Houssem Badreddine

Identification of fully coupled anisotropic plasticity and damage constitutive equations using a hybrid experimental–numerical methodology with various triaxialities

A hybrid experimental–numerical methodology is presented for the parameter identification of a mixed nonlinear hardening anisotropic plasticity model fully coupled with isotropic ductile damage accounting for microcracks closure effects. In this study, three test materials are chosen: DP1000, CP1200, and AL7020. The experiments involve the tensile tests with smooth and notched specimens and two types of shear tests. The tensile tests with smooth specimens are conducted in different directions with respect to the rolling direction. This helps to determine the plastic anisotropy parameters of the material when the ductile damage is still negligible. Also, in-plane torsion tests with a single loading cycle are used to determine separately the isotropic and kinematic hardening parameters. Finally, tensile tests with notched specimens and Shouler and Allwood shear tests are used for the damage parameters identification. These are conducted until the final fracture with the triaxiality ratio η lying between 0 and 1 / 3 (i.e. 0 ≤ η ≤ 1 / 3 ). The classical force–displacement curves are chosen as the experimental responses. However, for the tensile test with notched specimens, the distribution of displacement components is measured using a full field measurement technique (ARAMIS system). These experimental results are directly used by the identification methodology in order to determine the “best” values of material parameters involved in the constitutive equations. The inverse identification methodology combines an optimization algorithm which is coded within MATLAB together with the finite element (FE) code ABAQUS/Explicit. After optimization, good agreement between experimental and numerically predicted results in terms of force–displacement curves is obtained for the three studied materials. Finally, the applicability and validity of the determined material parameters are proved with additional validation tests.

Inverse Identification of CDM Model Parameters for DP1000 Steel Sheets Using a Hybrid Experimental-Numerical Methodology Spanning Various Stress Triaxiality Ratios

A hybrid experimental-numerical methodology is presented for the identification of the model parameters regarding a mixed hardening anisotropic finite plasticity fully coupled with isotropic ductile damage in which the micro-crack closure effect is given account for, for steel sheets made of DP1000. The experimental tests involve tensile tests with smooth and pre-notched specimens and shear tests with specimen morphologies recently proposed by D.R. Shouler, J.M. Allwood (Design and use of a novel sample design for formability testing in pure shear, Journal of Materials Processing Technology, Volume 210, Issue 10, 1 July 2010, Pages 1304-1313). These tests cover stress triaxiality ratios lying between 0 (pure shear) and 1/√3 (plane strain). To neutralize machine stiffness effects displacements of the chosen material surface pixels are kept track of using the digital image correlation system ARAMIS, where recorded inputs are synchronized with force measurements. On the numerical part, developed constitutive model is implemented as user defined material subroutine, VUMAT, for ABAQUS/Explicit. FE models for the test cases are built using 3D brick elements (rather than thin shells) and devising developed VUMAT for the constitutive model, model parameters are identified using an inverse parameter identification procedure where the objective function relies on the difference of experimentally observed-numerically predicted forces for the selected pixel displacements. The validity of the material model and transferability of its parameters are tested using tests involving complex strain paths.

Advanced Anisotropic Damage Model Fully Coupled with Anisotropic Plasticity

In this work, a thermodynamically-consistent framework is used to formulate a non-associative finite strain anisotropic elastoplastic model fully coupled with anisotropic ductile damage. The finite strain assumption is considered using specific large strains kinematics based on multiplicative decomposition of the total transformation gradient and assuming a small elastic strains. The objectivity principle fulfillment is assumed using the well-known rotating frame formulation. The effective variables are defined to introduce the effect of the anisotropic damage on the other variables through the total energy equivalence assumption. The non-associative plasticity framework, for which equivalent stresses in yield function and in plastic potential are separately defined, allows better plastic anisotropy description. The evolution equations for overall dissipative phenomena are deduced from the generalized normality rule applied to the plastic potential while the consistency condition is still applied to the yield function. Applications are made to an RVE with generic material parameters by considering non-proportional loading paths. For each loading path the effect of the anisotropic plasticity on the damage evolution is studied in the context of finite strains.

