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| | كتاب Mechanical Behavior of Materials - Engineering Methods for Deformation, Fracture, and Fatigue | |
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عدد المساهمات : 18959 التقييم : 35383 تاريخ التسجيل : 01/07/2009 الدولة : مصر العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
| موضوع: كتاب Mechanical Behavior of Materials - Engineering Methods for Deformation, Fracture, and Fatigue الجمعة 11 مايو 2012, 11:38 am | |
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تذكير بمساهمة فاتح الموضوع : أخوانى فى الله أحضرت لكم كتاب Mechanical Behavior of Materials - Engineering Methods for Deformation, Fracture, and Fatigue Fourth Edition Norman E. Dowling Frank Maher Professor of Engineering Engineering Science and Mechanics Department, and Materials Science and Engineering Department Virginia Polytechnic Institute and State University Blacksburg, Virginia International Edition contributions by Katakam Siva Prasad Assistant Professor Department of Metallurgical and Materials Engineering National Institute of Technology Tiruchirappalli R. Narayanasamy Professor Department of Production Engineering National Institute of Technology Tiruchirappalli
و المحتوى كما يلي :
Contents PREFACE 11 ACKNOWLEDGMENTS 17 1 Introduction 19 1.1 Introduction 19 1.2 Types of Material Failure 20 1.3 Design and Materials Selection 28 1.4 Technological Challenge 34 1.5 Economic Importance of Fracture 36 1.6 Summary 37 References 38 Problems and Questions 38 2 Structure and Deformation in Materials 40 2.1 Introduction 40 2.2 Bonding in Solids 42 2.3 Structure in Crystalline Materials 46 2.4 Elastic Deformation and Theoretical Strength 50 2.5 Inelastic Deformation 55 2.6 Summary 61 References 62 Problems and Questions 63 3 A Survey of Engineering Materials 65 3.1 Introduction 65 3.2 Alloying and Processing of Metals 66 3.3 Irons and Steels 72 3.4 Nonferrous Metals 80 3.5 Polymers 84 56 Contents 3.6 Ceramics and Glasses 94 3.7 Composite Materials 100 3.8 Materials Selection for Engineering Components 105 3.9 Summary 111 References 113 Problems and Questions 114 4 Mechanical Testing: Tension Test and Other Basic Tests 118 4.1 Introduction 118 4.2 Introduction to Tension Test 123 4.3 Engineering Stress–Strain Properties 128 4.4 Trends in Tensile Behavior 137 4.5 True Stress–Strain Interpretation of Tension Test 143 4.6 Compression Test 151 4.7 Hardness Tests 157 4.8 Notch-Impact Tests 164 4.9 Bending and Torsion Tests 169 4.10 Summary 175 References 176 Problems and Questions 177 5 Stress–Strain Relationships and Behavior 190 5.1 Introduction 190 5.2 Models for Deformation Behavior 191 5.3 Elastic Deformation 201 5.4 Anisotropic Materials 214 5.5 Summary 223 References 225 Problems and Questions 225 6 Review of Complex and Principal States of Stress and Strain 234 6.1 Introduction 234 6.2 Plane Stress 235 6.3 Principal Stresses and the Maximum Shear Stress 245 6.4 Three-Dimensional States of Stress 253 6.5 Stresses on the Octahedral Planes 260 6.6 Complex States of Strain 262 6.7 Summary 267 References 269 Problems and Questions 269Contents 7 7 Yielding and Fracture under Combined Stresses 275 7.1 Introduction 275 7.2 General Form of Failure Criteria 277 7.3 Maximum Normal Stress Fracture Criterion 279 7.4 Maximum Shear Stress Yield Criterion 282 7.5 Octahedral Shear Stress Yield Criterion 288 7.6 Discussion of the Basic Failure Criteria 295 7.7 Coulomb–Mohr Fracture Criterion 301 7.8 Modified Mohr Fracture Criterion 311 7.9 Additional Comments on Failure Criteria 318 7.10 Summary 321 References 322 Problems and Questions 323 8 Fracture of Cracked Members 334 8.1 Introduction 334 8.2 Preliminary Discussion 337 8.3 Mathematical Concepts 344 8.4 Application of K to Design and Analysis 348 8.5 Additional Topics on Application of K 359 8.6 Fracture Toughness Values and Trends 371 8.7 Plastic Zone Size, and Plasticity Limitations on LEFM 381 8.8 Discussion of Fracture Toughness Testing 390 8.9 Extensions of Fracture Mechanics Beyond Linear Elasticity 391 8.10 Summary 398 References 401 Problems and Questions 402 9 Fatigue of Materials: Introduction and Stress-Based Approach 416 9.1 Introduction 416 9.2 Definitions and Concepts 418 9.3 Sources of Cyclic Loading 429 9.4 Fatigue Testing 430 9.5 The Physical Nature of Fatigue Damage 435 9.6 Trends in S-N Curves 441 9.7 Mean Stresses 451 9.8 Multiaxial Stresses 463 9.9 Variable Amplitude Loading 468 9.10 Summary 478 References 479 Problems and Questions 4818 Contents 10 Stress-Based Approach to Fatigue: Notched Members 491 10.1 Introduction 491 10.2 Notch Effects 493 10.3 Notch Sensitivity and Empirical Estimates of k f 497 10.4 Estimating Long-Life Fatigue Strengths (Fatigue Limits) 501 10.5 Notch Effects at Intermediate and Short Lives 506 10.6 Combined Effects of Notches and Mean Stress 510 10.7 Estimating S-N Curves 520 10.8 Use of Component S-N Data 527 10.9 Designing to Avoid Fatigue Failure 536 10.10 Discussion 541 10.11 Summary 542 References 544 Problems and Questions 545 11 Fatigue Crack Growth 560 11.1 Introduction 560 11.2 Preliminary Discussion 561 11.3 Fatigue Crack Growth Rate Testing 569 11.4 Effects of R = Smin/Smax on Fatigue Crack Growth 574 11.5 Trends in Fatigue Crack Growth Behavior 584 11.6 Life Estimates for Constant Amplitude Loading 590 11.7 Life Estimates for Variable Amplitude Loading 601 11.8 Design Considerations 607 11.9 Plasticity Aspects and Limitations of LEFM for Fatigue Crack Growth 609 11.10 Environmental Crack Growth 616 11.11 Summary 621 References 623 Problems and Questions 624 12 Plastic Deformation Behavior and Models for Materials 638 12.1 Introduction 638 12.2 Stress–Strain Curves 641 12.3 Three-Dimensional Stress–Strain Relationships 649 12.4 Unloading and Cyclic Loading Behavior from Rheological Models 659 12.5 Cyclic Stress–Strain Behavior of Real Materials 668 12.6 Summary 681 References 683 Problems and Questions 684Contents 9 13 Stress–Strain Analysis of Plastically Deforming Members 693 13.1 Introduction 693 13.2 Plasticity in Bending 694 13.3 Residual Stresses and Strains for Bending 703 13.4 Plasticity of Circular Shafts in Torsion 707 13.5 Notched Members 710 13.6 Cyclic Loading 722 13.7 Summary 733 References 734 Problems and Questions 735 14 Strain-Based Approach to Fatigue 745 14.1 Introduction 745 14.2 Strain Versus Life Curves 748 14.3 Mean Stress Effects 758 14.4 Multiaxial Stress Effects 767 14.5 Life Estimates for Structural Components 771 14.6 Discussion 781 14.7 Summary 789 References 790 Problems and Questions 791 15 Time-Dependent Behavior: Creep and Damping 802 15.1 Introduction 802 15.2 Creep Testing 804 15.3 Physical Mechanisms of Creep 809 15.4 Time–Temperature Parameters and Life Estimates 821 15.5 Creep Failure under Varying Stress 833 15.6 Stress–Strain–Time Relationships 836 15.7 Creep Deformation under Varying Stress 841 15.8 Creep Deformation under Multiaxial Stress 848 15.9 Component Stress–Strain Analysis 850 15.10 Energy Dissipation (Damping) in Materials 855 15.11 Summary 864 References 867 Problems and Questions 868 Appendix A Review of Selected Topics from Mechanics of Materials 880 A.1 Introduction 880 A.2 Basic Formulas for Stresses and Deflections 88010 Contents A.3 Properties of Areas 882 A.4 Shears, Moments, and Deflections in Beams 884 A.5 Stresses in Pressure Vessels, Tubes, and Discs 884 A.6 Elastic Stress Concentration Factors for Notches 889 A.7 Fully Plastic Yielding Loads 890 References 899 Appendix B Statistical Variation in Materials Properties 900 B.1 Introduction 900 B.2 Mean and Standard Deviation 900 B.3 Normal or Gaussian Distribution 902 B.4 Typical Variation in Materials Properties 905 B.5 One-Sided Tolerance Limits 905 B.6 Discussion 907 References 908 ANSWERS FOR SELECTED PROBLEMS AND QUESTIONS 909 BIBLIOGRAPHY 920 INDEX 93 Index A A286 (superalloy), 83, 827 Absolute modulus, 858 Abusive grinding, 540 Accidental loads, 429 Acrylic (PMMA), 21, 139, 140, 202, 341 Activation energies, 811–812 defined, 809 evaluation of, 816–817 Adiabatic modulus, 860 AFGROW, 602 Aging. See Precipitation hardening Albert, W. A. J., 417 Allowable stress design, 31–32, 296, 321 Alloy steels. See Low-alloy steels Alloying, 66, 92, 111 Alloying and processing of metals, 66–72 annealing, 68–69 cold work, 68–69 grain refinement, 69 multiple phase effects, 70–72 precipitation hardening, 70–72 solid solution strengthening, 69–70 strengthening methods, 68 Alloys, 40–41, 43 Alpha iron, 47 Alternating stress, 419 Alumina (Al2O3), 41, 55, 96, 97, 161, 202, 341 Aluminum and alloys, 41, 66–67, 80–82, 101, 106, 111, 138, 152, 202, 296, 340, 343, 578, 582, 672, 751, 906 Aluminum bronze, 83 American Association of State Highway and Transportation Officials (AASHTO), 30, 534 bridge design code, 534–535 American Institute of Steel Construction, allowable stress design code of, 31–32 American Iron and Steel Institute (AISI), steel nomenclature, 73–75 AISI 304, 587 AISI 310, 73, 827 AISI 316, 78 AISI 403, 73, 78 AISI 1020, 73, 106, 109, 124, 133, 134–137, 138, 148, 150, 152 AISI 1040, 78 AISI 1045, 73, 77, 342–343, 751 AISI 1195, 73 AISI 1340, 74 AISI 4142, 138, 152, 751 AISI 4340, 73, 77–79, 106, 374–375, 578, 585, 589, 618, 620, 751 AISI T1, 73 933934 Index American Society for Testing and Materials (ASTM International), 73, 122 See also ASTM Standards American Welding Society (AWS) structural welding design code, 532–535 Amorphous materials, 98, 203 Amorphous thermoplastics, crystalline vs., 86–89 Amplitude, of stress, 418–419 Amplitude ratio, 419 Amplitude-mean diagram, 452–454 Andrade, 806 Anelastic damping, 855 Anelastic strain, 201, 855 Anisotropic Hooke’s law, 214–217 Anisotropic materials, 214–221 cubic material, 216 elastic modulus parallel to fibers, 219–220 elastic modulus transverse to fibers, 220–221 fibrous composites, 217–218 orthotropic materials, 215–217 stress–strain relationships, 214–224 yield criteria for, 298–299 Annealing, 69 Aramid, 86, 88 Aramid-aluminum laminate (ARALL), 41, 103–105 Areas, properties of, 882–884 Arrhenius equation, 811, 822, 864 ASTM Standards, 73, 78, 122–123, 131, 171, 314, 373, 398, 474, 569, 617, 668, 748 A242 steel, 78 A302 steel, 78 A395 cast iron, 73 A441 steel, 78 A514 steel, 138, 152 A517 steel, 78, 340 A533 steel, 78 A538-C steel, 73 A572 steel, 78 A588 steel, 78 A588-A steel, 73 E399, for fracture, 373, 390 E466, for fatigue, 430 E606 for low-cycle fatigue, 668, 748 E647 for crack growth, 569, 572 E1049 for cycle counting, 472, 474 E1290, for fracture, 398 E1681 for environmental cracking, 617 E1820, for fracture, 373, 394, 397–398 Ausforming process, 79 Austenite (γ -iron), 77 Austenitic stainless steels, 79 B Bailey bridges, 527 Bauschinger effect, 639–641, 664 Beach marks, 440–441 Beams, 884–885 Bend (fracture) specimen, 351, 371–373, 396–397 Bending shears, moments, deflections, 884–885 Bend strength, 170–171 Bending analysis for creep, 851–854 elastic analysis of, 694–696, 880–882 in cyclic loading, 722–724 plastic analysis of, 694–703, 891–895 residual stresses for, 703–707 Bending and torsion tests, 118–119, 169–175 bending (flexure) tests, 170–171 heat-deflection test, 171–172 modulus of rupture in bending, 171 testing of thin-walled tubes in torsion, 173–175 torsion test, 169–170 Beryllium, 47, 70 Beryllium copper, 83 Biaxial stresses. See Multiaxial stress effects; Three-dimensional states of stress Blending, defined, 92 Blunting line, 397–398 Body-centered cubic (BCC) structure, 46, 61, 376 Bolts, bolted joints, 536–537 Bonding in solids, 42–46 primary chemical bonds, 42–44 secondary chemical bonds, 44–46 Bone, 100 Borides, 59 Boron, 59, 66, 102 Boron carbide (B4C), 95, 161 Boron nitride (BN), 98 Boundary integral equation method, 354 Brale indenter, 162 Branching in polymers, 88 Brass, 41, 83, 202 Bridge Design Specifications (AASHTO), 30, 534–535 Bridge structures, cracks in, 336Index 935 Bridgman correction for hoop stress, 146–147 Bridgman, P. W., 146 Brinell hardness test, 159, 163, 175 British Standards Institution (BSI), 122 Brittle behavior, 21–22, 40, 894–895 effects of cracks on, 342–344 multiaxial criteria for, 299–320 in notch fatigue, 510–511 in tension tests, 126, 133 Brittle fracture, 23–24, 37, 334–400 safety factors against, 356 Bronze, 41, 83 Buckling, 22, 152, 174 Budynas, S-N curve estimate, 520, 522–523 Bulk modulus, 210 C Carbon, 44, 59, 66, 72, 74, 76–78, 84, 93, 101, 111 Carbon steel, 76–77 AISI–SAE designations for (table), 75 Carburizing, 447, 540 Cast irons, 72, 74–76, 126, 138, 152, 305 Casting, 66 Cellulose, 100 Cemented carbides, 41, 97–98, 112 Cementite, 76 Center-cracked plates, 342, 349, 352, 394, 569 Ceramics, 40–41, 59, 94–98, 112, 223, 298 chemical bonding in, 44, 94 clay products, 94–97 concrete, 94, 96–97 creep in, 802, 813 ductility, 137 elastic moduli of, 95, 137 engineering, 94, 97, 112 fatigue crack growth in, 585, 589, 592 fracture toughness of, 341, 344, 373, 376 hardness of, 160–161 natural stone, 94, 96 Cermets, 97–98, 112 Chain molecules, 40, 44–46, 61, 84, 88–90 Charpy V-notch test, 165–169 Chemical bonding in solids. See Bonding in solids Chemical vapor deposition, 97–98 Chromium, 66, 78–79, 82, 84, 803 plating, 447, 540 Circular cracks, 360 Circular shafts, torsion of, 707–710, 881–882, 894–895 Circumferential cracks, 352, 354 Clay products, 41, 94–96, 112 Cleavage, 376–378, 587 Climb (dislocation), 815 Closed-loop servohydraulic test system, 121–122, 435 Close-packed directions, planes, 57 Cobalt, 34, 66, 67, 83–84, 97–98, 111, 803 Coble creep, 814–815 Coefficient of tensile viscosity, 193 Coefficient of thermal expansion, 212–213 Coffin, L. F., 751, 834 Coffin–Manson relationship, 751 Coherent precipitate, 70, 102 Cold rolling, 539 Cold work, 68–69, 79, 80–83, 672 Collagen, 100 Combined stresses, yielding and fracture, 275–322 Comet passenger airliner, 343 Compact specimen, 353, 373–374, 396–397, 569 Completely reversed cycling, 420 Compliance method, 348, 395–396 Component, 33 Component S-N data, 527–535 Bailey bridge example, 527–529 curves for welded members, 531–535 matching to notched specimen data, 531 mean stress and variable amplitude cases life, 529 Component testing, 32–34 Composite materials, 40–41, 94, 100–105, 112 defined, 100 elastic constants for, 217–222 failure criteria for, 299 fibrous composites, 102–104 