Thermal and Phase-Transformation Stresses in Matrix-Whisker Composites I

The book develops mathematical models to describe stresses in two-component materials with cylindrical particles embedded in an isotropic matrix. These stresses arise either from differences in thermal expansion during cooling or from lattice changes during phase transformations. The model takes into account geometric and structural properties such as particle size, shape, and distribution. The derivations are based on the mechanics of elastic continua and make use of fundamental equations such as Hooke’s law and the Cauchy equations. In cases where multiple solutions are possible, the principle of minimum potential energy is applied. Finally, explicit mathematical formulas for thermal and phase-transformation-induced stresses are provided, supplemented by numerical calculations in the appendix.