A general micromechanics model, the bridging model, is incorporated with the unified Bodner–Partom constitutive theory to simulate the cyclic response of Titanium matrix based composite laminates subjected to arbitrary thermal–mechanical load. The Titanium matrix response at any strain rate, load level, and working temperature is best described using the differential Bodner–Partom unified theory. However, the bridging model has been developed based on an incremental solution strategy which is most applicable for engineering analysis. For this purpose, the incremental Prandtl–Reuss description for the matrix inelastic response has proved efficient. Thus, a conversion from the Bodner–Partom description to the Prandtl–Reuss description at every load level for the stress–strain response of the Titanium matrix material is necessary. In the present paper, the differential Bodner–Partom theory is used to obtain an equivalent one-dimensional entire stress–strain curve of the matrix at the current load condition (strain rate, load level, and working temperature) through a numerical integration. From this curve, the corresponding material parameters required by the Prandtl–Reuss description are successfully defined. A cross-ply laminate subjected to isothermal cyclic load at an elevated temperature of 650°C and to an in-phase thermo-mechanical fatigue from 150 to 650°C has been analyzed in this way. Correlation between the predicted and available experimental cyclic stress–strain responses is reasonably good.
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