Budynas-Nisbett:Shigley's ll.Failure Prevention 5.Failures Resulting from ©The McGraw-Hfl Mechanical Engineering Static Loading Companies,2008 Design,Eighth Edition 5 Failures Resulting from Static Loading Chapter Outline 5-1 Static Strength 208 5-2 Stress Concentration 209 5-3 Failure Theories 211 5-4 Maximum-Shear-Stress Theory for Ductile Materials 211 5-5 Distortion-Energy Theory for Ductile Materials 213 5-6 Coulomb-Mohr Theory for Ductile Materials 219 5-7 Failure of Ductile Materials Summary 222 5-8 Maximum-Normal-Stress Theory for Brittle Materials 226 5-9 Modifications of the Mohr Theory for Brittle Materials 227 5-10 Failure of Brittle Materials Summary 229 5-11 Selection of Failure Criteria 230 5-12 Introduction to Fracture Mechanics 231 5-13 Stochastic Analysis 240 5-14 Important Design Equations 246 205
Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition II. Failure Prevention 5. Failures Resulting from Static Loading © The McGraw−Hill 209 Companies, 2008 5Failures Resulting from Static Loading Chapter Outline 5–1 Static Strength 208 5–2 Stress Concentration 209 5–3 Failure Theories 211 5–4 Maximum-Shear-Stress Theory for Ductile Materials 211 5–5 Distortion-Energy Theory for Ductile Materials 213 5–6 Coulomb-Mohr Theory for Ductile Materials 219 5–7 Failure of Ductile Materials Summary 222 5–8 Maximum-Normal-Stress Theory for Brittle Materials 226 5–9 Modifications of the Mohr Theory for Brittle Materials 227 5–10 Failure of Brittle Materials Summary 229 5–11 Selection of Failure Criteria 230 5–12 Introduction to Fracture Mechanics 231 5–13 Stochastic Analysis 240 5–14 Important Design Equations 246 205
210 Budynas-Nisbett:Shigley's ll.Failure Prevention 5.Failures Resulting from T©The McGraw-Hill Mechanical Engineering Static Loading Companies,2008 Design,Eighth Edition 206 Mechanical Engineering Design In Chap.I we learned that strength is a property or characteristic of a mechanical element.This property results from the material identity,the treatment and processing incidental to creating its geometry,and the loading,and it is at the controlling or critical location. In addition to considering the strength of a single part,we must be cognizant that the strengths of the mass-produced parts will all be somewhat different from the others in the collection or ensemble because of variations in dimensions,machining, forming,and composition.Descriptors of strength are necessarily statistical in nature,involving parameters such as mean,standard deviations,and distributional identification. A static load is a stationary force or couple applied to a member.To be stationary, the force or couple must be unchanging in magnitude,point or points of application, and direction.A static load can produce axial tension or compression,a shear load,a bending load,a torsional load,or any combination of these.To be considered static,the load cannot change in any manner. In this chapter we consider the relations between strength and static loading in order to make the decisions concerning material and its treatment,fabrication,and geometry for satisfying the requirements of functionality,safety,reliability,competitiveness, usability,manufacturability,and marketability.How far we go down this list is related to the scope of the examples "Failure"is the first word in the chapter title.Failure can mean a part has sepa- rated into two or more pieces;has become permanently distorted,thus ruining its geometry:has had its reliability downgraded;or has had its function compromised, whatever the reason.A designer speaking of failure can mean any or all of these pos- sibilities.In this chapter our attention is focused on the predictability of permanent distortion or separation.In strength-sensitive situations the designer must separate mean stress and mean strength at the critical location sufficiently to accomplish his or her purposes. Figures 5-1 to 5-5 are photographs of several failed parts.The photographs exem- plify the need of the designer to be well-versed in failure prevention.Toward this end we shall consider one-,two-,and three-dimensional stress states,with and without stress concentrations,for both ductile and brittle materials. Figure 5-1 (a)Failure of a truck drive-shaft spline due to corrosion fatigue.Note that it was necessary to use clear tape to hold the pieces in place. (b)Direct end view of failure. (a)
Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition II. Failure Prevention 5. Failures Resulting from Static Loading 210 © The McGraw−Hill Companies, 2008 206 Mechanical Engineering Design In Chap. 1 we learned that strength is a property or characteristic of a mechanical element. This property results from the material identity, the treatment and processing incidental to creating its geometry, and the loading, and it is at the controlling or critical location. In addition to considering the strength of a single part, we must be cognizant that the strengths of the mass-produced parts will all be somewhat different from the others in the collection or ensemble because of variations in dimensions, machining, forming, and composition. Descriptors of strength are necessarily statistical in nature, involving parameters such as mean, standard deviations, and distributional identification. A static load is a stationary force or couple applied to a member. To be stationary, the force or couple must be unchanging in magnitude, point or points of application, and direction. A static load can produce axial tension or compression, a shear load, a bending load, a torsional load, or any combination of these. To be considered static, the load cannot change in any manner. In this chapter we consider the relations between strength and static loading in order to make the decisions concerning material and its treatment, fabrication, and geometry for satisfying the requirements of functionality, safety, reliability, competitiveness, usability, manufacturability, and marketability. How far we go down this list is related to the scope of the examples. “Failure” is the first word in the chapter title. Failure