The strength of brittle materials containing second phase dispersions

Abstract Cracks in brittle materials can be impeded by obstacles in the form of second phase dispersions. The crack tends to bow out between obstacles forming secondary semi-elliptical flaws. The strength is determined by the stress to propagate these secondary cracks. Stress calculations show that this depends on the ratios of the obstacle dimensions and the obstacle spacing and, except for large relative obstacle spacings, the stress is larger than the stress to extend the primary crack. Second phase dispersions will usually increase strength, therefore, through an effect equivalent to the ‘line tension effect’ observed for dislocation motion. A comparison of the calculated ‘line tension effect’ with observed increases in strength in brittle matrix composites shows that line tension is the major contribution to the strength increase for brittle obstacles, but only a minor contribution for fibre composites, and probably a minor contribution for ductile obstacles.