Constitutive Model for Anisotropic Creep Behaviors of Single-Crystal Ni-Base Superalloys in the Low-Temperature, High-Stress Regime

A crystallographic constitutive model is developed to capture orientation-sensitive primary and secondary creep behaviors within approximately 20 deg from the [0 0 1] orientation in single-crystal superalloys for the low-temperature and high-stress regime. The crystal plasticity-based constitutive formulations phenomenologically incorporate experimentally observed dislocation micromechanisms. Specifically, the model numerically delineates the nucleation, propagation, and hardening of a\( \langle 1 { 1 2} \rangle \) dislocations that shear multiple \( \gamma^{\prime } \) precipitates by creating extended stacking faults. Detailed numerical descriptions involve slip-system kinematics from a/2\( \langle 1 { 1 }0 \rangle \) dislocations shearing the \( \gamma \)-phase matrix, a\( \langle 1 { 1 2} \rangle \) stacking fault dislocation ribbons shearing the \( \gamma^{\prime } \)-phase precipitate, interactions between a/2\( \langle 1 { 1 }0 \rangle \) dislocations to nucleate a\( \langle 1 1 2\rangle \) dislocations, and interactions between the two types of dislocations. The new constitutive model was implemented in the finite-element method (FEM) framework and used to predict primary and secondary creep of a single-crystal superalloy CMSX-4 in three selected orientations near the [0 0 1] at 1023 K (750 °C) and 750 MPa. Simulation results showed a reasonable, qualitative agreement with the experimental data. The simulation results also indicated that a/2\( \langle 1 { 1 }0 \rangle \) matrix dislocations are important to limit the propagation of a\( \langle 1 { 1 2} \rangle \) dislocations, which leads to the transition to secondary creep.