Effect of Thermoelastic Characteristics of Components, Shape of Non-Isometric Inclusions, and Their Orientation on Average Stresses in Matrix Structures

The paper presents model calculations on which to predict volume-average external stress under changes of local internal stress in matrix composites with non-isometric inclusions. It is assumed that the rise of local stress owes to different coefficients of linear thermal expansion of non-isometric inclusions and matrix. The inclusions are taken as ellipsoids of rotation (disks, short fibers) and their principal semiaxes as oriented either along three mutually perpendicular directions x, y, and z of a rectangular coordinate system, only along x and y, or only along x. The average stress in the heterogeneous material and its local stress within an individual inclusion are related through a stress concentration operator (fourth rank tensor) for which an explicit expression is derived in a generalized singular approximation of random field theory. The relations obtained for external stress take into account thermoelastic characteristics of the two components as well as inclusion concentrations and orientations in the matrix. The calculation is applied to estimate the average stress along three axes in a composite consisting of an ED-20 epoxy binder and non-isometric copper inclusions.