The Strength of Two-Phase Ceramic/Glass Materials

The strengths of various glasses, with a range of expansion coefficients, containing 10 vol % thoria spheres, of diameter 50 to 700 mu m, have been measured. Stresses occur around the spheres, due to differences in the expansion coefficients of the glass and the spheres, on cooling from the fabrication temperature. Stress magnification occurs near the spheres, due to differences in elastic properties, in the presence of an applied stress. When the expansion coefficient of the sphere is greater than that of the glass, circumferential cracks form around the spheres but only when the sphere diameter is greater than a critical value. An approximate value for the critical diameter may be obtained by an energy balance criterion. Cracks may form around spheres smaller than the critical diameter under application of applied stress at stresses below the macroscopic fracture stress. In these cases the strength is governed by a Griffith relationship with the crack size equal to the sphere diameter. When the expansion coefficients of the spheres and glass are similar, the strength of the glass is reduced only when large spheres ((sic) 300 mu m diameter) are present. When the expansion coefficient of the spheres is less than that of the glass, linking radial cracks form between the spheres and the material has very low strength.