechanical Engineering Design In Chap. 5 we considered the analysis and design of parts subjected to static loading. The behavior of machine parts is entirely different when they are subjected to timevarying loading. In this chapter we shall examine how parts fail under variable loading and how to proportion them to successfully resist such conditions. 6–1 Introduction to Fatigue in Metals In most testing of those properties of materials that relate to the stress-strain diagram, the load is applied gradually, to give sufficient time for the strain to fully develop. Furthermore, the specimen is tested to destruction, and so the stresses are applied only once. Testing of this kind is applicable, to what are known as static conditions; such conditions closely approximate the actual conditions to which many structural and machine members are subjected. The condition frequently arises, however, in which the stresses vary with time or they fluctuate between different levels. For example, a particular fiber on the surface of a rotating shaft subjected to the action of bending loads undergoes both tension and compression for each revolution of the shaft. If the shaft is part of an electric motor rotating at 1725 rev/min, the fiber is stressed in tension and compression 1725 times each minute. If, in addition, the shaft is also axially loaded (as it would be, for example, by a helical or worm gear), an axial component of stress is superposed upon the bending component. In this case, some stress is always present in any one fiber, but now the level of stress is fluctuating. These and other kinds of loading occurring in machine members produce stresses that are called variable, repeated, alternating, or fluctuating stresses. Often, machine members are found to have failed under the action of repeated or fluctuating stresses; yet the most careful analysis reveals that the actual maximum stresses were well below the ultimate strength of the material, and quite frequently even below the yield strength. The most distinguishing characteristic of these failures is that the stresses have been repeated a very large number of times. Hence the failure is called a fatigue failure. When machine parts fail statically, they usually develop a very large deflection, because the stress has exceeded the yield strength, and the part is replaced before fracture actually occurs. Thus many static failures give visible warning in advance. But a fatigue failure gives no warning! It is sudden and total, and hence dangerous. It is relatively simple to design against a static failure, because our knowledge is comprehensive. Fatigue is a much more complicated phenomenon, only partially understood, and the engineer seeking competence must acquire as much knowledge of the subject as possible. A fatigue failure has an appearance similar to a brittle fracture, as the fracture surfaces are flat and perpendicular to the stress axis with the absence of necking. The fracture features of a fatigue failure, however, are quite different from a static brittle fracture arising from three stages of development. Stage I is the initiation of one or more microcracks due to cyclic plastic deformation followed by crystallographic propagation extending from two to five grains about the origin. Stage I cracks are not normally discernible to the naked eye. Stage II progresses from microcracks to macrocracks forming parallel plateau-like fracture surfaces separated by longitudinal ridges. The plateaus are generally smooth and normal to the direction of maximum tensile stress. These surfaces can be wavy dark and light bands referred to as beach marks or clamshell marks, as seen in Fig. 6–1. During cyclic loading, these cracked surfaces open and close, rubbing together, and the beach mark appearance depends on the changes in the level or frequency of loading and the corrosive nature of the environment. Stage III occurs during the final stress cycle when the remaining material cannot support the loads, resulting in
252 Budynas-Nisbett:Shigley's ll.Failure Prevention 6.Fatigue Failure Resulting ©The McGraw-Hill Mechanical Engineering from Variable Loading Companies,2008 Design,Eighth Edition Fatigue Failure Resulting from Variable Loading 259 Figure 6-1 Fatigue failure of a bolt due to repeated unidirectional bending.The failure started at the thread root at A, propagated across most of the cross section shown by the beach marks at B,before final fast fracture at C.(From ASM Handbook,Vol.12: Fractography,ASM Inter national,Materials Park,OH 440730002,fig50,p.120 Reprinted by permission of ASM Intemational www.asminternational.org.) a sudden,fast fracture.A stage IlI fracture can be brittle,ductile,or a combination of both.Quite often the beach marks,if they exist,and possible patterns in the stage IlI frac- ture called chevron lines,point toward the origins of the initial cracks. There is a good deal to be learned from the fracture patterns of a fatigue failure.! Figure 6-2 shows representations of failure surfaces of various part geometries under differing load conditions and levels of stress concentration.Note that,in the case of rotational bending,even the direction of rotation influences the failure pattern. Fatigue failure is due to crack formation and propagation.A fatigue crack will typ- ically initiate at a discontinuity in the material where the cyclic stress is a maximum. Discontinuities can arise because of: Design of rapid changes in cross section,keyways,holes,etc.where stress concen- trations occur as discussed in Secs.3-13 and 5-2. Elements