On the Behaviour of Materials with Binary Microstructures

Abstract

This paper deals with the stochastic analysis of the non-linear response of material systems having a binary microstructure. This type of material is of considerable interest in many engineering applications. Upon the application of an external influence, they show generally a non-linear response behaviour. The latter comprises, apart from the steady-state response (quasi-linear) two distinct transients, namely one that precedes the steady-state and another of importance since it ends with the fracture of the material. As shown schematically in Fig. la, the binary structure consists of an α-phase (or hard phase) of particles that are embedded in a β-phase (soft matrix), where these non-linear stages become more pronounced with an increase of the stress or temperature level (Fig. 1b.) They represent then the important class of high-temperature materials which have been investigated in previous work [1, 2]. An alternative analysis is proposed in this paper using some results of the theory of Markov chains [3]. The concepts of stochastic mechanics and definitions used in [5] will also be maintained throughout this study. They are based on the mathematical theory of probability [6] and the axioms of measure theory [7].