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Stresses in a long cylindrical conductor moving axially through a pair of electrode plates under stationary conditions
Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Applied Mechanics.
Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Applied Mechanics.
2013 (English)In: Journal of applied mechanics, ISSN 0021-8936, E-ISSN 1528-9036, Vol. 80, no 2, 021013- p.Article in journal (Refereed) Published
Abstract [en]

In a conductor carrying electric current, the Lorentz force gives rise to mechanical stresses. Here, we study a long elastic cylindrical conductor that moves axially with constant velocity through two electrode plates. The aims are to explore how the stresses in the conductor depend on the velocity in the stationary case of constant current and to assess the validity of the analytic method used. The diffusion equation for the magnetic flux density is solved by use of Fourier transform, and the current density is determined. The stresses, due to the Lorentz force, are found by use of an analytic method combining the solutions of a quasi-static radial problem of plane deformation and a dynamic axial problem of uniaxial stress. They are also determined through FE analysis. Radial field profiles between the plates indicate a velocity skin effect signifying that the current and the magnetic field are concentrated near the cylindrical surface up-stream and are more uniformly distributed downstream. The radial and hoop stresses are compressive, while the axial stress is tensile. The von Mises effective stress increases towards the symmetry axis, in the downstream direction, and with velocity. There are circumstances under which a large current can produce an effective stress in a copper conductor of the order of the yield stress without causing a significant temperature rise. The stresses obtained with the two methods agree well, even relatively near the electrode plates. The analytical method should be useful in similar cases as well as for the provision of test cases for more general simulation tools.

Place, publisher, year, edition, pages
2013. Vol. 80, no 2, 021013- p.
National Category
Applied Mechanics
Research subject
Engineering science with specialization in Applied Mechanics
Identifiers
URN: urn:nbn:se:uu:diva-187308DOI: 10.1115/1.4007221ISI: 000326175400026OAI: oai:DiVA.org:uu-187308DiVA: diva2:574205
Available from: 2012-12-04 Created: 2012-12-04 Last updated: 2017-12-07Bibliographically approved
In thesis
1. Interaction of Cylindrical Penetrators with Ceramic and Electromagnetic Armour
Open this publication in new window or tab >>Interaction of Cylindrical Penetrators with Ceramic and Electromagnetic Armour
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Alternative title[sv]
Växelverkan mellan cylindriska penetratorer och keramiska och elektromagnetiska pansar
Abstract [en]

Armoured vehicles have traditionally used steel armour as protection against penetrators such as projectiles and shaped charge jets. The latter produce a thin stretching metal jet, usually of copper, with a tip velocity of about 7-8 km/s. In order to obtain more weight-efficient solutions, there is a search for lighter materials and other protection techniques. In this thesis, ceramic and electromagnetic armours are studied. Ceramic materials are lighter than steel, and their high compressive strength makes them useful as armour materials. Electromagnetic armour consists of two metal plates connected to an electric power supply capable of delivering a strong current pulse. A conductive penetrator passing through both plates is destroyed by the effects of the resulting current.

Tests of the ceramic armour materials alumina and boron carbide were performed with reverse impact technique, which signifies that a target assembly (ceramic confined in a metal cylinder) was launched by a gun towards a projectile placed in front of the gun barrel. By this technique yaw was eliminated, but the geometric scale had to be very small. Therefore, we studied scaling laws for ceramic armour through a series of tests with direct impact technique and projectile diameters from 2 to 10 mm. The small scale has the advantage that flash X-ray photography can be used to photograph the projectile inside the ceramic target. The phenomenon of interface defeat or dwell was also demonstrated. It signifies that the ceramic, at least for a short time, can withstand the impact pressure so that the projectile just flows out onto the target surface. A transition velocity, above which dwell does not occur, was determined. Simulations were performed with the continuum-dynamic code Autodyn and by use of a model for the brittle ceramic materials by Johnson and Holmquist. The simulations reasonably well represented the penetration behaviour above the transition velocity. They also did below, if under this condition the ceramic model was forced to remain undamaged.

The performance of electromagnetic armour was tested against a shaped charge jet. The jet was registered with shadowgraph flash X-ray photography between the plates and after passing through the plates. The current through the jet and the voltage over the plates were also registered. The current caused heating leading to melting and even vaporization. The magnetic Lorentz force compressed the jet radially, and as this effect increases with decreasing jet radius, instability may arise. Explosions in the compressed regions resulted in a fragmented jet with disk-shaped fragments which are less effective penetrators than the elongated fragments obtained in the absence of current. We also performed a theoretical study, in which the penetrator was subjected to small elastic strains only and the current was constant. The magnetic field was determined by FFT, and the stresses due to the Lorentz force were calculated with a semi-analytical method. The velocity skin effect was demonstrated.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2013. 73 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1032
National Category
Interaction Technologies
Research subject
Engineering Science with specialization in Solid Mechanics
Identifiers
urn:nbn:se:uu:diva-197563 (URN)978-91-554-8633-4 (ISBN)
Public defence
2013-05-17, Polhemssalen, Ångström, Uppsala, 10:15 (Swedish)
Opponent
Supervisors
Available from: 2013-04-25 Created: 2013-03-27 Last updated: 2013-08-30Bibliographically approved

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Westerling, LarsLundberg, Bengt

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