Adhesive Boundary Element Method Using Virtual Crack Closure Technique

Yang Xu,Rongxin Zhou

doi:10.3389/fmech.2021.754782

Yang Xu, Rongxin Zhou

Open Access

https://doi.org/10.3389/fmech.2021.754782

Copy DOI

Abstract

In this study, a new adhesive contact model is built upon a boundary element method (BEM) model developed by Pohrt and Popov (2015). The strain energy release rate (SERR) on the edge of the bonding interface is evaluated using Virtual Crack Closure Technique (VCCT) which is shown to have better accuracy and weaker mesh-size dependency than the closed-form SERR formula derived by Pohrt and Popov. A composite delamination criterion is proposed for crack nucleation and propagation. Numerical results predicted by the present model are in good agreement with the analytical solutions of two classic problems, namely, the axisymmetric parabolic contact and the sinusoidal waviness contact in the plane strain condition. The model of Pohrt and Popov can achieve a similar accuracy for the axisymmetric parabolic contact where the mesh grid is non-conforming to the crack front. Once the conforming mesh grid is used, the accuracy of their model is significantly deteriorated, especially at high work of adhesion and high mesh density. In both BEM models, however, the crack nucleation is found to be mesh-dependent which may be solved by introducing an upper limit for the tensile normal traction.

Highlights

Two mating surfaces bond to each other through intermolecular attractions, even under the tensile loading
We have shown that 1) Virtual Crack Closure Technique (VCCT) is suitable for evaluating the strain energy release rate (SERR) in the purely normal adhesive contact problem; and 2) the composite delamination criterion is correctly implemented for the crack propagation stage
By revisiting two classic crack problems, it is shown that VCCT has better accuracy and weaker mesh-size dependency than the closed-form SERR formula adopted in the previous model

Summary

Introduction

Two mating surfaces bond to each other through intermolecular attractions, even under the tensile loading. If the intermolecular attraction outside the contact area is neglected (i.e., the JKR limit), the adhesive interface is equivalent to a brittle crack whose static equilibrium is governed by the Griffith’s criterion (Maugis and Barquins, 1978; Greenwood and Johnson, 1981; Johnson, 1995). The intermolecular attractions outside the contact area can be included through the cohesive zone modeling, and the closed-form solution may be obtained if simplified cohesive laws are used [e.g., the Dugdale model (Maugis, 1992; Ciavarella et al, 2019; Jin and Yue, 2020) or the double Hertzian/Westergaard model (Greenwood and Johnson, 1998; Jin et al, 2016)].

Results

Discussion

Conclusion