Kinetic model for prediction of subcritical crack growth, crack tip relaxation, and static fatigue threshold in silicate glass

Prediction of brittle fracture of amorphous oxide glasses continues to be a challenge due to the existence of multiple fracture mechanisms that vary with loading conditions. To address this challenge, we present a model for all three regimes of crack growth in glasses. Regimes I and III are controlled by Arrhenius processes while regime II is transport controlled along with a simple Arrhenius model for viscoelastic stress relaxation. Through dimensional arguments and physical reasoning, we propose a single mechanism which underlies both regime III subcritical crack growth and near-crack-tip viscoelastic relaxation. By combining the subcritical crack growth and viscoelastic models we obtain a prediction for a threshold stress intensity, $K_{\mathrm{th}}$, below which stresses around the crack relax faster than it propagates. For stress intensity $K_I<K_{\mathrm{th}}$, no subcritical crack growth is predicted to occur, allowing for the design of stable glass systems. The prediction is compared to measured subcritical fracture threshold data for soda-lime silica glasses.