Plane Analysis of Finite Multilayered Media With Multiple Aligned Cracks—Part I: Theory

[+] Author and Article Information
Linfeng Chen, Marek-Jerzy Pindera

Civil Engineering Department, University of Virginia, Charlottesville, VA 22904-4742

J. Appl. Mech 74(1), 128-143 (Apr 01, 2006) (16 pages) doi:10.1115/1.2201883 History: Received December 18, 2005; Revised April 01, 2006

Elasticity solutions are developed for finite multilayered domains weakened by aligned cracks that are in a state of generalized plane deformation under two types of end constraints. Multilayered domains consist of an arbitrary number of finite-length and finite-height isotropic, orthotropic or monoclinic layers typical of differently oriented, unidirectionally reinforced laminas arranged in any sequence in the plane in which the analysis is conducted. The solution methodology admits any number of arbitrarily distributed interacting or noninteracting cracks parallel to the horizontal bounding surfaces at specified elevations or interfaces. Based on half-range Fourier series and the local/global stiffness matrix approach, the mixed boundary-value problem is reduced to a system of coupled singular integral equations of the Cauchy type with kernels formulated in terms of the unknown displacement discontinuities. Solutions to these integral equations are obtained by representing the unknown interfacial displacement discontinuities in terms of Jacobi or Chebyshev polynomials with unknown coefficients. The application of orthogonality properties of these polynomials produces a system of algebraic equations that determines the unknown coefficients. Stress intensity factors and energy release rates are derived from dominant parts of the singular integral equations. In Part I of this paper we outline the analytical development of this technique. In Part II we verify this solution and present new fundamental results relevant to the existing and emerging technologies.

Copyright © 2007 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

A unidirectional composite layer rotated by an angle about axis perpendicular to its plane

Grahic Jump Location
Figure 2

Geometry of the finite multilayered media with multiple aligned cracks

Grahic Jump Location
Figure 3

A finite-dimension layer in the plane of analysis showing two types of end constraints: (a) Left and right ends horizontally pinned; (b) left and right ends vertically pinned





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