Elsevier

Acta Materialia

Volume 56, Issue 15, September 2008, Pages 4046-4061
Acta Materialia

Solute strengthening of both mobile and forest dislocations: The origin of dynamic strain aging in fcc metals

https://doi.org/10.1016/j.actamat.2008.04.027Get rights and content

Abstract

A full rate-dependent constitutive theory for dynamic strain aging is developed based on two key ideas. The first idea is that both solute strengthening and forest strengthening must exist and must exhibit aging phenomena. The second idea is that a single physical aging mechanism, cross-core diffusion within a dislocation core, controls the aging of both the solute and forest strengthening mechanisms. All the material parameters in the model, apart from forest dislocation density evolution parameters, are derivable from atomistic-scale studies so that the theory contains essentially no adjustable parameters. The model predicts the steady-state stress/strain/strain-rate/temperature/concentration dependent material response for a variety of Al–Mg alloys, including negative strain-rate sensitivity, in qualitative and quantitative agreement with available experiments. The model also reveals the origin of non-additivity of solute and forest strengthening, and explains observed non-standard transient stress behavior in strain-rate jump tests.

Introduction

In a companion paper [1], it was shown that a proper rate theory for thermally activated dislocation motion involving a single rate-dependent dislocation strengthening mechanism is unable to predict a regime of negative strain-rate sensitivity (nSRS), defined as m=d(ln(τ))/d(ln(ε˙)), where τ is the stress, and ε˙ is the strain rate. Previous theories [2], [3], [4], [5], [6], [7], [8], [9] have made invalid simplifications in the rate theory and assumptions in the underlying physics such that nSRS is predicted, as discussed in the companion paper, but such theories lack a direct connection to physical mechanisms of dynamic strain aging or to material parameters. Thus, while exhibiting features consistent with experiments, the theories remain phenomenological and are not predictive. Here, the analysis in the companion paper is extended in a crucial way by the incorporation of two concurrent strengthening mechanisms, solute strengthening and forest hardening, each of which is influenced by the same time-dependent mechanism of cross-core solute diffusion proposed by Curtin et al. [10]. That is, solute diffusion simultaneously influences both (i) temporarily arrested but otherwise mobile dislocations and (ii) forest dislocations formed during the plastic deformation. Solute strengthening controls the overall rate dependence, so that forest hardening enters the theory as a time-, strain- and strain-rate dependent “back-stress” acting on the mobile dislocations. The dynamic solute strengthening of the mobile dislocations assists in achieving overall nSRS by reducing the “normal” positive strain-rate sensitivity (SRS) parameter to nearly zero and also accounts for transients during strain-rate jumps. The dynamic forest strengthening mechanism, previously proposed and analyzed in general by Picu [11], [12], provides a nSRS such that the overall SRS is negative over a range of strain rates and temperatures. The present theory of strain aging thus relates the nanoscale solute/dislocation–core interactions to the macroscopic strain-rate behavior through relatively direct analytical expressions. Assuming a strain-dependent evolution of the forest dislocation density, the study shows that the theory can quantitatively predict the stress–strain behavior and steady-state SRS of Al–Mg alloys as a function of strain rate, plastic strain, temperature and solute concentration. Comparisons with experimental data on Al–Mg alloys show broad quantitative agreement. The model also predicts the well-known but unexplained non-additivity of solute strengthening and forest hardening at low strain rates [13], [14], the origin of which lies in the dynamic strengthening of the forest dislocations. And, the model predicts the transient behavior observed in strain–jump tests, which differs from the canonical behavior and is shown to arise from a combination of aging of the solute strengthening, with a fast transient, and aging of the forest strengthening, with a slower and asymmetric transient. The totality of predictions of the model suggests that the work here represents a major step forward in the understanding and predictability of dynamic strain aging in solute-strengthened materials.

Section snippets

Mobile and forest strengthening and aging

According to the rate-dependent theory described in a companion paper, the general constitutive equation relating the strain rate to the stress and time history for plastic flow due to pinning of dislocations, and including aging phenomena that can occur during the time of pinning, depends on the instantaneous rate of escape of a dislocation from its local pinning points, given byν(τ(t),t,tp)=ν0exp(-ΔE(τ(t),t,tp))Here, ν0 is a microscopic attempt frequency, and ΔE is the energy barrier

Predictions

It is now demonstrated that the constitutive model quantitatively predicts all the trends observed in the SRS of Al–Mg alloys with no adjustable parameters. Specifically, successive sections study the steady-state SRS vs. plastic strain, temperature and solute concentration. This spectrum of results represents various “cuts” through the parameter space of the full constitutive law, and is thus a subset of the full scope of possible results. Then non-steady-state strain-rate-jump tests and

Discussion and summary

This section briefly discusses aspects of the model with respect to previous models, other potential models and experiments, and then summarizes the work.

The collection of equations constituting the present theory appears similar to sets of equations proposed in the recent literature, e.g. Ref. [28]. Those models include some type of underlying rate-dependent phenomena, presumably solute strengthening, but not explicitly stated, a backstress due to forest dislocation strengthening that evolves

Acknowledgments

The authors acknowledge support of this work through the General Motors/Brown Collaborative Research Laboratory on Computational Materials Science and the NSF Materials Science Research and Engineering Center on “Nano and Micromechanics of Materials” at Brown University, Grant DMR-0520651. The authors thank Prof. C. Picu for useful discussions. W.A.C. thanks Prof. A. Benallal for conversations that led to the initiation of this work, performed while W.A.C. was a Visiting Professor at LMT, Ecole

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