Virtual Crack Closure Integral Method Research Articles

Damage Tolerance Behaviour of Stiffened Crown Panel of a Transport Aircraft Fuselage

Ever since the introduction of damage tolerance requirements in the aviation regulations, efforts continue to be made to prevent catastrophic failures due to damages present in the structure. It has also been realized that damage detection is the weakest link in the whole process of damage tolerance design to maintain continued airworthiness. The major components of the aircraft structure consist of both integral and riveted panels of sheets and stringers which are employed in fuselage skin panels, spar webs and stiffeners. In spite of all precautions, cracks or damages may arise in many of these primary structural members. These cracks cause stiffness degradation and reduce the total load-carrying capacity of the structure. In this paper, the damage tolerance behaviour of fuselage crown panel both integral and riveted stiffened panel configurations of Aluminium alloy 2024-T351 are studied using finite element based tools using crack growth analysis methods. The crack growth behaviour of both integral and riveted stiffened panels of aircraft fuselage having same geometrical configuration and subjected to uniformly distributed tensile loads is investigated. For this, a metallic stiffened panel with eight stringers, representative of crown panel of a transport aircraft fuselage is analysed with a centre skin crack propagating through the stringers. Stress intensity factors and fatigue crack propagation rates at the progressive crack tip of both types of the stiffened panels are computed by using Modified Virtual Crack Closure Integral (MVCCI) method. The stiffened panels fatigue crack growth rate was computed by using Paris law under constant amplitude fatigue loads. The analysis results show that integral stiffened panel causes higher stress intensity factor and less load bearing capability than riveted stiffened panel which has better damage tolerant capability in comparison to the integrally stiffened panel.

On the determination of SIF at a tip of an edge crack in an orthotropic material using FEM combined with a Virtual Crack Closure Integral Method

The paper discuss the way of dicision on stress intensity factor in the vicinity of crack on the center of plate which is a part of orthotropic cantilever on tension load and bending load by means of finite element analysis and virtual crack closure integral method.

A modified three-dimensional virtual crack closure technique for calculating stress intensity factors with arbitrarily shaped finite element mesh arrangements across the crack front

To obtain accurate stress intensity factors (SIFs) with arbitrarily shaped finite element mesh arrangements across the crack front, a modified three-dimensional virtual crack closure technique (modified 3D-VCCT) is proposed in this paper. This method is based on three-dimensional virtual crack closure technique (3D-VCCT) and finite element method. To increase the SIFs calculation accuracy for the crack with arbitrary shape, the length and shape of finite element meshes across the crack front are considered in this method. Then the SIFs with arbitrarily shaped finite element mesh arrangements across the crack front are calculated by three different methods, the modified 3D-VCCT in this paper, the extension of virtual crack closure-integral method proposed by Okada and the 3D-VCCT. The solutions of SIFs obtained by three methods are compared and the comparison results show the modified 3D-VCCT has better accuracy with arbitrarily shaped finite element mesh arrangements across the crack front. In addition, the simulations of fatigue crack growth are carried out by using the modified 3D-VCCT. Then the simulation results are compared with the test results, which shows good agreement.

Analysis of stress intensity factor for fatigue crack using bootstrap S-version finite element model

PurposeFailure of the materials occurs once the stress intensity factor (SIF) overtakes the material fracture toughness. At this level, the crack will grow rapidly resulting in unstable crack growth until a complete fracture happens. The SIF calculation of the materials can be conducted by experimental, theoretical and numerical techniques. Prediction of SIF is crucial to ensure safety life from the material failure. The aim of the simulation study is to evaluate the accuracy of SIF prediction using finite element analysis.Design/methodology/approachThe bootstrap resampling method is employed in S-version finite element model (S-FEM) to generate the random variables in this simulation analysis. The SIF analysis studies are promoted by bootstrap S-version Finite Element Model (BootstrapS-FEM). Virtual crack closure-integral method (VCCM) is an important concept to compute the energy release rate and SIF. The semielliptical crack shape is applied with different crack shape aspect ratio in this simulation analysis. The BootstrapS-FEM produces the prediction of SIFs for tension model.FindingsThe mean of BootstrapS-FEM is calculated from 100 samples by the resampling method. The bounds are computed based on the lower and upper bounds of the hundred samples of BootstrapS-FEM. The prediction of SIFs is validated with Newman–Raju solution and deterministic S-FEM within 95 percent confidence bounds. All possible values of SIF estimation by BootstrapS-FEM are plotted in a graph. The mean of the BootstrapS-FEM is referred to as point estimation. The Newman–Raju solution and deterministic S-FEM values are within the 95 percent confidence bounds. Thus, the BootstrapS-FEM is considered valid for the prediction with less than 6 percent of percentage error.Originality/valueThe bootstrap resampling method is employed in S-FEM to generate the random variables in this simulation analysis.

