On the stress analysis of cracked bodies by means of finite elements

The work described in this thesis deals with the development and application of a finite element program for the analysis of several cracked structures. In order to simplify the organisation of the material presented herein, the thesis has been subdivided into two Sections : In the first Section the development of a finite element program for the analysis of two-dimensional problems of plane stress or plane strain is described. The element used in this program is the six-mode isoparametric triangular element which permits the accurate modelling of curved boundary surfaces. Various cases of material aniftropy are included in the derivation of the element stiffness properties. A digital computer program is described and examples of its application are presented. In the second Section, on fracture problems, several cracked configurations are analysed by embedding into the finite element mesh a sub-region, containing the singularities and over which an analytic solution is used. The modifications necessary to augment a standard finite element program, such as that developed in Section I, are discussed and complete programs for each cracked configuration are presented. Several examples are included to demonstrate the accuracy and flexibility of the technique.

Separation of n-paraffins by selective adsorption

A study has been undertaken of the vapor-phase adsorptive separation of n-alkanes from Kuwait kerosene (Kuwait National Petroleum Company, heavy kerosene) using zeolite molecular sieves. Due to the shortage of information on the adsorption of multicomponent systems in the open literature, the present investigation was initiated to study the effect of feed flowrate, temperature, and zeolite particle size on the height of mass transfer zone (MTZ) and the dynamic capacity of the adsorbent for multicomponent n-alkanes adsorption on a fixed-bed of zeolite type-5A. The optimum operating conditions for separation of the n-alkanes has been identified so that the effluent would also be of marketable quality. The effect of multicycle adsorption-desorption stages on the dynamic behaviour of zeolite using steam as a desorbing agent has been studied and compared with n-pentane and n-hexane as desorbing agents. The separation process comprised one cycle of adsorption using a fixed-bed of zeolite type-5A. The bed was fed with vaporized kerosene until saturation had been achieved whereby the n-alkanes were adsorbed and the denormalized material eluted. The process of adsorption-desorption was carried out isobarically at one atmosphere. A mathematical model has been developed to predict the breakthrough time using the method of characteristics. The results were in a reasonable agreement with the experimental values. This model has also been utilized to develop the equilibrium isotherm. Optimum operating conditions were achieved at a feed flowrate of 33.33 x 10-9 m3/s, a temperature of 643 K, and a particle size of (1.0 - 2.0) x 10-3 m. This yielded an HMTZ value and a dynamic capacity of 0.206 m and 9.6S3 x 10-2 kg n-alkanes/kg of zeolite respectively. These data will serve as a basis for design of a commercial plant. The purity of liquid-paraffin product desorbed using steam was 83.24 wt%. The dynamic capacity was noticed to decrease sharply with the cycle number, without intermediate reactivation of zeolite, while it was kept unchanged by intermediate reactivation. Normal hexane was found to be the best desorbing agent, the efficiency of which was mounted to 88.2%.

Intumescent formulations incorporating melamine phosphate

Once familiar with the fire test rig constructed by M Kay, and modified to allow incorporation of both video and computer facilities, Melamine Phosphate production was scaled up from small to large laboratory scale, and then commercial scale production was considered. Samples produced at each stage were compared analytically, visually and in fire testing. The separation and drying stages on a commercial scale lay unresolved practically, due to lack of test facilities. Different cure regimes for the Araldite MY753 and Versamid system were investigated along with weathering tests and cured samples. Surface priming is suggested for large scale application, though on a small scale a clean unprimed surface was thought sufficient. Some samples heat, aired, cracked at the edges but remained bonded on fire testing. An intumescent sample containing Melamine Phosphate, Araldite and Versamid could not be applied to a vertical surface successfully, the viscosity had to be increased to allow application and curing, various additives were tested, two successful ones being fumed silica and a solvent, isopropanol. The low percentages fumed silica used was incorporated into the sample and the viscosity and fire test results compared with a `standard sample'. An expanding graphite incorporated into a standard sample made mixing and application increasingly difficult, due to the lubricating affect of graphite, but the char produced was a good quality, stable char. A suitable formulation could now be mixed, applied and cured, and assuming no adverse interaction between the additives would protect the sample in the event of a fire.

