Abstract
The problem of the interaction of a crack and a dislocation in a medium with a nonlinear stress-strain law is considered for the case of a semi-infinite crack in a displacement loaded strip under longitudinal shear deformation. A power law stress-strain relation is considered and the dislocation is assumed positioned so that the net effect of its interaction with the crack is to produce a zero stress intensity factor when combined with the effect of the applied displacements. Thus the Atkinson-Kay superdislocation model of a relaxed crack tip is extended to the situation where the material satisfies a power-law stress-strain relationship.
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References
Louat, N.P., Proc. 1st Intl. Conf. on Fracture, Sendai, Japan, (1965).
AtkinsonC., Int. Jnl. Fracture Mechanics, 2 (1966) 567–575.
AtkinsonC. & KayT.R., Acta Met., 19 (1971), 679–685.
AtkinsonC. & ClementsD.L., Acta Met., 21 (1973) 55–60.
AtkinsonC. & KanninenM.F., Int. Jnl. Fracture, 13 (1977) 151–163.
BilbyB.A., CottrellA.M. & SwindenK.H., Proc. Roy. Soc., Ser. A., 272 (1963) 304–314.
DugdaleD.S., J. Mech. Phys. Solids, 8 (1960) 100–104.
AtkinsonC. & ChampionC.R., Q. Jl. Mech. Appl. Math., 37 (1984) 401–419.
EshelbyJ.D., J. Elasticity, 5 (1975) 321–335.
AmazigoJ.C., Int. J. Solids Structures, 10 (1974) 1003–1015.
ChampionC.R. & AtkinsonC. Q. Jl. Mech. Appl. Math., 38 (1985) 461–483.
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Champion, C.R., Atkinson, C. On the interaction between a dislocation and a crack in a material with a nonlinear stress-strain law. J Elasticity 16, 349–365 (1986). https://doi.org/10.1007/BF00041760
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DOI: https://doi.org/10.1007/BF00041760