Fracture Analysis Methods Research Articles

An extended polygonal finite element method for large deformation fracture analysis

The modeling of large deformation fracture mechanics has been a challenging problem regarding the accuracy of numerical methods and their ability to deal with considerable changes in deformations of meshes where having the presence of cracks. This paper further investigates the extended finite element method (XFEM) for the simulation of large strain fracture for hyper-elastic materials, in particular rubber ones. A crucial idea is to use a polygonal mesh to represent space of the present numerical technique in advance, and then a local refinement of structured meshes at the vicinity of the discontinuities is additionally established. Due to differences in the size and type of elements at the boundaries of those two regions, hanging nodes produced in the modified mesh are considered as normal nodes in an arbitrarily polygonal element. Conforming these special elements becomes straightforward by the flexible use of basis functions over polygonal elements. Results of this study are shown through several numerical examples to prove its efficiency and accuracy through comparison with former achievements.

Failure Analysis on Leakage of the Circumferential Weld of Steel 20 Buried Pipeline

Nowadays, the welding quality of circumferntial welds is the main influencing factor of the service behaviors of long-distance transport pipeline, and the accidents caused by the circumferential welding defects have get extensive attention. To figure out the leaking reason of circumferential weld of the steel 20 buried pipeline, with macro inspection, nondestructive testing, physical and chemical properties, methods of medium leakage and fracture analysis, we found that the welding defects in the weld toe are mainly responsible for pipeline leaking. The welding defects of circumferential weld destroy the continuity of welding, which result in the stress concentration and cracks. Under the combined action of corrosion, erosion, working stress and welding residual stress, the cracks extend along the welding weak areas and penetrates the welding metal, finally leading to the leakage failure of the welds, also some suggestions are given to prevent similar accidents.

Some Recent Advances in Engineering Fracture Modeling for Turbomachinery

Recent advances in practical engineering methods for fracture analysis of turbomachinery components are described. A comprehensive set of weight function (WF) stress intensity factor (SIF) solutions for elliptical and straight cracks under univariant and bivariant stress gradients has been developed and verified. Specialized SIF solutions have been derived for curved through cracks, cracks at chamfered and angled corners, and cracks under displacement control. Automated fracture models are available to construct fatigue crack growth (FCG) life contours and critical initial crack size (CICS) contours for all nodal locations in two-dimensional or three-dimensional (2D or 3D) finite element (FE) models.

Linear and nonlinear analyses of femoral fractures: Computational/experimental study

This paper describes two new methods for computational fracture analysis of human femur using Quantitative Computed Tomography (QCT) voxel-based finite element (FE) simulation. The paper also reports comprehensive mechanical testing for validation of the methods and evaluation of the required material properties. The analyses and tests were carried out on 15 human femurs under 11 different stance-type loading orientations. Several classical forms of subcapital, transcervical, basicervical, and intertrochanteric fractures plus a specific type of subtrochanteric fracture were created and analyzed. A new procedure was developed for prediction of the strengths and the fracture initiation patterns using a FE-based linear scheme. The predicted and observed fracture patterns were in correspondence, and the FE predictions of the fracture loads were in very good agreement with the experimental results. Moreover, the crack initiation and growth behaviors of two subtrochanteric fractures were successfully simulated through a novel implementation of the cohesive zone model (CZM) within a nonlinear FE analysis scheme. The CZM parameters were obtained through a series of experimental tests on different types of specimens and determination of a variety of material properties for different anatomic regions and orientations. The presented results indicated that the locations and patterns of crack initiation, the sequences of crack growth on different paths, and the compatibility of growth increments agreed very well with the observed specifications. Also, very good agreements were achieved between the measured and simulated fracture loads.

