Finite element analysis of the tetragonal to monoclinic phase transformation during oxidation of zirconium alloys

Abstract

a b s t r a c tCorrosion is a key limiting factor in the degradation of zirconium alloys in light water reactors. Developing a mechanistic understanding of the corrosion process offers a route towards improving safety and efficiency as demand increases for higher burn-up of fuel. Oxides formed on zirconium alloys are composed of both monoclinic and meta-stable tetragonal phases, and are subject to a number of potential mechanical degradation mechanisms. The work presented investigates the link between the tetragonal to monoclinic oxide phase transformation and degradation of the protective character of the oxide layer. To achieve this, Abaqus finite element analysis of the oxide phase transformation has been carried out. Study of the change in transformation strain energy shows how relaxation of oxidation induced stress and fast fracture at the metal-oxide interface could destabilise the tetragonal phase. Central to this is the identification of the transformation variant most likely to form, and understanding why twinning of the transformed grain is likely to occur. Development of transformation strain tensors and analysis of the strain components allows some separation of dilatation and shear effects. Maximum principal stress is used as an indication of fracture in the surrounding oxide layer. Study of the stress distributions shows the way oxide fracture is likely to occur and the differing effects of dilatation and shape change. Comparison with literature provides qualitative validation of the finite element simulations.

Peridynamic simulations of the tetragonal to monoclinic phase transformation in zirconium dioxide

“…The phase transformation has been represented as a volumetric or dilatational expansion via the expansion of a central set of truss elements (Fig.1). Each truss element within this central region increases in length by 0.019 (1.9%) in line with the hydrostatic strain defined in Eq.2 and the calculated strain tensors in (Platt et al, 2014).…”

“…The impact of variant selection and anisotropic material properties are not the main focus of this work, therefore for simplicity, the phase transformation has been simulated as a dilatational volumetric expansion. This is implemented via the hydrostatic strain, calculated from the strain tensors defined in (Platt et al, 2014), and shown in equation 2. The phase transformation has been represented as a volumetric or dilatational expansion via the expansion of a central set of truss elements (Fig.1).…”

“…Both the surface and strain energies are positive whilst the chemical energy is negative. The change in total free energy must be negative for the transformation to proceed (Chevalier et al, 2009;Kelly and Francis Rose, 2002;Platt et al, 2014).…”

“…In both cases a key issue is the ingress of oxygen containing species. The tetragonal to monoclinic phase transformation is known to generate cracks (Chevalier et al, 2009;Kelly and Francis Rose, 2002), as a consequence of the ~6% volumetric expansion and ~16% shear strain upon transformation (Platt et al, 2014). Nano-scale cracks associated with this phase transformation have also been observed using transmission electron microscopy (TEM) in oxides formed on zirconium alloys (Bossis, 2002).…”

“…Previously, finite element analysis has been used to simulate the tetragonal to monoclinic phase transformation (Platt et al, 2014). This work highlighted how relaxation of the in-plane biaxial compressive stress, or the application of a triaxial tensile stress, could destabilise the tetragonal phase.…”