Virtual Crack Extension Method Research Articles

Mechanism of stress evolution in environmental barrier coatings considering the presence of crack channels

The roles of crack channel transitions and thermally grown oxides (TGO) in the failure of environmental barrier coatings (EBCs) should be clarified. Hence, in this study, the laws of penetration and delamination crack evolution were investigated using a virtual crack extension method for multilayer materials to gain insights into the transformation conditions with a framework for a coupled thermal/mechanical/chemical numerical model of TGO containing channel cracks developed based on this law. The framework integrates diffusion, TGO growth, and phase transformation of the oxides. A theoretical model for high-temperature gas corrosion of EBCs coupled with deformation, mass diffusion, and chemical reactions was proposed, with the results indicating that the cracks transitioned from vertical to exfoliation cracks in the ytterbium dibasic silicate (YbDS) layer. The coupling effect of cracks and stresses led to non-uniform growth of the TGO by affecting the oxygen diffusion and inflow rates. The y-direction stresses at the YbDS/TGO interface near the crack channel changed from compressive to tensile stresses after cooling, making the first location to undergo delamination failure. The proposed model can provide better guidance for designing EBCs systems and supporting the life prediction of EBCs in service environments.

Simulation on coupling effects between surface wear and fatigue in spur gear

A surface wear prediction method is used to determine the wear rate of the tooth surface. This method employs the Archard’s wear model together with the gear contact mechanics model. An equivalent calculation model based on Hertzian contact theory and fracture mechanics is used to investigate crack initiation and crack propagation. The virtual crack extension (VCE) method is employed to analyze the propagation process from the initial crack to occurrences of tooth surface pitting. A life prediction method on the wear-fatigue coupling is developed. The crack propagation process and pit shapes are determined by the iterative analysis. The relationship between service life and the remaining distance from the crack tips to the tooth surface is determined. The damage mechanism of wear-fatigue coupling is explored. The results of the comparative analysis show that the wear of tooth surface affects the cracks propagation characteristics, reduces the service life and even can change the failure mode. The simulated pit shapes and crack propagation process are in good agreement with the results of other literature. The analysis method of wear-fatigue coupling damage can well simulate the damage process and predict service life in spur gear.

Crack singular field evaluation with characteristic tensor considering residual stress

ABSTRACT To accurately evaluate the fracture behaviour and fatigue life of welded structures, it is necessary to consider welding residual stress in addition to the stress produced by the applied loads. Characteristic tensor, which has a proportional relationship to stress intensity factor (SIF), is one new approach to evaluate stress singularity caused by a crack. Characteristic tensor is the tensor that is easily calculated by integrating stresses in a simple sphere zone around a crack tip using coarse mesh without special limitation in the mesh division, even under general cases like mixed-mode loading conditions. In this study, the stress singularity in the welded plate is evaluated by characteristic tensor and its effectiveness with the residual stress field is verified. Firstly, the residual stress distribution in butt-welded plates is calculated by the finite element method. Secondly, the singular stress field is obtained by introducing a single straight crack in the welded plates. A crack with different lengths and the crack tip located at different residual stress states are considered in reproducing the stress singularity. In each case, SIF is estimated from the characteristic tensor calculated from stress distribution nearby a crack tip and compared to those from the Green’s function or virtual crack extension method. Additionally, the stress singularity caused by the external load is evaluated in the same manner. The estimated SIFs with coarse mesh are in good agreement with the conventional methods. The results suggest that characteristic tensor provides a practical approach to evaluating stress singularity in welding structures.

Computation of energy release rate for interfacial crack in orthotropic bimaterials

The interfacial crack in bimaterials is a very interesting problem for composite materials and which has received particular attention from several researchers. In this study, we will propose a numerical modeling of the interfacial crack between two orthotropic materials using a special mixed finite element. For the calculation of the energy release rate, a technique, based on the association of the present mixed finite element with the virtual crack extension method, was used. The numerical model proposed, in this work, was used to study a problem of interfacial crack in bimaterials. Two cases were treated: isotropic and orthotropic bimaterials. The results obtained, using the present element, were compared with the values of the analytical solution and other numerical models found in the literature.

