## Appendix A Gr91 Steel Constitutive Model  
The constitutive model for the Grade 91 steel studied in this work was taken from [48; 58]. Understanding the material's creep response under sustained and cyclic loading at high temperatures is important for certifying its longevity in these energy applications. From a survey of minimum creep strain rates in Grade 91 (Gr91) at 600 \({}^{\circ}\)C, a transition in mechanism seemed apparent between a stress-to-strain-rate power law exponent \(n=12\) above 100 MPa [59] and a smaller exponent \(n=1\) at lower applied loads [60]. This transition raised concerns about extrapolating short-duration creep test data to service conditions at lower temperatures and stresses. Therefore, a micromechanical modeling approach was adopted with a multi-mechanism inelastic rate extension of (8) to combine the effects of dislocation and diffusional creep as follows:  
\[\dot{\mathbf{t}}=\mathbf{C}_{0}:\left(\mathbf{d}-(\mathbf{d}^{(\mathrm{p})}+ \mathbf{d}^{(\mathrm{d})})\right)+\mathbf{R}\bar{\mathbf{w}}^{(\mathrm{p})} \mathbf{R}^{T}\mathbf{t}-\mathbf{t}\mathbf{R}\bar{\mathbf{w}}^{(\mathrm{p})} \mathbf{R}^{T}, \tag{1}\]  
where the diffusional strain rate \(\mathbf{d}^{(\mathrm{d})}\) arises from point defect migration postulated to occur independently from the line defect (dislocation) motion. The constitutive equations for these two mechanisms are summarized in the following paragraphs and discussed further in [48]. The first inelastic strain rate \(\mathbf{d}^{(\mathrm{P})}\) is expressed by a power-law relation between each slip rate and its associated resolved shear stress on the twelve primary \(\{110\}\big{<}\bar{1}11\big{>}\) body-centered cubic (BCC) slip systems. The power-law relation is indicative of alternating glide/climb of dislocations over microstructural barriers, with a large exponent \(n=12\) associated with the contributions of the precipitate network. The power-law drag stress \(\bar{\tau}\) is taken to increase by a Vocc hardening relation due to the immobilization of free dislocations during the creep process. These models take the form  
\[\dot{\gamma}^{(s)}(\tau^{(s)};\bar{\tau})=\frac{\dot{\bar{\tau}}}{\bar{\tau}} \Big{|}\frac{\tau^{(s)}}{\bar{\tau}}\Big{|}^{n-1}\tau^{(s)}, \tag{11}\]  
\[\bar{\tau}=\tau_{\mathrm{y}}+\tau_{\mathrm{w}}, \tag{12}\]  
\[\tau_{\mathrm{w}}=\theta_{0}\Big{(}1-\frac{\tau_{\mathrm{w}}}{\tau_{\mathrm{v} }}\Big{)}\sum_{s=1}^{n_{\mathrm{slip}}}\big{|}\dot{\gamma}^{(s)}\big{|}. \tag{13}\]  
In the slip-rate equation, \(\dot{\bar{\tau}}\) is the reference strain rate, \(\tau^{(s)}=\mathbf{t}:\Big{(}\mathbf{R}^{\mathrm{P}\bar{T}}\bar{\mathbf{m}}^{( s)}\mathbf{R}^{\mathrm{P}}\Big{)}\) is the resolved shear stress, and \(\bar{\mathbf{m}}^{(s)}=\mathrm{sym}\Big{(}\bar{\mathbf{b}}^{(s)}\otimes\bar{ \mathbf{n}}^{(s)}\Big{)}\) is the Schmid tensor. The drag stress \(\bar{\tau}\) is composed of an initial slip resistance \(\tau_{\mathrm{y}}\) and a strengthening resistance \(\tau_{\mathrm{w}}\) that evolves from \(0\) to the saturation stress \(\tau_{\mathrm{v}}\) with an initial slope equal to the flow modulus \(\theta_{0}\). The calibrated values of these parameters are taken from [48] and provided in Table 1.  
The second inelastic strain rate, denoted by \(\mathbf{d}^{(\mathrm{d})}\), is incorporated to capture the linear relationship between the applied stress and creep rate observed at lower applied loads [60]. Along with the motion of dislocation (line) defects, the movement of point defects such as atoms or vacancies is thought to play a role in this behavior. This diffusion can occur within grains, along grain boundaries, within dislocation cores, or in other regions of the complex Grade 91 microstructure. For simplicity, as discussed in [48], the rate of this diffusion is treated in an average sense using a generic diffusion coefficient \(D_{\eta}\).