that roll and/or slide against each other (bearings,gears,cams,etc.)under high contact pressure,developing concentrated subsurface contact stresses(Sec.3-19) that can cause surface pitting or spalling after many cycles of the load. Carelessness in locations of stamp marks,tool marks,scratches,and burrs;poor joint design;improper assembly;and other fabrication faults. .Composition of the material itself as processed by rolling,forging.casting,extrusion, drawing,heat treatment,etc.Microscopic and submicroscopic surface and subsurface discontinuities arise,such as inclusions of foreign material,alloy segregation,voids, hard precipitated particles,and crystal discontinuities. Various conditions that can accelerate crack initiation include residual tensile stresses, elevated temperatures,temperature cycling,a corrosive environment,and high-frequency cycling. The rate and direction of fatigue crack propagation is primarily controlled by local- ized stresses and by the structure of the material at the crack.However,as with crack formation,other factors may exert a significant influence,such as environment,tem- perature,and frequency.As stated earlier,cracks will grow along planes normal to the See the ASM Handbook,Fractograp/ry.ASM International.Metals Park,Ohio,vol.12,9th ed.,1987
Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition II. Failure Prevention 6. Fatigue Failure Resulting from Variable Loading 262 © The McGraw−Hill Companies, 2008 Fatigue Failure Resulting from Variable Loading 259 Figure 6–1 Fatigue failure of a bolt due to repeated unidirectional bending. The failure started at the thread root at A, propagated across most of the cross section shown by the beach marks at B, before final fast fracture at C. (From ASM Handbook, Vol. 12: Fractography, ASM International, Materials Park, OH 44073-0002, fig 50, p. 120. Reprinted by permission of ASM International ®, www.asminternational.org.) 1 See the ASM Handbook, Fractography, ASM International, Metals Park, Ohio, vol. 12, 9th ed., 1987. a sudden, fast fracture. A stage III fracture can be brittle, ductile, or a combination of both. Quite often the beach marks, if they exist, and possible patterns in the stage III fracture called chevron lines, point toward the origins of the initial cracks. There is a good deal to be learned from the fracture patterns of a fatigue failure.1 Figure 6–2 shows representations of failure surfaces of various part geometries under differing load conditions and levels of stress concentration. Note that, in the case of rotational bending, even the direction of rotation influences the failure pattern. Fatigue failure is due to crack formation and propagation. A fatigue crack will typically initiate at a discontinuity in the material where the cyclic stress is a maximum. Discontinuities can arise because of: • Design of rapid changes in cross section, keyways, holes, etc. where stress concentrations occur as discussed in Secs. 3–13 and 5–2. • Elements that roll and/or slide against each other (bearings, gears, cams, etc.) under high contact pressure, developing concentrated subsurface contact stresses (Sec. 3–19) that can cause surface pitting or spalling after many cycles of the load. • Carelessness in locations of stamp marks, tool marks, scratches, and burrs; poor joint design; improper assembly; and other fabrication faults. • Composition of the material itself as processed by rolling, forging, casting, extrusion, drawing, heat treatment, etc. Microscopic and submicroscopic surface and subsurface discontinuities arise, such as inclusions of foreign material, alloy segregation, voids, hard precipitated particles, and crystal discontinuities. Various conditions that can accelerate crack initiation include residual tensile stresses, elevated temperatures, temperature cycling, a corrosive environment, and high-frequency cycling. The rate and direction of fatigue crack propagation is primarily controlled by localized stresses and by the structure of the material at the crack. However, as with crack formation, other factors may exert a significant influence, such as environment, temperature, and frequency. As stated earlier, cracks will grow along planes normal to the
Budynas-Nisbett:Shigley's ll.Failure Prevention 6.Fatigue Failure Resulting T©The McGraw-Hil 23 Mechanical Engineering from Variable Loading Companies,2008 Design,Eighth Edition 260 Mechanical Engineering Design Figure 6-2 High nominol stress Low nominal stress Mild s Schematics of fatigue fracture surfaces produced in smooth 人 and notched components with round and rectangular cross 3274717288 赶只：0 88 sections under various loading t conditions and nominal stress levels.(From ASM Handbook Vol.11:Failure Analysis and Prevention,ASM Infemational, Materials Park,OH 440730002,fg18,p.111 Reprinted by permission of ASM Intemational www.asmintemational.org.) Tension-tension or tension-compression Reversed bending Rotational bending 带 Fast-fracture zone
Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition II. Failure Prevention 6. Fatigue Failure Resulting from Variable Loading © The McGraw−Hill 263 Companies, 2008 260 Mechanical Engineering Design Figure 6–2 Schematics of fatigue fracture surfaces produced in smooth and notched components with round and rectangular cross sections under various loading conditions and nominal stress levels. (From ASM Handbook, Vol. 11: Failure Analysis and Prevention, ASM International, Materials Park, OH 44073-0002, fig 18, p. 111. Reprinted by permission of ASM International ®, www.asminternational.org.)
