Bonded Double-Overlap Joints

Linear Material Properties, and No Bending.

Gerry Flanagan, Materials Sciences Corporation, Nov. 3, 1999

Introduction

This notebook shows the derivation of the governing equations for the simplest bonded joint, the double-overlap joint. The "double" configuration is used to avoid the issue of bending that occurs for a single overlap joint. Classical bonded joint assumptions are used. The key assumptions are that all shear occurs in the bondline, and all axial load is carried by the adherend. Given these assumptions, relatively simple differential equations can be derived. Several combinations of boundary conditions are possible. This notebook explores three of the most practical combinations of load and restraints.

These solutions are limited to the linear range of the adhesive. Actual adhesives are usually highly nonlinear before failure. This limits the utility of these solutions for predicting failure. However, they are of use in design a joint for fatigue. In that case, it is desirable to keep the adhesive operating in the linear regeme.

Solve Differential Equation

A force balance for a differential element of each adherend give the following two differential equations (See Fig 1)

The solution to this coupled pair of equations is

The coefficients C[1] - C[4] are determined from the boundary conditions. At the end of each adherend, we can either restrain displacement, or specify a load intensity (P, lb/in). The spccified load may be zero. Three cases are considered.

Case 1

Solve for the unknown coefficients, and substitute into the equations for and .

Shear stress

Load in adherend a

Load in adherend b

Numerical Examples

Plot of shear stress over length of joint

Plot of load intensity in two adherends. Red is adherend "a", and blue is adherend "b"

Case 2

Numerical Example

Case 3

Boudnary Conditions for Case 3

Numerical Example

Design Charts

By looking at the nondimensional combinations of parameters, the peak shear stress information can be summarized in simple charts. The key parameters are λ L, and R=

Case 1

Perform a series of substitutions that yield the ratio of the peak shear stress to average shear stress in terms of  q=λ L, and R.

Plot for a series of R values

for large λ L, these curves approach the following

     λ L R
     -----
     R + 1

Case 2

for large λ L,

Note that all three cases have the same limiting relation.

Case 3

for large λ L,