脆性材料裂纹扩展的分形运动学

大量实验结果表明脆性材料裂纹扩展路径是弯弯曲曲的，不规则的，断裂表面粗糙不平，表现出分形特征。本文应用分形几何推导出脆性材料裂纹扩展的分形运动学公式，得到了动、静态断裂韧性与分形裂纹扩展速度、裂纹长度、微结构特征量δ＿ｃ以及分形维数之间的关系；推导出了裂纹扩展速度的计算公式，得出宏观量测的裂纹扩展速度Ｖ＿０应小于分形裂纹扩展速度Ｖ；并推导出直接根据材料动、静态断裂韧性和裂纹扩展速度Ｖ＿０估算材料裂纹扩展路径的分维计算公式．本文理论分析结果与实验值在定性定量上达到了较好的一致。

FRACTAL KINEMAIICS OF CRACK PROPAGAtiON IN BRITTLE MAtERIALS

Experimental results indicate that the crack propagation path of a brittle mate-rials is irregular and tortuous,and fracture surfaces are roughness,which behave as fractal. Applied fractal geometry,the author derives formula of fractal kinematics of the crack prop-agation in brittle materials.The correlation of dynamic and static fracure toughnesses withcrack velocity,crack length,microstructure parameter and fractal dimension is obtained. From equations of estimating crack velocity and fractal dimension deduced in this paper,weconcluded that measured crack velocity V_0 should be less than the fractal crack velocity V, and the fractal dimension of the crack propagation path can be calculated directly from thecrack velocity V_0 and the fracture toughnesses.It is found that our analysis qualitativelyand/or quantitatively agrees with the experimental results.