Issue 38

A. Znaidi et alii, Frattura ed Integrità Strutturale, 38 (2016) 135-140; DOI: 10.3221/IGF-ESIS.38.18 136 I NTRODUCTION large majority of the metal parts are obtained by forming during which the material is plastically deformed. These forming processes are optimized to reduce cost; this requires manufacturers to increasingly use numerical simulation and therefore need to describe the material behavior. These simulations are often flawed by a simplified description of the plastic behavior of the material; particularly the anisotropy of rolled sheets [1-3]. Therefore, it is important to accurately model the plastic behavior of metals in large deformation in order to better predict the behavior of the part during the forming. The formulation of the anisotropic elasto-plastic behavior in large deformations is well understood now: using the formalism of rotating frame ensures the objectivity of the behavior law regardless of the constitutive model functions, [2-5]. To describe the plastic behavior of the material, it is necessary to clarify two concepts: (i) a load surface related to a plasticity criterion [6] that indicates the conditions of plastic flow, (ii) an anisotropy evolution. The experimental determination of these areas through various mechanical testing and mathematical modeling has been the subject of many research efforts such as using the Von Mises criterion: due to its implementation in most commercial finite element analysis codes. This criterion is called energy criterion in which the elastic deformation energy of the material must not exceed a limit value in order to remain within the elastic range. In the case sheet metal, the material is treated as having orthotropic plasticity where retained three preferred directions used in the expression of the Hill criterion. Also, in order to describe the asymmetric behavior in tension and compression such as the anisotropy of a structure of a sheet metal Cazacu, Barlat and al proposed in a new orthotropic criterion [7-11]. The objective of this work is to provide a model for the numerical simulation of forming processes by plastic deformation of thin metal sheets. Hence, the importance of developing a general framework for elasto-plastic orthotropic models (initial orthotropic and isotropic hardening) based on the choice of an equivalent stress, a hardening law and a plastic potential [12-14] and a model identification strategy using and experimental database [15]. This database consists of various hardening curves from various tests interpreted as homogeneous [2] and their Lankford coefficients. These plates are obtained from a hot-rolling process. At this point, the identification of constitutive parameters of the material behavior laws is an important step. A new identification strategy with its validation using Barlat's criterion will be presented. A NISOTROPIC ELASTO - PLASTIC CONSTITUTIVE LAWS n this work, we are interested in a plastic hardening behavior. The materials are treated as incompressible with negligible elastic deformations. The plastic hardening constitutive laws that we have to study fall within the following framework:   f ( , ) 0,      σ Q (1) with Q the transformation tensor between the initial time t 0 and the current time t. α Represents the internal hardening variable. h( , )    σ D (2) . 1( , )     σ (3) With λ plastic multiplier that can be determined from the consistency condition . f and D is the plastic strain rate tensor. This work is limited to plastic orthotropic behavior. Models are formulated for standard generalized materials with an isotropic hardening described by an internal hardening variable, a law of evolution and an equivalent deformation. The material is initially orthotropic and remains orthotropic; isotropic hardening is assumed to be captured by a single scalar internal hardening variable denoted by  . In particular, we will assume that the elastic range evolves homothetically, the yield criterion is then written as follows: A I