, Volume 152, Issue 2, pp 103-139

The Evolution of Stress Intensity Factors and the Propagation of Cracks in Elastic Media

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Abstract:

When a crack Γ s propagates in an elastic medium the stress intensity factors evolve with the tip x(s) of Γ s . In this paper we derive formulae which describe the evolution of these stress intensity factors for a homogeneous isotropic elastic medium under plane strain conditions. Denoting by ψ=ψ(x,s) the stress potential (ψ is biharmonic and has zero traction along the crack Γ s ) and by κ(s) the curvature of the crack at the tip x(s), we prove that the stress intensity factors A 1(s), A 2(s), as functions of s, satisfy: where , are stress intensity factors of the tangential derivative of in the polar coordinate system at x(s) with θ=0 in the direction of the crack at x(s). The case of antiplane shearing is also briefly considered; in this case ψ is harmonic.