This book presents original mathematical models of thermal-stress-field interactions in composite materials, along with mathematical models of thermal-stress induced micro/macro-strengthening and intercrystalline or transcrystalline crack formation. The mathematical determination results from mechanics of an isotropic elastic continuum.

The materials consist of an isotropic matrix with isotropic ellipsoidal inclusions. The thermal stresses are a consequence of different thermal expansion coefficients of the material components.

The interactions are determined by suitable mathematical boundary conditions, as well as by a suitable iteration method. The mathematical models include microstructural parameters of a real matrix-inclusion composite, and are applicable to composites with ellipsoidal inclusions of different morphology (e.

g. , dual-phase steel, martensitic steel).

In case of a real matrix-inclusion composite, such numerical values of the microstructural parameters can be determined, which result in maximum values of the strengthening, and which define limit states with respect to the crack formation. .