Virtual Crack Closure Technique Research Articles

Analysis of load-displacement curves of an adhesive-reinforced composite patch repaired plate using the combination of XFEM and CZM techniques

Since the development of the eXtended Finite Element Method (XFEM), Cohesive Zone Modelling (CZM), and the Virtual Crack Closure Technique (VCCT) for damage analysis in repaired structures, it has now become easy to validate experimental tensile tests carried out on damaged and repaired plates with a composite patch. In most cases, these tensile tests can be expensive and time-consuming due to surface preparation, cleaning, polishing, adhesive application, and the crosslinking time of the adhesive, which must be carefully considered. The analysis of damage in structures assembled by adhesive bonding is crucial to predicting their behavior under various loading conditions. Moreover, the analysis of experimental curves is in most cases translated a global behavior without taking into account the details that can influence the results. With the introduction of techniques (XFEM, CZM and VCCT), it is now possible to model different forms of damage, accounting for several mechanical and geometric parameters of the plate, patch, and adhesive. This work aims to analyze the behavior under tensile loading of a 2024-T3 aluminum plate presenting an initial crack of different lengths emanating from a central circular notch. This plate is repaired by a carbon/epoxy type patch through an adekit A140 adhesive. The combined use of XFEM to track damage in the plate and CZM for adhesive debonding allowed the acquisition of tensile load-elongation curves and the assessment of damage inflicted by loading on the plate. The results demonstrate that the combined use of XFEM and CZM techniques enables the identification of the adhesive debonding impact on the load transfer to the patch and consequently on the strength of the repaired structure. Furthermore, these highlight that the decrease in the effectiveness of the composite patch with increasing crack size is directly linked to the progressive deterioration of both the plate and the adhesive strength.

Structural fatigue crack propagation simulation and life prediction based on improved XFEM-VCCT

To simulate structural crack propagation and predict fatigue life, the extended finite element method (XFEM) combined with the virtual crack closure technique (VCCT) is adopted in this paper. Firstly, the underlying principles of the XFEM-VCCT framework are elaborated comprehensively, mainly including the calculation of crack tip energy release rate based on VCCT, the simulation of element cracking utilizing the phantom nodes, and the computation of structural responses under cyclic loading through the direct cyclic analysis. In addition, to calculate the crack propagation length, an interpolation method to obtain the crack tip coordinates is developed based on tracking and locating the crack by the level set functions. Meanwhile, to compensate the defect that the fatigue life is often overestimated when dealing with the complex mode crack in complex structure through XFEM-VCCT, a simple improved algorithm based on the average rate concept is proposed without altering the XFEM-VCCT framework. Based on specific examples, the necessity and accuracy of the improved algorithm are fully verified by comparing with the original method, and the fatigue life predicted by the improved algorithm is more consistent with reality. Finally, this method is successfully applied to the simulation and analyses for a typical ship stiffened plate structure, demonstrating good engineering applicability.

Investigation of a secondary bonded pultrusion composite laminate containing a ply-drop, Part 2: A novel two-dimensional hybrid fracture discrete element for producing debond failure

This is the second of two papers in which a novel numerical method to predict the debond failure of a secondary bonded pultrusion laminate is presented. In Part 1 of this study, experimental work was described which is used here in the development, calibration and validation of the numerical model. The structure investigated in this work may be represented by a bonded composite laminate with external ply-drops (PDs).In this part of the study, a fully coupled mixed mode cohesive zone model is developed which relies upon a traction-separation relation and the virtual crack closure technique to obtain the mode mixity. These are used to develop a hybrid fracture discrete element (HFDE). Fracture toughness tests, as well as tests on PD specimens are used to calibrate the model. Based on these tests, run-arrest fracture criteria are defined. The model is validated by comparing test results for two other PD specimen types to those obtained with the HFDE and finite element analyses.

