Jerzy Gawad

Evolving texture-informed anisotropic yield criterion for sheet forming

In this work we compare the predictions of the phenomenological anisotropic plane-stress plasticity model BBC2008, calibrated either classically by means of mechanical tests, or by crystal plasticity virtual experiments, to those of a HMS type model with continuous calibration of the same phenomenological model BBC2008. An industrial-grade aluminum alloy AA-6016 is chosen for the test case. Experimental part of the study includes tensile tests and deep drawing of cylindrical cups, preceded by measurements of crystallographic texture. It was found that the material exhibits a noticeable through-thickness gradient in terms of both the texture and plastic anisotropy. The classical calibration of the 16 parameters of BBC2008 was done from tensile experiments (yield stresses and Lankford coefficients) in directions every 15° from the rolling direction and the biaxial yield stress and anisotropy coefficient. The initial texture for the HMS-BBC2008 model was determined from as received samples. The ALAMEL model ...

A Coupled Multiscale Model of Texture Evolution and Plastic Anisotropy

In this paper we present a multiscale model of a plastic deformation process in which the anisotropy of plastic properties is related to the evolution of the crystallographic texture. The model spans several length scales from the macroscopic deformation of the workpiece to the microscale interactions between individual grains in a polycrystalline material. The macroscopic behaviour of the material is described by means of a Finite Element (FE) model. Plastic anisotropy is taken into account in a constitutive law, based on the concept of a plastic potential in strain rate space. The coefficients of a sixth‐order Facet equation are determined using the Taylor theory, provided that the current crystallographic texture at a given FE integration point is known. Texture evolution in the FE integration points is predicted by an ALAMEL micromechanical model. Mutual interactions between coarse and fine scale are inherent in the physics of the deformation process. These dependencies are taken into account by full ...

An Efficient Strategy to Take Texture-Induced Anisotropy Point-by-Point into Account during FE Simulations of Metal Forming Processes

Cup drawing of sheet material (carbon steel DC06 and aluminium alloy AA3103-O) is simulated using a Finite Element (FE) method configured as a hierarchical multi-scale model. It performs a two-way simulation of the interactions between the metal flow and the crystallographic textures of the polycrystalline material. In this, the evolution of the deformation textures is simulated by the Taylor and ALAMEL models, and this in every integration point of the FE mesh. The resulting textures have been compared with experimentally measured ones at different positions within the work-piece. An anisotropic constitutive model is used based on the Facet model identified from the current texture in every location by means of the Taylor and/or ALAMEL model. The updating procedure has been highly optimized. Simulated and experimental results (cup profiles, deformation textures) are compared. The effect of texture updating is assessed.

Anisotropic sheet forming simulations based on the ALAMEL model: Application on cup deep drawing and ironing

The grain interaction ALAMEL model [1] allows predicting the evolution of the crystallographic texture and the accompanying evolution in plastic anisotropy. A FE constitutive law, based on this multilevel model, is presented and assessed for a cup deep drawing process followed by an ironing process. A Numisheet2011 benchmark (BM‐1) is used for the application. The FE material model makes use of the Facet plastic potential [2] for a relatively fast evaluation of the yield locus. A multi‐scale approach [3] has been recently developed in order to adaptively update the constitutive law by accommodating it to the evolution of the crystallographic texture. The identification procedure of the Facet coefficients, which describe instantaneous plastic anisotropy, is accomplished through virtual testing by means of the ALAMEL model, as described in more detail in the accompanying conference paper [4]. Texture evolution during deformation is included explicitly by re‐identification of Facet coefficients in the course...

Identification of constitutive equation in hierarchical multiscale modelling of cup drawing process

In this paper we discuss extensions to a hierarchical multi‐scale model (HMS) of cold sheet forming processes. The HMS model is capable of predicting changes in plastic anisotropy due to the evolution of crystallographic textures. The ALAMEL polycrystal plasticity model is employed to predict the texture evolution during the plastic deformation. The same model acts as a multilevel model and provides “virtual experiments” for calibration of an analytical constitutive law. Plastic anisotropy is described by means of the Facet method, which is able to reproduce the plastic potential in the entire strain rate space. The paper presents new strategies for identification of the Facet expression that are focused on improving its accuracy in the parts of the plastic potential surface that are more extensively used by the macroscopic FE model and therefore need to be reproduced more accurately. In this work we also evaluate the applicability of identification methods that (1) rely exclusively on the plastic potenti...

The Application of Crystal Plasticity Material Files in Stamping Simulations

Representative material data are inevitable to execute accurate stamping simulations. These material data are generally generated by performing extensive mechanical material tests. In this research the generation and application of material data from a crystal plasticity-based multiscale model have been studied. The crystal plasticity model enables to generate detailed material properties which can be applied in various yield locus models. The evolution of the anisotropic properties during deformation can be readily taken into account with the crystal plasticity model. The generated material data have been applied in deep drawing simulations of a cross-die. The thickness distribution of the simulation has been compared with experiments. Results showed that crystal plasticity models are a viable alternative for material data generation, having as main advantage that extensive mechanical experiments are avoided.