An analytical damage tolerance method accounting for delamination in compression-loaded composites

An efficient damage tolerance (DT) analysis method is required for application during the preliminary design phase of a composite structure. In the present work, we describe an analytical, energy-based DT analysis method for compression-loaded composite laminates containing a delamination. Based on the sublaminate buckling as the driving phenomenon, the strain energy release rate is calculated through the virtual crack extension method. The consideration of the load transfer within the laminate allows calculating the strain energy release rate in two directions which permits an assessment of the damage propagation direction. Further, the developed method permits taking into account the effects of the laminate width and the damage eccentricity. The obtained results are compared with other analysis approaches and validated through experiments from the literature. This validation approves the method’s capability to assess the residual laminate properties, although the method turned out to be less accurate than methods presented in the literature.

On the computation of energy release rates by a peridynamic virtual crack extension method

A new peridynamic virtual crack extension (PVCE) method is developed to predict the energy release rate G in fracture mechanics, and the directionally and virtually broken bonds are uniquely applied to constitute the virtual crack for crack extension in the numerical implementation. An algorithm of the PVCE method considering serial crack extensions and quasi-static analysis is proposed, and the modified PVCE method is further introduced to reduce the computational error. As validation and application examples, the developed PVCE method is applied to compute the energy release rates of single edge-notched tension (SENT), double cantilever beam (DCB), and end loaded split (ELS) tests, and the results are compared with the existing analytical solutions and numerical finite element analysis. The new PVCE method builds a natural “bridge” for peridynamic fracture analysis between the peridynamics and classical fracture mechanics, and it is capable of accurately and effectively computing the energy release rates for both mode I and mode II fracture cases as well as predicting the critical load and displacement in fracture analysis.

A virtual crack extension method for thermoelastic fracture using a complex-variable finite element method

A virtual crack extension (VCE) technique using the complex-variable finite element method (ZFEM) has been developed and demonstrated for thermoelastic fracture problems. This VCE approach provides an accurate computation of the energy release rate (G) as a byproduct of the complex-variable finite element analysis and obviates the use of energy conservation integrals such as the J-integral. The crack extension is induced using imaginary coordinates and a single global estimate of G is obtained as a sum of the element contributions. Numerical examples are provided for 2D, including a bimaterial cracked plate, axisymmetric, and 3D structures. The results indicate that the complex-variable VCE approach is of the same accuracy as the J-integral formulation.

A virtual crack extension method to compute energy release rates using a complex variable finite element method

The complex-valued finite element method, ZFEM, is proposed as a new virtual crack extension method to compute the energy release rate. The energy release rate is computed as a numerical derivative of the strain energy with respect to a crack extension using the complex Taylor series expansion method (CTSE). This is accomplished using a finite element method with complex nodal coordinates and extending the crack by a very small quantity along the imaginary directions of the complex nodal coordinates. The resulting finite element formulation becomes complex valued with the imaginary component of the strain energy containing the energy release rate. This method retains the conceptual simplicity of numerical differentiation but eliminates numerical issues regarding perturbation of the crack size. Both two- and three-dimensional examples are provided. Numerical examples indicate that the energy release rate computed using ZFEM is of the same accuracy as the domain-based J integral formulation. The method is very general and can be applied to self-similar or non-self-similar crack extensions.

Decomposition of 3-D mixed-mode energy release rates using the virtual crack extension method

A technique was implemented for decomposing 3-D mixed-mode energy release rates using the Virtual Crack Extension (VCE) method. The technique uses a symmetric/anti-symmetric approach to decompose local crack-front displacements that are substituted into the global VCE energy release rate form. The subsequent expansion leads to the mixed-mode energy release rate expressions. As a result of the expansion, previously unaddressed modal–interaction coupling terms are found to impact the mixed-mode energy release rates. This development expands the VCE method’s advantages over similar procedures when simulating arbitrary crack growth by providing the means to calculate both mixed-mode energy release rates and their variations.

