Abstract
This chapter discusses the analysis of branched cracks under biaxial stresses. Branched cracks are often observed in brittle fracture and also in stress corrosion cracking. The reasons for these crack branching phenomena in brittle fracture can be explained on the basis of dynamic effects. A doubly symmetric branched crack is considered for the analysis. A conformal mapping function that maps the crack into a unit circle is given by a Schwartz–Christoffel transformation. The solutions for the branched crack under arbitrary biaxial stresses can be calculated by simply superimposing the solutions for the cracks under uniaxial stress. In a fracture process such that a symmetric branched crack can grow, there is a stable branching angle particular to a given biaxial stress state, which increases with increase of the lateral biaxial tensile stress. Using the solutions for the bent crack, the stability of the crack under various biaxial stresses can be determined. The crack has a particular stability, which may affect a crack extension behavior.
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