固-固转变中的非仿射场：产物液滴的结构和稳定性
Non-affine fields in solid-solid transformations: the structure and stability of a product droplet
摘要：
我们描述的微观结构，形状和动力学的马氏体成核的母奥氏体在固-固转变过程中的液滴的生长，使用朗道理论写在传统的仿射，弹性形变和{ \em非仿射}自由度。非亲和性，$ϕ$，作为一个来源的应变不相容性和屏幕远程弹性相互作用。它产生于局部应力超过阈值的地方，然后扩散退火。当可能在变换过程中产生的缺陷对之间的间隔很小时，根据$ϕ$的描述是不可避免的。使用变分计算，我们找到了三种类型的稳定的解决方案（{ \hv I}，{ \hv II}和{ \hv III}）的产品液滴的结构取决于缩放迁移率的$ϕ$平行和垂直于父产品界面和应力阈值。在{ \hv I}中，$ϕ$非常小，{ \hv II}涉及位于母体-产品界面内高应力区域的大$ϕ$，{ \hv III}中$ϕ$完全润湿母体-产品界面。虽然在解{ \hv I}中孪晶的宽度$l$和尺寸$W$遵循$l\propto\sqrt{W}$，但这种关系对于{ \hv II}或{ \hv III}不成立。我们获得了以这些溶液为特征的动态相图，并认为它们代表了特定的微观结构，例如孪生或错位的马氏体。
英文摘要：
We describe the microstructure, shape and dynamics of growth of a droplet of martensite nucleating in a parent austenite during a solid-solid transformation, using a Landau theory written in terms of conventional affine, elastic deformations and {\em non-affine} degrees of freedom. Non-affineness, $ϕ$, serves as a source of strain incompatibility and screens long-ranged elastic interactions. It is produced wherever the local stress exceeds a threshold and anneals diffusively thereafter. A description in terms of $ϕ$ is inevitable when the separation between defect pairs, possibly generated during the course of the transformation, is small. Using a variational calculation, we find three types of stable solutions ({\hv I}, {\hv II} and {\hv III}) for the structure of the product droplet depending on the scaled mobilities of $ϕ$ parallel and perpendicular to the parent-product interface and the stress threshold. In {\hv I}, $ϕ$ is vanishingly small, {\hv II} involves large $ϕ$ localized in regions of high stress within the parent-product interface and {\hv III} where $ϕ$ completely wets the parent-product interface. While width $l$ and size $W$ of the twins follows $l\propto\sqrt{W}$ in solution {\hv I}, this relation does not hold for {\hv II} or {\hv III}. We obtain a dynamical phase diagram featuring these solutions and argue that they represent specific microstructures such as twinned or dislocated martensites.
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