The Modified Void Nucleation and Growth Model (MNAG) for Damage Evolution in BCC Ta

Jie Chen,Saryu J Fensin,Darby J Luscher

doi:10.3390/app11083378

Abstract

A void coalescence term was proposed as an addition to the original void nucleation and growth (NAG) model to accurately describe void evolution under dynamic loading. The new model, termed as modified void nucleation and growth model (MNAG model), incorporated analytic equations to explicitly account for the evolution of the void number density and the void volume fraction (damage) during void nucleation, growth, as well as the coalescence stage. The parameters in the MNAG model were fitted to molecular dynamics (MD) shock data for single-crystal and nanocrystalline Ta, and the corresponding nucleation, growth, and coalescence rates were extracted. The results suggested that void nucleation, growth, and coalescence rates were dependent on the orientation as well as grain size. Compared to other models, such as NAG, Cocks–Ashby, Tepla, and Tonks, which were only able to reproduce early or later stage damage evolution, the MNAG model was able to reproduce all stages associated with nucleation, growth, and coalescence. The MNAG model could provide the basis for hydrodynamic simulations to improve the fidelity of the damage nucleation and evolution in 3-D microstructures.

Highlights

Ductile metals fail by nucleation of voids at weak regions in the microstructure followed by growth and coalescence of these voids until complete failure
The void nucleation term contributed to a steady increase in the total damage at the initial stage where void nucleation was dominant
The performance of a few common damage models was compared to the void number density and damage calculated from molecular dynamics (MD) simulations using shock-loaded singlecrystal and nanocrystalline Ta as model systems

Summary

Introduction

Ductile metals fail by nucleation of voids at weak regions in the microstructure followed by growth and coalescence of these voids until complete failure. In this process, many contributing factors, including the exact loading condition (which determines the stress history), the weak spots (heterogeneities such as pre-existing and as-nucleated defects and grain boundaries that act as void nucleation sites), as well as the required stress at which voids start to nucleate and grow, dictates where, when, and at what rate damage accumulates in the microstructure and the overall failure behavior. Many efforts have been devoted to understanding damage nucleation and evolution under such loading conditions [1,2]

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