Stephane Dumoulin

Determination of the equivalent stress–equivalent strain relationship of a copper sample under tensile loading

Abstract In this paper, a new method is used to determine the true stress–true strain curve. As this method still makes use of a tensile test, the results are compared with the results obtained with an extensometer on a copper sample for which the strain between the grips is supposed to be homogeneous. In the present case, the deformation is determined using a correlation method applied to successive images of one randomly painted sample face. The calculated strain field brings into evidence an increasing heterogeneity at high deformations. Taking this heterogeneity into account allows a more precise computation of the equivalent stress–equivalent strain curve which is used in a finite element simulation of the tensile test. Comparing the results of the simulation with those of image analysis, it appears that a corrected equivalent stress–equivalent strain relationship is sufficient to obtain a correct behaviour up to necking. The simulation also shows that the necking in the material is obtained when a necking criterion (Considere’s criterion) is verified. It indicates that in this case only the datum of the σ eq = f ( e eq ) relationship is sufficient to obtain the whole behaviour of the material.

Description of plastic anisotropy in AA6063-T6 using the crystal plasticity finite element method

The crystal plasticity finite element method has been used in combination with crystallographic texture data to predict the plastic anisotropy of the extruded aluminium alloy AA6063 in temper T6. The results are compared with experimental data from tensile tests at different angles between the tensile and extrusion directions. Inverse modelling based on the tensile test in a reference direction is used to identify the parameters of the work-hardening model at slip system level. To investigate the influence of grain interactions, various discretizations of the grains are applied in the representative volume element modelled with finite elements. In addition, alternative homogenization schemes, such as the full-constraint Taylor and viscoplastic self-consistent methods, are used to model the behaviour of the polycrystal. It is found that the grain discretization and the homogenization scheme have only minor influence on the predicted plastic anisotropy. While the crystal plasticity-based methods all give reasonable predictions of the directional variations of flow stresses and plastic strain ratios measured experimentally, there are still significant deviations, indicating there are other sources to the plastic anisotropy than crystallographic texture.

Modelling the plastic anisotropy of aluminum alloy 3103 sheets by polycrystal plasticity

The hood, doors and other panels of a car can be made by aluminium sheets, through complex forming operations. Design of forming processes requires trustable models and simulations.Forming properties are different in different directions. There are two principle ways to describe this plastic anisotropy of metals. The first one is the continuum theories for materials. The flow properties in various directions are described by the yield function. It is a parametric function calibrated by experimental tests. Unfortunately only a few mechanical tests can be directly used.The second approach takes into account that metals consist of many small crystals. The properties of each crystal are determined by crystal planes, but crystals are rotated in many directions. The crystal models either resolve all the details of thousands of crystals in a small volume element, requiring huge computer capacity, or simplified statistical models can be applied. In both cases the models are much more demanding than continuum models. In practice these models can be used to perform virtual experiments for calibration of continuum models.In his PhD work Kai Zhang (kai.zhang@ntnu.no) implemented and tested both type of models. More efficient numerical algorithms for computer simulations were developed and programmed for the detailed crystal plasticity approach. Three different cases were investigated experimentally. In one of the cases it was found that even for the detailed computer implementation the predictions could not replace experiments for design purposes. A combination of real and virtual experiments was recommended for calibration. For the other two cases the virtual experiments could be trusted.It was found that the best statistical models, that are more than thousand times faster, can replace detailed simulations of the crystal structure with high accuracy.

Influence of Texture and Grain Shape on the Yield Surface in Aluminium Sheet Material Subjected to Large Deformations

The crystal plasticity finite element method is used to investigate the combined effects of crystallographic texture and grain morphology on the shape of the yield surface computed for aluminium sheets subjected to large deformation. Two crystallographic textures (recrystallized and rolling) and two grain shapes (equiaxed and elongated) were modelled using a representative volume element (RVE) containing a large number of grains satisfying the periodicity conditions. Plane stress state is assumed and a rate‐dependent model of single crystal plasticity is used to compute the mechanical response of the individual grains within each RVE.

Quasi‐3D Strain Analysis in Equal Channel Angular Pressing

Although deformation features of ECAP have been widely studied and investigated through numerical approaches, experimental observations are very scarce in the literature. Therefore, in this paper, quasi‐3D strains in multi‐sectioned samples during one pass of ECAP are analyzed, for different friction conditions and material properties. From this study, it can be concluded that ECAP is a plane‐strain process and friction and material properties affect the strain distribution, strain homogeneity and also the work‐piece geometry. Furthermore, ECAP can be interpreted as a combination of shear and stretch.