The effect of flow regimes in the distillation of systems containing two liquid phases

Single phase solutions containing three components have been observed to exhibit foaminess near a single to two liquid phase boundary. It was seen, in a sintered plate column under mass transfer conditions, that distillation systems where the liquid appeared as one phase in one part of a column and two phases in another part, exhibited foaminess when the liquid concentration was near the one phase to two phase boundary. Various ternary systems have been studied in a 50 plate. 30mm i.d. Oldershaw column and it was observed that severe foaming occurred in the middle section of the column near the one liquid phase to two liquid phase boundary and no foaming occurred at the end of the column where liquid was either one phase or two phase. This is known as Ross type foam. Mass transfer experiments with Ross type ternary systems have been carried out in a perspex simulator with small and large hole diameter trays. It was observed that by removal of the more volatile component, Ross type foam did not build up on the tray. Severe entrainment of liquid was observed in all cases leading to a 'dry' tray, even with a low free area small diameter hole tray which was expected to produce a bubbly mixture. Entrainment was more severe for high gas superficial velocities and large hole diameters. This behaviour is quite different from the build up of foam observed when one liquid phase/two liquid phase Ross systems were contacted with air above a small sintered disc or with vapour in an Oldershaw distillation column. This observation explains why distillation columns processing mixtures which change from one liquid phase to two liquid phases (or vice versa) must be severely derated to avoid flooding. Single liquid phase holdups at the spray to bubbly transition were measured using a perspex simulator similar to that of Porter & Wong (17). i.e. with no liquid cross flow. A light transmission technique was used to measure the transition from spray regime to bubbly regime. The effect of tray thickness and the ratio of hole diameter to tray thickness on the transition was evaluated using trays of the same hole diameter and free area but having thickness of 2.38 mm, 4 mm, and 6.35 mm. The liquid holdup at the transition was less with the thin metal trays. This result may be interpreted by the theory of Lockett (101), which predicts the transition liquid holdup in terms of the angle of the gas iet leaving the holes in the sieve plate. All the existing correlations have been compared and none were found to be satisfactory and these correlations have been modified in view of the experimental results obtained. A new correlation has been proposed which takes into account the effect of the hole diameter to tray thickness ratio on the transition and good agreement was obtained between the experimental results and the correlated values of the liquid holdup at the transition. Results have been obtained for two immiscible liquids [kerosene and water] on trays to determine whether foaming can be eliminated by operating in the spray regime. Kerosene was added to a fixed volume of water or water was added to a fixed volume of kerosene. In both cases, there was a transition from spray to bubbly. In the water fixed system. the liquid holdup at the transition was slightly less than the pure kerosene system. Whilst for the kerosene fixed system, the transition occurred at much lower liquid holdups. Trends In the results were similar to those for single liquid phase. New correlations have been proposed for the two cases. It has been found that Ross type foams, observed in a sintered plate column and in the Oldershaw column can be eliminated by either carrying out the separation in a packed column or by the addition of defoaming additives.

Application of the finite element method to problems in fracture mechanics

Numerical techniques have been finding increasing use in all aspects of fracture mechanics, and often provide the only means for analyzing fracture problems. The work presented here, is concerned with the application of the finite element method to cracked structures. The present work was directed towards the establishment of a comprehensive two-dimensional finite element, linear elastic, fracture analysis package. Significant progress has been made to this end, and features which can now be studied include multi-crack tip mixed-mode problems, involving partial crack closure. The crack tip core element was refined and special local crack tip elements were employed to reduce the element density in the neighbourhood of the core region. The work builds upon experience gained by previous research workers and, as part of the general development, the program was modified to incorporate the eight-node isoparametric quadrilateral element. Also. a more flexible solving routine was developed, and provided a very compact method of solving large sets of simultaneous equations, stored in a segmented form. To complement the finite element analysis programs, an automatic mesh generation program has been developed, which enables complex problems. involving fine element detail, to be investigated with a minimum of input data. The scheme has proven to be versati Ie and reasonably easy to implement. Numerous examples are given to demonstrate the accuracy and flexibility of the finite element technique.

