Virtual Crack Closure Technique Research Articles

An Analytical Solution of the Total Strain Energy Release Rate and Mode Partitioning of a Beam Type Delamination Specimen under High Speed Mixed-Mode Loading

In this work an analytical solution for the calculation of the total Stain Energy Release Rate and mode partitioning of beam type delamination specimen, at crack initiation, under high speed, mixed-mode loading is obtained for the first time. The analytical model is based on the dynamic response of a Mixed-Mode End Load Split type specimen subjected to loading with a constant velocity. The Timoshenko beam theory is used to model the specimen's kinematics and the mode partitioning method used is based on the Virtual Crack Closure Technique. To model the bonded region a method based on Lagrangian multipliers is utilized. The specimen is considered as a waveguide and the waves that are allowed to propagate are analytically obtained. Due to the complexity of the analytical form of the wavenumbers for the bonded region of the specimen, which makes the calculation of eigenfrequencies intractable, a series approximation method is used. The results of the proposed analytical solution are verified using a 2D Finite Element Model. The results show the dependency of the Strain Energy Release Rate and the mode mixity on the eigenfrequencies and the eigenmodes of the specimen rendering the value of the mode mixity highly inconsistent through time.

Mixed-mode fatigue crack propagation simulation by means of [formula omitted] and walker models of the structural steel S355

In this paper, a numerical simulation method of mixed-mode fatigue crack propagation was explored using the extended finite element method (XFEM) and the Virtual Crack Closure Technique (VCCT). Both 2D and 3D numerical models were selected to simulate the fatigue crack propagation of steel specimens. Two coefficients were proposed to calculate the equivalent energy release rate (Geq) for a better simulation of the mixed-mode fatigue crack propagation of S355 steel. The Walker equation and the calculation formula of Geq were realized by a user-defined subroutine. A set of optimal correction coefficients of mode II energy release rate (GII) and mode III energy release rate (GIII) were quantitatively comparing the simulation results and test data. The results will contribute to fatigue crack propagation prediction of steel structures in the civil engineering field.

Delamination Propagation and Crack Growth Analysis of Composite Beams Using a Layer Wised Virtual Crack Closure Technique

Delamination Propagation and Crack Growth Analysis of Composite Beams Using a Layer Wised Virtual Crack Closure Technique

Experimental characterization and numerical study on the interlaminar fracture toughness of carbon fibre reinforced polymer laminates reinforced with carbon nanotubes

AbstractThe present study is focused on the nanoreinforcement of carbon fiber reinforced polymer laminates to evaluate its effect on delamination growth in double cantilever beam specimen. Multi‐walled carbon nanotubes were sprayed on the laminate interface using air‐brush spraying technique. Three nanofiller contents of 0.05 wt.%, 0.1 wt.%, and 0.5 wt.% were examined to evaluate the mode I fracture toughness (GIC) in a double cantilever beam specimen and the results were compared with the base laminate (0.0 % carbon nanotubes). The average mode I fracture toughness of composite laminates increased from 180.6 J/m2 to 270.92 J/m2 due to the addition of 0.05 wt.% multi‐walled carbon nanotubes, and to 268.27 J/m2 for 0.1 wt.% multi‐walled carbon nanotubes. Mechanisms for the increase in GIC of the nanofiller reinforced laminates are discussed based on the experimental results and microscopic study of fractured specimen surfaces from scanning electron microscopy. Energy dissipation from carbon nanotube bridging ahead of the crack front is the major toughening mechanism resulting in improved fracture toughness. Numerical simulations of delamination growth were performed as well by using virtual crack closure technique analysis in Abaqus. The R‐curve behaviour from the experiments is implemented in the finite element modeling of delamination growth to validate the effect of nanoreinforcements.

