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Plasticity and Textures - Wiktor Gambin

Plasticity and Textures

Hardcover Published: 31st December 2001
ISBN: 9781402002120
Number Of Pages: 240

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The classical, phenomenological theory of plastically anisotropic materials has passed a long way: from the work of von Mises presented in 1928, and the HilI formulation given in 1948, to the latest papers on large elastic-plastic deformations of anisotropic metal sheets. A characteristic feature of this approach is a linear flow rule and a quadratic yield criterion. Mathematical simplicity of the theory is a reason of its numerous applications to the analysis of engineering structures during the onset of plastic deformations. However, such an approach is not sufficient for description of the metal forming processes, when a metal element undergoes very large plastic strains. If we take an initially isotropic piece of metal, it becomes plastically anisotropic during the forming process, and the induced anisotropy progressively increases. This fact strongly determines directions of plastic flow, and it leads to an unexpected strain localization in sheet elements. To explain the above, it is necessary to take into account a polycrystalline structure of the metal, plastic slips on slip systems of grains, crystallographic lattice rotations, and at last, a formation of textures and their evolution during the whole deformation process. In short, it is necessary to introduce the plasticity of crystals and polycrystals. The polycrystal analysis shows that, when the advanced plastic strains take place, some privileged crystallographic directions, called a crystallographic texture, occur in the material. The texture formation and evolution are a primary reason for the induced plastic anisotropy in pure metals.

Introductionp. 1
Texture formation during the plastic flow processp. 1
Properties of materials with texturep. 2
Mathematical and physical theory of plasticityp. 2
General principlesp. 7
Motion and deformationp. 7
Motion description in material and spatial coordinatesp. 7
Deformation, strain-rate and spin measuresp. 9
Finite elastic-plastic deformationsp. 13
Stress statep. 18
Stress and stress-rate measuresp. 18
Conjugate stress and strain-rate measuresp. 21
Equilibrium equations and boundary conditionsp. 22
Principle of virtual velocitiesp. 23
Constitutive relationsp. 24
Physical admissibilityp. 24
Constitutive principlesp. 27
Material symmetryp. 28
Plastic flow rule and plastic spin rulep. 29
Anisotropic plasticityp. 34
Anisotropic yield conditions and hardening rulesp. 34
General form of anisotropic yield conditionp. 34
The Hill orthotropic criterionp. 40
Hardening evolution lawsp. 43
Generalized relations of anisotropic plasticityp. 48
Generalized plastic potentialp. 48
Conjugate flow rule and conjugate plastic spin rulep. 49
Generalized Prandtl-Reuss equationsp. 50
Models of plastically anisotropic materialsp. 56
Rigid-plastic materialsp. 56
Elastic-plastic materialsp. 59
Finite element formulationp. 60
Advanced plastic deformationsp. 64
Application to sheet metal forming processesp. 64
Differences between theoretical predictions and experimental resultsp. 69
More physical approach - theories with plastic corner effectp. 74
Sources of induced plastic anisotropyp. 80
Physical approachp. 80
Background of considerationsp. 80
Plastic behaviour of single crystalsp. 84
Plastic behaviour of crystalline aggregatesp. 93
Structure and kinematics of single crystalsp. 101
Crystallographic lattice frame and system of slip systemsp. 101
Stereographic projection of crystalline latticep. 106
Motion of the latticep. 110
Motion of the materialp. 113
Coupling of the lattice motion and the material motionp. 118
Uniform deformations of single crystalsp. 118
Finite elastic-plastic deformations of single crystalsp. 121
Plasticity of crystalsp. 125
Rigid-plastic crystals behaviourp. 125
General form of yield criterionp. 125
The Schmid law - independent slip systemsp. 127
Crystals with interacting slip systemsp. 131
Generalized plastic potential for strain rate and plastic spinp. 135
Regularized Schmid law - interacting slip systemsp. 137
Complete system of equationsp. 142
Elastic-plastic crystals behaviourp. 145
General form of constitutive relationsp. 145
The Schmid modelp. 148
Rate-dependent modelp. 150
Regularized Schmid modelp. 150
Lattice reorientationsp. 155
Latent hardeningp. 157
Complete system of equationsp. 159
From textures to plastic anisotropyp. 161
Elements of texture analysisp. 161
The Orientation Distribution Functionp. 161
Direct and inverse pole figuresp. 166
Methods of texture analysisp. 171
Continuous model of textured materialsp. 177
Preliminary remarksp. 177
Extended physical spacep. 180
Textured material bodyp. 181
The equation of texture evolutionp. 183
Global virtual power principlep. 186
Finite element analysis of crystal aggregatep. 188
Finite element analysis of textured continuump. 190
Deformation textures developmentp. 194
Fibre and rolling texturesp. 194
Single crystal behaviourp. 200
Polycrystal behaviourp. 203
Refined models of anisotropic plasticityp. 208
Non-quadratic plastic potentialsp. 208
Direct generalizationsp. 208
Tricomponent plane stress yield surfacep. 212
Six-component yield surfacep. 217
Dual plastic potentialsp. 220
Quadratic strain-rate potentialp. 220
Texture-adjusted strain-rate potentialp. 222
Convex non-quadratic strain-rate potentialp. 225
Referencesp. 229
Indexp. 237
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9781402002120
ISBN-10: 1402002122
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 240
Published: 31st December 2001
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.4 x 15.6  x 1.91
Weight (kg): 1.21