引入了强化系数描述多层膜结构的强化机制。强调了多层膜结构的强化是由于界面位错的约束和界面位错的聚集, 而弱化则是由于层内位错做层间运动引起的。在经典力学框架内, 把描述位错运动的Seeger方程化为带有固定力矩的摆方程。用Jacobian椭圆函数解析地刻划了扰动系统和无扰动系统的相平面特征; 并在相空间密度均匀分布的假设下, 利用相面积概念导出了多层膜结构的强化系数。结果表明, 当层内应力场小于界面位错约束时材料被强化。

In this paper, the enhancement factor is introduced to describe the strengthening mechanism of the multilayer structure. It is emphasized that the strengthening of the multilayer structure is caused due to the constraint and accumulation of interface dislocations, while weakening is caused due to the interlayer movement. In the framework of classical mechanics, the Seeger equation of motion of dislocations is reduced to be the pendulum equation with a constant moment. The phase plane properties are analytically characterized by the non-perturbed system and the perturbed system by using Jacobian elliptic function; and the enhancement factor of the multilayer structure is derived by the concept of phase area in the assumption of the uniform distribution of a phase space density. The results show that the material is strengthened when the stress field in layer is less than the inherent stress field on the interface.