Hyperbolic heat conduction based weight function method for thermal fracture of functionally graded hollow cylinders

This article introduces a weight function method for fracture analysis of a circumferentially cracked functionally graded hollow cylinder subjected to thermal loads. The non-Fourier hyperbolic heat conduction model is used to determine the transient temperature distribution in the functionally graded cylinder. Solutions for transient temperature and stress distributions in the uncracked cylinder are derived by converting the governing differential equations into Fredholm integral equations in the Laplace domain. A numerical Laplace inversion technique is used to calculate the wave-like temperature and stress solutions in the time domain. These solutions are utilized to determine stresses acting on the faces of the circumferential crack in the local perturbation problem. A weight function technique is developed to compute the corresponding mode I thermal stress intensity factors. Comparisons to the results generated by finite difference and finite element methods demonstrate the high level of accuracy attained by the application of the developed procedures. Further parametric analyses are presented to illustrate the influences of dimensionless time, crack depth to thickness ratio, power law index, and thermal relaxation time upon the stress intensity factors.

New kinematical constraints of cracked MITC4 shell elements based on the phantom-node method for fracture analysis

In this paper, the phantom-node method is developed for cracked plates and shells simulated by continuum mechanics based 4-node quadrilateral shell elements using the mixed interpolation of tensorial components (MITC) technique for the shear-locking removal. The proposed method permits an arbitrary crack to cut through elements. The discontinuity across the crack is described by continuous displacement fields of overlapping elements that are constructed by duplicating homologous nodes and realized on the real parts of the cracked elements. New kinematical constraints for the nodal displacements of the overlapping triple elements are derived to represent the displacement fields of the partially cracked elements. The interaction domain integral of cracked shell structures is formulated to extract the fracture parameters. Several numerical benchmark cracked plates and shells are analyzed to evaluate the accuracy and robustness of the proposed method.

Modelling of femur fracture using finite element procedures

During the last decades human femur fracture has been mainly analysed using an experimental approach focused on cadaveric or synthetic bones. Nowadays, advances in computational technologies allow using numerical methods, such as the finite element method for femur fracture analysis. However, fracture morphology has been scarcely studied using numerical methods despite the interest of this study due to the different clinical treatment required for each fracture type. In this work, different fracture modelling techniques have been analysed with the objective of predicting a realistic fracture path, which in the literature is often limited to the initial steps of fracture. The main goal of this article is to compare different numerical approaches and to provide a robust methodology for femur fracture simulation. Experimental work was carried out on a synthetic femur in order to validate the numerical models. Through this validation we verified that some numerical methods present convergence problems, and they are not useful to model long crack paths. The best results are obtained by simulating the crack growth by a local material property degradation applied through successive analyses. This technique has been applied to a real human femur, obtaining accurate results in fracture morphology prediction.

A Hamiltonian‐based analytical method for fracture analysis of linear thermo‐viscoelastic media

AbstractA Hamiltonian‐based methodology is presented to study the fracture behaviors of the thermo‐viscoelastic materials based on the Laplace transform. The governing equations and associated boundary conditions are rebuilt in a Hamiltonian form by using the symplectic mathematics in the frequency domain (s‐domain). The fundamental unknown vector composed of both displacements and stresses variables is expanded in terms of the symplectic eigensolutions. The corresponding unknown coefficients of the symplectic series are determined from the outer boundary conditions. Thus, the main unknowns are obtained and transformed into the time domain (t‐domain). The fracture parameters including stress intensity factors (SIFs) and J‐integrals are derived simultaneously. Numerical examples as well as convergence studies are given and are found to be in good agreement with the ANSYS results. A parametric study of thermo‐viscoelastic parameters is included also.

