上海交通大学：《Design and Manufacturing》课程教学资源（参考文献）Shigley's Mechanical Engineering Design ch6 fatigue failures resulting from variable loading

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 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 I 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 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 fre￾quency 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 Inter￾national, 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 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.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 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

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

Budynas-Nisbett:Shigley's ll.Failure Prevention 6.Fatigue Failure Resulting T©The McGraw-Hil 265 Mechanical Engineering from Variable Loading Companies,2008 Design,Eighth Edition 262 Mechanical Engineering Design Figure 6-5 Fatique fracture surface of a forged connecting rod of AlSI 8640 steel.The fatigue crack origin is at the left edge,at the flash line of the forging,but no unusual roughness of the flash trim was indicated.The fatigue crack progressed halfway around the oil hole at the left,indicated by the beach marks,before final fast racture occurred.Note the pronounced shear lip in the final fracture at the right edge. (From ASM Handbook, Vol.12:Fractography,ASM International,Materials Park, OH440730002,fig523, p.332.Reprinted by permission of ASM International www.asminterational.org.) Figure 6-6 Fatigue fracture surface of a 200-mm (8-in)diameter piston rod of an alloy steel steam hammer used for forging.This is an example ofa fatigue fracture caused by pure tension where surfoce stress concentrations are absent and a crack may initiate anywhere in the cross section.In this instance,the initial crack formed at a forging flake slightly below center,grew outward symmetrically,and ultimately produced a brittle fracture without warning. (From ASM Handbook,Vol.12:Fractography,ASM Interational,Materials Park,OH 44073-0002,fig 570,p.342.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 © The McGraw−Hill 265 Companies, 2008 262 Mechanical Engineering Design Figure 6–5 Fatigue fracture surface of a forged connecting rod of AISI 8640 steel. The fatigue crack origin is at the left edge, at the flash line of the forging, but no unusual roughness of the flash trim was indicated. The fatigue crack progressed halfway around the oil hole at the left, indicated by the beach marks, before final fast fracture occurred. Note the pronounced shear lip in the final fracture at the right edge. (From ASM Handbook, Vol. 12: Fractography, ASM International, Materials Park, OH 44073-0002, fig 523, p. 332. Reprinted by permission of ASM International ®, www.asminternational.org.) Figure 6–6 Fatigue fracture surface of a 200-mm (8-in) diameter piston rod of an alloy steel steam hammer used for forging. This is an example of a fatigue fracture caused by pure tension where surface stress concentrations are absent and a crack may initiate anywhere in the cross section. In this instance, the initial crack formed at a forging flake slightly below center, grew outward symmetrically, and ultimately produced a brittle fracture without warning. (From ASM Handbook, Vol. 12: Fractography, ASM International, Materials Park, OH 44073-0002, fig 570, p. 342. Reprinted by permission of ASM International ®, www.asminternational.org.)

26 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 263 Medium-carbon steel (ASTMA186) 30 dia Flange (1of2) Fracture (a)Coke- r wheel (c) Figure 6-7 Fatigue failure of an ASTMA186 steel double-flange trailer wheel caused by stamp marks.(a)Cokeoven car wheel showing position of stamp marks and fractures in the rib and web.(b)Stamp mark showing heavy impression and fracture extending along the base of the lower row of numbers.(c)Notches,indicated by arrows,created from the heavily indented stamp marks from which cracks initiated along the top at the fracture surface.(From ASM Handbook,Vol.1 1:Failure Analysis and Prevention,ASM International,Materials Park,OH 44073- 0002,fig 51,p.130.Reprinted by permission of ASM Intemational,www.asmintemational.org.) Figure 6-8 Aluminum alloy 7075-T73 .94 Rockwell B 85.5 Aluminum alloy 7075-T73 755 landing gear torquearm 10.200 assembly redesign to eliminate fatigue fracture at a lubrication hole.(a)Arm configuration, original and improved design [dimensions given in inches). Fracture b)Fracture surface where (1of2) arrows indicate multiple crack origins.(From ASM -Primary-fracture Handbook,Vol.11:Failure Lubrication hole surface Analysis and Prevention,ASM 1.750-in.-dia Lubrication hole International,Materials Park. 0.090-in.wall OH440730002,fig23, p.114.Reprinted by permission of ASM in International www.asminternationol.org.) 3.62 dia Secondary fracture Original design Improved design Detail A (a侧

Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition II. Failure Prevention 6. Fatigue Failure Resulting from Variable Loading 266 © The McGraw−Hill Companies, 2008 Fatigue Failure Resulting from Variable Loading 263 Figure 6–7 Fatigue failure of an ASTM A186 steel double-flange trailer wheel caused by stamp marks. (a) Coke-oven car wheel showing position of stamp marks and fractures in the rib and web. (b) Stamp mark showing heavy impression and fracture extending along the base of the lower row of numbers. (c) Notches, indicated by arrows, created from the heavily indented stamp marks from which cracks initiated along the top at the fracture surface. (From ASM Handbook, Vol. 11: Failure Analysis and Prevention, ASM International, Materials Park, OH 44073- 0002, fig 51, p. 130. Reprinted by permission of ASM International ®, www.asminternational.org.) Aluminum alloy 7075-T73 Rockwell B 85.5 Original design 10.200 A Lug (1 of 2) 25.5 4.94 Fracture 3.62 dia Secondary fracture 1.750-in.-dia bushing, 0.090-in. wall Primary-fracture Lubrication hole surface 1 in Lubrication hole Improved design Detail A (a) Figure 6–8 Aluminum alloy 7075-T73 landing-gear torque-arm assembly redesign to eliminate fatigue fracture at a lubrication hole. (a) Arm configuration, original and improved design (dimensions given in inches). (b) Fracture surface where arrows indicate multiple crack origins. (From ASM Handbook, Vol. 11: Failure Analysis and Prevention, ASM International, Materials Park, OH 44073-0002, fig 23, p. 114. Reprinted by permission of ASM International ®, www.asminternational.org.) Medium-carbon steel (ASTM A186) (a) Coke-oven-car wheel Web 30 dia Flange (1 of 2) Fracture Tread Fracture

Budynas-Nisbett:Shigley's ll.Failure Prevention 6.Fatigue Failure Resulting T©The McGraw-Hill 267 Mechanical Engineering from Variable Loading Companies,2008 Design,Eighth Edition 264 Mechanical Engineering Design 6-2 Approach to Fatigue Failure in Analysis and Design As noted in the previous section,there are a great many factors to be considered,even for very simple load cases.The methods of fatigue failure analysis represent a combi- nation of engineering and science.Often science fails to provide the complete answers that are needed.But the airplane must still be made to fly-safely.And the automobile must be manufactured with a reliability that will ensure a long and troublefree life and at the same time produce profits for the stockholders of the industry.Thus,while sci- ence has not yet completely explained the complete mechanism of fatigue,the engineer must still design things that will not fail.In a sense this is a classic example of the true meaning of engineering as contrasted with science.Engineers use science to solve their problems if the science is available.But available or not,the problem must be solved, and whatever form the solution takes under these conditions is called engineering. In this chapter,we will take a structured approach in the design against fatigue failure.As with static failure,we will attempt to relate to test results performed on sim- ply loaded specimens.However,because of the complex nature of fatigue,there is much more to account for.From this point,we will proceed methodically,and in stages. In an attempt to provide some insight as to what follows in this chapter,a brief descrip- tion of the remaining sections will be given here. Fatigue-Life Methods(Secs.6-3 to 6-6) Three major approaches used in design and analysis to predict when,if ever,a cyclically loaded machine component will fail in fatigue over a period of time are presented.The premises of each approach are quite different but each adds to our understanding of the mechanisms associated with fatigue.The application,advantages,and disadvantages of each method are indicated.Beyond Sec.6-6,only one of the methods,the stress-life method,will be pursued for further design applications Fatigue Strength and the Endurance Limit(Secs.6-7 and 6-8) The strength-life (S-N)diagram provides the fatigue strength S versus cycle life N of a material.The results are generated from tests using a simple loading of standard laboratory- controlled specimens.The loading often is that of sinusoidally reversing pure bending. The laboratory-controlled specimens are polished without geometric stress concentra- tion at the region of minimum area. For steel and iron,the S-N diagram becomes horizontal at some point.The strength at this point is called the endurance limit S and occurs somewhere between 106 and 107 cycles.The prime mark on S refers to the endurance limit of the controlled laboratory specimen.For nonferrous materials that do not exhibit an endurance limit,a fatigue strength at a specific number of cycles.S,may be given,where again,the prime denotes the fatigue strength of the laboratory-controlled specimen The strength data are based on many controlled conditions that will not be the same as that for an actual machine part.What follows are practices used to account for the differences between the loading and physical conditions of the specimen and the actual machine part. Endurance Limit Modifying Factors(Sec.6-9) Modifying factors are defined and used to account for differences between the speci- men and the actual machine part with regard to surface conditions,size,loading,tem- perature,reliability,and miscellaneous factors.Loading is still considered to be simple and reversing

Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition II. Failure Prevention 6. Fatigue Failure Resulting from Variable Loading © The McGraw−Hill 267 Companies, 2008 264 Mechanical Engineering Design 6–2 Approach to Fatigue Failure in Analysis and Design As noted in the previous section, there are a great many factors to be considered, even for very simple load cases. The methods of fatigue failure analysis represent a combi￾nation of engineering and science. Often science fails to provide the complete answers that are needed. But the airplane must still be made to fly—safely. And the automobile must be manufactured with a reliability that will ensure a long and troublefree life and at the same time produce profits for the stockholders of the industry. Thus, while sci￾ence has not yet completely explained the complete mechanism of fatigue, the engineer must still design things that will not fail. In a sense this is a classic example of the true meaning of engineering as contrasted with science. Engineers use science to solve their problems if the science is available. But available or not, the problem must be solved, and whatever form the solution takes under these conditions is called engineering. In this chapter, we will take a structured approach in the design against fatigue failure. As with static failure, we will attempt to relate to test results performed on sim￾ply loaded specimens. However, because of the complex nature of fatigue, there is much more to account for. From this point, we will proceed methodically, and in stages. In an attempt to provide some insight as to what follows in this chapter, a brief descrip￾tion of the remaining sections will be given here. Fatigue-Life Methods (Secs. 6–3 to 6–6) Three major approaches used in design and analysis to predict when, if ever, a cyclically loaded machine component will fail in fatigue over a period of time are presented. The premises of each approach are quite different but each adds to our understanding of the mechanisms associated with fatigue. The application, advantages, and disadvantages of each method are indicated. Beyond Sec. 6–6, only one of the methods, the stress-life method, will be pursued for further design applications. Fatigue Strength and the Endurance Limit (Secs. 6–7 and 6–8) The strength-life (S-N) diagram provides the fatigue strength Sf versus cycle life N of a material. The results are generated from tests using a simple loading of standard laboratory￾controlled specimens. The loading often is that of sinusoidally reversing pure bending. The laboratory-controlled specimens are polished without geometric stress concentra￾tion at the region of minimum area. For steel and iron, the S-N diagram becomes horizontal at some point. The strength at this point is called the endurance limit S e and occurs somewhere between 106 and 107 cycles. The prime mark on S e refers to the endurance limit of the controlled laboratory specimen. For nonferrous materials that do not exhibit an endurance limit, a fatigue strength at a specific number of cycles, S f , may be given, where again, the prime denotes the fatigue strength of the laboratory-controlled specimen. The strength data are based on many controlled conditions that will not be the same as that for an actual machine part. What follows are practices used to account for the differences between the loading and physical conditions of the specimen and the actual machine part. Endurance Limit Modifying Factors (Sec. 6–9) Modifying factors are defined and used to account for differences between the speci￾men and the actual machine part with regard to surface conditions, size, loading, tem￾perature, reliability, and miscellaneous factors. Loading is still considered to be simple and reversing.

