While the three-dimensional (3D) shape and stress field of a twin in hexagonal close-packed (HCP) metals have attracted considerable interest in recent years due to their substantial impact on internal stress and mechanical properties, a detailed understanding of their variation with twin size is still lacking. An analytical model that is not restricted by spatial scale is developed in this work by considering the effects of anisotropic boundary energy, elastic strain energy and plastic relaxation to predict the 3D shape with the minimum energy, and the stress field, of an isolated ellipsoidal twin of different sizes. The model is applied to Mg with a focus on the $\left\{10\overline{1}2\right\}$ twin type. The analytical results show that the nucleation of the nano-sized twin embryos is facilitated by the stress field near structural defects such as dislocations. During the expansion of this nano-sized twin embryo, the interplay between the elastic strain energy and interfacial energy changes the length of the twin along the twin shear (forward) direction from being shorter to longer than that along the lateral direction. In contrast to the current understandings, the maximum shear stress on the twin plane along the twin shear direction occurs at the lateral, rather than the forward, side of the twin. At the forward side, the maximum shear stress occurs at a distance ahead of the twin tip and this distance increases with increasing twin thickness.

虽然近年来六方密排 (HCP) 金属中孪晶的三维 (3D) 形状和应力场由于它们对内应力和机械性能的重大影响而引起了相当大的兴趣，但详细了解它们随时间的变化双尺寸仍然缺乏。在这项工作中，通过考虑各向异性边界能、弹性应变能和塑性松弛的影响，开发了一种不受空间尺度限制的分析模型，以预测具有最小能量的 3D 形状和应力场，孤立的椭球孪晶不同大小的。该模型适用于 Mg，重点是$\left\{10\overline{\mathrm{1个}}\mathrm{2个}\right\}$双胞胎类型。分析结果表明，位错等结构缺陷附近的应力场促进了纳米双胚的成核。在这个纳米尺寸的双胞胎胚胎膨胀过程中，弹性应变能和界面能之间的相互作用改变了双胞胎沿双剪切（向前）方向的长度，从短到长于沿横向的长度。与目前的理解相反，双平面上沿双剪切方向的最大剪应力发生在双晶的侧面，而不是前侧。在前侧，最大剪应力出现在双尖端前面的一段距离处，并且该距离随着双厚度的增加而增加。