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The Quarterly Journal of Mechanics and Applied Mathematics 1993 46(4):627-642; doi:10.1093/qjmam/46.4.627
© 1993 by Oxford University Press
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ON THE INTERACTION OF A SCREW DISLOCATION WITH A UNIFORM SHEAR FIELD IN A MATERIAL WITH A NONLINEAR STRESS—STRAIN LAW

C. R. CHAMPION

( Department of Mathematics, Imperial College London SW7 2AZ )

The interaction of a uniform shear field with a screw dislocation in a nonlinear elastic material is considered. For general isotropic stress—strain laws, the correction to the field at infinity is found, to leading order, and the virtual force on the dislocation is shown to be the same as for a linear material. It is noted that the correction to the stress field at the dislocation core is not, in general, equal to the stress applied at infinity, as would be true in the linear case. Exact solutions are obtained for two separate stress-strain laws, and these solutions are used to obtain the force on the dislocation by a local analysis near the dislocation core, with the results agreeing with the general case. It is noted that these simple results do not carry over to more general loading situations.


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