Stress Intensity Factors for a Randomly Located Arc-Shaped Crack in a Circular Disk in the Course of Rotation
- PDF / 821,613 Bytes
- 8 Pages / 594 x 792 pts Page_size
- 8 Downloads / 191 Views
STRESS INTENSITY FACTORS FOR A RANDOMLY LOCATED ARC-SHAPED CRACK IN A CIRCULAR DISK IN THE COURSE OF ROTATION О. P. Datsyshyn,1 H. P. Marchenko,1, 2 and І. А. Rudavs’ka1
UDC 539.375
We study a plane problem of the theory of elasticity for a circular disk containing a randomly located arc-shaped crack under the action of a rotating load. The problem is reduced to a singular integral equation, which is solved numerically by the method of mechanical quadratures. We determine the numerical values of the stress intensity factors and angles of initial propagation of the crack depending on its location and geometric parameters (curvature and length). Keywords: circular disk, arc-shaped crack, rotating load, centrifugal forces, method of singular integral equations, stress intensity factors.
Various contemporary machines and mechanisms have rotating parts in which centrifugal forces are formed in the course of rotation. This type of loading and the circular shape of rotating parts itself often play the role of causes of initiation of arc-shaped cracks, which may lead to emergency situations. This is especially important in the case of high-speed rotating loads typical, e.g., of the rotors of steam or gas turbines whose rotational speed can be as high as tens thousands revolutions per minute. This is why it is important to determine the stressed state of these parts of machines and mechanisms containing cracks, including the stress intensity factors (SIF). The stress intensity factors determined in the process of rotation of a disk weakened by a rectilinear crack about its center are known from the literature. Thus, in [1], the values of the SIF were obtained by the method of boundary collocations for a randomly located rectilinear crack and, for a special case of eccentrically located diametric crack, the results were described by approximating relations. However, the formation of arc-shaped cracks in a disk is possible under the action of rotating loads. For a concentric crack, the SIF were found by the boundary element method [2]. In what follows, we solve a plane problem of the theory of elasticity for a circular disk weakened by a crack randomly located along an arc of the circle rotating with a constant angular velocity. A rectilinear crack can be regarded as a special case of an arcshaped crack. We determine numerical values of the SIF and the angles of initial propagation of the crack. Formulation of the Problem Consider an elastic isotropic circular disk of radius R bounded by a contour L0 centered at the origin of the principal coordinate system xOy (Fig. 1). The disk is weakened by an internal arc-shaped crack randomly located along the contour L relative to a local coordinate system x1O1y1 . The O1x1 -axis of the local coordinate system is inclined to the Ox -axis at an angle α and the affix of its center O1 in the principal system is given by the formula z10 = r0 eiθ 0 .
1 2
Karpenko Physicomechanical Institute, Ukrainian National Academy of Sciences, Lviv, Ukraine. Corresponding author; e-mail: [email protected]
Data Loading...
