两相共格固体中晶界和沉淀物之间的弹性介导相互作用
Elastically-mediated interactions between grain boundaries and precipitates in two-phase coherent solids
摘要：
本文用解析和数值方法研究了在失配应变存在下两相共格固体中晶界和第二相沉淀物之间的相互作用。我们的数值研究使用振幅方程描述的成分和应力的相互作用[R。Spatschek和A. Karma，Phys. Rev. B { \bf 81}，214201（2010）]以及分别对应于表现出各向同性和各向异性弹性性质的二维六边形和三维BCC晶体结构的自由能。我们考虑两个实验动机的几何形状，其中（i）层状沉淀物成核沿平面晶界内的沉淀物为中心，和（ii）一个圆形的沉淀物成核内的晶粒在一个有限的距离，最初的平面晶界。对于第一种几何形状，我们发现，晶界变得形态不稳定，由于长期的弹性相互作用之间的晶界和组成域边界，和剪切耦合晶界运动的组合。我们通过扩展最近进行的线性稳定性分析来解析地描述这种不稳定性[P. - A. Geslin，Y. C. Xu，和A. Karma，Phys. Rev. Lett. { \bf 114}，105501（2015）]中描述的弹性各向异性的更一般情况。分析预测，弹性各向异性阻碍，但不抑制不稳定。模拟还表明，在一个发达的非线性政权，这种不稳定性可能会导致小角度晶界的破裂时，失配应变超过一个阈值，取决于晶界取向差。对于第二种几何形状，模拟表明，初始平面晶界和相邻的圆形沉淀物之间的弹性相互作用导致沉淀物迁移到晶界并锚定在晶界处。
英文摘要：
We investigate analytically and numerically the interaction between grain boundaries and second phase precipitates in two-phase coherent solids in the presence of misfit strain. Our numerical study uses amplitude equations that describe the interaction of composition and stress [R. Spatschek and A. Karma, Phys. Rev. B {\bf 81}, 214201 (2010)] and free-energies corresponding to two-dimensional hexagonal and three-dimensional BCC crystal structures that exhibit isotropic and anisotropic elastic properties, respectively. We consider two experimentally motivated geometries where (i) a lamellar precipitate nucleates along a planar grain boundary that is centered inside the precipitate, and (ii) a circular precipitate nucleates inside a grain at a finite distance to an initially planar grain boundary. For the first geometry, we find that the grain boundary becomes morphologically unstable due to the combination of long-range elastic interaction between the grain boundary and compositional domain boundaries, and shear-coupled grain boundary motion. We characterize this instability analytically by extending the linear stability analysis carried out recently [P.-A. Geslin, Y.-C. Xu, and A. Karma, Phys. Rev. Lett. {\bf 114}, 105501 (2015)] to the more general case of elastic anisotropy. The analysis predicts that elastic anisotropy hinders but does not suppress the instability. Simulations also reveal that, in a well-developed non-linear regime, this instability can lead to the break-up of low-angle grain boundaries when the misfit strain exceeds a threshold that depends on the grain boundary misorientation. For the second geometry, simulations show that the elastic interaction between an initially planar grain boundary and an adjacent circular precipitate causes the precipitate to migrate to and anchor at the grain boundary.
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