Identification of mode I fracture toughness in GFRP/Al and GFRP/Cu joints for structural batteries

Fiber metal laminates (FMLs) have been proposed as components of structural batteries, yet their elastic mismatch can lead to interface cracks, compromising structural integrity and both mechanical and electrochemical efficiency. To this end, the bonding between the metal and the composite layer is of utmost importance. In this study, the effect of various metal surface treatments on the mode I interlaminar fracture toughness of two FML configurations suitable for structural batteries — Glass Fiber Reinforced Polymer (GFRP)/aluminum laminate and GFRP/copper laminate — was examined. The surface treatments included sulfo-ferric etching, NaOH/HNO3 etching, and Sol–Gel anodizing for aluminum 2024-T3, as well as FeCl3/HCl/Glycerol treatment and Sol–Gel anodizing for copper alloy. The results were compared with untreated conditions and with the baseline GFRP/GFRP configuration. GFRP/metal coupons were designed to achieve pure mode I interlaminar fracture toughness in double cantilever beam (DCB) tests, and the designs were verified using the Virtual Crack Closure Technique (VCCT). The surface characterization of the metals was performed using contact angle tests to estimate the surface free energy, while Coherence Scanning Interferometry (CSI) was used to measure the surface roughness and topography.

Ply curving termination for enhancing tensile strength of composite ply drop-off: static evaluation and failure mechanism

Composite structures are optimized in shape by terminating specific plies gradually. However, stress concentration at the ply drop-off can cause interlaminar delamination from the ply edge. In this study, Ply Curving Termination (PCT), which is introduced by locally curving fibers at 0° ply edges, is used to enhance tensile strength of the ply drop-off. To clarify the dependence of the PCT strength on the curved fiber angle (PCT angle), static tensile tests using ply drop-off specimens are conducted, followed by detailed damage observations using X-ray CT. The results indicates that the strength significantly increases with PCT but the fracture behavior differs depending on the PCT angle. Interestingly, specimens with large PCT angles fail from the position where the fibers curve, away from the ply edge. This PCT-specific failure mechanism is then elucidated using finite element analysis and the virtual crack closure technique, indicating that shear lag caused by the stiffness change due to fiber curving is important. Finally, using the revealed PCT failure mechanism, PCT angles that are the most effective in enhancing tensile strength is discussed.

Post-buckling damage tolerance of welded omega-stiffened thermoplastic panels with initial damage

Welded omega-stiffened panels made of thermoplastic carbon composite with initial damage in the conduction welded joint are analysed and tested to investigate the damage tolerance in post-buckling. Finite element analyses are performed, using the virtual crack closure technique to investigate skin-stringer separation for both the pristine welded joint and joints with initial damage. A sensitivity study is executed for the initial damage size and location with different geometrical imperfections. Four omega-stiffened panels are tested, of which three have initial damage consisting of a foil at the welded skin-stringer interface. During the test, digital image correlation is used to measure the panels’ deformation to determine the evolution of the buckling shape and the interaction with the initial damage. A high-speed camera is placed on the stringer side of the panel to capture the final failure. The panels fail in post-buckling when skin-stringer separation occurs, starting from the initial damage. The finite element analysis is able to predict the overall structural behaviour well, with conservative failure load predictions for panels with initial damage in the middle stringer. Although the initial buckling shape is predicted well, the buckling shape evolution at higher loads is difficult to predict.

A method for modelling arbitrarily shaped delamination fronts with large and distorted elements

The simulation of delamination in layered composites is currently limited for large structures. Typically, the use of Cohesive Zone Modelling leads to a requirement of keeping the elements smaller than 1.0 mm. As an alternative, this article presents an Energy Release Rate-based cohesive method enabling the use of elements significantly larger (up to 5 mm). A novel algorithm is presented to use the Virtual Crack Closure Technique with distorted elements not aligned with the delamination front. When the propagation criterion is met, a cohesive law is introduced to model the progressive crack growth along the newly created crack surface, ensuring to dissipate the correct amount of energy. The method is validated for different propagation tests. Notably, Double Cantilever Beam and End-Notched Flexure tests are accurately modelled with large and distorted elements. Finally, a partially reinforced DCB test demonstrates the ability of the method in representing an evolving delamination front.

Formation of transverse cracks in cross ply laminates in an environment of nonuniformly distributed fibers

This work is concerned with extracting characteristic features of transverse crack formation in cross ply laminates under axial tension considering nonuniform distribution of fibers in the ply cross section. The fiber-matrix debond crack initiation sites are determined first by the dilatation induced cavitation criterion for an epoxy matrix. The growth of the debond cracks is analyzed by calculating the energy release rates using the virtual crack closure technique. The kink-out of the debond cracks into the matrix is determined in short incremental steps by the maximum energy release rate criterion. Different scenarios are considered for the linking up of the kinked-out cracks to form continuous transverse cracks. By studying two different degrees of fiber distribution nonuniformity, the interactive effects due to the fiber distribution on the transverse crack formation are clarified.

