Twinning

Twinning usually occurs sequentially in terms of twin nucleation (TN), twin propagation, and twin growth when stretching the Mg alloy along its c-axis or loading equivalently. The accommodation of finite shear deformation and abrupt lattice reorientation could contribute to both the ductility and the strength of Mg alloys. Recent studies using atomistic simulations have shed valuable light on understanding the atomistic mechanisms associated with deformation twinning.^{Reference Wang, Hirth and Tomé19,Reference Wang, Beyerlein and Tomé20} Extensive experimental observations and atomistic simulations have revealed that twins preferentially nucleate at local inhomogeneities, mostly at grain boundaries (GBs).^{Reference Beyerlein, Capolungo, Marshall, McCabe and Tomé21,Reference Niezgoda, Kanjarla, Beyerlein and Tomé22} TN models developed based on the statistical distribution of GB dislocations effectively describe the important influence of local stresses near GB area on TN.^{Reference Van Houtte23} Many models focus more on twin growth, and the associated reorientation and work hardening.^{Reference Van Houtte23,Reference Tomé, Maudlin, Lebensohn and Kaschner24} Handling the extremely large number of new orientations is difficult to address by twinning schemes.

The volume fraction transfer (VFT) scheme^{Reference Lebensohn and Tomé18} partitions the Euler space into a fixed number of discrete cells with appropriate weights to represent the texture of samples. The VFT scheme robustly accounts for the contribution to texture of every twinning system in every grain by transferring twin volume fractions (TVFs) from one cell to another. The main drawback is that the “grain” identity is lost, and the implementation of a realistic hardening scheme is not allowed.

The predominant twin reorientation (PTR) scheme treats twinning as a pseudo-slip mechanism and tracks the evolution of the TVF.^{Reference Tomé, Lebensohn and Kocks15,Reference Van Houtte23,Reference Tomé, Maudlin, Lebensohn and Kaschner24} A grain with TVF reaching a threshold value is completely reoriented into its predominant twin orientation. The threshold value depends statistically on the total TVF in the entire polycrystal to ensure that heavily twinned grains are reoriented. This scheme has been applied intensively to study the twinning behavior of Mg alloys.^{Reference Agnew and Duygulu25,Reference Wang, Raeisinia, Wu, Agnew and Tomé26} The major advantage is that the number of total grain orientations remains constant. However, multiple twinning variants can be simultaneously active in a grain, which cannot be predicted by the PTR scheme.

Kalidindi’s twin scheme allows tracking the evolution of multiple twinning systems in each grain.^{Reference Kalidindi27} The orientation of a twinned region is obtained according to the matrix–twin crystallographic relation that has mirror symmetry with respect to the twin boundary. The soundness of tracking multiple twinning systems and slip in both twinned and untwinned regions has been acknowledged by researchers, and the model has been applied to study the plasticity of hcp materials.^{Reference Proust, Tomé and Kaschner28,Reference Proust, Tomé, Jain and Agnew29} The disadvantage is the cumbersome implementation into the CP framework when taking accounting for the slip in twinned regions and the increase in the number of grains.

A twin nucleation, propagation, and growth model that explicitly takes into account the stress relaxation associated with twin initiation and propagation has also been developed (Figure 1).^{Reference Wu, Guo, Qiao and Lloyd30,Reference Qiao, Barnett and Wu31} This model relies on the fact that the resistance to twin growth is less than or equal to that for twin initiation.^{Reference Christian and Mahajan3} It has been rationalized that the stress relaxation drives a just-nucleated twin to propagate, while work hardening promotes twin growth after its propagation. The model demonstrates the processes of twin nucleation, propagation, growth, and transmission across GBs.^{Reference Qiao, Barnett and Wu31,Reference Xin, Liu, Sun, Wang, Guo, Ren and Liu32}

Figure 1.

Schematic representations of (a) twin nucleation, propagation, and growth in a grain, and (b) resistance to twin nucleation, propagation, and growth.^{Reference Wu, Guo, Qiao and Lloyd30} Note: ${{\rm{\hat{\tau }}}^{\rm{\alpha }}},{\rm{twinningresistance}};{f^{\rm{\alpha }}},$ twin volume fraction. At nucleation, the resolved shear stress must overcome a high resistance, ${\rm{\tau }}_0^{\rm{\alpha }}$. During twin propagation, the resistance to twinning decreases to its minimum ${\rm{\tau }}_{\rm{g}}^{\rm{\alpha }}$ at the twin volume fraction, ${f^{\rm{\alpha }}} = f_{\rm{g}}^{\rm{\alpha }}$.

