Modified Virtual Crack Closure Integral Research Articles

Generalization of Mvcci Approach for Lefm Problems Using Numerical Integration

Modified Virtual Crack Closure Integral (MVCCI) has become a valuable tool for estimation of mixed-mode fracture parameters in Linear Elastic Fracture Mechanics (LEFM) problems. When finite elements with fewer nodes and using polynomial shape functions are employed at the crack tip for fracture analysis, the expressions for MVCCI can easily be derived and many times also be expressed in closed form. For higher order elements they become unwieldy and so a numerical integration scheme is proposed and this can be used with any type of element. The scheme requires a two-step numerical integration: one to evaluate nodal forces exerted by the solid below the crack extension line on the portion above and the second to evaluate Strain Energy Release Rates. This development makes the post-processing for fracture parameters easy and computationally economical for 3-dimensional fracture problems. The technique is used to estimate fracture parameters in certain practical problems using higher order elements and typical numerical results are presented.

Enhanced Delamination Tolerance Levels by Hybridizing Carbon Laminates with Glass Plies: Parametric Study

Laminated composites are extensively used in the aerospace industry and one of the key issues is delamination tolerance in these configurations during the operational phase. This paper demonstrates that hybridization is an effective strategy to achieve higher delamination tolerance sizes. For the above purpose, this paper presents a method to hybridize two different practical laminated carbon composite panels with glass fibers and also a parametric study to evaluate the influence of various hybrid laminate parameters on the delamination tolerance. Geometrical non-linear finite element analysis is carried out on three-dimensional models of delaminated non-hybrid and hybrid composite laminates. The mode I Strain Energy Release Rate (SERR) is estimated using Modified Virtual Crack Closure Integral (MVCCI). The SERR components are compared for the hybrid and the non-hybrid laminates. It is demonstrated that an appropriate hybridization with glass plies in between a few top and bottom carbon layers enhances delamination tolerance levels without significantly affecting the stiffness of the laminate.

Effect of adhesive de-bond and crack in adherent plate on single lap joint with bi-adhesive

PurposeThis paper aims to study the benefits of use of bi-adhesive (combination of two different adhesives) over conventional single adhesive in bonded lap joints. Characterise damage severity due to cohesive and adherent failure as feedback for operating load levels that assist in developing damage tolerance design of the adhesively bonded joints.Design/methodology/approachSingle lap joint where the adherent plate is made up of aluminium alloy joined together with bi-adhesives is analysed. The nature of adhesives ranges from brittle, elastic-plastic, moderately ductile to largely ductile. Numerical analysis is performed considering the material and geometric non-linear behaviour of the joint. The optimum bond ratio of bi-adhesives and the effect of the location of adhesive on the stress distribution are studied. The cohesive zone modelling (CZM) is adopted to account for the cohesive failure of the joint. The adherent plate failure is also addressed by modelling and studying the behaviour of the crack at different locations in the plate using modified virtual crack closure integral (MVCCI).FindingsThe results obtained from the stress analysis show some important characteristic behaviour of the bi-adhesive joint. Although bi-adhesive is expected to result in improved joint strength, the purpose gets defeated if a brittle adhesive is used at the corners and ductile adhesive at the middle. The joint strength based on CZM, evaluated for a single adhesive, is in good comparison with the experimental results from the literature. Also, the location of the crack in the adherent plate plays a significant role in the failure of the joint.Originality/valueEstimating joint strength for the bi-adhesive model using CZM and evaluating damage severity in the presence of de-bond and crack in the bi-adhesive lap joint model assists in developing robust damage tolerance design models of such joints.

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.

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.

Fatigue de-bond growth in adhesively bonded single lap joints

The fatigue de-bond growth studies have been conducted on adhesively bonded lap joint specimens between aluminium and aluminium with Redux-319A adhesive with a pre-defined crack of 3 mm at the bond end. The correlations between fracture parameters and the de-bond growth data are established using both numerical and experimental techniques. In the numerical method, geometrically non-linear finite element analyses were carried out on adhesively bonded joint specimen for various de-bond lengths measured from the lap end along the mid-bond line of the adhesive. The finite element results were post processed to estimate the SERR components G I and G II using the Modified Virtual Crack Closure Integral (MVCCI) procedure. In experimental work, specimens were fabricated and fatigue de-bond growth tests were conducted at a stress ratio R = − 1. The results obtained from both numerical analyses and testing have been used to generate de-bond growth curve and establish de-bond growth law in the Paris regime for such joints. The de-bond growth rate is primarily function of mode-I SERR component G I since the rate of growth in shear mode is relatively small. The value of Paris exponent m is found to be 6.55. The high value of de-bond growth exponent in Paris regime is expected, since the adhesive is less ductile than conventional metallic materials. This study is important for estimating the life of adhesively bonded joints under both constant and variable amplitude fatigue loads.

