المحاضرة السادسة

Lec.6
Thermal Stresses and Thermal Expansion in MMCs
For simplicity, we will consider composites made of two-phases-a matrix phase and a reinforcement phase-with the possible additional presence of porosity (which may then be considered as a third phase). The reinforcement phase can have the shape of particles, fibers, platelets, or even consist of a continuous three-dimensional network. The degree of ?continuity? (or ?contiguity?) is an important feature of the configuration of the two phases. A phase may be continuous in one, two, or three dimensions. In MMCs, the matrix phase is usually three dimensional continuous (i.e., percolating), whereas the reinforcement phase may be discontinuous, one-dimensional continuous (continuous fibers), two dimensional-continuous, or three-dimensional-continuous. The distinction between matrix and reinforcement phases may become ambiguous in the case of some MMCs developed for low thermal expansion applications, which may contain a quite large reinforcement volume fraction, sometimes even exceeding 0.5.
Under uniform temperature change, stresses are induced in a composite due to the thermal expansion mismatch between the matrix and the reinforcing phase. Only these type of thermal stresses, the so-called ?phase stresses,? will be considered in this chapter: no account will be given of the type of thermal stresses which arise in any solid in the presence of temperature gradients. Temperature will always be assumed uniform throughout the composite.
Composite thermal stresses and thermal expansion depend in an intricate manner on the following:
(i) reinforcement volume fraction and ?morphology? (i.e., particle or fiber size, shape, orientation distribution, and continuity);
(ii) matrix crystallographic texture and porosity;
(iii) possible voids or lack of adhesion at matrix-reinforcement interfaces.
Matrix texture is most often neglected and the composite anisotropy is thus usually ascribed only to the anisotropy of the reinforcement orientation distribution. Being, in principle, a reversible phenomenon, thermal expansion at a given temperature should be determined only by the elastic constants and thermal expansion coefficients of the matrix and reinforcement, accounting for the possible presence of voids in matrix and/or at interfaces. However, the magnitude of internal stresses may be such that temperature change induces nonreversible phenomena such as plastic yielding, reinforcement fracture, void growth in the matrix, or interface decohesion. The apparent (nonreversible) thermal expansion then also depends on the plastic or visco-plastic strength of both the matrix and the reinforcement, as well on the damage resistance of the