An engineering approach to the fracture assessment of hopper wagons

A hopper wagon is a type of railroad freight car used to transport many types of materials such as coal, ore, grain, ballast and minerals and bulk cargo. It is a complicated welded structure. When performing a safety assessment of cracks in a hopper wagon, it is necessary to consider fatigue crack propagation and fracture among the possible modes of failure. In any such analysis the stress intensity factors at crack tips are important parameters for estimating both residual life and criticality (residual strength). The purpose of this paper is to present engineering fracture analysis method for calculating the stress intensities for cracks in a hopper wagon. The advantage of the present approach is that it negates the need to explicitly model cracks. A crack of any size can be analysed using the original (un-cracked) finite element model. Furthermore, as cracks are not modelled explicitly a coarse mesh can be used to minimise the number of degrees of freedom, thereby reducing the analysis time. As such solutions for the stress-intensity factors can then be obtained quickly and easily for a variety of cracks and crack lengths using the original uncracked finite element analysis. The interaction between neighbouring cracks growing towards each other have been considered in this paper. Comparing the values of stress intensity factors computed using traditional finite element, the results obtained by new method presented in this paper suggest an agreement of within 3.5%. Therefore, this approach is sufficiently satisfactory to enable engineering estimates for residual strength (safety) and residual life. The method used in this paper is approximately ten times faster than computationally expensive methods.

Fracture analysis of fiber reinforced concrete structures in the micropolar peridynamic analysis framework

In this study, an effective meshless model is proposed for fracture analysis of cracks in fiber reinforced concrete structures. The cementitious material is modeled using the micropolar peridynamic approach which is a generalized form of the bond-based peridynamics. A semi-discrete approach is incorporated in the micropolar peridynamic framework to study the effect of fiber reinforcement on the fracture analysis of cracks in cementitious materials. Therefore in the proposed fiber reinforced concrete modeling approach, the macro-scale fibers are randomly distributed in the cementitious material, and the forces developed in the fibers are indirectly applied to the cementitious material particles. This fracture analysis method used for fiber-cementitious material composites improves the computational efficiency. Furthermore in contrast to the finite element method, there is no need for mesh refinement and monitoring crack initiations/propagations in the proposed peridynamic framework. The crack development is an inherent feature of the proposed analysis framework. The accuracy of the proposed fracture analysis model is demonstrated through a comparison of available experimental results and simulation outcomes of fiber reinforced concrete beams with a notch at varying locations along the span.

A coupled meshless finite point/Peridynamic method for 2D dynamic fracture analysis

In this paper, a new coupled meshless method for 2D transient elastodynamic problems involving dynamic crack propagation is developed. The method is based on an efficient coupling between the finite point method (FPM) and a discretized form of Peridynamics. The solution domain is partitioned in three parts: one discretized by Peridynamics, one by FPM, and a transition part discretized by both methods where the switching between the two approaches is performed. The coupling adopts a local/nonlocal framework that benefits from the full advantages of both methods. The parts of domain where cracks either exist or are likely to propagate are described by Peridynamics; the remaining part of the domain is described by FPM that requires less computational effort. The capabilities of the proposed approach are demonstrated by means of the solution of dynamic problems including dynamic fracture as well as a ghost force test.

Weight function method for transient thermomechanical fracture analysis of a functionally graded hollow cylinder possessing a circumferential crack

ABSTRACTThis article introduces a weight function method for fracture analysis of a circumferentially cracked functionally graded hollow cylinder subjected to transient thermomechanical loading. Analytical solutions for transient temperature and stress distributions in the uncracked cylinder are derived by applying finite Hankel transformation. These solutions are utilized to determine stress acting on the faces of the circumferential crack in the local perturbation problem. Thermomechanical material properties are assumed to be power functions of the radial coordinate in the derivations. Coefficients of the weight function are found using reference stress intensity factors computed through the finite element method. Domain form of the J-integral is used in the finite element calculations. Comparisons of the numerical results calculated by the proposed weight function method to those generated by finite element analysis demonstrate the high level of accuracy attained by the application of the developed procedures. Further parametric analyses are presented to illustrate the influences of dimensionless time, crack depth to thickness ratio, power law index, and convection coefficient upon transient mode I thermomechanical stress intensity factors.

Cortical bone fracture analysis using XFEM - case study.

