An extended semi-analytical formulation for fast and reliable mode I/II stress analysis of adhesively bonded joints

Lélias, Guillaume; Paroissien, Éric; Lachaud, Frédéric; Morlier, Joseph; Schwartz, Sébastien; Gavoille, Cyril

doi:10.1016/j.ijsolstr.2014.12.027

Cited by 21 publications

(35 citation statements)

References 20 publications

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“…. But the elementary stiffness matrix corresponds to the relationship between the vector of nodal forces and the vector of nodal displacements ( Paroissien, 2006a;Paroissien et al, 2006bParoissien et al, , 2007Paroissien et al, , 2013Lélias et al, 2015 ), such as:…”

Section: Resultsmentioning

confidence: 99%

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Experimental characterization of cohesive zone models for thin adhesive layers loaded in mode I, mode II, and mixed-mode I/II by the use of a direct method

Lélias

Paroissien

Lachaud

et al. 2019

International Journal of Solids and Structures

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The demand for designing lightweight structures without any loss of strength or stiffness has conducted many engineers and researchers to seek for alternative joining methods. In this context, adhesive bonding may appear as an attractive joining method. However the interest of adhesive bonding remains while the structural integrity of the joint is ensured. According to recent literature the cohesive zone model (CZM) appears as a suitable approach able to predict both static and fatigue strength of adhesively bonded joints. This approach of the fracture process of adhesive layers is based on the modeling of the adhesive mechanical behavior through a set of adhesive cohesive properties in either mode I, mode II or mixed-mode I/II. The strength prediction of adhesively bonded joints is then highly dependent on the CZM parameters. The methods used to experimentally characterize them are thus essential. A new methodology, termed direct method, is presented and tested. It is based on the measurement of displacement field of bonded adherends at the crack tip of classical specimens allowing for the loading of the adhesive layer in pure mode I, pure mode II and mixed-mode I/II. The tested adhesive is a methacrylate-based two-component adhesive paste found under the reference SAF30 MIB manufactured by AEC Polymers (ARKEMA group). The adherends are in aluminium 6060. It is shown that it is possible to characterize the cohesive properties of the adhesive layer using the direct method. The numerical tests involve both adherends and adhesive nonlinearities. Nevertheless, the presented experimental implementation passes by the development of a dedicated data pre-processing to interpret the experimental measurements, highlighting the significance of the choice of the measurement means linked to the design of specimen.

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Section: Resultsmentioning

confidence: 99%

“…A particular emphasis is given to the ability of the suggested approach to provide both the experimental stiffness and the maximum load bearing capability of each adhesive specimen. All the numerical tests presented in this paper are based on the simplified stress analyses using ME, already presented in details in ( Lélias et al, 2015 ).…”

Section: Elasticmentioning

confidence: 99%

Experimental characterization of cohesive zone models for thin adhesive layers loaded in mode I, mode II, and mixed-mode I/II by the use of a direct method

Lélias

Paroissien

Lachaud

et al. 2019

International Journal of Solids and Structures

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“…A JE is a 4-nodes brick element allowing for the modelling of two bonded adherends [15][16][17]. Over a similar period of time, the first and third authors of the present papers and co-workers have been working on the development of the macro-element (ME) technique for the simplified stress analysis of bonded, bolted and hybrid (bonded/bolted) joints made of dissimilar and possibly laminated beams [18][19][20][21][22][23][24]. The JE and ME are based on the same modelling approach.…”

Section: Nomenclature and Unitsmentioning

confidence: 99%

“…The ME technique can be regarded as a mathematical procedure allowing for the resolution of the system of ODEs, under a less restricted application field of simplifying hypotheses, in terms of geometry, material behaviours, kinematics, boundary conditions and loads. Dedicated 4-nodes bonded-bars (BBa) and bonded-beams (BBe) have been formulated [18][19][20][21][22][23][24]. Once the stiffness matrix of the complete structure is assembled from the elementary stiffness matrices and the boundary conditions are applied, the minimization of the potential energy provides the solution, in terms of adhesive stress distributions along the overlap, internal forces and displacements in the adherends at any abscissa along the joint.…”

Section: Overview Of the Macro-element Technique And Applicationmentioning

confidence: 99%

“…The boundary conditions and loading are applied through the Augmented Lagrangian method [25][26]. Besides, an algorithm based on the Newton-Raphson iterative procedure has been developed to support nonlinear material behaviors of the adhesive and adherends [21][22][23][24]. In the case of nonlinear computation, the overlap length needs to be meshed with n_ME MEs along the overlap length (only) to allow for the update of the material properties within the iterative procedure ( Figure 2).…”

Section: Overview Of the Macro-element Technique And Applicationmentioning

confidence: 99%

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A comparison between macro-element and finite element solutions for the stress analysis of functionally graded single-lap joints

Paroissien

Lachaud

Silva

et al. 2019

Composite Structures

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comparison between macro-element and finite element solutions for the stress analysis of functionally graded single-lap joints. (2019) Composite Structures, 215.Abstract -The interest in functionally graded adhesive (FGA) joints has been increasing in recent years. For example, FGAs offer the opportunity to optimize the strength of multimaterial bonded joints by locally tailoring the adhesive properties and without modifying the design of the adherends to be joined. The development of dedicated stress analyses to predict the stress distribution is then of the highest interest to control the strength of such joints. The Finite Element (FE) method is able to address the stress analysis of FGA joints but is computationally costly. Simplified stress analyses have then been developed. The objective of this paper is to assess the prediction of simplified stress analyses, solved through the macroelement (ME) technique, with respect to those of FE models. It is shown that the predictions of ME models are in a sufficient agreement with the FE models to be employed at a pre-sizing stage. The influence of the overlap length is then investigated by the means of the simplified 2 stress analyses. A noticeable result is the existence of an overlap length for which the adhesive peak shear stress is minimal, in the 1D-bar kinematics framework.

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Formulation methodologies based on Taylor expansion power and Fourier expansion series for the macro‐element resolution scheme of enriched models for the stress analysis of adhesively bonded joints

Salaün,

Paroissien,

Schwartz

et al. 2023

Numerical Meth Engineering

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In recent years, interest in adhesive bonding has grown as it can be considered an efficient solution in terms of strength‐to‐mass ratio when applied to lightweight structures or an interesting solution to complement conventional technologies. The study of bonded adhered joints is carried out using a technique based on the macro‐element method (ME), the ME shape functions are modeled using Taylor expansion power and Fourier expansion series. The purpose of this work is to compare the stiffness matrix obtained first from the entire Taylor series and then with the entire Fourier series. The method has been developed so far for 1D‐bar and 1D‐beam kinematics frameworks.

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An extended semi-analytical formulation for fast and reliable mode I/II stress analysis of adhesively bonded joints

Cited by 21 publications

References 20 publications

Experimental characterization of cohesive zone models for thin adhesive layers loaded in mode I, mode II, and mixed-mode I/II by the use of a direct method

Experimental characterization of cohesive zone models for thin adhesive layers loaded in mode I, mode II, and mixed-mode I/II by the use of a direct method

A comparison between macro-element and finite element solutions for the stress analysis of functionally graded single-lap joints

Formulation methodologies based on Taylor expansion power and Fourier expansion series for the macro‐element resolution scheme of enriched models for the stress analysis of adhesively bonded joints

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