A tantalum strength model using a multiscale approach: version 2
A continuum strength model for tantalum was developed in 2007 using a multiscale approach. This was our first attempt at connecting simulation results from atomistic to continuum length scales, and much was learned that we were not able to incorporate into the model at that time. The tantalum model described in this report represents a second cut at pulling together multiscale simulation results into a continuum model. Insight gained in creating previous multiscale models for tantalum and vanadium was used to guide the model construction and functional relations for the present model. While the basic approach follows that of the vanadium model, there are significant departures. Some of the recommendations from the vanadium report were followed, but not all. Results from several new analysis techniques have not yet been incorporated due to technical difficulties. Molecular dynamics simulations of single dislocation motion at several temperatures suggested that the thermal activation barrier was temperature dependent. This dependency required additional temperature functions be included within the assumed Arrhenius relation. The combination of temperature dependent functions created a complex model with a non unique parameterization and extra model constants. The added complexity had no tangible benefits. The recommendation was to abandon the strict Arrhenius form and create a simpler curve fit to the molecular dynamics data for shear stress versus dislocation velocity. Functions relating dislocation velocity and applied shear stress were constructed vor vanadium for both edge and screw dislocations. However, an attempt to formulate a robust continuum constitutive model for vanadium using both dislocation populations was unsuccessful; the level of coupling achieved was inadequate to constrain the dislocation evolution properly. Since the behavior of BCC materials is typically assumed to be dominated by screw dislocations, the constitutive relations were ultimately built using only the screw relations. In light of this, the screw dislocation mobility relation is chosen as the starting point for the present tantalum model. Edge dislocations are not included explicitly in the current model. A significant change from the previous models is in the functional dependence of the dislocation evolution equations. The prior multiscale models assumed that the dislocation evolution rate depended on stress as well dislocation velocity. This crated an implicit dependence on the kinetic relation and required an iterative solution for the dislocation density. In the present model the integration scheme is simplified by casting the dislocation evolution terms of strain rate and current dislocation density. The final notable change was in the transition relation from the thermally activated regime to phonon drag. Historically, and in the prior models, this transition had been through a harmonic average on the strain rates making it impossible to determine the stress directly when given the plastic strain rate. After considering alternative transition relations, it was determined that an equally suitable fit to the molecular dynamics simulation data in the transition region could be constructed by averaging stresses rather than strain rates. The end result of these enhancements is a simpler (fewer parameters) and more straight forward model formulation where the material strength can be evaluated directly when given the plastic strain rate, temperature, pressure and the dislocation density at the beginning of the time step. This greatly improves the computational efficiency and robustness over the prior models where additional iteration loops were required.
- Research Organization:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 967734
- Report Number(s):
- LLNL-TR-417075; TRN: US200924%%169
- Country of Publication:
- United States
- Language:
- English
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