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Plastic deformation in crystalline materials results from the nucleation and non conservative motion of line defects called dislocations. Understanding the mechanical behavior metals requires an explicit treatment of dislocations. In the MMST the dislocation ensemble is represented by means of a scalar phase field, the value of which at a point of the slip plane represents the extent of slip on units of the Burgers vector. The phase field is an integer and its value records the number of dislocations, with their sign, that have crossed the point. The location of a dislocation line is associated with integer jumps in the value of the scalar field.
The model accounts for an arbitrary number and arrangement of dislocations over a slip plane, the long range elastic interactions between dislocation lines, the interaction of dislocations with obstacles and with an external applied stress.
The phase-field model of dislocations enables to simulate the nucleation and evolution of dislocations in ductile single crystals under cyclic and monotonic loading. The user can choose the initial configuration and simulate the evolution of dislocations under an external applied stress.
Dislocations may be individually tracked enabling the observation of the evolution of the dislocation ensemble, including nucleation of dislocations and the formation of Orowan loops and dislocation piles ups. At the same time characteristic features of the macroscopic response can be predicted, including strain hardening, dislocation multiplication under monotonic loading, Bauschinger effect, path dependency and hysteresis.
Code developed by Marisol Koslowski's group in Mechanical Engineering, Purdue University
This work was funded by NSF's Network for Computational Nanotechnology.
Research code development is supported with funds form DOE-Basic Energy Sciences, NSF-CMMI and NNSA.
The tool operation and its underlying physics is described in an associated nano 501 lecture entitled Plastic Deformation at Micron and Submicron Scales.