A crystal plasticity finite element model for flow stress anomalies in Ni₃Al single crystals

Abstract

This paper presents a dislocation density-based non-Schmid constitutive model to address the anomalous thermo-mechanical behaviour of the L1₂ intermetallic single-crystal Ni₃Al. Ni₃Al is used as a strengthening precipitate (γ′ phase) in Ni-based superalloys. Addressing such anomalous behaviour by accounting for temperature-dependent flow stress and hardening evolution, as well as orientation-dependent tension–compression asymmetry, is necessary for modelling superalloys across a range of temperatures. While hardening in cube-slip systems results from statistically stored dislocations (SSDs), hardening in octahedral slip systems is due to both SSDs and cross-slip dislocations (CSDs). The constitutive model incorporates hardening evolution due to SSDs and CSDs. Experimental data for Ni₃Al-type single crystals, available in the literature, are used to calibrate material parameters. Subsequently, results of crystal plasticity FEM simulations are compared with experimental data for several orientations under constant strain rate and creep loading conditions for a wide range of temperatures. The model is able to correctly predict the response of L1₂ intermetallic single crystals including features of anomalous flow stress and non-Schmid yield behaviour.

Keywords:

• intermetallic single crystals
• anomalous flow stress
• tension–compression asymmetry
• cross-slip
• non-Schmid yield

Acknowledgements

This work has been partially supported by the National Science Foundation, Civil and Mechanical Systems Division through grant number CMMI-1,200,231 (program director: Dr. Alexis Lewis). It has also been partially supported by the Air Force Office of Scientific research and Air Force Research Laboratories/RX through grant number FA9550-12-1-0445 to the Center of Excellence on Integrated Materials Modelling (CEIMM) at Johns Hopkins University (AFOSR program director: Dr. Ali Sayir and AFRL program monitors Drs. C. Woodward and C. Przybyla). This sponsorship is gratefully acknowledged. Computer use of the Hopkins High Performance Computing (HHPC) facilities is gratefully acknowledged.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work has been partially supported by the National Science Foundation, Civil and Mechanical Systems Division through [grant number CMMI-1200231] (program director: Dr. Alexis Lewis). It has also been partially supported by the Air Force Office of Scientific research and Air Force Research Laboratories/RX through [grant number FA9550-12-1-0445] to the Center of Excellence on Integrated Materials Modelling (CEIMM) at Johns Hopkins University (AFOSR program director: Dr. Ali Sayir and AFRL program monitors Drs. C. Woodward and C. Przybyla).