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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Grahic Jump Location
An elastic body under traction T in (a) and T in (b)
Grahic Jump Location
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.)
Grahic Jump Location
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+
Grahic Jump Location
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.)
Grahic Jump Location
Two different microscopic deformation mechanisms could produce the same macroscopic damage shear strain component ε̄12D
Grahic Jump Location
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.)
Grahic Jump Location
Arbitrary macroscopic stress components σ̄11o in (a) and σ̄22o=σ̄33o in (b) applied to the undamaged unidirectional composite
Grahic Jump Location
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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