Elsevier

International Journal of Plasticity

Volume 123, December 2019, Pages 208-223
International Journal of Plasticity

Understanding common grain boundary twins in Mg alloys by a composite Schmid factor

https://doi.org/10.1016/j.ijplas.2019.07.018Get rights and content

Highlights

  • A composite Schmid factor (CSF) is for the first time proposed to understand common-boundary twins in Mg alloys.

  • A CSF threshold for the activation of common-boundary twins is present, which decreases with the applied strain.

  • CSF is more effective in predicting twin variants than Schmid factor especially for small strain.

Abstract

It is well known that twinning likely nucleates and forms pairs at grain boundaries (GBs) during the deformation of Mg alloys. Therefore, the crystallography of GBs plays an important role in selecting twin variants. In this regard, the Schmid factor (SF) cannot predict from which GBs twinning prefers to nucleate. To solve this problem, a composite Schmid factor (CSF) is proposed in this paper that incorporates both the SF and a geometric compatibility factor (m'). First, the link of the CSF with the SF and m' is defined and discussed based on theoretical derivations, which is further verified in terms of crystal plasticity finite element simulations. Then, experiments were carried out to investigate the effects of this parameter in predicting {10–12} extension twins in AZ31 Mg alloys. A CSF threshold for the activation of common-boundary twins was noticed and it decreases with the applied strain. By contrast, the SF threshold and its dependence with strain is not obvious. Moreover, the CSF is more effective in predicting the variants of common-boundary twins especially for small strain.

Introduction

Twinning is an important deformation mode for hexagonal close packed (HCP) metals due to their insufficient number of slip systems. Therefore, in order to accurately predict the deformation behavior of HCP metals, it is necessary to incorporate twinning and detwining modes in crystal plasticity based models (Wang et al., 2013; Cheng and Ghosh, 2015; Abdolvand and Wilkinson, 2016; Siska et al., 2017; Barnett et al., 2015; Oppedal et al., 2012). Indeed, the main focus of recent simulation studies is modeling the processes of twinning nucleation, propagation and growth (Wang et al., 2018; Qiao et al., 2016; Liu et al., 2018; Ardeljan et al., 2017; Tadano et al., 2016; Xie et al., 2016). Moreover, systematic experiments were carried out to investigate twinning behavior under various loading conditions (Singh et al., 2019; Choi et al., 2007; Jin et al., 2015; Shi et al., 2017; Huang et al., 2019). Assisted with crystal plasticity simulations, the correlation between twinning and mechanical response was further understood. Despite of these great efforts on simulations, statistical experimental work is still needed to identify the key microstructural parameters on twin nucleation. It is known that GBs are the preferential sites for twin nucleation (Beyerlein et al., 2010). Twin transmission is also related to the crystallography of GBs (Khosravani et al., 2015). Statistical analyses on twinning behavior in Mg and Zr alloys were carried out by Beyerlein et al. (Beyerlein et al., 2010a; Capolungo et al., 2009). They revealed the angle of grain boundary (GB) has remarkable influence on twin nucleation. Based on experimental observations, a stochastic model has been proposed to nucleate twins at grain boundaries. The simulation results reveal that the accuracy of simulated twin activity can be improved by applying this model (Beyerlein and Tomé, 2010b; Beyerlein et al., 2011; Liu et al., 2018). This reflects the importance of integrating the GB effect on twin nucleation in crystal plasticity based models.

The activation ability of dislocation slip and twinning is commonly evaluated by calculating Schmid factors (SFs) based on grain orientation. However, many non-high SF twins were frequently observed in Mg, Ti and Zr alloys (Barnett et al., 2008; Koike et al., 2008; Luo et al., 2012; Bieler et al., 2014). This was attributed to the stress fluctuation or strain accommendation requirement at GBs. For HCP metals, generally there is one deformation mode dominant in each grain, and the others play minor roles due to the large difference in critical resolved shear stress (CRSS) and SFs. The compatibility between the dominant deformation modes in neighboring grains could therefore determine the ability of plasticity at GBs (Bieler et al., 2014; El et al., 2013; Lind et al., 2014; Xu et al., 2017). Based on this concept, the phenomenon of non-high Schmid twins has been succesfully explained by calculating the displacement gradient tensors associated with twinning and slip (Jonas et al., 2011; Shi et al., 2015). Such tensor analysis can be linked to a simple geometric compatibility factor m' that was initially used to assess slip transfer in Ni–Al alloys (Wang et al., 2009, 2010b; Guo et al., 2014; Xin et al., 2014; Luster and Morris, 1995). Although both SFs and m' have been confirmed being important parameters for predicting twin variants (Bieler et al., 2014; Hong et al., 2016), their relative importance has not been investigated to date. The purpose of the present investigation was therefore to consider the use of a single parameter that incorporates both SF and m'. The variant selection of twins during the compression of an AZ31 Mg alloy is analyzed below in a statistical manner.

