Initial and Boundary Conditions for the Lattice Boltzmann Method

A new approach of implementing initial and boundary conditions for the lattice Boltzmann method is presented. The new approach is based on an extended collision operator that uses the gradients of the fluid velocity. The numerical performance of the lattice Boltzmann method is tested on several problems with exact solutions and is also compared to an explicit finite difference projection method. The discretization error of the lattice Boltzmann method decreases quadratically with finer resolution both in space and in time. The roundoff error of the lattice Boltzmann method creates problems unless double precision arithmetic is used.Comment: 42 pages in Postscript, with additional 27 Postscript figures Physical Review E, Submitted December 92, Revised June 9

Multi-objective optimisation of the cure of thick components

This paper addresses the multi-objective optimisation of the cure stage of composites manufacture. The optimisation aims to minimise the cure process duration and maximum temperature overshoot within the curing part by selecting an appropriate thermal profile. The methodology developed combines a finite element solution of the heat transfer problem with a Genetic Algorithm. The optimisation algorithm approximates successfully and consistently the Pareto optimal front of the multi-objective problem in a variety of characteristic geometries of varying thickness. The results highlight the efficiency opportunities available in comparison with standard industrial cure profiles. In the case of ultra-thick components improvements of up to 70% in terms of overshoot and 14 h in terms of process time, compared to conventional cure profiles for ultra-thick components, can be achieved. In the case of thick components reduction up to 50% can be achieved in both temperature overshoot and process duration

Stochastic simulation of the influence of fibre path variability on the formation of residual stress and shape distortion

A stochastic cure simulation approach is developed and implemented to investigate the influence of fibre misalignment on cure. Image analysis is used to characterize fiber misalignment in a carbon non-crimp fabric. It is found that variability in tow orientation is significant with a standard deviation of 1.2°. The autocorrelation structure is modeled using the Ornstein-Uhlenbeck sheet and the stochastic problem is addressed by coupling a finite element model of cure with a Monte Carlo scheme. Simulation of the cure of an angle shaped carbon fiber-epoxy component shows that fiber misalignment can cause considerable variability in the process outcome with a coefficient of variation in maximum residual stress up to approximately 2% (standard deviation of 1 MPa) and qualitative and quantitative variations in final distortion of the cured part with the standard deviation in twist and corner angle reaching values of 0.4° and 0.05° respectively. POLYM. COMPOS., 2015. © 2015 The Authors Polymer Composites published by Wiley Periodicals, Inc. on behalf of Society of Plastics Engineer

Toward a constitutive model for cure dependent modulus of a high temperature epoxy during the cure

A constitutive model, based on Kohlrausch-Williams-Watts (KWW) equations, was developed to simulate the evolution of the dynamic relaxation modulus during the cure of a "high temperature' epoxy. The basic assumption of the modelling methodology proposed is the equivalence of the mechanisms underlying the evolution of the glass transition temperature and the relaxation time shift during the cure, leading to the use of a common potential function. This assumption is verified by the comparison of normalized glass transition data and principal relaxation times, which have been found to follow a single master curve. Results show satisfactory agreement between experimental data and model prediction over the range of chemical conversion considered

Percolation threshold of carbon nanotubes filled unsaturated polyesters

This paper reports on the development of electrically conductive nanocomposites containing multi-walled carbon nanotubes in an unsaturated polyester matrix. The resistivity of the liquid suspension during processing is used to evaluate the quality of the filler dispersion, which is also studied using optical microscopy. The electrical properties of the cured composites are analysed by AC impedance spectroscopy and DC conductivity measurements. The conductivity of the cured nanocomposite follows a statistical percolation model, with percolation threshold at 0.026 wt.% loading of nanotubes. The results obtained show that unsaturated polyesters are a matrix suitable for the preparation of electrically conductive thermosetting nanocomposites at low nanotube concentrations. The effect of carbon nanotubes reaggregation on the electrical properties of the spatial structure generated is discussed

Stochastic heat transfer simulation of the cure of advanced composites

A stochastic cure simulation approach is developed to investigate the variability of the cure process during resin infusion related to thermal effects. Boundary condition uncertainty is quantified experimentally and appropriate stochastic processes are developed to represent the variability in tool/air temperature and surface heat transfer coefficient. The heat transfer coefficient presents a variation across different experiments of 12.3%, whilst the tool/air temperatures present a standard deviation over 1℃. The boundary condition variability is combined with an existing model of cure kinetics uncertainty and the full stochastic problem is addressed by coupling a cure model with Monte Carlo and the Probabilistic Collocation Method and applied to the case of thin carbon epoxy laminates. The overall variability in cure time reaches a coefficient of variation of about 22%, which is dominated by uncertainty in surface heat transfer and tool temperature; with ambient temperature and kinetics contributing variability in the order of 1%

Stochastic simulation of the influence of cure kinetics uncertainty on composites cure

A stochastic cure simulation methodology is developed and implemented to investigate the influence of cure kinetics uncertainty due to different initial resin state on the process of cure. The simulation addresses heat transfer effects and allows quantification of uncertainty in temperature overshoot during the cure. Differential Scanning Calorimetry was used to characterise cure kinetics variability of a commercial epoxy resin used in aerospace applications. It was found that cure kinetics uncertainty is associated with variations in the initial degree of cure, activation energy and reaction order. A cure simulation model was coupled with conventional Monte Carlo and an implementation of the Probabilistic Collocation Method. Both simulation schemes are capable of capturing variability propagation, with the collocation method presenting benefits in terms of computational cost against the Monte Carlo scheme with comparable accuracy. Simulation of the cure of a carbon fibre–epoxy panel shows that cure kinetics uncertainty can cause considerable variability in the process outcome with a coefficient of variation in temperature overshoot of about 30%