Fracture analysis of base-edge-cracked reverse-tapered plates

Abstract

This paper presents a fracture mechanics analysis of the base-edge-cracked reverse-tapered (RT) fracture geometry. Motivation for this study was the use of this test geometry in Phase 1 of a recently completed jointindustry-agency project entitled 'Large-Scale Ice Fracture Experiments'. Underlying the choice of the RT fracture geometry for Phase 1 was the desirability of achieving crack propagation in a controlled and stable manner; such control would allow a number of observations to be made on one testpiece. Reverse tapering greatly improves not only crack growth stability but also crack path stability. The weight function method was used to provide accurate wide-ranging stress intensity factor (SIF), crack face displacement (COD) and crack opening area (COA) expressions for the RT subject to any loading. The required weight function was obtained through a finite element analysis of this geometry subject to a reference load case which determined the associated stress intensity factor and crack opening displacements. The Wu and Carlsson procedure was followed. A key modification to the latter procedure facilitated the attainment of the reference CMOD for all crack lengths, including the zero ligament limit; this was achieved by considering an additional reference solution. This modification is general in nature and could be pursued whenever the reference CMOD is not known analytically. An analytical solution for the crack opening area (COA) was also achieved for the special case of concentrated loading at the crack mouth. This solution can be applied to any geometry where the reference CMOD expression is known.

Fracture analysis of semi-circular and semi-circular-bend geometries

“…The ~i(a) functions are written in [2] in a form that explicitly reveals the singular behavior as a-+ 1. (12)…”

“…The above expressions actually apply to any geometry subject to concentrated loading at the crack mouth that is treated as outlined in [2]. The crack opening area for the reference solution is readily given by 27rcrA2~5(a) …”

“…The reference crack opening area is plotted in Figure 2 The SIF solution for a concentrated load at the crack mouth in terms of the reference SIF and CMOD solutions is then immediately available, as found in [2] 5. …”

“…The expression for •(a) stated in (14), given the form for f~ (a) stated in (8),, has been derived analytically for any arbitrary fT(a) and VT(a) in[2] for the RT geometry. A curve was fit to the expression to simplify the presentation here without compromising accuracy.…”

Radial cracking with closure

“…Similar to the approach used by Dempsey et al [15], a wide-ranging (exact) description of the compliance coefficients, c~;~ u is obtained by analytically integrating the expressions in (46); thus ;~u (k = 1,2, 14) are presented in Table 4; the functions The compliance coefficients gk ... 7k(a) (k = 1 ... 14) in (47) are given by Kinematic compatibility. The plate is considered to be rigid in the 0-direction; however, the circumferential displacement associated with the radial cracks requires further consideration.…”