Basic model for brittle fracture

The incorporation of material scientific approach to future accident analysis and the method of including it into analytical code are two new problems to clarify the unexpectedness of accidents. One example of going to catastrophe suddenly is brittle fracture. Brittleness is affected by crystalline defects, impurities, geometrical conditions, temperature, strain rate etc., and in case of nuclear reactors, the important problems are environmental embrittlement, hydrogen embrittlement, radiation embrittlement and so on. There are four methods to find out the relationship between the measurable physical properties and the limiting strength of materials. But the stress sufficiently small as compared with the ideal strength can break materials if cracks exist in them due to stress concentration at the crack ends. The stress functions in the stress field with cracks can be found by assuming three basic modes of stress and displacement. As breaking is irreversible phenomenon, the conditions of breaking must be derived from the second law of thermodynamics. The concept of Griffith is based on the first law of thermodynamics. Stress magnification factor must be determined in order to calculate strain energy release rate. The studies on the formation and growth of cracks reached only to the stage of qualitative analysis. The J integral by Rice bridges between continuum mechanics and thermodynamics in crack opening. The models for crack end region and non-linear region are given. (Kako, I.)