Contactless inductive flow tomography

The three-dimensional velocity field of a propeller driven liquid metal flow is reconstructed by a contactless inductive flow tomography (CIFT). The underlying theory is presented within the framework of an integral equation system that governs the magnetic field distribution in a moving electrically conducting fluid. For small magnetic Reynolds numbers this integral equation system can be cast into a linear inverse problem for the determination of the velocity field from externally measured magnetic fields. A robust reconstruction of the large scale velocity field is already achieved by applying the external magnetic field alternately in two orthogonal directions and measuring the corresponding sets of induced magnetic fields. Kelvin's theorem is exploited to regularize the resulting velocity field by using the kinetic energy of the flow as a regularizing functional. The results of the new technique are shown to be in satisfactory agreement with ultrasonic measurements.Comment: 9 Figures; to appear in Phys. Rev

Finite element analysis of small-scale hot compression testing

This paper models hot compression testing using a dilatometer in loading mode. These small-scale tests provide a high throughput at low cost, but are susceptible to inhomogeneity due to friction and temperature gradients. A novel method is presented for correcting the true stress-strain constitutive response over the full range of temperatures, strain-rates and strain. The nominal response from the tests is used to predict the offset in the stress-strain curves due to inhomogeneity, and this stress offset Δσ is applied piecewise to the data, correcting the constitutive response in one iteration. A key new feature is the smoothing and fitting of the flow stress data as a function of temperature and strain-rate, at multiple discrete strains. The corrected model then provides quantitative prediction of the spatial and temporal variation in strain-rate and strain throughout the sample, needed to correlate the local deformation conditions with the microstructure and texture evolution. The study uses a detailed series of 144 hot compression tests of a Zr-Nb alloy. While this is an important wrought nuclear alloy in its own right, it also serves here as a test case for modelling the dilatometer for hot testing of high temperature alloys, particularly those with dual α-β phase microstructures (such as titanium alloys)

Design and testing of an instrumented experimental rig for autogenous friction stir spot welding

This report presents the design and testing of an experimental rig, dedicated for testing lightweight alloys in autogenous friction stir spot welding. The rig is capable of accurate measurement of torque and downforce, simultaneously with temperature at several locations in the weld. The objective is to enable investigation of the high temperature deformation behaviour of different materials over a range of friction welding conditions in a controlled setting. An extensive range of trials explored empirically the sensitivity of the key outputs to variation in the process variables: plunge depth, plunge rate, dwell time, rotational speed, sample thickness and thermocouple arrangement. Four aluminium alloys and one magnesium alloy were tested: wrought Al 6082-T6, 2024-T3, 7449-T3 and cast AlSi10Mg, and cast Mg AM50. The recorded torque showed little scatter and no idling value, improving the quality of the measurements compared to the in-built machine data acquisition system, and allowing for future use with other non-instrumented FSSW machines

Finite element analysis of heat generation in dissimilar alloy ultrasonic welding

This paper presents a computationally efficient finite element analysis of the heat generation in ultrasonic welding (USW). The temperature field is predicted from a continuous thermal model, with the heat generation rate being calculated intermittently, using a deformation model for single cycles of oscillation. The model was applied to USW of Al 6111 to itself, and to DC04 steel and Ti6Al4V, with plastic deformation only occurring in the Al alloy. Ultrasonic softening was allowed for empirically in the constitutive plastic response of the Al alloy. The predicted heat generation rate for all three material combinations was consistent with that inferred from thermocouple data and the thermal model. Material deformation maps were developed as a means of illustrating the dominant deformation regime of temperature and strain-rate. The thermal and deformation models were then fully coupled, as a proof of concept, to demonstrate that the power and temperature histories can be predicted directly from the constitutive data for the alloy and a kinematic description of the process.EPSRC grant: Friction Joining – Low Energy Manufacturing for Hybrid Structures in Fuel Efficient Transport Applications (EP/G022674/1) University of Camridge Doctoral Training Account TWI Lt

Synchrotron x-ray measurement and finite element analysis of residual strain in TIG welded aluminium alloy 2024

