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.

The effect of the environment on the mechanical properties of medical grade silicones

Silicone spacers have been in use as replacement joints in the human hand for over 30 years. Since they were first used there has been a number of designs all of which have had problems with fracture. This may be due to a defect in the material caused during implantation, or by bony intrusions within the arthritic hand after implantation. The aim of this research was to investigate the effect of the environment on the mechanical properties of medical grade silicones used for human implantation. The materials were subjected to static tensile testing after various forms of ageing. The environmental conditions included temperatures of 37 and 80°C and the environments of Ringer's solution, distilled water, and air. The environmental conditions employed resulted in reduced mechanical strength with ageing time of the silicones. This research supports the view that failure of silicone implants in the hand could be partly attributed to the effects of environmental ageing of the material.

The application of finite element analysis to fracture mechanics.

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Mechanical properties of sheet metal under forming conditions

In the bulge test, a sheet metal specimen is clamped over a circular hole in a die and formed into a bulge by the hydraulic pressure on one side of the specirnen. As the unsupported part of the specimen is deformed in this way, its area is increased, in other words, the material is generally stretched and its thickness generally decreased. The stresses causing this stretching action are the membrane stresses in the shell generated by the hydraulic pressure, in the same way as the rubber in a toy balloon is stretched by the membrane stresses caused by the air inside it. The bulge test is a widely used sheet metal test, to determine the "formability" of sheet materials. Research on this forming process (2)-(15)* has hitherto been almost exclusively confined to predicting the behaviour of the bulged specimen through the constitutive equations (stresses and strains in relation to displacements and shapes) and empirical work hardening characteristics of the material as determined in the tension test. In the present study the approach is reversed; the stresses and strains in the specimen are measured and determined from the geometry of the deformed shell. Thus, the bulge test can be used for determining the stress-strain relationship in the material under actual conditions in sheet metal forming processes. When sheet materials are formed by fluid pressure, the work-piece assumes an approximately spherical shape, The exact nature and magnitude of the deviation from the perfect sphere can be defined and measured by an index called prolateness. The distribution of prolateness throughout the workpiece at any particular stage of the forming process is of fundamental significance, because it determines the variation of the stress ratio on which the mode of deformation depends. It is found. that, before the process becomes unstable in sheet metal, the workpiece is exactly spherical only at the pole and at an annular ring. Between the pole and this annular ring the workpiece is more pointed than a sphere, and outside this ring, it is flatter than a sphere. In the forming of sheet materials, the stresses and hence the incremental strains, are closely related to the curvatures of the workpiece. This relationship between geometry and state of stress can be formulated quantitatively through prolateness. The determination of the magnitudes of prolateness, however, requires special techniques. The success of the experimental work is due to the technique of measuring the profile inclination of the meridional section very accurately. A travelling microscope, workshop protractor and surface plate are used for measurements of circumferential and meridional tangential strains. The curvatures can be calculated from geometry. If, however, the shape of the workpiece is expressed in terms of the current radial (r) and axial ( L) coordinates, it is very difficult to calculate the curvatures within an adequate degree of accuracy, owing to the double differentiation involved. In this project, a first differentiation is, in effect, by-passed by measuring the profile inclination directly and the second differentiation is performed in a round-about way, as explained in later chapters. The variations of the stresses in the workpiece thus observed have not, to the knowledge of the author, been reported experimentally. The static strength of shells to withstand fluid pressure and their buckling strength under concentrated loads, both depend on the distribution of the thickness. Thickness distribution can be controlled to a limited extent by changing the work hardening characteristics of the work material and by imposing constraints. A technique is provided in this thesis for determining accurately the stress distribution, on which the strains associated with thinning depend. Whether a problem of controlled thickness distribution is tackled by theory, or by experiments, or by both combined, the analysis in this thesis supplies the theoretical framework and some useful experimental techniques for the research applied to particular problems. The improvement of formability by allowing draw-in can also be analysed with the same theoretical and experimental techniques. Results on stress-strain relationships are usually represented by single stress-strain curves plotted either between one stress and one strain (as in the tension or compression tests) or between the effective stress and effective strain, as in tests on tubular specimens under combined tension, torsion and internal pressure. In this study, the triaxial stresses and strains are plotted simultaneously in triangular coordinates. Thus, both stress and strain are represented by vectors and the relationship between them by the relationship between two vector functions. From the results so obtained, conclusions are drawn on both the behaviour and the properties of the material in the bulge test. The stress ratios are generally equal to the strain-rate ratios (stress vectors collinear with incremental strain vectors) and the work-hardening characteristics, which apply only to the particular strain paths are deduced. Plastic instability of the material is generally considered to have been reached when the oil pressure has attained its maximum value so that further deformation occurs under a constant or lower pressure. It is found that the instability regime of deformation has already occurred long before the maximum pressure is attained. Thus, a new concept of instability is proposed, and for this criterion, instability can occur for any type of pressure growth curves.