The prediction of fatigue crack growth of rotary kiln shell welded under cyclic loading

In this paper, fatigue crack propagation in the kiln shell welded under cyclic loading has been estimated using computerized finite element analysis (S-Version FEM). By using the S-FEM technique, it makes the local mesh which is re-meshed automatically, then it becomes easier to make a numerical study of crack growth on the welded kiln shell. Virtual crack closure integral method (VCCM) uses the stress intensity factor evaluated. From the results, it was observed that the crack depth grows faster as the number of cycles increased. It was found that the initial crack of welded shell propagates slowly, and beyond 8 × 105 cycles increase quickly. In addition, the effect of stress distribution and stress intensity factor on cracking have been discussed and evaluated. The life of the component depends on the initial crack depth, stress intensity factors and crack inclination angle.

Two bay crack arrest capability evaluation for metallic fuselage

Transport aircraft is a highly complex structure. The aircraft fuselage shell is composed of stressed skin, longitudinal stringers, and circumferential frames. The skin is connected to the stringers and frames mostly by rivets. The fuselage has a number of riveted joints and is subjected to a major loading of differential internal pressurization. When the fuselage is pressurized and depressurized during each take-off and landing cycle of aircraft, the metal skin of fuselage expands and contracts to result in metal fatigue. Due to the presence of a large number of rivet holes, the fuselage skin has a large number of high-stress locations and these are locations of potential crack initiation. The wide-bodied transport aircraft are designed to tolerate large fatigue cracks. This project focuses attention on damage tolerance design of a fuselage structure of transport aircraft. In this project, the stress intensity factor, quantifying the intensity of the stress field around a crack tip for a longitudinal crack under the pressurization load is studied. The objective of this project is to investigate crack initiation, crack growth, fast fracture and crack arrest features in the stiffened panel. The longitudinal crack is initiated from the rivet hole and stress intensity factor is calculated using modified virtual crack closure integral (MVCCI) method at each stage of crack propagation. In order to arrest crack propagation which is the capital importance of tear straps are used, which prevent the further crack propagation. In this project, the linear static stress analysis of the stiffened panel of a fuselage is performed using MSC NASTRAN solver. The pre-processing of the model is done by using MSC PATRAN software.

Fatigue crack growth behaviour of semi-elliptical surface cracks for an API 5L X65 gas pipeline under tension

The paper is presenting the fatigue crack growth (FCG) behavior of semi-elliptical surface cracks for API X65 gas pipeline using S-version FEM. A method known as global-local overlay technique was used in this study to predict the fatigue behavior that involve of two separate meshes each specifically for global (geometry) and local (crack). The pre-post program was used to model the global geometry (coarser mesh) known as FAST including the material and boundary conditions. Hence, the local crack (finer mesh) will be defined the exact location and the mesh control accordingly. The local mesh was overlaid along with the global before the numerical computation taken place to solve the engineering problem. The stress intensity factors were computed using the virtual crack closure-integral method (VCCM). The most important results is the behavior of the fatigue crack growth, which contains the crack depth (a), crack length (c) and stress intensity factors (SIF). The correlation between the fatigue crack growth and the SIF shows a good growth for the crack depth (a) and dissimilar for the crack length (c) where stunned behavior was resulted. The S-version FEM will benefiting the user due to the overlay technique where it will shorten the computation process.

