Virtual Crack Closure Technique Research Articles

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.

Numerical modelling of the mode I fracture behavior in composite laminates with significant R-curve effect

Significant R-curve effect is very common in the mode I fracture of composite laminates. Accurate simulation of fracture with R-curve effect is important for damage tolerance design of composite structures. However, traditional numerical methods usually do not consider the R-curve effect. In this work, four methods, including three phenomenological methods and cohesive zone model with multi-linear constitutive relation are presented. The three phenomenological methods are based on bilinear cohesive zone model, virtual crack closure technique and extended finite element method respectively with the consideration of R-curve. It is interesting to know which method is more suitable for modelling delamination growth with significant R-curve effect. To achieve this goal, double cantilever beam specimen is modeled and delamination growth is simulated using above four methods. Comparisons between the numerical results and the experimental results of laminates with different material types and stack sequences are made for these methods. Finally, the accuracy, computational efficiency and parameter acquisition of these methods are discussed with the goal of finding a suitable method for delamination modelling in laminated composites. It is shown that the cohesive zone model with multi-linear constitutive relation shows good accuracy in all studied cases.

Design, analysis and testing of thermoplastic welded stiffened panels to investigate skin-stringer separation in post-buckling

Thermoplastic composite three-stringer panels with omega stiffeners and conduction welded joints are designed, analysed and tested until final failure to investigate the performance of the welded joint in post-buckling. The three-stringer panels are designed to be structurally representative of the fuselage demonstrator of the Clean Sky 2 project STUNNING. A simplified model of the fuselage keel section is analysed by finite element analysis, using the virtual crack closure technique to model skin-stringer separation of the welded joint. The post-buckling and skin-stringer separation behaviour of the fuselage section is then adopted as the reference for the design of the three-stringer panels. Two panels are then tested. The test setup utilises digital image correlation to measure the deformation of the panels, and a high-speed camera to capture the final failure mode. The panels failed in post-buckling due to the separation of the middle stringer, with unstable separation growth followed by separation of the outer stringers and then stringer fracture. The numerical analysis of the panels, with geometrical imperfections included, is able to predict the structural behaviour accurately, with only minor differences in buckling shape and separation behaviour.

The Multi-Virtual Crack Closure Technique for three-dimensional interface crack problems

The Virtual Crack Closure Technique (VCCT) is a simple method that was found in the past to produce good results for determining stress intensity factors of cracks in homogeneous bodies and poor results for interface cracks. In recent papers, the VCCT was found to produce excellent results for two-dimensional interface cracks where many elements were used in the virtual crack extension (VCE). This approach is called here the Multi-VCCT. A criterion for the optimal number of elements used in the VCE was also found. Here, the M-VCCT is extended to three-dimensional interface crack problems. Results for three-dimensional problems containing a straight through finite length interface crack and a penny-shaped interface crack are presented. The interfaces include that between two homogeneous and isotropic dissimilar materials, as well as two transversely isotropic materials.

Mode I fracture toughness determination and environmental durability evaluation of adhesive bonds by wedge test

This paper presents a study of a method for determining the fracture toughness of adhesive bonds under Mode I loading using the wedge test. The slope of adhesively bonded specimen arms at loading points was used to provide an effective crack length for the wedge test specimen. A simple expression was derived based on beam theory for the Mode I energy release rate. Finite element analyses were conducted on wedge specimens with a range of material and geometrical properties. Good agreement was found between the energy release rates from the beam theory-based expression and the virtual crack closure technique (VCCT). A comparison of various energy release rate expressions showed that the present expression was more accurate than the other expressions available in the literature. The results of this study suggest that the environmental durability of adhesive bonds with composite adherends as well as metallic adherends can be assessed in terms of their fracture toughness using the present method. Experiments under hot and humid conditions were performed on wedge specimens with adherends made of carbon fiber reinforced polymer (CFRP) composite laminate and titanium alloy, and the fracture toughness results were obtained.

