Abstract
Powerful forces arise when a pulse of a magnetic field in the order of a few tesla diffuses into a conductor. Such pulses are used in electromagnetic forming, impact welding of dissimilar materials and grain refinement of solidifying alloys. Strong magnetic field pulses are generated by the discharge current of a capacitor bank. We consider analytically the penetration of such pulse into a conducting half-space. Besides the exact solution we obtain two simple self-similar approximate solutions for two sequential stages of the initial transient. Furthermore, a general solution is provided for the external field given as a power series of time. Each term of this solution represents a self-similar function for which we obtain an explicit expression. The validity range of various approximate analytical solutions is evaluated by comparison to the exact solution.
Highlights
High current pulses during the solidification may be useful for structure improvement of alloys.[1,2,3,4] Induced currents together with the magnetic field itself create powerful forces that may detach nuclei formed at the mould walls[2,3] or fracture the dendrites.[4]
We obtain a similar solution in the half-space for the capacitor discharge current generated magnetic field that follows the dacaying sine law
065014-4 Grants, Bojarevičs, and Gerbeth where f ′(ξ) e−ξ2/4 √. This approximate solution for the induced current is compared with the exact solution (7) in figure 2
Summary
High current pulses during the solidification may be useful for structure improvement of alloys.[1,2,3,4] Induced currents together with the magnetic field itself create powerful forces that may detach nuclei formed at the mould walls[2,3] or fracture the dendrites.[4]. We obtain a similar solution in the half-space for the capacitor discharge current generated magnetic field that follows the dacaying sine law In either case these exact solutions are rather difficult to comprehend. The same property holds for transient boundary conditions when their right-hand side is a half-integer power function of time.[8,10] a general analytical solution may be constructed by self-similar functions when the transient boundary conditions are given as a power series of time. These functions (see eq 3.2.54 in Ref. 8 or eq 4.2-23 in Ref. 10) are given by iterated integrals of the complementary error function in a form that is not immediately usable for higher power terms.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
