Abstract
In this paper we formulate the three-dimensional elastic problem of a half plane crack interacting with zones of transformation strain and dislocations. The stress intensity factors induced at the crack tip are discussed. The analysis is based on Rice's (Int. J. Solids Struct.21, 781, 1985b) development, using three-dimensional “weight function” theory, of elastic crack tip interactions with internal stress sources and on Bueckner's (Int. J. Solids Struct.23, 57, 1987) solution for the complete set of weight functions for a half plane crack. The formulae for the shear mode weight functions by Bueckner are simplified significantly. Explicit formulae are given for the intensity factors induced by arbitrarily distributed 3-D transformation strains, which reduce to the solutions known in the literature for 2-D transformation strains. Results are also specified to calculate the intensity factor distribution due to rectangular and semicircular crack-tip dislocation loops, and compared to those previously estimated by Anderson and Rice (J. Mech. Phys. Solids35, 743, 1987). The three-dimensional results are novel and in part II of this series (Gao and Rice, J. Mech. Phys. Solids37, 155, 1989) we use the formulations presented here to calculate the self energy of a 3-D shear dislocation loop emerging from the crack tip.
Published Version
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