Nonuniform deformations in polycrystals and aspects of the validity of the Taylor model. (English) Zbl 0669.73040
Full solutions to mixed rate boundary value problems over polycrystalline domains are performed via the finite element method. In oder to make these finite element calculations feasible, an idealized two-dimensional crystal structure is studied. These boundary value problems rigorously satisfy the averaging theorems of R. Hill [Proc. R. Soc. London. Ser. A 326, 131-147 (1972; Zbl 0229.73004)] so that well defined Taylor model analogue problems may be identified and solved. Comparisons between the finite element solutions and their corresponding Taylor model analogues yield a quantitative assessment of the Taylor model’s validity with respect to its predictions of texture development and global stress- strain response. The finite element calculations also provide physical insight into the mechanisms contributing to the development of nonuniform and localized deformations in polycrystals.
MSC:
| 74B99 | Elastic materials |
| 74C99 | Plastic materials, materials of stress-rate and internal-variable type |
| 74D99 | Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials) |
| 74H99 | Dynamical problems in solid mechanics |
| 74S05 | Finite element methods applied to problems in solid mechanics |
Keywords:
mixed rate boundary value problems; polycrystalline domains; idealized two-dimensional crystal structure; averaging theorems; Taylor model analogue problemsCitations:
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