Planar delamination behaviour of CFRP panels under quasi-static out-of-plane loading

In this study, a novel experimental approach was devised to investigate shear dominant and combined opening-shear planar delamination behaviours in composite laminates subjected to quasi-static out-of-plane loading. The patterns of planar delamination growth were depicted through different inspection techniques, including digital image correlation (DIC), C-scan, and microscopic observation. The artificially embedded delamination propagated in the direction parallel to the fibre orientation of the layer above the mid interface, but migrated to an upper interface in the direction transverse to the directing ply. A continuous stiffening process was recognized with increasing delamination area. Furthermore, a numerical analysis based on virtual crack closure technique (VCCT) indicated that the local mode II was dominant for delamination growth, while the local mode III triggered delamination migration.

Study of conduction welded C-struts for a thermoplastic composite fuselage

In this research, conduction welded C-struts, part of a thermoplastic composite fuselage designed and manufactured in the framework of the Clean Sky 2 STUNNING project, are investigated. Five specimens made of two C-section profiles are manufactured and welded using conduction welding in three different configurations with variations in the direction and distance of the two welded joints. Preliminary numerical analysis using the virtual crack closure technique are conducted to obtain an initial evaluation of the specimens behavior, in preparation of the tests. Experiments are performed under quasi-static loading conditions to measure the strength of the welds. Comparisons with the preliminary numerical analyses show a good agreement in terms of the predicted maximum load, while a clear difference is observed in the initial stiffness, due to the compliance of the support structure. The numerical model is updated, leading to results that closely match the experimental behavior. For all the analyzed specimens, the separation occurs suddenly and no signs of propagation are observed. Experimental and numerical data show no relevant difference in the joint strength among the different conduction welding configurations.

Influence of Failure-Load Prediction in Composite Single-Lap Joints with Brittle and Ductile Adhesives Using Different Progressive-Damage Techniques.

The usage of adhesively bonded joints, such as single-lap and double-lap joints, is increasing rapidly in aerospace composite structures as a popular alternative to bolts and rivets. Compared to the conventional joining methods such as fastening and riveting, adhesive-bonding technology better prevents damage to composite structures due to the smooth configuration and the mitigation of stress concentration around holes. In this work, the built-in progressive-damage-modeling techniques in Abaqus, including the cohesive zone model (CZM) and the virtual crack closure technique (VCCT), are used to predict the strength and progressive failure of composite single-lap joints subjected to tensile loading. Modeling of an adhesive layer by using a zero/non-zero-thickness cohesive element, cohesive surface, and VCCT is investigated, as is the effect of brittle and ductile adhesives. Two-dimensional finite-element models with different damage-modeling strategies are performed in this study. The failure-load predictions are compared with the experimental results obtained from the literature. For the ductile adhesive, the predicted failure loads using a zero/non-zero-thickness cohesive elements and a cohesive surface are all shown to be in good agreement with the experiments. However, the VCCT technique predicts higher failure loads. For a brittle adhesive, on the other hand, the predictions by zero/non-zero-thickness cohesive elements and cohesive surfaces reveal notable deviations compared to the experimental results. In contrast to the ductile adhesive, the VCCT technique is revealed to be accurate in predicting the brittle adhesive.

Energy release rate in bimaterial specimens tested in pure modes I and II

New closed-form analytical expressions of the energy release rate of a bimaterial cracked specimen are derived, when it experiences pure mode I in an asymmetric double cantilever test, and pure mode II in an asymmetric end-notched flexure test. The analysis is based on the strain coenergy and on the laminated beam theory. The results of the analytical approach are compared with those obtained using the finite element method in two ways: by the virtual crack closure technique at a test point and by cohesive elements during a virtual delamination test. The agreement is excellent in both cases.

Modelling of crack propagation in miniaturized and normal SENB specimens based on local failure criterion

The use of miniaturized specimen testing methods is a promising way to solve the problem of limited materials in RPV monitoring programs. The use of miniature specimens allows the evaluation of fracture toughness from other specimen materials used. In particular, the small-size compact tensile test specimen (0.16T CT) is promising for the determination of fracture toughness, as it can be produced from the standard size Charpy specimen that has already been tested. However, if we have only 0.16T CT test, we cannot investigate the dimensional response and also have only one restricted deformation state, which may pose problems in verifying geometry independence and determining local parameters for state-of-the-art analyses. It is therefore recommended to prepare at least two tests with two different restricted deformation specimens. Therefore, the testing of mini single edge notched bending (SENB) is also required and can be worked out from the Charpy specimens. The paper presents the determination of fracture toughness for these miniaturized specimens by modifying the virtual crack closure technique (VCCT) simulation method using GTN parameters instead of energy release as the driving force. This allows the calculation of the J-integral to proceed in parallel with the crack propagation.

