This paper presents a physically-based microstructural model for creep rupture at 600 °C for Grade 91 steel. The model includes constitutive equations that reflect various observed phenomena in Grade 91, and it is incorporated into a mesoscale finite element model with explicit geometry for the prior austenite grains and grain boundaries. Creep within the grains is represented using crystal plasticity for dislocation motion and recovery along with linear viscous diffusional creep for point defect diffusion. The grain boundary models include physics-based models for cavity growth and nucleation that accurately capture tertiary creep and creep rupture. Simulations of creep at 100 MPa are performed, and the contribution of each mechanism is analyzed. The overarching goal is to gain a mechanistic understanding of the material to improve the prediction of creep rupture for long service lives in elevated temperature operating conditions. The creep response of the material at different stress levels, stress states, and temperatures is studied in Part 2 of this paper in order to determine the implications of the simulations on high temperature design practice. Furthermore, the second part explores the effect of triaxial stress states on the creep response and finds a transition from notch-strengthening behavior at high stress to notch-weakening behavior at lower stresses.

This paper describes a series of physically-based crystal plasticity finite element method (CPFEM) simulations of long-term creep and creep rupture of Grade 91 steel. It is Part 2 of a two part series of papers. Part 1 describes the simulation framework; this part focuses on specific simulations and on how the predicted long-term creep properties of Grade 91 compare to the assumptions used in current high temperature design practices. This work extends the model developed in Part 1 to look at creep properties at different temperatures, principal stresses, and multiaxial stress states. The simulations show that empirically extrapolating creep rupture stresses from short-term experimental data may substantially over predict the actual long-term creep properties of Grade 91. Additionally, the CPFEM calculations predict a transition from notch strengthening creep behavior for high values of maximum principal stress and moderate notch severity to notch weakening behavior for low principal stresses and more severe notches. The latter regime better categorizes conditions in engineering components designed for long term elevated temperature use, which implies Grade 91 may be a notch weakening material in actual service. This would have a significant impact on high temperature design practices, though confirmatory test data on long-life, low stress notched specimens is difficult to obtain. Finally, one advantage of the physically-based modeling approach adopted here is that the simulation results also elucidate the microstructural mechanisms causing the macroscopic trends in engineering properties predicted by the simulations. This paper shows that the detailed micromechanical mechanisms predicted by the CPFEM simulations can be abstracted with a simple micromechanical model that can be used to both explain the detailed results and make improved predictions of engineering properties from experimental data.

Summary A computational method is developed for evaluating the plastic strain gradient hardening term within a crystal plasticity formulation. While such gradient terms reproduce the size effects exhibited in experiments, incorporating derivatives of the plastic strain yields a nonlocal constitutive model. Rather than applying mixed methods, we propose an alternative method whereby the plastic deformation gradient is variationally projected from the elemental integration points onto a smoothed nodal field. Crucially, the projection utilizes the mapping between Lie groups and algebras in order to preserve essential physical properties, such as orthogonality of the plastic rotation tensor. Following the projection, the plastic strain field is directly differentiated to yield the Nye tensor. Additionally, an augmentation scheme is introduced within the global Newton iteration loop such that the computed Nye tensor field is fed back into the stress update procedure. Effectively, this method results in a fully implicit evolution of the constitutive model within a traditional displacement‐based formulation. An elemental projection method with explicit time integration of the plastic rotation tensor is compared as a reference. A series of numerical tests are performed for several element types in order to assess the robustness of the method, with emphasis placed upon polycrystalline domains and multi‐axis loading. Copyright © 2016 John Wiley & Sons, Ltd.