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

摘要

The present work examines various aspects of the plastic behaviour of the 6000 series of aluminiumudalloys, including yield, work-hardening, diffuse necking, flow stress anisotropy andudplastic flow anisotropy. The alloys were investigated experimentally, using tensile tests, andudtheir behaviour was modelled using the finite element method (FEM). The material in the finiteudelement simulations was described either by anisotropic phenomenological plasticity or crystaludplasticity models. The aim of the work was to study the cases in which crystal plasticity modelsudmay improve the predictions compared to the phenomenological plasticity models or predictudnew aspects of the material’s behaviour. The first part of the thesis is a literature study on crystaludplasticity theory and phenomenological plasticity and a synopsis of the articles, which areudincluded in the second part.udIn Article 1 a method for finding the equivalent stress-strain curve from a uniaxial tensileudtest for a material with anisotropic plastic behaviour after necking is proposed. The forceudand cross-section diameter measurements in such test produce a true stress-strain curve untiludfracture, but this curve includes a triaxial stress field, which develops in the neck. To removeudthe influence of this triaxial field and obtain the equivalent stress-strain curve the reverse engineeringudmethod was utilized. A set of specimens produced from the AA6060 and AA6082udalloys with different heat treatments was tested under uniaxial tension condition. These testsudwere modelled using the FEM, with an anisotropic phenomenological plasticity material model.udThe work-hardening parameters of this model (which define its equivalent stress-strain curve)udwere set as the variables in the optimisation procedure. The anisotropic yield surfaces usedudin the phenomenological model were found using the crystal plasticity model and the crystallographicudtexture data obtained for the examined alloys. It was found that the equivalentudstress-strain curves obtained with this anisotropic plasticity model differ from the curves obtainedudwith an isotropic plasticity model, i.e. this method allows to account for the material’sudplastic anisotropy. The anisotropic yield surfaces obtained with the crystal plasticity model allowed to predict the plastic flow anisotropy reasonably well.udIn Article 2 the precipitation, yield stress and work-hardening model developed by Myhr etudal.1 is combined with a crystal plasticity model with Taylor type homogenisation. The sameudalloys as in Article 1 were used. The precipitation model provides the information about theudsolid solution and precipitate particles formed in the alloy, depending on its thermal history andudchemical composition. This information is then transformed into the parameters of the yieldudand work-hardening model, which predicts the global equivalent stress-strain curve of the alloy.udIn this work an alternative work-hardening rule was proposed, which also uses the informationudabout solid solution and precipitate particle data from the precipitation model. However, unlikeudthe rule proposed by Myhr et al. it is acting on the slip system level. The global equivalentudstress-strain is then calculated using the full constraint Taylor homogenisation model. In thisudcase the influence of crystallographic texture and its evolution on the yield strength and workudhardening is naturally accounted for. The results obtained by the two approaches were comparedudto these experimental data. The comparison showed that while some features of theudalloys’ plastic behaviour were captured somewhat better by the new approach, the overall improvementudwas not large and the results were influenced to a greater extent by the precipitationudmodel than by the crystallographic texture.udIn Article 3 the latent hardening and its influence on the plastic anisotropy of the aluminiumudalloys was studied. Phenomenological and physically based crystal plasticity hardening modelsuduse different descriptions of the latent hardening. The exact values of the latent hardeningudmatrix is a long-standing problem, which has been attempted to be solved both experimentallyudand numerically. These efforts produced quite a few different results. Some typical latentudhardening matrices found in the literature were tested. The experimental study consisted ofuduniaxial tensile tests in different material directions on an AA6060 alloy. These test wereudsimulated using the FEM with crystal plasticity. The results of the simulation were comparedudto the experimental data. In the experiments, the material demonstrated an evolution of theudanisotropy of both flow stress and plastic flow. It was shown that while models with differentudlatent hardening matrices all reproduced the main tendencies of the alloy’s behaviour, thereudwere noticeable differences in the responses.udIn Article 4 an AA6060 alloy sample is studied, in which an extremely sharp cube textureud1Myhr, O. R., Grong, Ø., and Pedersen, K. O. (2010). A combined precipitation, yield strength, and workudhardening model for Al–Mg–Si alloys. Metallurgical and Materials Transactions A, 41(9), 2276–2289. udis observed. The material demonstrated an anomalous rhomboid shape of the fracture surfaceudin the tensile test with a notched cylindrical specimen. The test was modelled using the FEM,udwith material described by the anisotropic phenomenological plasticity model and a crystaludplasticity model. The finite element model represented the specimen geometry and boundaryudconditions realistically, with the average size of the constituent grains in the model close toudthe real one. The combination of the realistic geometry and crystal plasticity model allowedudpredicting the rhomboid shape of the notched specimen’s cross-section at larger strains, whileudthe phenomenological FEM failed to do so.