颗粒增强复合材料的屈服极限

Initial Yield Limits of Particle-reinforced Composites

基于渐近均匀化方法,导出了颗粒增强复合材料的屈服准则,给出了初始屈服应力的解析表达式.因为颗粒增强体的弹性模量远比弹塑性基体的弹性模量高,这个模量差在增强体和基体中产生了装配刚度.解局部问题可以得到该装配刚度.从屈服应力的表达式可以看出,装配刚度和基体的剪切模量之比,以及增强体和基体两者的剪切模量之比决定了屈服极限的提高程度.给出了两个数值算例.采用菱形十二面体单胞求解了局部问题.取单胞形状为菱形十二面体的优点是增强体的体积比可以高达74%.

A yield criterion for particle-reinforced composites is developed based on the method of asymptotic homogenization.According to the yield criterion,the initial yield stresses are predicted in closed forms.Because the elastic modulus of the particle reinforcement is much higher than that of the elasto-plastic matrix,the difference between the elastic moduli results in an assembly stiffness in the composites.The assembly stiffness can be obtained by solving a local problem.It can be seen from the expressions of the yield stress that the increase of yield stress depends on the ratios between the average assembly stiffnesses and the shear moduli of both the reinforcement and the matrix.Two numerical examples are given.A rhombic dodecahedron cell is used to solve the local problem,by means of which the volume ratio of reinforcement can be as high as 74%.