Experimental and numerical study of rate-dependent mode-I failure of a structural adhesive

Copyright © 2022 The Author(s).. We present an experimental and numerical study of the rate dependence of the mode-I failure of adhesive joints, focussing on aluminium plates bonded with Araldite® 2015. For the experimental part, we tested 24 double-cantilever beams (DCB) at six different prescribed speeds, from 0.1 to 5000 mm/min. The numerical simulations use a previously proposed cohesive-zone model (CZM) based on fractional viscoelasticity and a novel finite element combining a Timoshenko beam and an interface element. The CZM had previously been validated for a rubber interface, so here we present a procedure to identify its input parameters and validate its capability to predict the failure of joints made with an epoxy adhesive. An effective procedure is also developed to evaluate the dependence of the fracture energy on the crack speed without experimentally measuring the crack speed. The adhesive response was found to be markedly rate dependent. Within the range of tested speeds, the fracture energy of the adhesive more than doubles its value and the shape of the ‘fracture energy-crack speed’ curve resembles a sigmoidal shape, but more tests are needed at higher speeds to better determine the maximum value of the fracture energy and the actual shape of the complete curve.European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 701032

On characterising fracture resistance in mode-I delamination

In this work we focus on the mode-I quasi-static crack propagation in adhesive joints or composite laminates. For this problems a number of di ff erent standards have been approved. The most widely used are based on the double cantilever beam (DCB) test and on linear elastic fracture mechanics (LEFM) but di ff er in some aspects of the testing procedure and the recommended data-reduction schemes. The applicability of these methods is still a matter of debate in the scientific community, particularly in the case of ductile interfaces. We revisit the accuracy of the most used standards and compare it with other methods based on either LEFM or J-integral theory. All the methods analysed in our work are based on either Euler-Bernoulli or Timoshenko beam theories. We present a number of numerical examples where we compare di ff erent expressions for fracture resistance obtained with di ff erent methods. The input for the analysis, which includes applied load, cross-head displacement and rotation, crack length and cohesive zone length, is obtained from the numerical model which simulates real experiments. In these simulations, we use a Timoshenko beam model with a bi-linear CZM, which allows us accurate comparison with analytical formulas for fracture resistance based on Euler-Bernoulli and Timoshenko beam theory

Enhanced simple beam theory for characterising mode-I fracture resistance via a double cantilever beam test

We study a double-cantilever beam (DCB), in which either the crack-mouth opening displacement or the end rotations are prescribed, in the linear-elastic-fracture-mechanics (LEFM) limit of an infinitely stiff and brittle interface.Wepresentanovel,yetextremelysimple,derivationoftheclosed-formsolutionofthisproblemwhen thearmsaremodelledwithTimoshenkobeamtheory.Weremovetheassumptionthatthecrosssectionsofthe DCB arms are assumed not to rotate (i.e. that they are clamped) at the crack tip, which is made in so-called ‘simple beam theory’(SBT).Therefore, with our‘ enhanced simple beam theory’(ESBT),in front of the crack tip, cross section sareallowedtorotate,althoughthebeamaxisstaysundeformed.Thus,wecandeterminethecracktiprotationcausedbythedeformationofthebeaminfrontofthecracktipalsointheLEFMlimit.Asaresult, mostoftheinaccuraciesoftheSBTareeliminated,withouttheneedforacrack-length correction, use dinthe ‘corrected beam theory’(CBT).Inthisway,wecanderiveaveryaccuratedatareductionformulaforthecritical energy release rate, Gc, which does not require the measurement of the crack length, unlike CBT. In our numerical results we show that, compared to the most effective data reduction methods currently available (including CBT), our formula is either as accurate or more accurate for the case of brittle delamination of thick compositeplates,inwhichsheardeformabilitycanplayasignificantrole

Characterisation of mode-I fracture resistance of adhesive layers with imperfections

Supplementary data are available on Brunelfigshare at: https://doi.org/10.17633/rd.brunel.25444726 [under a CC BY 4.0 license].In this work, a novel procedure to evaluate the influence of imperfections at the interface (such as voids and interfacial failure) on the fracture resistance of adhesive joints in mode-I debonding is proposed, based on an image-processing analysis of the crack surface. Its application to the characterisation of fracture resistance of aluminium DCB specimens bonded with an epoxy adhesive leads to a more accurate evaluation of the ‘effective’ fracture resistance by taking into account the distribution of imperfections along the interface, therefore also confirming that the typical oscillations and drops in the load–displacement curve can be attributed to the imperfections.TThis research is part of the project MOLAY-STRUDEL, funded from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement N. 701032

Complete analytical solutions for double cantilever beam specimens with bi-linear quasi-brittle and brittle interfaces

In thiswork we develop a complete analytical solution for a double cantilever beam (DCB) where the arms are modelled as Timoshenko beams, and a bi-linear cohesive-zone model (CZM) is embedded at the interface. The solution is given for two types of DCB; one with prescribed rotations (with steady-state crack propagation) and one with prescribed displacement (where the crack propagation is not steady state). Because the CZM is bi-linear, the analytical solutions are given separately in three phases, namely (i) linearelastic behaviour before crack propagation, (ii) damage growth before crack propagation and (iii) crack propagation. These solutions are then used to derive the solutions for the casewhen the interface is linear-elastic with brittle failure (i.e. no damage growth before crack propagation) and the case with infinitely stiff interface with brittle failure (corresponding to linear-elastic fracture mechanics (LEFM) solutions). If the DCB arms are shear-deformable, our solution correctly captures the fact that they will rotate at the crack tip and in front of it even if the interface is infinitely stiff. Expressions defining the distribution of contact tractions at the interface, as well as shear forces, bending moments and cross-sectional rotations of the arms, at and in front of the crack tip, are derived for a linear-elastic interface with brittle failure and in the LEFM limit. For a DCB with prescribed displacement in the LEFM limit we also derive a closed-form expression for the critical energy release rate, Gc. This formula, compared to the so-called ‘standard beam theory’ formula based on the assumptions that the DCB arms are clamped at the crack tip (and also used in standards for determining fracture toughness in mode-I delamination), has an additional term which takes into account the rotation at the crack tip. Additionally, we provide all the mentioned analytical solutions for the case when the shear stiffness of the arms is infinitely high, which corresponds to Euler–Bernoulli beam theory. In the numerical examples we compare results for Euler–Beronulli and Timoshenko beam theory and analyse the influence of the CZM parameters

On the Effectiveness of Higher-Order One-Dimensional Models for Physically Nonlinear Problems

The chapter presents numerical assessments of physically nonlinear problems through a class of refined one-dimensional theories based on the Carrera Unified Formulation (CUF). CUF is a hierarchical formulation to generate refined structural theories through a variable kinematic approach. Physical nonlinearities include von Mises plasticity and cohesive interface modeling for delamination of composites. This work aims to provide insights into the effect of kinematic enrichment on the overall nonlinear behavior of the structure. Guidelines stem from the evaluation of the accuracy and numerical efficiency of the proposed models against analytical and numerical approaches from the literature