Fatigue crack growth analysis on square prismatic with embedded cracks under tension loading

One of the most important issues yet to be overcome by engineers is the integrity and reliability of engineering structures. This is to ensure the safety of the engineering structure is at the greatest since the catastrophic failures usually occur due to fatigue crack growth. Due to insufficient studies on the fatigue embedded crack growth, the prismatic bar is chosen as the model of the structure. It is wise to select the solid bar since the analysis can be much simpler, thus making it easier to examine the behaviour of the fatigue crack growth. In this study, the metallic square prismatic with embedded cracks is analysed using S-version Finite Element Modelling (S-version FEM) under tension loading. The S-version FEM is an open source program, that is built from codes previously compiled as a program. The S-version FEM structured using the global-local overlay technique consists of two separate global and local meshes. By using the basic concept from the energy release rate and stress intensity factors (SIF), the behaviour of the fatigue crack growth is analysed. From the linear elastic fracture mechanics concept, the SIF is calculated using the virtual crack closure-integral method. The influences of different initial crack size and aspect ratios on the fatigue crack growth are investigated in this study. In addition, the SIF results from the S-version FEM are compared with the analytical solutions. From the analysis, the root mean square errors (RMSE) are performed to support the validation. The RMSE shows a very small error of 0.227, 0.086 and 0.3089 according to the aspect ratio of 0.5, 1.0 and 2.0, respectively. The results also show significant characteristics and behaviour of the SIF trend along the crack front, corresponding to different aspect ratios. From this study, the S-version FEM is suitable to be used to predict the fatigue crack growth for the cracks embedded in a structure. Subsequently, the S-version FEM is an open source program can be modified for increasingly complex engineering problems.

Stress and damage tolerance analysis of stiffened panel with passenger door cutout in airframe structure using FEA

It is very essential to design the airframe structure with minimum possible weight without compromising on the structural safety. Fuselage has many stress concentration areas. Passenger door cutout region is one among such critical regions. Current work includes stress and damage tolerance analysis of a critical region in the fuselage structure. The structure considered for the analysis includes a stiffened panel with a passenger door cutout and surrounding area with the presence of stiffening members. The present work also includes the damage tolerance analysis of the panel in presence of a crack emanating from the high stress location. The pressurization load case is one of the critical load cases considered for the design of the aircraft structure. The tensile loads at the edge of the panel corresponding to pressurization will be considered for the linear static analysis of the panel. A location of maximum tensile stress and its magnitude will be identified from the stress analysis. Stress intensity factor calculation is carried out for different incremental crack lengths for a crack emanating from the high stress location. Modified virtual crack closure integral method is used for stress intensity factor calculation.

Prediction of fatigue crack growth for semi-elliptical surface cracks using S-version fem under tension loading

The finite element method (FEM) is commonly used is solving engineering problems including fatigue crack growth. The S-version FEM is an extended version of the FEM to predict fatigue crack growth. This method was developed into open-source software written in C/C++ language and built based on the UNIX operating system. The objective of this study is to perform a prediction for fatigue crack growth using the S-version FEM. This S-version FEM was structured using the global-local overlay technique that consisted of two separate meshes for global and local. Therefore, the computation process was solely focused on the local area instead of whole geometries. This undoubtedly reduced computation time and dependency on conventional FEM software. The geometry of the problem was modelled in FAST (pre-post) program and referred to as a global mesh, and the mesh was automatically generated in FAST. The location of the crack refers to the local mesh and at this stage smaller elements and finer mesh were made at the crack area. Local mesh was overlaid with global mesh. Then the global-local overlay approach was used to compute the engineering problem. The stress intensity factor (SIF) was calculated using the virtual crack closure-integral method (VCCM). The prediction of the fatigue crack growth results are shown in this study as well as the behaviour of the SIF corresponding to the crack growth. Analytical solutions were compared with the S-version FEM to validate the results. A very good agreement was presented between the S-version FEM and analytical approach for the normalised SIF. In addition, regression analysis was performed to support the evidence. From the analysis, very small root mean square errors (RMSE) of 0.12 with high correlation coefficient (R2) of 99.74% were shown to confirm the findings. From this study, it can be concluded that the S-version FEM is suitable to be used to predict fatigue crack growth for semi-elliptical surface cracks. The application of the S-version FEM benefits the user because using the overlay approach shortens the computation process. Keywords: Fatigue crack growth (FCG), S-version Finite Element Method

Evaluation of crack propagation behaviors in a T-shaped tubular joint employing tetrahedral FE modeling

Crack growth in a T-shaped tubular joint is studied using a newly developed system to simulate three-dimensional crack propagation and fatigue testing results. Tetrahedral finite element (FE) modeling is adopted to analyze a tubular structure with a curved surface crack. The virtual crack closure-integral method is used to evaluate the fracture mechanics parameters. The FE crack modeling with a remeshing procedure using an automated mesh generation system greatly simplifies the crack propagation simulation. The calculation results are compared with the experiments.