Chemical reactions at nuclear fuel-clad interfaces

This thesis presents a study of the chemical reactions that may occur at the fuel- clad interfaces of fuel elements used in advanced gas-coooled reactors (A.G.R.) The initial investigation involved a study of the inner surfaces of irradiated stainless steel clad and evidence was obtained to show that fission products, in particular tellerium, were associated with reaction products on these surfaces. An accelerated rate of oxidation was observed on the inner surfaces of a failed A.G.R. fuel pin. It is believed that fission product caesium was responsible for this enhancement. A fundamental study of the reaction between 20%Cr/25%Ni/niobium stabilised stainless steel and tellerium was then undertaken over the range 350 - 850 degrees C. Reaction occurred with increasing rapidity over this range and long term exposure at ≤ 750 degrees resulted in intergranular attack of the stainless steel and chromium depletion. The reaction on unoxidised steel surfaces involved the formation of an initial iron-nickel-tellerium layer which subsequently transformed to a chromium telluride product during continued exposure. The thermodynamic stabilities of the steel tellurides were determined to be chromium telluride > nickel telluride > iron telluride. Oxidation of the stainless steel surface prior to tellerium exposure inhibited the reaction. However reaction did occur in regions where the oxide layer had either cracked or spalled.

Development of multiphase and multiscale mathematical models for thermal spray process

High velocity oxyfuel (HVOF) thermal spraying is one of the most significant developments in the thermal spray industry since the development of the original plasma spray technique. The first investigation deals with the combustion and discrete particle models within the general purpose commercial CFD code FLUENT to solve the combustion of kerosene and couple the motion of fuel droplets with the gas flow dynamics in a Lagrangian fashion. The effects of liquid fuel droplets on the thermodynamics of the combusting gas flow are examined thoroughly showing that combustion process of kerosene is independent on the initial fuel droplet sizes. The second analysis copes with the full water cooling numerical model, which can assist on thermal performance optimisation or to determine the best method for heat removal without the cost of building physical prototypes. The numerical results indicate that the water flow rate and direction has noticeable influence on the cooling efficiency but no noticeable effect on the gas flow dynamics within the thermal spraying gun. The third investigation deals with the development and implementation of discrete phase particle models. The results indicate that most powder particles are not melted upon hitting the substrate to be coated. The oxidation model confirms that HVOF guns can produce metallic coating with low oxidation within the typical standing-off distance about 30cm. Physical properties such as porosity, microstructure, surface roughness and adhesion strength of coatings produced by droplet deposition in a thermal spray process are determined to a large extent by the dynamics of deformation and solidification of the particles impinging on the substrate. Therefore, is one of the objectives of this study to present a complete numerical model of droplet impact and solidification. The modelling results show that solidification of droplets is significantly affected by the thermal contact resistance/substrate surface roughness.

Creep crack growth in cast steam turbine casing steels

The creep rupture properties of cast ½Cr½Mo¼V and 1Cr1Mo¼V alloy steel used in the manufacture of power station steam generating plant. have been investigated. The effects of constraint and geometry on the creep rupture properties are also considered. The validity of various criteria controlling macroscopic creep crack growth in cast CrMoV alloys has been examined. It is found that neither the stress intensity factor nor reference stress correlate satisfactorily the creep crack growth rates at the test temperature of 550°C. Certain minimum displacements must be achieved for crack initiation and propagation. It is found that this displacement as measured by crack opening displacement or crack aspect ratio, is the same in both compact tension and centre-cracked panel geometries, is invariant with crack length and decreases with increasing constraint. The effect of constraint on creep crack growth rate in the two geometries is less conclusive. A new model describing creep crack growth in cast CrMoV alloy steels has been developed. The model is based on the results from a numerical finite element creep analysis of the relaxation and redistribution of stress ahead of an incubating creep crack . It is found that macroscopic creep crack growth in a material undergoing either plane stress or plane strain deformation can be described by a fracture stress which is based on the Von Mises equivalent stress. It has been shown that this model is capable of rationalising all of the experimental crack velocity data from the cast CrMoV alloys. The resultant degree of data correlation is far superior to that obtained when using the stress intensity factor or reference stress. A cumulative damage creep fracture model based upon the results from the numerical analysis has been developed. It is found that the model is capable of predicting the behaviour of propagating creep cracks in cast CrMoV alloys from smooth bar creep rupture data.