Numerical simulation of sheet metal blanking based on fully coupled elastoplasticity-damage constitutive equations accounting for yield surface distortion-induced anisotropy

This paper deals with the numerical simulation of sheet metal blanking process based on fully coupled elastoplastic model accounting for the induced anisotropies due to the kinematic hardening and the yield surface distortion. The yield surface distortion is assumed to be controlled by the kinematic hardening leading additional extra hardening which enhances the predictive capabilities of the model. Series of finite element-based numerical simulations of blanking process with four kinds of assumed distortional hardening parameters have been conducted. Through the comparison between the experimentally observed responses and the numerically predicted ones with and without the yield surface distortion effect, the significance of the yield surface distortion-induced anisotropy on the estimation of the blanking edge quality has been investigated.

Interaction between ductile damage and texture evolution in finite polycrystalline elastoplasticity

In this paper, a multiscale model of ductile damage and its effects on the inelastic behavior of face centered cubic polycrystalline metallic materials, such as the evolution of their crystallographic textures, are investigated. The constitutive equations are written in the framework of rate-dependent polycrystalline plasticity at the microscopic scale. Plasticity and damage are coupled through a ductile damage variable introduced at the scale of the crystallographic slip systems of each grain. When homogenized to the macro-scale, this becomes an approximate phenomenological measure of the macroscopic ductile damage which can describe the material degradation by initiation, growth, and coalescence of micro-defects. In this paper, thermally activated intergranular (or creep) damage is not taken into account. Both theoretical and numerical aspects of the model are presented. The model is implemented into a general-purpose finite element code in order to analyze the effects of texture evolution and ductile damage initiation in the grains with favorably oriented slip systems. The capability of the proposed model to predict the plastic strain localization and the induced textural evolution, as well as the effects of the ductile damage and its evolution up to the final macroscopic failure are studied for a classical tensile loading path, applied to a representative volume element and to a 3D tensile specimen on which a parametric study has been carried out.

Non-Associative Finite Strain Plasticity Coupled With Anisotropic Ductile Damage for Metal Forming

This paper presents the formulation of an advanced mechanical model describing a wide class of anisotropic elastoplastic constitutive equations accounting for the strong coupling with the anisotropic ductile damage. This model is developed within the framework of thermodynamics of irreversible processes with state variables and the continuum damage mechanics. The plastic anisotropy is accounted for through a non-associative theory for which a plasticity yield criterion and the plastic potential are defined separately but considering the strong coupling between both phenomena. The damage anisotropy is defined by using a second rank tensor. The effect of damage on the mechanical fields (stress, hardening, plastic strain, etc…) is described by a fourth rank damage effect operator that is defined in the context of the hypothesis of total energy equivalence. A rotating frame formulation is used to fulfil the objectivity of the constitutive equations under finite transformation. Finally, in order to illustrate the predictive capabilities of the model, the parametric studies with some simple loading case are investigated and the results discussed on the light of the anisotropic character of the ductile damage and its interaction with the anisotropy of plastic flow.© 2012 ASME

Damage Prediction in Sheet Metal Forming

Ductile (or plastic) damage often occurs during sheet metal forming processes due to the large plastic flow localization. Accordingly, it is crucial for numerical tools, used in the simulation of that processes, to use fully coupled constitutive equations accounting for both hardening and damage. This can be used in both cases, namely to overcome the damage initiation during some sheet metal forming processes as deep drawing, … or to enhance the damage initiation and growth as in sheet metal cutting. In this paper, a fully coupled constitutive equations accounting for combined isotropic and kinematic hardening as well as the ductile damage is implemented into the general purpose Finite Element code for metal forming simulation. First, the fully coupled anisotropic constitutive equations in the framework of Continuum Damage Mechanics are presented. Attention is paid to the strong coupling between the main mechanical fields as elasto‐viscoplasticity, mixed hardening, ductile isotropic damage and contact wit...