Abstract
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.
Highlights
IntroductionA fine-grained material is stronger and harder than a coarse-grained one
Most of metals and metal alloys have polycrystalline nature
The Hall-Petch relationship and effects of its strengthening on the flow stress in metals are investigated through the strain gradient plasticity model
Summary
A fine-grained material is stronger and harder than a coarse-grained one. This can be described in the relation between grain size and yield stress through the Hall-Petch equation as follow [1, 2]: kk σσyy = σσ0 + √DD (1). Where σσyy denotes the yield stress, σσ0 denotes the material constant related to the resistance of lattice to dislocation motion, kk denotes the Hall-Petch strengthening coefficient, and DD denotes the average grain size. Strain gradient-enhanced flow rules are proposed to investigate the grain-size dependent flow stress of polycrystalline materials. The main aim of this work is to show that the proposed strain gradient-enhanced flow rule well captures the Hall-Petch relation. The two-dimensional finite element solution for finite deformation with considering the temperature effect is used to investigate the Hall-Petch relationship
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