Damage Mechanics in Metal Forming Advanced Modeling and Numerical Simulation

by Saanouni, Khemais

• ISBN13: 9781848213487
• ISBN10: 1848213484
• Edition: 1st
• Format: Hardcover
• Copyright: 2012-05-21
• Publisher: Wiley-ISTE

Summary

Virtual metal forming is nowadays inescapable when looking to optimize numerically various metal forming processes in order to design advanced mechanical components. To do this, highly predictive constitutive equations accounting for the full coupling between various physical phenomena at various scales under large deformation including the ductile damage occurrence are required. Also fully 3D adaptive numerical methods related to the time and space discretization are required in order to solve accurately the associated initial and boundary value problems are needed. This book focuses on these two main and complementary aspects with application to a wide range of metal forming and machining processes.

Author Biography

Khemais Saanouni is Professor of applied and computational mechanics at the University of Technology of Troyes (France), where he founded and leads a research group working on advanced modeling in virtual metal forming. He teaches theoretical and computational nonlinear mechanics with application to metal forming by large inelastic strains with ductile damage and is the author or co-author of more than 200 scientific publications with around 80 papers in major peer-reviewed journals in the field of applied and computational mechanics.

Table of Contents

Preface	p. xiii
Principle of Mathematical Notations	p. xix
Elements of Continuum Mechanics and Thermodynamics	p. 1
Elements of kinematics and dynamics of materially simple continua	p. 2
Homogeneous transformation and gradient of transformation	p. 2
Homogeneous transformation	p. 2
Gradient of transformation and its inverse	p. 4
Polar decomposition of the transformation gradient	p. 5
Transformation of elementary vectors, surfaces and volumes	p. 5
Transformation of an elementary vector	p. 6
Transformation of an elementary volume: the volume dilatation	p. 6
Transformation of an oriented elementary surface	p. 7
Various definitions of stretch, strain and strain rates	p. 8
On some definitions of stretches	p. 8
On some definitions of the strain tensors	p. 10
Strain rates and rotation rates (spin) tensors	p. 15
Volumic dilatation rate, relative extension rate and angular sliding rate	p. 17
Various stress measures	p. 19
Conjugate strain and stress measures	p. 23
Change of referential or configuration and the concept of objectivity	p. 23
Impact on strain and strain rates	p. 24
Impact on stress and stress rates	p. 26
Impact on the constitutive equations	p. 29
Strain decomposition into reversible and irreversible parts	p. 30
On the conservation laws for the materially simple continua	p. 33
Conservation of mass: continuity equation	p. 33
Principle of virtual power: balance equations	p. 34
Energy conservation. First law of thermodynamics	p. 36
Inequality of the entropy. Second law of thermodynamics	p. 37
Fundamental inequalities of thermodynamics	p. 38
Heat equation deducted from energy balance	p. 39
Materially simple continuum thermodynamics and the necessity of constitutive equations	p. 39
Necessity of constitutive equations	p. 40
Some fundamental properties of constitutive equations	p. 41
Principle of determinism or causality axiom	p. 42
Principle of local action	p. 42
Principle of objectivity or material indifference	p. 42
Principle of material symmetry	p. 43
Principle of consistency	p. 43
Thermodynamic admissibility	p. 44
Thermodynamics of irreversible processes. The local state method	p. 44
A presentation of the local state method	p. 44
Internal constraints	p. 52
Mechanics of generalized continua. Micromorphic theory	p. 55
Principle of virtual power for micromorphic continua	p. 58
Thermodynamics of micromorphic continua	p. 59
Thermomechanically-Consistent Modeling of the Metals Behavior with Ductile Damage	p. 63
On the main schemes for modeling the behavior of materially simple continuous media	p. 64
Behavior and fracture of metals and alloys: some physical and phenomenological aspects	p. 69
On the microstructure of metals and alloys	p. 69
Phenomenology of the thermomechanical behavior of polycrystals	p. 70
Linear elastic behavior	p. 71
Inelastic behavior	p. 72
