Continuum modeling of the response of a Mg alloy AZ31 rolled sheet during uniaxial deformation

Abstract

a b s t r a c tLightweight magnesium alloys, such as AZ31, constitute alternative materials of interest for many industrial sectors such as the transport industry. For instance, reducing vehicle weight and thus fuel consumption can actively benefit the global efforts of the current environmental industry policies. To this end, several research groups are focusing their experimental efforts on the development of advanced Mg alloys. However, comparatively little computational work has been oriented towards the simulation of the micromechanisms underlying the deformation of these metals. Among them, the model developed by Staroselsky and Anand [Staroselsky, A., Anand, L., 2003. A constitutive model for HCP materials deforming by slip and twinning: application to magnesium alloy AZ31B. International Journal of Plasticity 19 (10), 1843-1864] successfully captured some of the intrinsic features of deformation in Magnesium alloys. Nevertheless, some deformation micromechanisms, such as cross-hardening between slip and twin systems, have been either simplified or disregarded. In this work, we propose the development of a crystal plasticity continuum model aimed at fully describing the intrinsic deformation mechanisms between slip and twin systems. In order to calibrate and validate the proposed model, an experimental campaign consisting of a set of quasi-static compression tests at room temperature along the rolling and normal directions of a polycrystalline AZ31 rolled sheet, as well as an analysis of the crystallographic texture at different stages of deformation, has been carried out. The model is then exploited by investigating stress and strain fields, texture evolution, and slip and twin activities during deformation. The flexibility of the overall model is ultimately demonstrated by casting light on an experimental controversy on the role of the pyramidal slip hc + ai versus compression twinning in the late stage of polycrystalline deformation, and a failure criterion related to basal slip activity is proposed.

A polycrystal based numerical investigation on the temperature dependence of slip resistance and texture evolution in magnesium alloy AZ31B

“…It seems reasonable given the rather fine grain structures in our samples (see Fig. 1c), and this number is consistent with the reported values from several groups (Agnew et al, 2003(Agnew et al, , 2006Barnett et al, 2006;Fernandez et al, 2011;Hutchinson and Barnett, 2010;Muranskya et al, 2008). Hardening parameters for slip and twinning: In the power-law hardening, we have three parameters fh sl;0 ; S sl ; a sl g for slip induced hardening, and three parameters fh tw;0 ; S tw ; a tw g for twin induced hardening.…”

“…Given the strong correlation between plasticity in magnesium and its formability, many research groups have carried out experiments and theoretical analysis to explain and predict the deformation mechanisms of magnesium subjected to various boundary value problems (Agnew et al, 2006;Beyerlein et al, 2011;Choi et al, 2010;Cipoletti et al, 2011;Fernandez et al, 2011;Khan et al, 2006;Lévesque et al, 2010;Lee et al, 2008a;Li et al, 2010;Mayama et al, 2011;Proust et al, 2009;Staroselsky and Anand, 2003;Walde and Riedel, 2007a;Wang et al, 2010a). Theoretically, crystal plastic model has been proved to be an effective way to capture the activation of different plastic deformation mechanisms at the microscopic level.…”

“…Soon several versions of crystal plasticity model for HCP metals emerged, with new features to enrich the physics of modeling. For example, Fernandez et al considered cross-hardening between slip and twinning systems based on the constitutive model (Fernandez et al, 2011); a rate-sensitive crystal plasticity constitute model was also used by Lévesque et al (2010) to simulate the deformation in magnesium alloy AM30; Walde and Riedel used a viscoplastic self-consistent model to simulate the forming processes of a variety of materials where deformation twinning cannot be avoided (Walde and Riedel, 2007b); Li et al proposed a TWINLAW based on three phenomenological deformation modes (slip, twinning and de-twinning) (Li et al, 2010); Beyerlein et al developed a crystal plasticity constitutive model dealing with the nucleation of deformation twins (Beyerlein et al, 2011); Wang et al developed a large strain elastic-viscoplastic self-consistent model for polycrystalline materials and employed it into AZ31B sheet (Wang et al, 2010a,b); Kochmann and Le presented an energy-based micromechanical model and described the mechanical characteristics of deformation twinning (Kochmann and Le, 2009);and Mu et al used a modified grain interaction model to simulate the texture evolution of AZ31 at different temperatures (from 473 to 673 K) based on twin reorientation scheme of Tomé and the cluster type Taylor models (Mu et al, 2010(Mu et al, , 2011.…”

Influence of texture on the recrystallization mechanisms in an AZ31 Mg sheet alloy at dynamic rates

“…Accordingly, the grain size increases to 12|jim, as twin propagation has now basically encompassed the entire grains and very few twin boundaries remain. It is well known that the twinned regions, in which the compression axis is parallel to the c-axes, pyramidal (c + a) and basal slip are the predominant deformation mechanisms [39,40]. As shown in Figs.…”

Finite element simulations of notch tip fields in magnesium single crystals

“…Kalidindi (1998) extended the crystal plasticity theory formulated by Asaro (1983b) and Asaro and Rice (1977) to incorporate deformation twinning by considering it as a quasi-slip process, with the twin volume fraction as the important variable that evolves due to nucleation and growth of twins. This modified crystal plasticity theory, implemented in finite element solution procedures, has been widely used to analyze the deformation behavior, stress distributions, texture evolution and formability in HCP metals (Salem et al 2005;Brown et al 2005;Graff et al 2007;Knezevic et al 2010;Izadbakhsh et al 2011;Fernandez et al 2011;Choi et al 2011). Several hardening models have been proposed to represent slip and twin interactions in Mg for incorporation in the above crystal plasticity formulation (Graff et al 2007;Homayonifar et al 2009;Zhang and Joshi 2012).…”