원주방향 관통균열을 갖는 원통형 쉘 구조의 패치보강 해석

이 연구에서는 수치해석 실험을 통하여, 원주방향 관통균열을 갖는 원통형 쉘의 패치보강 전후의 거동에 대한 평가와 다양한 변수에 따른 패치보강 효과를 분석하였다. 해석 모델의 신뢰성을 높이기 위해, h-법 및 p-법에 기초한 모델링, 두 가지 방법이 동시에 고려되었다. 또한 선형탄성파괴역학 개념에 기초하여 에너지 방출률을 산정하기 위해, 등가영역적분법 및 가상균열확장법이 고려되었다. 해석 예제로서, 먼저 연구에서 수행된 h-법 및 p-법 유한요소 모델을 검증하기 위해, 패치 보강전의 인장력을 받는 관통 균열이 있는 쉘 구조물이 해석되었으며, 해석 결과값들과 여러 참고문헌 값들이 비교되었다. 그리고 패치 보강된 원통형 쉘 시스템에서의 접착제 두께, 접착제 전단탄성계수, 패치 두께, 패치 재료, 균열 길이 등의 여러 설계 변수에 대한 민감도 해석이 수행되었다. In this study, behavior of unpatched and patched cylindrical shells with through-wall cracks has been estimated using numerical experiments, and patching effect of them has been investigated according to various patching parameters. To show credibility of numerical models considered, two ways such as h- and p-methods have been adopted. Also, domain integral method and virtual crack extension method have been considered to calculate energy release rates based on linear elastic fracture mechanics. For examples, the unpatched cylindrical shells with circumferential cracks under remote tension have firstly been analyzed to show the validity of finite element modeling with h-method or p-method, and then the results have been compared with literature values published. Next, the sensitive analysis of patch repaired problems in terms of thickness of patch and adhesive, shear modulus of adhesive, composite material type of patch, crack length, etc. has been carried out.

Effect of Strength Matching Performance on J-Integral of Inhomogeneous Welded Joints

In this paper, J-integral of inhomogeneous welded joint is calculated by use of the combination of finite element method and virtual crack extension method, and the impact of strength matching on J-integral is studied as well. The analysis results show that the strength matching factor affects J-integral value greatly, that is, low matching of inhomogeneous welded joint of same steel can help to improve the ductility of the welded joint and the influence of the matching performance of dissimilar steel welded joint is more complex.

1210 高温環境下におけるSUS304平板の疲労き裂進展評価(G02-4 疲労の特性および評価,G02 機械材料・材料加工部門)

High-temperature plants, such as nuclear and thermal power plants are used under severe conditions. High temperature plants are susceptible to micro-cracks in its structure. This is because there is the effect of cyclic fatigue and creep fatigue. To prevent serious accidents, including small defects in the structure, we predicted the destruction, we must use safely. In particular, the evaluation of fatigue crack development is important. And, it is desirable to develop a more accurate assessment method. In this study, fatigue tests conducted for SUS304 which is often used in high temperature plant. Then observe the behavior of crack development, we examined the relationship between crack growth rate and the elastic-plastic fracture mechanics parameter, J-integral. In addition, the model plate with central crack, the J-integral analysis was performed by the virtual crack extension method.

