Singularities at the Tip of a Crack Terminating Normally at an Interface Between Two Orthotropic Media

[+] Author and Article Information
J. C. Sung, J. Y. Liou

Department of Civil Engineering, National Cheng Kung University, Tainan, Taiwan 70101, R.O.C.

J. Appl. Mech 63(2), 264-270 (Jun 01, 1996) (7 pages) doi:10.1115/1.2788859 History: Received May 26, 1994; Revised March 15, 1995; Online October 26, 2007


The order of stress singularities at the tip of a crack terminating normally at an interface between two orthotropic media is analyzed. Characteristic equation in complex form for the power of singularity s , where 0 < Re{s} < 1, is first set up for two general anisotropic materials. Attention is then focused on the problem that is composed by two orthotropic media where one of them (say, material #2 ) the material principal axes are aligned while the other one (say, material #1) the principal axes can have an angle γ relative to the interface. For such a problem, a real form of the characteristic equation is obtained. The roots are functions of γ in general. Two real roots exist for most values of γ; however, there are possible ranges of γ that the complex roots will occur. The roots s are found to be independent of γ when material #1 has the property that δ(1) = 1. When γ = 0, two roots are always real. Furthermore, each of these two roots is associated with symmetric or antisymmetric mode and they become equal when Δ = 1. Many other features of the effects of the material parameters on the behaviors of the roots s are further investigated in the present work, where the six generalized Dundurs’ constants, expressed in terms of Krenk’s parameters, play an important role in the analysis.

Copyright © 1996 by The American Society of Mechanical Engineers
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