L. Zhao, J. Tong, University of Portsmouth, Portsmouth, United Kingdom
Modelling of crack tip deformation and crack growth in a nickel-based superalloy at elevated temperature has been carried out for a compact tension (CT) specimen using the finite element method. A unified viscoplastic model with non-linear kinematic and isotropic hardening rules has been adopted to describe the material constitutive behaviour. The material model was implemented in the finite element software ABAQUS via a user-defined material subroutine (UMAT). Finite element analyses for stationary cracks showed distinctive strain ratchetting behaviour near the crack tip at selected load ratios, leading to progressive accumulation of tensile strain normal to the crack growth plane. Results also showed that low frequencies and superimposed hold periods at peak loads significantly enhanced strain accumulation at crack tip.Finite element simulation of crack growth was carried out under a constant ΔK-controlled loading condition. Similar to stationary crack analysis, crack tip deformation for a growing crack also shows the distinctive feature of strain accumulation. Lower frequency and longer dwell period enhance strain ratchetting and strain accumulation. This is consistent with the observed dependency of crack growth rate on frequency and dwell period from the experimental results, i.e., faster crack growth rate at lower frequency and longer dwell period. A crack growth criterion based on strain-accumulation is proposed where a crack is assumed to grow when the accumulated strain ahead of the crack tip reaches a critical value over a characteristic distance. The criterion has been utilised in the prediction of crack growth rates in a CT specimen at selected loading ranges, frequencies and dwell periods, and the predictions were compared with the experimental results. During crack growth simulation, crack closure behaviour was also examined using the standard compliance offset method for both plane strain and plane stress cases, and confirmed the lack of crack closure for plane strain condition.
Summary: The fundamental deformation behaviour near a crack tip in a nickel-based superalloy RR1000 at elevated temperature has been studied using the viscoplastic constitutive model. Detailed finite element analyses were carried out to study the stress-strain fields near a crack tip in a CT specimen under mode I cyclic loading conditions. Distinctive ratchetting behaviour has been observed near the crack tip for stationary cracks, leading to progressive accumulation of tensile strain normal to the crack growth plane. The ratchetting behaviour largely depends on the loading range, ratio, frequency and dwell period. Low frequencies and superimposed hold periods at peak loads significantly enhanced strain accumulation at crack tip.
Fatigue crack growth was simulated under a constant ΔK-controlled condition using a node release algorithm. Similar to stationary crack analysis, crack tip deformation for a growing crack also shows the distinctive feature of strain accumulation, and fatigue crack growth at elevated temperature seems to be strongly related to ratchetting strain accumulation near the crack tip. It is proposed that crack growth occurs when the accumulated strain ahead of the crack tip reaches a critical value over a characteristic distance. This crack growth criterion was reasonably successful in predicting the crack growth rate at selected loading range, frequency and dwell period, although for crack growth at lower frequencies and longer dwell periods, oxidation gains significance which should be taken into account in future model development.
Also, crack closure behaviour was examined from the crack opening profiles and the monitored load-displacement trace at crack mouth, using the standard compliance offset method (ASTM Standard 1995) for both plane strain and plane stress cases, and confirmed the lack of crack closure for plane strain condition.
