Magneto-elastic stress induced by an electric current in an infinite thin plate with an elliptical hole

Abstract

Two-dimensional magnetic field and stress analyses have been presented for soft ferromagnetic, paramagnetic, and diamagnetic materials of an infinite thin plate with an elliptical hole under steady electric current. The magnetic stress has been analyzed in the Maxwell Stress Model. Except for the approximation of the plane stress state since the plate is the thin plate, any assumption is not made for the stress analysis, though the Maxwell stress components are expressed by nonlinear terms. The boundary condition expressed by Maxwell's stress is completely satisfied without any linear assumptions on the boundary. Two ways for the boundary condition are stated. The analysis of σ z in the direction of the plate thickness is also carried out. Figures of the magnetic field and stress distribution are shown. Stress intensity factors are also derived, and the magnitude of the stress intensity factor for the magnetic stress and thermal stress due to the Joule heat caused by the electric current is discussed.

Magnetic field and magneto elastic stress in an infinite plate containing an elliptical hole with an edge crack under uniform electric current

“…This fact was already stated in (Hasebe et al, 2007;Hasebe, 2009b). Therefore, if the magneto elastic stress state at the remote field can be obtained, the stress analysis of stress state (a) can be carried by usual stress analysis under uniform shear stress.…”

“…Fig. 7a and b show Maxwell stress components symmetric and asymmetric to the z = 0 plane, respectively, of which mechanical properties under the electric current were investigated in (Hasebe, 2009b). The results are briefly mentioned here.…”

“…The intensity was investigated in (Hasebe et al, 2010a). It is noticed from (21) that the magnetic field intensities H x (x, y, z), H y (x, y, z) have the same singularity as that of the electric current at the crack tip (Hasebe, 2009b where r is the distance from the crack tip and h is the angle measured in the counterclockwise direction. The intensity H f is obtained using the magnetic complex potential function A(f), (21), as follows:…”

“…The line of e K Ibeq in Fig. 14 shows SIF of the equivalent crack length 2a cr = 2a + c. The equivalent SIF is defined from that of a crack (Hasebe, 2009b) as follows:…”

“…The stress intensity factors (SIF), K Ia , K IIa for stress state (a) are calculated by the following equations using (56) (Hasebe and Horiuchi, 1978): 13 shows non-dimensional SIF for stress state (a) and the line of e K Iaeq is that for the equivalent crack length 2a cr = (2a + c). The equivalent SIF is defined from that of a crack (Hasebe, 2009b) as follows:…”