Collinear unequal crack series in magnetoelectroelastic materials: Anti-plane case

• Published in: Zeitschrift für angewandte Mathematik und Mechanik 2011-09, Vol.91 (9), p.743-752
• Main Authors: Li, Y.-D., Lee, K.Y., Pan, J.-W.
• Format: Article
• Language: English
• Subjects: Collinear unequal cracks; Exact sciences and technology; Functional analysis; Functions of a complex variable; generalized dislocations; Green's function; magnetoelectroelastic materials; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Ordinary differential equations; Sciences and techniques of general use; singular integral equations
• ISSN: 0044-2267; 1521-4001
• DOI: 10.1002/zamm.201000053

The purpose of the present work is to study collinear unequal crack series in magnetoelectroelastic materials, which are of more practical significance than the widely studied collinear equal cracks. Fracture analysis is performed by the combined methods of distributed generalized dislocations, Green's function and singular integral equations (SIEs). The theoretical derivation is validated by the degeneration of SIEs in special cases. Parametric studies on the numerical results of mechanical strain energy release rate (MSERR) yield the following conclusions. (a) As two unequal cracks approach each other, interference occurs in crack tip fields, resulting in an obvious increase of MSERR. The ratio between the crack space and the length of the shorter crack is a main factor affecting the interference. (b) Negative or positive electric loading may shield or enhance crack growth, respectively. In the case of positive magnetic permeability, the effect of magnetic loading is analogous to that of electric loading; however, if magnetic permeability is negative, the result is completely opposite. (c) Positive values of magnetic permeability are found to be more reasonable than the negative values. The purpose of the present work is to study collinear unequal crack series in magnetoelectroelastic materials, which are of more practical significance than the widely studied collinear equal cracks. Fracture analysis is performed by the combined methods of distributed generalized dislocations, Green's function and singular integral equations (SIEs). The theoretical derivation is validated by the degeneration of SIEs in special cases.