No abstract

It is shown here that ultrasonic measurements can provide accurate information on an adhesive layer whose thickness is negligible compared with the wavelength. In this case, the adhesive layer can be considered as a simple interface between two elastic solids. This kind of contact enables small discontinuities of stresses or displacements between both substrates. A simple formulation is introduced to take into account these discontinuities expressed in terms of imperfect boundary conditions. It is shown that this formulation is consistent with exact calculation in layered media. The range of applications of this model and its limits is also investigated. This model is used to infer quantitative data on the changes in mechanical properties of a thin bonding layer (about 5 pm) from reflection coefficient measurements during its hardening process. The results obtained are in excellent agreement with ultrasonic measurement in bulk. 3264

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

No abstract

The uniaxial constitutive law for an adhesive is studied by constant strain rate tensile, creep and relaxation tests. The S-D effect of the adhesive is taken into account by using the Raghava yielding criterion in a three dimensional constitutive formulation. The obtained constitutive law is then used to analyze a single lap joint and a butt joint by a finite element method. Constant cross head speed tensile and creep loading cases are examined. For a butt joint, the results show that the viscous effect and the influence of the hydrostatic stress must be taken into account due to the variation of the hydrostatic stress and of the loading rate in the adhesive layer as function of its thickness. A comparison with experimental results is also given. A good agreement between viscoplastic calculations and experimental results is obtained for single-lap joints. A reasonable result is obtained for butt joints and the discrepancy is attributed to interfacial debonding.