同轴与非同轴渐进变形几何解析

GEOMETRICAL ANALYSIS FOR COAXIAL AND NONCOAXIAL PROGRESSIVE DEFORMATION

应用变形梯度莫尔圆,把同轴渐进变形与非同轴渐进变形及其特点以图解的方法,定量地、明确地表示出来。得到这样的结论:同轴渐进变形的变形梯度圆圆心总是在D_(ii)轴上,在D_(ii)-D_(ij)(i≠j)坐标系中,圆心的轨迹是一条直线,非同轴渐进变形的变形梯度圆圆心在变形的不同瞬时都在变化,在初始未变形状态,它位于D_(ii)轴上,在渐进变形过程中,圆心沿某一路线移动,其轨迹在D_(ii)-D_(ij)(i≠j)坐标系中为某一特征曲线,对于简单剪切这种特殊的有旋变形,圆心轨迹为平行于D_(ij)(i≠j)轴的直线。藉此可鉴定、反映渐进变形的性质。

The character and quantities of a progressive deformation in coaxial and noncoaxial may be graphically ,quantitatively, clearly expressed by moans of the delonnalion gradient Mohr circles. The conclusion of geometrical character is that the comers of deformation gradient circles for a coaxial progressive deformation are always on the D axis, the trajectory of circle centres is a straight line in Dij-Dij(i≠j) coordinate system; for a noncoaxial progressive deformation ,they are located at Dij axis in initial undeformed state and then shift with time along some path .the trajectory of circle centres, in general case ,is a curve in Dij-Dij(i≠j) coordinate svsiem. For a simple shear which is a rotational deformation, the trajectory of circle centres is a straight line parallel to Dij(i≠j) axis.