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 |  موضوع: كتاب Mechanical Behavior of Materials - Engineering Methods for Deformation, Fracture, and Fatigue الجمعة 11 مايو 2012, 11:38 am | |
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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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