Gradient-dependent deformation of two-phase single crystals. (English) Zbl 0994.74012
Summary: We propose a gradient- and rate-dependent crystallographic formulation to investigate the macroscopic behaviour of two-phase single crystals. The slip-system-based constitutive formulation relies on strain-gradient concepts to account for the additional strengthening mechanism associated with the deformation gradients within a single crystal with a high volume fraction of dispersed inclusions. The resulting total slip resistance in each active system is assumed to be due to a mixed population of forest obstacles arising from both statistically stored and geometrically necessary dislocations. The non-local theory is implemented numerically into the finite element method, and is used to investigate the effect of relevant microstructural (i.e., size and volume fraction of precipitated inclusions) and deformation-gradient-related length scales on the macroscopic behaviour of a typical nickel-based superalloy single crystal. We also propose an analytical framework to link the strain-gradient effects at the microscopic level with macroscopic behaviour of an equivalent homogeneous single crystal.
MSC:
| 74E15 | Crystalline structure |
| 74C10 | Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity) |
| 74S05 | Finite element methods applied to problems in solid mechanics |
Keywords:
constitutive behaviour; crystal plasticity; inclusion; gradient- and rate-dependent crystallographic formulation; two-phase single crystals; strain-gradient concepts; deformation gradients; non-local theory; finite element method; nickel-based superalloyReferences:
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