Effect of Adhesive Compliance in the Assessment of Soft Adhesives with the Wedge Test

Abstract

Wedge tests are usually analysed assuming that the free, unbonded members may be treated as encastré cantilever beams. However, if the adhesive layer is sufficiently flexible (e.g., due to low elastic modulus), then significant strain in the bonded region may occur and lead to modification of the behaviour outside this region. Using in conjunction a sensitive strain gauge method on asymmetric wedge tests and a mathematical analysis developed from the work of Winkler, we conclude that the standard, simple beam theory approach significantly overestimates crack length for a supple adhesive layer. The present contribution mainly considers strain effects in the intact, bonded zone, rather than fracture per se. However, it is concluded that, if in fracture tests, the incorrect values of crack length obtained from the encastré beam assumption are employed to calculate fracture energy using the simpler model, there will be some self-compensation and little error in estimates of the latter will result (at least in the cases presently studied).

Pre-cracking behaviour in the single cantilever beam adhesion test

“…5. The initial idea for the following analysis stems from Winkler in the nineteenth century (Winkler 1867), who studied reactions in railway ballast, but the concept has since been developed several times in conjunction with adhesive bonds (Gillis and Gilman 1964;Kanninen 1973;Kendall 1973;Williams 1993;Kendall 2001;Sargent 2005;Cotterell et al 2006;Budzik et al 2011).We here present the rudiments necessary for application to the SCB test: more detail is given in (Budzik et al 2011).…”

“…The constants A 1 , B 1 , A 2 , B 2 , C 2 , and D 2 can be found from boundary conditions of geometry and continuity of functions (Budzik et al 2011), and derivatives up to order 3, leading to the rather complicated expressions:…”

Fracture energy of bonded joints with 2D elastic adhesive layer

“…Winkler approach was apparently the first developed to describe the root rotation effect [14] and has recently been employed to consider the influence of adhesive compliance [15]. Considering again Fig.2., we take a beam bonded in the range a < x < +∞, and free over 0 < x < a.…”

“…Taking into account the influence of Poisson's ratio (confinement), we have [15]: The bracketed terms in ν A are to allow for essentially plane strain conditions existing in a thin adhesive layer (e/b<<1). The correction is not negligible, since an adhesive could easily have a Poisson's ratio of 0.4, leading to ca.…”

“…These models do not take adhesive layer into account which is specifically required when compliant adhesives are used. Compliance effect can be introduced by treating adhesive layer as a Winkler elastic foundation [14,15]. Numerical and experimental observations proves that also other effects affecting fracture could be present when the joint is submitted to rather simple 1D loading [16,17].…”