Constitutive modeling of δ-phase zircaloy hydride

Based on strain rate dependent nanoindentation and nano-scale impact dataset

Significance 

Cladding materials are the thin-walled metal tube that forms the outer jacket of a nuclear fuel rod. Its purpose is to prevent corrosion of the fuel by the coolant and the release of fission products into the coolant. Aluminum, stainless steel, and zirconium alloys are common cladding materials. Of the three, zirconium alloys (zircaloy) are more popular credit to their outstanding thermomechanical properties and corrosion resistance. Nonetheless, during the operation of nuclear reactors, zircaloy cladding chemically reacts with the high temperature coolant water, producing zirconium oxide and hydrogen. A small amount of hydrogen diffuses into the cladding. After the critical solubility limit of hydrogen, a second phase precipitate forms known as zirconium hydride. In particular, δ-phase zirconium hydride is most common in many reactors. The problem with these precipitates is that they significantly degrade the tensile strength, ductility, fracture toughness, and creep behavior of the zircaloy cladding. To be specific, one of the most significant issues is ductile to brittle transition in the failure mechanism after hydride formation. At present, owing to the intricate microstructural features related to the hydride formation at different length scales, definitive examination of ductile to brittle transition remains challenging.

A review of related technical scripts reveals that many scientists have deemed it worthwhile to embark on constitutive models that incorporate local mechanical properties of embedded hydride precipitates. In line with this, Purdue University researchers: Dr. Hao Wang, Dr. Jonova Thomas, Dr. Maria A. Okuniewski and led by Professor Vikas Tomar developed one such constitutive model for zircaloy-4 embedded with δ-hydride rim/blister structures (δ-Phase zircaloy hydride). Specifically, they focused on using nanoindentation and nano-scale impact techniques to obtain the stress-strain constitutive relation of the δ-phase hydrides and zircaloy matrix at elevated temperatures. Their works is currently published in the research journal, International Journal of Plasticity.

In their approach, a combination of experiments based on nanoindentation and nano-scale impact with FEM simulations was used to develop a viscoplastic constitutive relation of zircaloy-4 embedded with δ-phase hydride rim/blister structures (δ-phase zircaloy hydride). In this work, a power law viscoplastic constitutive model was chosen to represent the strain rate dependent behavior.

The authors reported that the strength coefficient and the strain hardening exponent in the power law relation were found to decrease with increase in temperature indicating softening behavior at higher temperatures. In addition, the researchers here also reported that the strain rate exponent remained constant with increase in temperature indicating that the rate dependent ductility does not change significantly at higher temperatures.

In summary, the study demonstrated the development of new constitutive model for zircaloy-4 embedded with δ-phase hydride rim/blister structures (δ-phase zircaloy hydride). The constitutive model was implemented in another FEM model to analyze the failure strength of hydride phase at different temperatures to understand ductile to brittle transition mechanism in zircaloy-4 embedded with δ-phase hydride rim/blister structures. Remarkably, the model was shown to predict the ductile to brittle transition behavior along with the hydride cracking. In a statement to Advances in Engineering, Professor Vikas Tomar emphasized that their model predicted that fracture strength of δ-phase zircaloy hydride decreases linearly with increase in temperature, however, limited sample availability remained an issue that affects such large-scale data analyses.

Reference

Hao Wang, Jonova Thomas, Maria A. Okuniewski, Vikas Tomar. Constitutive modeling of δ-phase zircaloy hydride based on strain rate dependent nanoindentation and nano-scale impact dataset. International Journal of Plasticity; volume 133 (2020) 102787.

Go To International Journal of Plasticity

Check Also

3D-printed short carbon fibre reinforced perforated structures with negative Poisson's ratios: Mechanisms and design - Advances in Engineering

3D-printed short carbon fibre reinforced perforated structures with negative Poisson’s ratios