Dedicated finite element analysis for refractory composites
This thesis presents a material model that has been designed to simulate the behaviour of certain refractory consumables used in the steel making industry. It is based on the principles of linear elasticity and isotropy, and a constitutive equation is developed that describes a non-linear mechanical response in tension with developing anisotropy. The mathematics of the model is firmly based on the physicality of the observed material behaviour, including the stable growth of microcracks. The residual stress that develops in some dual phase ceramics with thermal mismatch is quantified from the thermal properties of each phase and used to determine the change in the properties of the composite when undergoing damage as a result of cooling after firing and applied tensile stress. Energy principles and a crack orientation density function that can be plotted on the surface of a sphere are used to ensure that the model is invariant to changes in the reference axes, while a simplification to ensure that matrices are always positive definite ensures computational robustness. A one dimensional constitutive equation is developed and then extended through a single phase isothermal model to establish a three dimensional, dual phase, thermal model that was incorporated as a subroutine into a commercial finite element analysis package and can be used to simulate the behaviour of real components subjected to thermal and mechanical load. Creep at high temperatures was modelled, somewhat crudely, by reducing (effectively to zero) the stiffness and load carrying capacity of material that was operating at temperatures above a critical value. The computer subroutine was validated analytically and against physical tests that were conducted at room temperature. Appropriate high temperature material data was not available. The model's ability to simulate the observed features of the tests to a useful degree of accuracy with suitable material properties was demonstrated. An optimisation routine to enable the model to be calibrated quickly was developed. Finally the limitations of the model are explored and possible further work outlined.