Mechanism-based modeling of solute strengthening:Application to thermal creep in Zr alloy

In this work, a crystallographic thermal creep model is proposed for Zr alloys that accounts for the hardening contribution of solutes via their time-dependent pinning effect on dislocations. The core-diffusion model proposed by Soare and Curtin (2008a) is coupled with a recently proposed constitutive modeling framework (Wang et al., 2017, 2016) accounting for the heterogeneous distribution of internal stresses within grains. The Coble creep mechanism is also included. This model is, in turn, embedded in the effective medium crystallographic VPSC framework and used to predict creep strain evolution of polycrystals under different temperature and stress conditions. The simulation results reproduce the experimental creep data for Zircaloy-4 and the transition between the low (n∼1), intermediate (n∼4) and high (n∼9) power law creep regimes. This is achieved through the dependence on local aging time of the solute-dislocation binding energy. The anomalies in strain rate sensitivity (SRS) are discussed in terms of core-diffusion effects on dislocation junction strength. The mechanism-based model captures the primary and secondary creep regimes results reported by Kombaiah and Murty (2015a, 2015b) for a comprehensive set of testing conditions covering the 500–600 °C interval, stresses spanning 14–156 MPa, and steady state creep rates varying between 1.5·10−9s−1 to 2·10−3s−1. There are two major advantages to this model with respect to more empirical ones used as constitutive laws for describing thermal creep of cladding: 1) specific dependences on the nature of solutes and their concentrations are explicitly accounted for; 2) accident conditions in reactors, such as RIA and LOCA, usually take place in short times, and deformation takes place in the primary, not the steady-state creep stage. As a consequence, a model that accounts for the evolution with time of microstructure is more reliable for this kind of simulation

A Physics-Based Crystallographic Modeling Framework for Describing the Thermal Creep Behavior of Fe-Cr Alloys

In this work, a physics-based thermal creep model is developed based on the understanding of the microstructure in Fe-Cr alloys. This model is associated with a transition state theory-based framework that considers the distribution of internal stresses at sub-material point level. The thermally activated dislocation glide and climb mechanisms are coupled in the obstacle-bypass processes for both dislocation and precipitate-type barriers. A kinetic law is proposed to track the dislocation densities evolution in the subgrain interior and in the cell wall. The predicted results show that this model, embedded in the visco-plastic self-consistent framework, captures well the creep behaviors for primary and steady-state stages under various loading conditions. The roles of the mechanisms involved are also discussed

Mechanism-based modeling of thermal and irradiation creep behavior:An application to ferritic/martensitic HT9 steel

In this work, the creep behavior of HT9 steel in both thermal and irradiation environments is predicted using an integrated modeling framework. Multiple physical mechanisms such as diffusional creep and dislocation climb are incorporated into crystal plasticity calculations using the Visco-Plastic Self-Consistent (VPSC) approach. Climb velocities are informed by mean field rate theory laws in place of empirical power law formulations. More interestingly, the climb velocities explicitly consider the contribution of irradiation-induced point defects, i.e., stress induced preferential absorption (SIPA) effect. The developed expressions are shown to apply under conventional thermal creep and to the more complex irradiation conditions as well. This physically-informed, mechanism-based model is used to simulate the creep strain evolution of HT9 pressurized tubes under various loading conditions. It is demonstrated that the experimental behavior of this material reported in the literature is well described by this theoretical framework. The role of each relevant mechanism is discussed

Mechanical behavior of low carbon steel subjected to strain path changes:Experiments and modeling

The mechanical response of a low carbon steel under complex strain path changes is analyzed here in terms of dislocation storage and annihilation. The mechanical tests performed are cyclic shear and tensile loading followed by shear at different angles with respect to the tensile axis. The material behavior is captured by a dislocation-based hardening model, which is embedded in the Visco-Plastic Self-Consistent (VPSC) polycrystal framework taking into account the accumulation and annihilation of dislocations, as well as back-stress effects. A new and more sophisticated formulation of dislocation reversibility is proposed. The simulated flow stress responses are in good agreement with the experimental data. The effects of the dislocation-related mechanisms on the hardening response during strain path changes are discussed

