Analysis Of Portevin-Le Chatelier Effect On The Nonlinear Dynamical System

When in certain range of temperature and strain rate, as well as proper initial deforming, various alloy materials can display special plastic instability phenomenon in tension experiment, and it performs to be the serrated stress flow in temporal field and the localized strain band in spatial field, which is called the Portevin-Le Chatelier (PLC) effect. PLC effect belongs to some kind of collective phenomenon and is considered to originate from the dynamical strain aging effect in the meso-structure evolution process of materials, also known as the dynamical interaction among mobile dislocation, forest dislocation and solute atoms. It is found that the characteristic parameters distribution of stress curve turns out to change when strain rate increases in PLC effect, specially, which displays the crossover from peak type to scaling type. From the point of nonlinear dynamics, such change implies the transition of different dynamical modes. Therefore, this paper is mainly focused on investigating the underlying dynamical mechanism of PLC effect via nonlinear dynamics, and takes three kinds of nonlinear analysis tools including the attractor trajectory analysis of reconstructed phase space, multiscale analysis based on wavelet transform and multifractal analysis, in order to characterize dynamical behavior of PLC effect.In section 2, it is mainly the attractor analysis in low strain rate (corresponding to type C band) by means of reconstructed phase space technology. However, it is suggested that there exists shortcomings for the traditional method which makes use of the self-correlation function in determining time lag in stress series of PLC effect. Therefore, the advanced combine average method is taken as the theorem for determination of time lag in this paper, and for comparison, it also displays the relevant trajectory in phase space. Finally, it is confirmed the given stress series posses the characteristic structure of chaotic attractor.In section 3, it is mainly the multiscale analysis of PLC effect based on the wavelet transform technology. Firstly, the self-similarity and its source are analyzed when PLC effect displays chaotic behavior. Secondly, considered the inevitable analysis error for the obtaining characteristic parameters due to personal reasons, wavelet transform as pure mathematical tool can get rid of such problem easily, for the usage of wavelet transform in PLC effect, this paper also gives the specific discussion from the physical meaning of wavelet coefficient. Thirdly, when stress curves in different solution temperature disposed on wavelet decomposition, it can found that wavelet coefficients display non-monotonous changing type as the temperature increases, similar to the traditional statistical result, which also further proves that the feasibility of application of wavelet transform in the study of PLC effect for fulfilling multiscale investigation and errorless statistics of characteristic parameters about the temporal structure.In section 4, based on the achievements of PLC effect study from the point of nonlinear dynamics, this paper employs multifractal analysis to classify the underlying dynamical mechanism for different types of PLC bands including type A, type B and type C. The result suggests, whatever the type is, there exists multifractal behavior in certain scales, and specifically, the signal of type B band owns the highest homogeneity, which can be explained by the different deforming conditions, for the reason that when type B band exists, the plastic strain incompatibility can be homogenized by the release of strain within the reloading interval, and therefore, the stability of dynamical in type B band is higher than the other types. Such phenomenon can be ascribed to the fact that the crossover from self-organization to quasi-periodicity and finally to chaos for the dynamical system when strain rate decreases.