Predicting the Hall-Petch Effect in FCC Metals Using Non-Local Crystal Plasticity

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Counts, William A.
Saxena, Ashok
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It is well documented that the mechanical response of polycrystalline metals depends on the metal's microstructure, for example the dependence of yield strength on grain size (Hall-Petch effect). Local continuum approaches do not address the sensitivity of deformation to microstructural features, and are therefore unable to capture much of the experimentally observed behavior of polycrystal deformation. In this work, a crystal plasticity model is developed that predicts a dependence of yield strength on grain size without grain size explicitly entering into the constitutive equations. The grain size dependence in the model is the result of non-local effects of geometrically necessary dislocations (GNDs), i.e. GNDs harden both the material at a point and the surrounding material. The conventional FeFp kinematics for single crystals have been augmented based on a geometric argument that accounts for the grain orientations in a polycrystal. The augmented kinematics allows an initial GND state at grain boundaries and an evolving GND state due to sub-grain formation within the grain to be determined in a consistent manner. Numerically, these non-local affects are captured using a non-local integral approach rather than a conventional gradient approach. The non-local crystal plasticity model is used to simulate the tensile behavior in copper polycrystals with grain sizes ranging from 14 to 244 micron. The simulation results show a grain size dependence on the polycrystal's yield strength, which are qualitatively in good agreement with the experimental data. However, the Hall-Petch exponent predicted by the simulations is more like d-1 rather than d-0.5. The effects of different simulation parameters including grain shape and misorientation distribution did not greatly affect the Hall-Petch exponent. The simulation results indicate that the Hall-Petch exponent is sensitive to the grain boundary strength: the Hall-Petch exponent decreases as grain boundary strength decreases. The intragrain misorientations predicted by the non-local model were compared with experiments on polycrystalline nickel. Experimentally, the intragrain misorientations were tracked by electron back scatter diffraction (EBSD) at various strain levels from the same location. On average, the simulation results predicted enough misorientation throughout the sample. However, the model did not correctly predict the spatial details of the intragrain misorientation.
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