History dependence of the microstructure on time-dependent deformation during in-situ cooling of a nickel-based single crystal superalloy

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Colleges, School and Institutes

External organisations

  • Rolls Royce
  • Nanyang Technological University, Singapore
  • National Physical Laboratory


Time-dependent plastic deformation through stress relaxation and creep deformation during in-situ cooling of the as-cast single crystal superalloy CMSX-4 has been studied via neutron diffraction, transmission electron microscopy (TEM), electro-thermal miniature testing (ETMT) and analytical modelling across two temperature regimes. Between 1000oC and 900oC stress relaxation prevails and gives rise to softening as evidenced by a decreased dislocation density and the presence of long segment stacking faults in γ phase. Lattice strains decrease in both the γ matrix and γ' precipitate phases. A constitutive viscoplastic law derived from in-situ isothermal relaxation test under-estimates the equivalent plastic strain in the prediction of the stress and strain evolution during cooling in this case. It is thereby shown that the history dependence of the microstructure needs to be taken into account while deriving a constitutive law and which becomes even more relevant at high temperatures approaching the solvus. Higher temperature cooling experiments have also been carried out between 1300oC and 1150oC to measure the evolution of stress and plastic strain close to the γ' solvus temperature. In-situ cooling of samples using ETMT shows that creep dominates during high temperature deformation between 1300oC and 1220oC, but below a threshold temperature, typically 1220oC work hardening begins to prevail from increasing γ' fraction and resulting in a rapid increase in stress. The history dependence of prior accumulated deformation is also confirmed in the flow stress measurements using a single sample while cooling. The saturation stresses in the flow stress experiments show very good agreement with the stresses measured in the cooling experiments when viscoplastic deformation is dominant. This study demonstrates that experimentation during high temperature deformation as well as the history dependence of the microstructure during cooling plays a key role in deriving an accurate viscoplastic constitutive law for the thermo-mechanical process during cooling from solidification.


Original languageEnglish
Pages (from-to)3963–3972
Number of pages10
JournalMetallurgical and Materials Transactions A
Issue number9
Early online date31 May 2018
Publication statusPublished - 1 Sep 2018