Computations of stress intensity factors for semi-elliptical cracks with high aspect ratios by using the tetrahedral finite element (fully automated parametric study)

The stress intensity factor (SIF) solutions of semi-elliptical cracks with high aspect ratios in plate and thick wall cylinder have been investigated under various assumed stress distributions. The authors have developed an automated analysis procedure to perform parametric studies on crack shapes and loading conditions. It consists of programs to perform automatic mesh generation, analysis execution including assignments of boundary conditions and SIF evaluations by VCCM (virtual crack closure-integral method). It was also found that SIF solutions for the thick wall cylinder and for the complex structure could be estimated by those for the flat plate.

Development of Stress Intensity Factors for Surface Cracks With Large Aspect Ratio in Plates

A number of surface cracks with large aspect ratio have been detected in components of nuclear power plants (NPPs) in recent years. The depths of these cracks are even larger than the half of crack lengths. When a crack is detected during in-service inspections, methods provided in ASME Boiler and Pressure Vessel Code Section XI or JSME Rules on fitness-for-service for NPPs can be used to assess the structural integrity of cracked components. The solution of the stress intensity factor (SIF) is very important in the structural integrity assessment. However, in the current codes, the solutions of the SIF are provided for semi-elliptical surface cracks with a limitation of a/ℓ ≤ 0.5, where a is the crack depth, and ℓ is the crack length. In this study, the solutions of the SIF were calculated using finite element analysis (FEA) with quadratic hexahedron elements for semi-elliptical surface cracks with large aspect ratio in plates. The crack dimensions were focused on the range of a/ℓ = 0.5–4.0 and a/t = 0.0–0.8, where t is the wall thickness. Solutions were provided at both the deepest and the surface points of the surface cracks. Furthermore, some of solutions were compared with the available existing results as well as with solutions obtained using FEA with quadratic tetrahedral elements and the virtual crack closure-integral method (VCCM). Finally, it was concluded that the solutions proposed in this paper are applicable in engineering applications.

Failure analysis of carbon nanotube/epoxy composites having a broken carbon nanotube

In the present work, multi-scale finite element analysis of carbon nanotube/epoxy composites having a broken carbon nanotube has been performed to assess the severity of such a fiber (i.e. carbon nanotube) break. A square representative volume element having nine-carbon nanotubes has been considered for the analysis. Considering a small debonding around the broken fiber as a crack front, stress redistribution around the break is studied. Using the concept of linear elastic fracture mechanics, strain energy release rates around the debonding have been calculated using virtual crack closure integral method. Quadratic stress criterion has been used to assess the delamination initiation at the interface of broken carbon nanotube and the matrix. Virtual crack closure integral along with quadratic stress criterion has been used to determine the critical strain energy release rate. Results from the present analysis show that the fiber volume fraction does not have significant influence on the ineffective length of the broken carbon nanotube. A high magnitude of interfacial shear stress is observed to have developed in the vicinity of the fiber break indicating the chances of debonding. All the three components of strain energy release rate have been determined and the influences of important parameters on the value of strain energy release rate have also been studied.

Stress Analysis and Damage tolerance evaluation for wing structure with a large cutout in the bottom skin

Wings are the lift generating components in the airframe structure. Wings are also used as fuel tanks in the transport aircraft. From the functional requirements point of view, cutouts are introduced in the bottom skin of the wing structure. Bottom skin is under tension stress field during flight. Cutouts in the bottom skin will act as stress risers due to stress concentration effect. The current project includes the stress analysis of a wing box with large cutouts in the bottom skin to identify the critical location for fatigue crack initiation. Damage tolerance evaluation includes the stress intensity factor calculations at crack tip. This is carried out by simulation of the crack in the finite element model. Stress intensity factor (SIF) at different crack lengths will be calculated using Modified Virtual Crack Closure Integral (MVCCI) method.

