Virtual Crack Extension Method Research Articles

Stress Intensity Factor Analysis of an Interface Crack between Dissimilar Materials under Thermal Stress Condition by Virtual Crack Extension Method.

A new method is presented for stress intensity factor analysis of interface crack problems under thermal stress conditions. The virtual crack extension method, which is used with the finite element method, is a powerful tool for estimation of the energy release rate. The virtual crack extension method is applied to stress intensity factor analyses of thermal interface crack problems. The energy release rate obtained by the virtual crack extension method is separated into individual stress intensity factors, K1 and KII, by the principle of superposition. The presented method is applied to several thermal stress interface crack problems. The results are compared with those obtained by the displacement and stress interpolation methods. It is found from these analyses that the present method gives very accurate results which are insensitive to the size of finite elements.

Stress Intensity Factors of 3-D Interface Crack under Mixed-Mode Loading.

Three-dimensional finite element analysis has been carried out on the compact normal and shear specimens under mixed-mode loading. The complex stress-intensity factor K associated with an elastic interface crack is discussed via three different approaches : the virtual crack extension method, the modified crack-closure integral and displacement extrapolation. The effect of Young's modulus ratio on stress intensity factors is discussed under various kinds of mixed-mode loading. The distribution of stress intensity factors along the crack front is investigated. A comparison between stress-intensity factor KI and KII, obtained by these three methods, is carried out.

A comparative numerical review of cracked materials

The prediction of the behaviour of cracked structures submitted to various kinds of actions is an important problem for their safety; therefore, it is necessary to have a good knowledge of the possibility for an existing crack to growth and, if it is the case, in which direction. The fracture mechanics concept with numerical modelling, by finite element model, is kept for this study. Linear fracture mechanics in static loading and crack propagation is investigated in this paper. There are a lot of numerical methods to determine the cracking parameters which characterize the behaviour of the cracked structures. A comparative analysis of some main numerical methods aims to assess each of them, with the possibility of their application in a homogeneous material and bi-materials. The virtual crack extension method, used very often at the present time, is more acceptable for the case of multilayered structures when the crack tip is near the interface; it enables us to obtain accurate results. A crack propagating through the interface between two layers (with a specific homogeneous material) of a structure is studied by this method. It has been shown that the propagation depends on the nature of the mechanical characteristics of these materials. In the case of crack propagation in mixed mode, it is very difficult, by the current numerical methods, to follow the propagation of a crack until the failure of the structure. New formulations — T integral and A integral — solve these kinds of difficulty, by separation of the failure modes, and can treat thermoelastic problems. The crack propagation can be followed until the failure of the studied structure without great modification of the finite element mesh. Thus, it becomes easy to get a crack propagation in mixed mode through a computational analysis.

On the computation of the J-integral for three-dimensional geometries in inhomogeneous materials

An analytical expression of the J-integral for inhomogeneous materials is presented in a form suitable for the numerical analysis of arbitrary three-dimensional (3-D) mode-I crack configurations. This integral is given using the principle of virtual work and Eshelby's energy moment tensor. The virtual crack extension method was developed from finite element considerations and was based on the calculations of the released energy when a crack in a finite element model was extended by a small amount Δa. For numerical calculations, the 3-D analogue of the volume integral appears to be an attractive approach for obtaining pointwise values of the stress intensity factors along a crack front. The formulation is easily incorporated into a finite element program, but can also conveniently be used as part of a post-processing program, which uses stress and displacement data from a finite element analysis to calculate the stress intensity factors. Numerical examples are presented, using twenty node, isoparametric, quarter-point elements, for the compact tension specimen, homogeneous and inhomogeneous materials. Stress intensity factors are calculated for various moduli of the inclusion and distances of the crack from the interface. Numerical results are compared with results obtained by two-dimensional models.

Stress Intensity Factors of a Mixed-Mode Interface Crack by a Finite Element Analysis.

Two-dimensional finite element analysis has been carried out on compact tension and shear specimens under mixed-mode loading. The complex stress-intensity factor K associated with an elastic interface crack is discussed via three different approaches : virtual crack extension method, modified crack-closure integral and displacement extrapolation. A comparison of stress-intensity factors KI and KII obtained by these three methods is carried out. The accuracy of these methods is discussed for specimens comprised of various dissimilar materials under various kinds of mixed-mode loading. The accuracy of the virtual crack extension method was revealed by comparison with the J-integral. The modified crack-closure integral varies markedly depending on the mesh length at the crack tip. However, the stress-intensity factor can be estimated with high accuracy using an appropriate mesh length.

Fracture analysis of cracked rubber components in two and three dimensions

This paper presents a non-linear fracture analysis of cracked rubber components. The fracture parameter, tearing energy for rubber materials is computed for two- and three-dimensional bodies using the virtual crack extension method. The crack propagation direction is found by a maximum tearing energy fracture criterion. To illustrate the finite element procedures developed, three design applications were studied. The results obtained are compared to those available in the literature. The procedures developed predict the crack propagation direction in cracked rubber solids.

