An 1D-Beam Approach for Both Stress Analysis and Fatigue Life Prediction of Bonded Joints

Abstract

An approach for both stress analysis and fatigue life prediction of bonded joints, based on a 1D-beam model, is presented. Only the adhesive is supposed to fail. The Goland and Reissner framework [1] is extended to unbalanced laminar or monolithic adherends under thermal loads. The J-integral is derived and employed in a modified Paris law, leading to fatigue lives, which are assessed w.r.t. published experimental results [2, 3] .

Modelling load transfer in single-lap adhesively bonded and hybrid (bolted / bonded) joints

“…[74,75,77] assumed two similar linear elastic adherends. The formulation for the bonded-beams ME with dissimilar laminated adherends was published from 2011 [79,[81][82][83][84][85]. The initial methodology employed for the formulation focuses on closed-form equations, as for the bonded-bars ME.…”

“…( 40) are the solutions to be considered for all geometrical and material parameters having a physical meaning [45,50] when the adherends are dissimilar and B 1 =B 2 =0. The adherend displacements and internal forces can be written as functions of the expressions for adhesive stresses and their derivatives as well as polynomial expressions [79,[81][82][83][84][85]. In addition to the first thirteen integration constants K 1 to K 13 , fourteen new integration constants appear.…”

“…It has been shown in Refs. [79,[81][82][83][84][85] that the stiffness matrix of beam elements representing the adherend outside the overlap takes the following shape:…”

“…Macro-element (ME) modelling has been developed since 2004 for the simplified stress analysis of HBB joints [74][75][76][77][78][79][80][81]. Applied to pure bonded joints, ME modelling is a semi-analytical method extending the scope of models belonging to the first family.…”

“…Applied to pure bonded joints, ME modelling is a semi-analytical method extending the scope of models belonging to the first family. It offers the advantage of providing a solution for geometrical, material and loading configurations for which there are no closed-form solutions [81][82][83][84][85][86][87][88][89][90][91][92][93]. As demonstrated in sections 4 and 5, ME modelling is an attractive approach to support the variation and associated growing complexity of simplifying hypotheses at low computational cost.…”