Fracture Mechanics Online Class

SIF Computation

This chapter introduces the existing different methods available to compute the Stress Intensity factor (SIF), which are

SIF Computation > Analytical methods: Reminder of Linear Elasticity

Under the assumptions of 2D linear elasticity, the problem can be stated in terms of the Airy function and is thus governed by the bi-harmonic equation:

\begin{equation} \nabla^2 \nabla^2 \Phi = 0. \label{eq:biharmonic}\end{equation}

One solution of this equation has the form:

\begin{equation} \Phi = \frac{\bar{\zeta}\Omega+\zeta\bar{\Omega} + \omega + \bar{\omega}}{2} ,\label{eq:PhiCrack}\end{equation}

where the functions $\omega(\zeta)$ and $\Omega(\zeta)$ have to be determined so that the boundary conditions are satisfied. The solution fields can be expressed in terms of these functions as: