By an analytical method, we examine non-uniform multiple slip near a grain boundary plane in fcc bicrystals. To analyse the multiple slip deformation, we develope a new computer code of finite element structure analyses that utilizes models for movement and interaction of dislocations to have a quantitative constitutive relation for fee crystals. In this method, the critical resolved shear stresses for activation of slip systems are assumed to be given by a linear combination of twelve functions that are proportional to 1/2 power of the density of accumulated dislocations on slip systems. And these functions are weighted with constants which represent interaction intensity between dislocations on twelve slip systems.
We analyse deformation of isoaxial bicrystals of nominal strain incompatible type and discuss in detail on the formation process and structure of the multiply slipped region. Results of the analyses are summarized as follows:
(1) At a very early stage of the activation of secondary slip systems, shear strain on the systems is in the order of 10
−7 and it is about 1/100 of the one on the primary system.
(2) At a deformation stage when the nominal strain is about 12 times as large as the one at the elastic limit, the multiply slipped region consists of rather uniform distribution of shear strain on the primary slip system and non-uniform shear strain on the secondary systems. Shear strain on the secondary systems range from 10
−7 to a value comparable to the one on the primary system.
(3) When the interaction intensity between moving and forest dislocations is doubled, the growing rate of the multiple slip region and shear strain on the secondary systems are reduced to about 1/1.6 and 1/2, respectively.
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