Crack-tip field on mode II interface crack of double dissimilar orthotropic composite materials

Abstract

Two systems of non-homogeneous linear equations with 8 unknowns are obtained. This is done by introducing two stress functions containing 16 undetermined coefficients and two real stress singularity exponents with the help of boundary conditions. By solving the above systems of non-homogeneous linear equations, the two real stress singularity exponents can be determined when the double material parameters meet certain conditions. The expression of the stress function and all coefficients are obtained based on the uniqueness theorem of limit. By substituting these parameters into the corresponding mechanics equations, theoretical solutions to the stress intensity factor, the stress field and the displacement field near the crack tip of each material can be obtained when both discriminants of the characteristic equations are less than zero. Stress and displacement near the crack tip show mixed crack characteristics without stress oscillation and crack surface overlapping. As an example, when the two orthotropic materials are the same, the stress singularity exponent, the stress intensity factor, and expressions for the stress and the displacement fields of the orthotropic single materials can be derived.

The Fracture Analysis around Anti-plane Crack in An Infinite Piezoelectric Plate

“…Thus, near the crack tip, it can be seen that (19) where r is polar radius and θ is polar angle, as shown in figure 1.…”

“…Wang, Liu, Zhang and Jaroon analyzed intensity factor around the crack embedded in an infinite piezoelectric material under a far-field anti-plane mechanical load and a far-field in-plane electrical load using permeable boundary condition [13][14][15][16] . Using the complex variable function method and the technique of the conformal mapping, Xue, Lu and Guo discussed the fracture problem of two semi-infinite collinear cracks in a piezoelectric strip under the anti-plane shear stress and in-plane electric load on the partial crack surface [17][18][19] . The stress intensity factors (SIFs) of interface crack in a piezoelectric bi-material is found by a combination of the Stroh formalism and the Williams eigenfunction method [20][21][22] .…”

Fracture analysis of mode-II crack perpendicular to imperfect bimaterial interface

“…Besides, a pure mode-II crack was dominated under some conditions shown by some experimental and theoretical results [25][26] , and the crack-tip field for a mode-II interface crack was obtained [27] . In the present paper, the problem of a mode-II crack perpendicular to an imperfect interface of two bonded dissimilar materials is considered.…”

Mode III Stress Singularity Analysis of Isotropic and Orthotropic Bi-material near the Interface End

“…By solving the above systems of non-homogeneous linear equations, the two real stress singularity exponents can be determined when the double material parameters meet certain conditions. The expression of the stress function and all coefficients are obtained based on the uniqueness theorem of limit [7].…”