An explicit integration scheme for hypo-elastic viscoplastic crystal plasticity

Abstract An explicit integration scheme for rate-dependent crystal plasticity (CP) was developed. Additive decomposition of the velocity gradient tensor into lattice and plastic parts is adopted for describing the kinematics; the Cauchy stress is calculated by using a hypo-elastic formulation, applying the Jaumann stress rate. This CP scheme has been implemented into a commercial finite element code (CPFEM). Uniaxial compression and rolling processes were simulated. The results show good accuracy and reliability of the integration scheme. The results were compared with simulations using one hyper-elastic CPFEM implementation which involves multiplicative decomposition of the deformation gradient tensor. It is found that the hypo-elastic implementation is only slightly faster and has a similar accuracy as the hyper-elastic formulation.

A microstructure-based yield stress and work-hardening model for textured 6xxx aluminium alloys

Abstract The plastic properties of an aluminium alloy are defined by its microstructure. The most important factors are the presence of alloying elements in the form of solid solution and precipitates of various sizes, and the crystallographic texture. A nanoscale model that predicts the work-hardening curves of 6xxx aluminium alloys was proposed by Myhr et al. The model predicts the solid solution concentration and the particle size distributions of different types of metastable precipitates from the chemical composition and thermal history of the alloy. The yield stress and the work hardening of the alloy are then determined from dislocation mechanics. The model was largely used for non-textured materials in previous studies. In this work, a crystal plasticity-based approach is proposed for the work hardening part of the nanoscale model, which allows including the influence of the crystallographic texture. The model is evaluated by comparison with experimental data from uniaxial tensile tests on two textured 6xxx alloys in five temper conditions.

Numerical Study on the Influence of Crystallographic Texture and Grain Shape on the Yield Surface of Textured Aluminum Sheet Material

The paper investigates by numerical modeling the effects of crystallographic texture and grain shape on the shape of the yield surface of aluminum sheet material at small strains. Different representative volume elements (RVEs) of the material are considered. Plane stress state is assumed in the sheet. A rate-dependent model of crystal plasticity (CP) is used in combination with either the full-constraint (FC) Taylor model or the finite element method (FEM) to compute the volume averaged stress of the material. The effect of different crystallographic textures observed in aluminum alloys on the shape of the yield surface is firstly investigated. An analytical yield function is used to generate yield surfaces for the different crystallographic textures. The deviation between the stress states at yielding computed by FC-Taylor model and the analytical yield surface is used to evaluate the capability of the yield function to fit the anisotropic yield surfaces representing different strong crystallographic textures. Two different shapes of the grains are introduced in the RVEs of CP-FEM in order to study the effect of the grain morphology. Small effects of grain shape are found at small strain compared with the marked influence of crystallographic texture.

Slip system interaction matrix and its influence on the macroscopic response of Al alloys.

In numerical models based on the crystal plasticity theory, various rules are implemented to describe hardening on the slip system level. The rules used are often variations of the Mecking-Kocks law, where the statistically stored dislocation density is the single internal variable. The dislocation density evolution equation consists of two terms representing accumulation and annihilation of dislocations. The accumulation term depends on a scalar parameter and an interaction matrix, which describes the contribution of all slip systems to the accumulation of the dislocations on a given slip system. Physically this matrix represents the relative strength of various dislocation locks which form when dislocations from different slip systems interact. The numerical values of the elements of the interaction matrix are rather hard to establish, but this has been done experimentally for different alloys and also based on numerical simulations. The obtained values, found in literature, are very different from each other. We use some new experimental data in an attempt to establish the influence of the numerical values of the elements of the interaction matrix on the hardening of a polycrystal.

3D Crystal Plasticity Modelling of Complex Microstructures in Extruded Products

The current study relates to the modelling of plastic anisotropy in aluminium alloy AA6063‐W using a rate‐dependent crystal plasticity finite element approach. A virtual microstructure, in which grains are explicitly resolved, was first generated based on experimental data using a grain growth algorithm. The texture was obtained by sampling the experimental ODF. The microstructure was then meshed using three different methods and appropriate boundary conditions were used in order to simulate uniaxial tensile testing in different directions. The results obtained from the different meshes were finally compared with experimental true stress‐true strain curves and discussed.