Quantitative non-destructive testing

The work undertaken during this period included two primary efforts. The first is a continuation of theoretical development from the previous year of models and data analyses for NDE using the Optical Thermal Infra-Red Measurement System (OPTITHIRMS) system, which involves heat injection with a laser and observation of the resulting thermal pattern with an infrared imaging system. The second is an investigation into the use of the thermoelastic effect as an effective tool for NDE. As in the past, the effort is aimed towards NDE techniques applicable to composite materials in structural applications. The theoretical development described produced several models of temperature patterns over several geometries and material types. Agreement between model data and temperature observations was obtained. A model study with one of these models investigated some fundamental difficulties with the proposed method (the primitive equation method) for obtaining diffusivity values in plates of thickness and supplied guidelines for avoiding these difficulties. A wide range of computing speeds was found among the various models, with a one-dimensional model based on Laplace's integral solution being both very fast and very accurate

Invited Article: CO_2 laser production of fused silica fibers for use in interferometric gravitational wave detector mirror suspensions

In 2000 the first mirror suspensions to use a quasi-monolithic final stage were installed at the GEO600 detector site outside Hannover, pioneering the use of fused silica suspension fibers in long baseline interferometric detectors to reduce suspension thermal noise. Since that time, development of the production methods of fused silica fibers has continued. We present here a review of a novel CO_2 laser-based fiber pulling machine developed for the production of fused silica suspensions for the next generation of interferometric gravitational wave detectors and for use in experiments requiring low thermal noise suspensions. We discuss tolerances, strengths, and thermal noise performance requirements for the next generation of gravitational wave detectors. Measurements made on fibers produced using this machine show a 0.8% variation in vertical stiffness and 0.05% tolerance on length, with average strengths exceeding 4 GPa, and mechanical dissipation which meets the requirements for Advanced LIGO thermal noise performance

Thermal distortions of non-Gaussian beams in Fabry–Perot cavities

Thermal effects are already important in currently operating interferometric gravitational wave detectors. Planned upgrades of these detectors involve increasing optical power to combat quantum shot noise. We consider the ramifications of this increased power for one particular class of laser beams—wide, flat-topped, mesa beams. In particular we model a single mesa beam Fabry–Perot cavity having thermoelastically deformed mirrors. We calculate the intensity profile of the fundamental cavity eigenmode in the presence of thermal perturbations, and the associated changes in thermal noise. We also outline an idealized method of correcting for such effects. At each stage we contrast our results with those of a comparable Gaussian beam cavity. Although we focus on mesa beams the techniques described are applicable to any azimuthally symmetric system

Aspects of mirrors and suspensions for advanced gravitational wave detectors

Gravitational waves were first predicted by Albert Einstein's Theory of general relativity, published in 1916. These waves are perturbations in the curvature of space-time. Indirect evidence of their existence has been obtained via observations of binary pulsar system inspirals by Hulse and Taylor. Research is now focussed on achieving direct detection of gravitational waves, giving a new way of observing astronoomical events in the universe. Gravitational waves are quadrupole in nature, causing tidal strains in space. The weak nature of gravity means that the magnitude of these strains is very small. Only astronomical scale sources are likely to produce waves of sufficient amplitude to be detected on Earth. In the frequency band of a few Hz to a few kHz, the expected strain amplitude for violent sources is of the order of 10[superscript -22]. Detection is most likely to be achieved using long baseline interferometer detectors. Currently several such detectors are in operation worldwide, including the GEO600 detector, built in a collaboration involving the Institute for Gravitational Research at the University of Glasgow, the Albert Einstein Institute (Hannover and Golm), and the University of Cardiff. In America the LIGO detector network has three large interferometric detectors - two of 4 km arm length and one with 2 km arms. In Italy a European collaboration has constructed the 3 km VIRGO detector. Currently GEO600 and LIGO have undertaken 5 data taking science runs with the most recent year long run, also involving VIRGO, concluding in November 2007. No detections have yet been confirmed, but analysis on the results of the most recent GEO600/LIGO/VIRGO run is ongoing. These detectors are now operating at, or close to their design sensitivities, so research is focussed on reduction of various noise sources by upgrading of the detectors. One important noise source is thermal noise (both Brownian and thermo-elastic) - a limiting factor at midband frequencies. Reduction of mechanical loss in mirrors and their suspensions will help lessen the impact of thermal noise in future detectors. The research detailed in this thesis was aimed at reducing thermal noise. In particular, it covers work undertaken to investigate the mechanical loss of suspension ribbons and fibres, test mass mirror coatings and also diffractive surfaces on test masses to evaluate their suitability for employment in future advanced gravitational wave detectors. Upgrade of LIGO to "Advanced LIGO" will aim to reduce thermal noise by implementing mirror suspension techniques pioneered in GEO600. Specifically, it was initially proposed that test masses be suspended from silica ribbon fibres, a key choice that will be re-evaluated in this thesis. Ribbons (or fibres) will be fabricated by a CO[subscript 2] laser pulling machine being developed in Glasgow, with control programming being undertaken by the author. Characterising the dimensions, strength and vertical bounce frequencies of the ribbons is important to confirm their suitability for use in detector mirror suspensions. A dimensional characterisation machine was constructed to measure the ribbon's cross sectional dimensions, with emphasis being placed on achieving high resolution in the ribbon neck regions, where the most bending occurs. Also, a bounce testing machine was constructed to experimentally measure the ribbon's vertical bounce frequency. Finally a proof load test was constructed to verify that ribbons could support the required weight. Results showed that ribbons could be fabricated successfully with the required strength and bounce frequency, though shaping of the cross section still requires further research to achieve the optimum. In a pendulum system most of the energy is stored as gravitational potential energy rather than bending energy of the suspension fibres or ribbons. Thus the effective loss of the suspension fibres/ribbons is reduced or "diluted" and thermal noise is lower than may be naively expected. Dilution of the mechanical loss of the pendulum suspensions was investigated using finite element modelling. Methods for importing data from the dimensional characterisation machine were developed, and it was observed that the dilution resulting from ribbon suspensions was not as high as had been initially expected, with bending in the neck region of the ribbon being seen to significantly reduce dilution. It was observed that the rectangular ribbons had inferior dilution to equivalent cross section circular fibres for necks of the length typically being produced. A typical 7.5 mm necked ribbon was seen to have a dilution 1.5 times lower than an equivalent fibre, despite the ribbons having 3.3 times greater dilution with no necks. Ribbons were only seen to have this superior dilution for very short necks. Bending in the necks resulted in an increased amount of bending strain energy occurring which caused the lower dilution factors. Additionally, bending occurring in the ears that join the fibres or ribbons to the masses was seen to further reduce the dilution. In the light of low dilution factors, reduction (ideally nulling) of thermoelastic noise was studied. Reduction in thermal noise in this way is proposed through the use of tapered fibres, which showed that a lower overall noise level than that from the baseline ribbons planned for Advanced LIGO can be achieved, despite lower dilution factors. In the light of this work tapered fibres have now been adopted as the baseling for Advanced LIGO. Measurement of test mass mirror samples showed that the mechanical loss of mirror coatings can be significantly reduced by doping the high refractive index layer, with reduction up to a factor of 2.5 in measured mechanical loss observed, when compared to equivalent undoped coatings. In order to perform these measurements an interferometric read out system was constructed. Future detectors will use higher laser powers which may cause thermal distortions in transmissive optical components. Use of all reflective components may be required to reduce this problem, possibly via diffractive mirrors. Measurements were undertaken on samples to discover if introducing a diffraction grating to an optic's surface increased the mechanical loss. However, the grating was not seen to do this, and also did not increase the mechanical loss of an optical coating applied on top of its surface, which verified that diffractive optics are viable for use in future detectors

