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.pdf_P6-P10

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 combination 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 science 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 simply 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 description 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 laboratorycontrolled specimens. The loading often is that of sinusoidally reversing pure bending. The laboratory-controlled specimens are polished without geometric stress concentration 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 specimen and the actual machine part with regard to surface conditions, size, loading, temperature, 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 sN<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 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 behavior depends on the static stress concentration factor and the component material’s sensitivity 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 combined 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 provided 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 implement 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 practical when applied to large structures in conjunction with computer codes and a periodic 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 rotatingbeam 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 higheststress 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 available 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 bending 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 ultimate 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