Cyclic elastoplasticity and XFEM based fatigue life assessment of out-of-plane gusset welded joints

Conventional design methods for high-cycle fatigue failure of engineering components often assume a linear-elastic material behaviour. The different driving forces of crack initiation and propagation fail to be considered, resulting in less accurate predictions of fatigue life. To address this issue, the present study proposes a novel method to predict the fatigue life of out-of-plane gusset welded joints based on cyclic elastoplasticity and extended finite element method (XFEM). Incorporating the welding residual stress simulated by thermal–mechanical analysis, the cyclic stress–strain response of out-of-plane gusset welded joints was assessed by Fatigue SS (FSS) constitutive model. The crack initiation life was therefore predicted by the local strain approach considering the mean stress correction. Based on the converged cyclic stress–strain response, the crack propagation behaviour and life were predicted by XFEM in combination with Virtual Crack Closure Technique (VCCT). The influence of mean stress, mixed-mode crack and residual stress on crack initiation and propagation life was also investigated. The results show that the proposed method can predict the fatigue life of out-of-plane gusset welded joints under the pure tension loading with high accuracy against experimental results.

On adhesively bonded joints with a mixed failure mode—An experimental and numerical study

Cohesive zone model (CZM) has been extensively used to study interfacial failure behaviors such as fracture of adhesively bonded joints (ABJs). Accurate and efficient identification of traction–separation law (TSL) in CZM signifies an important issue for design and analysis of adhesive structures. In this study, a modified Arcan fixture was developed and employed to investigate the mixed mode failure behaviors of ABJs for carbon fiber reinforced plastic (CFRP) substrates under a tensile-shear coupling load, in which the double cantilever beam (DCB) test was carried out to characterize fracture toughness for benchmark data. With the help of digital image correlation (DIC) technique, the interfacial displacement field was obtained. The virtual crack closure technique (VCCT) was adopted to decouple the mode mixture at different tension-shear angles of the Arcan specimens. Based on the traction–separation law for each mixed ratio of failure mode, a refined CZM was established. In this study, the Arcan and DCB specimens bonded with a flexible adhesive of 3M DP190 were prepared and tested. The experiments were carried out for the ABJs with two adhesive layer thicknesses of 0.3 mm and 1 mm, respectively, to investigate the influence of bonding thickness. Based on the extracted CZM parameters, a finite element (FE) analysis model was developed and validated with the experimental results. Unlike the traditional predetermined damage evolution law, a new CZM was established without a priori cohesive damage evolution; and the effectiveness of the proposed model for the TSL extraction was verified. By using this method, the mechanical response of the bonding interface under complex stress state was well predicted and the FE modeling of ABJ’s fracture was accurately achieved. The study is anticipated to gain new understanding and fundamental data on mixed failure mode, thereby enabling better design of ABJs for engineering applications.

FRACTURE PARAMETERS EVALUATION FOR THE CRACKED NONHOMOGENEOUS ENAMEL BASED ON THE FINITE ELEMENT METHOD AND VIRTUAL CRACK CLOSURE TECHNIQUE

To accurately solve the fracture parameters of enamel, we have established computational nonhomogeneous enamel models and constructed the fracture element of enamel dumb nodes, based on the enamel mineral concentration, nonhomogeneous mechanical properties, and virtual crack closure technique. Through the commercial finite element software ABAQUS and the fracture element of the enamel dumb nodes, we have established the user subroutines UMAT and UEL, which enabled solving of the energy release rates of the nonhomogeneous enamel structure with cracks. The stress intensity factors of central cracks, three-point bend and compact stretched enamels, and double-edge notched stretched enamels are determined. By comparing them with analytical solutions, we have proved that the fracture element of the enamel dumb nodes is highly accurate, simple, and convenient. In addition, the cracks can be other elements rather than singular or special elements; they show versatility and other advantages. The stress intensity factor of the dental enamel can be solved more realistically. Thus, a new numerical method for prevention and treatment of dental diseases is provided.