3D-Modeling and Numerical Analysis of Fracture Behavior in AFM-Specimen on Mixed-Mode I-II Loading Condition

The computational analysis of a three-dimensional (3D) finite element model of all fracture modes (AFM) specimen on mixed-mode I-II fracture was presented in this paper. The separated energy release rates (SERRs) along the crack front of the AFM-model were calculated by the modified virtual crack closure integral (MVCCI)-method and commercially available software ANSYS. The influence of finite geometry and loading angles on mixed mode I-II fracture was investigated.

Crack Initiation Predictions of the AFM-Specimen under Bend and Torsion Loading

In this paper, the computational predictions of crack initial breakpoint and deflection angles under bend and torsion loading conditions are investigated in conjunction with the modified virtual crack closure integral (MVCCI)-method by using the all fracture modes (AFM) specimen and commercial software ANSYS. The separated strain energy release rates (SERRs) along the crack front are calculated and subsequently converted to the stress intensity factors (SIFs) by using Irwin´s equations. Based on the SIFs results, the crack initiation predictions are presented by the maximum principal stress σ1'-criterion. Results show that when the AFM-model under a series of combined proportional bend and torsion loading conditions, asymmetrical stress fields are produced along the crack front. The presented investigation also shows that the maximum principal stress σ1'-criterion in conjunction with the MVCCI-method provides a powerful numerical tool for general computational approach to the fracture analysis of complex loading conditions.

Computational Analysis of the AFM Specimen on Mixed-Mode I+II+III Fracture

The computational analysis of an all fracture modes (AFM) specimen on mixed-mode I+II+III fracture is presented in this paper. The separated energy release rates (SERRs) along the crack front of the AFM-model are calculated by the modified virtual crack closure integral (MVCCI)-method and the commercially available software ANSYS. A transition model is built by adopting several 3D elements of SOLID45 and one point element of MASS21 in the ANSYS program. Under the related constraint conditions, the separate force and moments are respectively applied on the point element of the transition model, so the corresponding desired reaction forces can be obtained. When the desired loads are superimposed and applied on the AFM-model, the mixed-mode I+II+III fracture can then be achieved. Thereby, the SERR results are calculated. The calculation results show that the facture behavior of GII and GIII appears complex due to the global deformation and Poisson’s ratio, although the distribution of SEERs GI is symmetrical with respect to the middle point along the crack front. The total SERRs, GTn-values increase along the crack front with the minim value at one corner and the maxim value at the other corner. It can therefore be predicted that the fracture will occur initially at one corner on the crack front of the AFM-specimen in this case.

Computational fracture analysis of an AFM-specimen under mixed mode loading conditions

Fracture processes in ship-building structures are in many cases of a 3-D character. A finite element (FE) model of an all fracture mode (AFM) specimen was built for the study of 3-D mixed mode crack fracture behavior including modes I, II, and III. The stress intensity factors (SIFs) were calculated by the modified virtual crack closure integral (MVCCI) method, and the crack initiation angle assessment was based on a recently developed 3-D fracture criterion—the Richard criterion. It was shown that the FE model of the AFM-specimen is applicable for investigations under general mixed mode loading conditions, and the computational results of crack initiation angles are in agreement with some available experimental findings. Thus, the applicability of the FE model of the AFM-specimen for mixed mode loading conditions and the validity of the Richard criterion can be demonstrated.

Computational Analysis of the AFM Specimen on Mixed-Mode II and III Fracture

Some results of 3D finite element analyses of the all fracture modes (AFM) specimen on mixed-mode II and III fracture are presented in this paper. The computational fracture analysis is based on the calculation of separated strain energy release rates (SERRs) along the crack front by the modified virtual crack closure integral (MVCCI)-method and the commercially available FE-code ANSYS. Calculation results show that under pure in-plane shear loading (mode II), not only the mode II, but also the mode III loading conditions, are generated owing to the Poission’s ratio effects. Similarly, under pure out-of-plane shear loading (mode III), besides the mode III, the mode II loading conditions are induced due to the global deformation. Nevertheless, once in-plane and out-of-plane shear loadings are superimposed, the fracture behavior appears more complex. Further discussion is given associate with some previous study.