258 Budynas-Nisbett:Shigley's ll.Failure Prevention 6.Fatigue Failure Resulting I©The McGraw-Hil Mechanical Engineering from Variable Loading Companies,2008 Design,Eighth Edition Fatigue Failure Resulting from Variable Loading 265 Stress Concentration and Notch Sensitivity(Sec.6-10) The actual part may have a geometric stress concentration by which the fatigue behav- ior depends on the static stress concentration factor and the component material's sensi- tivity to fatigue damage. Fluctuating Stresses (Secs.6-11 to 6-13) These sections account for simple stress states from fluctuating load conditions that are not purely sinusoidally reversing axial,bending,or torsional stresses. Combinations of Loading Modes(Sec.6-14) Here a procedure based on the distortion-energy theory is presented for analyzing com- bined fluctuating stress states,such as combined bending and torsion.Here it is assumed that the levels of the fluctuating stresses are in phase and not time varying. Varying,Fluctuating Stresses;Cumulative Fatigue Damage (Sec.6-15) The fluctuating stress levels on a machine part may be time varying.Methods are pro- vided to assess the fatigue damage on a cumulative basis. Remaining Sections The remaining three sections of the chapter pertain to the special topics of surface fatigue strength,stochastic analysis,and roadmaps with important equations. 6-3 Fatigue-Life Methods The three major fatigue life methods used in design and analysis are the stress-life method,the strain-life method,and the linear-elastic fracture mechanics method.These methods attempt to predict the life in number of cycles to failure,N,for a specific level of loading.Life of 1 sN103 cycles.The stress-life method, based on stress levels only,is the least accurate approach,especially for low-cycle applications.However,it is the most traditional method,since it is the easiest to imple- ment for a wide range of design applications,has ample supporting data,and represents high-cycle applications adequately. The strain-life method involves more detailed analysis of the plastic deformation at localized regions where the stresses and strains are considered for life estimates.This method is especially good for low-cycle fatigue applications.In applying this method, several idealizations must be compounded,and so some uncertainties will exist in the results.For this reason,it will be discussed only because of its value in adding to the understanding of the nature of fatigue. The fracture mechanics method assumes a crack is already present and detected.It is then employed to predict crack growth with respect to stress intensity.It is most prac- tical when applied to large structures in conjunction with computer codes and a peri- odic inspection program. 6-4 The Stress-Life Method To determine the strength of materials under the action of fatigue loads,specimens are subjected to repeated or varying forces of specified magnitudes while the cycles or stress reversals are counted to destruction.The most widely used fatigue-testing device

Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition II. Failure Prevention 6. Fatigue Failure Resulting from Variable Loading 268 © The McGraw−Hill Companies, 2008 Fatigue Failure Resulting from Variable Loading 265 Stress Concentration and Notch Sensitivity (Sec. 6–10) The actual part may have a geometric stress concentration by which the fatigue behav￾ior depends on the static stress concentration factor and the component material’s sensi￾tivity to fatigue damage. Fluctuating Stresses (Secs. 6–11 to 6–13) These sections account for simple stress states from fluctuating load conditions that are not purely sinusoidally reversing axial, bending, or torsional stresses. Combinations of Loading Modes (Sec. 6–14) Here a procedure based on the distortion-energy theory is presented for analyzing com￾bined fluctuating stress states, such as combined bending and torsion. Here it is assumed that the levels of the fluctuating stresses are in phase and not time varying. Varying, Fluctuating Stresses; Cumulative Fatigue Damage (Sec. 6–15) The fluctuating stress levels on a machine part may be time varying. Methods are pro￾vided to assess the fatigue damage on a cumulative basis. Remaining Sections The remaining three sections of the chapter pertain to the special topics of surface fatigue strength, stochastic analysis, and roadmaps with important equations. 6–3 Fatigue-Life Methods The three major fatigue life methods used in design and analysis are the stress-life method, the strain-life method, and the linear-elastic fracture mechanics method. These methods attempt to predict the life in number of cycles to failure, N, for a specific level of loading. Life of 1 ≤ N ≤ 103 cycles is generally classified as low-cycle fatigue, whereas high-cycle fatigue is considered to be N > 103 cycles. The stress-life method, based on stress levels only, is the least accurate approach, especially for low-cycle applications. However, it is the most traditional method, since it is the easiest to imple￾ment for a wide range of design applications, has ample supporting data, and represents high-cycle applications adequately. The strain-life method involves more detailed analysis of the plastic deformation at localized regions where the stresses and strains are considered for life estimates. This method is especially good for low-cycle fatigue applications. In applying this method, several idealizations must be compounded, and so some uncertainties will exist in the results. For this reason, it will be discussed only because of its value in adding to the understanding of the nature of fatigue. The fracture mechanics method assumes a crack is already present and detected. It is then employed to predict crack growth with respect to stress intensity. It is most prac￾tical when applied to large structures in conjunction with computer codes and a peri￾odic inspection program. 6–4 The Stress-Life Method To determine the strength of materials under the action of fatigue loads, specimens are subjected to repeated or varying forces of specified magnitudes while the cycles or stress reversals are counted to destruction. The most widely used fatigue-testing device

