An analysis of the effect of process parameters on the formability of sheet metal

This investigation is in two parts, theory and experimental verification. (1) Theoretical Study In this study it is, for obvious reasons, necessary to analyse the concept of formability first. For the purpose of the present investigation it is sufficient to define the four aspects of formability as follows: (a) the formability of the material at a critical section, (b) the formability of the material in general, (c) process efficiency, (d) proportional increase in surface area. A method of quantitative assessment is proposed for each of the four aspects of formability. The theoretical study also includes the distinction between coaxial and non-coaxial strains which occur, respectively, in axisymmetrical and unsymmetrical forming processes and the inadequacy of the circular grid system for the assessment of formability is explained in the light of this distinction. (2) Experimental Study As one of the bases of the experimental work, the determination of the end point of a forming process, which sets the limit to the formability of the work material, is discussed. The effects of three process parameters on draw-in are shown graphically. Then the delay of fracture in sheet metal forming resulting from draw-in is analysed in kinematical terms, namely, through the radial displacements, the radial and the circumferential strains, and the projected thickness of the workpiece. Through the equilibrium equation of the membrane stresses, the effect on the shape of the unsupported region of the workpiece, and hence the position of the critical section is explained. Then, the effect of draw-in on the four aspects of formability is discussed throughout this investigation. The triangular coordinate system is used to present and analyse the triaxial strains involved. This coordinate system has the advantage of showing all the three principal strains in a material simultaneously, as well as representing clearly the many types of strains involved in sheet metal work.

The behaviour of granular material in pure shear, direct shear and simple shear

In biaxial compression tests, the stress calculations based on boundary information underestimate the principal stresses leading to a significant overestimation of the shear strength. In direct shear tests, the shear strain becomes highly concentrated in the mid-plane of the sample during the test. Although the stress distribution within the specimen is heterogeneous, the evolution of the stress ratio inside the shear band is similar to that inferred from the boundary force calculations. It is also demonstrated that the dilatancy in the shear band significantly exceeds that implied from the boundary displacements. In simple shear tests, the stresses acting on the wall boundaries do not reflect the internal state of stress but merely provide information about the average mobilised wall friction. It is demonstrated that the results are sensitive to the initial stress state defined by K0 = sh/sv. For all cases, non-coaxiality of the principal stress and strain-rate directions is examined and the corresponding flow rule is identified. Periodic cell simulations have been used to examine biaxial compression for a wide range of initial packing densities. Both constant volume and constant mean stress tests have been simulated. The characteristic behaviour at both the macroscopic and microscopic scales is determined by whether or not the system percolates (enduring connectivity is established in all directions). The transition from non-percolating to percolating systems is characterised by transitional behaviour of internal variables and corresponds to an elastic percolation threshold, which correlates well with the establishment of a mechanical coordination number of ca. 3.0. Strong correlations are found between macroscopic and internal variables at the critical state.

A study of the micro-mechanics of granular media

The development of more realistic constitutive models for granular media, such as sand, requires ingredients which take into account the internal micro-mechanical response to deformation. Unfortunately, at present, very little is known about these mechanisms and therefore it is instructive to find out more about the internal nature of granular samples by conducting suitable tests. In contrast to physical testing the method of investigation used in this study employs the Distinct Element Method. This is a computer based, iterative, time-dependent technique that allows the deformation of granular assemblies to be numerically simulated. By making assumptions regarding contact stiffnesses each individual contact force can be measured and by resolution particle centroid forces can be calculated. Then by dividing particle forces by their respective mass, particle centroid velocities and displacements are obtained by numerical integration. The Distinct Element Method is incorporated into a computer program 'Ball'. This program is effectively a numerical apparatus which forms a logical housing for this method and allows data input and output, and also provides testing control. By using this numerical apparatus tests have been carried out on disc assemblies and many new interesting observations regarding the micromechanical behaviour are revealed. In order to relate the observed microscopic mechanisms of deformation to the flow of the granular system two separate approaches have been used. Firstly a constitutive model has been developed which describes the yield function, flow rule and translation rule for regular assemblies of spheres and discs when subjected to coaxial deformation. Secondly statistical analyses have been carried out using data which was extracted from the simulation tests. These analyses define and quantify granular structure and then show how the force and velocity distributions use the structure to produce the corresponding stress and strain-rate tensors.