Finite element based interfacial failure analysis of PVC and laminated FRP composite pipe socket joints subjected to internal pressure

Present study reports a comparison of stress, failure and failure growth behaviour of polyvinyl chloride (PVC) and fiber reinforced plastic (FRP) made pipe socket joints. Finite element based Ansys codes have been developed and validated with experiment and literature based analytical results. Various stress based failure criteria (parabolic yield criterion, and Tsai-Wu failure criteria), and Strain Energy Release Rates (SERRs) as the fracture parameters determined using Virtual Crack Closure Technique (VCCT) have been used to simulate the onset of failure and its growth, respectively. Stress and failure analysis suggested, the pipe-adhesive interface at the junction of the joints to be the most vulnerable location for failure under internal pressure. Pre‐embedded adhesion failure growth along the axial length and circumferential width has been simulated. Adhesion failure growth in axial direction was found more susceptible to mode I failure whereas mode III was dominating in circumferential direction. It was also evident from the studies that axial direction is the dominating direction for adhesion failure growth. Unidirectional ply [90]4 was observed to be the optimum stacking sequence for adhesion failure growth resistance.

Experimental and Numerical Research of Delamination Process in CFRP Laminates with Bending-Twisting Elastic Couplings.

This paper aims at experimental and numerical research of delamination process in carbon/epoxy composite laminates with different fiber orientation angles in stacking sequence exhibiting the bending-twisting elastic couplings. Experimental specimens were subjected to the double cantilever beam (DCB) tests according to the ASTM D5528 regulations. Values of the mode I strain energy release rates were calculated by using three different data reduction schemes: the modified beam theory, the compliance calibration method and the modified compliance calibration. Determination of delamination initiation point was conducted in twofold way: by visual observation of crack tip using high resolution camera and by utilization of the acoustic emission technique. Numerical analyss were prepared in Abaqus/CAE Software environment by using the virtual crack closure technique (VCCT). The numerical beam model consisted of SC8R continuum shell elements. Obtained outcomes revealed that extensive fiber bridging phenomenon occurring during delamination process pronouncedly affected propagation values of strain energy release rate (GIprop) and numerically obtained load-displacement curves. Nevertheless, in initial stage of delamination, results obtained by using the VCCT were in agreement with experimental data. The greatest value of the mode I fracture toughness equal 0.56 N/mm was obtained for the BT45 laminate.

Determination of Paris parameters from S−N curve in the simulation of fatigue in Nomex honeycomb sandwich structures

Determination of S-N and Paris parameters form the two primary approaches as far as fatigue testing is concerned. With many economic factors and complexities involved in experimentation, these approaches are not related to each other and require implementation of separate test standards for both of them. In this work, an attempt is made on the interconvertibility of these experimental parameters and a numerical technique based on the virtual crack closure technique (VCCT) is proposed for the evaluation of Paris parameters from S−N curve, corresponding to four-point bending end notched flexural (4ENF) sandwich specimen made up of Nomex® aramid honeycomb core with glass fibre reinforced composite (GFRP) facesheets. VCCT was effectively utilised for the estimation of strain energy release rates (SERR), in both 2D plane stress/strain and 3D conditions, which were compared with each other, and the resultant was incorporated with the S−N data for the determination of parameters of the Paris curve. These determined parameters were employed for the simulation of fatigue delamination growth by using ‘Direct Cyclic’ step and compared with the results obtained from the literature. The comparison revealed a good agreement between the two, thereby validating the proposed technique.

Mixed mode failure curve for an interface crack between single crystal silicon and silicone rubber

An interface crack between single crystal silicon (SC-Si) and silicone rubber was examined. Mixed mode fracture tests were performed on Arcan-type specimens at different mode mixities. It was observed during the tests that silicone rubber underwent large deformations before crack propagation. Nonlinear finite element analyses (FEAs) of the fracture tests were carried out in Abaqus. A cubic (anisotropic), linear elastic material model was used for SC-Si, while a Mooney–Rivlin (hyperelastic) model was used for the silicone rubber. The virtual crack closure technique (VCCT) which has been adopted for large deformations was employed to determine the energy release rates from the FEAs. A mixed mode failure criterion was obtained from the energy release rate data.

Skin-stringer separation in post-buckling of butt-joint stiffened thermoplastic composite panels

Two aeronautical thermoplastic composite stiffened panels are analysed and tested to investigate the buckling behaviour, the skin-stringer separation and the final failure mode. The panels are made of fast crystallising polyetherketoneketone carbon composite, have three stringers with an angled cap on one side, and are joined to the skin by a short-fibre reinforced butt-joint. The panels contain an initial damage in the middle skin-stringer interface representing barely visible impact damage. Finite element analysis using the virtual crack closure technique are conducted before the test to predict the structural behaviour. During the tests, the deformation of the panels is measured by digital image correlation, the damage propagation is recorded by GoPro cameras and the final failure is captured by high speed cameras. The panels show an initial three half-wave buckling shape in each bay, with damage propagation starting shortly after buckling. A combination of relatively stable and unstable damage propagation is observed until final failure, when the middle stringer separates completely and the panels fail in an unstable manner. The test results are compared to the numerical prediction, which shows great agreement for both the buckling and failure behaviour.

