Modelling dynamic cracking of graphite

  • Timothy Crump

    Student thesis: Doctor of Engineering


    Advances in dynamic fracture modelling have become more frequent due to increases in computer speed, meaning that its application to industrial problems has become viable. From this, the author has reviewed current literature in terms of graphite material properties, structural dynamics, fracture mechanics and modelling methodologies to be able to address operational issues related to the ageing of Advanced Gas-cooled Reactor (AGR) cores. In particular, the experimentally observed Prompt Secondary Cracking (PSC) of graphite moderator bricks which has yet to be observed within operational reactors, with the objective of supporting their plant life extension. A method known as eXtended Finite Element Method with Cohesive Zones (XCZM) was developed within Code_Aster open-source FEM software. This enabled the incorporation of velocity toughening, irradiation-induced material degradation effects and multiple 3D dynamic crack initiations, propagations and arrests into a single model, which covers the major known attributes of the PSC mechanism. Whilst developing XCZM, several publications were produced. This started with first demonstrating XCZM's ability to model the PSC mechanism in 2D and consequently that methane holes have a noticeable effect on crack propagation speeds. Following on from this, XCZM was benchmarked in 2D against literature experiments and available model data which consequently highlighted that velocity toughening was an integral feature in producing energetically correct fracture speeds. Leading on from this, XCZM was taken into 3D and demonstrated that it produced experimentally observed bifurcation angle from a literature example. This meant that when a 3D graphite brick was modelled that the crack profile was equivalent to an accepted quasi-static profile. As a consequence of this validation, the XCZM approach was able to model PSC and give insight into features that could not be investigated previously including: finer-scale heterogeneous effects on a dynamic crack profile, comparison between Primary and Secondary crack profiles and also, 3D crack interaction with a methane hole, including insight into possible crack arrest. XCZM was shown to improve upon previous 2D models of experiments that showed the plausibility of PSC; this was achieved by eliminating the need for user intervention and also incorporation of irradiation damage effects through User-defined Material properties (UMAT). Finally, while applying XCZM to a full-scale 3D graphite brick including reactor effects, it was shown that PSC is likely to occur under LEFM assumptions and that the Secondary crack initiates before the Primary crack arrests axially meaning that modal analysis would not be able to fully model PSC.
    Date of Award1 Aug 2018
    Original languageEnglish
    Awarding Institution
    • The University of Manchester
    SupervisorAndrey Jivkov (Supervisor) & Paul Mummery (Supervisor)


    • Structural integrity
    • AGR
    • Prompt Secondary Cracking
    • meso
    • XCZM
    • graphite
    • Cohesive zone
    • XFEM
    • dynamic fracture
    • Nuclear

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