摘要
假设裂纹顶端沿着分形轨迹运动，建立了裂纹扩展的分形弯折（ｋｉｎｋｉｎｇ）模型来描述裂纹的动态扩展。根据这个模型，我们推导了分形裂纹扩展对劝态应力强度和裂纹速度的影响．动态应力强度因子与表观应力强度因子之比Ｋ（ｌ（ｔ），Ｖ）／Ｋ（Ｌ（ｔ），Ｏ）是表观裂纹速度Ｖ＿Ｏ，材料微结构参数（ｄ／Δａ），分维Ｄ和裂纹扩展路径的弯折角θ的函数。本文研究结果表明：在分形裂纹扩展中，表观（或量测）的裂纹速度Ｖ＿Ｏ很难接近Ｒａｙｌｅｉｇｈ波速Ｃ＿ｒ．动态断裂实验中Ｖ＿Ｏ明显低于Ｃ＿ｒ的原因可能是分形裂纹扩展效应所致。材料的微结构，裂纹扩展路径的分维和弯折角均很强地影响动态应力强度因子和裂纹扩展速度。
Crack extension paths are often irregular, producing rough fracture surfaceswhich have a fractal geometry.In this paper, crack tip motion along a fractal crack trace isanalysed. A fractal kinking model of the crack extension path is established to describe ir-regular crack growth. A formula is derived to describe the effects of fractal crack propagationon the dvnamic stross intensity factor and on crack velocity. The ratio of the dvnamic stressintensity factor to the applied stress intensity factor,K(l(t),V)/K(L(t),0), is a function ofthe apparent crack velocity,V_O, microstructure parameter,d/Δa(grain size/crack incrementstep length), fractal dimension,D, and fractal kinking angle of crack extension path,θ. Forfractal crack propagation, the apparent (or measured)crack velocity,V_O,cannot approachthe Rayleigh wave speed,C_r. Why V_O is significantly lower than C_r in dynamic fractureexperiments can be explained by the effects of fractal crack propagation. The dynamic stressintensity factor and apparentcrack velocity are strongly affected by the microstructure pa-rameter,(d/Δa), fractal dimension,D, and fractal kinking angle of crack extension path,θ.This is in good agreement witb experimental findings.
出处
《力学学报》
EI
CSCD
北大核心
1995年第1期18-27,共10页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金项目
国家重大基础性理论课题"非线性科学"
国家教育委员会跨世纪优秀人才计划项目资助
关键词
裂纹扩展
动态断裂
分形效应
断裂力学
crack propagation, dynamic fracture, fractal crack path, fractal kinked model,fractal effect
