Hexagonal close-packed (HCP) metals show highly anisotropic mechanical responses due to twinning, slip and the interaction among various slip and twin systems. Each HCP metal shows different sets of activated slip and twin systems. The interaction among slip and twin systems causes highly nonlinear and rapidly changing hardening behaviors in the critical resolved shear stress (CRSS) of each slip/twin system. To accurately understand the anisotropic mechanical response of HCP metals, both single-crystal and polycrystal tests must be performed. The interaction among different slip and twin systems shows different behaviors in the single-crystal and polycrystal settings since the interacting environments are different. The fitting process of the single crystal and polycrystal stress–strain data involves a series of trials and errors to find the correct interaction patterns among various slip and twin systems. The fitting procedures used in previous researches take a lot of times of trials and errors and are not guided by any physical property. Therefore, this study employs a recently proposed new fitting procedure, which is based on a physical property, the saturation strength of the material, to fit magnesium experimental data more efficiently with a less number of trials and errors. Compared to the slip process, twinning is computationally more difficult to take into account due to the directionality of the twin process, i.e., twinning occurs only in one direction, not in the opposite direction unlike the slip process. The rapidly changing highly nonlinear interaction hardening behaviors among various slip and twin systems are computationally challenging. Both of the above computational difficulties require a more robust and accurate numerical scheme than previously used ones to obtain accurate representations of experimental data. Therefore, this study proposes a more accurate and robust numerical scheme for the hardening strengths (CRSS) of twin/slip systems and interaction hardening. The newly proposed scheme is based upon implicit time integration, which enhances accuracy and stability. Using the proposed fitting procedure and the implicit integration scheme for hardening strength (CRSS) and interaction hardening, the experimental stress–strain data of polycrystal magnesium shown in Kelley and Hosford (The plastic deformation of magnesium. Technical report, 1967, Trans Metall Soc AIME 242:5–13, 1968) are successfully reproduced.

由于孪晶，滑移以及各种滑移和孪生系统之间的相互作用，六方密堆积（HCP）金属显示出高度各向异性的机械响应。每种HCP金属均显示不同组的激活滑移和双胎系统。滑移和孪生系统之间的相互作用会在每个滑移/孪生系统的临界分辨剪切应力（CRSS）中引起高度非线性和快速变化的硬化行为。为了准确了解HCP金属的各向异性机械响应，必须执行单晶和多晶测试。由于相互作用的环境不同，不同的滑移和孪生系统之间的相互作用在单晶和多晶环境中表现出不同的行为。单晶和多晶应力应变数据的拟合过程涉及一系列试验和错误，以找到各种滑移和孪生系统之间的正确相互作用模式。以前的研究中使用的拟合过程需要大量的试验和错误，并且不受任何物理性质的指导。因此，这项研究采用了最近提出的一种新的拟合方法，该方法基于物理特性，材料的饱和强度，以较少的试验和错误次数更有效地拟合了镁的实验数据。与滑动过程相比，由于孪生过程的方向性，孪生在计算上更加难以考虑，即，孪生仅在一个方向上发生，而不像滑动过程那样在相反的方向上发生。各种滑移和孪生系统之间快速变化的高度非线性相互作用硬化行为在计算上具有挑战性。与先前使用的计算困难相比，以上两个计算困难都需要更健壮和准确的数字方案，以获得实验数据的精确表示。因此，本研究提出了一种更为精确和鲁棒的数值方案，用于孪晶/滑动系统的硬化强度（CRSS）和相互作用硬化。新提出的方案基于隐式时间积分，从而提高了准确性和稳定性。使用拟议的拟合程序以及硬化强度和相互作用硬化的隐式积分方案，在Kelley和Hosford中展示了多晶镁的实验应力-应变数据（镁的塑性变形。