By Khemais Saanouni
The target of this e-book is to summarize the present most excellent equipment for modeling, simulating, and optimizing steel forming strategies, and to offer the most positive aspects of recent, cutting edge equipment at present being constructed so that it will doubtless be the economic instruments of the following day. It discusses harm (or disorder) prediction in digital steel forming, utilizing complex multiphysical and multiscale absolutely coupled constitutive equations. Theoretical formula, numerical facets in addition to program to varied sheet and bulk steel forming are provided in detail.
Virtual steel forming is these days inescapable while trying to optimize numerically a variety of steel forming approaches in an effort to layout complex mechanical elements. to do that, hugely predictive constitutive equations accounting for the total coupling among a variety of actual phenomena at numerous scales lower than huge deformation together with the ductile harm incidence are required. moreover, absolutely 3D adaptive numerical equipment regarding time and area discretization are required with the intention to clear up safely the linked preliminary and boundary price difficulties. This booklet makes a speciality of those major and complementary points with program to quite a lot of steel forming and machining processes.
1. parts of Continuum Mechanics and Thermodynamics.
2. Thermomechanically-Consistent Modeling of the Metals habit with Ductile Damage.
3. Numerical tools for fixing steel Forming Problems.
4. program to digital steel Forming.
Chapter 1 parts of Continuum Mechanics and Thermodynamics (pages 1–62): Khemais Saanouni and Pierre Devalan
Chapter 2 Thermomechanically?Consistent Modeling of the Metals habit with Ductile harm (pages 63–242): Khemais Saanouni and Pierre Devalan
Chapter three Numerical tools for fixing steel Forming difficulties (pages 243–354): Khemais Saanouni and Pierre Devalan
Chapter four program to digital steel Forming (pages 355–492): Khemais Saanouni and Pierre Devalan
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Additional info for Damage Mechanics in Metal Forming
Dx 2dX . dX 2dx. 45]. 46] and after some algebraic transformations, we easily obtain the following relationship between the Eulerian strain rate D and the Lagrangian strain rate E : C F T . F or also E 1 T F . U 2 D R. RT R. R T R. R T R. 54], the rotation of the rigid body affects the strain rate and that pure dilatation affects the material rotation rate ȍ , which is distinct from the proper rotation rate W . 4. 57] This proves that the rate of volume variation, or the variation of volume in relation to the elementary volume in current configuration Ct , is equal to the trace of the strain rate tensor D , ( tr( D ) D : 1 ), or to the divergence of the velocity vector v .
Q T ) f( , , ) Q. f ( , , ) f ( , Q. , Q. Q T ) Q. 103] f ( , Q. , Q. 7. Strain decomposition into reversible and irreversible parts For solids exhibiting irreversible strains ((visco)plasticity) in addition to reversible deformations (elasticity), it is essential to know how to decompose the Eulerian and/or the Lagrangian strain measures into their reversible, or elastic parts, and their irreversible, or anelastic (plastic or viscoplastic) parts. This will be the focus of Chapter 2, devoted to the modeling of thermo-elasto-(visco)plastic behavior with damage.
S ) Q. 93] We will now look at the derivatives of the objective stress tensors. e. Q T . 96] initial conditions This result can cause problems of objectivity when formulating nonlinear constitutive equations under finite strains, and in particular for those that are expressed in the form of tensorial relationships between stress rates and strain rates. This is the case in (visco)plasticity, where objective relationships are sought and the strain rate tensor D. It is thus between the Cauchy stress rate tensor essential to use objective derivatives of any objective tensor in order to ensure the independence of the constitutive equations with regard to observer changes, that is, changes of triad, referential or configuration.
Damage Mechanics in Metal Forming by Khemais Saanouni