The strain energy release rates in adhesively bonded balanced and unbalanced specimens and lap joints

Abstract

a b s t r a c tAn analytical model is developed to determine the strain energy release rate in adhesive joints of various configurations such as the double-cantilever beam and single-lap joints. The model is based on asymptotic analysis of adhesive layer stresses and Irwin's crack closure integral. Closed-form solutions are presented for balanced and unbalanced joints under mode I, II and mixed-mode I/II that take into account the influence of the shear force on the adhesive stresses, and its influence on the strain energy release rate. The accuracy of the model is tested against the classical beam theory expressions for double-cantilever beam and end-notch flexure specimens. In fact, classical beam theory's expressions are found to be the lower bound of the proposed model solutions, and the two methods converge as the adhesive layer thickness decreases. Analysis of single-lap joints reveals the influence of edge shear forces on the total strain energy release rate, and more importantly on the ratio between modes I and II. Results from the proposed analytical model are in good agreement with finite element results and with analytical models found in the literature.

A linear elastic-brittle interface model: application for the onset and propagation of a fibre-matrix interface crack under biaxial transverse loads

“…Nevertheless, in the current (may be the most straightforward) formulation of constitutive law and failure criterion for LEBIM, with no traction singularity at a crack tip, these two criteria somewhat surprisingly become equivalent. It appears that this quite surprising observation has been repeatedly rediscovered by many researchers during the last 50 years showing (apparently independently), in different ways that the ERR at a crack tip (actually the endpoint of an undamaged interface zone) is determined by the interface tractions at this very crack tip point (Entov and Salganik 1968;Fernlund and Spelt 1991;Krenk 1992;Bank-Sills and Salganik 1994;Erdogan 1997;Lenci 2001;Bruno and Greco 2001;Shahin and Taheri 2008;Carpinteri et al 2009). Actually, as will be shown in Section 2.2, ERR can be defined for breaking of any small undamaged portion of the linear elastic-brittle interface (not necessarily the crack tip point) and is determined by tractions at the point where the breakage initiates and just at the moment before the breakage occurs.…”

“…Although several proofs for the formulae (2b) and (2c) for ERR of a crack at a linear elastic interface have (apparently independently) been published in the past in Entov and Salganik (1968);Fernlund and Spelt (1991); Krenk (1992); Erdogan (1997); Lenci (2001); Bruno and Greco (2001); Shahin and Taheri (2008);Carpinteri et al (2009), see also Bank-Sills and Salganik (1994), the present authors believe that the mechanical interpretation, (given below), of Irwin's Crack Closure Technique (Irwin 1957) applied to any unbroken point of this interface, given below, still deserves to be presented. Let us consider two linear, elastic solids (adherents) A and B bonded along a straight interface, located at the x-axis.…”

Energy release rate and phase angle of delamination in sandwich beams and symmetric adhesively bonded joints

“…The former approach, which has been used for over seven decades, focuses on the prediction of interfacial peel and shear stresses within the adhesive layer (Goland and Reissner, 1944;Delale et al, 1981;Wang and Zhang, 2009). In the latter approach, which has been used more recently (Krenk, 1992;Alfredsson and Hogberg, 2007;Fernlund, 2007;Shahin and Taheri, 2008), two fracture mechanics parameters, ERR and its phase angle, are calculated. Three methods are 0020-7683/$ -see front matter Ó 2009 Elsevier Ltd. All rights reserved.…”

“…Three methods are 0020-7683/$ -see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijsolstr.2009.09.003 commonly used to calculate the ERR and its phase angle: (1) a finite element analysis (FEA); (2) a classical interface fracture solution (Suo and Hutchinson, 1990;Østergaard and Sørensen, 2007); and (3) an interface stress-based method (Krenk, 1992;Alfredsson and Hogberg, 2007;Fernlund, 2007;Shahin and Taheri, 2008). In the interface stress-based method, the maximum interface peel and shear stresses at the delamination tip (within the adhesive layer) are first obtained using the aforementioned strength of materials method.…”

“…The ERR in mode I or II is then calculated as half the product of the square of the peel stress (or shear stress) at the crack tip and the stiffness of peel (or shear). This approach was originally developed for symmetric adhesive bonded joints (Krenk, 1992), and recently it has been used for asymmetric joints by a few researchers (Alfredsson and Hogberg, 2007;Fernlund, 2007;Shahin and Taheri, 2008). However, the validation of such an extension is questionable because the phase angle obtained through the interface stress-based method is not reliable for an asymmetric joint (Alfredsson and Hogberg, 2007).…”