A numerical multi-scale model to predict macroscopic material anisotropy of multi-phase steels from crystal plasticity material definitions

A numerical multi-scale model is being developed to predict the anisotropic macroscopic material response of multi-phase steel. The embedded microstructure is given by a meso-scale Representative Volume Element (RVE), which holds the most relevant features like phase distribution, grain orientation, morphology etc., in sufficient detail to describe the multi-phase behavior of the material. A Finite Element (FE) mesh of the RVE is constructed using statistical information from individual phases such as grain size distribution and ODF. The material response of the RVE is obtained for selected loading/deformation modes through numerical FE simulations in Abaqus. For the elasto-plastic response of the individual grains, single crystal plasticity based plastic potential functions are proposed as Abaqus material definitions. The plastic potential functions are derived using the Facet method for individual phases in the microstructure at the level of single grains. The proposed method is a new modeling framework...

Experimental validation and effect of modelling assumptions in the hierarchical multi-scale simulation of the cup drawing of AA6016 sheets

An essential step in the improvement of design strategies for a wide range of industrial deep drawing applications is the development of methods which allow for the precise prediction of shape and processing parameters. Earlier work has demonstrated, in a clear but qualitative manner, the capabilities of the hierarchical multiscale (HMS) model, which predicts the anisotropic plastic properties of metallic materials based on a statistical analysis of microstructure-based anisotropy and a continuous description of the yield locus. The method is implemented into the ABAQUS finite-element software but, until recently, little attention had been paid to other factors which determine the accuracy of a finite element prediction in general, such as mesh size, friction coefficient and rigid/elastic modelling of the tools. Through the analysis of cup drawing, which is a well-established laboratory-scale test relevant to industrial applications, a quantitative comparison is provided between measured cup geometry and punch force and modelling results for commercial AA6016T4 aluminium sheets. The relatively weak earing behaviour of these materials serves to emphasise the small differences still found between model and experiment, which may be addressed by future refinement of the micromechanical component of the HMS. Average cup height and punch force, which is an important process parameter omitted in earlier studies, depend primarily on the friction coefficient and assumptions in the modelling of the tools. Considering the balance between accuracy and precision, it is concluded that the proposed methodology has matured sufficiently to be used as a design tool at industrial level.

Accelerating multi-scale sheet forming simulations by exploiting local macroscopic quasi-homogeneities

Multi-scale simulations are computationally expensive if a two-way coupling is employed. In the context of sheet metal forming simulations, a fine-scale representative volume element (RVE) crystal plasticity (CP) model would supply the Finite Element analysis with plastic properties, taking into account the evolution of crystallographic texture and other microstructural features. The main bottleneck is that the fine-scale model must be evaluated at virtually every integration point in the macroscopic FE mesh. We propose to address this issue by exploiting a verifiable assumption that fine-scale state variables of similar RVEs, as well as the derived properties, subjected to similar macroscopic boundary conditions evolve along nearly identical trajectories. Furthermore, the macroscopic field variables primarily responsible for the evolution of fine-scale state variables often feature local quasi-homogeneities. Adjacent integration points in the FE mesh can be then clustered together in the regions where the field responsible for the evolution shows low variance. This way the fine-scale evolution is tracked only at a limited number of material points and the derived plastic properties are propagated to the surrounding integration points subjected to similar deformation. Optimal configurations of the clusters vary in time as the local deformation conditions may change during the forming process, so the clusters must be periodically adapted. We consider two operations on the clusters of integration points: splitting (refinement) and merging (unrefinement). The concept is tested in the Hierarchical Multi-Scale (HMS) framework [1] that computes macroscopic deformations by means of the FEM, whereas the micro-structural evolution at the individual FE integration points is predicted by a CP model. The HMS locally and adaptively approximates homogenized stress responses of the CP model by means of analytical plastic potential or yield criterion function. Our earlier work investigated simple test cases [2]. In this contribution we present a deep drawing process simulated using the HMS framework improved to exploit local quasi-homogeneities. We conclude that large performance gains (e.g. a speedup of 25) are obtained at the expense of introducing only a minor (e.g. below 1%) modelling error compared to the HMS simulation with no clustering of integration points.

SPATIAL CLUSTERING STRATEGIES FOR HIERARCHICAL MULTI-SCALE MODELLING OF METAL PLASTICITY

In multi-scale simulations of material forming processes, macroscopic zones of nearly homogeneous strain response occur. In such zones the evolution of plastic anisotropy at each finite element integration point can be approximated from the properties at a represen- tative point. We show how these zones can be identified by a clustering algorithm and can be utilized to reduce the computational cost of the simulation.