As reported by Beyerlein et al. (2010), twins often form as adjoining pairs at GBs of pure Mg after compression deformation at room temperature in the in-plane transverse direction. In what follows, these kinds of twin pairs are referred to as common - GB twins or adjoining twins. Modeling of trans-grain twin transmission in AZ31 has been conducted via a neighborhood-based viscoplastic self-consistent model, which indicates the significance of incorporating twin transmission as a twin formation mode in predictive models (Chelladurai et al., 2018). Transmission of {332}<113> twins across GBs in a metastable β-Ti alloy was also studied by a crystal plasticity finite element (CPFE) model, which also reveals the influence of GB parameters on twin transmission (Lin et al., 2018). In previous studies, common - GB twins were frequently studied in Mg alloys with basal textures. In the present case, however, an extruded AZ31 alloy with a basal fiber texture was employed instead. This has the advantage that the latter has a broader distribution of GB misorientation (Xin et al., 2015). Furthermore, as pointed out by Khosravani et al. (2015), the activation and propagation behavior of twins in the early stages of deformation may differ from that pertaining to fully developed twins. To clarify such an effect of strain, the twins formed at two different strains were analyzed. Based on the experimental results and on the analysis described below, the advantages of using the single parameter proposed here will be described and discussed.

Section snippets

Local Schmid factor

Two neighboring grains G1 and G2 containing twins are illustrated in Fig. 1a. When T1 impinges on the common GB, it causes local stress concentration, which can either stimulate or retard the formation of a twin in G2. This effect can be evaluated by resolving the shear stress induced by T1 onto the potential twin systems in G2. As shown in Fig. 1b, the shear and habit plane normal of the twinning system in G1 are represented by sA and nA (T1), while those of the twinning system in G2 are sB

Experimental results and analysis

The material studied was a Mg-3wt.% Al-1wt.% Zn (AZ31) alloy, which was produced by hot extrusion. Microstructure and texture of the alloy were examined by electron backscatter diffraction (EBSD). The samples for EBSD analysis were mechanically polished and followed by electrochemical polishing with a commercial electrolyte (AC2) at 20 V and −20 °C. A typical microstructure of the as-received material is shown in Fig. 7a. The average grain size was determined to be about 12 μm by a linear

CSF map vs. SF map

As mentioned earlier, CSF1 and CSF2 are associated with the twins with the higher and lower SFs, respectively. The differences in the CSF between adjoining twins are displayed in Fig. 12. Here ΔCSF = CSF1 − CSF2 is plotted against GB misorientation angles for the 106 twin pairs studied in the sample strained to 1.2%. It can be seen that there is little difference between the two CSF values. For example, about 88% of the twin pairs have a ΔCSF below 0.03 and 81% have a value below 0.02.

Conclusions

A new orientation factor (CSF) is proposed to assess the selection of twin variants and twin transmission in Mg alloys subjected to uniaxial compression. This CSF takes into account global stress and the shear stress from one dominant deformation mode in neighboring grains. A statistical analysis on more than one hundred twin pairs reveals that the activated twins correspond to a CSF threshold, which decreases with the applied strain.

CSF for twinning is closely related to GB misorientation. The

Acknowledgements

This project was supported financially by the National Natural Science Foundation of China (Project No. 51571045, 51871036 and 51421001) and the National Key Research and Development Program of China (2016YFB0301102). HW acknowledges the support of the Foundation of State Ley Laboratory of Solidification Processing (SKLSP201810), the Shanghai Pujiang Program (18PJ1405000) and the Research Project of State Key Laboratory of Mechanical System and Vibration (MSVZD201911). RLX would like to thank

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