Detwinning

Subjected to strain path change, Mg alloys often undergo detwinning subsequent to twinning, which necessitates the model to handle both phenomena. The composite grain model, which treats twins as parallel lamellae, allows for detwinning, but it only takes into account the predominant twinning system.^{Reference Proust, Tomé and Kaschner28} The twinning and detwinning (TDT) model acknowledges and approximates the key fact that the stress on the twin boundary (TB) drives the twins.^{Reference Wang, Wu, Tomé and Wang33} Consequently, mechanisms for twin initiation (which comprises twin nucleation and propagation) and twin growth are introduced for twinning, while mechanisms for twin shrinkage and retwinning (twinning of a twinned region) model detwinning.^{Reference Wang, Wu, Tomé and Wang33,Reference Wang, Wu, Wang and Tomé34} The TDT model can simulate twinning and detwinning behaviors in hcp metals and capture key features such as texture evolution and hardening behavior.^{Reference Guo, Wu, Wu, Qiao, An and Liaw35–Reference Ma, Wang, Hama, Guo, Mao, Wang and Wu39} Secondary twinning occurs when the retwinning variant is not the same as the one that created the twin in the first place. The most frequently observed {10$\bar{1}$1}–{10$\bar{1}$2} double twin structure is a particular type of secondary twinning, which may cause rapid flow localization and failure in Mg alloys.^{Reference Ma, El Kadiri, Oppedal, Baird, Horstemeyer and Cherkaoui40,Reference Niknejad, Esmaeili and Zhou41} The TDT model has been extended to account for and demonstrate the nontrivial role of secondary twinning behavior under complex loading conditions.^{Reference Qiao, Guo, Hong and Wu42}

Dynamic recrystallization

Discontinuous DRX (DDRX) and continuous DRX (CDRX) are important DRX mechanisms for Mg alloys at high temperatures. These mechanisms generate new grains that alter the microstructure and mechanical behavior of the alloys. The nucleation of recrystallized grains and the long-range migration of GBs are two major features of DDRX.^{Reference Doherty43,Reference Sakai, Belyakov, Kaibyshev, Miura and Jonas44} A DDRX scheme has been proposed to correlate the nucleation probability to the loading rate, GB area, and temperature once a critical dislocation density has been reached.^{Reference Tang, Zhou, Li, Li, Peng, Peng, Wu, Wang and Lee10} The growth of the nucleated grains is determined by the GB mobility and relative difference in dislocation density across the GB. The results of simulations, realized at different temperatures, with respect to plastic deformation, grain orientation, and grain size, are a reflection of the low flow stress, high ductility, and weak anisotropy associated with Mg alloys at higher temperatures (Figure 2).

Figure 2.

Experimental and predicted (a) stress–strain curves at a strain rate of 10 per s and a temperature of 673 K and (b) textures at a strain of 0.9 shown in terms of the inverse pole figures.^{Reference Tang, Zhou, Li, Li, Peng, Peng, Wu, Wang and Lee10} Note that temperature rises with loading at a high strain rate. Better agreement with experimental results was obtained if the temperature rise was considered. The inverse pole figures were obtained through a stereographic projection to reflect the distribution of the grain orientations. Both experimental and simulation results revealed that the {10$\bar{1}$0} crystal directions were developed preferentially along the loading direction.

CDRX is favorable for fine-grained Mg alloys at elevated temperatures ranging from 200°C to 450°C. New grains are generated by the continuous increase in misorientation inside a given grain, which leads to the development of high-angle grain boundaries (HAGBs) without obvious GB migration.^{Reference Sakai, Belyakov, Kaibyshev, Miura and Jonas44,Reference Park, Oh and Kim45} These characteristics have been described in the CDRX scheme, where the misorientation between the core and boundary of a grain is tracked through lattice distortion.^{Reference Zhou, Li, Li, Peng, Wang and Wu46} Once the misorientation reaches a critical value, HAGBs form and new grains are born. Contrary to DDRX, the growth of grains generated from CDRX is negligible.

Future directions

Some recent experimental findings need to be implemented in the CP models. For example, CP-based models view twins as two-dimensional (2D) domains. Recently, the three-dimensional structure of twins has been characterized, and the growth and structure along the lateral direction were found to be different from those developed from the 2D point of view.^{Reference Liu, Li, Shao, Gong, Wang, McCabe, Jiang and Tomé47} Additionally, twin–twin interactions and junctions, also not accounted for in any model, influence the hardening behavior of Mg alloys.^{Reference Yu, Zhang and Jiang7} The failure in predicting the internal stresses demands better characterization of the stress state of newly created twins.^{Reference Qiao, Agnew and Wu36} It has been shown that twin pairs form when a twin crosses the GB, which affects the macroscopic behavior. GB sliding, a deformation mechanism that involves displacement of grains against each other, is another important mechanism of Mg alloy deformation at a high temperature, especially when the grain size is below the submicrometer scale. The quantitative description of the entities previously mentioned and their implementation into mesoscale material models are still lacking and are good areas for future work.