Abstract
The present paper deals with the consideration of the rate-sensitivity mechanical behavior of metallic materials, in the framework of mean field and full field homogenization approaches. We re-examine the possibility of describing properly this rate sensitivity with a simple and widely used power law expressed at the level of the slip system, and we propose a methodology to accelerate the identification of the global material constitutive law for Finite Element (FE) simulations. For such an aim, simulations of a tensile test are conducted, using a simple homogenization model (the Taylor one, used in a relaxed constraint form) and an FE code (Abaqus), both using the same single-crystal rate-dependent constitutive law. It is shown that, provided that the identification of this law is performed with care and well adapted to the examined case (rate-sensitive or insensitive materials, static and/or dynamic ranges), the simple power law can be used to simulate the macroscopic behavior of polycrystalline aggregates in a wide range of strain rate (including both static and dynamic regimes) and strain-rate sensitivity values (up the rate-insensitive limit).
Highlights
As the objective is to deal with strain-rate sensitivity in the framework of Finite Element (FE) codes, some simulations have been performed with the FE code Abaqus, which is increasingly used for the simulation of the VP behavior of polycrystalline materials, with the very same description of the single-crystal constitutive law
This first study has highlighted the fact that the only way to really neglect rate sensitivity with the power law is to set γ0 = E von Mises (VM), and to keep the macroscopic strain-rate constant; this is well known from experienced users of VP mean field or full field methods, but much less from new FE code users, if we look at the recent bibliography on the subject
The aim of the present study was to rationalize the use of the simple VP power law, still widely used for its simplicity with mean field and full field approaches, to model the behavior of polycrystalline samples in a wide range of strain rates or temperatures
Summary
For the modeling of the global and local mechanical behaviors of polycrystalline metals in a wide range of temperature or strain rate—with polycrystalline models, such as Taylor [1,2,3] or selfconsistent models [4,5,6], with Finite Element (FE) codes [7,8,9,10], or with multiscale approaches coupling discrete dislocations dynamic approaches with FE codes [11, 12]—it is quite usual to use a rate-dependent crystalline constitutive law, which generally takes the form of the following power law expressed on the slip system s [1]1 γs = γ0s τs τ0s n (1) In this expression, n (or more often 1/n = m) characterizes the material rate sensitivity, γs is the slip rate, and τs the resolved shear stress. By construction, the local strain rate is allowed to differ from one grain to another and may be quite different from the macroscopic imposed one
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