Numerical studies on ductile failure of aluminium alloys
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Numerical modelling and simulation are becoming increasingly important for structural design and assessment, and they are essential tools for engineers facing the challenges and demands imposed by the modern society. Using numerical models in place of physical experiments may represent significant savings for the industry, since material testing campaigns are associated with substantial economic costs. Also, predictive material models yield the ability to better understand and utilize the material capacity, which is favourable from both economical and environmental perspectives. The work in this thesis is concerned with numerical modelling of ductile failure under quasi-static loading conditions. Aluminium alloys have been the focus of this work, but the numerical tools that have been developed are rather general. The thesis consists of four individual parts which all contain a single journal article either published in (Part 1-3), or submitted to (Part 4), international peer-reviewed journals. They are contextualized by a synopsis which links the parts together. The synopsis presents the background and motivation, a brief overview of the main aspects concerning ductile fracture, the objectives and scope of this thesis, and overall conclusions and suggestions for further work. In Part 1, we examined the influence of loading path on ductile failure of tensile specimens. Experimental data from four quasi-isotropic aluminium alloys were used as the background material. Finite element simulations of smooth tensile specimens were used to evaluate the local loading path attained in the critical material element. Further, the stress triaxiality from this element was assigned in unit cell calculations either as a strain-weighted average value or as a continuous function of the equivalent strain. We found that using the non-proportional loading path changed the ductility predictions and brought them in closer agreement with the experimental results. Unit cell analyses were further employed to estimate the initial porosity for the four different aluminium alloys. The Gurson porous plasticity model was then used to simulate both smooth and two notched tensile specimens. We carried out two sets of simulations; the first using identical initial porosity for all materials and the second using the calibrated initial porosities from the unit cell calculations. While the behaviour of the smooth tensile specimens were rather well predicted, the true stress was somewhat overestimated for the notched tensile specimens. The predictions of material failure were generally enhanced when we employed the calibrated initial porosities in the Gurson model. Part 2 deals with effects of matrix plastic anisotropy on the macroscopic response of an idealized material microstructure. Five strong textures for face-centred cubic polycrystals and one random texture were examined. First, we carried out unit cell simulations to elucidate the influence of matrix anisotropy on the global stress-strain behaviour and void evolution. We found pronounced effects of the matrix anisotropy on the microstructural evolution and macroscopic mechanical response. In particular, the void shape evolution was related to the direction of plastic flow and the void growth rate was influenced by the radius of the matrix yield surface. Further, we employed a heuristic extension of the Gurson model in which the equivalent stress measure accounts for the underlying matrix plastic anisotropy. This model was seen to provide reasonable predictions when compared to the unit cell simulations. However, we observed that the conformity between the porous plasticity model and the unit cell was generally deteriorated for low stress triaxiality ratios and we found some disparity in the accuracy of the porous plasticity model for different loading states. Part 3 deals with the influence of yield surface curvature on macroscopic yielding and strain localization predictions for isotropic porous ductile solids. Unit cell calculations of an idealized material microstructure with a non-quadratic isotropic matrix description were conducted and used to calibrate a heuristic modification of the Gurson model. The porous plasticity model was able to retrieve some of the effects observed in the unit cell simulations, however it was somewhat inaccurate for the lower stress triaxialities. Further, we conducted strain localization analyses using three different modelling approaches: (i) unit cell model, (ii) imperfection band analyses, and (iii) bifurcation analyses. While the bifurcation analyses gave higher strain levels at localization, the imperfection band analyses were in reasonable agreement with the unit cell calculations. In general, we observed that the non-quadratic matrix yield function had a prominent influence on the failure strain predictions. The quadratic and the non-quadratic matrix yield surface gave rather similar ductility predictions around generalized shear, while the non-quadratic matrix yield surface lowered the failure strain levels for generalized tension and generalized compression. This was attributed to the curvature of the yield surface, allowing the plastic flow direction to shift more readily towards the favourable direction for localization. In Part 3, we found that the matrix description governed by the J2 flow theory gave rise to a monotonous decrease of the void growth rate with increasing Lode parameter. Using some salient features of an existing shear-modified Gurson model, the study in Part 4 examines a potential way of including a Lode parameter dependency in the Gurson model which yields predictions in closer agreement with the unit cell calculations. The proposed void evolution model was found to provide reasonably good agreement between the unit cell calculations and the porous plasticity model. Further, we compared strain localization analyses using the Gurson model, the shear-modified Gurson model, and the new Lode-dependent Gurson model. We observed that the void evolution model proposed in this work gave enhanced ductility predictions when compared to unit cell studies previously reported in the literature.