Residual strains have been measured in a tungsten inert gas (TIG) butt-welded 2024 aluminum alloy plate using synchrotron X-ray diffraction. Novel two-dimensional strain maps spanning the entire plate reveal steep gradients in residual stress and provide detailed validation data for finite element (FE) analysis. Two variants of a FE model have been used to predict the residual strain distributions, incorporating different levels of plate constraint. The model uses decoupled thermal and elastic- plastic mechanical analyses and successfully predicts the longitudinal and transverse residual strain field over the entire weld. For butt weld geometries, the degree of transverse constraint is shown to be a significant boundary condition, compared to simpler bead-on-plate analyses. The importance of transverse residual strains for detailed model validation is highlighted, together with the need for care in selecting the location for line scans. The residual stress is largest in the heat-affected zone (HAZ), being equal to the local postweld yield stress, though the strength increases subsequently by natural aging. In addition, a halving of the diffraction line width has been observed local to the weld, and this correlates with the microstructural changes in the region

Large-wavelength instabilities in free-surface Hartmann flow at low magnetic Prandtl numbers

We study the linear stability of the flow of a viscous electrically conducting capillary fluid on a planar fixed plate in the presence of gravity and a uniform magnetic field. We first confirm that the Squire transformation for MHD is compatible with the stress and insulating boundary conditions at the free surface, but argue that unless the flow is driven at fixed Galilei and capillary numbers, the critical mode is not necessarily two-dimensional. We then investigate numerically how a flow-normal magnetic field, and the associated Hartmann steady state, affect the soft and hard instability modes of free surface flow, working in the low magnetic Prandtl number regime of laboratory fluids. Because it is a critical layer instability, the hard mode is found to exhibit similar behaviour to the even unstable mode in channel Hartmann flow, in terms of both the weak influence of Pm on its neutral stability curve, and the dependence of its critical Reynolds number Re_c on the Hartmann number Ha. In contrast, the structure of the soft mode's growth rate contours in the (Re, alpha) plane, where alpha is the wavenumber, differs markedly between problems with small, but nonzero, Pm, and their counterparts in the inductionless limit. As derived from large wavelength approximations, and confirmed numerically, the soft mode's critical Reynolds number grows exponentially with Ha in inductionless problems. However, when Pm is nonzero the Lorentz force originating from the steady state current leads to a modification of Re_c(Ha) to either a sublinearly increasing, or decreasing function of Ha, respectively for problems with insulating and conducting walls. In the former, we also observe pairs of Alfven waves, the upstream propagating wave undergoing an instability at large Alfven numbers.Comment: 58 pages, 16 figure

Constrained flow around a magnetic obstacle

Many practical applications exploit an external local magnetic field -- magnetic obstacle -- as an essential part of their constructions. Recently, it has been demonstrated that the flow of an electrically conducting fluid influenced by an external field can show several kinds of recirculation. The present paper reports a 3D numerical study whose some results are compared with an experiment about such a flow in a rectangular duct.Comment: accepted to JFM, 26 pages, 14 figure

Modelling and visualisation of material flow in friction stir spot welding

The material flow in friction stir spot welding of aluminium to both aluminium and steel has been investigated, using pinless tools in a lap joint geometry. The flow behaviour was revealed experimentally using dissimilar Al alloys of similar strength. The effect on the material flow of tool surface features, welding conditions (rotation speed, plunge depth, dwell time), and the surface state of the steel sheet (un-coated or galvanized) have been systematically studied. A novel kinematic flow model is presented, which successfully predicts the observed layering of the dissimilar Al alloys under a range of conditions. The model and the experimental observations provide a consistent interpretation of the stick-slip conditions at the tool-workpiece interface, addressing an elusive and long-standing issue in the modelling of heat generation in friction stir processing.The authors wish to thank the EPSRC for funding this research through the following grants: Friction Joining – Low Energy Manufacturing for Hybrid Structures in Fuel Efficient Transport Applications (EP/G022402/1 and EP/G022674/1); and LATEST2, Light Alloys Towards Environmentally Sustainable Transport (EP/H020047/1).This is the author accepted manuscript. The final version is available from Elsevier at http://dx.doi.org/10.1016/j.jmatprotec.2015.06.02

Measurement and control systems for an imaging electromagnetic flow meter

Electromagnetic flow metres based on the principles of Faraday's laws of induction have been used successfully in many industries. The conventional electromagnetic flow metre can measure the mean liquid velocity in axisymmetric single phase flows. However, in order to achieve velocity profile measurements in single phase flows with non-uniform velocity profiles, a novel imaging electromagnetic flow metre (IEF) has been developed which is described in this paper. The novel electromagnetic flow metre which is based on the ‘weight value’ theory to reconstruct velocity profiles is interfaced with a ‘Microrobotics VM1’ microcontroller as a stand-alone unit. The work undertaken in the paper demonstrates that an imaging electromagnetic flow metre for liquid velocity profile measurement is an instrument that is highly suited for control via a microcontroller