We aim to achieve an accurate simulation of human cortical bone fracture using the extended finite element method within a commercial finite element software abaqus. A two-dimensional unit cell model of cortical bone is built based on a microscopy image of the mid-diaphysis of tibia of a 70-year-old human male donor. Each phase of this model, an interstitial bone, a cement line, and an osteon, are considered linear elastic and isotropic with material properties obtained by nanoindentation, taken from literature. The effect of using fracture analysis methods (cohesive segment approach versus linear elastic fracture mechanics approach), finite element type, and boundary conditions (traction, displacement, and mixed) on cortical bone crack initiation and propagation are studied. In this study cohesive segment damage evolution for a traction separation law based on energy and displacement is used. In addition, effects of the increment size and mesh density on analysis results are investigated. We find that both cohesive segment and linear elastic fracture mechanics approaches within the extended finite element method can effectively simulate cortical bone fracture. Mesh density and simulation increment size can influence analysis results when employing either approach, and using finer mesh and/or smaller increment size does not always provide more accurate results. Both approaches provide close but not identical results, and crack propagation speed is found to be slower when using the cohesive segment approach. Also, using reduced integration elements along with the cohesive segment approach decreases crack propagation speed compared with using full integration elements. Copyright © 2016 John Wiley & Sons, Ltd.

Advanced Methodologies for Fracture Analysis and Damage Tolerant Evaluation

The objective of the paper is to present the advanced methodologies for fracture analysis and damage tolerant evaluation of metallic structural components for efficient and safe design of structural systems meeting the functional criteria. An efficient and novel Numerically Integrated-Modified Virtual Crack Closure Integral (NI-MVCCI) technique has been demonstrated for 4-noded bilinear, 8-noded (regular & quarter-point), 9-noded Lagrangian and 12-noded cubic isoparametric family of finite elements. Another advanced numerical method, Extended Finite Element Method (XFEM) for fracture analysis of cracked stiffened panels has been discussed. Methodologies for crack growth and remaining life assessment of structural components under constant and variable amplitude loading have been presented. Brief description on residual strength evaluation has been provided. Numerical studies on fracture analysis to compute Strain Energy Release Rate (SERR), G and stress intensity factor (SIF) and remaining life assessment and residual strength evaluation have been conducted and the results are compared with the respective analytical/experimental results.

Edge-based smoothed extended finite element method for dynamic fracture analysis

In this paper, the edge-based smoothed extended finite element method (ES-XFEM) is applied to the dynamic fracture analysis of two-dimensional elastic solids. The dynamic stress intensity factor (DSIF) is deduced from J-integral with the train smoothing method. With the deduced DSIF, the implementation of numerical integration and sub-smoothing regions are numerically verified in dynamic fracture behaviors of linear elastic solids. The analysis shows that ES-XFEM is an efficient numerical approach to simulate the dynamic fracture problems.

The impact velocity and bone fracture pattern: Forensic perspective

Studies on bone-energy interaction are meager and revealed only a general correlation between the fracture pattern and the mechanism of the insult.This study has two objectives, to establish a usable fracture analysis method and to reveal the association between the energy of the force and the fracture pattern. Dynatup Model POE 2000 (Instron Co.) low energy pendulum impact machine was utilized to apply impact loading on fresh pig femoral bones (n=30). The bone clamp shaft was adjusted to position the bone for three-point bending with additional bone compression. Three different velocities of the forced applied were carried out. On average, the number, length and the curviness of the fracture lines created under moderate and high-energy impact is significantly higher compared to a low-energy impact. Most fractures lines were located on the impacted aspect in bones subjected to moderate- and high-velocity impact. Four oblique-radial fracture lines running from the point of impact creating a double butterfly pattern were found in bones subjected to moderate and high-velocity impact. Only “false” wedge-shaped (butterfly) fragments were found in the current study. Our results suggest an association between fracture pattern and the velocity of the impact.

