Thermo-mechanical contributions to pellet-clad interaction (PCI) in advanced gas-cooled reactors (AGR) are modelled in the ABAQUS finite element (FE) code. User supplied subroutines permit the modelling of the non-linear behaviour of AGR fuel through life. Through utilization of ABAQUS's well-developed pre-and post-processing ability, the behaviour of the axially constrained steel clad fuel was modelled. The 2D axisymmetric model includes thermomechanical behaviour of the fuel with time and condition dependent material properties. Pellet cladding gap dynamics and thermal behaviour are also modelled. The model treats heat up as a fully coupled temperature-displacement study. Dwell time and direct power cycling was applied to model the impact of online refuelling, a key feature of the AGR. The model includes the viscoplastic behaviour of the fuel under the stress and irradiation conditions within an AGR core and a non-linear heat transfer model. A multiscale fission gas release model is applied to compute pin pressure; this model is coupled to the PCI gap model through an explicit fission gas inventory code. Whole pin, whole life, models are able to show the impact of the fuel on all segments of cladding including weld end caps and cladding pellet locking mechanisms (unique to AGR fuel). The development of this model in a commercial FE package shows that the development of a potentially verified and future-proof fuel performance code can be created and used. Keywords: Fuel Performance, ABAQUS, Finite Element, AGR Introduction Pellet-cladding interactionNumerous authors have investigated the phenomenon of PCI in the past [1][2][3][4][5][6][7][8][9][10]. These studies have included the AGR system. The AGR studies from the early 90s offer insight into the effective bonding forces between AGR cladding and fuel, albeit that these studies were for a very simplified geometry and material properties. Walker's models were two dimension r-T segments of a pellet and cladding in a coupled thermo-mechanical transient analysis. This analysis showed that the expected bond between pellet and clad will fail and cause the debonding of about 6% of the pellet-clad surface producing sufficient stress relief to prevent further debonding. Walker also shows that a failure of this size was sufficient to cause a two orders of magnitude reduction in the number of pellet cracks to propagate in the adjacent cladding. Most work in recent years has focussed on water cooled systems [2][3][11][12][13]. Marchal [11] showed through 3D modelling of PCI, in the CAST3M FE code, that the while pellet fracture did produce stress concentrations in the cladding there was also a significant stress remaining in the fuel fragment. These pellet fragments had sufficient remaining stresses that later interaction with the cladding through friction contact produced further radial cracking. Marchal's smeared crack model emphasises the non-linear behaviour of PCI cracking and that it is strongly dependent on fuel-cladding friction. *Manuscript Click here ...
Whether present as a manufactured stabilised ceramic, or as an oxide layer on zirconium alloys, mechanical degradation in zirconia is influenced by the tetragonal to monoclinic phase transformation.Peridynamic theory was implemented within the Abaqus finite element framework to understand how the tetragonal to monoclinic phase transformation can itself cause fracture in zirconia. In 2D these simulations represent a single grain, transforming via an isometric dilational expansion, surrounded by a homogenous monoclinic oxide. The effect of transformation time, applied bi-axial pressure, and the fracture strain were assessed using the change in strain energy and the amount of damage in the oxide surrounding the transformed grain. Reducing the applied compressive stress or applying a tensile stress reduces the transformation strain energy. The introduction of a fracture strain leads to damage in the surrounding oxide region largely in the form of cracks, and reduces the transformation strain energy further by reducing the constraint on the transforming grain. The extent of the fracture, and reduction in constraint on the transformed grain, is more significant with the application of a biaxial tensile pressure.
The concept of ‘contact stress’, as introduced by Cauchy, is a special case of a nonlocal stress tensor. In this work, the nonlocal stress tensor is derived through implementation of the bond-based formulation of peridynamics that uses an idealised model of interaction between points as bonds. The method is sufficiently general and can be implemented to study stress states in problems containing stress concentration, singularity, or discontinuities. Two case studies are presented, to study stress concentration around a circular hole in a square plate and conventionally singular stress fields in the vicinity of a sharp crack tip. The peridynamic stress tensor is compared with finite element approximations and available analytical solutions. It is shown that peridynamics is capable of capturing both shear and direct stresses and the results obtained correlate well with those obtained using analytical solutions and finite element approximations. A built-in MATLAB code is developed and used to construct a 2D peridynamic grid and subsequently approximate the solution of the peridynamic equation of motion. The stress tensor is then obtained using the tensorial product of bond force projections for bonds that geometrically pass through the point. To evaluate the accuracy of the predicted stresses near a crack tip, the J-integral value is computed using both a direct contour approximation and the equivalent domain integral method. In the formulation of the contour approximation, bond forces are used directly while the proposed peridynamic stress tensor is used for the domain method. The J-integral values computed are compared with those obtained by the commercial finite element package Abaqus 2018. The comparison provides an indication on the accurate prediction of the state of stress near the crack tip.
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