Σύνθετα υλικά με διαβαθμισμένες θερμομηχανικές ιδιότητες υπό διαξονική καταπόνηση

Abstract

In this thesis we study the deformation regime of plates, made by functionally graded materials with viscoplastic and thermoviscoplastic properties, under biaxial loading. We are interested in examining the possible instability modes that can appear, characterized by strain localization. More speci?cally, we study emergence of multiple necking under special conditions, and we also examine problems of shear banding appearance. Moreover, we introduce a type of homogenization of functionally graded viscoplastic materials. In Chapter 2 we make a brief introduction to non-homogeneous materials, focusing our attention to composite materials and especially to functionally graded materials. The ways of production, as well as the potential uses of such materials are presented. In Chapter 3 we refer to the strain localization that is observed in a plate, made by homogeneous material, when it is subjected to biaxial loading. The plate appears a small hole at its center, which allows the 00release00 of unstable behaviours of the material. Also we present the static elastic theory and the plastic theory of plane stress, which are accompanied by numerical examples of biaxial loading of an elastic and elastoplastic plate correspondingly. From the analyses follows that, while in the elastic condition we have a simple increase of stress in a narrow region, when the material enters the plastic region, we observe strain localization and formation of shear band with incli- nation which depends on the ratio of the boundary loads. The chapter closes with the presentation of a numerical analysis of a plate, made by thermo- plastic material, under isothermal conditions, where we have similar results with the elastoplastic analysis, as well as that the ?nal temperature seems be independent of the ratio of the boundary loads. Chapter 4 introduces the main part of this PhD thesis. We formulate the problem of biaxial loading of a material of non-homogeneous nature, under quasi-static conditions, showing the basic equations that govern the problem. We study the behaviour of viscoplastic and thermoviscoplastic materials in 00large00 times, from where we observe that under special initial and boundary conditions, thermoviscoplastic and some cases of viscoplastic materials can show unstable behaviour. The time of appearance, in the cases of non-homogeneous materials, di®ers from point to point. Next we formulate a special solution of the problem corresponding to appropriate initial and boundary conditions of physical interest. This special solution is the reference solution on which we apply the instability analysis. In Chapter 5 we present the theory of e®ective instability analysis of Dudzinski - Molinari, formulating conveniently the equations for the case of non-homogeneous viscoplastic and thermoviscoplastic material. We also present the instability analysis in the case of homogeneous viscoplastic ma- terial with a slight band of inhomogeneity.