Numerical analysis of cracked aluminium panel repaired with functionally graded adhesively bonded patch

Aircraft maintenance is becoming more important as a means of enhancing structural integrity and prolonging the service life of older aircraft. The bonded composite repair is the most popular among the various repair processes because of its ability to join similar and dissimilar materials. In the present research, the performance of a single sided functionally graded adhesively bonded patch on a centre crack aluminium panel was evaluated using 3D FE analysis. The integrity of a graded crack patch repair system is investigated using the fracture mechanics principle. The strain energy release rate (SERR) GI is used to analyse damage/crack growth and evaluated by utilising the virtual crack closure technique (VCCT), which is based on the concept of linear elastic fracture mechanics (LEFM). The gradation of patch is carried out with linear profile with different modulus ratios in the preferred direction such that using more flexible adhesive at centre of crack and stiffer adhesive ahead of crack/damage. From exhaustive finite element analyses, substantial reduction in crack growth driving forces (SERR) is observed in functionally graded crack-patch repair system. Effect of different modulus ratios on SERR has been also studied. In view of above, graded crack-patch repair system can be recommended for designer.

Fatigue driven delamination in composite structures: Definition and assessment of a novel fracture mechanics based computational tool

The development of numerical methodologies to investigate material damages is a crucial aspect of aerospace components design. The advent of composite materials has made this aspect more critical due to their anisotropic properties, which result in damage mechanisms difficult to control and predict. Despite the progress made in the development of computational approaches for composites failure assessment, fatigue damage remains an open issue. This work deals with the development of a robust and efficient computational tool to simulate the fatigue driven delamination in complex composite structures. The main objective is to exploit the peculiarities, in terms of mesh and load step size independency, of the well-established SMart–time XB procedure, based on the Virtual Crack Closure Technique approach, to develop a Paris Law-based module to mimic the delamination growth rate due to cyclic loads. The implemented fatigue block interacts with the already existing modules, thus simulating the fatigue driven delamination without mesh dependency and potentially accounting for the R-curve behaviour of the material. The procedure takes advantage of the solver of the commercial Finite Element code Ansys Mechanical but is fully implemented in the Ansys Parametric Design Language, resulting in an absolutely versatile and parametric procedure. The promoted numerical tool has been firstly validated at coupon level considering the literature available Single Leg Bending-based benchmark. Then, the post–buckling behaviour of a typical aeronautical stiffened panel, based on a literature experimental test, has been studied under non-constant cyclic load conditions. Comparison against literature numerical and experimental data have proved the efficiency of the proposed computational tool to simulate fatigue-driven delamination both at coupon level and in complex structures.This work deals with the development of a robust and efficient computational tool to simulate the fatigue driven delamination in complex composite structures. The main objective is to exploit mesh and load independency peculiarities of the well-established SMart–time XB procedure, to develop a Paris Law-based module to mimic the delamination growth due to cyclic loads. The procedure is fully implemented in the Ansys Parametric Design Language, resulting in a versatile and parametric procedure. The promoted tool has been firstly validated at coupon level. Then, the post–buckling behaviour of a stiffened panel, based on a literature experimental test, has been investigated.

A hierarchical quadrature element method for energy release rate calculation in combination with the virtual crack closure technique

In this paper, the virtual crack closure technique (VCCT) is combined with a hierarchical quadrature element method (HQEM) with p-convergence for the evaluation of strain energy release rate (SERR) for the first time. A universal SERR formula suitable for HQEM is proposed, regardless of the node arrangements and the number of nodes per element boundary. The validity of the present formula is evaluated by the typical cases of mode I and II fracture of homogeneous materials, as well as the bimaterial interface crack problem. A comprehensive comparison with several widely-acknowledged h-version elements shows that the present approach can significantly improve the accuracy and efficiency of SERR calculation even with a relatively coarse mesh and thus be readily used as a viable and effective tool for fracture analysis.

