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Rheology, Physical and Mechanical Behavior of Materials 5 studies fractures and fatigue in metallic materials and composites. It analyzes the mechanisms at work according to the types of damage and fractures observed.
This book covers the formation of cracks around inclusions or precipitates, ductile and cup fracture facies, abrupt or intergranular fractures, cleavage and the influence of strain rates in striction and fracture. It also looks at the formability limit curves of metals under dynamic actions and techniques used.
Regarding metals, the book studies the types of tests, cracking mechanisms, and laws relating to uncracked and cracked parts, as well as endurance limits. As for composites, fracture mechanisms for unidirectional and laminate materials, successive layer fractures, maximum and quadratic stress and/or strain criteria, and fracture envelopes are analyzed.
Contents
Chapter 1 Damage 1
1.1 Definition 1
1.2 Damage variables 2
1.3 Effective stress 3
1.4 Principle of strain equivalence 5
1.5 Experimental characterization of the damage 6
1.5.1 Changes in mechanical characteristics 6
1.5.2 Modifications of the material 7
1.5.3 Wear rate 7
1.6 Models of the progression of the damage D 9
1.6.1 Dissipation 9
1.6.2 Types of damage 10
Chapter 2 Ductile Fracture 17
2.1 Stages of ductile tearing 17
2.1.1 First step: damage by decohesion, cracking of inclusions, impurities, precipitates, cavity formation 17
2.1.2 Second stage: growing cavities, formation of peduncles followed by necking, giving rise to ductile tearing 18
2.2 Linear ductile plastic damage during strain 20
2.3 Formation of cracks around inclusions or precipitates, cavities in ductile fracture 23
2.3.1 Formation of cracks from particles for Figure 2.5(b): the case of multiple metals 28
2.3.2 Aluminum-silicon alloy 29
2.4 Analysis of facies of ductile fractures of trichite and metals according to the purity and the state of the stresses 30
2.4.1 Whisker fracture (Cu and Fe) 30
2.4.2 Polycrystals CC and CFC in ductile fracture: influence of stress states and purity 33
2.4.3 Ductile fracture of steel test pieces without notches 34
2.4.4 Fracture of pure iron specimens 35
2.4.5 Ductile fracture of industrial copper specimens of purity 4N and 5N 36
2.4.6 Cases of zones of melted Fe, Cu (4N, 5N and industrial), aluminum (3N, 5N and industrial) - uniaxial and triaxial stresses 40
2.5 Relationship between the density of inclusions and ductility 44
2.5.1 Sintered copper made up of particles 44
2.5.2 Alumina 46
Chapter 3 Sudden Fracture, Fracture Energy 53
3.1 Analysis of the fracture 53
3.2 Sudden fracture and energy criterion 54
3.2.1 Energy balance causing the crack to advance 54
3.2.2 Obtaining Gc 56
3.2.3 Data for Gc and Kc 58
3.2.4 Examples of sudden fractures 64
Chapter 4 Description and Modeling of Physical Mechanisms 73
4.1 Expansion of cracks 73
4.2 Calculation of rp : the case of confined plasticity 74
4.3 Elastoplastic zone at the end of a crack 76
4.4 Stress and strain field at the end of the crack 77
Chapter 5 Fractures due to Cleavages and Intergranularity 81
5.1 Fractures from cleavages 81
5.1.1 Examples of fractures by cleavage 82
5.1.2 Change of micromechanisms 84
5.2 Intergranular fracture 85
5.2.1 Fractures along interfaces, grain boundary 85
5.2.2 Intergranular brittle fracture 86
5.2.3 Metal fracture transition parameter 87
5.2.4 Influence of the grain boundary 91
5.2.5 Cleavage strain of steels 92
5.2.6 Influence of the addition elements on the brittle-ductile transition 93
Chapter 6 Concentration of Stresses K t 97
6.1 Introduction 97
6.2 Measure of Kt 99
6.2.1 By extensometry gauges 99
6.2.2 By photoelasticimetry 100
6.3 Solids with equal resistances 101
6.4 Notching effect 102
6.5 Reduction of the stress concentration factor: the case of notched objects 104
