The effect of crack interactions on stress intensity factors is examined for a periodic array of coplanar penny-shaped cracks. Kachanov's approximate method for crack interactions (Int. J. Solid. Struct. 1987; 23(1):23-43) is employed to analyze both hexagonal and square crack configurations. In approximating crack interactions, the solution converges when the total truncation number of the cracks is 109. As expected, due to high density packing crack interaction in the hexagonal configuration is stronger than that in the square configuration. Based on the numerical results, convenient fitting equations for quick evaluation of the mode I stress intensity factors are obtained as a function of crack density and angle around the crack edge for both crack configurations. Numerical results for the mode II and III stress intensity factors are presented in the form of contour lines for the case of Poisson's ratio ν =0.3. Possible errors for these problems due to Kachanov's approximate method are estimated. Good agreement is observed with the limited number of results available in the literature and obtained by different methods.

中文翻译：

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相互作用的共面便士形裂纹的周期性阵列的应力强度因子

裂纹相互作用对应力强度因子的影响被检查为共面便士形裂纹的周期性阵列。Kachanov 的裂纹相互作用近似方法（Int. J. Solid. Struct. 1987; 23(1):23-43）用于分析六角形和方形裂纹配置。在近似裂纹相互作用中，当裂纹的总截断数为 109 时，解收敛。正如预期的那样，由于高密度堆积，六边形配置中的裂纹相互作用比方形配置中的强。根据数值结果，获得了方便的拟合方程，用于快速评估 I 型应力强度因子，作为两种裂纹配置的裂纹密度和裂纹边缘角度的函数。对于泊松比 ν = 0.3 的情况，模式 II 和 III 应力强度因子的数值结果以等高线的形式呈现。由于 Kachanov 的近似方法，这些问题的可能错误被估计。与文献中可用的有限数量的结果和通过不同方法获得的结果一致。