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Concurrent multiscale modeling and theory of solute-strengthening for dilute and complex concentrated alloys

Shankha Nag

Under common processing conditions, both dilute and complex concentrated alloys are often realized as random alloys, with no correlation in the occupancy of lattice sites by the constituent atom types. The current thesis primary addresses two problems in random alloys, namely (1) the application of concurrent multiscale modeling and (2) solute-strengthening. For accurate functioning of a forced-based atomistic-continuum (a/c) couple, it is important that the underlying material description of the two domains are the same near the a/c interface. A/c coupling of random alloys violates this criterion since the atomistic domain is inherently inhomogeneous with local fluctuations in atomic configuration and elastic stiffness, while the continuum is defined with the average elastic constants of the alloy. The resulting coupling errors are of the order of 100 MPa in long-range spurious stresses and spurious stress fluctuations near the interface. Two methods of constructing the coupled problem are proposed in this thesis to mitigate coupling errors. In Method 1, the pad atoms are relaxed with respect to the atoms in the atomistics domain in the initial construction of the a/c couple, which eliminates spurious stresses in absence of external loading. Negligible spurious stresses (â 5 MPa) arise on loading the coupled problem. Method 2 replaces the random pad atoms with average atoms, thus explicitly eliminating fluctuations in the pad region which causes coupling errors. This methods also yield coupling errors of â 5 MPa, which are negligible relative to stresses arising in realistic mechanical problems of interest. The latter part of the thesis deals with solute-strengthening in random alloys. In random alloys, strengthening is caused by the pinning of dislocation segments in favourable solute environments. The length scales of dislocation undulation and the energy barrier for unpinning local segments are controlled by solute-dislocation interactions (SDIs) and solute-solute interactions (SSIs). The SDIs are modeled as the interaction of solute misfit volume with dislocation pressure field, under anisotropic elasticity assumption. Comparison of the anisotropic theory with isotropic theory shows that the Voigt-averaged elastic constants best reproduce the anisotropic predictions. SSIs are accounted for in the strengthening theory and it is found to cause significant additional strengthening (â 70% at 10% Al) in dilute Ni(Al) alloys with strong Al-Al repulsion, but only a negligible increase in strength (â 2%) in bcc MoNbTaW complex alloy with larger solute misfit volumes and lower SSIs. Finally, the thesis also studies the role of short-range order (SRO) on alloy strengthening and predicts the average strengthening due to SRO, in terms of solute pair interaction energies, the well-known Warren-Cowley SRO parameters and alloy composition. The theory accounting for SRO is in progress, however, the theory in its current state lays the groundwork for realizing the most comprehensive strengthening theory for alloys of any compositional complexity.

EPFL2020

Effect of solute-solute interactions on strengthening of random alloys from dilute to high entropy alloys

William Curtin, Shankha Nag

The yield strength of random metal alloys, i.e. alloys with random occupation of the crystalline lattice sites by the elemental constituent atoms all considered as solutes, is primarily understood as controlled by solute/dislocation interactions. Solute-solute interactions exist and provide the energetic driving force for both short-range and long-range order but can then also affect yield strength even in the random alloy. Here, a recent theory for random alloys is extended to include solute-solute interactions described by pair-wise interactions. The new theory involves the standard deviation in total solute-solute interaction energies as a dislocation segment glides through the material, which changes specific solute-solute pairs across the glide plane at every pair distance. An analytic expression is derived for the above standard deviation and validated against numerical simulations on a wide range of model random alloys consisting of 2-5 elements interacting via Lennard-Jones pair potentials. The theory is applied to the bcc MoNbTaW high entropy alloy, using solute-solute interactions computed via first-principles, and a model NbTaV alloy, described by EAM potentials, where the strength increases negligibly by 2% and 0.45%, respectively. Application to random dilute fcc Ni-Al, where the first-neighbor Al-Al interaction is very strongly repulsive, shows significant strengthening of 60-100% at 10% Al, depending on the origin of the inputs. Some connections to literature atomistic simulations on Ni-Al are also presented. Overall, the present theory provides a quantitative framework for assessing the relative roles of solute-dislocation and solute-solute interactions on strengthening in random alloys. (C) 2020 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

PERGAMON-ELSEVIER SCIENCE LTD2020