Keywords: finite transformation, anisotropic plasticity, Hill criterion, isotropic ductile damage, sheet metal forming.

Sheet metal drawing is an industrial process widely used in automotive production. Motivated by the high cost of experimentation combined with the great capability of numerical simulation to give more and more accurate results, the deep drawing processes are now widely modelled and numerically simulated using various specialized or general finite element (FE) codes. The incremental approach is the most used approach in the FE codes because of its capability to deal with high non linearity caused by various phenomena as elastoplasticity, finite transformation, hardening, damage, friction and so on.

Recently some new works [1,2] have shown the high performance of the coupled models accounting for the ductile damage in optimizing any sheet metal forming with respect to defects (damage) predictions. The present work shows the ability of using continuum damage mechanics in order to predict the ductile damage (or fracture) occurrence during the deep drawing of anisotropic thin sheets. For this purpose a constitutive equations accounting for anisotropic elasto-plasticity coupled with the isotropic damage and a combined isotropic and kinematic hardening are derived from the thermodynamic of irreversible processes. The quadratic Hill yield criterion is used in order to take into account the initial plastic anisotropy of the sheet metal. Numerical aspects related to the associated initial and boundary values problem are presented. To preserve the objectivity requirement, the rotational objective rates are used to calculate the derivatives of any tensorial variables. This consists to rephrase the small strain elastoplastic-damage model in the deformed configuration rotated by the orthogonal rotation tensor. This rotated description keeps unchanged the basic structure of the constitutive equations as formulated in small strain hypothesis. Hence, along this paper the constitutive equations will be formulated in the rotated frame.

For the local integration, an iterative implicit scheme is used together with a reduction in the number of the integrated constitutive equations and a fully implicit Return Mapping Algorithm. These are the anisotropic yield function and tensorial equation governing the evolution of the unit normal to the yield surface. At the global level, a Dynamic Explicit scheme is used to solve the equilibrium problem defined by the principle of virtual power using ABAQUS/Explicit software.

Application has been made to the damage prediction in deep drawing. First, the material parameters (17 parameters for elasticity, anisotropic plasticity, isotropic and kinematic hardening and isotropic ductile damage) are determined by numerical identification with experimental results in term of force-displacement curves from tensile tests conducted until the final fracture.

Some classical deep drawing and hydro-forming processes are then simulated and the distribution of the mechanical fields carefully analyzed. A special cure is given to the ductile damage distribution inside the formed anisotropic sheet in order to predict when and where macroscopic cracks take place. Qualitative comparisons with available experimental results are made.

1

M. Khelifa, H. Badreddine, N. Belamri, M. A. Gahbiche, K. Saanouni, A. Cherouat, A. Dogui. "Effect of anisotropic plastic flow on the ductile damage evolution in sheet metal forming. Application to circular bulging test", International Journal of Forming Processes, 2003.

2

K. Saanouni, J.L. Chaboche, "Computational damage mechanics. Application to metal forming", ISBN 0-08-043749-4, Elsevier, 321-376, 2003.

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