Mechanical response, twinning, and texture evolution of WE43 magnesium-rare earth alloy as a function of strain rate: Experiments and multi-level crystal plasticity modeling

Highlights

• A multi-level grain-to-polycrystalline aggregate-to-macro-level model, T-CPFE, is adapted for modeling of WE43.

• EBSD, neutron diffraction, and mechanical testing data are used to calibrate and validate the model.

• Anisotropy in mechanical response induced by microstructural evolution is predicted.

• Role of deformation modes on the mechanical behavior and texture evolution is discussed.

• Formation of contraction twins is identified to increase the rate of strain hardening under high strain rate deformation.

Abstract

This work adapts a recently developed multi-level constitutive model for polycrystalline metals that deform by a combination of elasticity, crystallographic slip, and deformation twinning to interpret the deformation behavior of alloy WE43 as a function of strain rate. The model involves a two-level homogenization scheme. First, to relate the grain level to the level of a polycrystalline aggregate, a Taylor-type model is used. Second, to relate the aggregate level response at each finite element (FE) integration point to the macro-level, an implicit FE approach is employed. The model features a dislocation-based hardening law governing the activation stress at the slip and twin system level, taking into account the effects of temperature and strain rate through thermally-activated recovery, dislocation debris formation, and slip-twin interactions. The twinning model employs a composite grain approach for multiple twin variants and considers double twinning. The alloy is tested in simple compression and tension at a quasi-static deformation rate and in compression under high strain rates at room temperature. Microstructure evolution of the alloy is characterized using electron backscattered diffraction and neutron diffraction. Taking the measured initial texture as inputs, it is shown that the model successfully captures mechanical responses, twinning, and texture evolution using a single set of hardening parameters, which are associated with the thermally activated rate law for dislocation density across strain rates. The model internally adjusts relative amounts of active deformation modes based on evolution of slip and twin resistances during the imposed loadings to predict the deformation characteristics. We observe that WE43 exhibits much higher strain-hardening rates under high strain rate deformation than under quasi-static deformation. The observation is rationalized as primarily originating from the pronounced activation of twins and especially contraction and double twins during high strain rate deformation. These twins are effective in strain hardening of the alloy through the texture and barrier hardening effects.

Introduction

Magnesium (Mg) alloys containing rare earth (RE) elements have been developed to increase ductility and strength while reducing the plastic anisotropy and tension vs. compression asymmetry in comparison to common Mg alloys such as AZ31 (Bhattacharyya et al., 2016; Cho et al., 2009; Hidalgo-Manrique et al., 2017; Jahedi et al., 2018a, 2018b; Jiang et al., 2016). Asymmetry refers to the difference in the mechanical response between tension vs. compression, while anisotropy is more generic and refers to a property being directionally dependent, which implies different properties in different directions, as opposed to isotropy. The major underlying mechanisms responsible for these improvements are related to precipitates, which influence the ratio between the activation stress for basal, prismatic, and pyramidal slip modes. As a result, slip systems belonging to these slip modes can simultaneously activate. Moreover, reduced twinning activity reduces tension vs. compression asymmetry and propensity to strain localization. Finally, texture in these alloys is moderately strong causing small anisotropy in mechanical behavior (Al-Samman and Li, 2011; Bohlen et al., 2007; Hadorn et al., 2012; Hantzsche et al., 2010; Imandoust et al., 2017; Sandlöbes et al., 2014; Stanford and Barnett, 2008). According to ASTM B951-11, 2011, King, 2007, in the WE Mg alloy series W stands for Yttrium (Y) and E stands for rare earth (RE) elements such as Neodymium (Nd), which influences age hardening and strength at elevated temperatures (Avedesian and Baker, 1999; Li et al., 2007). The alloy WE43 is based on the Mg–Y-Nd system (Nie, 2012); and amongst the WE series, WE43 alloy shows high static and fatigue strength, creep resistance, corrosion resistance, and flame resistance (Castellani et al., 2011; Gavras et al., 2016; Ghorbanpour et al., 2019a, Ghorbanpour et al., 2019b; Li et al., 2010; Mengucci et al., 2008; Nie and Muddle, 2000; Nie et al., 2001).

Various crystal plasticity-based models have been developed and used to model the constitutive response of metals and alloys. These models have proven to be successful especially for low symmetry crystal structure metals such as Mg alloys with hexagonal close-packed (HCP) structure which exhibit pronounced anisotropy and asymmetry in their mechanical response. In crystal plasticity models, the homogenization relationships relating the deformation of the constituent crystal to that of the polycrystalline aggregate can be achieved using mean-field and full-field theories. In either case, activation of deformation models (i.e. slip and twinning modes) is governed by a hardening model, which describes their resistance to activation. The former class of models (Kalidindi, 1998; Knezevic et al., 2008, 2009, 2014a; Knezevic and Landry, 2015; Lebensohn and Tomé, 1993; Taylor, 1938; Van Houtte, 1988; Wu et al., 2007; Zecevic and Knezevic, 2018; Zecevic et al., 2015, 2016c, 2017b, 2018b, 2019) have often been used due to their computational efficiency and ease of implementation. These are commonly referred to as Taylor-type and self-consistent-type models. However, explicit grain-to-grain interactions are not considered by these models. The latter class of models (Abdolvand et al., 2015; Fernández et al., 2013; Jahedi et al., 2015; Keshavarz and Ghosh, 2015; Lebensohn et al., 2012; Staroselsky and Anand, 2003) accounts for grain-to-grain interactions and, as a result, better resolves local mechanical fields arising from the explicit grain structure. These models include the crystal plasticity finite element (CPFE) models and Green's function fast Fourier transform crystal plasticity models (Eghtesad et al., 2018; Lebensohn et al., 2012).