Simulation of Destructive Test for Arch Reinforcement Area of Tunnel Lining by MSIM

Meshless Shepard interpolation method (MSIM) is used to simulate the destruction process within the arch reinforcement area of tunnel lining. In this method, the shape functions are formed by the partition of unity and the finite cover technology, which is not affected by discontinuous domains, with delta property at any desired node, and applies boundary conditions in an easy and correct way. The MSIM method combines the advantages of both the conventional meshless method and the numerical manifold method. The finite cover technology enables the shape functions to not be affected by the discontinuities in the solution domain, which overcomes the difficulty resulting from the conventional meshless method. The finite covers and the partition of unity functions are formed using the influence domains of a series of nodes, which removes the obstacle from conventional numerical manifold method and has simpler formation of finite covers than numerical manifold method. Virtual crack closure technique is used to calculate the intensity factor of crack-tip stress. The results of progressive destruction process simulation on the cracking patterns within the arch reinforcement area indicate that the method is suitable for tracking the crack propagation in complex stress conditions.

A numerical study on the effect of delamination on composite cylindrical shells subjected to hydrostatic pressure

This paper deals with the delamination damage and the effect of buckling behavior on delamination propagation of the composite cylindrical shell subjected to hydrostatic pressure. The model of the composite shell with initial delamination and geometric imperfection is elaborated numerically by using the finite element method. The virtual crack closure technique is employed to calculate the strain energy release rate, and the linear fracture criterion is used to determine the onset and growth of the delamination. The buckling deformation and delamination propagation are monitored by performing the nonlinear buckling analysis. In addition, a parametric study is carried out to investigate the influence of the initial delamination shape, area, depth, and ply orientation on ultimate pressure and delamination propagation path. The results show that local or global buckling of the shell promotes the propagation of delamination, and the ultimate buckling pressure of the shell is more sensitive to the axial initial delamination length. The initial delamination shape, depth, and ply orientation have different influences on the ultimate pressure of the shell and the delamination propagation path, and the corresponding explanations are given in this paper.

Asphalt concrete crack propagation parameters from XFEM modelling of the Texas Overlay Test

ABSTRACT Paris’ power law is commonly used to describe transverse thermal cracking propagation in asphalt concrete (AC) pavements. In its most common format, it relates the rate of change in the crack length per cycle to changes in either the stress intensity factor K or the energy release. The parameters defining this relationship for ACs can be obtained using the Texas cyclic Overlay Test (OTR). This paper describes two numerical approaches for simulating the OTR using the extended finite element method (XFEM). The first uses the direct low-cyclic fatigue (LCF) approach and the second uses the virtual crack closure technique (VCCT). Comparisons of the model predictions to laboratory OTR measurements for six mixtures suggest that the XFEM model coupled with VCCT is better suited for simulating the OTR. The model output includes the crack length and the energy release rate ERR (i.e. Δ J R ) as cracks propagate. This data was used to fit the modified Paris’ law parameters A ′ and n ′ as a function Δ J R . Subsequently, the traditional A and n Paris’ power law parameters were fitted by estimating the corresponding ΔK. Using this model, it was possible to efficiently estimate the AC cracking parameters using as input only the tensile modulus and the critical ERR.

Numerical analysis of the residual ultimate strength of composite laminates under uniaxial compressive load

In the current study, the residual ultimate strength of a composite laminate with delamination is determined under in-plane compressive loading numerically. The delamination growth is predicted and modelled using the finite element method. The method that has been used to extend the delaminated area is based on linear fracture mechanics and the applied tool is the virtual crack closure technique. The results show that due to the expansion of the delaminated area in a composite laminate, the load-carrying capacity of the structure is reduced. Despite the simplicity and efficiency of this method, the strain energy release rates at different fracture modes in the delamination region can be calculated and predicted.

