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A physically-based elasto-viscoplastic constitutive model is proposed to examine the size effects of the precipitate and blocks on the creep for martensitic heat-resistant steels with both the dislocation creep and diffusional creep mechanisms considered.

The model relies upon the initial dislocation density and the sizes of M₂₃C₆ carbide and MX carbonitride, through the use of internal variable based governing equations to address the dislocation density evolution and precipitate coarsening processes. Most parameters of the model can be obtained from existing literature, while a small subset requires calibration. Based on the least-squares fitting method, the calibration is successfully done by comparing the modeling and experimental results of the steady state creep rate at 600° C across a wide range of applied stresses.

The model predictions of the creep responses at various stresses and temperatures, the carbide coarsening and the dislocation density evolution are consistent with the experimental data in literature. The modeling results indicate that considerable effect of the sizes of precipitates occurs only during the creep at relatively high stress levels where dislocation creep dominates, while the martensite block size effect happens during creep at relatively low stress levels where diffusion creep dominates. The size effect of M₂₃C₆ carbide on the steady creep rate is more significant than that of MX precipitate.

The present study also reveals that the two creep mechanisms compete such that at a given temperature the contribution of the diffusion creep mechanism decreases with increasing stress, while the contribution of the dislocation creep mechanism increases.