Mechanical behavior of Mg subjected to strain path changes:Experiments and modeling

Two-step tension tests with reloads along different directions are performed on rolled Mg alloy sheet at room temperature. The experimental yield stress at reloading is systematically lower than before unloading. Such a behavior is captured by a microstructure-based hardening model accounting for dislocation reversibility and back-stress. This formulation, embedded in the Visco-Plastic Self-Consistent (VPSC) model, links the dislocation density evolution throughout the deformation with hardening. The predicted results agree well with the experimental data in terms of flow stress response and texture evolution. The effects of texture anisotropy and back-stress on the mechanical response during the strain path change are discussed

Mechanical response of stainless steel subjected to biaxial load path changes:Cruciform experiments and multi-scale modeling

We propose a multi-scale modeling approach that can simulate the microstructural and mechanical behavior of metal/alloy parts with complex geometries subjected to multi-axial load path changes. The model is used to understand the biaxial load path change behavior of 316L stainless steel cruciform samples. At the macroscale, a finite element approach is used to simulate the cruciform geometry and numerically predict the gauge stresses, which are difficult to obtain analytically. At each material point in the finite element mesh, the anisotropic viscoplastic self-consistent model is used to simulate the role of texture evolution on the mechanical response. At the single crystal level, a dislocation density based hardening law that appropriately captures the role of multi-axial load path changes on slip activity is used. The combined approach is experimentally validated using cruciform samples subjected to uniaxial load and unload followed by different biaxial reloads in the angular range [27 degrees, 90 degrees]. Polycrystalline yield surfaces before and after load path changes are generated using the full-field elasto-viscoplastic fast Fourier transform model to study the influence of the deformation history and reloading direction on the mechanical response, including the Bauschinger effect, of these cruciform samples. Results reveal that the Bauschinger effect is strongly dependent on the first loading direction and strain, intergranular and macroscopic residual stresses after first load, and the reloading angle. The microstructural origins of the mechanical response are discussed

Individual tree growth models for eucalyptus in northern Brazil

The diameter and height growth model is one of three submodels used for simulating individual tree growth. In Brazil, there are few studies on the dimensional growth of individual trees be they native or exotic species, despite their potential. This study aimed to evaluate diameter and height growth models for individual trees for eucalyptus stands and to validate the best fitting model. Tree diameter and height data were obtained from 48 permanent plots of unthinned stands of Eucalyptus grandis × Eucalyptus urophylla hybrid located in northern Brazil. The evaluation of the diameter and height growth models was based on adjusted coefficient of determination, standard error of estimate as a percentage, trend, root mean square error and Akaike Information Criterion. Analysis also included distribution of residual percentage, statistical significance and signs of the coefficients. The Lundqvist-Korf model provided the most accurate estimates for diameter and height growth, in comparison with the other models, providing better statistical values, greater proximity to observed values and better distribution of residual percentages. The use of this type of model is feasible and can result in significant improvements in the accuracy of yield estimates

A comparative study between micro- and macro-mechanical constitutive models developed for complex loading scenarios

Constitutive models developed for simulating plastic response upon strain path changes are combined: 1) a macro-mechanical model based on anisotropic yield function, associated flow rule and distortional hardening using Homogeneous Anisotropic Hardening (HAH) approach; 2) a micro-mechanical model using self-consistent crystal plasticity in conjunction with crystallographic dislocation-density based hardening. The micro-mechanical model is employed to probe the yield surface in order to gain the insight required to construct empirical rules appropriate for the macro-mechanical model. Simulation results of the micro-mechanical model under various loading conditions involving strain path changes and different crystallographic textures are presented. The trends captured in the yield surface evolution predicted by the micro-mechanical model were used to validate and improve the empirical rules used in the HAH model