Finite Element Analyses of Modified Compact Tension Shear (MCTS)-Specimens under Mixed-Mode Loading Conditions

In this paper a detailed 3D-finite element analyses results of modified compact tension shear (MCTS)-specimens with an inclined crack plane or crack front under mixed-mode loading conditions are presented. It is found that under mixed-mode loading, a superposition of all fracture modes I, II and III can be generated along the straight crack front of MCTS-specimens, and the maximum of the total SERR along the crack front of two different MCTS-specimens is found at right hand side of crack front corner，where the risk of crack initial growth is highest. The computational fracture analysis is based on the calculation of separated energy release rates GI, GII and GIII along the crack front by the numerically highly effective modified virtual crack closure integral(MVCCI)-method.

Crack observation methods, their application and simulation of curved fatigue crack growth

Abstract The observation of cracks with curved crack path has to be done optically. It is shown that a modified commercial flat bed scanner and a combination of a high-resolution scanner camera system with 10,000 × 10,000 pixels with a telecentric lens are appropriate for high-resolution (up to 8 μm/pixel) optical recording of multiple crack ends on sample areas up to 210 mm × 290 mm. The high-resolution photographs are suitable for determination of crack lengths. It is also possible to observe crack paths or geometrical crack tip parameters and strain fields by image correlation. The method is used to determine static crack resistance and cyclic crack growth curves on center crack tension and biaxial cruciform samples. Furthermore, the paper presents an improved finite element technique for the simulation of curved fatigue crack growth in a multiple arbitrarily pre-cracked isotropic sheet under biaxial plane stress loading applying a predictor–corrector procedure in combination with the modified virtual crack closure integral (MVCCI) method including the consideration of the plastic limit loads. For this, the program PCCS-2D was extended to analyse the crack growth and the plastic limit load for each crack propagation step in a fully automatic simulation. The proposed solution algorithm provides a powerful tool for flaw assessment with the failure assessment diagram procedure in combination with a numerical crack path simulation. Finally, the simulation is verified experimentally.

Computational Fracture Analyses of a Compact Tension Shear (CTS) Specimen with an Inclined Crack Front

In this paper some results of 3D-finite element analyses of a modified CTS-specimen(MCTS) with an inclined crack front are presented. It will be shown, that through the inclination of the crack front, even under pure in-plane shear loading of the specimen, mixed-mode II and III loading conditions can be generated along the straight inclined crack front. Furthermore a superposition of all fracture modes I, II and III can be generated, if this MCTS-specimen is subject to an in-plane tension/shear loading. The computational fracture analysis is based on the calculation of separated energy release rates GI, GII and GIII along the crack front by the numerically highly effective modified virtual crack closure integral(MVCCI)-method and for the finite element(FE)-modelling the commercially available FE-code ANSYS is utilized.

Computational Fracture Analyses of a Compact Tension Shear (CTS) Specimen with an Inclined Crack Plane

In this paper some results of 3D-finite element analyses of a modified CTS-specimen with an inclined crack plane are presented. It will be shown, that through the inclination of the crack plane, even under pure tension loading of the specimen, a superposition of all fracture modes I, II and III can be generated along the straight crack front of the inclined crack plane. Furthermore, mixed-mode I, II and III loading conditions can also be generated if this modified CTS-specimen is subject to an in-plane tension/shear loading. The computational fracture analysis is based on the calculation of separated energy release rates GI, GII and GIII along the crack front by the numerically highly effective modified virtual crack closure integral(MVCCI)-method and for the finite element(FE)-modelling the commercially available FE-code ANSYS is utilized.