Fatigue crack growth characterization of composite-to-steel bonded interface using ENF and 4ENF tests

In this paper, mode II fatigue crack growth properties of the composite-to-steel interface are characterised through different test configurations, namely ENF and 4ENF tests. Different loading types including force control and displacement control methods are compared. An innovative shear strain based method is proposed for monitoring the mode II crack growth at the bi-material interface through Digital Image Correlation (DIC). A 3D finite element model with Virtual Crack Closure Technique (VCCT) is built and used for obtaining the strain energy release rate (SERR) to investigate the effect of geometrical nonlinearity, friction at the interface and steel yielding, as well as to verify the mode mixity. The results show that the standard 3-point bending ENF specimen can be unstable under force control and sweeps narrow SERR range by a single test under displacement control. The 4-point bending 4ENF test shows stable crack propagation and clear SERR developing trend. More pronounced geometrical nonlinearity and friction effect exist for 4ENF test which can be considered when interpreting the Paris curves by a nonlinear finite element model.

Effects of Thermal-Moisture Coupled Field on Delamination Behavior of Electronic Packaging

Abstract Delamination failure is one of the most prevalent and serious reliability issues in micro-electronic packaging. To understand this phenomenon further, this study constructs an experimental test system consisting of a double cantilever beam (DCB) fixture, an MTS-Acumen microforce tester, and a temperature and humidity controller. The system is employed to investigate the effects of coupled moisture-thermal loading on the critical strain energy release rate (SERR) at the epoxy molding compound (EMC)/Cu leadframe (LF) interface of a very thin quad flat no-lead package (WQFN) assembly. A three-dimensional computational model with hygro-thermal loading conditions is developed to evaluate the moisture diffusion, thermal stress, and integrated stress of a multichip WQFN package under typical processing conditions and precondition tests. The validated simulation model is then applied with the virtual crack closure technique (VCCT) to investigate the fracture behavior at the EMC/Cu LF interface in the WQFN package. The effects of three design parameters on the SERR performance of the package are identified through a parametric analysis. Finally, a Genetic Algorithm (GA) optimization method is employed to examine the effects of the main structural design parameters of the WQFN package on its delamination reliability. The results are used to determine the optimal packaging design that minimizes the SERR and hence enhances the package reliability.

New investigation of delamination using the VCCT method to predict the damage in bonded composite repair plates subjected to tensile load

PurposeThis study provides an analysis of patch repair for cracked aircraft structures. Delamination is a type of damage that affects the patch's behavior. The purpose of this study is to assess the influence of delamination on repair performance.Design/methodology/approachAn analytical and numerical study using the finite element method was conducted for a cracked plate repaired with a patch containing a pre-existing delamination defect. The method for defining the contact pair surfaces and modeling the delamination interaction within the patch interface is specified using the virtual crack closure technique (VCCT) approach.FindingsThe efficiency of the repair is measured in terms of the J-integral. The effects of delamination initiation, mechanical loading, crack length and patch stacking sequences are presented. It is noted that in mode I, delamination propagation is only significant at node A. The numerical results are in good agreement with those of the analytical solution found in the literature. It is observed that the patch's behavior is strongly dependent on loading, crack size and stacking sequences in terms of reducing the structure's lifespan, especially in the presence of delamination.Originality/valueThe numerical modeling presented by the VCCT approach is highly valuable for studying delamination evolution. The influence of loading, crack size and stacking sequences on repair performance is discussed in this work.

