A DISLOCATION-BASED MULTISCALE MODELING OF PLASTICITY AND CONTROLLING MECHANISMS
Taheri Nassaj, Nasrin
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The objective of this research is to investigate the plastic deformation and its controlling mechanisms in order to model and predict the material microstructure either dislocation pileups as a feature of plasticity or spatio-temporal dislocations pattern as another feature of plastic deformation using a hierarchical multiscale modeling approach from discrete dislocation dynamic to continuum dislocation dynamics and continuum mechanics. Investigation of size-dependent phenomenon in single crystals as well as polycrystals is the other objective of this research. We studied this size effect at small scales using the dislocation pileups within a stress-gradient plasticity theory and also using a continuum dislocation dynamic model coupled with a viscoplastic self-consistent (VPSC) model by introducing strain-gradient plasticity and stress-gradient plasticity models, also a combined model into viscoplasticity theory. In strain-gradient plasticity, the length scale controlling size effect has been attributed to so-called geometrically necessary dislocations. This size dependency in plasticity can also be attributed to dislocation pileups in source-obstacle configurations. This has led to the development of stress-gradient plasticity models in the presence of stress gradients. In this work, we re-examine this pileup problem by investigating the double pileup of dislocations emitted from two sources in an inhomogeneous state of stress using both discrete dislocation dynamics and a continuum method which resulted in a dislocation-based stress-gradient plasticity model, leading to an explicit expression for flow stress. Our findings show that this expression depends on obstacle spacing, as in the Hall–Petch effect, as well as higher-order stress gradients. In addition, we developed a physically-based mesoscale model for dislocation dynamics systems to predict the deformation and spontaneous formation of spatio-temporal dislocation patterns over microscopic space and time. This mesoscale model includes a set of nonlinear partial differential equations of reaction-diffusion type. Here we consider the equations within a one-dimensional framework and analyze the stability of steady-state solutions for these equations to elucidate the associated patterns with their intrinsic length scale. The numerical solution to the model in one-dimension as well as two-dimension yields the spatial distribution of dislocation patterns over time.
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