Modeling Inter-Laminar Failure in Composite Structures: Illustration on an Industrial Case Study

This paper presents a solution procedure made available at an industrial level to study delamination in composites. Two approaches are presented. The first one is based on an original VCE (Virtual Crack Extension) method used to provide a quick estimate of the propagation load and the critical inter-laminar cracks, in a linear finite element analysis. The second approach relies on cohesive elements, and implies a non linear analysis. More general than the fracture mechanics (VCE) approach, the cohesive elements technique allows to provide the value of the maximum load that can be sustained by the structure, and to predict the residual strength and stiffness over the fracture process. Those two methods are first compared in a DCB test case to show that the results agree well with those from the literature or with the analytical solutions. Finally, a multi-delaminated industrial test case is solved with both approaches.

Fatigue crack initiation and propagation under cyclic contact loading

A computational model for contact fatigue damage analysis of gear teeth flanks is presented in this paper. The model considers the conditions required for the surface fatigue crack initiation and then allows for proper simulation of the fatigue crack propagation that leads to the appearance of small pits on the contact surface. The fatigue process leading to pitting is divided into crack initiation and a crack propagation period. The model for prediction of identification of critical material areas and the number of loading cycles, required for the initial fatigue crack to appear, is based on Coffin–Manson relations between deformations and loading cycles, and comprises characteristic material fatigue parameters. The computational approach is based on continuum mechanics, where a homogenous and elastic material model is assumed and results of cyclic loading conditions are obtained using the finite element method analysis. The short crack theory together with the finite element method is then used for simulation of the fatigue crack growth. The virtual crack extension (VCE) method, implemented in the finite element method, is used for simulating the fatigue crack growth from the initial crack up to the formation of the surface pit. The relationship between the stress intensity factor K and crack length a, which is needed for determination of the required number of loading cycles N p for a crack propagation from the initial to the critical length, is shown.

The influence of surface morphology on the interfacial adhesion and fracture behavior of vacuum infused carbon fiber reinforced polymeric repairs

AbstractThe current work is focused on the adhesion characteristics of vacuum infused repair patches on variously pretreated composite surfaces, given that the impregnation resin acts both as a consolidation agent of the reinforcement as well as a very thin bonding medium on a composite substrate. Initially, the pretreated surfaces, on which the repair patches were infused, were characterized with a number of surface analysis techniques such as X‐ray Photoelectron Spectroscopy (XPS), scanning electron microscopy (SEM), laser profilometry, dynamic contact angle and surface energy analysis. Double cantilever beam (DCB) repairs were then considered as the macroscopic method of assessment by infusing layers of carbon woven fabric onto the surface pretreated composite laminates. The behavior of the asymmetric DCB configuration was also studied by finite element modeling, for cohesive crack growth within the bondline, using the virtual crack extension (VCE) method. DCB testing results showed that the fracture resistance curves obtained from the repairs were lower than the numerical resistance curves. This was attributed to the preferential crack trajectory at the receptive infusion resin/pretreated composite interface. Correlation of the experimental fracture energies with the surface property data, revealed an explicit relationship between the surface roughness and the interfacial adhesion of the repair patches during crack initiation and propagation. The strain energy release rates of the DCB repairs were increased with increased surface roughness without dramatic change of the failure mode, as verified by the post‐failure examination of the fractured surfaces using scanning electron micrographs. POLYM. COMPOS., 29:92–108, 2008. © 2007 Society of Plastics Engineers

Stress intensity factor analysis of an interface crack between dissimilar anisotropic materials under thermal stress using the finite element analysis

New numerical methods were presented for stress intensity factor analyses of two-dimensional interfacial crack between dissimilar anisotropic materials subjected to thermal stress. The virtual crack extension method and the thermal M-integral method for a crack along the interface between two different materials were applied to the thermoelastic interfacial crack in anisotropic bimaterials. The moving least-squares approximation was used to calculate the value of the thermal M-integral. The thermal M-integral in conjunction with the moving least-squares approximation can calculate the stress intensity factors from only nodal displacements obtained by the finite element analysis. The stress intensity factors analyses of double edge cracks in jointed dissimilar isotropic semi-infinite plates subjected to thermal load were demonstrated. Excellent agreement was achieved between the numerical results obtained by the present methods and the exact solution. In addition, the stress intensity factors of double edge cracks in jointed dissimilar anisotropic semi-infinite plates subjected to thermal loads were analyzed. Their results appear reasonable.

