The yield behavior of crystalline solids is determined by the motion of defects like dislocations, twin boundaries and coherent phase boundaries. These solids are hardened by introducing precipitates—small particles of a second phase. It is generally observed that the motion of line defects like dislocations are strongly inhibited or pinned by precipitates while the motion of surface defects like twin and phase boundaries are minimally affected. In this article, we provide insight into why line defects are more susceptible to the effect of precipitates than surface defects. Based on mathematical models that describe both types of motion, we show that for small concentrations of a nearly periodic arrangement of precipitates, the critical force that is required for a surface defect to overcome a precipitate is smaller than that required for a line defect. In particular, the critical forces for surface and line defects scale with the radius of precipitates to the second and first power, respectively.

晶体固体的屈服行为取决于位错，孪晶界和相干相界等缺陷的运动。这些固体通过引入沉淀物（第二相的小颗粒）而硬化。通常观察到，诸如位错的线缺陷的运动被沉淀物强烈抑制或固定，而诸如孪晶和相界的表面缺陷的运动受到的影响最小。在本文中，我们提供了有关为什么线缺陷比表面缺陷更容易受到沉淀影响的见解。基于描述两种运动类型的数学模型，我们表明，对于小浓度的近乎周期性的沉淀物，表面缺陷克服沉淀所需的临界力小于线缺陷所需的临界力。特别是，表面缺陷和线缺陷的临界力分别与析出物的半径成比例地增大到第二和第一幂。