Finite element simulation of heat flow in decomposing polymer composites
Polymer composite materials, particularly glass reinforced plastics (GRP), are increasingly being used in the offshore industry and their behaviour in fire is studied using mathematical and numerical modelling. A generalised finite element method is developed to analyse the thermally induced response of a widely used GRP, consisting of polyester resin and glass fibre reinforcement. GRP panels, pipes and joins subject to hydrocarbon fires (i.e. high temperatures) are studied. One- and two-dimensional mathematical models are developed to study the fire performance of: (i) single-skinned GRP panels, (ii) twin-skinned GRP-Vermiculux sandwich panels, and (iii) thin and thick GRP joins (step panels). The models involve thermochemical decomposition of the material (pyrolysis) and include: (i) transient heat conduction, (ii) gas mass movement and internal heat convection of pyrolysis gases, (iii) mass loss and Arrhenius rate decomposition of the resin material into gases and char, and (iv) endothermicity of pyrolysis. The effect of imperfect bonding on heat transfer in sandwich panels and the accumulation of pyrolysis gases and internal pressurisation in thick step panels are also included. The models may be used with any combination of steady or time-dependent boundary conditions including temperature, radiation, chemical reactions, mass diffusion and free and forced convections. Various positions of panels, i.e. vertical, horizontal and inclined are studied. The material is assumed homogeneous and orthotropic with respect to thermal and transport properties which may vary with temperature, pore pressure and moisture. The finite element models use weighted residual approach with linear elements for one- dimensional and quadrilateral elements for two-dimensional. Non-linear terms and coefficients are evaluated explicitly using an iterative-updating method and nodal temperatures and pore pressures implicitly using Crank-Nicolson solution. The classical finite difference time stepping algorithm is used where an efficient solution is achieved using variable time step. Numerical results are presented in the form of temperature versus time, temperature versus distance, pore pressure versus distance, mass loss versus distance and moisture versus distance and compared with experimental data where available. It is shown that the decomposition of the material, endothermicity of pyrolysis and the movement of pyrolysis gases make substantial contributions towards the cooling behaviour and delaying the bum-through. The effect of gas mass movement and surface chemical reactions across the boundary layer adjacent to the fire-exposed surface is very important in introducing a theoretical boundary condition. An investigation into the effect of inclusion the variable thermal properties reveals considerable improvement in thermal predictions. Sandwich panels consisting of GRP/Vermiculux/GRP offer good thermal insulation. Thermal contact resistance at an imperfect bonding is important where an average difference of 12% can be found between the thermal responses of sandwich panels with perfect and imperfect bonding. For thin GRP step panels, a one-dimensional solution is found adequate to predict the fire resistance behaviour of the material. For thick GRP step panels, the effect of internal pressurisation coupled with temperature on the thermal response is considerable.