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扩展裂纹裂尖附近场的现有渐近解存在一系列数学物理上异常的情况。为此,本文从奇异摄动理论观点对现有渐近分析的有效性作了考察。文章第一次揭示了当渐近展开式为γ、θ变量可分离型且在γ→0时满足条件时,渐近分析对θ为非一致有效;无论裂纹模式、材料类型如何不同,也无论是准静态扩展还是动力学扩展,在裂纹扩展线和裂纹表面都存在着现有文献分析不适用的边界层。对这些边界层存在的意义作了讨论。指出,在平面应变Ⅰ型裂纹问题中,用一角层代替θ=π/4处的边界是必要的,以得到一相容的渐近场解。
The existing asymptotic solutions of the field near the crack tip have a series of mathematical and physical anomalies. For this reason, this paper examines the validity of the existing asymptotic analysis from the singular perturbation theory point of view. The paper first reveals that asymptotic expansion is non-uniform for θ when the asymptotic expansion is separable for the γ and θ variables and satisfies the conditions for γ → 0. Asymptotic analysis is non-uniform for θ regardless of the crack mode and the type of material Is quasi-static or dynamic expansion of the extension of the crack line and crack surface exist in the existing literature analysis of the boundary layer does not apply. The significance of these boundary layers is discussed. It is pointed out that it is necessary to replace the boundary at θ = π / 4 with a corner layer in order to obtain a compatible asymptotic field solution.