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Predicting the Hall-Petch effect in fcc metals using non-local crystal plasticity. (English) Zbl 1154.74007

Summary: Many conventional continuum approaches to solid mechanics do not address the size sensitivity of deformation to microstructural features like grain boundaries, and are therefore unable to capture much of the experimentally observed behavior of polycrystal deformation. We propose a non-local crystal plasticity model, in which the geometrically necessary dislocation (GND) density is calculated using a non-local integral approach. The model is based on augmented \(\mathbf F^{\mathbf e}\mathbf F^{\mathbf p}\) kinematics, which account for the initial microstructure (primarily grain boundaries) present in the polycrystal. With the augmented kinematics, the initial GND and the evolving GND state are determined in a consistent manner. The expanded kinematics and the non-local crystal plasticity model are used to simulate the tensile behavior in copper polycrystals with different grain sizes ranging from \(14\, \mu \)m to \(244\, \mu \)m. The simulation results show a grain size dependence on the polycrystal’s yield strength, which are in good agreement with the experimental data.

MSC:

74C99 Plastic materials, materials of stress-rate and internal-variable type
74E15 Crystalline structure
74S05 Finite element methods applied to problems in solid mechanics
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