Typical Calculation Method of Stress Intensity Factors and Crack Growth Criterions on Infinite Plate Containing Hole-Edge Cracks

This paper introduces a finite element analysis software FRANC2D/L to calculate the stress intensity factor (SIF) and simulate the crack growth. Samples with infinite plate containing center crack, one hole-edge crack and two symmetrical hole-edge cracks were analyzed by this software. Comparing the SIF calculation results of the three samples based on displacement correlation method, J-integral method and virtual crack closure integral method, the results show that the three methods are all suitable for calculating the SIF problems, and the calculation precision of J-integral method and virtual crack closure integral method are better. Comparing the three crack growth criterion of maximum circumferential stress, maximum strain energy release rate and minimum strain energy density, the calculation velocity and precision of maximum circumferential stress criterion and minimum strain energy density criterion are prior to maximum strain energy release rate criterion. The calculating time and angle error of maximum strain energy release rate criterion is larger than that of the other two criterions．

Fully automated mixed mode crack propagation analyses based on tetrahedral finite element and VCCM (virtual crack closure-integral method)

The authors have been developing a crack propagation analysis system that can deal with arbitrary shaped cracks in three-dimensional solids. The system is consisting of mesh generation software, a large-scale finite element analysis program and a fracture mechanics module. To evaluate the stress intensity factors, virtual crack closure-integral method (VCCM) for the quadratic tetrahedral finite element is adopted and is included in the fracture mechanics module. The rate and direction of crack propagation are predicted by using appropriate formulae based on the stress intensity factors. In this paper, the crack propagation system is briefly described and some numerical results are presented.

CM-JP-4 Propagation analyses of multiple and arbitrary shaped cracks in complex structures

In this paper,the authors' recent developments on the crack propagation analysis software system are presented.The system has been developed based on three main parts i) finite element model generation,ii) finite element analysis and iii) stress intensity factor computations.We adopt the quadratic tetrahedral finite element and the processes in the finite element model generation are fully automated by using the Delaunay tessellation technique.The stress intensity factors are evaluated by using the virtual crack closure-integral method(VCCM) for the tetrahedral finite element.In this presentation,the outlines of the software system and the results of single and multiple crack analyses are presented.When the multiple crack analyses are performed,the coalescences of the cracks are considered.To do so,the net-section yield criterion is adopted to judge the coalescence of adjacent cracks.

Study on Mixed-Mode Interlaminar Fracture of Laminated Composites

The superposition-finite element method is developed to analyze the mixed-mode delamination in laminated composites. Both a coarse global mesh and an overlaying fine local mesh are integrated into the finite element analysis model. The whole design domain is discretized by a uniform global mesh, while the high stress regions are discretized by fine local meshes. Local mesh is built independently from the global mesh, which greatly simplifies the model generation procedures. Strain energy release rate is calculated based on the modified virtual crack closure-integral method, which is used to describe the propagation of delamination in laminated composites. Mixed-mode bending tests are performed for unidirectional and cross-ply carbon fiber reinforced laminated composites to characterize the interlaminar fracture behavior under mixed-mode I/II loading conditions. The interlaminar fracture toughness is also given for different mixed-mode ratio. It is seen that fracture resistance for laminated composites exhibit R-curve behavior (increase as delamination propagation). However, once the delamination is sufficiently long, the interfacial fracture toughness changes slightly as the delamination extended and become almost independent of the delamination length. The results of finite element method are in good agreement with the experimental results and provides a basis for establishing failure criterion used in damage tolerance analysis of composite structures.

Crack growth analysis in a weld-heat-affected zone using S-version FEM

The objective of this study is the prediction of crack propagation under thermal, residual stress fields using S-Version FEM (S-FEM). By using the S-FEM technique, only the local mesh should be re-meshed and it becomes easy to simulate crack growth. By combining with an auto-meshing technique, the local mesh is re-meshed automatically, and a curved crack path is modeled easily. Virtual crack closure integral method (VCCM) is used to evaluate energy release rate at the crack tip. For crack growth analyses, crack growth rate and growth direction are determined using criteria for mixed mode loading condition. In order to confirm the validity of this analysis, some comparisons with previously reported analyses were done, and good agreement obtained. In this study, residual stress data were provided by JAEA, Japan Atomic Energy Agency, based on their numerical simulation. Stress corrosion crack (SCC) growth analyses in a pipe are conducted in two-dimensional and three-dimensional fields. Two cases, for an axi-symmetric distribution of residual stress in the pipe wall and a non-axisymmetric one are assumed. Effects of residual stress distribution patterns on SCC cracking are evaluated and discussed.