An extended element free Galerkin method for fracture analysis of functionally graded materials

ABSTRACTAn extended element free Galerkin method (XEFGM) has been adopted for fracture analysis of functionally graded materials (FGMs). Orthotropic enrichments functions are used along with the sub-triangle technique for enhancing the Gauss quadrature accuracy near the crack, and the incompatible interaction integral method is employed to calculate the stress intensity factors. Numerical simulations have proved that XEFGM provides more accurate results by less number of nodes (DOFs) in comparison with the unenriched EFGM and other conventional methods for several FGM problems with different crack locations and loadings. The results have been compared with the reference results, showing the reliability, stability, and efficiency of present XEFGM.Received 9 June 2014 Accepted 17 September 2014.

An effective fracture analysis method based on the virtual crack closure-integral technique implemented in CS-FEM

In this work, the virtual crack closure integral technique (VCCT) is formulated in the framework of cell-based smoothed finite element (CS-FEM) for evaluating stress intensity factors and for modeling the crack propagation in solids. In the present CS-FEM, the strain smoothing technique is operated over the smoothing domains which are constructed based on elements, and each element is further subdivided into several smoothing cells. The smoothed strain is then obtained by a boundary integral along the boundaries of the smoothing cells. Only shape function itself is involved in computing the strains and no derivatives of the shape functions or coordinate transformation is required for the computation of the discretized stiffness matrix, and thus ideal for fracture mechanics problems to evaluate the stress intensity factors, we utilize the one-step-analysis approach of the VCCT based on the assumption that an infinitesimal perturbation of crack-tip location shall not significantly affect the stress/displacement field. The significant feature of the present CS-FEM method equipped with VCCT is that it requires no domain integration in the analysis of fracture mechanics problems. Several numerical examples are presented to validate the effectiveness of the present method. It uses only the information for displacement openings behind the crack-tip and the nodal forces at the crack-tip for stress intensity factor evaluation. The comparison study has shown that is as accuracy as the FEM-Q4 that need domain integrations for both stiffness matrix computation and interaction integral methods for stress intensity factor evaluation. The present method is further used to successfully predict the crack growth trajectory with excellent agreement between numerical results and the experimental observations.

Stochastic fracture analysis of cracked structures with random field property using the scaled boundary finite element method

This paper presents a stochastic fracture analysis method for random non-homogenous cracked structures using the scaled boundary finite element method (SBFEM). The analyzed cracked domain is divided into polygon-based sub-domains such that the material property of each sub-domain can be modeled differently in the SBFEM. The spatial variability of the material property is represented as random field which is then incorporated directly into the coefficient matrices of the SBFEM. The stochastic global stiffness matrix and the stochastic equilibrium equation of the SBFEM through which the stochastic structural responses can be successfully calculated are further formulated. The stochastic stress intensity factors (SIFs) considering the spatial variability of the material property are then directly extracted from the stress solution of the cracked polygon. Numerical examples are given to demonstrate the validity of the proposed method and investigate the effect of the spatial distribution of the material property on the SIFs.

Applicability of VCCT in mode I loading of yielding adhesively bonded joints—a case study

Virtual Crack Closure Technique (VCCT) is a fracture analysis method that is typically utilised when plastic dissipation does not exist. This paper studies the applicability of VCCT for crack growth analyses of an adhesively bonded joint with a ductile adhesive and self-similar crack growth. Analyses were performed for a Double Cantilever Beam (DCB) specimen with epoxy adhesive. Reference data for the analysis case existed. The precrack cycle of the DCB test was first analysed assuming linear elastic behaviour of the adhesive and by using the measured average fracture energy as a critical value. The computed force–displacement curve was noted to match well with the experimental data. In the next step, a nonlinear analysis was performed by using a linear elastic – ideally plastic material model for the adhesive and by selecting the critical energy release rate value so that the computed force–displacement curve fit the experimental and linear analysis data. The approach allowed for extracting plastic dissipation from the measured fracture energy to obtain an estimate for the critical energy release rate. The nonlinear analysis results were further studied using the Energy Derivate Technique (EDT) as a post-processing tool. The EDT analysis results confirmed that plastic dissipation remains at a constant level for the entire crack propagation phase of the precrack cycle analysis.