非线性损伤材料中Ⅲ型裂纹尖端场

Tip field of mode Ⅲ crack in nonlinear damage material

为了研究损伤对裂纹尖端场的影响,在Krajcinovic一维脆性材料损伤模型的基础上,从宏观的唯象角度出发,采用连续损伤力学中的热力学内变量理论,推导出三维空间非线性损伤材料的本构方程,建立了一种非线性应变损伤模型,得出非线性损伤材料Ⅲ型裂纹尖端应力、应变和损伤场的解析表达式及其数值计算结果.经过分析得出损伤指数n和损伤变量D对裂尖场的影响较大,应力、应变为有限值,不具有奇异性,从而在理论上解释了实际材料在有限应力下破坏的现象,与工程实际相符.

In order to investigate the influence of damage on cracktip field,constitutive equations have been derived with a nonlinear strain damage model established for 3D nonlinear damage material using the 1D Krajcinovie's damage evolution model for brittle material and the thermodynamic internal variable theory of continuous damage mechanics so that analytic expressions and their calculated numeric values are obtained for the tip stress,strain and damage fields of mode Ⅲ cracks in nonlinear damage material.Analyses indicate that damage exponent n and damage variable D have significant influence on carktip feld;stress and strain have limited values,and are not singular,thereby giving a theoretical explanation to the failure of material under limited stress in line with actual engineering practice.