Budynas-Nisbett:Shigley's Il.Failure Prevention 6.Fatigue Failure Resulting ©The McGraw-Hill Mechanical Engineering from Variable Loading Companies,2008 Design,Eighth Edition Fatigue Failure Resulting from Variable Loading 261 maximum tensile stresses.The crack growth process can be explained by fracture mechanics (see Sec.6-6). A major reference source in the study of fatigue failure is the 21-volume ASM Metals Handbook.Figures 6-1 to 6-8,reproduced with permission from ASM International,are but a minuscule sample of examples of fatigue failures for a great variety of conditions included in the handbook.Comparing Fig.6-3 with Fig.6-2,we see that failure occurred by rotating bending stresses,with the direction of rotation being clockwise with respect to the view and with a mild stress concentration and low nominal stress. Figure 6-3 Fatigue fracture of an AlSl 4320 drive shaft.The fatigue failure initiated at the end of the keyway at points B and progressed to final rupture at C.The final rupture zone is small,indicating that loads were low.(From ASM Handbook,Vol.11:Failure Analysis and Prevention,ASM International,Materials Park. OH440730002,fig18, p.111.Reprinted by permission of ASM International www.asminternational.org.) Figure 6-4 Fatigue fracture surface of an AISI 8640 pin.Sharp corners of the mismatched grease holes provided stress concentrations that initiated two fatigue cracks indicated by the arrows.(From ASM Handbook,Vol.12: Fractography,ASM International,Materials Park, OH440730002,fig520, p.331.Reprinted by permission of ASM International www.asminternational.org.]
Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition II. Failure Prevention 6. Fatigue Failure Resulting from Variable Loading 264 © The McGraw−Hill Companies, 2008 Fatigue Failure Resulting from Variable Loading 261 Figure 6–3 Fatigue fracture of an AISI 4320 drive shaft. The fatigue failure initiated at the end of the keyway at points B and progressed to final rupture at C. The final rupture zone is small, indicating that loads were low. (From ASM Handbook, Vol. 11: Failure Analysis and Prevention, ASM International, Materials Park, OH 44073-0002, fig 18, p. 111. Reprinted by permission of ASM International ®, www.asminternational.org.) Figure 6–4 Fatigue fracture surface of an AISI 8640 pin. Sharp corners of the mismatched grease holes provided stress concentrations that initiated two fatigue cracks indicated by the arrows. (From ASM Handbook, Vol. 12: Fractography, ASM International, Materials Park, OH 44073-0002, fig 520, p. 331. Reprinted by permission of ASM International ®, www.asminternational.org.) maximum tensile stresses. The crack growth process can be explained by fracture mechanics (see Sec. 6–6). A major reference source in the study of fatigue failure is the 21-volume ASM Metals Handbook. Figures 6–1 to 6–8, reproduced with permission from ASM International, are but a minuscule sample of examples of fatigue failures for a great variety of conditions included in the handbook. Comparing Fig. 6–3 with Fig. 6–2, we see that failure occurred by rotating bending stresses, with the direction of rotation being clockwise with respect to the view and with a mild stress concentration and low nominal stress