A temporary connection for an aluminium space frame

This thesis examines theoretically and experimentally the behaviour of a temporary end plate connection for an aluminium space frame structure, subjected to static loading conditions. Theoretical weld failure criterions are derived from basic fundamentals for both tensile and shear fillet welds. Direct account of weld penetration is taken by incorporating it into a more exact poposed weld model. Theoretical relationships between weld penetration and weld failure loads, failure planes and failure lengths are derived. Also, the variation in strength between tensile and shear fillet welds is shown to be dependent upon the extent of weld penetration achieved/ The proposed tensile weld failure theory is extended to predict the theoretical failure of the welds in the end plate space frame connection. A finite element analysis is conducted to verify the assumptions made for this theory. Experimental hardness and tensile tests are conducted to substantiate the extent and severity of the heat affected zone in aluminium alloy 6082-T6. Simple transverse and longitudinal fillet welded specimens of the same alloy, are tested to failure. These results together with those of other authors are compared to the theoretical predictions made by the proposed weld failure theories and by those made using Kamtekar's and Kato and Morita's failure equations, the -formula and BS 8118. Experimental tests are also conducted on the temporary space frame connection. The maximum stresses and displacements recorded are checked against results obtained from a finite element analysis of the connection. Failure predictions made by the proposed extended weld failure theory, are compared against the experimental results.

Design of sway frames

The aim of the work presented in this thesis is to produce a direct method to design structures subject to deflection constraints at the working loads. The work carried out can be divided into four main parts. In the first part, a direct design procedure for plane steel frames subjected to sway limitations is proposed. The stiffness equations are modified so that the sway in each storey is equal to some specified values. The modified equations are then solved by iteration to calculate the cross-sectional properties of the columns as well as the other joint displacements. The beam sections are selected initially and then altered in an effort to reduce the total material cost of the frame. A linear extrapolation technique is used to reduce this cost. In this design, stability functions are used so that the effect of axial loads in the members are taken into consideration. The final reduced cost design is checked for strength requirements and the members are altered accordingly. In the second part, the design method is applied to the design of reinforced concrete frames in which the sway in the columns play an active part in the design criteria. The second moment of area of each column is obtained by solving the modified stiffness equations and then used to calculate the mlnlmum column depth required. Again the frame has to be checked for all the ultimate limit state load cases. In the third part, the method is generalised to design pin-jointed space frames for deflection limitatlions. In these the member areas are calculated so that the deflection at a specified joint is equal to its specified value. In the final part, the Lagrange multiplier technique is employed to obtain an optimum design for plane rigidly jointed steel frames. The iteration technique is used here to solve the modified stiffness equations as well as derivative equations obtained in accordance to the requirements of the optimisation method.

Crystallographic studies of magnetite and titanomaghemite

The crystal structure of natural magnetite has been investigated on the basis of previously published X-ray intensity data and a newly acquired, more extensive data base. Both investigations show that the structure does not conform to the centrosymmetrical space group Fd3m, as is normally assumed, but the non-centrosymmetrical space group F43m. The structure refinement provides values for the atom positions, anisotropic thermal parameters and bond lengths. A study of Friedel related pairs of X-ray intensities shows that Friedel's law is violated in magnetite, further confirming that the space group is non-centrosymmetrical. It was found that the octahedral site cations in magnetite do not occupy special positions at the centres of the octahedral interstices as they should under the space group Fd3m, but are displaced along <111 > directions leading to F43m symmetry. A mechanism is known for the origin of these displacements and the likelihood of similar displacements occurring in other natural and synthetic spinels is discussed. The crystal structure of a natural titanomaghemite was determined by a combination of X-ray diffraction and Mõssbauer spectroscopy. This was confirmed as possessing a primitive cubic Bravais lattice with the space group P4332 and the structural formula: Fe3+.0.96 0 0.04 [Fe2+0.23 Fe3+0.99 Ti4+0.42 0 0.37 ] 042 - where 0 represents a cation vacancy. As the above formula shows, there are cation vacancies on both tetrahedral arrl octahedral sites, the majority being restricted to octahedral sltes. No tetrahedral site Fe2+ or Ti4+ was observed. Values for the atom positions, anisotropic thermal parameters and bond lengths have been determined for this particular specimen.

The mechanics of creep crack growth in a Magnox alloy

Magnox AL80 has been used for a study of creep crack propagation. A number of variables have been considered such as specimen geometry,notch root radius, material thickness, creep prestrain and stress level.The work has covered the material behaving under two values of the creep exponent, n=3.5 and n=7, according to the stress level. As well as observing initiation times and crack growth rates, scribed grids have been used to examine the near crack tip strain levels and distributions. It was shown that estimations of COD from notch flank opening can give misleading indications of material behaviour and that a more informative method was to monitor displacements in the material surrounding the crack tip. Strong evidence was found for crack advance being displacement controlled, however it was shown that the COD approach should be considered geometry dependant. The summation of ∈xx and ∈yy provided the most successful description of crack advance as it produced a single value that described propagation in all the cases concidered. The strain distributions indicates that σyy was related to distance from a point ahead of the crack tip by the exponent - (l/n+l) and that σxx is proportional to σyy. The constraint stresses arising in the DEN and CN specimens were evaluated. Initiation time was found to be principally affected by the stress level but was modified by the constraints arising from specimen geometry. Crack growth was found not to obey either the empirical K or σpett relationships but was reviewed in context of the observed strain behaviour.

