PSI - Issue 82

Abhijit Joshi et al. / Procedia Structural Integrity 82 (2026) 91–97 A. Joshi et al./ Structural Integrity Procedia 00 (2026) 000–000

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2.2. Creep laws Abaqus software supports number of creep laws such as time- and strain-hardening models, a time-power law model and a power-law model. Other advanced models such as the hyperbolic-sine law, double power law, Anand law, and Darveaux law are also available. The creep tests completed on CGI showed good curve fits for the creep strain using the Bailey-Norton creep equation (Joshi et al., 2025): ! = " # (1) In this equation the creep strain ! is expressed in terms of stress and time . The equation includes parameter , which is the creep exponent, and and are two parameters dependent on the material and temperature. The parameters , and for the CGI material used in the current research are reported in our previous work (Joshi et al., 2025). The Bailey-Norton equation can be rewritten in the form of creep strain rate ̇ ! with same parameters , and : ̇ ! = " #$% (2) The time hardening law available in Abaqus ̇ ! = " & (3) is similar to the Bailey-Norton creep strain rate equation. Here, the creep strain rate ̇ ! is expressed as a function of uniaxial equivalent deviatoric stress , time , and the creep exponent . Eq. (3) can be written in the form of creep strain as ! = &( ' % " &(% (4) where and are parameters dependent on the material and temperature, and they can be derived from the parameters and using in the following form: = (5) = − 1 (6) The creep exponent is identical in Eqs. (1)-(4). The time-hardening creep-rate equation given in Eq. 3 can be modified to eliminate the time factor: ̇ ! = ( " ) "# ! ! 1( + 1) ! 3 " " #! (7) In this equation, also known as strain hardening law , the creep strain rate is defined as a function of stress and creep strain, with the time factor fully removed from the equation. In applications with a constant stress, the time- and strain hardening creep laws are equivalent (Naumenko and Altenbach, 2016). The experimental results with variable loading are generally more aligned with strain-hardening law (Naumenko and Altenbach, 2016) and so the simulations discussed in this paper are based on this law. 2.3. Material properties The matrix was simulated using the Young’s modulus of 125 GPa based on our tensile tests at 500 °C reported in (Joshi et al., 2025). The Poisson’s ratio of 0.25 was taken from the literature (Cao et al., 2025; Palkanoglou et al.,