分形下材料裂纹的临界表面能

Critical Surface Energy of Materials Crack in Fractal

分形理论在金属断裂分析方面的应用越来越广,针对材料裂纹临界表面能与实际表面能存在较大误差的现象,分析并修正了临界表面能与分形尺度的关系。将裂纹临界表面能准则的裂纹平直路径扩展假设修正为分形路径扩展,采用分形理论建立了沿晶断裂、穿晶断裂、沿晶和穿晶混合断裂的分形模型,并根据自相似性分别计算其Hausdorff维数。最后在裂纹路径分形扩展的假设下,对裂纹临界表面能进行了修订,得出了韧性材料断裂的临界表面能与分形尺度的关系式。

The fractal theory is widely used to analysis the fracture of metal. The relation of critical surface and fractal dimensions was analyzed and revised to solve the deviation problem of the critical surface energy and the actual surface energy. The fractal model of the inter granular fracture, transgranular fracture and blended fracture of the two kinds were created after it was revised that hypothesis of flat extension o{ the fissure surface energy rule to {ractal exten- sion path. The Hausdorf{ dimension was quantitatively calculated based on the self-similarity of the fractal model. At last the critical surface energy of the crack was revised under the assumption of fractal extension path of the crack, the relational expression of the surface energy of the ductile material and fractal scale was obtained.