粉末冶金材料两个屈服条件几何性质

Geometrical Properties of Two Yield Criteria for Powder Metallurgical Materials

粉末冶金材料屈服条件是广义塑性理论的重要基础。介绍了粉末冶金材料2个常用屈服条件的基本形式,通过物理和数学分析揭示了它们的几何性质,确定了二次函数屈服面为椭球面、线性函数屈服面为六棱锥面。当粉末冶金材料成为全致密材料时,椭球面和六棱锥面分别成为圆柱面和六棱柱面。研究了单向拉伸(压缩)、平面应力和平面应变条件下的屈服性质,导出了屈服轨迹方程,并确定了相应屈服轨迹的几何形状。揭示了粉末冶金材料2个常用屈服条件的相互关系。

The yield criterion for powder metallurgical materials was a key basis of generalized plasticity theory. Therefore, the basic forms of two important yield criteria for powder metallurgical materials were introduced in the paper. Based upon the physical and mathematical analyses, it was deduced that the yield surfaces of square yield function and linear yield function were elliptical sphere and hexagonal pyramid respectively. If powder metallurgical materials were changed into fully dense materials, then the elliptical sphere and hexagonal pyramid would evolve into cylinder and hexagon bar respectively. The yield properties in uni-axial elongation or compression, plane stress and plane strain were intensively researched, the related yield track equations were derived and the geometrical forms of the yield tracks were determined. Some relationships between the two yield criteria for powder metallurgical materials were revealed in detail.