Nonlocal thermoelastic vibrations for variable thermal conductivity nanobeams due to harmonically varying heat

This article constructs a new model of nonlocal thermoelasticity beam theory with phase-lags considering the thermal conductivity to be variable. A nanobeam subjected to a harmonically varying heat is considered. The nonlocal theories of coupled thermoelasticity and generalized thermoelasticity with one relaxation time can be extracted as limited and special cases of the present model. The effects of the variable thermal conductivity parameter, the nonlocal parameter, the phase-lags and the angular frequency of thermal vibration on the lateral vibration, the temperature, the displacement, and the bending moment of the nanobeam are investigated

A Study of Transversely Isotropic Thermoelastic Beam with Green-Naghdi Type-II and Type-III Theories of Thermoelasticity

The present research deals with the study of transversely isotropic thermoelastic beam in the context of Green-Naghdi (GN) theory of thermoelasticity of Type-II and Type-III. The mathematical model is prepared for the thin beam in a closed form with the application of Euler Bernoulli beam theory. The Laplace Transform technique has been used to find the expressions for displacement component, lateral thermal moment, deflection and axial stress in transformed domain. The general algorithm of the inverse Laplace Transform is developed to compute the results numerically in physical domain. The effect of two theories of thermoelasticity Green-Naghdi-II and Green-Naghdi-III has been depicted on the various quantities. Some particular cases have also been deduced

Multi-scale analysis of thermoelastic properties of graphene foam/PDMS composites

In macroscopic applications, the production of graphene foam (GF) can be an attractive way to utilize the combined advantages of graphene sheets and porous materials. The porosity level significantly affects mechanical and thermal properties by changing the specific surface area. In this study, a multi-scale method is used to calculate the coefficient of thermal expansion (CTE) and heat capacity of GF/polymer composites. Molecular dynamics have calculated the properties of 3D GFs. In particular, four types of GF with increasing mass density and decreasing porosity are investigated. The thermoelastic properties are calculated as temperature-dependent for all groups of GF. Mechanics of structure genome (MSG) based on Carrera unified formulation (CUF) is used to calculate the effective properties of the GF/polymer composites. It was found that the composite consisting of GF with the highest density and lowest porosity has the minimum CTE. Also, the heat capacity of the composite depends not only on the heat capacity of the components but also on their Young modulus, CTE, and geometry

Diffusive and wavelike phenomena in thermal processing of materials

Contemporary materials science abounds with novel processing methods. Devices such as lasers, microwave sources, and electron beam guns, provide unprecedented control over the deposition of energy within a material. The modern materials scientist has the ability to deposit energy volumetrically, to precisely control the location of energy deposition within a material, and to deposit energy in extremely short intervals of time. While making possible numerous thermal processing methods, these devices also push the limits of our understanding of the response of materials to energy deposition. In order to optimize and control these processing methods, it becomes necessary to further our understanding of this response. Here, we investigate several problems, motivated by the study of thermal processing methods, whose analyses further our understanding of these new parameter regimes. First, we consider two classes of problems arising in microwave processing of ceramics. These problems are characterized by volumetric energy deposition and a weak coupling between thermal diffusion and electromagnetic wave propagation. Next, we investigate a sequence of problems motivated by and arising in the study of an electron beam joining process. These problems are characterized by rapid volumetric energy deposition and a strong coupling between thermal diffusion and elastic wave propagation