This book presents original mathematical models of • thermal and phase-transformation stresses, which originate during a cooling process in model material systems, i.e., multi-particle-envelope-matrix and multi-particle-matrix systems, corresponding to real three- and two-component materials respectively, • intercrystalline and transcrystalline crack formation in components of these model material systems, including mathematical definitions of critical limit states with respect to the material crack formation, which isinduced by these stresses. • material micro- and macro-strengthening in components of these model systems, which is induced by these stresses.