The effects of metallurgical variables on the mechanical properties of high-chromium cast irons

The.use of high-chromium cast irons for abrasive wear resistance is restricted due to their poor fracture toughness properties. An.attempt was made to improve the fracture characteristics by altering the distribution, size and.shape of the eutectic carbide phase without sacrificing their excellent wear resistance. This was achieved by additions of molybdenum or tungsten followed by high temperature heat treatments. The absence of these alloying elements or replacement of them with vanadium or manganese did not show any significant effect and the continuous eutectic carbide morphology remained the same after application of high temperature heat treatments. The fracture characteristics of the alloys with these metallurgical variables were evaluated for both sharp-cracks and blunt notches. The results were used in conjunction with metallographic and fractographic observations to establish possible failure mechanisms. The fracture mechanism of the austenitic alloys was found to be controlled not only by the volume percent but was also greatly influenced by the size and distribution of the eutectic carbides. On the other hand, the fracture mechanism of martensitic alloys was independent of the eutectic carbide morphology. The uniformity of the secondary carbide precipitation during hardening heat treatments was shown to be a reason for consistant fracture toughness results being obtained with this series of alloys although their eutectic carbide morphologies were different. The collected data were applied to a model which incorporated the microstructural parameters and correlated them with the experimentally obtained valid stress intensity factors. The stress intensity coefficients of different short-bar fracture toughness test specimens were evaluated from analytical and experimental compliance studies. The.validity and applicability of this non-standard testing technique for determination of the fracture toughness of high-chromium cast irons were investigated. The results obtained correlated well with the valid results obtained from standard fracture toughness tests.

The mechanical properties and formability of dual-phase steel

In recent years dual phase steels comprising of 5-20% martensite in a ferrite matrix have come into the limelight of high strength cold formable steels because of their potential for vehicle weight saving. They show the following features: no yield point; relatively low initial flow stress; high initial workhardening rate; well sustained work hardening. As a consequence of these characteristics, dual phase steels exhibit a better combination of strength and elongation than other HSLA steels. In this thesis, a broad view of the factors which influence their properties is presented. Mechanical properties and forming ability of a commercially available dual phase steel and an AL-Si killed steel processed to dual phase form are investigated to ascertain the effect of their microstructure on their properties. It is found that the yield phenomena are masked by the transformation induced stresses present during processing and so yield point could be recovered under suitable ageing treatment; that apart from giving the above properties dual phasing gives rise to very low strain-rate sensitivity and a low R value ~ 1; that the mechanical response under rolling conditions is not different from those under tension; that there is a danger of damage to tooling during forming operations of these steels if fracture should precede instability as a result of grain size dependent strength found for these steels. It is also found that very little deformation of the martensite islands took place during deformation except at high strains. The work-hardening and the strength levels can be controlled by either decreasing the grain size or increasing the martensite volume fraction, but it is found that increasing martensite has a detrimental effect on ductility and the ductility and fracture strength can be controlled better by refining the grain size. A remarkable effect found in the dual phase steel tested is that the compressive strength is higher than the tensile strength. The reason for this observation is not yet clear but it is suggested that it might be due to the introduction of emissary type dislocations into the ferrite lattice as a result of twins formed in the martensite during transformation from austenite. The twins are envisaged to be {111} <112> in character.

Transglutaminase mediated grafting of silk proteins onto wool fabrics leading to improved physical and mechanical properties

Transglutaminases have the ability to incorporate primary amines and to graft peptides (containing glutamine or lysine residues) into proteins. These properties enable transglutaminases to be used in the grafting of a range of compounds including peptides and/or proteins onto wool fibres, altering their functionality. In this paper we investigated the transglutaminase mediated grafting of silk proteins into wool and its effect on wool properties. A commercial hydrolysed silk preparation was compared with silk sericin. The silk sericin protein was labelled with a fluorescent probe which was used to demonstrate the efficiency of the TGase grafting of such proteins into wool fibres. The TGase mediated grafting of these proteins led to a significant effect on the properties of wool yarn and fabric, resulting in increased bursting strength, as well as reduced levels of felting shrinkage and improved fabric softness. Also observed was an accumulation of deposits on the surface of the treated wool fibres when monitored by SEM and alterations in the thermal behaviour of the modified fibres, in particular for mTGase/sericin treated fibres which, with the confocal studies, corroborate the physical changes observed on the treated wool fabric. © 2006 Elsevier Inc. All rights reserved.