Decomposition of Eshelby’s energy momentum tensor and application to path and domain independent integrals for the crack extension force of a plane circular crack in Mode III loading

Vanishing divergence of Eshelby’s (energy momentum) tensor allows formulation of path or domain independent integral expressions of the crack extension force. In this work, a decomposition scheme of this tensor is presented, which results in zero divergence decomposed parts that allow formulation of expressions yielding the Mode I, II and III crack tip parameters J and K, with particular emphasis on Mode III, at present. By using the Mode III decomposed part of Eshelby’s tensor and the virtual crack extension method, a path and a domain independent integral, both new, for the crack extension force of a plane circular crack in axi-symmetric Mode III loading, are derived as examples of application.

Comparison of virtual crack extension and strain energy density methods applied to contact surface crack growth

The paper is concerned with comparison of two crack propagation methods applied to a two-dimensional computational model of the surface initiated crack growth in the lubricated contact area of meshing gears. The virtual crack extension method and the minimum strain energy density criterion are used for simulation of the crack propagation in the framework of the finite element analysis. The discretised equivalent contact model, with the assumed size and orientation of the initial crack, is subjected to contact loading conditions, accounting for the elasto-hydro-dynamic lubrication effects, tangential loading due to sliding and the influence of lubricating fluid, driven into the crack by hydraulic mechanism. The computational results show that both crack propagation methods give comparable results, although the virtual crack extension method has some clear advantages due to its theoretical superiority in dealing with mixed-mode short crack propagation close to the loading boundary.

Evaluation of the Interfacial Fracture Toughness of Anodic Bonds

The interfacial fracture toughness of anodic bonds between silicon and glass is quantitatively evaluated using the stress intensity factors of an interfacial crack between dissimilar anisotropic materials. Partial delaminations of anodic bonds were introduced using the photolithography and the BHF-etching. To investigate the effect of crystal anisotropy on the fracture toughness of an anodic bond, both the (100) and the (111) silicon wafers were used. The tensile fracture tests of anodic bonds between silicon chips and Pyrex glasses were performed to measure the fracture load. The stress intensity factors of interfacial cracks in anodic bonds at fracture were calculated using the combination between the finite element method and the modified virtual crack extension method which was developed in our previous study. The fracture mode of tensile tests were mixed mode and cracks kinked into Pyrex glass. The fracture toughness of specimens using the (100) and the (111) silicon wafers was almost identical. The thermal shock tests of anodic bonds between silicon chips and soda glasses were performed. The temperatures when the anodic bonds were broken were measured. The stress intensity factor under the thermal stress was almost pure mode II, and cracks were extended along the cleavage planes of silicon chips. The fracture toughness of an anodic bond using the (111) silicon wafer was higher than that using the (100) silicon wafer.

Pitting formation due to surface and subsurface initiated fatigue crack growth in contacting mechanical elements

A computational model for simulation of surface and subsurface initiated fatigue crack growth due to contact loading is presented. The model is based on fracture mechanics theory where the required materials properties are obtained from common fatigue tests. For computational simulations an equivalent model of two contacting cylinders is used instead of simulating the actual contact of mechanical elements. The discretised model with the initial crack on or under the surface is then subjected to normal contact pressure, which takes into account the EHD-lubrication conditions, and tangential loading due to friction between contacting surfaces. The model considers also the moving contact of mechanical elements and for the surface initiated crack also the fluid trapped in the crack. The virtual crack extension method, implemented in the finite element method is then used for simulating the fatigue crack growth from the initial crack up to the formation of the surface pit. The numerical results correspond well with available experimental data. The described model can be used for simulation of pitting phenomenon of contacting mechanical elements like gears, bearings, wheels, etc.