On the calculation of energy release rate and mode mixity in delaminated laminated beams

Abstract

A method is presented for the analysis of laminated beams with general stacking sequences and arbitrarily located, through-the-width delaminations. First, the relative displacements and concentrated forces at the crack tip are determined based on classical lamination theory and Timoshenko beam kinematics. Next, new quantities, called crack-tip displacement rates, are defined as the relative displacements per unit increase in crack length. The previously computed quantities are then used to calculate the energy release rate and its mode I and II contributions via an adaptation of the virtual crack closure technique. Results for homogeneous and bimaterial delaminated beams are presented and compared to the predictions of other methods in the literature. Lastly, applications to some non-standard delamination test specimens are illustrated

The Effects of Shear on Mode II Delamination

“…(22) and (23) with (20) and (21) shows that Valvo's method [24] reduces to Wang and Qiao's method [20], if the crack-tip bending moment, MC, is disregarded. In general, however, MC gives a contribution to both modes I and II.…”

“…(20) and (21), shear forces and shear deformation contribute only to mode I. Valvo [24] extended Williams' method from homogeneous beams to general laminated beams. He determined the modal contributions to G based on a modified virtual crack closure technique.…”

“…If the delaminated beam is modelled as an assemblage of rigidly connected sublaminates, the total energy release rate can be evaluated based on beam theory [21][22][23][24]. Thus, an analytical expression for G is determined depending on the values of the internal forces acting on the crack-tip segment: the axial forces, N i , shear forces, Q i , and bending moments, M i (i = 1, 2, 3).…”

“…The delamination is not necessarily placed on the mid-plane, but divides the laminate into two sublaminates with thicknesses H1 = 2h1 and H2 = 2h2 (Fig. 5b) [24]. …”

“…Besides the adoption of a more or less refined structural theory for the sublaminates, the connection between them has to be suitably described. To this aim, models of growing complexity can be chosen, ranging from rigid connections [15][16][17][18][19][20][21][22][23][24] to elastic interfaces [25][26][27][28][29][30][31][32][33][34][35][36][37][38] and cohesive zone models [39][40][41][42][43][44][45][46][47]. This choice is relevant not only for the accurate prediction of the laminate structural response -e.g.…”