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Variable Energy Cyclotron Centre, Kolkata

Understanding of the basic mechanisms of the plastic instability in Portevin-Le Chatelier effect

Many materials when subjected to deformation exhibits unstable plastic flow beyond the elastic limit. In certain range of strain rates and temperatures many solid solutions, both substitutional and interstitial, exhibit serrated yielding which is also referred as the Portevin-Le Chatelier (PLC) effect in literature. The origin of the PLC effect stems from the interaction of dislocations with solute atoms. Dislocation is the line defect within the crystal structure, along which some atoms are misaligned. In metallic alloys, the added solute atoms have their own strain fields. These strain fields interact with the strain field of the dislocations through various mechanisms and under certain experimental conditions the collective movement of the dislocations translates into PLC instabilities. The PLC effect is characterized by inhomogeneous deformation and results in serrated stress-strain characteristics as shown in Fig.1. The strains are localized as deformation bands and with increasing strain rate and/or decreasing temperature, the band character changes from static type C to hopping type B and finally to continuously propagating type A. 

Fig. 1

 

Fig. 2 

The intriguing spatio-temporal dynamics of the PLC effect has fascinated the researchers over several past decades. Moreover, it has some detrimental effects on the mechanical properties of the material. Hence, a huge amount of works are being done to understand the underlying dynamics of this phenomenon. In our section, several techniques of nonlinear dynamics and time series analyses have been adopted to study the dynamics of the PLC effect in different band regime indirectly from the stress-time series data. The tensile tests are performed on substitutional Al-2.5%Mg alloy and interstitial low carbon steel using the Universal tensile Testing Machine INSTRON over a wide range of strain rate. Analyses of the stress-time data reveals that the PLC dynamics in type A band regime has the memory less Markov property and the effective dimension of the dynamics is found to decrease with strain as shown in Fig.2. In the type B band regime, PLC dynamics exhibits deterministic chaos. The differences in relative positions of the solutes in substitutional and interstitial alloys are reflected in difference in the degrees of freedom of the dynamics. Moreover, a transition regime from type A to type B band could be identified and further analyses revealed that both type A and type B band does not exist simultaneously, instead a single band changes its character during deformation. Even though the band characters are different in different experimental conditions, the stress data recorded during the PLC effect is a macroscopic output of the dynamics. Thus the data should possess some general characteristics independent of the strain rate. This motivated  to search for a common feature in the PLC dynamics with imposed strain rate and two different techniques of time series analysis were adopted for this purpose: (1) Scaling analysis and (2) Quantification of complexity. The result of scaling analyses clearly suggests that the scaling behavior of the overall dynamics of the PLC effect at all strain rates follow Levy-walk property. Fig.3 exhibits the scaling nature of the Standard deviation Analysis (SDA) and Diffusion entropy Analysis (DEA) of the stress vs. time data obtained from Al-2.5%Mg alloy during tensile deformation at a strain rate of 3.85x10-4 Sec-1.

 

Fig. 3 

The complexity of the PLC dynamics is estimated through Multi Scale Entropy (MSE) analysis and it is observed that MSE analyses can be successfully employed to identify the type A and type B band regime. The transition regime could also be identified with this technique.