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.

Relaxation procedures for an iterative MFS algorithm for the stable reconstruction of elastic fields from Cauchy data in two-dimensional isotropic linear elasticity

We investigate two numerical procedures for the Cauchy problem in linear elasticity, involving the relaxation of either the given boundary displacements (Dirichlet data) or the prescribed boundary tractions (Neumann data) on the over-specified boundary, in the alternating iterative algorithm of Kozlov et al. (1991). The two mixed direct (well-posed) problems associated with each iteration are solved using the method of fundamental solutions (MFS), in conjunction with the Tikhonov regularization method, while the optimal value of the regularization parameter is chosen via the generalized cross-validation (GCV) criterion. An efficient regularizing stopping criterion which ceases the iterative procedure at the point where the accumulation of noise becomes dominant and the errors in predicting the exact solutions increase, is also presented. The MFS-based iterative algorithms with relaxation are tested for Cauchy problems for isotropic linear elastic materials in various geometries to confirm the numerical convergence, stability, accuracy and computational efficiency of the proposed method.

A relaxation method of an alternating iterative algorithm for the Cauchy problem in linear isotropic elasticity

We propose two algorithms involving the relaxation of either the given Dirichlet data (boundary displacements) or the prescribed Neumann data (boundary tractions) on the over-specified boundary in the case of the alternating iterative algorithm of Kozlov et al. [16] applied to Cauchy problems in linear elasticity. A convergence proof of these relaxation methods is given, along with a stopping criterion. The numerical results obtained using these procedures, in conjunction with the boundary element method (BEM), show the numerical stability, convergence, consistency and computational efficiency of the proposed method.

Does rebound tonometry probe misalignment modify intraocular pressure measurements in human eyes?

Purpose. To examine the influence of positional misalignments on intraocular pressure (IOP) measurement with a rebound tonometer. Methods. Using the iCare rebound tonometer, IOP readings were taken from the right eye of 36 healthy subjects at the central corneal apex (CC) and compared to IOP measures using the Goldmann applanation tonometer (GAT). Using a bespoke rig, iCare IOP readings were also taken 2 mm laterally from CC, both nasally and temporally, along with angular deviations of 5 and 10 degrees, both nasally and temporally to the visual axis. Results. Mean IOP ± SD, as measured by GAT, was 14.7±2.5 mmHg versus iCare tonometer readings of 17.4±3.6 mmHg at CC, representing an iCare IOP overestimation of 2.7±2.8 mmHg (P<0.001), which increased at higher average IOPs. IOP at CC using the iCare tonometer was not significantly different to values at lateral displacements. IOP was marginally underestimated with angular deviation of the probe but only reaching significance at 10 degrees nasally. Conclusions. As shown previously, the iCare tonometer overestimates IOP compared to GAT. However, IOP measurement in normal, healthy subjects using the iCare rebound tonometer appears insensitive to misalignments. An IOP underestimation of <1 mmHg with the probe deviated 10 degrees nasally reached statistical but not clinical significance levels. © 2013 Ian G. Beasley et al.

EP4 prostanoid receptor-mediated vasodilatation of human middle cerebral arteries

1 Dilatation of the cerebral vasculature is recognised to be involved in the pathophysiology of migraine. Furthermore, elevated levels of prostaglandin E2 (PGE2) occur in the blood, plasma and saliva of migraineurs during an attack, suggestive of a contributory role. In the present study, we have characterised the prostanoid receptors involved in the relaxation and contraction of human middle cerebral arteries in vitro. 2 In the presence of indomethacin (3μM) and the TP receptor antagonist GR32191 (1 μM), PGE2 was found to relax phenylephrine precontracted cerebral arterial rings in a concentration-dependent manner (mean pEC50 8.0 ± 0.1, n = 5). 3 Establishment of a rank order of potency using the EP4 > EP2 agonist 11-deoxy PGE1, and the EP2 > EP4 agonist PGE1-OH (mean pEC 50 of 7.6 ± 0.1 (n = 6) and 6.4 ± 0.1 (n = 4), respectively), suggested the presence of functional EP4 receptors. Furthermore, the selective EP2 receptor agonist butaprost at concentrations < 1 μM failed to relax the tissues. 4 Blockade of EP 4 receptors with the EP4 receptor antagonists AH23848 and EP4A caused significant rightward displacements in PGE2 concentration-response curves, exhibiting pA2 and pKB values of 5.7 ± 0.1, n = 3, and 8.4, n = 3, respectively. 5 The IP receptor agonists iloprost and cicaprost relaxed phenylephrine precontracted cerebral arterial rings (mean pEC50 values 8.3 ± 0.1 (n = 4) and 8.1 ± 0.1 (n = 9), respectively). In contrast, the DP and FP receptor agonists PGD2 and PGFα2 failed to cause appreciable relaxation or contraction at concentrations of up to 30 μM. In the absence of phenylephrine contraction and GR32191, the TP receptor agonist U46619 caused concentration-dependent contraction of cerebral artery (mean pEC50 7.4 ± 0.3, n = 3). 6 These data demonstrate the presence of prostanoid EP4 receptors mediating PGE2 vasodilatation of human middle cerebral artery. IP receptors mediating relaxation and TP receptors mediating contraction were also functionally demonstrated.