Three-dimensional analysis of interface cracks in rubber materials

Three-dimensional and plane stress finite element analyses were carried out to investigate the stress fields and fracture parameters of interface cracks in rubber materials. The tearing energy computations for any arbitrarily shaped 3D crack front in dissimilar materials were obtained using the virtual crack extension method. The finite element results obtained are validated against existing alternate solutions and experimental data for cracks in homogeneous as well as bimaterial cases. The effects of different rubber material models, tearing energy distributions, crack extension angles, and three-dimensional regions at the crack tip for interface cracks are presented and discussed. It is shown that nonlinear materials have larger three-dimensional effects near the interface crack front, and that this effect increases as the material mismatch increases.

On the determination of mixed mode stress intensity factors of an angled crack in a disc using FEM

This paper is concerned with the rigorous determination of the stress intensity factors of an arbitrary located and oriented angled crack in discs using the finite element method. Three different loading conditions are examined: boundary loadings resulting from disc attachments and/or interference fit with a rotating shaft, body forces resulting from rotation at a constant angular velocity and thermal stresses associated with a quadratic radial temperature distribution. Three techniques are adopted in the evaluation of the resulting mixed-mode stress intensity factors: direct extrapolation methods, virtual crack extension and J-integral method. Verification with available referenced solutions for the simple case of a radial crack is provided and merits and limitations associated with the above three methods are discussed.

On the calculation of energy release rate for curved cracks of rubbery materials

The energy release rate G for 2-D rubbery material problems with curved cracks is calculated with finite element solutions in this paper. Two approaches, a generalized domain integral method and the virtual crack extension method, are investigated. The generalized domain integral method is demonstrated to be “patch independent” and therefore a complicated finite element mesh adjacent to the crack tip area is not required.

Stress intensity factors for 3-D axisymmetric bodies containing cracks by p-version of F.E.M.

A new axisymmetric crack model is proposed on the basis of p-version of the finite element method limited to theory of small scale yielding. To this end, axisymmetric stress element is formulated by integrals of Legendre polynomial which has hierarchical nature and orthogonality relationship. The virtual crack extension method has been adopted to calculate the stress intensity factors for 3-D axisymmetric cracked bodies where the potential energy change as a function of position along the crack front is calculated. The sensitivity with respect to the aspect ratio and Poisson locking has been tested to ascertain the robustness of p-version axisymmetric element. Also, the limit value that is an exact solution obtained by FEM when degree of freedom is infinite can be estimated using the extrapolation equation based on error prediction in energy norm. Numerical examples of thick-walled cylinder, axisymmetric crack in a round bar and internal part-thorough cracked pipes are tested with high precision.

Maximum tearing energy computation for 3D rubber fracture

This paper presents a finite element procedure for computing tearing energy for any arbitrarily shaped 3D crack front in rubber solids using the virtual crack extension method. The magnitude and direction of maximum tearing energy can be evaluated from the specified virtual crack extensions in three dimensions defined by spherical coordinates for any type of crack front. This finite element procedure was applied to a double pure shear fracture specimen. The results obtained for tearing energy are in good agreement with those calculated with the J-integral as well as with the experimental data. It is shown that a sinusoidal tearing energy distribution occurs within the crack front normal plane for a double pure shear fracture specimen.

A new method for evaluation of stress intensities for interface cracks

A new method is presented for calculating the values of K I and K II in the elasticity solution at the tip of an interface crack. The method is based on an evaluation of the J-integral by the virtual crack extension method. Expressions for calculating K I and K II by using the displacements and the stiffness derivative of the finite element solution and asymptotic crack tip displacements are derived. The method is shown to produce very accurate solutions even with coarse element mesh.

Stress Intensity Factor Analyses of an Interface Crack in an Adhesive Joint by Combination of the Boundary Element and Finite Element Methods.

In this paper, a combination of the boundary element method and the finite element method was applied to the stress intensity factor analyses of an interface crack in adhesive joints. The virtual crack extension method was utilized for finite elements allocated around a crack tip to obtain the energy release rate of a crack. The superposition technique proposed by Matos was utilized for the mode separation of the stress intensity factor of the interface crack. We applied the present method not only to a bimaterial plate with a center interface crack, but also to adhesive joints with a center interface crack or a slant interface crack to show the effectiveness of the present method for analyses of an interface crack in a very thin adhesive layer. Furthermore, the fracture toughness of an adhesive joint with an edge crack for various adhesive thicknesses was experimentally determined using the present analytical method. As a result, we obtained a constant fracture toughness regardless of the thickness of the adhesive layer.