Modeling deformation twinning in the plasticity models for Mg alloys is vital. Modeling discrete twins and the growing domains of reoriented crystal lattice orientation accommodating the plastic strain using spatially resolved models have been attempted only recently (Ardeljan et al., 2015, 2017; Ardeljan and Knezevic, 2018; Cheng et al., 2018; Kumar et al., 2015). However, these models have yet to be advanced to model the formation, propagation, and growth of twin domains in a practical way. In contrast, several micromechanical approaches have been developed to incorporate the reorientation and shear due to twinning in mean-field models: the predominant twin reorientation approach (Jain and Agnew, 2007; Tomé et al., 1991, 2001; Van Houtte, 1978; Wang et al., 2010), total Lagrangian approach (Kalidindi, 1998; Wu et al., 2007), and composite-grain (CG) approach (Knezevic et al., 2013a; Proust et al., 2007; Tomé and Kaschner, 2005). Here, deformation twinning is considered as pseudo-slip (Kalidindi, 1998; Van Houtte, 1978) followed by reorientation and volume transfer from a parent grain containing a twin to the independent twin grain.

In the present work, the full-field finite element and Taylor-type crystal plasticity models are combined (T-CPFE), where the first level of meso-scale homogenization is performed using the Taylor model (T-), while the second level of macro-scale homogenization is performed using crystal plasticity finite elements (CPFE). The second level of the homogenization is relaxing the intrinsic assumption of the Taylor model pertaining to the iso deformation gradient or iso velocity gradient applied over a polycrystal. Thus, every constituent grain experiences the same applied deformation. The applied deformation varies spatially over finite elements but is the same for all grains embedded per FE integration point. A polycrystalline material is split over a number of FE integration points interrogating a subset of grains belonging to the sub-polycrystal. The overall FE homogenization is over many Taylor-type models running at FE integration points. The added advantage of the T-CPFE model over the Taylor-type homogenization is that it can simulate geometrical changes. The T-CPFE model is similar to the FE-VPSC (visco-plastic self-consistent) (Knezevic et al., 2013b, 2013c, 2014c; Zecevic et al., 2016b) and FE-EPSC (elasto-plastic self-consistent) (Zecevic et al., 2017a) formulations since both approaches embed a sub-polycrystal at every FE integration point. The latter models rely on the self-consistent (SC) homogenization of individual grains, while the T-CPFE model embeds the Taylor-type homogenization. In general, the SC approach is more accurate and versatile but is slower than T-CPFE because of the SC iterations. Therefore, typically the number of grains embedded at each FE integration point is smaller for FE-VPSC/FE-EPSC than in T-CPFE. The individual grains deform by crystallographic slip and deformation twinning. The CG formulation (Proust et al., 2007) within the total Lagrangian numerical scheme of the T-CPFE model is used for handling twinning, where multiple twin variants per grain are allowed. Every variant is a new grain undergoing the Taylor-type homogenization per FE integration point. A recently developed dislocation density (DD) hardening law is used for evolving the slip/twin resistances (Beyerlein and Tomé, 2008). The T-CPFE modeling approach integrating the sub-crystalline scale and the scale of the sample operating concurrently, has been successfully applied to AZ31 (Ardeljan et al., 2016a) and is adapted here to alloy WE43. An EPSC model for predicting the mechanical behavior of the alloy WE43 has been proposed in (Bhattacharyya et al., 2016); and while the model successfully captured strain hardening evolution of the material as a function of testing direction using a set of material parameters at a given strain rate, it did not consider secondary or double twinning. As a result, the origins of strain hardening across strain rates, which are in the core of the present paper, have not been described.

Mechanical response of the alloy is measured in simple compression and tension under a quasi-static deformation rate and in compression under high strain rates at room temperature. The testing results are presented here along with texture and twinning evolution of the alloy. These are characterized using electron backscattered diffraction (EBSD) and neutron diffraction. Taking the measured initial texture and average grain size data as inputs, it is shown that the model successfully captures across strain rates the mechanical responses, twinning, and texture evolution of the alloy using a single set of hardening parameters associated with the DD hardening law. The complete set of material hardening parameters for the law for the WE43 alloy is established. The model internally adjusts relative amounts of active deformation modes based on the evolution of slip and twin resistances during the imposed loadings to predict the deformation characteristics. The predictions show that the deformation is accommodated by a combination of multiple slip and twinning modes governing the flow stress and texture evolution. It is seen that WE43 exhibits much higher strain-hardening rates under high strain rate deformation then under quasi-static deformation. The observation is rationalized here to originate from the pronounced activation of twinning and especially contraction and double twinning during high strain rate deformation. These twins are effective in strain hardening of the alloy through the texture and barrier effects.