Energy-based delamination theory for biaxial loading in the presence of thermal stresses

Abstract This paper addresses the issue of using energy balance methods and crack closure concepts to predict the growth of delaminations associated with ply cracks during the progressive loading of cross-ply laminates subject to a combination of in-plane biaxial stresses and thermal residual stresses. When the effective applied stresses and the temperature are held fixed during delamination growth, and there is negligible interaction of the delamination tips with the ply cracks, very simple analytical formulae for the energy release rate can be derived for unconstrained and generalised plane strain conditions, which are exact when the ply crack separation tends to infinity. In some practical applications, such as for wide plates, delamination growth is constrained transversely by surrounding undamaged laminate and this has an effect on energy release rates. An analytical method is described that determines the energy release rate for delamination growth under such constrained conditions. This result is also exact in the limit of ply crack separations tending to infinity. The boundary element method (BEM) has been used to investigate energy release rates for constrained conditions for a range of ply crack densities, both in the presence and absence of thermal residual stresses, for a special case where the delamination tips are mid-way between neighbouring ply cracks. BEM results show a slight dependence of the energy release rate on ply crack separation, and predictions for the maximum ply crack separation considered are within 1.6% of the exact limiting analytical predictions valid for infinite separation. This agreement indicates the validity of both the analytical methods used, and the numerical analysis based on the BEM.