近置多裂纹相互作用的渐近分析方法

考虑到近置裂纹的强相互作用，提出了一种多裂纹相互作用的渐近分析方法. 经典Kachanov 方法将裂纹表面伪面力分解为两部分：均匀分布部分和非均匀部分，并假设裂纹的相互作用 仅由均匀部分引起，而忽略非均匀部分的影响. 该假设大大简化了分析过程，而且当裂纹间 距不是很小时，有很好的精度. 但当裂纹非常靠近或者沿主荷载方向重叠时，由于裂纹尖端 进入了其它裂纹的应力强化区或者应力屏蔽区，强相互作用使得该假设不再合理，从而带来 较大的误差. 为了提高分析近置多裂纹问题的精度，将裂纹表面伪面力分解为抛物线型分布 部分及高阶部分，考虑抛物线型分布张力对其他裂纹的影响，同样忽略高阶部分的影响. 通 过对三共线裂纹及两平行偏置裂纹两个实例的分析，验证了对于近置裂纹，新渐近方法具有 良好的精度.

Asymptotic Analysis of Interaction of Closely-spaced Cracks

An approximate method of stress analysis in elastic solids with multiple cracks is proposed to improve the accuracy of the Kachanov method in analyzing closely-spaced cracks. Classical Kachanov method assumed that traction in each crack can be represented as a sum of a uniform component and a non-uniform one, and the interaction among the cracks is only due to the uniform components. The assumptions simplify considerably the mathematics. However, the assumptions may not be valid when the cracks are very close and overlap along the direction of load. because each crack may be embedded in the stress-amplifying region as well as the stress-shielding region of the other cracks at this time To improve the accuracy of the Kachanov method, a new asymptotic method, in which the influence on a crack of the quadratic parabola pseudo tractions rather than the average ones on the other crack are taken into account, is proposed. Applications to the problem of three collinear cracks and two offset parallel closely-spaced cracks are considered to validate the accuracy of the new method