Inelastic behavior sensitive to the loading rate	p. 74
Initial and induced anisotropies	p. 76
Other phenomena linked to the shape of the loading paths	p. 77
Phenomenology of the inelastic fracture of metals and alloys	p. 82
Micro-defects nucleation	p. 84
Micro-defects growth	p. 85
Micro-defects coalescence and final fracture of the RVE	p. 85
A first definition of the damage variable	p. 86
From ductile damage at a material point to the total fracture of a structure by propagation of macroscopic cracks	p. 89
Summary of the principal phenomena to be modeled	p. 90
Theoretical framework of modeling and main hypotheses	p. 91
The main kinematic hypotheses	p. 91
Choice of kinematics and compliance with the principle of objectivity	p. 92
Decomposition of strain rates	p. 94
On some rotating frame choices	p. 99
Implementation of the local state method and main mechanical hypotheses	p. 102
Choice of state variables associated with phenomena being modeled	p. 103
Definition of effective variables: damage effect functions	p. 108
State potential: state relations	p. 113
State potential in case of damage anisotropy	p. 114
Formulation in strain space: Helmholtz free energy	p. 114
Formulation in stress space: Gibbs free enthalpy	p. 121
State potential in the case of damage isotropy	p. 124
Formulation in strain space: Helmholtz free energy	p. 124
Formulation in stress space: Gibbs free enthalpy	p. 128
Microcracks closure: quasi-unilateral effect	p. 129
Concept of micro-defect closure: deactivation of damage effects	p. 129
State potential with quasi-unilateral effect	p. 132
Dissipation analysis: evolution equations	p. 139
Thermal dissipation analysis: generalized heat equation	p. 140
Heat flux vector: Fourier linear conduction model	p. 141
Generalized heat equation	p. 141
Intrinsic dissipation analysis: case of time-independent plasticity	p. 143
Damageable plastic dissipation: anisotropic damage with two yield surfaces	p. 144
Damageable plastic dissipation: anisotropic damage with a single yield surface	p. 157
Incompressible and damageable plastic dissipation: isotropic damage with two yield surfaces	p. 162
Incompressible and damageable plastic dissipation: single yield surface	p. 169
Intrinsic dissipation analysis: time-dependent plasticity or viscoplasticity	p. 174
Damageable viscoplastic dissipation without restoration: anisotropic damage with two viscoplastic potentials	p. 176
Viscoplastic dissipation with damage: isotropic damage with a single viscoplastic potential and restoration	p. 182
Some remarks on the choice of rotating frames	p. 186
Modeling some specific effects linked to metallic material behavior	p. 189
Effects on non-proportional loading paths on strain hardening evolution	p. 190
Strain hardening memory effects	p. 191
Cumulative strains or ratchet effect	p. 191
Yield surface and/or inelastic potential distortion	p. 192
Viscosity-hardening coupling: the Piobert-Lüders peak	p. 192
Accounting for the material microstructure	p. 193
Some specific effects on ductile fracture	p. 193
Modeling of the damage-induced volume variation	p. 194
On the compressibility induced by isotropic ductile damage	p. 195
Concept of volume damage	p. 195
State coupling and state relations	p. 196
Dissipation coupling and evolution equations	p. 197
Modeling of the contact and friction between deformable solids	p. 200
Kinematics and contact conditions between solids	p. 201
Impenetrability condition	p. 203
Equilibrium condition of contact interface	p. 204
Contact surface non-adhesion condition	p. 205
Contact unilaterality condition	p. 205
On the modeling of friction between solids in contact	p. 206
Time-independent friction model	p. 206
Nonlocal modeling of damageable behavior of micromorphic continua	p. 215
Principle of virtual power for a micromorphic medium: balance equations	p. 217
State potential and state relations for a micromorphic solid	p. 218
Dissipation analysis: evolution equations for a micromorphic solid	p. 221
Continuous tangent operators and thermodynamic admissibility for a micromorphic solid	p. 223
Transformation of micromorphic balance equations	p. 224
On the micro-macro modeling of inelastic flow with ductile damage	p. 226
Principle of the proposed meso-macro modeling scheme	p. 227
Definition of the initial RVE	p. 230
Localization stages	p. 230
