The Hall-Petch relationship in metals is investigated using the strain gradient plasticity theory within the finite deformation framework. For this purpose, the thermodynamically consistent constitutive formulation for the coupled thermomechanical gradient-enhanced plasticity model is developed. The corresponding finite element method is performed to investigate the characteristics of the Hall-Petch relationship in metals. The proposed model is established based on an extra Helmholtz-type partial differential equation, and the nonlocal quantity is calculated in a coupled method based on the equilibrium conditions. An excellent agreement between the simulation results and the test data is resulted in the Hall-Petch graph. Furthermore, it is observed that the Hall-Petch constants do not remain unchanged but vary with the strain level.
Song, Yooseob, "Investigation of the Hall-Petch Relationship Using Strain Gradient Plasticity Model for Finite Deformation Framework" (2020). Civil Engineering Faculty Publications and Presentations. 17.
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Journal of Materials and Applications