Role of Self-Organization of Dislocations in the Onset and Kinetics of Macroscopic Plastic Instability
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DUCTION
THE interaction of dislocations with solute atoms in dilute alloys can lead to instability of uniform plastic flow. This phenomenon, known as the Portevin–Le Chatelier effect (PLC),[1] is manifested by jerky deformation curves and strain localization in deformation bands.[2,3] The generally accepted mechanism of the PLC effect is based on the concept of dynamic strain aging (DSA) considering solute pinning of mobile dislocations arrested on obstacles during the waiting time tw for thermal activation.[4–15] Due to such additional pinning, the strain-rate sensitivity (SRS) of the flow stress r, Sf ¼ ð@r=@ lnð_ep ÞÞep ;T , becomes negative in a certain range of strain ep , strain rate, and temperature T, thus giving rise to instability.[5] One of the long-standing challenges concerns an adequate description of the critical conditions for onset of plastic instability, in particular, the critical strain ec . Early models based on the DSA predicted the so-called ‘‘normal’’ behavior consisting of an increase in ec with an increase in the applied strain rate e_ a or a decrease in temperature.[6–8] Experimental studies showed a nonmonotonic dependence including ‘‘inverse’’ behavior at low e_ a -values (e.g., References 9, 16, and 17). Although
NIKOLAY P. KOBELEV is with Institute of Solid State Physics, Russian Academy of Sciences, Chernogolovka, Russia 142432. MIKHAIL A. LEBYODKIN and TATIANA A. LEBEDKINA are with Laboratoire d’Etude des Microstructures et de Me´canique des Mate´riaux (LEM3), UMR CNRS 7239, Universite´ de Lorraine, Ile du Saulcy, 57045 Metz Cedex 01, France. Contact e-mail: [email protected] Manuscript submitted July 24, 2016. Article published online January 3, 2017 METALLURGICAL AND MATERIALS TRANSACTIONS A
the latter can be caused by specific mechanisms, e.g., associated with precipitates,[18] non-monotonic behavior was recently explained in a unique framework of DSA modified to allow for its dependence on strain.[19,20] In spite of this success, several fundamental issues were not fully addressed. It was shown quite early that the negative value of SRS does not suffice to generate a macroscopic instability because a finite time is needed for the strain rate to localize into a deformation band.[6] In McCormick,[6] the conditions of the growth of a local perturbation of the uniform strain state were examined to find criteria for the onset of flow localization. An important feature of the model is a characteristic relaxation time s for the SRS, which is of the order of tw and can be estimated from the transient kinetics of the flow stress upon abrupt changes in e_ a . The linear stability analysis provided two new criteria corresponding to either oscillating or exponential growth of the small perturbation, respectively, at eu and eh , where eh >eu >e0 , and e0 is the critical strain obtained for the condition Sf < 0. The available experimental data for ec were found to lie between these two criteria. Recent finite-element modeling rendered ec values rather close to eh .[20] In any case, the ph
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