Determination of the Fracture Parameters in a Stiffened Composite Panel

Abstract

A modified J-integral, namely the equivalent domain integral, is derived for athree-dimensional anisotropic cracked solid to evaluate the stress intensity factor alongthe crack front using the finite element method. Based on the equivalent domain integralmethod with auxiliary fields, an interaction integral is also derived to extract the secondfracture parameter, the T-stress, from the finite element results. The auxiliary fields arethe two-dimensional plane strain solutions of monoclinic materials with the plane ofsymmetry at x3=0 under point loads applied at the crack tip. These solutions areexpressed in a compact form based on the Stroh formalism. Both integrals can beimplemented into a single numerical procedure to determine the distributions of stressintensity factor and T-stress components, T11, T13, and thus T33, along a three-dimensionalcrack front.The effects of plate thickness and crack length on the variation of the stressintensity factor and T-stresses through the thickness are investigated in detail for through-thicknesscenter-cracked plates (isotropic and orthotropic) and orthotropic stiffenedpanels under pure mode-I loading conditions. For all the cases studied, T11 remains negative. For plates with the same dimensions, a larger size of crack yields largermagnitude of the normalized stress intensity factor and normalized T-stresses. The resultsin orthotropic stiffened panels exhibit an opposite trend in general. As expected, for thethicker panels, the fracture parameters evaluated through the thickness, except the regionnear the free surfaces, approach two-dimensional plane strain solutions. In summary, thenumerical methods presented in this research demonstrate their high computational effectiveness and good numerical accuracy in extracting these fracture parameters fromthe finite element results in three-dimensional cracked solids.