laminated composites, 104–105 particulate composites, 100–102 tensile behavior of, 137, 140 uses of, 100–101 Compression tests, 118, 151–156, 175 materials properties in compression, 153–154 strengths from, 95, 97 trends in compressive behavior, 154–156, 299–300 with lateral pressure, 156 Concrete, 41, 94, 96–97, 100, 112, 305, 341, 906 creep in, 820–821936 Index Constant amplitude loading (of cracked members) life estimates for, 590–601 closed-form solutions, 593–594 crack length at failure, 594–595 solutions by numerical integration, 598–601 Constant amplitude stressing, 418–420 Constant-life diagram, 452–453 Constitutive equations. See Stress–strain relationships Constraint, geometric, 212, 293–295, 387–389, 717–718 Copolymerization, 93 Copper and alloys, 41, 67, 68, 83, 202 Corner crack, 360–361 Corrected true stress, 146–149 Corrosion, 20, 28 Corrosion fatigue, 28, 449, 589, 621 Corten–Dolan cumulative damage method, 542 Costs of fracture, 36–37, 417 Costs of materials, relative, 106, 110 Coulomb–Mohr (C–M) fracture criterion, 301–311, 321–322 development of, 302–307 effective stress for, 309–310 graphical representation of, 307–309 Covalent bonding, 42–44, 47–48, 94 Crack growth. See Environmental crack growth; Fatigue crack growth Crack growth analysis, need for, 561–563 Crack growth effect on k f , 495–496 Crack growth retardation, 606 Crack surface displacement, modes of, 344 Crack velocity, 616–617 Cracked members, fracture of, 334–400 Cracks application of K to design and analysis, 348–370 cases of special practical interest, 359–364 leak-before-break in pressure vessels, 369–371 safety factors, 356–359 superposition for combined loading, 366–367 behavior at crack tips in real materials, 338–339 effects on brittle vs. ductile behavior, 342–344 effects on strength, 339–341 growing from notches, 364–366 inclined or parallel to an applied stress, 367–369 inspection for, 336, 616 periodic inspections for, 562–563 internally flawed materials, 344 mathematical concepts, 344–348 mixed mode, 381 nonpropagating, 496 strain energy release rate G, 344–346 stress intensity factor K , 346–348 as stress raisers, 337–338 See also Fracture mechanics; Fracture toughness Crack-tip opening displacement (CTOD), 338, 392, 397–400 Crack-tip plastic zone. See Plastic zone (at crack tip) Crazing, craze zone, 140, 338 Creep, 190–191, 196–198, 223, 802–866 activation energies, evaluation of, 816–817 Coble type, 814–815 in concrete, 820–821 in crystalline materials, 61, 813–816 cycle-dependent type, 678–679 defined, 22–23, 60 deformation mechanism maps, 817–819 dislocation type, 813–816 fracture mechanism maps, 807, 810 isochronous stress–strain curves, 809, 836–838, 850–854, 864–865 Nabarro–Herring type, 814–815 physical mechanisms of, 809–820 in polymers, 813 power-law type, 814–816 rheological models for, 196–198, 836–838 steady-state (secondary) stage, 191–193, 805, 847 stress-strain analysis of components for linear viscoelasticity, 850–853 nonlinear behavior, 853–855 tertiary stage, 805–806 transient (primary) stage, 192–194, 805 viscous type, 810–813, 815 Creep cavitation, 821 Creep deformation, 22–23, 37, 40, 55, 60–61, 196–198, 200–201, 802–803 application involving (example), 23 for linear viscoelasticity, 836–838 for multiaxial stress, 848–850 for nonlinear behavior, 838–841 recovery of, 841–842 for varying stress, 841–848 for linear viscoelastic models, 844–846 stress relaxation, 842–844 time- and strain-hardening rules, 846–848Index 937 Creep failure under varying stress, 833–836 creep rupture under step loading, 833–834 creep–fatigue interaction, 834–836 Creep rupture, 25, 37, 804, 821 for multiaxial stress, 833 safety factors for, 831–833 for step loading, 833–834 time-temperature parameters and life estimates, 821–833 Creep tests, 804–806 behavior observed in, 804–806 presentation of results, 806–809 Creep–fatigue interaction, 27, 757, 834–836 Critical plane approach, 466, 769–771 Cross-links, 89–91, 92, 112 Crystal structure, defined, 46 Crystalline grains, 48 Crystalline materials basic crystal structures, 46–47 complex crystal structures, 47–48 creep in, 60–61, 813–816 structure in, 46–50 Crystalline polymers, 86, 88 Crystals, defects in, 48–50 Cubic crystal, 46 Cubic material, 216 Cumulative fatigue damage. See Palmgren–Miner rule; Variable amplitude loading Cycle counting, 469, 471–475, 677, 775–776, 780–781, 789 Cycle-dependent creep, 678–679 Cycle-dependent hardening, 668–669, 732 Cycle-dependent relaxation, 678–681 Cycle-dependent softening, 668–669, 732 Cyclic bending, analyzing, 722–724 Cyclic loading, 416–418 accidental loads, 429 alternating stress, 419 closed-loop servohydraulic testing machines, 435 completely reversed cycling, 419–420 constant amplitude stressing, 418–419 and fatigue crack growth, 560, 569 fatigue under, 25–27 fatigue crack growth, 560–615, 621–622 strain-based approach, 745–790 stress-based approach, 416–479, 491–543 rheological modeling for, 640–641, 659–661, 664–668 sources of, 429–430 and static loads, 429 stress amplitude, 418–419 stress range, 418–419 stress ratio R, 419 stress–strain analysis of, 722–733 bending, 722–725 generalized methodology, 725–728 irregular load vs. time histories, 728–732 stress–strain behavior during, 640, 668–681 and time-dependent deformation, 803, 833–836 vibratory loads, 429 working loads, 429 zero-to-tension cycling, 419–420 Cyclic plastic zone, 611–612 Cyclic stress–strain behavior of materials cyclic stress–strain curves, 671–673, 747 cyclic stress–strain tests and behavior, 668–671 cyclic yield strength, 671–673, 680 hysteresis loop curve shapes, 673–677 mean stress relaxation, 678–681 D Damage intensification, 438 Damage tolerant design, 343, 563, 607–608 Damping in materials, 804, 855–863 anelastic type, 855 from rheological models, 855–857 definitions of variables describing, 858 in engineering components, 862–863 importance of, 855 low-stress mechanisms in metals, 858–860 magnetoelastic type, 860 plastic strain type, 860–863 Snoek effect, 858 thermal current type, 859 Deformation, 19–20, 66, 190, 223 characteristics of the various types of (table), 201 creep, 22–23, 25, 37, 60–61, 190, 223, 802–866 elastic type, 21–22, 37, 50–53, 191, 201–213, 223–224 plastic type, 21–22, 37, 55–59, 190, 223 behavior and models for materials, 638–683 Deformation behavior models creep deformation, 190–194, 196–198, 836–838 discussion of, 200–201 elastic deformation, 191–193938 Index Deformation behavior models (Continued) plastic deformation, 191–193, 194–196, 648–649, 659–668 relaxation behavior, 198–199, 842–844 rheological models, defined, 191 Deformation mechanism maps, 817–820 Deformation plasticity theory, 641, 650–659 incremental plasticity theory vs., 658–659 Delaminations in layered materials, 335 Delta iron, 47 Design, 28–34 allowable stress, 32, 296 creep, 802–803 defined, 28–29, 37 durability, 29 environmental cracking, 618–619 fatigue, 448, 536–542 fatigue crack growth, 563, 607–609 load factor, 32, 296–297 material selection, 66, 105–111 safety factors, 29, 30–32 service experience, 34 Design truck, 534 Diamond cubic structure, of carbon, 48 Diffusion, 810–811 Diffusional flow, 60, 813–815 Dimpled rupture, 376, 378 Direction cosines, 253 Disc, rotation stresses, 887–889 Discontinuous stress–strain curves, 699–701 Dislocation climb, 815 Dislocation creep, 815–816 Dislocation motion, plastic deformation by, 56–58 Dislocations, 50 Dispersion hardening, 101–102 Distortion energy criterion. See Octahedral shear stress yield criterion Drawing, 66, 68–69 Ductile behavior, 21–22 effects of cracks on, 342–343 multiaxial stress effect, 318–320 in notched members, 894–898 in notch fatigue, 506–513 in a tension test, 126–127 Ductile fracture, 24–25, 37, 391–399 Ductile iron. See Cast irons Ductility engineering fracture strain, 131 engineering measures of, 130–132 and necking, 131–132 percent elongation, 22, 131 percent reduction in area, 131 Durability, durability testing, 29, 33 Dynamic modulus, 858 Dynamic recrystallization, 821 Dynamic tear test, 165 E Ebonite, 92 Economics of fracture, 36–37, 417 Edge dislocation, 50 Edge-cracked tension member, 349, 353–354 Effective mean stress, 465–466 Effective plastic strain, 650 Effective strain rate, 849 Effective stress, 278–279, 281, 283, 290, 309–310, 314, 650–651, 653, 849 Effective stress amplitude, 465 Effective stress–strain curve, 653–654 Effective total strain, 650–651, 653 for fatigue life, 768–769 Elastic bending, 694–696, 880–882 Elastic constants, 128–129, 202–204, 214–218 Elastic deformation, 21, 37, 50–53, 190–191, 201–224 anisotropic case, 214–218 bulk modulus, 210–211 hydrostatic stress, 209–211 isotropic case, 201–213 orthotropic case, 215–217 physical mechanisms of, 51–52 and theoretical strength, 53–55 thermal strains, 211–213 and volume change, 209–210, 213 volumetric strain, 209–211 Elastic limit, 130 Elastic, linear-hardening stress-strain relationship, 194–195, 643–644 Elastic modulus, 21, 52–53, 105, 128, 193, 201–204 parallel to fibers, 219–220 for polymers, 88, 91 time dependent type, 837–838, 851, 865 transverse to fibers, 220–221 values, trends in, 52–53Index 939 Elastic, perfectly plastic stress–strain relationship, 194–195, 641–643 in bending, 699 in notched members, 715 residual stresses in bending, 704–707 in torsion, 710 Elastic, power-hardening stress-strain relationship, 644 Elastic strain. See Elastic deformation Elastic strains, Hooke’s law for, 204–206, 649–650 Elastic stress concentration factor, 337–338, 420, 493, 508–509, 511–513, 536–537, 712, 889–891 Elastically calculated stresses, 717 Elastomers, 84, 88, 90–91, 111, 861 elastic moduli of, 137 Elliptic integral of the second kind, 360–362 Elliptical cracks, 360–364, 392 Elongation, percent, 22, 130–132, 138–140 Embrittlement, 616 Endo, T., 471 Endurance limits. See Fatigue limits Energy capacity, engineering measures of, 132–134 Energy dissipation. See Damping in materials Energy, impact, 164–169 Engineering ceramics, 94, 97, 112 Engineering components materials selection for, 105–111 Engineering design. See Design Engineering fracture strain, 131 Engineering fracture strength, 129 Engineering materials, 40 classes and examples of, 41 general characteristics of (table), 41 size scales for, 41–42 survey of, 65–112 Engineering metals, 66, 72–84 Engineering plastics, 86 Engineering shear strains, 262, 650 Engineering size crack, 787–788 Engineering stress and strain, 125–137, 149–150, 175 Engineering stress–strain properties (from tension tests), 128–136 ductility, 130–132 elastic constants, 128–129 elastic limit, 130 elastic (Young’s) modulus, 21, 128 elongation, 22, 131–132 engineering fracture strength, 129 engineering measures of ductility, 130–132 engineering measures of energy capacity, 132–134 versus fracture toughness, 134 engineering measures of strength, 129–130 lower yield point, 130 necking behavior and ductility, 131–132 offset yield strength, 130 proportional limit, 130 reduction in area, 131–132 strain hardening, 134 tangent modulus, 129 trends in 137–143 ultimate tensile strength, 22, 129 upper yield point, 130 yielding, 21, 129–130 Environmental crack growth, 560–561, 616–621, 622 static loading, life estimates for, 616–618 Environmental cracking, 25, 36, 616–621 and creep, 803 Environmental effects in creep-fatigue, 834–836 in fatigue, 445 in fatigue crack growth, 587–589 in static fracture, 320–321 Epoxies, 41, 90, 102–103, 105, 139, 202, 341 Equivalent completely reversed stress amplitude, 456, 478, 760 Equivalent completely reversed uniaxial stress, 466 Equivalent constant amplitude stress, 475–476, 479, 535, 603 and safety factors, 475–477 Equivalent life, for zero-mean stress, 760–762, 765 European Standards (European Union), 122 Extensometers, 122 Extrusion, 68 F Face-centered cubic (FCC) structure, 46–47, 61 Factor of safety. See Safety factors Failure criteria, 275–322 brittle vs. ductile behavior, 318–320 comparison of, 295–296 cracks, time-dependent effects of, 320–321 fracture in brittle materials, 299–301 load factor design, 296–297940 Index Failure criteria (Continued) stress raiser effects, 297–298 See also Fracture criteria; Yield criteria Failure envelope, for Mohr’s circle, 301 Failure surface, 278 Fatigue, 25–27, 36, 416–479, 491–543 corrosion with, 28, 445, 589 crack initiations in, 25–26, 435–441, 757, 787–789 cyclic loading, 418–420 sources of, 429–430 definitions for, 418–421 designs for, 536–537 fatigue damage, physical nature of, 435–441 fatigue limit behavior, 447–449 fatigue testing apparatus and specimens, 430–435 fracture mechanics approach, 417, 560–622 fretting, 27–28, 536 high-cycle and low-cycle types, 26, 423–424, 754 mean stresses, 451–462 life estimates with, 456–461 normalized amplitude-mean diagrams, 452–454 presentation of mean stress data, 451–452 safety factors with, 461–462 multiaxial stresses, 463–467 effective mean stress, 465–466 effective stress amplitude, 465–466 equivalent completely reversed uniaxial stress, 466 notch effects, 443, 491–501, 506–513, 771–785 point stresses versus nominal stresses, 420–421 prevention of, 25–26 residual stress effects, 446–447, 539–541, 785 safety factors for S-N curves, 427–429 size effects, 503, 758 statistical scatter in, 449–451 strain-based approach, 417, 745–790 stress versus life (S-N) curves, 421–426 equations for, 423 estimating, 520–527 trends in, 441–451 stress-based approach, 416–479, 491–543 surface finish effects, 503, 757 variable amplitude loading, 468–477 cycle counting for irregular histories, 471–474 equivalent stress level and safety factors, 475–477, 535 Palmgren–Miner rule, 468–470, 786–787 Fatigue crack growth, 27, 560–622 arrested, 606 behavior, 584–590 trends with material, 584–587 trends with temperature and environment, 587–590 behavior, describing, 564–568 constant amplitude loading, life estimates for, 590–601 crack growth analysis, need for, 561–563 damage-tolerant design, 563, 607–609 definitions for, 564 design considerations, 607–609 fatigue crack growth tests, 569–574 geometry independence of da/dN vs. K curves, 573 test methods and data analysis, 569–572 test variables, 572–573 Forman equation, 580–581 Paris equation, 564–565 plasticity aspects and limitations of LEFM for, 609–615 limitations for small cracks, 613–615 plasticity at crack tips, 610–612 thickness effects, 612–613 R-ratio effects, 574–584, 590 sequence effects on, 606–607 and stiffeners, 608–609 threshold value Kth, 565, 621 variable amplitude loading, life estimates for, 601–607 Walker equation, 574–580 Fatigue crack growth rate, 560, 569–570 Fatigue Design Handbook (SAE), 455, 474, 540, 694 Fatigue failure design details, 536–539 designing to avoid, 536–541, 607–609 surface residual stresses, 539–541 Fatigue limits, 423 behavior of, 447–449 and engineering design, 448 estimating, 501–506 factors affecting, 502–503 reduction factors, 504–506 load type, size, and surface finish, 504 in variable amplitude fatigue, 449, 469, 534–535, 787Index 941 Fatigue notch factor, 493–501, 788–789 at short life, 506–510, 783 for mean stress, 510–513, 783 Fatigue strength, 423–424 Fatigue testing, 430–435 component tests, 526–529 crack growth tests, 569–574 reciprocating bending test, 433–434 resonant vibration test, 434–435 rotating bending test, 430–433 strain-life tests, 668–671, 748–753 test apparatus and specimens, 430–435 Ferrite (α-iron), 76 Ferritic stainless steel, 79 Ferromagnetic metals, 862 Ferrous alloys, 72 Fiberglass, 41, 94 Fibrous composites, 102–104, 217–218 Finite element analysis, 191, 298, 354, 420, 694, 717 Fir tree design, 492, 536 Flaw shape factor, 360 Flexure tests and strength, 170–171 Fluctuating dipole bond, 45 Forging, 66, 68, 335 Forman equation, 580–581 Fracture, 19–20 brittle, 23, 299–300 cleavage, 376–378 costs of, 36–37, 417 of cracked members, 334–400 dimpled rupture, 376–378 ductile, 24–25 intergranular, 610–611, 619 modes, 344 for static and impact loading, 23–25 in torsion tests, 172 transgranular, 611 types of, 20 Fracture criteria, 275, 279–281, 299–301 Coulomb-Mohr, 301–311 maximum normal stress, 279–282, 314 modified Mohr, 311–318 Fracture mechanics, 23–24, 37, 277, 334–336, 417 application to design and analysis, 348–371 for environmental cracking, 616–621 extensions of, 391–398 crack-tip opening displacement (CTOD), 398 fracture toughness tests for JI c, 395–398 J-integral, 393–400 plastic zone adjustment, 392–393 for fatigue crack growth, 560–615 plasticity limitations, 386–390, 612–613 plastic zone size, 381–386, 611–612 strain energy release rate G, 345, 348 stress intensity factor K, 346–348 Fracture mechanism map, 807 Fracture strain engineering type, 131 true type, 149–151 Fracture strength, true, 149–151 Fracture surface, 278 Fracture toughness, 23–24, 134, 168–169, 334, 339 effects of cyclic loading, 583 effects of temperature and loading rate, 376–379 effect of thickness on, 387–389 microstructural influences, 379–381 mixed-mode fracture, 381 values and trends, 371–381 Fracture toughness testing, 371–381, 390–391, 395–398 Frequency-modified fatigue approach (Coffin), 834 Fretting, 27–28, 536 Full yielding (in fatigue), 508–510 Fully plastic limit load (force or moment), 357, 392, 400, 700–701, 890–899 Fully plastic yielding, 594, 713–714 F-111 aircraft crash (1969), 343 G Gage length, 125 Gamma iron, 47 Gas-turbine engines, 34 Gaussian distribution, 451, 902–904 Generalized Hooke’s law, 204–206, 223–224 Generalized plane stress, 234, 244–246 Generalized Poisson’s ratio, 653, 718 Geometric constraint, 212–213, 293–295, 385–386, 388, 717–718 Geometric discontinuities, 491 Gerber parabola, 455 Glass, 40–41, 93–100, 102, 112, 126, 161, 202, 223, 341 chemical bonding in, 40 creep in, 810 ductility, 137942 Index Glass transition temperature, 52–53, 88–91 Glass-fiber-reinforced thermoplastics, 106, 443 Glinka’s rule, 717 Goodman equation, 454 for notched members, 510–511 Grain boundaries, 48, 50, 59–60, 813–815 Grain boundary sliding, 813–814 Grain refinement, 69 Graphite, 55, 102 Graphite-epoxy, 41, 106, 218 Gray cast iron. See Cast irons Griffith, A. A., 344 H Hardening cycle-dependent, 668 dispersion, 101–102 isotropic, 641 kinematic, 641, 661 precipitation, 70–72, 79–84, 101 strain, 134 surface hardening treatments, 540 Hardness correlations and conversions, 163–164 Hardness tests, 157–164 Brinell hardness test, 159, 175 Mohs hardness scale, 157 Rockwell hardness test, 162–163, 175 Scleroscope hardness test, 157 Vickers hardness test, 160–162, 175 Haynes 188 (superalloy), 83 Heat treatment, 66, 76–77, 81 Heat-deflection temperature, 172 Heat-deflection test, 171–172 Hexagonal close-packed (HCP) crystal structure, 47, 61, 82 High-carbon steels, 76–77 High-cycle fatigue, 26, 423–424, 754 High-impact polystyrene (HIPS), 93 High-performance composites, 100, 103–104, 106, 112 High-strength low-alloy (HSLA) steels, 78 High-temperature creep, 817 Hill anisotropic yield criterion, 298–299 Homogeneous material, 202 Hooke’s law, 213, 264, 277, 848 anistropic case, 214–218 for elastic strains (with plasticity), 649–651 isotropic case, 204–213 orthotropic case, 215–216 Hot isostatic pressing, 97 Hydrogen bond, 45–46 Hydrogen embrittlement, 616 Hydrostatic stress, 210 effect on fracture, 318–320 effect on yielding, 285–286, 291, 295 as octahedral normal stress, 261 Hysteresis loops, 664–667, 722, 725–733, 748–749, 775–781, 860 curve shapes, 673–677 elliptical, 856–857 I Impact energy tests, 164–169 Impact loading, fracture under, 23 Impurity (interstitial, substitutional), 48–49 Inclusions, fracture effect, 335, 379–381 for fatigue, 436, 438 Inconel 736(superalloy), 83, 582 Incremental plasticity theory, 641, 658 deformation plasticity theory vs., 658–659 Indentation hardness, 157–164 Inelastic deformation, 55–61 Initial yielding (in fatigue), 512–513 Initial yielding force or moment, 700, 713, 891–894 Inspection for cracks, 336–337, 561–563, 607–609 Instron Corp. testing machine, 121 Intergranular fracture, 25, 610–611, 619–620 Intermetallic compounds, 44, 48, 70 Internal combustion engine, 34 Internal friction. See Damping in materials Internally flawed materials, 344 International Organization for Standardization (ISO), 122 Interstitial, 49 Invariant quantities, 211, 257, 261 Ionic bonding, 42–44, 47–48 Irons, cast. See Cast irons Irregular load vs. time histories. See Variable amplitude loading Irwin, G. R., 345, 386 Isochronous stress–strain curves, 809, 836–838, 850–854, 864–865 Isothermal modulus, 860 Isotropic behavior, 191, 202–203Index 943 Isotropic hardening, 641 Izod tests, 139, 165 J Jet engines, 34 J-integral, JI c tests, 393–400 Juvinall, R. C. mean stress approach, 513 S-N curve estimate, 520, 522–523 K Kevlar, 85–86, 93, 103, 105, 218 K-field, 386–387 Kinematic hardening, 641, 661 L Laminated composites, 101, 102–105 Langer, B. F., 468 Larson–Miller (L-M) time-temperature parameter, 822, 825–830 Lattice plane and site, 48 Lead, 66, 67, 202 Leak-before-break condition, 369–371 Liberty Ships and tankers, 343 Lignin, 100 Line defects (dislocations), 48, 50 Linear-elastic fracture mechanics (LEFM), 339, 347, 386, 398 See also Fracture mechanics Linear elastic material, 203 Linear hardening, 194, 643–644 Linear polymers, 87–88 Linear variable differential transformers (LVDTs), 122 Linear viscoelasticity, 196, 223, 836–838 component analysis for, 850–853 damping for, 855–863, 865–866 step loading for, 844–846 Liquid metal embrittlement, 616 Load cells, 122 Load factor design, 32, 296–297, 318, 321 in fatigue, 461–462, 476, 534 Loading path dependence, 658–659 Local yielding, 508–509, 511–513, 710, 714–717 Log decrement, 858 Lognormal distribution, 451, 908 Loss coefficient, 858 Low-alloy steels, 34, 74, 77–78 AISI-SAE designations for (table), 75 Low-carbon steel, 76 Low-cycle fatigue, 26, 423–424, 754 Low-density polyethylene (LDPE), 91–92, 139 Lower yield point, 130 Low-temperature creep, 817 M Magnesium and alloys, 41, 47, 66–67, 83, 111, 138, 152, 202 Magnetoelastic damping, 860 Major Poisson’s ratio, 221 Malleable iron, 76 Manganese, 47, 66, 76 Manson, S. S., 750, 834 Maps, for creep mechanisms, 807, 817 Maraging steels, 79, 138, 152, 340 MARM 302 (superalloy), 83 Martensite, 77 Martensitic stainless steel, 79 Materials damping, 804, 855–862, 865–866 See also Damping in materials Materials selection, 66, 105–112 Maximum normal stress fracture criterion, 279–282, 311, 314 Maximum shear stress, 246–251 Maximum shear stress yield criterion, 282–286 development of, 282–284 graphical representation of, 284–285 hydrostatic stresses and, 285–286 Mean stress, 418–419 discussion of, 765, 782–785 effects of, 451–452, 758–767 equivalent life for, 761–762, 765 in fatigue crack growth, 574–583 life estimates with, 456–461 mean stress equations, 454–456, 760–765 mean stress tests, 759 normalized amplitude-mean diagrams, 452–454 for notched members, 510–520, 523 presentation of mean stress data, 451–452 safety factors with, 461–462 in strain-based fatigue, 758–767 modified Morrow approach, 762–763944 Index Mean stress (Continued) Morrow equation, 761–762, 765 Smith, Watson, and Topper (SWT) parameter, 763–764 Walker relationship, 764–765 Mean stress relaxation, 678–681, 783–785 Mechanical behavior of materials, 19, 37 Mechanical testing, 118–176 bending and torsion tests, 169–175 closed-loop servohydraulic test system, 121–122 compression tests, 151–156 creep tests, 804–809 cyclic stress–strain tests, 668–671 engineering stress–strain properties (in tension), 128–137 environmental crack growth tests, 616–618 extensometers, 122 fatigue tests crack growth, 569–574 strain-life, 748–753 stress–life (S-N), 430–435, 527–529 fracture toughness tests, 371–374, 390–391, 395–398 hardness tests, 157–164 hardness correlations and conversions, 163–164 Instron Corp. testing machine, 121 linear variable differential transformers (LVDTs), 122 load cells, 122 MTS Systems Corp., 121 notch-impact tests, 164–169 specimens, 118–119 standard test methods, 122–123 strain gages, 122 tensile behavior, 137–143 tension tests, 123–128 test equipment, 119–122 true stress–strain curves and properties, 148–150 universal testing machines, 119–121 Medium-carbon steels, 76–77 Memory effect, 196, 661, 677, 730, 734, 775–776, 789 Metallic bonding, 43–44 Metals, 40–41 alloying/processing of, 66–72 creep in, 802, 813–819 cyclic deformation in, 668–676 environmental crack growth in, 616–621 fatigue in, 435–451, 754–757 fatigue crack growth in, 584–590 fracture in, 374–381 irons and steels, 72–79 low-stress damping in, 858–862 nonferrous metals, 80–84 strengthening methods for, 68–72 Microcracks, 338, 786, 820–821 Microstrain, 126 Microvoid coalescence. See Dimpled rupture Mild steel, 76 Miner, M. A., 468 Minimum detectable crack length, 562 Mixed-mode fracture, 381 Models. See Rheological models Modified Goodman equation and line, 454 Modified Mohr fracture criterion, 311–314, 321–322 Modulus of elasticity. See Elastic modulus Mohr, Otto, 240, 255 Mohr’s circle, 240–244, 247, 250–251, 255, 263–264 as failure envelope, 301 Mohs hardness scale, 157 Molybdenum, 66, 79 Monotonic loading, 639 Monotonic plastic zone, 611 Monotonic proportional loading, 658–659 Monotonic straining, 194 Morrow, J., 455, 761 Morrow mean stress relationship, 455–456, 761–763 MTS Systems Corp., 121 Multiaxial stress effects creep, 833, 848–850 elastic deformation, anisotropic case, 214–223 elastic deformation, isotropic case, 204–213 fatigue, 463–467, 767–771 fracture, cracked members, 381, 387–389 fracture, uncracked members, 279–282, 299–318 plastic deformation, 649–659, 717–718 yielding, 282–295 See also Three-dimensional stress–strain relationships N Nabarro–Herring creep, 814–815 NASGRO, 602 Natural stone, 94, 96, 112 Naval brass, 83Index 945 Necking, 131–132, 138–140, 805 Network modifiers, 98 Neuber constant, 499 Neuber, H., 499 Neuber’s rule, 694, 714–717, 720, 727, 733, 772–774, 789 strain-based fatigue method, 771–781 residual stresses and strains at notches, 719–722 Neutron radiation effects, 381 Nickel, 34, 47, 49, 66, 67, 70, 83–84, 98, 587, 803, 807, 817 plating, 447 Nickel-base superalloys, 41, 83, 582, 751, 824, 827 Niobium, 66 Nitrides, 59 Nitriding of steels, 447, 540 Nodular iron, 75 Nominal stresses, 420 point stresses vs., 420–421 Nonferrous metals, 80–84 aluminum alloys, 80–82, 111 copper alloys, 83 magnesium alloys, 83, 111 superalloys, 83, 111 titanium alloys, 82–83, 111 Nonlinear creep equations, 838–841 Nonlinear hardening, rheological modeling of, 648–649 Nonpropagating cracks, 496, 789 Nonproportional loading, 463, 466, 658–659, 732–733, 769–770, 780 Normal distribution, 451, 902–904 Normal stress fracture criterion, 279–282, 311, 314 Normalized amplitude-mean diagram, 452–454 Notch effects in fatigue, 443, 491–497 crack growth effect, 495–496 fatigue notch factor, 493–494, 497–501 at intermediate and short lives, 506–510 and mean stress, 510–520 process zone size and weakest-link effects, 494–495 reversed yielding effect, 496–497 Notch sensitivity, 497–501 Notched members, 710–722 elastic behavior and initial yielding, 712–713 elastic stress concentration factor, 337–338, 420, 889–890 fracture criteria for, 297–298 fully plastic yielding, 713–714, 894–899 local yielding analysis Neuber’s rule, 694, 714–717, 720, 727, 733, 772, 774, 789 strain energy (Glinka) method, 717 residual stresses and strains in, 539–540, 719–722, 732 strain-based fatigue method, 771–785 stress-based fatigue method, 491–543 yield criteria for, 297–298 Notched specimens, 119, 435, 531 Notch-impact tests, 164–169, 336 Charpy V-notch test, 165 dynamic tear test, 165 fracture toughness vs., 168–169, 379 Izod tests, 165 temperature-transition behavior, 168 Numerical integration (for crack growth), 598–601 Nylons, 41, 86, 111, 139, 140, 202 O Octahedral planes, stresses on, 260–262 Octahedral shear stress yield criterion, 288–295 development of, 288–290 energy of distortion, 292 graphical representation of, 290–292 Offset yield strength, 130 Opening mode crack, 344 Orthotropic materials, 215–217 Overall range, 471 Overload effects. See Sequence effects in fatigue Oxidation, and creep, 803 Oxides, 59, 94, 96–99 P Palmgren, A., 468 Palmgren–Miner rule, 468–469, 475, 478, 527, 529, 535, 542, 775–776, 786–787, 833–834 Paris equation, 564–565, 621 Particulate composites, 100–102 Peaks, 471 Pearlite, 76 Percent elongation, 22, 131–132 Percent reduction in area (%RA), 131–132946 Index Perfectly plastic stress–strain curve, 194–196, 641–643 See also Elastic, perfectly plastic stress–strain relationship Periodic inspections for cracks, 562–563, 607 Periodic overstrains (in fatigue), 449, 787 Peterson constant, 497–499 Phase angle, 856, 858 Plain-carbon steels, 72, 76 Plane strain fracture toughness, 339, 373–381, 390–391, 399–400 Plain strain, 263 crack plastic zone, 385–386 fracture effect, 373–374, 387–389, 391 in notch, 717–718 Plane stress, 235–245, 249–253 crack plastic zone, 384–385 fracture effect, 387–389, 391 generalized, 244–245, 263–264 Mohr’s circle for, 240–242 plastic deformation for, 654–657 principal stresses, 237–239 rotation of coordinate axes, 236–237 Plastic collapse, 693, 700, 890–899 Plastic deformation, 21–22, 55–59, 190, 194–196, 200–201, 223 behavior and models for materials, 638–683 in bending, 694–703 analysis by integration, 696–698 discontinuous stress–strain curves, 699–701 elastic bending, 694–696 Ramberg–Osgood Stress–strain curve, 701–703 rectangular cross sections, 698 of components under cyclic loading, 722–734 cyclic stress–strain behavior of materials, 668–681 cyclic stress–strain curves and trends, 671–673 cyclic stress–strain tests and behavior, 668–670 hysteresis loop curve shapes, 673–677 mean stress relaxation, 678–681 by dislocation motion, 56–58 fracture methods for, 391–398 memory effect in, 196, 661, 677, 730, 775, 776, 789 in notched members, 496, 506–513, 710–722 rheological modeling of, 194–196, 641–644, 648–649, 659–668 cyclic loading behavior, 664–667 irregular strain versus time histories, 667–668 unloading behavior, 661–664 significance of, 638–639 stress-strain curves, 641–649, 681 elastic, linear-hardening relationship, 643–644 elastic, perfectly plastic relationship, 641–643, 681, 699, 710, 715 elastic, power-hardening relationship, 644, 716 Ramberg–Osgood relationship, 644–645, 671, 701–703, 708, 710, 716, 771 simple power-hardening relationship, 698, 709 three-dimensional stress–strain relationships, 649–659 application to plane stress, 654–656 deformation plasticity theory, 650–653 deformation vs. incremental theories, 658–659 effective stress–strain curve, 653–654 time dependence of, 639 in torsion, 707–710 unloading and cyclic loading behavior from rheological models, 659–668 Plastic hinge, 700–701 Plastic modulus, 651–652 Plastic strain, 21, 190, 200–201, 638 See also Plastic deformation Plastic strain damping, 860–862 Plastic zone (at crack tip), 338, 381–390, 392 for cyclic loading, 610–612 for plane strain, 385–386 for plane stress, 384–385 plane stress versus plane strain, 387–389 plasticity limitations on LEFM, 386–387 Plasticity. See Plastic deformation Plasticizers, 93 Plastics. See Polymers Plating, 447, 540 Plywood, 41, 104 Point defects, 48–49 interstitial impurity, 49 self interstitial, 49 substitutional impurity, 48 vacancy, 48–49 Poisson’s ratio, 129, 202–204, 213, 682 for anistropic materials, 216–217, 221 generalized, 653 and Hooke’s law, 204–206, 652 Polaris missile, 343 Polycarbonate (PC), 86, 88, 106, 139, 202Index 947 Polycrystalline materials, 48 Polyethylene (PE), 41, 44, 55, 85–86, 88, 111, 139, 202, 813, 839 crystal structure of, 87 Polyethylene terephthalate (PET), 86 Polyisoprene, 88, 90 Polymers, 40–41, 84–94, 111, 203 amorphous, 48, 88 atactic, isotactic, syndiotactic, 88 classes, examples, and uses of (table), 85 combining and modifying, 92–94 covalent bonds in, 46 creep in, 802–803, 813 crystalline, 88 and cyclic loading, 445, 672–673 damping in, 861 elastomers, 84, 90–91 fatigue in, 441, 445, 752 fatigue crack growth in, 585 fracture toughness of, 373, 376 linear, 88 molecular structures of, 84–86, 91 naming conventions, 84 strengthening effects, 91–92 tensile stress-strain curves for, 126–127, 130–131 thermoplastics, 84–86 crystalline versus amorphous, 86–88 molecular structure of, 84–86 thermosetting plastics, 84, 89–90 yield criteria for, 299 yield strengths in compression, 299 yield strengths in tension, 130 Polymethyl methacrylate (PMMA), 84–85, 88 Polyoxymethylene (POM), 86, 88 Polyphenylene oxide (PPO), 86 Polypropylene (PP), 85–86, 88 Polystyrene (PS), 41, 85–86, 88, 139, 341 Polytetrafluoroethylene (PTFE), 84–86, 140 Polyurethane elastomers, 90 Polyvinyl chloride (PVC), 41, 46, 85, 86, 88, 139, 341 Poncelet, J. V., 417 Pop-in crack, 390 Porcelain, 94, 95, 112, 161 Potential drop method, 396, 569 Potential energy, in fracture, 345, 393–394 Power-hardening stress–strain relationship, 148, 644 in bending, 698 in notched members, 716 in torsion, 709 Power-law creep, 813–816 in bending, 854 relaxation for, 843–844 Precipitate, coherent, 70, 102 Precipitation hardening, 70–72, 79–83, 101 Precipitation-hardening stainless steels, 73, 79, 578, 582 Precrack, 390, 395–396, 569 Prepregs, 103 Presetting, 446–447, 539 Pressure effect. See Hydrostatic stress Pressure vessels cracks in, 336 leak-before-break design, 369–371 stresses in, 884–888 Primary chemical bonds, 42–44 Primary stage of creep, 805 See also Transient creep Primitive cubic (PC) structure, 46–47 Principal axes, 235, 255 Principal strains, 263 Principal stresses, 235, 237–240, 256–257 directions for, 235, 237–240, 257–260 and the maximum shear stress, 245–253 principal normal stresses, 237, 245, 255 principal shear stresses, 246–251 Process zone size, 494–495 Product liability costs, 36 Proportional limit, 130 Proportional loading, 280, 658–659 Prototype, 32–34 Q Quality factor, 858 Quasi-isotropic material, 221 Quenching and tempering of steels, 72–73, 76–77, 79 R Radiation embrittlement, 381 Rainflow cycle counting, 471–474, 677, 775–777 Ramberg–Osgood relationship, 148, 644–648 in bending, 701–703 for biaxial stress, 656 for cyclic stress–strain curve, 671, 747948 Index Ramberg–Osgood relationship (Continued) in notched members, 716 in pure shear, 708 for tension test, 148–151 time variable added, 840 in torsion, 710 Range of stress, 418–419, 471, 564 Ratchetting, 678–679 R-curve, 397–398 Reaction bonding, 97 Reciprocating bending test, 433–434 Recovery of creep strain, 198, 201, 223, 813, 820–821, 841–842 Redistributed stress, 298, 338, 384 Reduction in area, 131, 132, 149 Refractory metals, 66 Region of K -dominance, 386 Reinforcement in polymers, 93–94 Relative P-M rule, 542 Relaxation behavior, 198–199, 223, 842–844 for mean stress, 678–680, 783–785 Remnant displacement, 856, 858 Repeating unit in polymers, 84 Residual stresses and strains, 446–447, 536 for bending, 703–707 analysis for interior of the beam, 706–707 and fatigue, 446–447, 539–541 at notches, 539–541, 719–722 and plastic deformation, 638–640 Resonant vibration, 434 Reversed yielding (at notches), 496–497, 511–513 Rheological models, 190–200, 223, 640, 659–661 damping behavior of, 855–857 creep in, 191–194, 196–198, 836–838, 844 linear viscoelastic behavior of, 836–838 plastic deformation in, 194–196, 641–644, 648–649 recovery in, 198, 813–814 relaxation in, 198–200, 842–844 unloading and cyclic loading behavior from cyclic loading behavior, 664–665 irregular strain versus time histories, 667–668 unloading behavior, 661–663 Rockwell hardness test, 162–163, 175 Rolling, 66, 68 Rosettes, strain gage, 266–267 Rotating bending test, 430–433 Rotating disc, stresses, 887–889 R-ratio, 419–420 effects in crack growth, 574–584 in mean stress equations, 455–456, 514, 516–517, 765 Rubbers, 41, 90–91 Rupture in creep, 25, 37, 804–807, 821–834 dimpled, 376, 378 modulus of, in bending, 171 S SAE Fatigue Design Handbook, 455, 474, 540, 694 SAE steel nomenclature, 73–75 Safety, 29 Safety factors, 30–32, 278 for crack growth, 562–563 for cracked members, 356–359 for creep rupture, 831–833 in design, 30–32 for fatigue, 427–429, 461, 475–477 for uncracked member fracture, 279–281, 310, 314, 321 for yielding, 284, 290, 296 Safety margin in temperature, 831 Sandwich materials, 105 Scarf joints, 537 Scleroscope hardness test, 157 Screw dislocation, 50 Secant modulus, 652, 653 Secondary chemical bonds, 44–46 Secondary stage of creep, 805 Self interstitial, 49 Sequence effects in fatigue, 449, 469, 542, 601, 606–607, 785–787, 790 Service experience, 34 Servo-hydraulic machines, 121–122, 435 Shear center, 695 Shear lip, 441 Shear modulus, 106, 173, 205, 216 for composite materials, 216–217, 221 Shear stress yield criterion, 282–288 Sherby–Dorn (S-D) time-temperature parameter, 822–825 Shigley, J. E., S-N curve estimate, 520 Ship structures, cracks in, 336, 343 Short cracks, defined, 613–614 Shot peening, 446, 539Index 949 SiC-aluminum composite, 41, 102, 140 Silica (SiO2), 98 Silica glasses. See Glass Silicon, 55, 59, 66 Silicon carbide (SiC), 55, 95, 102, 104, 161, 202, 341 Silicon nitride (Si3N4), 95, 97, 161, 341 Simple range, 471 Simpson’s rule, 598 Simulated service testing, 33 Sintering, 97 Size effect, in fatigue, 494–495, 503–505, 758 Sliding mode crack, 344 Slip (in crystals), 56–58, 436–437, 815 Slope reduction factor, 643, 649 Slow-stable crack growth, 390–391, 399 Small cracks, defined, 613–615 limitations for, 613–615 transition length, 615 Small-strain theory, 204 Smith, Watson, and Topper (SWT) equation, 455 for notched members, 510, 513–516 for strain-life curves, 763–764 Smooth specimens, 118, 435 S-N (stress vs. fatigue life) curves, 421–426, 746, 750 component S-N data, use of, 527–535 Bailey bridge example, 527–529 curves for welded members, 531–535 matching to notched specimen data, 531 mean stress and variable amplitude cases, 529 equations for, 423, 443, 456–457, 516–520, 531–535 estimating, 520–527 safety factors for, 427–429, 461, 476, 535 trends in, 441–451 environment and frequency effects, 445 geometry, 443 mean stress, 443 microstructure, effects of, 445–446 ultimate strength, 441–443 Walker equation fit, 516–520 Snoek effect, 858–859 S-N-P curves, 451 Solid solution strengthening, 69–70, 80, 82, 83 Solution heat treatment. See Precipitation hardening Specimens, test, 118–119, 169 for bending, 170 for compression, 151 for fatigue, 434–435, 748 for fatigue crack growth, 569 for fracture toughness, 371–373 for notch-impact, 165–166 for tension, 123–124 for torsion, 172–175 Spherulites, 87 Spring and slider rheological models, 194–196, 659–668 Stacking fault, 50 Stainless steels, 34, 72, 78–79 Standard test methods, 122–123 See also ASTM Standards State-of-stress effects. See Multiaxial stress effects Static loading fracture under, 23 life estimates for crack growth, 616–621 Static loads, 429 Stationary loading, 602 Statistical variation in fatigue, 449–451 in fracture toughness, 376, 906 in materials properties, 900–908 Steady-state creep, 191–194, 196–197, 805 Steam engines, 34 Steels, 41, 72–79, 98, 111, 298, 343 as-quenched, 77 carbon, 76–77 high-carbon, 76–77 low-alloy, 34, 72, 77–78 low-carbon, 76 medium-carbon, 76–77 mild, 76, 202 naming system for, 73–75 plain-carbon, 72, 76 quenching and tempering, 77 stainless, 34, 72, 78–79, 202 tool, 72, 79 Step loading creep deformation under, 844–848 creep rupture under, 833–834 of linear viscoelastic models, 844–846 Stiffness, 94, 105, 112 See also Elastic modulus Storage modulus, 858 Strain, 21, 125–128 complex states of, 262–267 engineering shear strains, 262, 650950 Index Strain (Continued) engineering type, 125 plane stress, special considerations for, 263–266 principal strains, 263 strain gage rosettes, 266–267 tensor shear strains, 262, 650 transformation of axes, 262 true type, 144 units for, 126 Strain-based approach to fatigue, 417, 745–790 crack growth effects, 787–789 development of, 746 discussion, 781–789 life estimates for structural components, 771–781 constant amplitude loading, 771–774 irregular load vs. time histories, 775–780 simplified procedure for irregular histories, 780–781 local mean stress, sequence effects related to, 785 mean stress effects, 758–767, 782–785 mean stress tests, 759 multiaxial stress effects, 767–771 critical plane approaches, 769–771 effective strain approach, 768–769 physical damage to the material, sequence effects related to, 786–787 stress-based approach compared to, 745–746, 781–782 Strain energy density (Glinka) method, 717 Strain energy release rate G, 345, 348, 393–394 Strain gages, 122 rosettes, 266–267 Strain hardening, 134, 194, 643–649 Strain hardening exponent, 148, 644 Strain-hardening rule, in creep, 846–848 Strain–life data, availability of, 750–752 Strain-range partitioning approach, 834–836 Strain versus life curves, 746, 748–758 creep–fatigue interaction, 757 engineering metals, trends for, 754–757 factors affecting, 757–759 strain–life tests and equations, 748–754 surface finish and size effects, 757–758 transition fatigue life, 753–754 mean stress effects, 758–767 Strength, 20, 105, 111, 129–130, 149–150 in bending, 170–171 in compression, 154–156 in tension, 129–130, 149–150 theoretical, 53–55 in torsion, 172–173 Strength coefficient, 148 Strengthening effects in polymers, 91–92 Strengthening methods for metals, 66–72 Stress, 20, 124–128 basic formulas for, 880–882 components of, 235–236 definitions for cycling, 418–420 engineering type, 125 generalized plane stress, 244–245 Mohr’s circle for, 240–244 nominal type, 420 on octahedral planes, 260–262 plane stress, 235–236, 249–253 point stress vs. nominal stress, 420–421 in pressure vessels, tubes, discs, 884–889 principal stresses, 235, 237–240, 245–247, 253–257 three-dimensional states of, 253–260 transformation of axes, 236–237 true type, 143–144 von Mises stress, 298 Stress amplitude, 418–419 Stress and strain concentration factors, 710, 712, 714–717 See also Elastic stress concentration factor; Notched members Stress corrosion cracking, 25, 616 Stress field, at crack, 346–347 Stress gradient, 494 Stress intensity factor, 339, 346–348 range for fatigue crack growth, 564, 571 See also Fracture mechanics Stress invariants, 211, 257, 261 Stress raisers, 491, 889–892 and design details, 536–539 effects of, 297–298 and fatigue strength reduction, 443, 493–500, 541–542 from surface roughness, 503 from welding, 447, 531 See also Notch effects in fatigue; Notched members Stress range, 418–419 Stress ratio R, 419 Stress redistribution, 298, 338, 384Index 951 Stress relaxation, 198–199, 223, 2842–844 Stress relief, 540 Stress-based approach to fatigue, 416–479, 491–543 fatigue failure, designing to avoid, 536–541 See also Fatigue limits; Fatigue testing; Mean stress, effects of; Notch effects in fatigue; S-N (stress vs. fatigue life) curves Stress–life curves for creep, 806–808, 831 for fatigue, 421–426 See also S-N (stress vs. fatigue life) curves Stress–strain analysis for creep, 850–855 for cyclic loading, 722–728 in bending, 722–725 with irregular load vs. time histories, 728–732 of notched members, 710–722 elastic behavior and initial yielding, 712–713 estimates of notch stress and strain for local yielding, 714–717 fully plastic yielding
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أخوانى فى الله أحضرت لكم كتاب Mechanical Behavior of Materials - Engineering Methods for Deformation, Fracture, and Fatigue Fourth Edition Norman E. Dowling Frank Maher Professor of Engineering Engineering Science and Mechanics Department, and Materials Science and Engineering Department Virginia Polytechnic Institute and State University Blacksburg, Virginia International Edition contributions by Katakam Siva Prasad Assistant Professor Department of Metallurgical and Materials Engineering National Institute of Technology Tiruchirappalli R. Narayanasamy Professor Department of Production Engineering National Institute of Technology Tiruchirappalli
و المحتوى كما يلي :
Contents PREFACE 11 ACKNOWLEDGMENTS 17 1 Introduction 19 1.1 Introduction 19 1.2 Types of Material Failure 20 1.3 Design and Materials Selection 28 1.4 Technological Challenge 34 1.5 Economic Importance of Fracture 36 1.6 Summary 37 References 38 Problems and Questions 38 2 Structure and Deformation in Materials 40 2.1 Introduction 40 2.2 Bonding in Solids 42 2.3 Structure in Crystalline Materials 46 2.4 Elastic Deformation and Theoretical Strength 50 2.5 Inelastic Deformation 55 2.6 Summary 61 References 62 Problems and Questions 63 3 A Survey of Engineering Materials 65 3.1 Introduction 65 3.2 Alloying and Processing of Metals 66 3.3 Irons and Steels 72 3.4 Nonferrous Metals 80 3.5 Polymers 84 56 Contents 3.6 Ceramics and Glasses 94 3.7 Composite Materials 100 3.8 Materials Selection for Engineering Components 105 3.9 Summary 111 References 113 Problems and Questions 114 4 Mechanical Testing: Tension Test and Other Basic Tests 118 4.1 Introduction 118 4.2 Introduction to Tension Test 123 4.3 Engineering Stress–Strain Properties 128 4.4 Trends in Tensile Behavior 137 4.5 True Stress–Strain Interpretation of Tension Test 143 4.6 Compression Test 151 4.7 Hardness Tests 157 4.8 Notch-Impact Tests 164 4.9 Bending and Torsion Tests 169 4.10 Summary 175 References 176 Problems and Questions 177 5 Stress–Strain Relationships and Behavior 190 5.1 Introduction 190 5.2 Models for Deformation Behavior 191 5.3 Elastic Deformation 201 5.4 Anisotropic Materials 214 5.5 Summary 223 References 225 Problems and Questions 225 6 Review of Complex and Principal States of Stress and Strain 234 6.1 Introduction 234 6.2 Plane Stress 235 6.3 Principal Stresses and the Maximum Shear Stress 245 6.4 Three-Dimensional States of Stress 253 6.5 Stresses on the Octahedral Planes 260 6.6 Complex States of Strain 262 6.7 Summary 267 References 269 Problems and Questions 269Contents 7 7 Yielding and Fracture under Combined Stresses 275 7.1 Introduction 275 7.2 General Form of Failure Criteria 277 7.3 Maximum Normal Stress Fracture Criterion 279 7.4 Maximum Shear Stress Yield Criterion 282 7.5 Octahedral Shear Stress Yield Criterion 288 7.6 Discussion of the Basic Failure Criteria 295 7.7 Coulomb–Mohr Fracture Criterion 301 7.8 Modified Mohr Fracture Criterion 311 7.9 Additional Comments on Failure Criteria 318 7.10 Summary 321 References 322 Problems and Questions 323 8 Fracture of Cracked Members 334 8.1 Introduction 334 8.2 Preliminary Discussion 337 8.3 Mathematical Concepts 344 8.4 Application of K to Design and Analysis 348 8.5 Additional Topics on Application of K 359 8.6 Fracture Toughness Values and Trends 371 8.7 Plastic Zone Size, and Plasticity Limitations on LEFM 381 8.8 Discussion of Fracture Toughness Testing 390 8.9 Extensions of Fracture Mechanics Beyond Linear Elasticity 391 8.10 Summary 398 References 401 Problems and Questions 402 9 Fatigue of Materials: Introduction and Stress-Based Approach 416 9.1 Introduction 416 9.2 Definitions and Concepts 418 9.3 Sources of Cyclic Loading 429 9.4 Fatigue Testing 430 9.5 The Physical Nature of Fatigue Damage 435 9.6 Trends in S-N Curves 441 9.7 Mean Stresses 451 9.8 Multiaxial Stresses 463 9.9 Variable Amplitude Loading 468 9.10 Summary 478 References 479 Problems and Questions 4818 Contents 10 Stress-Based Approach to Fatigue: Notched Members 491 10.1 Introduction 491 10.2 Notch Effects 493 10.3 Notch Sensitivity and Empirical Estimates of k f 497 10.4 Estimating Long-Life Fatigue Strengths (Fatigue Limits) 501 10.5 Notch Effects at Intermediate and Short Lives 506 10.6 Combined Effects of Notches and Mean Stress 510 10.7 Estimating S-N Curves 520 10.8 Use of Component S-N Data 527 10.9 Designing to Avoid Fatigue Failure 536 10.10 Discussion 541 10.11 Summary 542 References 544 Problems and Questions 545 11 Fatigue Crack Growth 560 11.1 Introduction 560 11.2 Preliminary Discussion 561 11.3 Fatigue Crack Growth Rate Testing 569 11.4 Effects of R = Smin/Smax on Fatigue Crack Growth 574 11.5 Trends in Fatigue Crack Growth Behavior 584 11.6 Life Estimates for Constant Amplitude Loading 590 11.7 Life Estimates for Variable Amplitude Loading 601 11.8 Design Considerations 607 11.9 Plasticity Aspects and Limitations of LEFM for Fatigue Crack Growth 609 11.10 Environmental Crack Growth 616 11.11 Summary 621 References 623 Problems and Questions 624 12 Plastic Deformation Behavior and Models for Materials 638 12.1 Introduction 638 12.2 Stress–Strain Curves 641 12.3 Three-Dimensional Stress–Strain Relationships 649 12.4 Unloading and Cyclic Loading Behavior from Rheological Models 659 12.5 Cyclic Stress–Strain Behavior of Real Materials 668 12.6 Summary 681 References 683 Problems and Questions 684Contents 9 13 Stress–Strain Analysis of Plastically Deforming Members 693 13.1 Introduction 693 13.2 Plasticity in Bending 694 13.3 Residual Stresses and Strains for Bending 703 13.4 Plasticity of Circular Shafts in Torsion 707 13.5 Notched Members 710 13.6 Cyclic Loading 722 13.7 Summary 733 References 734 Problems and Questions 735 14 Strain-Based Approach to Fatigue 745 14.1 Introduction 745 14.2 Strain Versus Life Curves 748 14.3 Mean Stress Effects 758 14.4 Multiaxial Stress Effects 767 14.5 Life Estimates for Structural Components 771 14.6 Discussion 781 14.7 Summary 789 References 790 Problems and Questions 791 15 Time-Dependent Behavior: Creep and Damping 802 15.1 Introduction 802 15.2 Creep Testing 804 15.3 Physical Mechanisms of Creep 809 15.4 Time–Temperature Parameters and Life Estimates 821 15.5 Creep Failure under Varying Stress 833 15.6 Stress–Strain–Time Relationships 836 15.7 Creep Deformation under Varying Stress 841 15.8 Creep Deformation under Multiaxial Stress 848 15.9 Component Stress–Strain Analysis 850 15.10 Energy Dissipation (Damping) in Materials 855 15.11 Summary 864 References 867 Problems and Questions 868 Appendix A Review of Selected Topics from Mechanics of Materials 880 A.1 Introduction 880 A.2 Basic Formulas for Stresses and Deflections 88010 Contents A.3 Properties of Areas 882 A.4 Shears, Moments, and Deflections in Beams 884 A.5 Stresses in Pressure Vessels, Tubes, and Discs 884 A.6 Elastic Stress Concentration Factors for Notches 889 A.7 Fully Plastic Yielding Loads 890 References 899 Appendix B Statistical Variation in Materials Properties 900 B.1 Introduction 900 B.2 Mean and Standard Deviation 900 B.3 Normal or Gaussian Distribution 902 B.4 Typical Variation in Materials Properties 905 B.5 One-Sided Tolerance Limits 905 B.6 Discussion 907 References 908 ANSWERS FOR SELECTED PROBLEMS AND QUESTIONS 909 BIBLIOGRAPHY 920 INDEX 93 Index A A286 (superalloy), 83, 827 Absolute modulus, 858 Abusive grinding, 540 Accidental loads, 429 Acrylic (PMMA), 21, 139, 140, 202, 341 Activation energies, 811–812 defined, 809 evaluation of, 816–817 Adiabatic modulus, 860 AFGROW, 602 Aging. See Precipitation hardening Albert, W. A. J., 417 Allowable stress design, 31–32, 296, 321 Alloy steels. See Low-alloy steels Alloying, 66, 92, 111 Alloying and processing of metals, 66–72 annealing, 68–69 cold work, 68–69 grain refinement, 69 multiple phase effects, 70–72 precipitation hardening, 70–72 solid solution strengthening, 69–70 strengthening methods, 68 Alloys, 40–41, 43 Alpha iron, 47 Alternating stress, 419 Alumina (Al2O3), 41, 55, 96, 97, 161, 202, 341 Aluminum and alloys, 41, 66–67, 80–82, 101, 106, 111, 138, 152, 202, 296, 340, 343, 578, 582, 672, 751, 906 Aluminum bronze, 83 American Association of State Highway and Transportation Officials (AASHTO), 30, 534 bridge design code, 534–535 American Institute of Steel Construction, allowable stress design code of, 31–32 American Iron and Steel Institute (AISI), steel nomenclature, 73–75 AISI 304, 587 AISI 310, 73, 827 AISI 316, 78 AISI 403, 73, 78 AISI 1020, 73, 106, 109, 124, 133, 134–137, 138, 148, 150, 152 AISI 1040, 78 AISI 1045, 73, 77, 342–343, 751 AISI 1195, 73 AISI 1340, 74 AISI 4142, 138, 152, 751 AISI 4340, 73, 77–79, 106, 374–375, 578, 585, 589, 618, 620, 751 AISI T1, 73 933934 Index American Society for Testing and Materials (ASTM International), 73, 122 See also ASTM Standards American Welding Society (AWS) structural welding design code, 532–535 Amorphous materials, 98, 203 Amorphous thermoplastics, crystalline vs., 86–89 Amplitude, of stress, 418–419 Amplitude ratio, 419 Amplitude-mean diagram, 452–454 Andrade, 806 Anelastic damping, 855 Anelastic strain, 201, 855 Anisotropic Hooke’s law, 214–217 Anisotropic materials, 214–221 cubic material, 216 elastic modulus parallel to fibers, 219–220 elastic modulus transverse to fibers, 220–221 fibrous composites, 217–218 orthotropic materials, 215–217 stress–strain relationships, 214–224 yield criteria for, 298–299 Annealing, 69 Aramid, 86, 88 Aramid-aluminum laminate (ARALL), 41, 103–105 Areas, properties of, 882–884 Arrhenius equation, 811, 822, 864 ASTM Standards, 73, 78, 122–123, 131, 171, 314, 373, 398, 474, 569, 617, 668, 748 A242 steel, 78 A302 steel, 78 A395 cast iron, 73 A441 steel, 78 A514 steel, 138, 152 A517 steel, 78, 340 A533 steel, 78 A538-C steel, 73 A572 steel, 78 A588 steel, 78 A588-A steel, 73 E399, for fracture, 373, 390 E466, for fatigue, 430 E606 for low-cycle fatigue, 668, 748 E647 for crack growth, 569, 572 E1049 for cycle counting, 472, 474 E1290, for fracture, 398 E1681 for environmental cracking, 617 E1820, for fracture, 373, 394, 397–398 Ausforming process, 79 Austenite (γ -iron), 77 Austenitic stainless steels, 79 B Bailey bridges, 527 Bauschinger effect, 639–641, 664 Beach marks, 440–441 Beams, 884–885 Bend (fracture) specimen, 351, 371–373, 396–397 Bending shears, moments, deflections, 884–885 Bend strength, 170–171 Bending analysis for creep, 851–854 elastic analysis of, 694–696, 880–882 in cyclic loading, 722–724 plastic analysis of, 694–703, 891–895 residual stresses for, 703–707 Bending and torsion tests, 118–119, 169–175 bending (flexure) tests, 170–171 heat-deflection test, 171–172 modulus of rupture in bending, 171 testing of thin-walled tubes in torsion, 173–175 torsion test, 169–170 Beryllium, 47, 70 Beryllium copper, 83 Biaxial stresses. See Multiaxial stress effects; Three-dimensional states of stress Blending, defined, 92 Blunting line, 397–398 Body-centered cubic (BCC) structure, 46, 61, 376 Bolts, bolted joints, 536–537 Bonding in solids, 42–46 primary chemical bonds, 42–44 secondary chemical bonds, 44–46 Bone, 100 Borides, 59 Boron, 59, 66, 102 Boron carbide (B4C), 95, 161 Boron nitride (BN), 98 Boundary integral equation method, 354 Brale indenter, 162 Branching in polymers, 88 Brass, 41, 83, 202 Bridge Design Specifications (AASHTO), 30, 534–535 Bridge structures, cracks in, 336Index 935 Bridgman correction for hoop stress, 146–147 Bridgman, P. W., 146 Brinell hardness test, 159, 163, 175 British Standards Institution (BSI), 122 Brittle behavior, 21–22, 40, 894–895 effects of cracks on, 342–344 multiaxial criteria for, 299–320 in notch fatigue, 510–511 in tension tests, 126, 133 Brittle fracture, 23–24, 37, 334–400 safety factors against, 356 Bronze, 41, 83 Buckling, 22, 152, 174 Budynas, S-N curve estimate, 520, 522–523 Bulk modulus, 210 C Carbon, 44, 59, 66, 72, 74, 76–78, 84, 93, 101, 111 Carbon steel, 76–77 AISI–SAE designations for (table), 75 Carburizing, 447, 540 Cast irons, 72, 74–76, 126, 138, 152, 305 Casting, 66 Cellulose, 100 Cemented carbides, 41, 97–98, 112 Cementite, 76 Center-cracked plates, 342, 349, 352, 394, 569 Ceramics, 40–41, 59, 94–98, 112, 223, 298 chemical bonding in, 44, 94 clay products, 94–97 concrete, 94, 96–97 creep in, 802, 813 ductility, 137 elastic moduli of, 95, 137 engineering, 94, 97, 112 fatigue crack growth in, 585, 589, 592 fracture toughness of, 341, 344, 373, 376 hardness of, 160–161 natural stone, 94, 96 Cermets, 97–98, 112 Chain molecules, 40, 44–46, 61, 84, 88–90 Charpy V-notch test, 165–169 Chemical bonding in solids. See Bonding in solids Chemical vapor deposition, 97–98 Chromium, 66, 78–79, 82, 84, 803 plating, 447, 540 Circular cracks, 360 Circular shafts, torsion of, 707–710, 881–882, 894–895 Circumferential cracks, 352, 354 Clay products, 41, 94–96, 112 Cleavage, 376–378, 587 Climb (dislocation), 815 Closed-loop servohydraulic test system, 121–122, 435 Close-packed directions, planes, 57 Cobalt, 34, 66, 67, 83–84, 97–98, 111, 803 Coble creep, 814–815 Coefficient of tensile viscosity, 193 Coefficient of thermal expansion, 212–213 Coffin, L. F., 751, 834 Coffin–Manson relationship, 751 Coherent precipitate, 70, 102 Cold rolling, 539 Cold work, 68–69, 79, 80–83, 672 Collagen, 100 Combined stresses, yielding and fracture, 275–322 Comet passenger airliner, 343 Compact specimen, 353, 373–374, 396–397, 569 Completely reversed cycling, 420 Compliance method, 348, 395–396 Component, 33 Component S-N data, 527–535 Bailey bridge example, 527–529 curves for welded members, 531–535 matching to notched specimen data, 531 mean stress and variable amplitude cases life, 529 Component testing, 32–34 Composite materials, 40–41, 94, 100–105, 112 defined, 100 elastic constants for, 217–222 failure criteria for, 299 fibrous composites, 102–104 laminated composites, 104–105 particulate composites, 100–102 tensile behavior of, 137, 140 uses of, 100–101 Compression tests, 118, 151–156, 175 materials properties in compression, 153–154 strengths from, 95, 97 trends in compressive behavior, 154–156, 299–300 with lateral pressure, 156 