Panel without patch

1.1 Analytical procedure

In the present analysis, the Irwin – Westergaard model (Pook, 2000) is used to calculate SIF in the panels without patch. The basic relationships are herein reported. The linear elastic fracture mechanics (LEFM) for a plate of infinite size and central crack (opening mode I) is given by the following expression:

The stress intensity factor, Ki, completely characterizes the stress distribution at the crack tip in a linear elastic material where a is the asymptotic tensile stress perpendicular to the crack plane and a is the crack half-length. Since the plate is of finite size, the boundary conditions introduce an higher stress intensification at the crack tip. The mode I stress intensity factor is given by (Jukes & Vogwell, 1995; Feddersen, 1996):

K,=Aa^[sec(^)]2 (2)

The elastic stress analysis becomes highly inaccurate as the inelastic region at the crack tip grows up. Simple corrections to the linear elastic fracture mechanics are available when moderate crack tip yielding occurs (Tada et al., 1985; Burdekin & Stone; McClintock & Irwin, 1965). The size of the crack tip yielding zone can be estimated by the Irwin approach, where the elastic stress analysis is used to estimate the elastic plastic boundary. A first order estimation of the plastic zone size, Ty, is

Panel without patch(3)

The stress intensity factor with plasticity correction is given by:

Щ = Aajn(a-ry) [sec g;)]2 (4)

The estimation of KI’, in Eq.(4), needs an iterative approach.

If this plastic zone is small compared to the crack size, then the linear elastic assumptions are correct. If not, the linear elastic fracture mechanics (LEFM) is not applicable and the elasto-plastic fracture mechanics (EPFM) should be used. The value of KI* can be related to Gi, the energy release rate for similar crack growth, in the usual way:

к; = (5)

Подпись: G, Подпись: 1 dU tp da Подпись: (6)

Where, from the results of Griffith (Griffith, 1924) the energy released normalized with respect to the new crack surface created during the crack extension, namely the strain energy release rate, is given by

An increase in the crack length leads to a decrease of the stored elastic strain energy AU.