ICME Multi-scale Modeling of Copper-Tantalum Nanocrystalline Material

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The proposed research aims to explore the stress-strain response of a copper-tantalum (Cu-Ta) nanocrystalline material by implementing a multiscale approach. By design, nanocrystalline materials achieve high hardness values by exploiting the Hall-Petch relationship and suppressing grain growth. In the Cu-Ta alloy, the suppression of grain growth has been attributed to the low solubility of tantalum in copper. However, the observed resiliency to grain growth has been profound. A nanocrystalline material of copper and 10 at.% tantalum maintained an average grain size of 111 nm up to 1173 K, 87% of the melting point of copper [1]. The effectiveness of the suppression of grain growth during deformation has not been addressed.


T. Frolov et al. [1] performed (MD) simulations of a small nanocrystal with dimensions of 11 x 15 x 10 nm3 to observe the thermal stability of Cu- 6.5 at.% Ta. The interatomic potentials of copper and tantalum were based of the potentials for pure copper and pure tantalum. MD simulations were performed of uniformly distributed Ta at 750 K, 1000 K, 1100 K, and 1200 K. Results of the simulations showed the tantalum atoms remaining uniformly distributed at 750 K, diffusing to the grain boundaries of copper at 1000 K and 1100K, and dispersed clusters as the copper liquefied at 1200 K. The suppression of grain growth was determined to be caused by migration of tantalum to the copper grain boundaries thus increasing the thermal stability. However, the effects of strain on grain size stability has not been addressed.
Multiscale modeling diagram example for the Cu-Ta nanocrystalline material. The diagram distinguishes the information passed between the different length scales.

Multiscale Approach

The framework for developing the stress-strain curve will consist of four different length scales due to the lack of computational resources. Because the grain-boundary-area-to-volume ratio is large, the highest length scale will consist of a crystal plasticity (CP) formulation. In order to determine the hardness rules required by the crystal plasticity model, simulations of dislocation motion and interaction will be conducted using the dislocation dynamics (DD) method. The mobility of dislocations required for the DD method subdivides into dislocation mobility in pure copper, pure tantalum, and grain boundaries. Molecular dynamics (MD) simulations using calibrated modified embedded atom method (MEAM) potentials will provide the mobility of dislocations of each category. Lattice parameter, general stacking fault energy (GSFE), cohesive energy, and elastic modulus of copper and tantalum are calculated by solving Schrödinger’s equation using density functional theory (DFT) to calibrate MEAM potentials.


  1. 1.0 1.1 T. Frolov, K.A. Darling, L.J. Kecskes, and Y. Mishin, Stabilization and strengthening of nanocrystalline copper by alloying with tantalum, Acta Materialia, vol. 60, pp. 2158-2168, 2012.
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