Fluctuation-Induced Nucleation of PLC Bands
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Fluctuation-Induced Nucleation of PLC Bands P. Sapalidis1, D. Dodou1, P. Hahner2, M. Zaiser3 and E.C. Aifan tis1;4 1
Aristotle Univ ersity of Thessaloniki, Polytechnic School, 54006 Thessaloniki, Greece
2 European Commission, JR C-IAM, P .O. Box 2, NL-1755ZG Petten, The Netherlands 3 Max-Planc k-Institut f ur Metallforsc hung, Heisenbergstr. 1, D-70569 Stuttgart, German 4 Center for the Mec hanics of Materials and Instabilities, Mic higan echnological T
y
University, Houghton, MI 49931
ABSTRACT The in uence of mesoscopic strain-rate uctuations on the n ucleation of localized deformation bands (PLC bands) in dynamically strain ageing materials is discussed. It is shown that uctuations ma y lead to a macroscopic localization of plastic ow even if linear stability analysis (LSA) of the macroscopic constitutiv e equations predicts stable deformation beha vior. The resulting quantitative corrections to linear stability analysis are evaluated, and implications for the reliabilit y of LSA results are discussed.
INTR ODUCTION
The deformation of man y alloys is, in a certain range of temperatures and strain rates, characterized by serrations in the stress-strain curves which go along with the formation of localized deformation bands. This so-called P ortevin-le Chatelier phenomenon is explained by the interaction of mobile dislocations with di using solute atoms which may lead to a negative strain-rate sensitivity of the ow stress [1,2] and a behavior that is very similar to stick-slip instabilities associated with negative di erential friction. While early models [3] of the PLC phenomenon have used a single constitutive equation relating ow stress, strain, and strain rate, it has become apparent that such models must be generalized to capture essential features of the observations: (i) to model the spatio-temporal dynamics of plastic o w in the unstable regime, gradient terms must be introduced into the constitutive equations [4,5,6]; (ii) experimen tally observed retardation e ects in the response of a dynamically strain ageing material to a strain-rate c hange can be described only if at least two constitutive variables are used [7,8]. Recently, a model has been proposed by Hahner et. al. [9] which accounts for the experimen tally observed characteristics of static and dynamic strain ageing in terms of t wo constitutive equations which describe the dynamics of dislocations and solutes and include a spatial coupling term to accoun t for the collective nature of dislocation depinning from solute clouds. This model is brie y discused belo w and serves as a starting point for the present investigation. By analogy with other strain-rate softening instabilities [8,10], one expects that mesoscopic uctuations of plastic ow may in uence the stability of deformation close to the PLC regime, leading to an extension of the PLC domain. This has been sho wn to be a relevant e ect in thermomec hanical instabilities of plastic ow at low temperatures [11]. In the present work we investigate the uctuation-induced nucleation of lo
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