Experimental and Numerical Study of Yielding, Work- Hardening and Anisotropy in Textured AA6xxx Alloys Using Crystal Plasticity Models

Abstract

The present work examines various aspects of the plastic behaviour of the 6000 series of aluminium alloys, including yield, work-hardening, diffuse necking, flow stress anisotropy and plastic flow anisotropy. The alloys were investigated experimentally, using tensile tests, and their behaviour was modelled using the finite element method (FEM). The material in the finite element simulations was described either by anisotropic phenomenological plasticity or crystal plasticity models. The aim of the work was to study the cases in which crystal plasticity models may improve the predictions compared to the phenomenological plasticity models or predict new aspects of the material’s behaviour. The first part of the thesis is a literature study on crystal plasticity theory and phenomenological plasticity and a synopsis of the articles, which are included in the second part. In Article 1 a method for finding the equivalent stress-strain curve from a uniaxial tensile test for a material with anisotropic plastic behaviour after necking is proposed. The force and cross-section diameter measurements in such test produce a true stress-strain curve until fracture, but this curve includes a triaxial stress field, which develops in the neck. To remove the influence of this triaxial field and obtain the equivalent stress-strain curve the reverse engineering method was utilized. A set of specimens produced from the AA6060 and AA6082 alloys with different heat treatments was tested under uniaxial tension condition. These tests were modelled using the FEM, with an anisotropic phenomenological plasticity material model. The work-hardening parameters of this model (which define its equivalent stress-strain curve) were set as the variables in the optimisation procedure. The anisotropic yield surfaces used in the phenomenological model were found using the crystal plasticity model and the crystallographic texture data obtained for the examined alloys. It was found that the equivalent stress-strain curves obtained with this anisotropic plasticity model differ from the curves obtained with an isotropic plasticity model, i.e. this method allows to account for the material’s plastic anisotropy. The anisotropic yield surfaces obtained with the crystal plasticity model allowed to predict the plastic flow anisotropy reasonably well. In Article 2 the precipitation, yield stress and work-hardening model developed by Myhr et al.1 is combined with a crystal plasticity model with Taylor type homogenisation. The same alloys as in Article 1 were used. The precipitation model provides the information about the solid solution and precipitate particles formed in the alloy, depending on its thermal history and chemical composition. This information is then transformed into the parameters of the yield and work-hardening model, which predicts the global equivalent stress-strain curve of the alloy. In this work an alternative work-hardening rule was proposed, which also uses the information about solid solution and precipitate particle data from the precipitation model. However, unlike the rule proposed by Myhr et al. it is acting on the slip system level. The global equivalent stress-strain is then calculated using the full constraint Taylor homogenisation model. In this case the influence of crystallographic texture and its evolution on the yield strength and work hardening is naturally accounted for. The results obtained by the two approaches were compared to these experimental data. The comparison showed that while some features of the alloys’ plastic behaviour were captured somewhat better by the new approach, the overall improvement was not large and the results were influenced to a greater extent by the precipitation model than by the crystallographic texture. In Article 3 the latent hardening and its influence on the plastic anisotropy of the aluminium alloys was studied. Phenomenological and physically based crystal plasticity hardening models use different descriptions of the latent hardening. The exact values of the latent hardening matrix is a long-standing problem, which has been attempted to be solved both experimentally and numerically. These efforts produced quite a few different results. Some typical latent hardening matrices found in the literature were tested. The experimental study consisted of uniaxial tensile tests in different material directions on an AA6060 alloy. These test were simulated using the FEM with crystal plasticity. The results of the simulation were compared to the experimental data. In the experiments, the material demonstrated an evolution of the anisotropy of both flow stress and plastic flow. It was shown that while models with different latent hardening matrices all reproduced the main tendencies of the alloy’s behaviour, there were noticeable differences in the responses. In Article 4 an AA6060 alloy sample is studied, in which an extremely sharp cube texture 1Myhr, O. R., Grong, Ø., and Pedersen, K. O. (2010). A combined precipitation, yield strength, and work hardening model for Al–Mg–Si alloys. Metallurgical and Materials Transactions A, 41(9), 2276–2289. is observed. The material demonstrated an anomalous rhomboid shape of the fracture surface in the tensile test with a notched cylindrical specimen. The test was modelled using the FEM, with material described by the anisotropic phenomenological plasticity model and a crystal plasticity model. The finite element model represented the specimen geometry and boundary conditions realistically, with the average size of the constituent grains in the model close to the real one. The combination of the realistic geometry and crystal plasticity model allowed predicting the rhomboid shape of the notched specimen’s cross-section at larger strains, while the phenomenological FEM failed to do so.