can mean a part has separated into two or more pieces; has become permanently distorted, thus ruining its geometry; has had its reliability downgraded; or has had its function compromised, whatever the reason. A designer speaking of failure can mean any or all of these possibilities. In this chapter our attention is focused on the predictability of permanent distortion or separation. In strength-sensitive situations the designer must separate mean stress and mean strength at the critical location sufficiently to accomplish his or her purposes. Figures 5–1 to 5–5 are photographs of several failed parts. The photographs exemplify the need of the designer to be well-versed in failure prevention. Toward this end we shall consider one-, two-, and three-dimensional stress states, with and without stress concentrations, for both ductile and brittle materials. Figure 5–1 (a) Failure of a truck drive-shaft spline due to corrosion fatigue. Note that it was necessary to use clear tape to hold the pieces in place. (b) Direct end view of failure
Budynas-Nisbett:Shigley's ll.Failure Prevention 5.Failures Resulting from ©The McGraw-Hil 21 Mechanical Engineering Static Loading Companies,2008 Design,Eighth Edition Failures Resulting from Static Loading 207 Figure 5-2 Impact failure of a lawn mower blade driver hub.The blade impacted a surveying pipe marker. Figure 5-3 Failure of an overhead-pulley retaining bolt on a weightlifting mochine.A manufacturing error caused a gap that forced the bolt to take the entire moment load. (a) (b) Figure 5-4 Chain test fixture that failed in one cycle.To alleviate complaints of excessive wear,the manufacturer decided to case-harden the material.(a)Two halves showing fracture;this is an excellent example of brittle fracture initiated by stress concentration.(b)Enlarged view of one portion to show cracks induced by stress concentration at the support-pin holes
Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition II. Failure Prevention 5. Failures Resulting from Static Loading © The McGraw−Hill 211 Companies, 2008 Figure 5–2 Impact failure of a lawnmower blade driver hub. The blade impacted a surveying pipe marker. Figure 5–3 Failure of an overhead-pulley retaining bolt on a weightlifting machine. A manufacturing error caused a gap that forced the bolt to take the entire moment load. Figure 5–4 Chain test fixture that failed in one cycle. To alleviate complaints of excessive wear, the manufacturer decided to case-harden the material. (a) Two halves showing fracture; this is an excellent example of brittle fracture initiated by stress concentration. (b) Enlarged view of one portion to show cracks induced by stress concentration at the support-pin holes. Failures Resulting from Static Loading 207
212 Budynas-Nisbett:Shigley's ll.Failure Prevention 5.Failures Resulting from T©The McGraw-Hil Mechanical Engineering Static Loading Companies,2008 Design,Eighth Edition 208 Mechanical Engineering Design Figure 5-5 Valve-spring failure caused by spring surge in an oversped engine.The fractures exhibit the classic 45 shear failure 5-1 Static Strength Ideally,in designing any machine element,the engineer should have available the results of a great many strength tests of the particular material chosen.These tests should be made on specimens having the same heat treatment,surface finish,and size as the ele- ment the engineer proposes to design;and the tests should be made under exactly the same loading conditions as the part will experience in service.This means that if the part is to experience a bending load,it should be tested with a bending load.If it is to be subjected to combined bending and torsion,it should be tested under combined bending and torsion.If it is made of heat-treated AISI 1040 steel drawn at 500C with a ground finish,the specimens tested should be of the same material prepared in the same manner. Such tests will provide very useful and precise information.Whenever such data are available for design purposes,the engineer can be assured of doing the best possible job of engineering. The cost of gathering such extensive data prior to design is justified if failure of the part may endanger human life or if the part is manufactured in sufficiently large quan- tities.Refrigerators and other appliances,for example,have very good reliabilities because the parts are made in such large quantities that they can be thoroughly tested in advance of manufacture.The cost of making these tests is very low when it is divid- ed by the total number of parts manufactured. You can now appreciate the following four design categories: 1 Failure of the part would endanger human life,or the part is made in extremely large quantities:consequently,an elaborate testing program is justified during design. The part is made in large enough quantities that a moderate series of tests is feasible. 3 The part is made in such small quantities that testing is not justified at all;or the design must be completed so rapidly that there is not enough time for testing
Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition II. Failure Prevention 5. Failures Resulting from Static Loading 212 © The McGraw−Hill Companies, 2008 208 Mechanical Engineering Design Figure 5–5 Valve-spring failure caused by spring surge in an oversped engine. The fractures exhibit the classic 45◦ shear failure. 5–1 Static Strength Ideally, in designing any machine element, the engineer should have available the results of a great many strength tests of the particular material chosen. These tests should be made on specimens having the same heat treatment, surface finish, and size as the element the engineer proposes to design; and the tests should be made under exactly the same loading conditions as the part will experience in service. This means that if the part is to experience a bending load, it should be tested with a bending load. If it is to be subjected to combined bending and torsion, it should be tested under combined bending and torsion. If it is made of heat-treated AISI 1040 steel drawn at 500◦C with a ground finish, the specimens tested should be of the same material prepared in the same manner. Such tests will provide very useful and precise information. Whenever such data are available for design purposes, the engineer can be assured of doing the best possible job of engineering. The cost of gathering such extensive data prior to design is justified if failure of the part may endanger human life or if the part is manufactured in sufficiently large quantities. Refrigerators and other appliances, for example, have very good reliabilities because the parts are made in such large quantities that they can be thoroughly tested in advance of manufacture. The cost of making these tests is very low when it is divided by the total number of parts manufactured. You can now appreciate the following four design categories: 1 Failure of the part would endanger human life, or the part is made in extremely large quantities; consequently, an elaborate testing program is justified during design. 2 The part is made in large enough quantities that a moderate series of tests is feasible. 3 The part is made in such small quantities that testing is not justified at all; or the design must be completed so rapidly that there is not enough time for testing
Budynas-Nisbett:Shigley's ll.Failure Prevention 5.Failures Resulting from T©The McGraw-Hill 213 Mechanical Engineering Static Loading Companies,2008 Design,Eighth Edition Failures Resulting from Static Loading 209 4 The part has already been designed,manufactured,and tested and found to be unsatisfactory.Analysis is required to understand why the part is unsatisfactory and what to do to improve it. More often than not it is necessary to design using only published values of yield strength,ultimate strength,percentage reduction in area,and percentage elongation, such as those listed in Appendix A.How can one use such meager data to design against both static and dynamic loads,two-and three-dimensional stress states,high and low temperatures,and very large and very small parts?These and similar questions will be addressed in this chapter and those to follow,but think how much better it would be to have data available that duplicate the actual design situation. 5-2 Stress Concentration Stress concentration (see Sec.3-13)is a highly localized effect.In some instances it may be due to a surface scratch.If the material is ductile and the load static,the design load may cause yielding in the critical location in the notch.This yielding can involve strain strengthening of the material and an increase in yield strength at the small criti- cal notch location.Since the loads are static and the material is ductile,that part can carry the loads satisfactorily with no general yielding.In these cases the designer sets the geometric (theoretical)stress concentration factor K,to unity. The rationale can be expressed as follows.The worst-case scenario is that of an idealized non-strain-strengthening material shown in Fig.5-6.The stress-strain curve rises linearly to the yield strength Sy,then proceeds at constant stress,which is equal to Sy.Consider a filleted rectangular bar as depicted in Fig.A-15-5,where the cross- section area of the small shank is 1 in2.If the material is ductile,with a yield point of 40 kpsi,and the theoretical stress-concentration factor(SCF)K,is 2, A load of 20 kip induces a tensile stress of 20 kpsi in the shank as depicted at point A in Fig.5-6.At the critical location in the fillet the stress is 40 kpsi,and the SCF is K=0max/onom=40/20=2. Figure 5-6 An idealized stress-strain curve.The dashed line depicts a strain-strengthening material. Tensile strain.e
Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition II. Failure Prevention 5. Failures Resulting from Static Loading © The McGraw−Hill 213 Companies, 2008 Failures Resulting from Static Loading 209 4 The part has already been designed, manufactured, and tested and found to be unsatisfactory. Analysis is required to understand why the part is unsatisfactory and what to do to improve it. More often than not it is necessary to design using only published values of yield strength, ultimate strength, percentage reduction in area, and percentage elongation, such as those listed in Appendix A. How can one use such meager data to design against both static and dynamic loads, two- and three-dimensional stress states, high and low temperatures, and very large and very small parts? These and similar questions will be addressed in this chapter and those to follow, but think how much better it would be to have data available that duplicate the actual design situation. 5–2 Stress Concentration Stress concentration (see Sec. 3–13) is a highly localized effect. In some instances it may be due to a surface scratch. If the material is ductile and the load static, the design load may cause yielding in the critical location in the notch. This yielding can involve strain strengthening of the material and an increase in yield strength at the small critical notch location. Since the loads are static and the material is ductile, that part can carry the loads satisfactorily with no general yielding. In these cases the designer sets the geometric (theoretical) stress concentration factor Kt to unity. The rationale can be expressed as follows. The worst-case scenario is that of an idealized non–strain-strengthening material shown in Fig. 5–6. The stress-strain curve rises linearly to the yield strength Sy , then proceeds at constant stress, which is equal to Sy . Consider a filleted rectangular bar as depicted in Fig. A–15–5, where the crosssection area of the small shank is 1 in2 . If the material is ductile, with a yield point of 40 kpsi, and the theoretical stress-concentration factor (SCF) Kt is 2, • A load of 20 kip induces a tensile stress of 20 kpsi in the shank as depicted at point A in Fig. 5–6. At the critical location in the fillet the stress is 40 kpsi, and the SCF is K = σmax/σnom = 40/20 = 2. 50 0 Sy Tensile strain, Tensile stress , kpsi A B D E C Figure 5–6 An idealized stress-strain curve. The dashed line depicts a strain-strengthening material.