On the Behaviour of Materials with Binary Microstructures

  • D. R. Axelrad
  • Y. M. Haddad
Chapter
Part of the NATO ASI Series book series (ASHT, volume 43)

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].

Keywords

Stochastic Analysis Hard Phase Soft Matrix Field Quantity Binary Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • D. R. Axelrad
    • 1
  • Y. M. Haddad
    • 2
  1. 1.Micromechanics Research LaboratoryMcGill UniversityMontrealCanada
  2. 2.Dept. of Mechanical EngineeringUniversity of OttawaOttawaCanada

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