Analysis of weld toe radius effects on fatigue weld toe cracks

Stress analysis of as-welded and weld toe ground fillet welded joints was carried out for four different weld toe radii (0·5, 1·0, 2·5 and 5·0 mm). This provided the stress distributions through the thickness of the plate and the stress concentration factor was determined by extrapolation to the weld toe surface. Closed form stress distribution equations were curve-fitted to the finite element results. Stress intensity factor computations for weld toe cracks were carried out using a weight function method and finite element techniques. Short weld toe cracks with crack depth to plate thickness ratios between a T = 0·001 and a T = 0·1 , were modelled and analysed for the weld toe radii of 0·5, 1·0, 2·5 and 5·0 mm. For the finite element analysis a virtual crack extension method was employed in computing the linear elastic J-integral and the average value for three contours was used to calculate the stress intensity factor. The stress intensity factor is presented as a stress concentration magnification factor (Mk) multiplied by the basic crack geometry for a single edge cracked plate (SECP). This was employed in a fatigue crack propagation analysis where the fatigue endurance curves were evaluated.

Fracture mechanical analysis of a reactor pressure vessel under thermal shock loading

Improved knowledge of cooling conditions in nuclear power plants in the case of potential emergencies and increasing irradiation embrittlement of reactor pressure vessel materials are two reasons for the fact that the safety of plant components is under permanent observation. In a loss-of-coolant accident it is possible that the injected cooling water runs in stripes down the vessel wall. This causes high thermal stresses and high stress gradients in the wall combined with a decrease of fracture toughness of the ferritic material. Assuming a circumferential crack in this region the temperature and loadtime-dependent stress intensity factors along the crack front are to be determined and compared with the temperature and life-time-dependent material toughness for the evaluation of pressure vessel safety against unstable crack propagation. Considering a reactor pressure vessel in operation the necessary ADINA finite element analyses of (i) transient heat transfer through the wall of the vessel and (ii) the stress and strain fields for thermoelastic-plastic material behaviour are presented. The virtual crack extension method was used for the calculation of J-integral values along the crackfront, which were converted into the stress intensity factors being compared with the material toughness.

Numerical analysis of cyclic deformations and crack growth of pre-cracked steel components using the adina program system

Our aim was to achieve a basic understanding of the vessel investigations under cyclic deformations and to validate ductile fracture mechanics concepts concerned with the cyclic J-integral. Several three-dimensional finite element analyses have been performed for components subjected to cyclic plastic deformations. Based on the slightly modified virtual crack extension method, cyclic J-integral values were computed and have been discussed. As long as the material plasticity around the crack tip is confined, the J-integral method is applicable and appears to be a suitable parameter for handling low-cycle fatigue problems.

Comparisons of fracture parameter evaluations for power law hardening creep

Convergence properties of various finite element based methods for the evaluation of the crack-tip field amplitude in creep C are examined on some representative examples. In particular, the case of non-steady-state creep, when C is contour-dependent with significant interior convergence properties, is studied. It is demonstrated that the virtual crack extension (VCE) implementation exhibits significantly better convergence properties than the conventional domain and contour integral methods. The VCE method also exhibits very good convergence for J evaluation, which does not have any direct physical interpretation for dominating creep but can be useful for C estimates. The background for these estimates is summarised.

Double virtual crack extension method for crack growth stability assessment

The second variation of energy corresponding to crack length is required in the stability analysis of crack growth. For determining such an energy gradient, an efficient finite element method extending the classical virtual crack extension concept is described in this paper. In elasticity, the method can be used for the prediction of the growth pattern of one single crack, and especially a system of interacting cracks as well from the results of a single strain-stress analysis. Example computations are performed for (1) a center-cracked plate and (2) a finite width strip containing two interacting cracks. Close agreement between the numerical results given by our method and reference solutions has been found in all testing cases.

Maximum energy release rate distribution from a generalized 3D virtual crack extension method

This paper presents a generalized 3D virtual crack extension (VCE) technique for determining the distribution of the maximum energy release rate along a general 3D crack front. The method allows for VCEs at any inclination to the local crack plane. By taking the component of the extension in the crack front's local normal plane it evaluates the local energy release rate, G, in that component's direction. Repeated VCEs applied to the crack front at different inclinations enable the maximum G and its associated direction in the normal plane to be determined. This technique has been applied to a quarter-circular crack in a square cross-section bar under axial and torsional loading. The evaluated maximum energy release rates show the expected antisymmetric direction and symmetric magnitude distributions. The test case also demonstrates a sinusoidal G distribution within the normal plane which would imply that the maximum G and its direction could be evaluated from only two local G values.

Finite element calculation of energy release rate for 2‐D rubbery material problems with non‐conservative crack surface tractions

AbstractThe energy release rate G for 2‐D rubbery material problems with non‐conservative crack surface tractions is calculated by a modified version of virtual crack extension method with finite element solutions. The formulation is demonstrated to be ‘patch‐independent’ and therefore a complicated finite element model around the crack tip is not required.