摘要
采用应变损伤模型,对应变损伤材料Ⅲ型动态扩展裂纹尖端的弹塑性场进行了研究。在假定材料服从J_2流动理论的前提下,应用应变弱化形式给出了近似损伤结果,推导了反平面剪切情况下的本构方程,并且给出了Ⅲ型动态扩展裂纹尖端场的渐近方程。分析结果表明,在裂纹尖端,应变具有(1n R/r)~δ奇异性,应力具有(1n R/r)^(-nδ)奇异性。从而揭示了应变损伤材料Ⅲ型动态扩展裂纹尖端场的渐近行为。
Adopting damage constitutive model elastoplastic field near a dynamic propagating crack-tip of mode Ⅲ in a strain-damaged material is investigated. Assuming that the medium obeys the J_2 flow theory, the damage rule is given asymptotically in the form of power-law strain softening. For anti-plane shear problem, the constitutive relation is derived.The asymptotic equations of the dynamic elastoplastic field are given for mode Ⅲ crack. It is shown that the stress and strain singularities are, respectively, of the order of lnR/r)~δ and (lnR/r)^(-nδ). Therefore the asymptotic behaviour near a dynamic propagating crack-tip field of mode Ⅲ in a strain-damaged material is revealed.
关键词
应变损伤材料
动态扩展
奇异性
strain-damaged material
dynamic propagation
singularity
