Effect of homogenisation conditions on recrystallisation in the Al-Mg-Mn alloy AA5454

The purpose of the present work is to understand the microstructure development and, particularly, to control the progress of recrystallisation in hot strip in the Al-Mg-Mn alloy AA 5454, which is typically used for the manufacture of structural automotive components. The chemical composition, together with the thermomechanical processing history of this material, has a strong influence on the microstructure of the product and the resulting properties as it is supplied to the customer. Electrical conductivity measurements, thermal analysis and electron microscopy have been carried out to characterise the evolution of precipitation state at various stages in the processing route. The conditions of the homogenisation heat treatment have been varied, and the effect on subsequent recrystallisation after hot rolling has been evaluated in both the as cast and rough rolled condition by optical microscopy techniques. Results indicate that the conditions of homogenisation heat treatment and roughing rolling are critical for the generation of a suitable recrystallised microstructure in AA 5454 hot strip. A new two stage homogenisation practice has been developed to expedite post-rolling recrystallisation in this alloy

High frequency homogenisation for elastic lattices

A complete methodology, based on a two-scale asymptotic approach, that enables the homogenisation of elastic lattices at non-zero frequencies is developed. Elastic lattices are distinguished from scalar lattices in that two or more types of coupled waves exist, even at low frequencies. Such a theory enables the determination of effective material properties at both low and high frequencies. The theoretical framework is developed for the propagation of waves through lattices of arbitrary geometry and dimension. The asymptotic approach provides a method through which the dispersive properties of lattices at frequencies near standing waves can be described; the theory accurately describes both the dispersion curves and the response of the lattice near the edges of the Brillouin zone. The leading order solution is expressed as a product between the standing wave solution and long-scale envelope functions that are eigensolutions of the homogenised partial differential equation. The general theory is supplemented by a pair of illustrative examples for two archetypal classes of two-dimensional elastic lattices. The efficiency of the asymptotic approach in accurately describing several interesting phenomena is demonstrated, including dynamic anisotropy and Dirac cones.Comment: 24 pages, 7 figure

Tensor-based numerical method for stochastic homogenisation

This paper addresses the complexity reduction of stochastic homogenisation of a class of random materials for a stationary diffusion equation. A cost-efficient approximation of the correctors is built using a method designed to exploit quasi-periodicity. Accuracy and cost reduction are investigated for local perturbations or small transformations of periodic materials as well as for materials with no periodicity but a mesoscopic structure, for which the limitations of the method are shown. Finally, for materials outside the scope of this method, we propose to use the approximation of homogenised quantities as control variates for variance reduction of a more accurate and costly Monte Carlo estimator (using a multi-fidelity Monte Carlo method). The resulting cost reduction is illustrated in a numerical experiment with a control variate from weakly stochastic homogenisation for comparison, and the limits of this variance reduction technique are tested on materials without periodicity or mesoscopic structure

Effect of homogenisation on milk fouling in a tubular heat exchanger : a thesis presented in partial fulfilment for the requirements for the degree of Master of Food Engineering, Massey University, Palmerston North, New Zealand

Fouling of equipment surfaces in milk processing has been a costly problem for many years. In spite of an increasing body of knowledge of the fouling mechanism, the problem is not fully understood yet. Recent investigations suggest that the role of fat in whole milk fouling seems to be very important. The state and form of the fat globules, processing conditions as well as the orientation of heating surfaces may affect the fouling mechanism. Homogenisation of milk is known to cause disruption of fat globules and prevent creaming. The present work aimed to investigate the effect of homogenisation on the rate of fouling, composition and structure of fouling layers. Homogenised and un-homogenised milk were used as test fluids. Milk was heated from 4°C to 60°C in a plate heat exchanger then to 70°C and 80°C in a double pipe heat exchanger consisted of a horizontal and a vertical tube. The fouling rate in the double pipe heat exchanger was calculated and expressed as the rate of increase of the overall resistance to heat transfer, normalised using the initial heat transfer coefficient at the beginning of the run. Composition analysis of fouling layers was carried out using standard methods of moisture, ash, fat and protein tests. Resistance to deformation analysis was performed using texture tests; coverage measurement was determined by digital image analysis. Within the experimental conditions used in this work, the effect of homogenisation on the fouling rate could not be ascertained conclusively because of large variations in the values obtained but it had a significant effect in the composition of fouling layers. In all experimental runs, the amount of fat in the fouling layer was higher for un-homogenised milk compared to homogenised milk. In fact, the fat contents of fouling layers were found to be very high (between 30%-60% on a dry weight basis), which agrees with observations of other researches in New Zealand. The coverage and thickness of fouling layers were more influenced by the orientation of heated surfaces than by homogenisation. The strength of fouling layers is affected by their thickness, which decreases with increasing milk temperature

High contrast homogenisation in nonlinear elasticity under small loads

We study the homogenisation of geometrically nonlinear elastic composites with high contrast. The composites we analyse consist of a perforated matrix material, which we call the "stiff" material, and a "soft" material that fills the pores. We assume that the pores are of size $0<\varepsilon\ll 1$ and are periodically distributed with period $\varepsilon$. We also assume that the stiffness of the soft material degenerates with rate $\varepsilon^{2\gamma},$ $\gamma>0$, so that the contrast between the two materials becomes infinite as $\varepsilon\to 0$. We study the homogenisation limit $\varepsilon\to 0$ in a low energy regime, where the displacement of the stiff component is infinitesimally small. We derive an effective two-scale model, which, depending on the scaling of the energy, is either a quadratic functional or a partially quadratic functional that still allows for large strains in the soft inclusions. In the latter case, averaging out the small scale-term justifies a single-scale model for high-contrast materials, which features a non-linear and non-monotone effect describing a coupling between microscopic and the effective macroscopic displacements.Comment: 31 page