Constitutive equations at different scales	p. 233
State potential and state relations	p. 233
Intrinsic dissipation analysis: evolution equations	p. 235
Homogenization and the mean values of fields at the aggregate scale	p. 239
Summary of the meso-macro polycrystalline model	p. 240
Numerical Methods for Solving Metal Forming Problems	p. 243
Initial and boundary value problem associated with virtual metal forming processes	p. 244
Strong forms of the initial and boundary value problem	p. 245
Posting a fully coupled problem	p. 245
Some remarks on thermal conditions at contact interfaces	p. 250
Weak forms of the initial and boundary value problem	p. 252
On the various weak forms of the IBVP	p. 252
Weak form associated with equilibrium equations	p. 254
Weak form associated with heat equation	p. 257
Weak form associated with micromorphic damage balance equation	p. 258
Summary of the fully coupled evolution problem	p. 258
Temporal and spatial discretization of the IBVP	p. 259
Time discretization of the IBVP	p. 259
Spatial discretization of the IBVP by finite elements	p. 260
Spatial semi-discretization of the weak forms of the IBVP	p. 260
Examples of isoparametric finite elements	p. 266
On some global resolution scheme of the IBVP	p. 270
Implicit static global resolution scheme	p. 272
Newton-Raphson scheme for the solution of the fully coupled IBVP	p. 273
On some convergence criteria	p. 275
Calculation of the various terms of the tangent matrix	p. 276
The purely mechanical consistent Jacobian matrix	p. 280
Implicit global resolution scheme of the coupled IBVP	p. 282
Dynamic explicit global resolution scheme	p. 284
Solution of the mechanical problem	p. 284
Solution of thermal (parabolic) problem	p. 286
Solution of micromorphic damage problem	p. 288
Sequential scheme of explicit global resolution of the IBVP	p. 288
Numerical handling of contact-friction conditions	p. 291
Lagrange multiplier method	p. 293
Penalty method	p. 295
On the search for contact nodes	p. 296
On the numerical handling of the incompressibility condition	p. 300
Local integration scheme: state variables computation	p. 304
On numerical integration using the Gauss method	p. 304
Local integration of constitutive equations: computation of the stress tensor and the state variables	p. 305
On the numerical integration of first-order ODEs	p. 306
Choice of constitutive equations to integrate	p. 308
Integration of time-independent plastic constitutive equations: the case of a von Mises isotropic yield criterion	p. 313
Integration of time-independent plastic constitutive equations: the case of a Hill quadratic anisotropic yield criterion	p. 326
Integration of the constitutive equation in the case of viscoplastic flow	p. 328
Calculation of the rotation tensor: incremental objectivity	p. 333
Remarks on the integration of the micromorphic damage equation	p. 335
On the local integration of friction equations	p. 335
Adaptive analysis of damageable elasto-inelastic structures	p. 337
Adaptation of time steps	p. 339
Adaptation of spatial discretization or mesh adaptation	p. 341
On other spatial discretization methods	p. 347
An outline of non-mesh methods	p. 348
On the FEM-meshless methods coupling	p. 353
Application to Virtual Metal Forming	p. 355
Why use virtual metal forming?	p. 356
Model identification methodology	p. 359
Parametrical study of specific models	p. 360
Choosing typical constitutive equations	p. 360
Isothermal uniaxial tension (compression) load without damage	p. 364
Accounting for ductile damage effect	p. 383
Accounting for initial anisotropy in inelastic flow	p. 396
Identification methodologies	p. 413
Some general remarks on the issue of identification	p. 414
Recommended identification methodology	p. 416
Illustration of the identification methodology	p. 422
Using a nonlocal model	p. 429
Some applications	p. 431
Sheet metal forming	p. 431
Some deep drawing processes of thin sheets	p. 432
Some hydro-bulging test of thin sheets and tubes	p. 441
Cutting processes of thin sheets	p. 447
Bulk metal forming processes	p. 463
Classical bulk metal forming processes	p. 463
Bulk metal forming processes under severe conditions	p. 476
Toward the optimization of forming and machining processes	p. 484
Appendix: Legendre-Fenchel Transformation	p. 493
Bibliography	p. 499
Index	p. 515
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