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Re-examination of crack opening model of interface fracture

机译：界面裂缝裂纹开口模型的再检验

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The complex singularity associated with a crack at the interface between two dissimilar, isotropic and homogeneous materials leads to mathematical artefacts. such as stress oscillations and crack face interpenetrations in the vicinity of the crack tip. TQ avoid these unrealistic features, Sinclair (Sinclair GB. On the stress singu1arity at an interface crack. International Journal of Fracture 1980; 16(2): 111-9) assumed a finite crack opening angle (COA) such that the singularity λ became real equal to 1/2. This paper extends the COA model by considering real singularities not necessary equal to 1/2. When COA is 0°, the interface crack singularity is complex with a real part equal to 1/2. On increasing COA, the imaginary part of the singularity decreases and becomes zero at a threshold value of COA; at this point, the singularity is a real, repeated value. A further increase in COA results in a pair of real singularities. Different crack opening configurations and material combinations are studied, and results presented for threshold COAs and associated values of singularity. Stress analyses for these three regimes: (a) complex, (b) real pair and (c) real repeated singularities, are reported. It is seen that additional complexities are present in the last case. Typical results for stress fields are also included for comparing with standard fields.
机译：与两种不同，各向同性和均质材料之间的界面处的裂纹相关的复杂奇异性导致了数学假象。例如应力振荡和裂纹尖端附近的裂纹面互穿。 TQ避免了这些不切实际的特征，Sinclair（Sinclair GB。关于界面裂纹的应力弯曲性。InternationalJournal of Fracture 1980; 16（2）：111-9）假定裂纹的开度为有限值（COA），使得奇异性λ变为实数等于1/2。本文通过考虑不一定等于1/2的实际奇点来扩展COA模型。当COA为0°时，界面裂纹奇异度很复杂，实部等于1/2。随着COA的增加，奇异性的虚部减小，并在COA阈值处变为零;在这一点上，奇点是真实的重复值。 COA的进一步增加会导致一对真实的奇点。研究了不同的裂纹开口构型和材料组合，并给出了阈值COA和相关奇异值的结果。报告了这三种情况的应力分析：（a）复杂，（b）真实对，（c）真实重复的奇点。可以看出，在最后一种情况下还存在其他复杂性。还包括应力场的典型结果，用于与标准场进行比较。

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