Proposed Fracture Theory of a Dispersion‐Strengthened Glass Matrix

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Abstract
A fracture theory is proposed for a composite system based on a continuous glass matrix. It is hypothesized that hard crystalline dispersions within the glass matrix will limit the size of Griffith flaws and strengthen the composite. Quantitative relations are derived for the effect of a dispersed phase on composite strength. At low volume fractions of the dispersed phase, the average flaw size is statistically reduced independent of the size of the dispersed particles. At high volume fractions of the dispersed phase, the average flaw size is governed by the average distance between particles dispersed in the matrix. The strength of a composite should, therefore, be a function of the volume fraction of the dispersed phase at low volume fractions and dependent on both the volume fraction and particle size of the dispersed phase at high volume fractions. For verification of the theory, cross‐bending strengths were measured on a sodium borosilicate glass containing varying volume fractions of spheroidized alumina over a range of particle sizes. The average distance between dispersed particles ranged from approximately 15 to 500μ. Good agreement with theory was found. Values of glass surface energy calculated from the experimental data agree well with literature data.

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