Experiment-based validation and uncertainty quantification of coupled multi-scale plasticity models

Highly anisotropic zirconium is a material used in the cladding of nuclear fuel rods, ensuring containment of the radioactive material within. The complex material structure of anisotropic zirconium requires model developers to replicate not only the macro-scale stresses but also the meso-scale material behavior as the crystal structure evolves; leading to strongly coupled multi-scale plasticity models. Such strongly coupled models can be achieved through partitioned analysis techniques, which couple independently developed constituent models through an iterative exchange of inputs and outputs. Throughout this iterative process, biases, and uncertainties inherent within constituent model predictions are inevitably transferred between constituents either compensating for each other or accumulating during iterations. The paper aims to discuss these issues.

A finite element model at the macro-scale is coupled in an iterative manner with a meso-scale viscoplastic self-consistent model, where the former supplies the stress input and latter represents the changing material properties. The authors present a systematic framework for experiment-based validation taking advantage of both separate-effect experiments conducted within each constituent’s domain to calibrate the constituents in their respective scales and integral-effect experiments executed within the coupled domain to test the validity of the coupled system.

This framework developed is shown to improve predictive capability of a multi-scale plasticity model of highly anisotropic zirconium.

For multi-scale models to be implemented to support high-consequence decisions, such as the containment of radioactive material, this transfer of biases and uncertainties must be evaluated to ensure accuracy of the predictions of the coupled model. This framework takes advantage of the transparency of partitioned analysis to reduce the accumulation of errors and uncertainties.