Prediction of Plastic Flow by Means of a Continuum Dislocation Approach
ABTRACT A continuum dislocation approach is presented in this paper to model the plastic flow from crystallographic slips. The expression of the plastic strain rate contains two contributions: the first contribution is due to statistically stored dislocations, and the second one is from geometrically necessary dislocations. Furthermore, the plastic strain rate is governed by the dislocation mobility coefficient, and its simplified expression is obtained for one single slip system. The model is used to simulate the response of a Ta BCC single crystal under pure shearing. INTRODUCTION: Conventional theories of plasticity fail to capture the stress-strain behavior in the plastic range when the specimen whose dimensions are about a fraction of a micron to tens of microns is subjected to a strain gradient, or when the specimen contains a specific dislocation structure. The size-dependent behavior was evidenced and modeled by a number of authors such as e.g. [Fleck and Hutchinson, 1997], [Gao et al., 1999]. Conventional theories cannot predict the plastic behavior at the micron scale because they incorporate no material length scale, and consequently, cannot capture the size effect. Starting from the fundamental findings in dislocation theory, which suggest that hardening is due to the combined presence of statistically stored dislocations (SSD) associated with plastic strain and geometrically necessary dislocations (GND) associated with a plastic strain gradient, a continuum modeling approach is presented in this paper to determine the plastic flow from crystallographic slips in single crystals. Furthermore, motivated by a recent discrete dislocation analysis in [Rhee et al., 1998], which has shown the effect of the dislocation mobility on the dislocation structure giving rise to a hardening behavior, the approach developed here attempts to make a link with a discrete dislocation modeling through the mobility coefficient.
- Research Organization:
- Pacific Northwest National Laboratory (PNNL), Richland, WA (US)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC05-76RL01830
- OSTI ID:
- 909485
- Report Number(s):
- PNNL-SA-35386; KJ0200000
- Country of Publication:
- United States
- Language:
- English
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