裂尖曲率对裂纹前缘塑性区的影响

Plastic Zone Affected by Crack Tip Curvature

考虑尖端为圆弧形的钝头裂纹模型 ,在外围取线弹性无裂纹体的解 ,应用线场分析方法 ,形成一套估计钝头裂纹前缘塑性区尺寸的方法。对含径向裂纹和圆弧形裂尖的圆盘受均匀张力作用情况 ,给出了塑性区的裂纹前缘尺寸与裂纹尖端曲率的关系。得到的结论是 ,塑性区的裂纹前缘尺寸与裂纹尖端曲率有关 ;对于给定的塑性区的裂纹前缘尺寸 ,载荷反比于外缘尺寸的平方。前一结论说明了塑性区的裂前尺寸作为裂纹失稳扩展判断的局限性 ;后一结论说明了裂纹体强度失效的尺寸效应规律 :抗断强度与总体线尺寸的平方成反比。

A dull crack model, with a circular curve on the tip, was investigated. An elastic solution without crack was taken in the periphery of the crack tip, the line field analysis method was adopted and a method for computing plastic zone forward crack tip was proposed. For a circular disk with radial crack uniformly subjected to tension in outer circular boundary, the relation between size of plastic zone forward crack tip and curvature radio of crack tip was obtained. It is concluded that the relationship between size of plastic zone forward crack tip and curvature radio of crack tip exists, if the size of plastic zone forward crack tip keeps as a constant, the uniform tension in out circular boundary is inverse proportional to the square of outer radius. The former conclusion indicates that there exists limitation when size of plastic zone forward crack tip is regarded as criterion of unstable expanding of a crack, and the latter shows the size effect of strength of a body with crack: strength of a body with crack is inverse proportional to the square of line dimension size.