Geodesic
Interaction of cracks in an elastic two-component material under anti-plane shear loading
Matematičeskaâ fizika i kompʹûternoe modelirovanie, no. 3 (2016), pp. 53-62

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The paper deals with a problem of the interaction of an interface crack with internal cracks in two-component materials (bimaterials) subjected to antiplane shear loading. The problem is formulated by means of the singular integral equations, where the unknowns are the derivatives of displacement jumps on the crack lines. The regular kernels of the equations contain the geometry of the problem, i.e. the coordinates of the crack centers, the inclination angles of the cracks to the interface and crack lengths. The singular integral equations were solved numerically using the quadrature formulas based on the Chebyshev polynomials. Then, the stress intensity factors Mode III (shear mode) were obtained. The stress intensity factors (SIFs) are the local characteristics of the stress-strain state in the vicinity of the crack tips. The higher SIF—the higher stresses are near the crack tips. If the SIF exceeds the critical value, the crack starts to propagate. At the same time the small crack near the interface crack tip can suppress the crack propagation and it was observed for some crack arrangements and for some combination of the materials in the considered problem. A parametric analysis of the effects of the location and orientation of the internal cracks on the SIF in the interface crack tips was performed for different shear moduli of the constituent materials. The following combinations of the materials were considered: $\mathrm{Al_2 O_3/Ni, Al_2 O_3/SiC, TiC/Al, Al_2 O_3/ZrO_2, TiC/SiC}$. It was shown that the SIFs in the interface crack tip can be amplified or shielded by the internal cracks, besides, the shear moduli of the constituent materials notably affect the SIFs of the interface crack.
Mots-clés : interface
Keywords: shear modulus, stress intensity factor, anti-plane shear loading, singular integral equation. 
@article{VVGUM_2016_3_a5,
     author = {M. G. Ordyan and V. E. Petrova},
     title = {Interaction of cracks in an elastic two-component material under anti-plane shear loading},
     journal = {Matemati\v{c}eska\^a fizika i kompʹ\^uternoe modelirovanie},
     pages = {53--62},
     publisher = {mathdoc},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VVGUM_2016_3_a5/}
}
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M. G. Ordyan; V. E. Petrova. Interaction of cracks in an elastic two-component material under anti-plane shear loading. Matematičeskaâ fizika i kompʹûternoe modelirovanie, no. 3 (2016), pp. 53-62. http://geodesic.mathdoc.fr/item/VVGUM_2016_3_a5/