Concrete, 41, 94, 96–97, 100, 112, 305, 341, 906 creep in, 820–821936 Index Constant amplitude loading (of cracked members) life estimates for, 590–601 closed-form solutions, 593–594 crack length at failure, 594–595 solutions by numerical integration, 598–601 Constant amplitude stressing, 418–420 Constant-life diagram, 452–453 Constitutive equations. See Stress–strain relationships Constraint, geometric, 212, 293–295, 387–389, 717–718 Copolymerization, 93 Copper and alloys, 41, 67, 68, 83, 202 Corner crack, 360–361 Corrected true stress, 146–149 Corrosion, 20, 28 Corrosion fatigue, 28, 449, 589, 621 Corten–Dolan cumulative damage method, 542 Costs of fracture, 36–37, 417 Costs of materials, relative, 106, 110 Coulomb–Mohr (C–M) fracture criterion, 301–311, 321–322 development of, 302–307 effective stress for, 309–310 graphical representation of, 307–309 Covalent bonding, 42–44, 47–48, 94 Crack growth. See Environmental crack growth; Fatigue crack growth Crack growth analysis, need for, 561–563 Crack growth effect on k f , 495–496 Crack growth retardation, 606 Crack surface displacement, modes of, 344 Crack velocity, 616–617 Cracked members, fracture of, 334–400 Cracks application of K to design and analysis, 348–370 cases of special practical interest, 359–364 leak-before-break in pressure vessels, 369–371 safety factors, 356–359 superposition for combined loading, 366–367 behavior at crack tips in real materials, 338–339 effects on brittle vs. ductile behavior, 342–344 effects on strength, 339–341 growing from notches, 364–366 inclined or parallel to an applied stress, 367–369 inspection for, 336, 616 periodic inspections for, 562–563 internally flawed materials, 344 mathematical concepts, 344–348 mixed mode, 381 nonpropagating, 496 strain energy release rate G, 344–346 stress intensity factor K , 346–348 as stress raisers, 337–338 See also Fracture mechanics; Fracture toughness Crack-tip opening displacement (CTOD), 338, 392, 397–400 Crack-tip plastic zone. See Plastic zone (at crack tip) Crazing, craze zone, 140, 338 Creep, 190–191, 196–198, 223, 802–866 activation energies, evaluation of, 816–817 Coble type, 814–815 in concrete, 820–821 in crystalline materials, 61, 813–816 cycle-dependent type, 678–679 defined, 22–23, 60 deformation mechanism maps, 817–819 dislocation type, 813–816 fracture mechanism maps, 807, 810 isochronous stress–strain curves, 809, 836–838, 850–854, 864–865 Nabarro–Herring type, 814–815 physical mechanisms of, 809–820 in polymers, 813 power-law type, 814–816 rheological models for, 196–198, 836–838 steady-state (secondary) stage, 191–193, 805, 847 stress-strain analysis of components for linear viscoelasticity, 850–853 nonlinear behavior, 853–855 tertiary stage, 805–806 transient (primary) stage, 192–194, 805 viscous type, 810–813, 815 Creep cavitation, 821 Creep deformation, 22–23, 37, 40, 55, 60–61, 196–198, 200–201, 802–803 application involving (example), 23 for linear viscoelasticity, 836–838 for multiaxial stress, 848–850 for nonlinear behavior, 838–841 recovery of, 841–842 for varying stress, 841–848 for linear viscoelastic models, 844–846 stress relaxation, 842–844 time- and strain-hardening rules, 846–848Index 937 Creep failure under varying stress, 833–836 creep rupture under step loading, 833–834 creep–fatigue interaction, 834–836 Creep rupture, 25, 37, 804, 821 for multiaxial stress, 833 safety factors for, 831–833 for step loading, 833–834 time-temperature parameters and life estimates, 821–833 Creep tests, 804–806 behavior observed in, 804–806 presentation of results, 806–809 Creep–fatigue interaction, 27, 757, 834–836 Critical plane approach, 466, 769–771 Cross-links, 89–91, 92, 112 Crystal structure, defined, 46 Crystalline grains, 48 Crystalline materials basic crystal structures, 46–47 complex crystal structures, 47–48 creep in, 60–61, 813–816 structure in, 46–50 Crystalline polymers, 86, 88 Crystals, defects in, 48–50 Cubic crystal, 46 Cubic material, 216 Cumulative fatigue damage. See Palmgren–Miner rule; Variable amplitude loading Cycle counting, 469, 471–475, 677, 775–776, 780–781, 789 Cycle-dependent creep, 678–679 Cycle-dependent hardening, 668–669, 732 Cycle-dependent relaxation, 678–681 Cycle-dependent softening, 668–669, 732 Cyclic bending, analyzing, 722–724 Cyclic loading, 416–418 accidental loads, 429 alternating stress, 419 closed-loop servohydraulic testing machines, 435 completely reversed cycling, 419–420 constant amplitude stressing, 418–419 and fatigue crack growth, 560, 569 fatigue under, 25–27 fatigue crack growth, 560–615, 621–622 strain-based approach, 745–790 stress-based approach, 416–479, 491–543 rheological modeling for, 640–641, 659–661, 664–668 sources of, 429–430 and static loads, 429 stress amplitude, 418–419 stress range, 418–419 stress ratio R, 419 stress–strain analysis of, 722–733 bending, 722–725 generalized methodology, 725–728 irregular load vs. time histories, 728–732 stress–strain behavior during, 640, 668–681 and time-dependent deformation, 803, 833–836 vibratory loads, 429 working loads, 429 zero-to-tension cycling, 419–420 Cyclic plastic zone, 611–612 Cyclic stress–strain behavior of materials cyclic stress–strain curves, 671–673, 747 cyclic stress–strain tests and behavior, 668–671 cyclic yield strength, 671–673, 680 hysteresis loop curve shapes, 673–677 mean stress relaxation, 678–681 D Damage intensification, 438 Damage tolerant design, 343, 563, 607–608 Damping in materials, 804, 855–863 anelastic type, 855 from rheological models, 855–857 definitions of variables describing, 858 in engineering components, 862–863 importance of, 855 low-stress mechanisms in metals, 858–860 magnetoelastic type, 860 plastic strain type, 860–863 Snoek effect, 858 thermal current type, 859 Deformation, 19–20, 66, 190, 223 characteristics of the various types of (table), 201 creep, 22–23, 25, 37, 60–61, 190, 223, 802–866 elastic type, 21–22, 37, 50–53, 191, 201–213, 223–224 plastic type, 21–22, 37, 55–59, 190, 223 behavior and models for materials, 638–683 Deformation behavior models creep deformation, 190–194, 196–198, 836–838 discussion of, 200–201 elastic deformation, 191–193938 Index Deformation behavior models (Continued) plastic deformation, 191–193, 194–196, 648–649, 659–668 relaxation behavior, 198–199, 842–844 rheological models, defined, 191 Deformation mechanism maps, 817–820 Deformation plasticity theory, 641, 650–659 incremental plasticity theory vs., 658–659 Delaminations in layered materials, 335 Delta iron, 47 Design, 28–34 allowable stress, 32, 296 creep, 802–803 defined, 28–29, 37 durability, 29 environmental cracking, 618–619 fatigue, 448, 536–542 fatigue crack growth, 563, 607–609 load factor, 32, 296–297 material selection, 66, 105–111 safety factors, 29, 30–32 service experience, 34 Design truck, 534 Diamond cubic structure, of carbon, 48 Diffusion, 810–811 Diffusional flow, 60, 813–815 Dimpled rupture, 376, 378 Direction cosines, 253 Disc, rotation stresses, 887–889 Discontinuous stress–strain curves, 699–701 Dislocation climb, 815 Dislocation creep, 815–816 Dislocation motion, plastic deformation by, 56–58 Dislocations, 50 Dispersion hardening, 101–102 Distortion energy criterion. See Octahedral shear stress yield criterion Drawing, 66, 68–69 Ductile behavior, 21–22 effects of cracks on, 342–343 multiaxial stress effect, 318–320 in notched members, 894–898 in notch fatigue, 506–513 in a tension test, 126–127 Ductile fracture, 24–25, 37, 391–399 Ductile iron. See Cast irons Ductility engineering fracture strain, 131 engineering measures of, 130–132 and necking, 131–132 percent elongation, 22, 131 percent reduction in area, 131 Durability, durability testing, 29, 33 Dynamic modulus, 858 Dynamic recrystallization, 821 Dynamic tear test, 165 E Ebonite, 92 Economics of fracture, 36–37, 417 Edge dislocation, 50 Edge-cracked tension member, 349, 353–354 Effective mean stress, 465–466 Effective plastic strain, 650 Effective strain rate, 849 Effective stress, 278–279, 281, 283, 290, 309–310, 314, 650–651, 653, 849 Effective stress amplitude, 465 Effective stress–strain curve, 653–654 Effective total strain, 650–651, 653 for fatigue life, 768–769 Elastic bending, 694–696, 880–882 Elastic constants, 128–129, 202–204, 214–218 Elastic deformation, 21, 37, 50–53, 190–191, 201–224 anisotropic case, 214–218 bulk modulus, 210–211 hydrostatic stress, 209–211 isotropic case, 201–213 orthotropic case, 215–217 physical mechanisms of, 51–52 and theoretical strength, 53–55 thermal strains, 211–213 and volume change, 209–210, 213 volumetric strain, 209–211 Elastic limit, 130 Elastic, linear-hardening stress-strain relationship, 194–195, 643–644 Elastic modulus, 21, 52–53, 105, 128, 193, 201–204 parallel to fibers, 219–220 for polymers, 88, 91 time dependent type, 837–838, 851, 865 transverse to fibers, 220–221 values, trends in, 52–53Index 939 Elastic, perfectly plastic stress–strain relationship, 194–195, 641–643 in bending, 699 in notched members, 715 residual stresses in bending, 704–707 in torsion, 710 Elastic, power-hardening stress-strain relationship, 644 Elastic strain. See Elastic deformation Elastic strains, Hooke’s law for, 204–206, 649–650 Elastic stress concentration factor, 337–338, 420, 493, 508–509, 511–513, 536–537, 712, 889–891 Elastically calculated stresses, 717 Elastomers, 84, 88, 90–91, 111, 861 elastic moduli of, 137 Elliptic integral of the second kind, 360–362 Elliptical cracks, 360–364, 392 Elongation, percent, 22, 130–132, 138–140 Embrittlement, 616 Endo, T., 471 Endurance limits. See Fatigue limits Energy capacity, engineering measures of, 132–134 Energy dissipation. See Damping in materials Energy, impact, 164–169 Engineering ceramics, 94, 97, 112 Engineering components materials selection for, 105–111 Engineering design. See Design Engineering fracture strain, 131 Engineering fracture strength, 129 Engineering materials, 40 classes and examples of, 41 general characteristics of (table), 41 size scales for, 41–42 survey of, 65–112 Engineering metals, 66, 72–84 Engineering plastics, 86 Engineering shear strains, 262, 650 Engineering size crack, 787–788 Engineering stress and strain, 125–137, 149–150, 175 Engineering stress–strain properties (from tension tests), 128–136 ductility, 130–132 elastic constants, 128–129 elastic limit, 130 elastic (Young’s) modulus, 21, 128 elongation, 22, 131–132 engineering fracture strength, 129 engineering measures of ductility, 130–132 engineering measures of energy capacity, 132–134 versus fracture toughness, 134 engineering measures of strength, 129–130 lower yield point, 130 necking behavior and ductility, 131–132 offset yield strength, 130 proportional limit, 130 reduction in area, 131–132 strain hardening, 134 tangent modulus, 129 trends in 137–143 ultimate tensile strength, 22, 129 upper yield point, 130 yielding, 21, 129–130 Environmental crack growth, 560–561, 616–621, 622 static loading, life estimates for, 616–618 Environmental cracking, 25, 36, 616–621 and creep, 803 Environmental effects in creep-fatigue, 834–836 in fatigue, 445 in fatigue crack growth, 587–589 in static fracture, 320–321 Epoxies, 41, 90, 102–103, 105, 139, 202, 341 Equivalent completely reversed stress amplitude, 456, 478, 760 Equivalent completely reversed uniaxial stress, 466 Equivalent constant amplitude stress, 475–476, 479, 535, 603 and safety factors, 475–477 Equivalent life, for zero-mean stress, 760–762, 765 European Standards (European Union), 122 Extensometers, 122 Extrusion, 68 F Face-centered cubic (FCC) structure, 46–47, 61 Factor of safety. See Safety factors Failure criteria, 275–322 brittle vs. ductile behavior, 318–320 comparison of, 295–296 cracks, time-dependent effects of, 320–321 fracture in brittle materials, 299–301 load factor design, 296–297940 Index Failure criteria (Continued) stress raiser effects, 297–298 See also Fracture criteria; Yield criteria Failure envelope, for Mohr’s circle, 301 Failure surface, 278 Fatigue, 25–27, 36, 416–479, 491–543 corrosion with, 28, 445, 589 crack initiations in, 25–26, 435–441, 757, 787–789 cyclic loading, 418–420 sources of, 429–430 definitions for, 418–421 designs for, 536–537 fatigue damage, physical nature of, 435–441 fatigue limit behavior, 447–449 fatigue testing apparatus and specimens, 430–435 fracture mechanics approach, 417, 560–622 fretting, 27–28, 536 high-cycle and low-cycle types, 26, 423–424, 754 mean stresses, 451–462 life estimates with, 456–461 normalized amplitude-mean diagrams, 452–454 presentation of mean stress data, 451–452 safety factors with, 461–462 multiaxial stresses, 463–467 effective mean stress, 465–466 effective stress amplitude, 465–466 equivalent completely reversed uniaxial stress, 466 notch effects, 443, 491–501, 506–513, 771–785 point stresses versus nominal stresses, 420–421 prevention of, 25–26 residual stress effects, 446–447, 539–541, 785 safety factors for S-N curves, 427–429 size effects, 503, 758 statistical scatter in, 449–451 strain-based approach, 417, 745–790 stress versus life (S-N) curves, 421–426 equations for, 423 estimating, 520–527 trends in, 441–451 stress-based approach, 416–479, 491–543 surface finish effects, 503, 757 variable amplitude loading, 468–477 cycle counting for irregular histories, 471–474 equivalent stress level and safety factors, 475–477, 535 Palmgren–Miner rule, 468–470, 786–787 Fatigue crack growth, 27, 560–622 arrested, 606 behavior, 584–590 trends with material, 584–587 trends with temperature and environment, 587–590 behavior, describing, 564–568 constant amplitude loading, life estimates for, 590–601 crack growth analysis, need for, 561–563 damage-tolerant design, 563, 607–609 definitions for, 564 design considerations, 607–609 fatigue crack growth tests, 569–574 geometry independence of da/dN vs. K curves, 573 test methods and data analysis, 569–572 test variables, 572–573 Forman equation, 580–581 Paris equation, 564–565 plasticity aspects and limitations of LEFM for, 609–615 limitations for small cracks, 613–615 plasticity at crack tips, 610–612 thickness effects, 612–613 R-ratio effects, 574–584, 590 sequence effects on, 606–607 and stiffeners, 608–609 threshold value Kth, 565, 621 variable amplitude loading, life estimates for, 601–607 Walker equation, 574–580 Fatigue crack growth rate, 560, 569–570 Fatigue Design Handbook (SAE), 