Subcritical crack growth, surface energy, fracture toughness, stick-slip and embrittlement

Abstract

It is proposed that the difficulties encountered with the meaning of subcritical crack growth arose from a misunderstanding of the Griffith equation. This equation is G=2γ for an equilibrium crack (stable or unstable) where γ is the intrinsic surface energy. When G>2γ the crack has a velocity v depending on the crack extension force G−2γ, even in a vacuum, and the following equation, well verified for adherence of elastomers, G−2γ=2γφT(v) where φT(v) is related to viscoelastic losses or internal friction at the crack tip, is generalized to other materials. At a critical speed vc, dφ/dv becomes negative; as a negative branch cannot be observed the velocity jumps to high values on a second positive branch, so that G=Gc is a criterion for crack speed discontinuity, not the Griffith criterion. The multiplicative factor 2γ on the right-hand side accounts for the shift of the v-K curves with environment. No stress corrosion is needed to explain subcritical crack growth. Subcritical crack growth in glasses and ceramics and velocity jump in brittle polymers are shown to agree with this proposal. This model can also explain stick-slip motion when a mean velocity is imposed in the negative branch. Occurrence of velocity jump or stick-slip depends on the geometry tested and the stiffness of the apparatus. A second kind of stick-slip associated with cavitation in liquid-filled cracks is discussed. When the surrounding medium can reach the crack tip and reduce the surface energy, even at the critical speed vc, the critical strain energy release rate Gc is reduced in the same proportion as γ, and a loading which would have given subcritical growth will give a catastrophic failure. Reduction of surface energy in the Rehbinder effect and in embrittlement by segregation is discussed. Finally, the evolution of ideas concerning the Irwin-Orowan formula and fracture toughness is examined.