含棒状共晶团复合陶瓷细观强度模型研究

Mesomechanical Strength Model of Composite Ceramics Containing Stick Eutectic Colony

以剪滞法为基础推导了棒状共晶团外加远场拉伸应力与共晶团界面极限剪应力、共晶团体积含量、共晶团长径比之间关系的解析表达式,进而得到含棒状共晶团复合材料的拉伸强度与基体极限剪应力之间的理论表达式。计算过程中将共晶团长径比的概率统计分布规律引入到计算模型中,并考虑了棒状共晶团方位的随机分布。定义了共晶团达到最大剪应力的共晶团长度占共晶团整个长度的比值β,当加权平均的β值超过材料的许用值[β]时,材料发生剪切破坏。[β]的取值由材料自身的性质决定,可以通过试验确定。分析了复合材料的[β]的取值与其强度的关系,并在MATLAB中实现了编程计算。

Based on shear-lag method, the relationships of the far field stress of the stick eutectic colony,the interface shear stress of the stick eutectic colony, the volume content of the stick eutectic colony and the slenderness ratio of the stick eutectic colony were derived. And then the tensile- strength of composite ceramics was got. The probability distribution of the slenderness ratio of the stick eutectic colony was leaded in the strength model. And the random orientation of stick eutectic colony was considered. The ratio β which stands for the length ratio maximizing the interface shear stress of the stick eutectic colony was leaded in the strength model. The ratio [β] was decided according to the material and can be got by experiments. The influences ofβ on the composite ceramics were analyzed. And the calculation programming was compiled in MATLAB.