455, 474, 540, 694 Fatigue failure design details, 536–539 designing to avoid, 536–541, 607–609 surface residual stresses, 539–541 Fatigue limits, 423 behavior of, 447–449 and engineering design, 448 estimating, 501–506 factors affecting, 502–503 reduction factors, 504–506 load type, size, and surface finish, 504 in variable amplitude fatigue, 449, 469, 534–535, 787Index 941 Fatigue notch factor, 493–501, 788–789 at short life, 506–510, 783 for mean stress, 510–513, 783 Fatigue strength, 423–424 Fatigue testing, 430–435 component tests, 526–529 crack growth tests, 569–574 reciprocating bending test, 433–434 resonant vibration test, 434–435 rotating bending test, 430–433 strain-life tests, 668–671, 748–753 test apparatus and specimens, 430–435 Ferrite (α-iron), 76 Ferritic stainless steel, 79 Ferromagnetic metals, 862 Ferrous alloys, 72 Fiberglass, 41, 94 Fibrous composites, 102–104, 217–218 Finite element analysis, 191, 298, 354, 420, 694, 717 Fir tree design, 492, 536 Flaw shape factor, 360 Flexure tests and strength, 170–171 Fluctuating dipole bond, 45 Forging, 66, 68, 335 Forman equation, 580–581 Fracture, 19–20 brittle, 23, 299–300 cleavage, 376–378 costs of, 36–37, 417 of cracked members, 334–400 dimpled rupture, 376–378 ductile, 24–25 intergranular, 610–611, 619 modes, 344 for static and impact loading, 23–25 in torsion tests, 172 transgranular, 611 types of, 20 Fracture criteria, 275, 279–281, 299–301 Coulomb-Mohr, 301–311 maximum normal stress, 279–282, 314 modified Mohr, 311–318 Fracture mechanics, 23–24, 37, 277, 334–336, 417 application to design and analysis, 348–371 for environmental cracking, 616–621 extensions of, 391–398 crack-tip opening displacement (CTOD), 398 fracture toughness tests for JI c, 395–398 J-integral, 393–400 plastic zone adjustment, 392–393 for fatigue crack growth, 560–615 plasticity limitations, 386–390, 612–613 plastic zone size, 381–386, 611–612 strain energy release rate G, 345, 348 stress intensity factor K, 346–348 Fracture mechanism map, 807 Fracture strain engineering type, 131 true type, 149–151 Fracture strength, true, 149–151 Fracture surface, 278 Fracture toughness, 23–24, 134, 168–169, 334, 339 effects of cyclic loading, 583 effects of temperature and loading rate, 376–379 effect of thickness on, 387–389 microstructural influences, 379–381 mixed-mode fracture, 381 values and trends, 371–381 Fracture toughness testing, 371–381, 390–391, 395–398 Frequency-modified fatigue approach (Coffin), 834 Fretting, 27–28, 536 Full yielding (in fatigue), 508–510 Fully plastic limit load (force or moment), 357, 392, 400, 700–701, 890–899 Fully plastic yielding, 594, 713–714 F-111 aircraft crash (1969), 343 G Gage length, 125 Gamma iron, 47 Gas-turbine engines, 34 Gaussian distribution, 451, 902–904 Generalized Hooke’s law, 204–206, 223–224 Generalized plane stress, 234, 244–246 Generalized Poisson’s ratio, 653, 718 Geometric constraint, 212–213, 293–295, 385–386, 388, 717–718 Geometric discontinuities, 491 Gerber parabola, 455 Glass, 40–41, 93–100, 102, 112, 126, 161, 202, 223, 341 chemical bonding in, 40 creep in, 810 ductility, 137942 Index Glass transition temperature, 52–53, 88–91 Glass-fiber-reinforced thermoplastics, 106, 443 Glinka’s rule, 717 Goodman equation, 454 for notched members, 510–511 Grain boundaries, 48, 50, 59–60, 813–815 Grain boundary sliding, 813–814 Grain refinement, 69 Graphite, 55, 102 Graphite-epoxy, 41, 106, 218 Gray cast iron. See Cast irons Griffith, A. A., 344 H Hardening cycle-dependent, 668 dispersion, 101–102 isotropic, 641 kinematic, 641, 661 precipitation, 70–72, 79–84, 101 strain, 134 surface hardening treatments, 540 Hardness correlations and conversions, 163–164 Hardness tests, 157–164 Brinell hardness test, 159, 175 Mohs hardness scale, 157 Rockwell hardness test, 162–163, 175 Scleroscope hardness test, 157 Vickers hardness test, 160–162, 175 Haynes 188 (superalloy), 83 Heat treatment, 66, 76–77, 81 Heat-deflection temperature, 172 Heat-deflection test, 171–172 Hexagonal close-packed (HCP) crystal structure, 47, 61, 82 High-carbon steels, 76–77 High-cycle fatigue, 26, 423–424, 754 High-impact polystyrene (HIPS), 93 High-performance composites, 100, 103–104, 106, 112 High-strength low-alloy (HSLA) steels, 78 High-temperature creep, 817 Hill anisotropic yield criterion, 298–299 Homogeneous material, 202 Hooke’s law, 213, 264, 277, 848 anistropic case, 214–218 for elastic strains (with plasticity), 649–651 isotropic case, 204–213 orthotropic case, 215–216 Hot isostatic pressing, 97 Hydrogen bond, 45–46 Hydrogen embrittlement, 616 Hydrostatic stress, 210 effect on fracture, 318–320 effect on yielding, 285–286, 291, 295 as octahedral normal stress, 261 Hysteresis loops, 664–667, 722, 725–733, 748–749, 775–781, 860 curve shapes, 673–677 elliptical, 856–857 I Impact energy tests, 164–169 Impact loading, fracture under, 23 Impurity (interstitial, substitutional), 48–49 Inclusions, fracture effect, 335, 379–381 for fatigue, 436, 438 Inconel 736(superalloy), 83, 582 Incremental plasticity theory, 641, 658 deformation plasticity theory vs., 658–659 Indentation hardness, 157–164 Inelastic deformation, 55–61 Initial yielding (in fatigue), 512–513 Initial yielding force or moment, 700, 713, 891–894 Inspection for cracks, 336–337, 561–563, 607–609 Instron Corp. testing machine, 121 Intergranular fracture, 25, 610–611, 619–620 Intermetallic compounds, 44, 48, 70 Internal combustion engine, 34 Internal friction. See Damping in materials Internally flawed materials, 344 International Organization for Standardization (ISO), 122 Interstitial, 49 Invariant quantities, 211, 257, 261 Ionic bonding, 42–44, 47–48 Irons, cast. See Cast irons Irregular load vs. time histories. See Variable amplitude loading Irwin, G. R., 345, 386 Isochronous stress–strain curves, 809, 836–838, 850–854, 864–865 Isothermal modulus, 860 Isotropic behavior, 191, 202–203Index 943 Isotropic hardening, 641 Izod tests, 139, 165 J Jet engines, 34 J-integral, JI c tests, 393–400 Juvinall, R. C. mean stress approach, 513 S-N curve estimate, 520, 522–523 K Kevlar, 85–86, 93, 103, 105, 218 K-field, 386–387 Kinematic hardening, 641, 661 L Laminated composites, 101, 102–105 Langer, B. F., 468 Larson–Miller (L-M) time-temperature parameter, 822, 825–830 Lattice plane and site, 48 Lead, 66, 67, 202 Leak-before-break condition, 369–371 Liberty Ships and tankers, 343 Lignin, 100 Line defects (dislocations), 48, 50 Linear-elastic fracture mechanics (LEFM), 339, 347, 386, 398 See also Fracture mechanics Linear elastic material, 203 Linear hardening, 194, 643–644 Linear polymers, 87–88 Linear variable differential transformers (LVDTs), 122 Linear viscoelasticity, 196, 223, 836–838 component analysis for, 850–853 damping for, 855–863, 865–866 step loading for, 844–846 Liquid metal embrittlement, 616 Load cells, 122 Load factor design, 32, 296–297, 318, 321 in fatigue, 461–462, 476, 534 Loading path dependence, 658–659 Local yielding, 508–509, 511–513, 710, 714–717 Log decrement, 858 Lognormal distribution, 451, 908 Loss coefficient, 858 Low-alloy steels, 34, 74, 77–78 AISI-SAE designations for (table), 75 Low-carbon steel, 76 Low-cycle fatigue, 26, 423–424, 754 Low-density polyethylene (LDPE), 91–92, 139 Lower yield point, 130 Low-temperature creep, 817 M Magnesium and alloys, 41, 47, 66–67, 83, 111, 138, 152, 202 Magnetoelastic damping, 860 Major Poisson’s ratio, 221 Malleable iron, 76 Manganese, 47, 66, 76 Manson, S. S., 750, 834 Maps, for creep mechanisms, 807, 817 Maraging steels, 79, 138, 152, 340 MARM 302 (superalloy), 83 Martensite, 77 Martensitic stainless steel, 79 Materials damping, 804, 855–862, 865–866 See also Damping in materials Materials selection, 66, 105–112 Maximum normal stress fracture criterion, 279–282, 311, 314 Maximum shear stress, 246–251 Maximum shear stress yield criterion, 282–286 development of, 282–284 graphical representation of, 284–285 hydrostatic stresses and, 285–286 Mean stress, 418–419 discussion of, 765, 782–785 effects of, 451–452, 758–767 equivalent life for, 761–762, 765 in fatigue crack growth, 574–583 life estimates with, 456–461 mean stress equations, 454–456, 760–765 mean stress tests, 759 normalized amplitude-mean diagrams, 452–454 for notched members, 510–520, 523 presentation of mean stress data, 451–452 safety factors with, 461–462 in strain-based fatigue, 758–767 modified Morrow approach, 762–763944 Index Mean stress (Continued) Morrow equation, 761–762, 765 Smith, Watson, and Topper (SWT) parameter, 763–764 Walker relationship, 764–765 Mean stress relaxation, 678–681, 783–785 Mechanical behavior of materials, 19, 37 Mechanical testing, 118–176 bending and torsion tests, 169–175 closed-loop servohydraulic test system, 121–122 compression tests, 151–156 creep tests, 804–809 cyclic stress–strain tests, 668–671 engineering stress–strain properties (in tension), 128–137 environmental crack growth tests, 616–618 extensometers, 122 fatigue tests crack growth, 569–574 strain-life, 748–753 stress–life (S-N), 430–435, 527–529 fracture toughness tests, 371–374, 390–391, 395–398 hardness tests, 157–164 hardness correlations and conversions, 163–164 Instron Corp. testing machine, 121 linear variable differential transformers (LVDTs), 122 load cells, 122 MTS Systems Corp., 121 notch-impact tests, 164–169 specimens, 118–119 standard test methods, 122–123 strain gages, 122 tensile behavior, 137–143 tension tests, 123–128 test equipment, 119–122 true stress–strain curves and properties, 148–150 universal testing machines, 119–121 Medium-carbon steels, 76–77 Memory effect, 196, 661, 677, 730, 734, 775–776, 789 Metallic bonding, 43–44 Metals, 40–41 alloying/processing of, 66–72 creep in, 802, 813–819 cyclic deformation in, 668–676 environmental crack growth in, 616–621 fatigue in, 435–451, 754–757 fatigue crack growth in, 584–590 fracture in, 374–381 irons and steels, 72–79 low-stress damping in, 858–862 nonferrous metals, 80–84 strengthening methods for, 68–72 Microcracks, 338, 786, 820–821 Microstrain, 126 Microvoid coalescence. See Dimpled rupture Mild steel, 76 Miner, M. A., 468 Minimum detectable crack length, 562 Mixed-mode fracture, 381 Models. See Rheological models Modified Goodman equation and line, 454 Modified Mohr fracture criterion, 311–314, 321–322 Modulus of elasticity. See Elastic modulus Mohr, Otto, 240, 255 Mohr’s circle, 240–244, 247, 250–251, 255, 263–264 as failure envelope, 301 Mohs hardness scale, 157 Molybdenum, 66, 79 Monotonic loading, 639 Monotonic plastic zone, 611 Monotonic proportional loading, 658–659 Monotonic straining, 194 Morrow, J., 455, 761 Morrow mean stress relationship, 455–456, 761–763 MTS Systems Corp., 121 Multiaxial stress effects creep, 833, 848–850 elastic deformation, anisotropic case, 214–223 elastic deformation, isotropic case, 204–213 fatigue, 463–467, 767–771 fracture, cracked members, 381, 387–389 fracture, uncracked members, 279–282, 299–318 plastic deformation, 649–659, 717–718 yielding, 282–295 See also Three-dimensional stress–strain relationships N Nabarro–Herring creep, 814–815 NASGRO, 602 Natural stone, 94, 96, 112 Naval brass, 83Index 945 Necking, 131–132, 138–140, 805 Network modifiers, 98 Neuber constant, 499 Neuber, H., 499 Neuber’s rule, 694, 714–717, 720, 727, 733, 772–774, 789 strain-based fatigue method, 771–781 residual stresses and strains at notches, 719–722 Neutron radiation effects, 381 Nickel, 34, 47, 49, 66, 67, 70, 83–84, 98, 587, 803, 807, 817 plating, 447 Nickel-base superalloys, 41, 83, 582, 751, 824, 827 Niobium, 66 Nitrides, 59 Nitriding of steels, 447, 540 Nodular iron, 75 Nominal stresses, 420 point stresses vs., 420–421 Nonferrous metals, 80–84 aluminum alloys, 80–82, 111 copper alloys, 83 magnesium alloys, 83, 111 superalloys, 83, 111 titanium alloys, 82–83, 111 Nonlinear creep equations, 838–841 Nonlinear hardening, rheological modeling of, 648–649 Nonpropagating cracks, 496, 789 Nonproportional loading, 463, 466, 658–659, 732–733, 769–770, 780 Normal distribution, 451, 902–904 Normal stress fracture criterion, 279–282, 311, 314 Normalized amplitude-mean diagram, 452–454 Notch effects in fatigue, 443, 491–497 crack growth effect, 495–496 fatigue notch factor, 493–494, 497–501 at intermediate and short lives, 506–510 and mean stress, 510–520 process zone size and weakest-link effects, 494–495 reversed yielding effect, 496–497 Notch sensitivity, 497–501 Notched members, 710–722 elastic behavior and initial yielding, 712–713 elastic stress concentration factor, 337–338, 420, 889–890 fracture criteria for, 297–298 fully plastic yielding, 713–714, 894–899 local yielding analysis Neuber’s rule, 694, 714–717, 720, 727, 733, 772, 774, 789 strain energy (Glinka) method, 717 residual stresses and strains in, 539–540, 719–722, 732 strain-based fatigue method, 771–785 stress-based fatigue method, 491–543 yield criteria for, 297–298 Notched specimens, 119, 435, 531 Notch-impact tests, 164–169, 336 Charpy V-notch test, 165 dynamic tear test, 165 fracture toughness vs., 168–169, 379 Izod tests, 165 temperature-transition behavior, 168 Numerical integration (for crack growth), 598–601 Nylons, 41, 86, 111, 139, 140, 202 O Octahedral planes, stresses on, 260–262 Octahedral shear stress yield criterion, 288–295 development of, 288–290 energy of distortion, 292 graphical representation of, 290–292 Offset yield strength, 130 Opening mode crack, 344 Orthotropic materials, 215–217 Overall range, 471 Overload effects. See Sequence effects in fatigue Oxidation, and creep, 803 Oxides, 59, 94, 96–99 P Palmgren, A., 468 Palmgren–Miner rule, 468–469, 475, 478, 527, 529, 535, 542, 775–776, 786–787, 833–834 Paris equation, 564–565, 621 Particulate composites, 100–102 Peaks, 471 Pearlite, 76 Percent elongation, 22, 131–132 Percent reduction in area (%RA), 131–132946 Index Perfectly plastic stress–strain curve, 194–196, 641–643 See also Elastic, perfectly plastic stress–strain relationship Periodic inspections for cracks, 562–563, 607 Periodic overstrains (in fatigue), 449, 787 Peterson constant, 497–499 Phase angle, 856, 858 Plain-carbon steels, 72, 76 Plane strain fracture toughness, 339, 373–381, 390–391, 399–400 Plain strain, 263 crack plastic zone, 385–386 fracture effect, 373–374, 387–389, 391 in notch, 717–718 Plane stress, 235–245, 249–253 crack plastic zone, 384–385 fracture