PSI - Issue 18

Sergey Uvarov et al. / Procedia Structural Integrity 18 (2019) 309–313 Author name / Structural Integrity Procedia 00 (2019) 000–000

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1. Introduction

In classical continuum plasticity, plastic deformation of a crystalline solid is viewed as smooth and quasi-laminar flow. The crystalline solid is considered to be a homogeneous continuum, where material flows in a spatially homogeneous manner in the absence of any plastic instabilities (such as occur with strain softening). In this paradigm, fluctuations are averaged (smoothed) out on any length scale above that of a representative volume element, which is small in comparison to the dimensions of the specimen. As it noticed in D’Anna paper plastic deformation process can be unstable and inhomogeneous even if the loading conditions are monotonous and stress distribution is uniform at the beginning of the test. This leads to the appearance of the Chernov-Luders bands, Portevin–Le Chatelier effect and adiabatic shear bands formation in the case of dynamic loading [Marchand (1988)]. According to the traditional view of classical continuum plasticity, wherein the flow of material is homogeneous, spatial-temporal fluctuations occur only in the advent of instabilities brought about by anomalous strain (or strain rate) softening. An alternative mechanism that may be responsible for the development of spatial-temporal fluctuation is the development of shear bands and subsequent pronounced correlations between these bands. Instead of a number of uncorrelated dislocation motions resulting in homogeneous flow, numerous localized bursts of deformation occur under the conditions of pronounced long-range spatial-temporal correlations. The nucleation and evolution of these regions of localized flow are associated with plastic instabilities possessing qualitatively new features. Instead of coordinated spatial-temporal oscillations, the stochastic bursts of localized plasticity are observed on scales that are spatially and temporally free. This means that the development of plastic deformation has a nature similar to certain criticality phenomena (e.g., phase transitions), and, as a consequence, pronounced self-similarity features of plastic flow may be established. As it mentioned in Froustey (2016) two characteristic stages of defects kinetics are responsible for adiabatic shear failure: formation of solitary wave collective modes and the following transforming into the blow-up dissipative structure of damage localization and crack nucleation. The same approach can be applied to the PLC effect where serrated yielding can be related to the repetitive bursts of the localized plasticity caused by blow-up dissipative structures formation. 2. Experiment

The geometry of the specimen was the same as in D’Anna (2000) except dimensions (fig. 1):

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b)

Fig. 1. (a) specimen drawing (dimensions in mm); (b) specimen between the loading plates.