Singularities, interfaces and cracks in dissimilar anisotropic media
Singularities, interfaces and cracks in dissimilar anisotropic media
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DOI：
10.1098/rspa.1990.0016
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发表时间：
1990-02
期刊：
影响因子：
--
通讯作者：
Z. Suo
中科院分区：
文献类型：
--
作者：
Z. Suo
对于界面裂纹不表现出振荡行为的非病理性双材料，观察到除了可能的应力强度因子外，两个块体的近尖端场的结构与另一个块体的弹性模量无关。在这种非振荡条件下分析了共线界面裂纹，并给出了一个简单的规则，它允许人们从各向同性均匀介质中的III型解构造完整的解。一般的界面裂纹尖端场由二维振荡奇点和一维平方根奇点组成。分别提出了一个复应力强度因子和一个实应力强度因子来衡量这两个奇异性。由于各向异性，一个特殊的事实是，当双材料退化到非病理性时，无论如何定义，标度振荡场的复应力强度因子都不能恢复经典的应力强度因子。在这种情况下，共线裂纹问题也被表述出来，并且确定了一个非常简单的数学结构。得到了奇异界面和奇异界面裂纹的交互解。一般结果专用于解耦的反平面变形和平面内变形。对于这种重要的情况，发现如果一个材料对界面和两个固体的一组相对取向是非病态的，那么对于任何一组取向它都是非病态的。对于粘结的正交各向异性材料，弹性各向异性和相异度的主要度量的直观选择是合理的。给出了一类简并的正交各向异性材料的复变量表示。在整篇文章中，强调了Lekhnitskii和Stroh形式主义的等价性。文章最后给出了各向异性固体界面断裂力学的形式表述。
For a non-pathological bimaterial in which an interface crack displays no oscillatory behaviour, it is observed that, apart possibly from the stress intensity factors, the structure of the near-tip field in each of the two blocks is independent of the elastic moduli of the other block. Collinear interface cracks are analysed under this non-oscillatory condition, and a simple rule is formulated that allows one to construct the complete solutions from mode III solutions in an isotropic, homogeneous medium. The general interfacial crack-tip field is found to consist of a two-dimensional oscillatory singularity and a one-dimensional square root singularity. A complex and a real stress intensity factors are proposed to scale the two singularities respectively. Owing to anisotropy, a peculiar fact is that the complex stress intensity factor scaling the oscillatory fields, however defined, does not recover the classical stress intensity factors as the bimaterial degenerates to be non-pathological. Collinear crack problems are also formulated in this context, and a strikingly simple mathematical structure is identified. Interactive solutions for singularity-interface and singularity interface-crack are obtained. The general results are specialized to decoupled antiplane and in-plane deformations. For this important case, it is found that if a material pair is non-pathological for one set of relative orientations of the interface and the two solids, it is non-pathological for any set of orientations. For bonded orthotropic materials, an intuitive choice of the principal measures of elastic anisotropy and dissimilarity is rationalized. A complex-variable representation is presented for a class of degenerate orthotropic materials. Throughout the paper, the equivalence of the Lekhnitskii and Stroh formalisms is emphasized. The article concludes with a formal statement of interfacial fracture mechanics for anisotropic solids.