The relation between dislocation density and stress

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Read has recently derived for the special case of simple bending a relation between the lattice curvature and stress gradient in a solid containing dislocations. It is shown that this relation follows at once from the fundamental relation in the theory of continuous distributions of dislocations. As a further example the relations between the stress gradient, dislocation density and lattice curvature in twisted cylindrical bars are given. It is also shown that the properties of linear dislocation arrays used by Read follow from the general expression for the dislocation tensor of a surface dislocation.