A STATISTICAL MODEL FOR LINKING OF MICROCRACKS

The problem of the formation of large cracks by coalescence of separately nucleated smaller cracks is approached by statistical methods. The stress concentration from existing cracks is neglected in order to obtain a manageable solution and it is thus assumed that nucleation of the cracks is random and independent of other cracks. If a crack aggregate of n cracks is required for fracture in a specimen with N grains, the fraction cracked grains for fracture is given by: Thus there exists a limiting value for p of 0.2. Cracks tending to infinite size are obtained as this value is approached. The expression is applied to transgranular cleavage cracks, to intercrystalline wedge cracks and to small intercrystalline pores. Good agreement is obtained with experimentally determined values for creep cracks and cavities. The expression should be regarded as an upper limit for crack density since the cracks have been assumed to be independent of each other. © 1969.