Improving the solubility and dissolution of poorly soluble drugs by salt formation and the consequent effect on mechanical properties

The bioavailability of BCS II compounds may be improved by an enhanced solubility and dissolution rate. Four carboxylic acid drugs were selected, which were flurbiprofen, etodolac, ibuprofen and gemfibrozil. The drugs were chosen because they are weak acids with poor aqueous solubility and should readily form salts. The counterions used for salt formation were: butylamine, pentylamine, hexylamine, octylamine, benzylamine, cyclohexylamine, tert-butylamine, 2-amino-2-methylpropan­2-ol, 2-amino-2-methyl propan-1,3-ol and tromethamine. Solubility was partially controlled by the saturated solution pH with the butylamine counterion increasing the solution pH and solubility and dissolution to the greatest extent. As the chain length increased, solubility was reduced due to the increasing lipophilic nature of the counterion. The benzylamine and cyclohexylamine counterions produced crystalline, stable salts but did not improve solubility and dissolution significantly compared to the parent compound. The substitution of hydroxyl groups to tert-butylamine counterions produced an increase in solubility and dissolution. AMP2 resulted in the most enhanced solubility and dissolution compared to the parent drug but using the tris salt did not further improve solubility due to a very stable crystal lattice structure. The parent drugs were very difficult to compress due to orientation effects and lamination. Compacts were prepared of each parent drug and salt and their modulus of elasticity values were measured using a three-point bend (Young’s modulus, E0) were extrapolated to zero porosity and compared. Compressibility and E0 were improved with the butylamine, tert-butylamine, cyclohexylamine and AMP2 counterions. The most significant improvement in compression and E0 was with the AMP2 salts. Mechanical properties were related to the hydrogen bonding within the crystal lattice structure for the gemfibrozil salt series.

The chemical structure and mechanical properties of phenolic resins and related polymers

Paper-based phenolic laminates are used extensively in the electrical industry. Many small components are fabricated from these materials by the process known as punching. Recently an investigation was carried out to study the effect of processing variables on the punching properties. It was concluded that further work would be justified and that this should include a critical examination of the resin properties in a more controlled and systematic manner. In this investigation an attempt has been made to assess certain features of the resin structure in terms of thermomechanical properties. The number of crosslinks in the system was controlled using resins based on phenol and para-cresol formulations. Intramolecular hydrogen bonding effects were examined using substituted resins and a synthetically derived phenol based on 1,3-di-(o-hydroxyphenyl) propane.. A resin system was developed using the Friedel Crafts reaction to examine inter-molecular hydrogen bonding at the resin-paper interface. The punching properties of certain selected resins were assessed on a qualitative basis. In addition flexural and dynamic mechanical properties were determined in a general study of the structure-property relationships of these materials. It has been shown that certain features of the resin structure significantly influenced mechanical properties. :F'urther, it was noted that there is a close relationship between punching properties, mechanical damping and flexural strain. This work includes a critical examination of the curing mechanism and views are postulated in an attempt to extend knowledge in this area of the work. Finally, it is argued that future work should be based on a synthetic approach and that dynamic mechanical testing would provide a powerful tool In developing a deeper understanding of the resin fine structure.

Automobile friction materials: a test instrument and technique for determining dynamic mechanical properties in relation to brake squeal

This study is primarily concerned with the problem of break-squeal in disc brakes, using moulded organic disc pads. Moulded organic friction materials are complex composites and due to this complexity it was thought that they are unlikely to be of uniform composition. Variation in composition would under certain conditions of the braking system, cause slight changes in its vibrational characteristics thus causing resonance in the high audio-frequency range. Dynamic mechanical propertes appear the most likely parameters to be related to a given composition's tendency to promote squeal. Since it was necessary to test under service conditions a review was made of all the available commercial test instruments but as none were suitable it was necessary to design and develop a new instrument. The final instrument design, based on longitudinal resonance, enabled modulus and damping to be determined over a wide range of temperatures and frequencies. This apparatus has commercial value since it is not restricted to friction material testing. Both used and unused pads were tested and although the cause of brake squeal was not definitely established, the results enabled formulation of a tentative theory of the possible conditions for brake squeal. The presence of a temperature of minimum damping was indicated which may be of use to braking design engineers. Some auxilIary testing was also performed to establish the effect of water, oil and brake fluid and also to determine the effect of the various components of friction materials.