Study on fatigue and energy-dissipation properties of nanolayered Cu/Nb thin films

Energy dissipation and fatigue properties of nano-layered thin films are less well studied than bulk properties. Existing experimental methods for studying energy dissipation properties, typically using magnetic interaction as a driving force at different frequencies and a laser-based deformation measurement system, are difficult to apply to two-dimensional materials. We propose a novel experimental method to perform dynamic testing on thin-film materials by driving a cantilever specimen at its fixed end with a bimorph piezoelectric actuator and monitoring the displacements of the specimen and the actuator with a fibre-optic system. Upon vibration, the specimen is greatly affected by its inertia, and behaves as a cantilever beam under base excitation in translation. At resonance, this method resembles the vibrating reed method conventionally used in the viscoelasticity community. The loss tangent is obtained from both the width of a resonance peak and a free-decay process. As for fatigue measurement, we implement a control algorithm into LabView to maintain maximum displacement of the specimen during the course of the experiment. The fatigue S-N curves are obtained.

Researching with, not on:using photography in researching street children in Accra, Ghana

What is discussed in this chapter is work-in-progress, an opportunity for reflection upon elements of an on-going research project examining the lives of street children in Accra, Ghana. Street children have received much research in recent years but our project is, we believe, distinctive in two respects. The first of these is that access to reliable data on the growing presence of children on the streets of African cities is often problematic. Available research is often diffuse and hard to access, it is more often than not driven by the short-term requirements of specific programmes and interventions and as a consequence can be lacking in depth, rigour and innovation. Without the means to provide a sufficiently self-conscious and critical engagement with accepted understandings of the lives of street children, consideration of the experience of street children in Africa continues to rely heavily on the more capacious and better disseminated research from the Americas (e.g., Mickelson, 2000). At the very least, Africa's specific experience of large population displacements, diversity of family forms, rapid urbanisation, vigorous structural adjustment and internal conflict raise important questions about the appropriateness of such ready generalisations. Judith Ennew (2003, p. 4) is clear that caution is needed in an uncritical endorsement of the “globalisation of the street child based on Latin American work”. She is equally mindful, however, that as far as Africa is concerned the absence of reliable evidence continues to hinder debate.

Heavy ion irradiation effects in zirconium nitride

Polycrystalline zirconium nitride (ZrN) samples were irradiated with He +, Kr ++, and Xe ++ ions to high (>1·10 16 ions/cm 2) fluences at ∼100 K. Following ion irradiation, transmission electron microscopy (TEM) and grazing incidence X-ray diffraction (GIXRD) were used to analyze the microstructure and crystal structure of the post-irradiated material. For ion doses equivalent to approximately 200 displacements per atom (dpa), ZrN was found to resist any amorphization transformation, based on TEM observations. At very high displacement damage doses, GIXRD measurements revealed tetragonal splitting of some of the diffraction maxima (maxima which are associated with cubic ZrN prior to irradiation). In addition to TEM and GIXRD, mechanical property changes were characterized using nanoindentation. Nanoindentation revealed no change in elastic modulus of ZrN with increasing ion dose, while the hardness of the irradiated ZrN was found to increase significantly with ion dose. Finally, He + ion implanted ZrN samples were annealed to examine He gas retention properties of ZrN as a function of annealing temperature. He gas release was measured using a residual gas analysis (RGA) spectrometer. RGA measurements were performed on He-implanted ZrN samples and on ZrN samples that had also been irradiated with Xe ++ ions, in order to introduce high levels of displacive radiation damage into the matrix. He evolution studies revealed that ZrN samples with high levels of displacement damage due to Xe implantation, show a lower temperature threshold for He release than do pristine ZrN samples.