Ductile fracture mechanisms in a structural steel

Microstructural fracture processes in a BS4360 Grade 50D structural steel with lower sulphur content were studied in smooth tensile specimen tests and Charpy-size bend bar tests. Based on the experimental analysis, an experimental void growth relation with the plastic strain and stress triaxiality and multiplying factor on void growth were determined. Experimental results show that the void growth relation can be reasonably used to estimate the constraint in the specimens containing the notch or crack, also they can be used to evaluate the variations of the stress triaxiality in front of the notch and crack tip under general yielding condition. Side-grooves obviously increase the constraint of the CVN specimens. Strain hardening leads to increasing the stress triaxiality, and decelerating the net void growth. This is especially true for the values of stress triaxiality more than about one. Additionally, the effect of the stress triaxiality on the critical void growth corresponding to the onset of ductile tearing was preliminarily investigated. In this work, a large number of smaller specimens were tested to investigate the ductile-brittle transition behaviour of the structural steel. A void growth rate explanation was suggested for evaluating the temperature transition behaviour. The elastic-plastic fracture tough-ness values based on small specimen tests, such as pre-cracked side-grooved bending specimen and short bar tensile specimen, may give large overestimates of the plane strain fracture toughness.

The intermediate pyrolysis and catalytic steam reforming of brewers spent grain

Brewers spent grain (BSG) is a widely available feedstock representing approximately 85% of the total by-products generated in the brewing industry. This is currently either disposed of to landfill or used as cattle feed due to its high protein content. BSG has received little or no attention as a potential energy resource, but increasing disposal costs and environmental constraints are now prompting the consideration of this. One possibility for the utilisation of BSG for energy is via intermediate pyrolysis to produce gases, vapours and chars. Intermediate pyrolysis is characterised by indirect heating in the absence of oxygen for short solids residence times of a few minutes, at temperatures of 350-450 °C. In the present work BSG has been characterised by chemical, proximate, ultimate and thermo-gravimetric analysis. Intermediate pyrolysis of BSG at 450 °C was carried out using a twin coaxial screw reactor known as Pyroformer to give yields of char 29%, 51% of bio-oil and 19% of permanent gases. The bio-oil liquid was found to separate in to an aqueous phase and organic phase. The organic phase contained viscous compounds that could age over time leading to solid tars that can present problems in CHP application. The quality of the pyrolysis vapour products before quenching can be upgraded to achieve much improved suitability as a fuel by downstream catalytic reforming. A Bench Scale batch pyrolysis reactor has then been used to pyrolyse small samples of BSG under a range of conditions of heating rate and temperature simulating the Pyroformer. A small catalytic reformer has been added downstream of the reactor in which the pyrolysis vapours can be further cracked and reformed. A commercial reforming nickel catalyst was used at 500, 750 and 850 °C at a space velocity about 10,000 L/h with and without the addition of steam. Results are presented for the properties of BSG, and the products of the pyrolysis process both with and without catalytic post-processing. Results indicate that catalytic reforming produced a significant increase in permanent gases mainly (H2 and CO) with H2 content exceeding 50 vol% at higher reforming temperatures. Bio-oil yield decreased significantly as reforming temperature increased with char remaining the same as pyrolysis condition remained unchanged. The process shows an increase in heating value for the product gas ranging between 10.8-25.2 MJ/m as reforming temperature increased. © 2012 Elsevier B.V. All rights reserved.

