Thermal-stress induced phenomena in two-component material:Part Ⅱ

The paper deals with analytical models of the elastic energy gradient Wsq representing an energy barrier. The energy barrier is a surface integral of the elastic energy density Wq. The elastic energy density is induced by thermal stresses acting in an isotropic spherical particle （q = p） with the radius R and in a cubic cell of an isotropic matrix （q = m）. The spherical particle and the matrix are components of a multi-particle-matrix system representing a model system applicable to a real two-component material of a precipitation-matrix type. The multi-particle-matrix system thus consists of periodically distributed isotropic spherical particles and an isotropic infinite matrix. The infinite matrix is imaginarily divided into identical cubic cells with a central spherical particle in each of the cubic cells. The dimension d of the cubic cell then corresponds to an inter-particle distance. The parameters R, d along with the particle volume fraction v = v（R, d） as a function of R, d represent micro- structural characteristics of a real two-component material. The thermal stresses are investigated within the cubic cell, and accordingly are functions of the microstructural charac- teristics. The thermal stresses originate during a cooling pro- cess as a consequence of the difference am - ap in thermal expansion coefficients between the matrix and the particle, am and ap, respectively. The energy barrier Wsq is used for the determination of the thermal-stress induced strengthening aq. The strengthening represents resistance against com- pressive or tensile mechanical loading for am - ap 〉 0 or am - ap 〈 0. respectively.

Thermal-stress induced phenomena in two-component material: Part II

The paper deals with analytical models of the elastic energy gradient W _sq representing an energy barrier. The energy barrier is a surface integral of the elastic energy density w _q . The elastic energy density is induced by thermal stresses acting in an isotropic spherical particle (q = p) with the radius R and in a cubic cell of an isotropic matrix (q = m). The spherical particle and the matrix are components of a multi-particle-matrix system representing a model system applicable to a real two-component material of a precipitation-matrix type. The multi-particle-matrix system thus consists of periodically distributed isotropic spherical particles and an isotropic infinite matrix. The infinite matrix is imaginarily divided into identical cubic cells with a central spherical particle in each of the cubic cells. The dimension d of the cubic cell then corresponds to an inter-particle distance. The parameters R, d along with the particle volume fraction v = v(R,d) as a function of R, d represent microstructural characteristics of a real two-component material. The thermal stresses are investigated within the cubic cell, and accordingly are functions of the microstructural characteristics. The thermal stresses originate during a cooling process as a consequence of the difference α _m ? α _p in thermal expansion coefficients between the matrix and the particle, α _m and α _p , respectively. The energy barrier W _sq is used for the determination of the thermal-stress induced strengthening σ _q . The strengthening represents resistance against compressive or tensile mechanical loading for α _m ? α _p  > 0 or α _m ? α _p  < 0, respectively.