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

Abstract

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 lying between 0 and 1= ffiffi ffi 3 p (i.e. 0 1= ffiffi ffi 3 p ). 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.

Simulation of Sheet Metal Forming Processes Using a Fully Rheological-Damage Constitutive Model Coupling and a Specific 3D Remeshing Method

“…The importance of this identification procedure is proportional to the increasing of the so-called advanced constitutive equations describing many coupled physical phenomena. The identification of the isotropic, isothermal elastoplastic constitutive equations accounting for isotropic hardening and ductile damage is based on the following steps [22,55]:…”

“…The titanium alloy was used, but the plastic hardening and damage parameters are estimated from the experimental shear curve (see Table 4). With these parameters, the maximum equivalent stress is about σ max = 1340 MPa, and a ductility of ε p max = 0.297 [55,56]. As shown in Figure 8, the coupled material model had fit the experiment value well when equivalent plastic strain less than ε p = 0.21 and the material damage accumulate rapidly to D max = 0.99 when equivalent plastic strain ε p = 0.297.…”

“…The elastic-plastic and damage parameters of the aluminum alloy (5086) are given in Table 6. The plastic parameters of the material are obtained, from the experimental curves, in which the maximum stress is about σ max = 366 MPa for equivalent plastic strain ε p = 0.17 and then the material stiffness deteriorates to zero when equivalent plastic strain equal to ε p max = 0.27 ( Figure 12) [55,56]. The numerical meshing parameters of the compression test are presented in Table 7.…”

“…Table 9. Elasto-plastic and damage parameters of the oxygen-free-high-conductivity copper [55,56]. Table 10.…”

“…The internal roughness of SPIF shaped component is influenced primarily by the tool (dp) and step (∆Z) sizes, as other factors such as, sheet thickness, material properties, forming angle, feed rate and etc., may affect both the internal and external roughness [54][55][56][57][58]. The influence of forming speed, both rotational spindle speed N and feed rate V f had an important effect on the heat generation due to the friction with the sheet.…”