Low severity Fischer-Tropsch synthesis for the production of synthetic hydrocarbon fuels

Currently, the main source for the production of liquid transportation fuels is petroleum, the continued use of which faces many challenges including depleting oil reserves, significant oil price rises, and environmental concerns over global warming which is widely believed to be due to fossil fuel derived CO2 emissions and other greenhouse gases. In this respect, lignocellulosic or plant biomass is a particularly interesting resource as it is the only renewable source of organic carbon that can be converted into liquid transportation fuels. The gasification of biomass produces syngas which can then be converted into synthetic liquid hydrocarbon fuels by means of the Fischer-Tropsch (FT) synthesis. This process has been widely considered as an attractive option for producing clean liquid hydrocarbon fuels from biomass that have been identified as promising alternatives to conventional fossil fuels like diesel and kerosene. The resulting product composition in FT synthesis is influenced by the type of catalyst and the reaction conditions that are used in the process. One of the issues facing this conversion process is the development of a technology that can be scaled down to match the scattered nature of biomass resources, including lower operating pressures, without compromising liquid composition. The primary aims of this work were to experimentally explore FT synthesis at low pressures for the purpose of process down-scaling and cost reduction, and to investigate the potential for obtaining an intermediate FT synthetic crude liquid product that can be integrated into existing refineries under the range of process conditions employed. Two different fixed-bed micro-reactors were used for FT synthesis; a 2cm3 reactor at the University of Rio de Janeiro (UFRJ) and a 20cm3 reactor at Aston University. The experimental work firstly involved the selection of a suitable catalyst from three that were available. Secondly, a parameter study was carried out on the 20cm3 reactor using the selected catalyst to investigate the influence of reactor temperature, reactor pressure, space velocity, the H2/CO molar ratio in the feed syngas and catalyst loading on the reaction performance measured as CO conversion, catalyst stability, product distribution, product yields and liquid hydrocarbon product composition. From this parameter study a set of preferred operating conditions was identified for low pressure FT synthesis. The three catalysts were characterized using BET, XRD, TPR and SEM. The catalyst selected was an unpromoted Co/Al2O3 catalyst. FT synthesis runs on the 20cm3 reactor at Aston were conducted for 48 hours. Permanent gases and light hydrocarbons (C1-C5) were analysed in an online GC-TCD/FID at hourly intervals. The liquid hydrocarbons collected were analyzed offline using GC-MS for determination of fuel composition. The parameter study showed that CO conversion and liquid hydrocarbon yields increase with increasing reactor pressure up to around 8 bar, above which the effect of pressure is small. The parameters that had the most significant influence on CO conversion, product selectivity and liquid hydrocarbon yields were reactor temperature and catalyst loading. The preferred reaction conditions identified for this research were: T = 230ºC, P = 10 bar, H2/CO = 2.0, WHSV = 2.2 h-1, and catalyst loading = 2.0g. Operation in the low range of pressures studied resulted in low CO conversions and liquid hydrocarbon yields, indicating that low pressure BTL-FT operation may not be industrially viable as the trade off in lower CO conversions and once-through liquid hydrocarbon product yields has to be carefully weighed against the potential cost savings resulting from process operation at lower pressures.

Fatigue crack growth behaviour in molten-metal processed SiC particle-reinforced aluminium alloys

Fatigue crack initiation and subsequent short crack growth behaviour of 2014-5wt%SiC aluminium alloy composites has been examined in 4-point bend loading using smooth bar specimens. The growth rates of long fatigue cracks have also been measured at different stress ratios using pre-cracked specimens. The distributions of SiC particles and of coarse constituent particles in the matrix (which arise as a result of the molten-metal processing and relatively slow cooling rate) have been investigated. Preferential crack initiation sites were found to be SiC-matrix interfaces, SiC particles associated with constituent particles and the coarse constituent particles themselves. For microstructurally short cracks the dispersed SiC particles also act as temporary crack arresters. In the long crack growth tests, higher fatigue crack growth rates were obtained than for monolithic alloys. This effect is attributed to the contribution of void formation, due to the decohesion of SiC particles, to the fatigue crack growth process in the composite. Above crack depths of about 200 μm 'short' crack growth rates were in good agreement with the long crack data, showing a Pris exponent, m = 4 in both cases. For the long crack and short crack growth tests little effect of specimen orientation and grain size was observed on fatigue crack growth rates, but, specimen orientation affected the toughness. No effect of stress ratio in the range R = 0.2-0.5 was seen for long crack data in the Paris region.