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金属塑性变形过程中产生的位错组态的基本特征是高低位错密度区交替出现的空间周期性有序结构,位错组态演化是典型的非线性现象.针对刃位错与螺位错组成的系统,考虑到螺位错通过交滑移作用对刃位错密度的贡献及位错间的反应特点,以反应-扩散方程为基础建立了一个反映变形过程中局部应力变化的包含高阶微分项的非线性偏微分方程,该方程具有非线性系统方程的一般特征,并利用这一特点,避免了建立位错组态演化模型时对复杂的位错反应项的表示.通过理论分析,得到了相邻高密度位错区之间距离(位错胞尺寸或位错墙之间的距离)与应力或位错密度之间的关系.利用该关系对亚微米晶铜和铝的流变应力进行了预测,所得到的结果与前人的实验结果吻合.
The basic feature of the dislocation configuration generated during the plastic deformation of metal is the spatial periodic ordered structure in which the high and low dislocation density regions alternate. The dislocation configuration evolution is a typical nonlinear phenomenon. Considering the contribution of screw dislocation to the dislocation density by cross slip and the reaction characteristics between dislocations, a new method is proposed based on the reaction-diffusion equation that reflects the local stress changes during deformation, The nonlinear partial differential equations of differential terms, which have the general characteristics of nonlinear system equations, can be used to avoid the representation of complex dislocation reaction terms in the establishment of dislocation configuration evolutionary models. By theoretical analysis, The relationship between the distance between adjacent high-density dislocation regions (the dislocation cell size or the distance between dislocation walls) and the stress or dislocation density was obtained.The rheological behavior of submicron copper and aluminum The stress is predicted, and the result is in good agreement with the previous experimental results.