Journal
APPLIED MATHEMATICAL MODELLING
Volume 77, Issue -, Pages 1460-1473Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2019.09.026
Keywords
Integral equation method; Orthotropic material; Doubly periodic crack; Stress intensity factor; Crack tearing displacement; Effective shear modulus
Funding
- Fund of Natural Science Foundation of China [11802225]
- Natural Science Basic Research Plan in the Shaanxi Province of China [2019JQ-261]
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The doubly periodic arrays of cracks represent an important mesoscopic model for analysis of the damage and fracture mechanics behaviors of materials. Here, in the framework of a continuously distributed dislocation model and singular integral equation approach, a highly accurate solution is proposed to describe the fracture behavior of orthotropic solids weakened by doubly periodic strip-like cracks on rectangular lattice arrays under a far-field longitudinal shear load. By fully comparing the current numerical results with known analytical and boundary element solutions, the high precision of the proposed solution is verified. Furthermore, the effects of periodic parameters and orthotropic parameter ratio on the stress intensity factor, crack tearing displacement, and effective shear modulus are studied, and an analytically polynomial estimation for the equivalent shear modulus is proposed in a certain range. The interaction distances among the vertical and horizontal periodic cracks are quite different, and their effects vary with the orthotropic parameter ratio. In addition, the dynamic problem is discussed briefly in the case where the material is subjected to harmonic longitudinal shear stress waves. Further work will continue the in-depth study of the dynamics problem of the doubly periodic arrays of cracks. (C) 2019 Elsevier Inc. All rights reserved.
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