Albert Van Bael

Finite element modeling of plastic anisotropy induced by texture and strain-path change

Abstract Consideration of plastic anisotropy is essential in accurate simulations of metal forming processes. In this study, finite element (FE) simulations have been performed to predict the plastic anisotropy of sheet metals using a texture- and microstructure-based constitutive model. The effect of crystallographic texture is incorporated through the use of an anisotropic plastic potential in strain-rate space, which gives the shape of the yield locus. The effect of dislocation is captured by use of a hardening model with four internal variables, which characterize the position and the size of the yield locus. Two applications are presented to evaluate the accuracy and the efficiency of the model: a cup drawing test and a two-stage pseudo-orthogonal sequential test (biaxial stretching in hydraulic bulging followed by uniaxial tension), using an interstitial-free steel sheet. The experimental results of earing behavior in the cup drawing test, maximum pressure and strain distribution in bulging, and transient hardening in the sequential test are compared against the FE predictions. It is shown that the current model is capable of predicting the plastic anisotropy induced by both the texture and the strain-path change. The relative significance of texture and strain-path change in the predictions is discussed.

Measurement and analysis of yield locus and work hardening characteristics of steel sheets wtih different r-values

Abstract Biaxial tensile experiments of six kinds of steel sheet with different r-values are carried out using a servo-controlled biaxial tensile testing machine. Successive contours of plastic work in the biaxial stress space and the plastic strain rate vectors are precisely measured for linear loading paths. The measured data are compared with the theoretical predictions based on the Taylor–Bishop–Hill model with the full constraints and relaxed constraints assumptions using the experimentally determined crystallographic textures. Comparisons with the Hill quadratic and Hosford yield criteria are also made. It is found that (1) the TBH model with the full constraints assumption is superior to that with the relaxed constraints assumption in predicting the plastic deformation characteristics of steel sheets; (2) The Hosford yield criterion is an effective phenomenological model for predicting the plastic deformation characteristics of steel sheets.

Prediction of forming limit strains under strain-path changes: Application of an anisotropic model based on texture and dislocation structure

Abstract Strain-path changes strongly influence the forming limit strains of sheet metals. The value of the limit strains is greatly affected by material-related effects such as initial anisotropy, transient. hardening, Bauschinger effect and cross hardening. A model which can describe these mechanical behaviours has been developed on the physical basis of texture and dislocation structure, and applied in conjunction with the Marciniak-Kuczynski analysis of the forming limit strains. The results are represented in forming limit diagrams (FLDs) in which the forming limit strains are indicated. The calculation successfully predicts some of the experimental tendencies which cannot be reproduced by conventional phenomenological models. Furthermore, the model has been used to discuss the effects of texture and dislocation structure on the FLDs. Especially, it is suggested that transient hardening caused by the latent part of the persistent dislocation structure significantly reduces the forming limit strain for a strain-path change from equi-biaxial stretching to uniaxial tension.

Finite element modeling of incremental forming of aluminium sheets

Incremental forming is an innovative and flexible sheet metal forming technology for small batch production and prototyping, which does not require any dedicated die or punch to form a complex shape. This paper investigates the process of single point incremental forming of an aluminum cone with a 50-degree wall angle both experimentally and numerically. Finite element models are established to simulate the process. The output of the simulation is given in terms of final geometry, the thickness distribution of the product, the strain history and distribution during the deformation as well as the reaction forces. Comparison between the simulation results and the experimental data is made.

Comparison of FEM simulations for the incremental forming process

Incremental forming is an innovative and highly flexible sheet metal forming technology for small batch production and prototyping that does not require any adapted dies or punches to form a complex shape. The purpose of this article is to perform FEM simulations of the forming of a cone with a 50-degree wall angle by incremental forming and to investigate the influence of some crucial computational parameters on the simulation. The influence of several parameters will be discussed: the FEM code used (Abaqus or Lagamine, a code developed at the University of Liège), the mesh size, the potential simplification due to the symmetry of the part and the friction coefficient. The output is given in terms of final geometry (which depends on the springback), strain history and distribution during the deformation, as well as reaction forces. It will be shown that the deformation is localized around the tool and that the deformations constantly remain close to a plane strain state for this geometry. Moreover, the tool reaction clearly depends on the way the contact is taken into account.

Analytical Representation of Polycrystal Yield Surfaces

A new yield function of the form \( f\left( {{S_i}} \right) = {\sum\limits_S^N {\left| {P_i^S\,{S_i}} \right|}^{{h + 1}}}/W_s^h \) is proposed to describe the yield surface of textured polycrystals. The parameters of this function can be derived from the rate of plastic work obtained from polycrystal models. f is strictly convex and approximates the yield surface with high precision.

Determination of Strain in Incremental Sheet Forming Process

A simplified method to determine the strain distribution during incremental forming of a cone is proposed in this paper. Because of the symmetry of the deformed part, the strain can be derived using the results obtained from a limited number of consecutive tool contours instead of going through the whole process. Comparisons made between the measured and simulated results show that the proposed method can be applied to determine the strain encountered in such kind of incremental forming process where axi-symmetric parts are formed.

The Application of Multiscale Modelling for the Prediction of Plastic Anisotropy and Deformation Textures

Finite element models for metal forming and models for the prediction of forming limit strains should be as accurate as possible, and hence should take effects due to texture, microstructure and substructure (dislocation patterns) into account. To achieve this, a hierarchical type of modelling is proposed in order to maintain the balance between calculation speed (required for engineering applications) and accuracy. This means that the FE models work with an analytical constitutive model, the parameters of which are identified using results of multilevel models. The analytical constitutive model will be discussed, as well as the identification procedure. The multilevel models usually connect the macro-scale with a meso-scale (grain level) via a homogenisation procedure. They can also be used to make predictions of deformation textures. These will be quantitatively compared with experimentally obtained rolling textures of steel and aluminium alloys. It was found that only models which to some extent take both stress and strain interactions between adjacent grains into account perform well. Finally an example of a three level model, also including the micro-scale (i.e. the dislocation substructure), will be given.

Texture-Based Explicit Finite-Element Analysis of Sheet Metal Forming

An explicit integration algorithm using a texture-based plastic potential and isotropic hardening has been developed and implemented into a commercial explicit finite-element software program through a user material subroutine (VUMAT in ABAQUS/Explicit). Simulations of cup drawing of an IF-steel are presented and compared to both experimental data and calculation results obtained with a previously developed fully implicit approach (UMAT in ABAQUS/Standard). The explicit formulation has the advantage of being more stable, but local sheet thickness variations cannot be reproduced with the same accuracy.

Analysis and Prediction of the Earing Behaviour of Low Carbon Steel Sheet

The earing behaviour during a cup drawing test was studied for a wide range of low carbon steel sheets, in order to check the validity of an existing model for the earing of anisotropic metal sheets. The modelling of the anisotropic behaviour of the metal sheet was made using the Taylor theory of polycrystal plasticity, which was implemented in a simplified cinematic model for the material flow during a cup-drawing test.