Plane Problem of Magnetoelasticity for a Piezomagnetic Medium with Cracks
- PDF / 1,245,381 Bytes
- 9 Pages / 594 x 792 pts Page_size
- 56 Downloads / 174 Views
PLANE PROBLEM OF MAGNETOELASTICITY FOR A PIEZOMAGNETIC MEDIUM WITH CRACKS L. А. Fil’shtyns'kyi,1,2 D. M. Nosov,1 and H. A. Eremenko1
UDC 539.3
We solve a boundary-value problem of magnetoelasticity for a piezomagnetic plane weakened by cracks. For this purpose, we generalize the method aimed at the solution of similar problems for anisotropic media. The boundary-value problem is reduced to a matrix singular integral equation and the solution of this equation is found in the class of vector functions unbounded at the ends of the notches. The numerical solution of this equation is obtained by the method of mechanical quadratures. The proposed numerical-analytic algorithm is used to investigate the influence of magnetoelastic fields on the stress intensity factors in the vicinity of the crack tips. Keywords: piezomagnetic ceramic, macrocracks, singular integral equations, intensity factors of the field quantities.
As a result of the development of artificial piezomagnetic ceramics with enormously high magnetostriction [1, 2], the interest of the researchers in magnetoelasticity strongly increased. In particular, it was shown that the significant mutual influence of coupled elastic and magnetic fields in ceramic alloys of rare-earth elements should be taken into account in the problems of fracture mechanics of piezomagnetic bodies. This kind of problems for cracks was considered in [3, 4]. The solutions of two-dimensional problems of concentration of magnetoelastic fields in bodies with holes and cracks are presented in [5]. In what follows, we generalize the formalism proposed in [6] to the plane boundary-value problems of magnetoelasticity for bodies with cracks. Statement of the Problem In a Cartesian coordinate system Ox1x 2 , we consider a flat plane made of a piezomagnetic material weakened by macrocracks Γ n (n = 1, M ). Assume that a normal pressure pn acts on its lips and that uniform
fields of tensile and shear stresses σ ij∞ and uniform fields of magnetic induction B ∞ j , i, j = 1, 2 are given at infinity. Suppose that Γ n are two-sided Lyapunov arcs that begin and end at the points an and bn (Fig. 1a).
We propose an efficient numerical-analytic algorithm with an aim to study coupled mechanical and magnetic fields in the body, to determine the stress intensity factors (SIF) K I and K II and the magnetic-induction intensity factor K B at the cracks tips, and to evaluate the mutual influence of the mechanical and magnetic fields in ceramics (alloys of rare-earth materials). 1 2
Sumy State University, Sumy, Ukraine.
Corresponding author; e-mail: [email protected].
Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 51, No. 2, pp. 109–115, March–April, 2015. Original article submitted July 7, 2014. 1068-820X/15/5102–0267
© 2015
Springer Science+Business Media New York
267
L. А. FIL’SHTYNSKYI, D. M. NOSOV,
268
AND
H. A. EREMENKO
Fig. 1. Piezomagnetic plane weakened by macrocracks. We represent the field quantities in the model [7–10] as follows [4]: 3
{ σ11, σ12 , σ 22 } = 2 Re ∑
Data Loading...
