Abstract
In order to quantify the crack branching morphology of brittle materials under axisymmetric tension, the “branching dimension” was defined in the present paper, and the relation between the branching dimension and fracture mechanics parameters was introduced.The branching dimension Db is defined as: Db=d(logLi)/d(logai), where Li is the total crack length after i-th crack branching has occurred and ai is the crack length which corresponds to the distance from crack nucleation point to crack tip. When the nominal stress σi varies with increasing crack length ai according to the relation, σi/σ0=(ai/a0)m, the branching dimension Db can be expressed by:Db=2+2m=2+2·d{log(σi)}/d{log(ai)}where σ0 and a0 are the stress and the crack length at crack initiation. Moreover, Db can be expressed by the change of the number of cracks, n, with increasing crack length, ai:Db=1+d{log(n)}/d{log(ai)}The branching dimension can well characterize the branching patterns obtained from the flexural test of Pyrex glass, ceramic and high strength steel specimens.
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