Evaluation of mode II fracture toughness under high loading rate conditions for composite bonded joints

Composite bonded joints are widely used in the aircraft components, which are frequently subjected to impact loading. The present paper intends to evaluate the mode II fracture behavior of composite bonded joints under high loading rate conditions. Dynamic loading was applied on the end-notched flexure (ENF) specimen at 10 m/s and 15 m/s via an electromagnetic split Hopkinson pressure bar system. Then the dynamic fracture toughness was evaluated using an experimental-numerical hybrid method according to the virtual crack-closure technique and compared to the fracture toughness under quasi-static loading rate (2 × 10−5 m/s and 2 × 10−4 m/s). Results indicate that the mode II fracture toughness of adhesively bonded composite joints shows a positive rate-dependent trend. The mode II fracture toughness can increase about 31.5% when the loading rate increases to 15 m/s. At last, fracture surface inspections using scanning electron microscopy (SEM) were conducted to reveal the physical mark of such an effect.

A Numerical Study on the Influence of Nanosilica‐Reinforced Epoxy Resin on the Delamination Behavior of Composite Laminates

AbstractThe use of nanomodified epoxy resins can potentially increase composites application to aeronautical structural components, thanks to the potential enhancement, in terms of physical and mechanical properties, when compared to the neat epoxy matrix. In this work, the effects of silica nanoparticles (NPs) on the fracture toughness and, consequently, the crack growth resistance of fiber‐reinforced polymers (FRPs) have been numerically investigated. The skin‐stringer debonding initiation and growth have been studied by a tailored innovative numerical procedure considering an aeronautical panel reinforced with a single T‐shape stringer, made of carbon fibers/epoxy resin material, and subjected to compressive load. An analytical model has been used to evaluate the Mode I fracture toughness value of the nanomodified resin, and the Virtual Crack Closure Technique methodology has been employed to assess the delamination growth in the frame of a Finite Elements (FE) analysis performed in the Ansys FE environment. Numerical results presenting the comparison between charged and neat configurations have been assessed to provide a first understanding of the influence of nanoparticles on the static delamination growth in geometrically complex composite structures.

A Numerical Study on Mode II Fatigue Delamination Growth in Composite Laminates

AbstractIn this paper, a numerical tool, able to mimic the delamination growth under cyclic loading conditions, has been adopted to investigate the mode II interlaminar damage growth in composite laminates. An improved Virtual Crack Closure Technique based model, mesh and time step independent, has been combined with a Paris‐Law equations‐based model to account for the effects of cycling loading conditions on the structural behavior of a specimen under an End‐Notched Flexure (ENF) test. The ANSYS FEM environment has been adopted for the numerical simulations and the numerical model has been implemented in ANSYS by adopting the Ansys Parametric Design Language (APDL). Comparisons at the coupon level with literature experimental data on unidirectional ENF samples have demonstrated the ability of the numerical model to simulate the Mode II fatigue delamination growth. Actually, useful indications on the damage propagation under fatigue loading condition have been provided by the proposed numerical model in conjunction with the experimental data taken from literature.

Study on fracture behaviour of basalt fibre reinforced asphalt concrete with plastic coupled cohesive model and enhanced virtual crack closure technique model

ABSTRACT In this study, the plastic coupled cohesive model and enhanced virtual crack closure technique (VCCT) are used to investigate the fracture behaviour of the basalt fibre reinforced asphalt concrete (BFRAC). In the plastic coupled cohesive model, the separation and traction response along the cohesive zone advance ahead of a crack tip is governed by an exponential cohesive law. The double-K fracture theory is integrated into the enhanced VCCT model. It is shown that the simulated load-cracking mouth opening displacement (P-CMOD) curves from both the plastic coupled cohesive model and the enhanced VCCT model compares favourably with the measured curves from the single-edge notched beam. The parameters used in the plastic coupled cohesive model cannot directly be obtained from the standard test, and the inverse analysis method is always necessary for identifying the fracture parameters. On the contrary, the fracture parameters in the enhanced VCCT method can be directly calculated from the P-CMOD curves based on the double-K fracture theory and the finite plastic fracture theory (Hutchinson, Rice, Rosengren singular crack tip fields, abbreviated as HRR field). Meanwhile, compared with the plastic coupled cohesive model, the enhanced VCCT model coupled with the Ramberg–Osgood elasto-plastic harden model is promising for investigating the physical mechanism underlying the nonlinear fracture of BFRAC. This paper proposed two concrete and valuable models in the finite element method for simulating the fracture behaviour of the huge structure with asphalt and asphalt concrete.