IntroductionAdhesive bonded joints for composite or metal joining are being used in many structural applications. Among the most significant concerns regarding the structural design and reliability of the joints are the possible defects like debonds or voids which occur during manufacturing or service. These defects can severely reduce the bond strength. Their presence will increase the peak stress levels which occur at the joint ends and near the flaw itself. The joint may fail at the ends of the joint at the ultimate stress or it may fail under cyclic loading where local debonding near the flaw can grow. Also, the subsequent redistribution of stress, due to debonding, may lead to possible delamination in the composite adherend itself'. The stress concentration, therefore, near a void or disbond is important, and any thermal mismatch between the adherend and the adhesive will also contribute to the increased stress levels which occur.Past work, related to the present study, was performed by Erdogan and Ratwani (1971), Hart-Smith (1973, 1981, Kan and Ratwani (1983, 1986), and Rossettos and Zang (1993 on axial stress as well as shear. A modified shear lag model used by Rossettos and Shishesaz (1987) is adopted here for this purpose.As such, a quadratic distribution of axial displacement is assumed in the adhesive. Based on appropriate equilibrium, stress-strain and strain-displacement relations, the problem is reduced to two coupled second order differential equations for the axial loads in the adherends. A subsequent nondimensionalization of quantities in the equation leads to several parameters which are seen to govern the stress distribution in the joint. A structural mechanics rather than a continuum approach is used, where the loading mechanisms are restricted to net axial and shear deformation in the components, and where a given quadratic displacement distribution is taken over the thickness of the adhesive layer. This avoids the corner singularity at the overlap ends. Since the general solution of the structural model contains exponential terms, the steep stress gradients near the overlap ends and at the defect edges can be calculated accurately.It is also remarked that if transverse shear in the adherends is also included in a higher order analysis (Renton and Vinson, 1977) the peak shear stress values will occur very near the overlap ends, dropping sharply to zero at the ends themselves.The conclusions of the present paper, however, regarding these peak shear stresses, will change very tittle, if at all.
AnalysisThe model consists of a simple lap joint as shown in Fig. l(a, b) made of two plates, which take only axial loads, bonded by an adhesive layer. Plates I and 2 can be made of composite materials with orthotropic characteristics, although either ad- Let pl (x), P2 (x) and P3 (x) be the resultant forces per unit width in adherend 1, adherend 2, and the adhesive respectively, while P0 is the corresponding force applied to the adherends away from the joint. For any value of x we have
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