Numerical Simulation of Fatigue Crack Growth for Curved Cracks Emanating from Fastener Holes in Sheets by the MVCCI Method

The paper presents the results of a continued study of curved fatigue crack growth in a multiple arbitrarily pre-cracked isotropic sheet under plane stress loading. The predictor-corrector method (PCM) was extended in order to analyse the growth of multiple crack systems in a finite 2D structure. Together with the recently proposed improved modified virtual crack closure integral (MVCCI) method we can obtain accurate SIF values also for interacting cracks, and furthermore we can simulate fatigue crack growth of multiple crack systems in plane sheets under proportional mixed mode loading conditions. As a result, the program PCCS-2D is written to run within ANSYS to simulate interacting curved cracks. In order to check the accuracy and efficiency of the proposed method several example problems are solved. Especially curved cracks emanating from loaded fastener holes in sheets are analysed.

Fracture Analysis of Delaminated Composite Panels in Compression Using Numerically Integrated MVCCI

Delamination tolerance is one of the key issues in laminated composites used in high technology structures. Delamination in these structures could grow due to repeated in-plane compressive loading during operation and the delamination tolerance levels are obtained by comparing mode-I SERR component with the corresponding fatigue threshold values. The Modified Virtual Crack Closure Integral (MVCCI) is used to estimate individual mode SERR components in a mixed-mode situation, which occurs at an embedded delamination. The present work proposed a numerical integration for the first time to evaluate the MVCCI for Hexa20 elements used in three-dimensional finite element analysis. Extensive numerical results are presented including a parametric study on a typical laminate.

Numerically integrated modified virtual crack closure integral technique for 2-D crack problems

Modified virtual crack closure integral (MVCCI) technique has become very popular for computation of strain energy release rate (SERR) and stress intensity factor (SIF) for 2-D crack problems. The objective of this paper is to propose a numerical integration procedure for MVCCI so as to generalize the technique and make its application much wider. This new procedure called as numerically integrated MVCCI (NI-MVCCI) will remove the dependence of MVCCI equations on the type of finite element employed in the basic stress analysis. Numerical studies on fracture analysis of 2-D crack (mode I and II) problems have been conducted by employing 4-noded, 8-noded (regular & quarter-point), 9-noded and 12-noded finite elements. For non-singular (regular) elements at crack tip, NI-MVCCI technique generates the same results as MVCCI, but the advantage for higher order regular and singular elements is that complex equations for MVCCI need not be derived. Gauss numerical integration rule to be employed for 8-noded singular (quarter-point) element for accurate computation of SERR and SIF has been recommended based on the numerical studies.

Numerical and Experimental Investigations of Curved Fatigue Crack Growth under Proportional Cyclic Loading

The present paper demonstrates that the common computer‐aided two‐dimensional crack path prediction can be considerably improved in accuracy by using a new predictor‐corrector procedure in combination with the modified virtual crack closure integral (MVCCI) method. The numerical crack growth simulation is still based on a step‐by‐step technique, but uses a piecewise curved approximation of the crack path. By this method, both the new locus of the crack tip and the slope of the crack path at the crack tip can be computed simultaneously by the mode I and II stress intensity factors for only one virtual tangential crack extension with respect to the previous step. Furthermore, the paper presents a new finite element technique of calculating stress intensity factors of mixed mode problems by MVCCI Method. The procedure is devised to calculate the separated strain energy release rates by using the convergence of two separate calculations with different element sizes in the neighbourhood of the crack. The method provides robust calculation ability, even in the case of very coarse meshes. In order to evaluate the validity and efficiency of the proposed higher order crack path simulation method in relation to the well‐established basic strategies, experiments of curved fatigue crack growth are carried out with a specially designed specimen under proportional lateral force bending. In all investigated cases the computationally predicted crack trajectories show an excellent agreement with the different types of curved cracks that are obtained in the experiments as a function of the position of crack initiation.

Fracture analyses and experimental results of crack growth under general mixed mode loading conditions

In this paper detailed results of 3D finite element (FE) and mixed mode analyses of different fracture specimens are presented and discussed. Special interest is taken in 3D and mode coupling effects to be found in strain energy release rate (SERR) results along crack fronts, in particular adjacent to corners, where a crack front intersects a free surface of a specimen. It will be shown that these effects stay small if they are related to Poisson’s ratio but that they can also be considerably pronounced if they are related to the global deformation behaviour of the specimen. The computational fracture analysis is based on the calculation of separated energy release rates (SERRs) by the aid of the modified virtual crack closure integral (MVCCI)-method in order to calculate the local SERR-distributions along the crack front. Furthermore some qualitative experimental results will show the influence of these variable mixed mode I, II and III loading conditions along the crack front on crack initiation and on the further development of 3D crack growth in the specimens.