Modelling the static and fatigue behavior of hybrid spot welded-adhesively bonded single lap joints

Hybrid joints formed by combining two or more joining methods, including spot welding and adhesive bonding, are relatively new joints designed especially for use in the automotive industry. The aim of this work is to study numerically the static and fatigue behavior of ultrasonically spot-welded, adhesively bonded and hybrid spot welded – adhesive bonded joints. The Virtual Crack Closure Technique was used to model the experimental static and fatigue tests for single lap joints reported in the literature. By introducing a short fictitious initial crack, in static loading the simulations matched the experimental results, characterized by a higher stiffness and static strength of the bonded and hybrid joints compared to the just spot-welded ones, and by an approximately similar static strength of the bonded and the hybrid joints. By the same method, a good match between the numerical and the experimental fatigue strengths was found, with the hybrid joints providing higher strength compared to the just spot-welded joints at 0.1 load ratio. According to the numerical analyses, S–N curves of bonded joints are expected to be statistically similar to those of the hybrid joints. This indicates that the adhesive plays the major role in the fatigue behaviour of the hybrid joint. Finally, the fatigue strength of hybrid joints was simulated at 0.3 load ratio. It was found a reasonable agreement between the experimental and numerical observations at 0.3 load ratio. The VCCT proved to be capable of simulating the static and the fatigue behaviour of the hybrid joints, thus proving to be a tool useful for the interpretation of the results and for the design of other hybrid joint configurations.

Experimental determination of the interlayer fracture toughness of a composite material

Modeling the propagation of interlaminar defects in multilayer composite materials requires knowledge of the characteristics of the material under study associated with the fracture processes. The goal of the study is determination of the interlaminar fracture toughness in the case of normal traction (GIc). Finite element modeling of testing was carried out proceeding from the data obtained. The delamination process was modeled using the most common approaches within the finite element method: VCCT (virtual crack closure technique) and CZM (cohesive zone model), wherein the fracture toughness is used as the main parameter for the occurrence of delamination. The obtained data are compared with the experiment. To confirm the correctness of the obtained experimental data on the fracture toughness GIc, modeling of the process of compression testing of a strut-type specimen with a defect in the form of a through-the-width delamination was carried out. This problem includes a nonlinear static solution with buckling and subsequent post-buckling behavior, and, as a result, the spread of the delamination zone. The data obtained using finite element modeling are consistent with the available experimental data.

Predictive methods for initiation of delamination and intra-laminar damage in carbon fibre reinforced polymer laminates subject to impact

AbstractA comparison of the modelling methodologies to capture the damage onset and delamination initiation in Abaqus and LS-Dyna is presented. A quasi-isotropic carbon fibre reinforced polymer laminate is modelled under a low-energy impact scenario. Hashin, Puck and Cuntze criteria are implemented for assessing intra-laminar damage in Abaqus in the linear elastic regime without damage evolution, with Virtual Crack Closure Technique being used for inter-laminar failure. In LS-Dyna, the Chang-Chang criterion is used for the intra-lamina failure with damage evolution, whereas delamination is captured using cohesive zone model and the tiebreak contact algorithm. The implementations carried out by both finite element software result in a modelling work well set to analyse and predict the impact response at the initial stages of delamination and damage within the plies. The composite damage criteria used in both finite element codes overall predict stiffer results when compared with the experimental data, however, remain in close agreement with each other.

Analysis of Interlayer Crack Propagation and Strength Prediction of Steel Bridge Deck Asphalt Pavement Based on Extended Finite Element Method and Cohesive Zone Model (XFEM–CZM) Coupling

The extended finite element method (XFEM) was employed for the computational modeling of internal defects within a bond layer. Furthermore, a cohesive zone model (CZM) was implemented to characterize the behavior of the bond layer in response to interactions at both the bond layer/steel plate and bond layer/asphalt paving layer interfaces. The coupling of XFEM and CZM was used for a comprehensive analysis of crack propagation within the bond layer as well as the assessment of phenomena associated with interfacial debonding and delamination. The feasibility and accuracy of the XFEM–CZM coupling method were verified by comparing it with the virtual crack closure technique (VCCT), CZM, XFEM–VCCT, and experiments. A double cantilever beam experimental model was established to simulate the process of interlayer-type cracks expanding from the inside of the bond layer to the interface between the bond layer and the upper and lower layers, causing debonding. This was undertaken to analyze the damage failure mechanism of interlayer-type cracks in asphalt paving layers of steel bridge decks; to discuss the impacts of the initial crack length, the interface stiffness, the interface strength, and the thickness of the bond layer on the performance of the overall interlayer bond strength; and to carry out the significance analysis. The results showed that the initial crack length, interface stiffness, and bond layer thickness had different effects on the expansion path of interlayer cracks. The interlayer strength decreased with an increase in the initial crack length and interface stiffness, increased with an increase in the interface strength, and decreased with an increase in the thickness of the bond layer. The interface stiffness had the most significant effect on the strength.