Deformation of Inhomogeneous Elastic Solids With Two-Dimensional Damage

[+] Author and Article Information
J. J. Luo, I. M. Daniel

Robert R. McCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL 60208

J. Appl. Mech 68(4), 528-536 (Jan 01, 2001) (9 pages) doi:10.1115/1.1380384 History: Received March 20, 2000; Revised January 01, 2001
Copyright © 2001 by ASME
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An elastic body under traction T in (a) and T in (b)
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A representative volume element in a solid with crack-like brittle damage occurring on two-dimensional surfaces. (The damage surfaces can be curved and possibly opened by the load T . Typical sizes of the damage and constituents are assumed to be much smaller than the element size.)
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Solid with crack-like damage in (a) damaged configuration with or without friction and sliding, and (b) undamaged configuration with fictitious damage surfaces recovered or closed by tractions To on Sk, and −To on Sk+
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For homogeneous materials the macroscopic damage strain component ε̄11D is equivalent to the damage deformation tensor component β11 which is the crack-opening volume ratio in the x1-direction. (Note that ε̄22D=ε̄33D2233=0 when all damage surface normals are in the x1-direction.)
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Two different microscopic deformation mechanisms could produce the same macroscopic damage shear strain component ε̄12D
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Common damage modes in unidirectional brittle matrix composites under longitudinal tension: matrix cracking (mode M), interface debonding/sliding (mode I), and fiber breakage (mode F). (The theory does not require the matrix crack spacing, interface debonding length, or fiber break spacing to be uniform or periodic.)
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Arbitrary macroscopic stress components σ̄11o in (a) and σ̄22o=σ̄33o in (b) applied to the undamaged unidirectional composite
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Stress-strain curves and calculated crack-opening volume ratios βm and βi of two batches of unidirectional composite (SiC/CAS) under longitudinal tension




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