Solute strengthening of both mobile and forest dislocations: The origin of dynamic strain aging in fcc metals
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 , where τ is the stress, and 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 byHere, 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
References (54)
- et al.
Acta Metall Mater
(1990) Mat Sci Eng A
(2005)- et al.
Int J Plasticity
(2004) Acta Mater
(2004)Mat Sci Eng A
(1996)Mat Sci Eng A
(1996)- et al.
J Mech Phys Sol
(2006) - et al.
Acta Metall Mater
(1993) - et al.
Acta Mater
(2004) - et al.
Phys Lett
(1983)
Physics Rep
Mat Sci Eng A
Eur J Mech A/Solids
Mat Sci Eng
Scripta Metall
Acta Mater
Acta Mater
Mat Sci Eng A
Acta Metall
Mat Sci Eng A
Acta Metall
Mat Sci Eng A
Scripta Metall Mater
Acta Metall Mater
Acta Mater
Proc Royal Soc London. Series A, Math Phys Sci
Acta Metall
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