A third-order state-space model for fatigue crack growth

A second‐order state‐space model of fatigue crack growth in ductile alloys was presented by Patankar et al., 1 - 4 where the crack length and the crack opening stress were treated as two state variables. Simulation results showed that this model gave good predictions when compared with experimental data for aluminium alloy 7075‐T6 and 2024‐T3 at constant‐amplitude load as well as with overloads. These model predictions were, however, poor for cases with over/under load or under/over load sequences where load excursion effects were underestimated. A third‐order state‐space model is presented is this paper that is believed to be more accurate for predictions of fatigue crack growth for ductile alloys under various loadings. The constraint factor calculated from an algebraic equation in the second‐order state‐space model is treated as the third state variable in this model. Through simulations, it is shown that the third‐order state‐space model gives better predictions than the second‐order state‐space model and FASTRAN II, especially when the effects of over/under load and under/over load are necessary considerations.