6.6 Effect of notches under fatigue 105
6.7 Stress concentration values Kt : useful cases in practice 107
Chapter 7 The Intensity Factor of Stresses K 111
7.1 Introduction 111
7.2 Fields of stresses and movements 113
7.2.1 Mode I 113
7.2.2 Mode II 115
7.2.3 Mode III 117
7.2.4 Values of K for flat cracked medium 118
7.2.5 Area at the bottom of the crack 121
7.2.6 Influence of the plastic zone undergoing cracking 124
7.3 Remarks regarding K = σ √πa 125
7.4 Values of the stress intensities KI , KII , KIII for the three modes: for cases related to the subject and useful cases in practice 126
7.4.1 Typical values of stress intensity factors KI , KII , KIII 126
7.4.2 Values of KI = f(λ).σ√πa 131
Chapter 8 Fracture Zones in Photoelasticimetry 137
8.1 Photoelasticity 137
8.1.1 Primary stresses and isostatic lines 137
8.1.2 Birefringence by strain 138
8.2 Propagation of light vibrations 139
8.2.1 Propagation of light in a vacuum 139
8.2.2 Propagation of light in a transparent medium 140
8.2.3 Wave in a dielectric 141
8.2.4 Values of the constants C and K of photoelastic materials 142
8.2.5 Choice of a photoelastic coating 144
8.2.6 Ellipsoid of the indices 146
8.3 Photoelasticimetry 149
8.3.1 Photoelasticimeter 149
8.3.2 Isochromatic lines, difference between the primary stresses 151
8.3.3 Example of physical parts under stresses: a three-dimensional case using the freezing method 159
Chapter 9 The Influence of Strain Speeds 161
9.1 Types of dynamic loads 161
9.2 Examples of fast fractures 163
9.3 Damage, domain between necking and fracture, the case between FLCS and LCFF 168
9.3.1 Definition 168
9.3.2 Large strains and damage 169
9.4 Forming limit curves: static stamping (under a press) and dynamic stamping (magnetoforming and electrohydroforming) 171
9.4.1 Measurement of strains 171
9.4.2 Description of an electrohydraulic (EH) test 172
9.4.3 Types of test pieces 176
9.4.4 Example of LCFFs 177
9.5 Shock by intense pulsed magnetic field on aluminum alloys 180
9.6 Test results 183
9.6.1 Strain trajectories, change of ε1 according to ε2 ; comparison of low and high speeds 184
9.6.2 Influence of strain speeds on FLCs, formability in static and dynamic states 187
9.6.3 Comparison of the values for necking Z and fracture F 189
Chapter 10 Metal Fatigue 197
10.1 Introduction 197
10.2 Endurance curve: plot of the endurance curve or Wöhler curve 197
10.3 Conventional endurance limit 199
10.4 Classification of fatigue tests 201
10.4.1 Definition 201
10.4.2 Tests in practice 203
10.4.3 Combined stress tests 205
10.4.4 Application of a criterion in planar stress 212
10.4.5 Examples of influences on endurance 216
10.4.6 Influence of temperature 217
10.5 Physical aspects of fatigue 219
10.5.1 Physical mechanisms 219
10.5.2 Fatigue fracture surfaces, microscope images 222
10.5.3 Change of the streak spacing 223
10.5.4 Examples of micrograph images of fractures 224
10.6 Types of fatigue 225
10.6.1 Behavior of non-cracked parts under fatigue 226
10.6.2 Behavior of non-cracked parts under fatigue 230
10.7 Plasticity, fast fracture by fatigue: a case study 235
10.8 Propagation of corrosion cracks under fatigue-corrosion stress and influence of cycle frequencies 241
Chapter 11 Fracture of Composites 247
11.1 Fracture mechanisms 247
11.1.1 Unidirectional composite (UD) 247
11.1.2 Fracture of laminates 252
11.2 Criteria for fracture 254
11.2.1 Data describing the resistance of a UD or a fabric 254
11.2.2 Successive fractures of layers 256
11.2.3 Strength/stress ratio: coefficient of resistance R 256
11.2.4 Criteria for maximum stress and/or maximum strain 257
11.2.5 Quadratic criterion: in the stress space 259
11.2.6 Fracture envelopes 264
11.3 Design in primary strains 266
11.3.1 Principal stresses and strains 266
11.3.2 Constants of stresses and strains 267
11.3.3 Scaling of isotropes 268
Appendices 275
References 331
Index 335