Budynas-Nisbett:Shigley's ll.Failure Prevention 6.Fatigue Failure Resulting ©The McGraw-Hil 269 Mechanical Engineering from Variable Loading Companies,2008 Design,Eighth Edition 266 Mechanical Engineering Design is the R.R.Moore high-speed rotating-beam machine.This machine subjects the specimen to pure bending (no transverse shear)by means of weights.The specimen,shown in Fig.6-9,is very carefully machined and polished,with a final polishing in an axial direction to avoid circumferential scratches.Other fatigue-testing machines are avail- able for applying fluctuating or reversed axial stresses,torsional stresses,or combined stresses to the test specimens. To establish the fatigue strength of a material,quite a number of tests are necessary because of the statistical nature of fatigue.For the rotating-beam test,a constant bend- ing load is applied,and the number of revolutions(stress reversals)of the beam required for failure is recorded.The first test is made at a stress that is somewhat under the ulti- mate strength of the material.The second test is made at a stress that is less than that used in the first.This process is continued,and the results are plotted as an S-N diagram (Fig.6-10).This chart may be plotted on semilog paper or on log-log paper.In the case of ferrous metals and alloys,the graph becomes horizontal after the material has been stressed for a certain number of cycles.Plotting on log paper emphasizes the bend in the curve,which might not be apparent if the results were plotted by using Cartesian coordinates. 3品n 0.30in 9in R. Figure 6-9 Test-specimen geometry for the R.R.Moore rotating beam machine.The bending moment is uniform over the curved at the higheststressed portion,a valid test of material,whereas a fracture elsewhere(not at the highes stress level)is grounds for suspicion of material flaw. Figure 6-10 -Low cycle .High cycle An SN diagram plotted from Finite life Infinite the results of completely life reversed axial fatigue tests. Material:UNS G41300 steel,normalized; 100 Sur =116 kpsi;maximum Sut =125 kpsi.(Data from NACA Tech.Note 3866, December 1966.] 50 10P 10 102 105 10105 10. 107 10 Number of stress cycles.N

Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition II. Failure Prevention 6. Fatigue Failure Resulting from Variable Loading © The McGraw−Hill 269 Companies, 2008 266 Mechanical Engineering Design 7 16 3 0.30 in in 9 in R. 7 8 Figure 6–9 Test-specimen geometry for the R. R. Moore rotating￾beam machine. The bending moment is uniform over the curved at the highest-stressed portion, a valid test of material, whereas a fracture elsewhere (not at the highest￾stress level) is grounds for suspicion of material flaw. 100 50 100 101 102 103 104 105 106 107 108 Number of stress cycles, N Se Sut Fatigue strength Sf , kpsi Low cycle High cycle Finite life Infinite life Figure 6–10 An S-N diagram plotted from the results of completely reversed axial fatigue tests. Material: UNS G41300 steel, normalized; Sut = 116 kpsi; maximum Sut = 125 kpsi. (Data from NACA Tech. Note 3866, December 1966.) is the R. R. Moore high-speed rotating-beam machine. This machine subjects the specimen to pure bending (no transverse shear) by means of weights. The specimen, shown in Fig. 6–9, is very carefully machined and polished, with a final polishing in an axial direction to avoid circumferential scratches. Other fatigue-testing machines are avail￾able for applying fluctuating or reversed axial stresses, torsional stresses, or combined stresses to the test specimens. To establish the fatigue strength of a material, quite a number of tests are necessary because of the statistical nature of fatigue. For the rotating-beam test, a constant bend￾ing load is applied, and the number of revolutions (stress reversals) of the beam required for failure is recorded. The first test is made at a stress that is somewhat under the ulti￾mate strength of the material. The second test is made at a stress that is less than that used in the first. This process is continued, and the results are plotted as an S-N diagram (Fig. 6–10). This chart may be plotted on semilog paper or on log-log paper. In the case of ferrous metals and alloys, the graph becomes horizontal after the material has been stressed for a certain number of cycles. Plotting on log paper emphasizes the bend in the curve, which might not be apparent if the results were plotted by using Cartesian coordinates