Feridun Delale

Stresses in Adhesively Bonded Joints: A Closed-Form Solution

In this paper the general plane strain problem of adhesively bonded struc tures which consist of two different orthotropic adherends is considered. Assuming that the thicknesses of the adherends are constant and are small in relation to the lateral dimensions of the bonded region, the adherends are treated as plates. Also, assuming that the thickness of the adhesive is small compared to that of the adherends, the thickness variation of the stresses in the adhesive layer is neglected. However, the transverse shear effects in the adherends and the in-plane normal strain in the adhesive are taken into ac count. The problem is reduced to a system of differential equations for the adhesive stresses which is solved in closed form. A single lap joint and a stif fened plate under various loading conditions are considered as examples. To verify the basic trend of the solutions obtained from the plate theory and to give some idea about the validity of the plate assumption itself, a sample pro blem is solved by using the finite element method and by treating the adherends and the adhesive as elastic continua. It is found that the plate theory used in the analysis not only predicts the correct trend for the adhesive stresses but also gives rather surprisingly accurate results. The solution is ob tained by assuming linear stress-strain relations for the adhesive. In the Ap pendix the problem is formulated by using a nonlinear material for the adhesive and by following two different approaches.

Interface crack in a nonhomogeneous elastic medium

The linear elasticity problem for an interface crack between two bonded half planes is reconsidered. It is assumed that one of the half planes is homogeneous and the second is nonhomogeneous in such a way that the elastic properties are continuous throughout the plane and have discontinuous derivatives along the interface. The problem is formulated in terms of a system of integral equations and the asymptotic behavior of the stress state near the crack tip is determined. The results lead to the conclusion that the singular behavior of stresses in the nonhomogeneous medium is identical to that in a homogeneous material provided the spacial distribution of material properties is continuous near and at the crack tip. The problem is solved for various values of the nonhomogeneity parameter and for four different sets of crack surface tractions, and the corresponding stress intensity factors are tabulated.

Line-spring model for surface cracks in a reissner plate☆

In this paper the line-spring model developed by Rice and Levy for a surface crack in elastic plates is reconsidered. The problem is formulated by using Reissners plate bending theory. For the plane strain problem of a strip containing an edge crack and subjected to tension and bending new expressions for stress intensity factors are used which are valid up to a depth-to-thickness ratio of 0.8. The stress intensity factors for a semi-elliptic and a rectangular crack are calculated. Considering the simplicity of the technique and the severity of the underlying assumptions, the results compare rather well with the existing finite element solutions.

Effect of transverse shear and material orthotropy in a cracked spherical cap

The elastostatic problem for a relatively thin-walled spherical cap containing a through crack is considered. The problem is formulated for a specially orthotropic material within the confines of a linearized, shallow shell theory. The theory used is equivalent to Reissners theory of flat plates and hence permits the consideration of all five physical conditions on the shell boundaries separately. The solution of the problem is reduced to that of a pair of singular integral equations and the asymptotic stress state around the crack tips is investigated. The numerical solution of the problem is given for an isotropic shell and for two specially orthotropic shells. The results indicate that the material orthotropy as well as the shell curvature and thickness may have a considerable effect on the stress intensity factors at the crack tips.

The crack problem for a half plane stiffened by elastic cover plate

Abstract In this paper the problem of an elastic half plane containing a crack and stiffened by a cover plate is considered. First, the asymptotic nature of the stress state in the half plane around an end point of the stiffner is studied in order to determine the likely orientation of a possible fracture initiation and growth. The problem is then formulated for an arbitrarily oriented radial crack in terms of a system of singular integral equations. For an internal crack and for an edge crack, the problem is solved and the stress intensity factors at the crack tips and the interface stress are calculated. The case of a cracked half plane for two symmetrically localted cover plates is then considered. From a fracture viewpoint, the case of two stiffeners appears to be more severe than that of a single stiffner.

Stress intensity factors for an internal or edge crack in a circular elastic disk subjected to concentrated or distributed loads

Abstract Stress intensity factors for an internal or edge crack in a circular elastic disk subjected to concentrated or distributed loads are obtained using the singular integral equation technique. First, a solution for the uncracked case is obtained using the complex variable method, and then employing the superposition technique the crack problem is reduced to a perturbation problem. By integrating the dislocation solution along the crack, a singular integral equation is obtained, which in turn is solved numerically. The stress intensity factors are calculated for various crack geometries and loading conditions.

Time-Temperature Effect in Adhesively Bonded Joints

In this paper the viscoelastic analysis of an adhesively bonded lap joint is reconsidered. The adherends are approximated by essentially Reissner plates and the adhesive is assumed to be linearly viscoelastic. The hereditary in tegrals are used to model the adhesive. The problem is reduced to a system of linear integral-differential equations for the shear and the tensile stress in the adhesive. For a constant operating temperature, the equations are shown to have constant coefficients and are solved by using Laplace transforms. It is also shown that if the temperature variation in time can be approximated by a piecewise constant function, then the method of Laplace transforms could still be used to solve the problem. A numerical example is given for a single lap joint under various loading conditions and operating at temperatures 70, 100, 140 and 180°F.

The crack problem in a specially orthotropic shell with double curvature

Abstract In this paper the crack problem of a shallow shell with two nonzero curvatures is considered. It is assumed that the crack lies in one of the principal planes of curvature and the shell is under Mode I loading condition. The material is assumed to be specially orthotropic. After giving the general formulation of the problem the asymptotic behavior of the stress state around the crack tip is examined. The analysis is based on Reissners transverse shear theory. Thus, as in the bending of cracked plates, the asymptotic results are shown to be consistent with that obtained from the plane elasticity solution of crack problems. Rather extensive numerical results are obtained which show the effect of material orthotropy on the stress intensity factors in cylindrical and spherical shells and in shells with double curvature. Other results include the stress intensity factors in isotropic toroidal shells with positive or negative curvature ratio, the distribution of the membrane stress resultant outside the crack and the influence of the material orthotropy on the angular distribution of the stresses around the crack tip.

An Experimental Study of Self-diagnosis of Interlaminar Damage in Carbon-fiber Composites

An experimental study was conducted to sense interlaminar delamination in carbon-fiber composites utilizing inherent material piezoresistivity. Mode I and II interlaminar fracture tests were carried out on double cantilever beam and end-notched-flexure specimens following ASTM standards. The traditional DC-sourcing two-point probe technique was employed to measure the through-thickness electrical resistance change. For comparison, optical marker method and acoustic emission technique were also applied to detect interlaminar crack growth. The investigation demonstrates the application potential of the self-sensing capabilities of carbon-fiber composites for structural health monitoring.

Critical fiber size for microcrack suppression in ceramic-fiber/ceramic-matrix composites

Abstract In this paper the microcracking of ceramic-fiber/ceramic-matrix composites due to residual stresses is studied. Starting with the model of a single fiber embedded in an infinite matrix, the critical fiber size for suppression of interface and radial matrix cracking is determined. The relationship between critical fiber size and the parameters governing microcracking (such as cooling temperature, thermal expansion coefficients of fiber and matrix, Youngs moduli of the constituents, etc.) is established. It is shown that a smaller difference between the thermal expansion coefficients of matrix and fiber leads to a larger critical fiber size. Cooling temperature and the elastic properties of the constituents also affect microfracture.