The simplified analytical approaches based on beam or plates theories are commonly used to solve the stress field in bonded laminates. However, to be correctly applied, these methods require an appropriate fracture criterion. In this paper, the use of J-integral as a fracture parameter in these simplified analytical approaches is discussed. After examining its path independence, the J-integral is calculated along two particular paths showing first that this integral is equal to the product of the strain energy at the end of the joint (i.e. at the debond tip) by its thickness. This relationship reveals the partitioning of the opening mode I and the shearing mode II. Secondly, the general expression of J as a function of the loading conditions is derived. It is shown that this parameter can be related to the strain energy release rate in the cases of small scale yielding conditions and for usual fracture mechanics specimens.
NomenclatureJ = Rice integral W = Strain energy density T = Tension vector s = Curvilinear abscissa u = Displacement vector U, V = x, y-components of the displacement = Stress tensor h0 = Adhesive thickness r, a~. = Shear and normal stresses in the adhesive 7, ey = Shear and normal strains in the adhesive h~ = Adherend thickness Ni, Q/ = Normal and shear forces in the adherend i Mi = Bending moment in the adherend i u~, v/ = x, y displacements of the neutral line fl~ = Bending rotation a~,, zx~. = Components of stress tensor in the adherends e, xx, 7xy = Components of strain tensor in the adherends