Plastic Flow in Two-Dimensional Solids

A time-dependent Ginzburg-Landau model of plastic deformation in two-dimensional solids is presented. The fundamental dynamic variables are the displacement field \bi u and the lattice velocity {\bi v}=\p {\bi u}/\p t. Damping is assumed to arise from the shear viscosity in the momentum equation. The elastic energy density is a periodic function of the shear and tetragonal strains, which enables formation of slips at large strains. In this work we neglect defects such as vacancies, interstitials, or grain boundaries. The simplest slip consists of two edge dislocations with opposite Burgers vectors. The formation energy of a slip is minimized if its orientation is parallel or perpendicular to the flow in simple shear deformation and if it makes angles of $\pm \pi/4$ with respect to the stretched direction in uniaxial stretching. High-density dislocations produced in plastic flow do not disappear even if the flow is stopped. Thus large applied strains give rise to metastable, structurally disordered states. We divide the elastic energy into an elastic part due to affine deformation and a defect part. The latter represents degree of disorder and is nearly constant in plastic flow under cyclic straining.Comment: 16pages, Figures can be obtained at http://stat.scphys.kyoto-u.ac.jp/index-e.htm

Numerical Simulation of Ultrasonic Surface Treatment

A dynamic model for the behavior of ultrasonically treatment materials is suggested. The microplastic strain piling up is related to the redistribution of the available defects and emergence of new ones on the microscale level as well as to the evolution of the available substructures and formation of new ones on the mesoscale level. The behavior of mild steel specimens subjected to ultrasonic shock wave treatment and to machining where the ultrasonic vibrations are applied directly by concentrator or magnetostrictive converter has been evaluated. The results obtained are reported

Numerical modeling of multi-scale shear stability loss in polycrystals under shock wave loading

Presented in this paper is numerical modeling of polycrystalline aluminum behavior under the weak shock waves. Plastic deformation is considered as a process of shear stability loss on the different scale levels : micro, meso, and macro. A dislocation kinetics equation describes micro scale processes. For the meso scale deformation to be simulated we use two different models. One of them takes into account a generation of plastic shears on grain boundaries and the other allows us to describe "independent rotation" of mesofragments. On the macro level we calculate impact interaction the aluminum flyer plate with perfectly rigid wall. The results of 2D calculations are reported and discussed