Motion and nucleation of steps along phase boundary
We study the motion of steps along a martensitic phase boundary in a cubic lattice undergoing anti-plane shear deformation. To enable analytical calculations, we model a phase transforming material by assuming a stress-strain law mat is piecewise linear with respect to one component of shear strain and linear with respect to another. Under these assumptions we derive a semi-analytical solution describing a steady sequential motion of the steps under an external loading. Our analysis yields kinetic relations between the driving force, the velocity of the steps and other characteristic parameters of the motion. These are studied in detail for the two-step configurations. We show mat the kinetic relations are significantly affected by the material anisotropy. Our results indicate the existence of multiple solutions exhibiting sequential step motion. Numerical simulations show mat some of these solutions can be stable, provided that the velocity of the steps is below a certain critical value that depends on material parameters and the step configuration. Above this value we observe a cascade nucleation of multiple steps, which then join sequentially moving groups.
Yu-bao Zhen Anna Vainchtein
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA;School of Astronautic Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA
国际会议
The 5th International Conference on Nonlinear Mechanics(第五届国际非线性力学会议)
上海
英文
1457-1463
2007-06-11（万方平台首次上网日期，不代表论文的发表时间）