弹粘塑性材料中Ⅲ型动态扩展裂纹尖端场的构造研究

Investigation Into Field Structure at Mode Ⅲ Dynamically Propagating Crack Tip in Elastic-Visco-Plastic Materials

采用弹粘塑性力学模型,对弹粘塑性材料中Ⅲ型动态扩展裂纹尖端场进行了渐近分析.在线性硬化条件下,裂纹尖端的应力和应变场具有相同的幂奇异性,奇异性指数由材料的粘性系数唯一确定.数值计算结果表明,运动参量裂纹扩展速度本身对裂尖场的分区构造影响很小.材料的硬化系数主导裂尖场的分区构造,但二次塑性区对裂尖场的影响较小.材料的粘性主导裂纹尖端应力和应变场的强度,同时对裂尖场的构造有一定影响.当裂纹扩展速度为0时,动态解退化为相应的准静态解;当硬化系数为0时,线性硬化解还原为相应的理想塑性解.

An elastic-viscoplastic mechanics model was adopted to investigate asymptotically the mode Ⅲ dynamically propagating crack tip field in elastic-viscoplastic materials. The stress and strain fields at crack tip possess the same power-law singularity under linear-hhardening condition. And the singularity exponent is uniquely determined by the viscosity coefficient of the material. Numerical calculation results indicate that the motion parameter of creek propagating speed has little effect itself on zone structure at crack tip. The hardening coefficient dominates the structure of crock-tip field but the secondary plastic zone has little influence on the field. The viscosity of the material dominates the strength of stress and strain fields at crack tip while it does have certain influence on crack-tip field structure. The dynamic crack-tip field degenerates into the relevant quasi-static solution when the crack moving speed is zero. And the cording perfectly-plastic solution is recovered from the linear-hardening solution when the hardening coefficient becomes zero.