Elastic energy of slit cracks in hexagonal crystals
The elastic energy of a two-dimensional slit crack in an infinite linear-elastic medium may be given by E = 1/2 ..integral../sub -a//sup a/sigma/sub i2/..delta..u/sub 'i/dx/sub 1/, where a Cartesian coordinate system for the slit crack is chosen such that parallel x/sub 1/ parallel < a,x/sub 2/ = 0, - infinity < x/sub 3/ < infinity, the crack width is 2a,sigma/sub i2/ denotes a component of the applied stress, and ..delta..u/sub i/ is a component of the displacement discontinuity across the crack plane x/sub 2/ = 0. The formal treatment of the elastic energy in a general anisotropic medium has been given by Stroh who used the method of Fourier transforms and dual integral equations, and more recently by Barnett and Asaro who used the method of a double-ended pile-up of continuously distributed infinitesimal dislocations. In the special case when the applied stresses are uniform, the elastic energy is E = -..pi../2 a/sup 2/B/sub ij/sigma/sub i2/sigma/sub j2/, and the crack extension force is G = par. delta E/par. delta a = ..pi..aB/sub ij/sigma/sub i2/sigma/sub j2/, where B/sub ij/ is the symmetrical second-rank tensor, the elastic compliance factor, which depends only on the elastic constants and the orientation of a crack. The crack extension forces for mode I (opening), mode II (shearing), and mode III (tearing) are G/sub I/ = ..pi..a sigma/sub 22/ (B/sub 22/sigma/sub 22/ + B/sub 23/sigma/sub 23/ + B/sub 12/sigma/sub 12/), G/sub II/ = ..pi..a sigma/sub 12/(B/sub 11/sigma/sub 12/ + B/sub 12/sigma/sub 22/ + B/sub 13/sigma/sub 23/), G/sub III/ = ..pi..a sigma/sub 23/(B/sub 33/sigma/sub 23/ + B/sub 13/sigma/sub 12/ + B/sub 23/sigma/sub 22/).
- Research Organization:
- Oak Ridge National Lab., TN
- OSTI ID:
- 6410264
- Journal Information:
- Scr. Metall.; (United States), Vol. 13:2
- Country of Publication:
- United States
- Language:
- English
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