Analysis of Taper-Taper Adhesive-Bonded Joints in Composite Plates Under Tension and Cylindrical Bending.

Abstract

A taper-taper adhesive-bonded joint between two composite plates has been analyzed under tension and cylindrical bending. Two tension models were derived. The first model was based on mechanics of materials and the second model used laminated plate theory and shear correction factors. For the mechanics of materials model the condition of plane strain was assumed for the adherends and adhesive. Average stresses were used in the adherends and point-wise stresses were used in the adhesive. The model derived consisted of four second-order ordinary differential equations with variable coefficients. The adherends were characterized by the extensional Young's modulus. The equations were solved numerically using the Linear Shooting Method and the solutions were compared with finite element models developed using the COSMOS/M commercial software package. The model was accurate in the area away from the sharp end of the taper and predicted strains within about 5-10% of the finite element models. The second analytical model was developed to improve prediction near the sharp end of the taper. The model was derived using first-order, laminated plate theory and included transverse shear deformation effects. The assembly was divided into three areas to facilitate the analysis, the two sections of laminate away from the joint and the joint itself. The first two sections were modeled by three first-order differential equations each. The joint was modeled by six second-order, ordinary differential equations with variable coefficients. The six equations were reduced to a set of twelve first-order differential equations, which were solved numerically with the six first-order equations from the areas away from the joint. Finite element models were developed using the COSMOS/M commercial software package for verification of the model. The model was accurate and predicted the peak stresses within about 5-8% of the values calculated with finite element analysis. A laminated plate model of the taper-taper joint was also derived for the case of cylindrical bending. The FORTRAN program was modified to numerically solve the resulting system of twelve first-order differential equations with variable coefficients. The adhesive stresses predicted were within about 2% of the results from the finite element models.