effect, 387–389, 391 generalized, 244–245, 263–264 Mohr’s circle for, 240–242 plastic deformation for, 654–657 principal stresses, 237–239 rotation of coordinate axes, 236–237 Plastic collapse, 693, 700, 890–899 Plastic deformation, 21–22, 55–59, 190, 194–196, 200–201, 223 behavior and models for materials, 638–683 in bending, 694–703 analysis by integration, 696–698 discontinuous stress–strain curves, 699–701 elastic bending, 694–696 Ramberg–Osgood Stress–strain curve, 701–703 rectangular cross sections, 698 of components under cyclic loading, 722–734 cyclic stress–strain behavior of materials, 668–681 cyclic stress–strain curves and trends, 671–673 cyclic stress–strain tests and behavior, 668–670 hysteresis loop curve shapes, 673–677 mean stress relaxation, 678–681 by dislocation motion, 56–58 fracture methods for, 391–398 memory effect in, 196, 661, 677, 730, 775, 776, 789 in notched members, 496, 506–513, 710–722 rheological modeling of, 194–196, 641–644, 648–649, 659–668 cyclic loading behavior, 664–667 irregular strain versus time histories, 667–668 unloading behavior, 661–664 significance of, 638–639 stress-strain curves, 641–649, 681 elastic, linear-hardening relationship, 643–644 elastic, perfectly plastic relationship, 641–643, 681, 699, 710, 715 elastic, power-hardening relationship, 644, 716 Ramberg–Osgood relationship, 644–645, 671, 701–703, 708, 710, 716, 771 simple power-hardening relationship, 698, 709 three-dimensional stress–strain relationships, 649–659 application to plane stress, 654–656 deformation plasticity theory, 650–653 deformation vs. incremental theories, 658–659 effective stress–strain curve, 653–654 time dependence of, 639 in torsion, 707–710 unloading and cyclic loading behavior from rheological models, 659–668 Plastic hinge, 700–701 Plastic modulus, 651–652 Plastic strain, 21, 190, 200–201, 638 See also Plastic deformation Plastic strain damping, 860–862 Plastic zone (at crack tip), 338, 381–390, 392 for cyclic loading, 610–612 for plane strain, 385–386 for plane stress, 384–385 plane stress versus plane strain, 387–389 plasticity limitations on LEFM, 386–387 Plasticity. See Plastic deformation Plasticizers, 93 Plastics. See Polymers Plating, 447, 540 Plywood, 41, 104 Point defects, 48–49 interstitial impurity, 49 self interstitial, 49 substitutional impurity, 48 vacancy, 48–49 Poisson’s ratio, 129, 202–204, 213, 682 for anistropic materials, 216–217, 221 generalized, 653 and Hooke’s law, 204–206, 652 Polaris missile, 343 Polycarbonate (PC), 86, 88, 106, 139, 202Index 947 Polycrystalline materials, 48 Polyethylene (PE), 41, 44, 55, 85–86, 88, 111, 139, 202, 813, 839 crystal structure of, 87 Polyethylene terephthalate (PET), 86 Polyisoprene, 88, 90 Polymers, 40–41, 84–94, 111, 203 amorphous, 48, 88 atactic, isotactic, syndiotactic, 88 classes, examples, and uses of (table), 85 combining and modifying, 92–94 covalent bonds in, 46 creep in, 802–803, 813 crystalline, 88 and cyclic loading, 445, 672–673 damping in, 861 elastomers, 84, 90–91 fatigue in, 441, 445, 752 fatigue crack growth in, 585 fracture toughness of, 373, 376 linear, 88 molecular structures of, 84–86, 91 naming conventions, 84 strengthening effects, 91–92 tensile stress-strain curves for, 126–127, 130–131 thermoplastics, 84–86 crystalline versus amorphous, 86–88 molecular structure of, 84–86 thermosetting plastics, 84, 89–90 yield criteria for, 299 yield strengths in compression, 299 yield strengths in tension, 130 Polymethyl methacrylate (PMMA), 84–85, 88 Polyoxymethylene (POM), 86, 88 Polyphenylene oxide (PPO), 86 Polypropylene (PP), 85–86, 88 Polystyrene (PS), 41, 85–86, 88, 139, 341 Polytetrafluoroethylene (PTFE), 84–86, 140 Polyurethane elastomers, 90 Polyvinyl chloride (PVC), 41, 46, 85, 86, 88, 139, 341 Poncelet, J. V., 417 Pop-in crack, 390 Porcelain, 94, 95, 112, 161 Potential drop method, 396, 569 Potential energy, in fracture, 345, 393–394 Power-hardening stress–strain relationship, 148, 644 in bending, 698 in notched members, 716 in torsion, 709 Power-law creep, 813–816 in bending, 854 relaxation for, 843–844 Precipitate, coherent, 70, 102 Precipitation hardening, 70–72, 79–83, 101 Precipitation-hardening stainless steels, 73, 79, 578, 582 Precrack, 390, 395–396, 569 Prepregs, 103 Presetting, 446–447, 539 Pressure effect. See Hydrostatic stress Pressure vessels cracks in, 336 leak-before-break design, 369–371 stresses in, 884–888 Primary chemical bonds, 42–44 Primary stage of creep, 805 See also Transient creep Primitive cubic (PC) structure, 46–47 Principal axes, 235, 255 Principal strains, 263 Principal stresses, 235, 237–240, 256–257 directions for, 235, 237–240, 257–260 and the maximum shear stress, 245–253 principal normal stresses, 237, 245, 255 principal shear stresses, 246–251 Process zone size, 494–495 Product liability costs, 36 Proportional limit, 130 Proportional loading, 280, 658–659 Prototype, 32–34 Q Quality factor, 858 Quasi-isotropic material, 221 Quenching and tempering of steels, 72–73, 76–77, 79 R Radiation embrittlement, 381 Rainflow cycle counting, 471–474, 677, 775–777 Ramberg–Osgood relationship, 148, 644–648 in bending, 701–703 for biaxial stress, 656 for cyclic stress–strain curve, 671, 747948 Index Ramberg–Osgood relationship (Continued) in notched members, 716 in pure shear, 708 for tension test, 148–151 time variable added, 840 in torsion, 710 Range of stress, 418–419, 471, 564 Ratchetting, 678–679 R-curve, 397–398 Reaction bonding, 97 Reciprocating bending test, 433–434 Recovery of creep strain, 198, 201, 223, 813, 820–821, 841–842 Redistributed stress, 298, 338, 384 Reduction in area, 131, 132, 149 Refractory metals, 66 Region of K -dominance, 386 Reinforcement in polymers, 93–94 Relative P-M rule, 542 Relaxation behavior, 198–199, 223, 842–844 for mean stress, 678–680, 783–785 Remnant displacement, 856, 858 Repeating unit in polymers, 84 Residual stresses and strains, 446–447, 536 for bending, 703–707 analysis for interior of the beam, 706–707 and fatigue, 446–447, 539–541 at notches, 539–541, 719–722 and plastic deformation, 638–640 Resonant vibration, 434 Reversed yielding (at notches), 496–497, 511–513 Rheological models, 190–200, 223, 640, 659–661 damping behavior of, 855–857 creep in, 191–194, 196–198, 836–838, 844 linear viscoelastic behavior of, 836–838 plastic deformation in, 194–196, 641–644, 648–649 recovery in, 198, 813–814 relaxation in, 198–200, 842–844 unloading and cyclic loading behavior from cyclic loading behavior, 664–665 irregular strain versus time histories, 667–668 unloading behavior, 661–663 Rockwell hardness test, 162–163, 175 Rolling, 66, 68 Rosettes, strain gage, 266–267 Rotating bending test, 430–433 Rotating disc, stresses, 887–889 R-ratio, 419–420 effects in crack growth, 574–584 in mean stress equations, 455–456, 514, 516–517, 765 Rubbers, 41, 90–91 Rupture in creep, 25, 37, 804–807, 821–834 dimpled, 376, 378 modulus of, in bending, 171 S SAE Fatigue Design Handbook, 455, 474, 540, 694 SAE steel nomenclature, 73–75 Safety, 29 Safety factors, 30–32, 278 for crack growth, 562–563 for cracked members, 356–359 for creep rupture, 831–833 in design, 30–32 for fatigue, 427–429, 461, 475–477 for uncracked member fracture, 279–281, 310, 314, 321 for yielding, 284, 290, 296 Safety margin in temperature, 831 Sandwich materials, 105 Scarf joints, 537 Scleroscope hardness test, 157 Screw dislocation, 50 Secant modulus, 652, 653 Secondary chemical bonds, 44–46 Secondary stage of creep, 805 Self interstitial, 49 Sequence effects in fatigue, 449, 469, 542, 601, 606–607, 785–787, 790 Service experience, 34 Servo-hydraulic machines, 121–122, 435 Shear center, 695 Shear lip, 441 Shear modulus, 106, 173, 205, 216 for composite materials, 216–217, 221 Shear stress yield criterion, 282–288 Sherby–Dorn (S-D) time-temperature parameter, 822–825 Shigley, J. E., S-N curve estimate, 520 Ship structures, cracks in, 336, 343 Short cracks, defined, 613–614 Shot peening, 446, 539Index 949 SiC-aluminum composite, 41, 102, 140 Silica (SiO2), 98 Silica glasses. See Glass Silicon, 55, 59, 66 Silicon carbide (SiC), 55, 95, 102, 104, 161, 202, 341 Silicon nitride (Si3N4), 95, 97, 161, 341 Simple range, 471 Simpson’s rule, 598 Simulated service testing, 33 Sintering, 97 Size effect, in fatigue, 494–495, 503–505, 758 Sliding mode crack, 344 Slip (in crystals), 56–58, 436–437, 815 Slope reduction factor, 643, 649 Slow-stable crack growth, 390–391, 399 Small cracks, defined, 613–615 limitations for, 613–615 transition length, 615 Small-strain theory, 204 Smith, Watson, and Topper (SWT) equation, 455 for notched members, 510, 513–516 for strain-life curves, 763–764 Smooth specimens, 118, 435 S-N (stress vs. fatigue life) curves, 421–426, 746, 750 component S-N data, use of, 527–535 Bailey bridge example, 527–529 curves for welded members, 531–535 matching to notched specimen data, 531 mean stress and variable amplitude cases, 529 equations for, 423, 443, 456–457, 516–520, 531–535 estimating, 520–527 safety factors for, 427–429, 461, 476, 535 trends in, 441–451 environment and frequency effects, 445 geometry, 443 mean stress, 443 microstructure, effects of, 445–446 ultimate strength, 441–443 Walker equation fit, 516–520 Snoek effect, 858–859 S-N-P curves, 451 Solid solution strengthening, 69–70, 80, 82, 83 Solution heat treatment. See Precipitation hardening Specimens, test, 118–119, 169 for bending, 170 for compression, 151 for fatigue, 434–435, 748 for fatigue crack growth, 569 for fracture toughness, 371–373 for notch-impact, 165–166 for tension, 123–124 for torsion, 172–175 Spherulites, 87 Spring and slider rheological models, 194–196, 659–668 Stacking fault, 50 Stainless steels, 34, 72, 78–79 Standard test methods, 122–123 See also ASTM Standards State-of-stress effects. See Multiaxial stress effects Static loading fracture under, 23 life estimates for crack growth, 616–621 Static loads, 429 Stationary loading, 602 Statistical variation in fatigue, 449–451 in fracture toughness, 376, 906 in materials properties, 900–908 Steady-state creep, 191–194, 196–197, 805 Steam engines, 34 Steels, 41, 72–79, 98, 111, 298, 343 as-quenched, 77 carbon, 76–77 high-carbon, 76–77 low-alloy, 34, 72, 77–78 low-carbon, 76 medium-carbon, 76–77 mild, 76, 202 naming system for, 73–75 plain-carbon, 72, 76 quenching and tempering, 77 stainless, 34, 72, 78–79, 202 tool, 72, 79 Step loading creep deformation under, 844–848 creep rupture under, 833–834 of linear viscoelastic models, 844–846 Stiffness, 94, 105, 112 See also Elastic modulus Storage modulus, 858 Strain, 21, 125–128 complex states of, 262–267 engineering shear strains, 262, 650950 Index Strain (Continued) engineering type, 125 plane stress, special considerations for, 263–266 principal strains, 263 strain gage rosettes, 266–267 tensor shear strains, 262, 650 transformation of axes, 262 true type, 144 units for, 126 Strain-based approach to fatigue, 417, 745–790 crack growth effects, 787–789 development of, 746 discussion, 781–789 life estimates for structural components, 771–781 constant amplitude loading, 771–774 irregular load vs. time histories, 775–780 simplified procedure for irregular histories, 780–781 local mean stress, sequence effects related to, 785 mean stress effects, 758–767, 782–785 mean stress tests, 759 multiaxial stress effects, 767–771 critical plane approaches, 769–771 effective strain approach, 768–769 physical damage to the material, sequence effects related to, 786–787 stress-based approach compared to, 745–746, 781–782 Strain energy density (Glinka) method, 717 Strain energy release rate G, 345, 348, 393–394 Strain gages, 122 rosettes, 266–267 Strain hardening, 134, 194, 643–649 Strain hardening exponent, 148, 644 Strain-hardening rule, in creep, 846–848 Strain–life data, availability of, 750–752 Strain-range partitioning approach, 834–836 Strain versus life curves, 746, 748–758 creep–fatigue interaction, 757 engineering metals, trends for, 754–757 factors affecting, 757–759 strain–life tests and equations, 748–754 surface finish and size effects, 757–758 transition fatigue life, 753–754 mean stress effects, 758–767 Strength, 20, 105, 111, 129–130, 149–150 in bending, 170–171 in compression, 154–156 in tension, 129–130, 149–150 theoretical, 53–55 in torsion, 172–173 Strength coefficient, 148 Strengthening effects in polymers, 91–92 Strengthening methods for metals, 66–72 Stress, 20, 124–128 basic formulas for, 880–882 components of, 235–236 definitions for cycling, 418–420 engineering type, 125 generalized plane stress, 244–245 Mohr’s circle for, 240–244 nominal type, 420 on octahedral planes, 260–262 plane stress, 235–236, 249–253 point stress vs. nominal stress, 420–421 in pressure vessels, tubes, discs, 884–889 principal stresses, 235, 237–240, 245–247, 253–257 three-dimensional states of, 253–260 transformation of axes, 236–237 true type, 143–144 von Mises stress, 298 Stress amplitude, 418–419 Stress and strain concentration factors, 710, 712, 714–717 See also Elastic stress concentration factor; Notched members Stress corrosion cracking, 25, 616 Stress field, at crack, 346–347 Stress gradient, 494 Stress intensity factor, 339, 346–348 range for fatigue crack growth, 564, 571 See also Fracture mechanics Stress invariants, 211, 257, 261 Stress raisers, 491, 889–892 and design details, 536–539 effects of, 297–298 and fatigue strength reduction, 443, 493–500, 541–542 from surface roughness, 503 from welding, 447, 531 See also Notch effects in fatigue; Notched members Stress range, 418–419 Stress ratio R, 419 Stress redistribution, 298, 338, 384Index 951 Stress relaxation, 198–199, 223, 2842–844 Stress relief, 540 Stress-based approach to fatigue, 416–479, 491–543 fatigue failure, designing to avoid, 536–541 See also Fatigue limits; Fatigue testing; Mean stress, effects of; Notch effects in fatigue; S-N (stress vs. fatigue life) curves Stress–life curves for creep, 806–808, 831 for fatigue, 421–426 See also S-N (stress vs. fatigue life) curves Stress–strain analysis for creep, 850–855 for cyclic loading, 722–728 in bending, 722–725 with irregular load vs. time histories, 728–732 of notched members, 710–722 elastic behavior and initial yielding, 712–713 estimates of notch stress and strain for local yielding, 714–717 fully plastic yielding
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