Method For Crack Propagation Research Articles

Coupling of Complex Function Theory and Finite Element Method for Crack Propagation Through Energetic Formulation: Conformal Mapping Approach and Reduction to a Riemann–Hilbert Problem

In this paper we present a theoretical background for a coupled analytical–numerical approach to model a crack propagation process in two-dimensional bounded domains. The goal of the coupled analytical–numerical approach is to obtain the correct solution behaviour near the crack tip by help of the analytical solution constructed by using tools of complex function theory and couple it continuously with the finite element solution in the region far from the singularity. In this way, crack propagation could be modelled without using remeshing. Possible directions of crack growth can be calculated through the minimization of the total energy composed of the potential energy and the dissipated energy based on the energy release rate. Within this setting, an analytical solution of a mixed boundary value problem based on complex analysis and conformal mapping techniques is presented in a circular region containing an arbitrary crack path. More precisely, the linear elastic problem is transformed into a Riemann–Hilbert problem in the unit disk for holomorphic functions. Utilising advantages of the analytical solution in the region near the crack tip, the total energy could be evaluated within short computation times for various crack kink angles and lengths leading to a potentially efficient way of computing the minimization procedure. To this end, the paper presents a general strategy of the new coupled approach for crack propagation modelling. Additionally, we also discuss obstacles in the way of practical realisation of this strategy.

Simulating quasi-static crack propagation by coupled peridynamics least square minimization with finite element method

In this work, we present an innovative simulation method for quasi-static crack propagation in mixed-mode, within a new framework of coupled peridynamics least square minimization and finite element method (PDLSM–FEM). As the inertia effect is neglected for quasi-static problems, the governing equations for PDLSM–FEM can be solved implicitly without iterations. Displacements and stresses from PDLSM–FEM are used to compute the interaction integral, an extended version of the J-integral. The stress intensity factors (SIFs) are derived from the interaction integral and used in the maximum circumferential tensile stress failure criterion to predict the onset of crack propagation and the direction of propagation. New contributions in this work include the following: (1) developing a new framework for coupling PDLSM and FEM; (2) pioneering a quasi-static method for simulating crack propagation in peridynamics; (3) developing an element-based approach for selecting the interaction integral contour; and (4) proposing and implementing an innovative method for handling peridynamic bond breakage and crack growth. Quasi-static crack propagation simulation in this work provides a computationally efficient way to find the shape of the crack, and the current PDLSM–FEM model is straightforward and can be easily introduced into commercial finite element codes. Three numerical examples are carried out, and the results show that the proposed method evaluates SIFs accurately and captures crack growth as expected.

A field-enriched finite element method for crack propagation in fiber-reinforced composite lamina without remeshing

A field-enriched finite element method for crack propagation in fiber-reinforced composite lamina without remeshing is proposed. In the field-enriched finite element method, the propagation and evolution of cracks are controlled by fracture criteria, and the physical location of cracks and the influence on the whole model are realized by the field variables enriched at the nodes. Then, field-enriched finite element method is used to investigate the influence of fiber orientation on the constant stiffness and variable stiffness composite lamina under different loading conditions and configurations. The numerical results obtained by the field-enriched finite element method are in good agreement with those obtained by experimental observation and other numerical methods. Moreover, the crack propagation path is roughly along the fiber orientation direction, which means that for the fiber reinforced composite lamina, the crack propagation path is mainly dominated by the fiber orientation rather than the configuration and loading conditions of the specimen. Compared with the phase field method, the calculation efficiency of the proposed method is higher. Compared with the extended finite element method, the proposed method is easier to characterize cracks. Therefore, the field-enriched finite element method is a very promising method for simulating the fracture behavior of fiber-reinforced composite lamina.

Fatigue crack separation and merging simulation using the smoothed particle hydrodynamics

The present paper proposes a new computational method for the fatigue crack propagation in a metallic structure using the smoothed particle hydrodynamics (SPH). First, we discuss how to model the crack front line with C0 continuous elements called chained crack front lines, which resemble those that were experimentally observed. In the second, the detailed algorithm for the chained crack front line is proposed and implemented into the fatigue crack propagation analysis program based on the SPH named as SPH-Fatigue. Third, the present method is applied to the fatigue crack propagation problems with crack separation and merging phenomena, such as the crack propagation passing through a hole or passing through a slit in a T-joint structure. The calculated results show an excellent agreement with time-dependent crack shapes experimentally obtained. We conclude that the idea of chained crack front line discussed in this paper is useful to estimate the time dependent crack shape of real materials and structures.

A non-intrusive stochastic phase field method for crack propagation in functionally graded materials

This work presents a framework to study the quasi-static brittle fracture in functionally graded materials with random material properties using a non-intrusive phase field method. The model accounts for variation in the material and fracture properties. Further, the effective Young’s modulus, the gradient index and the fracture properties of the constituent materials are considered as random input variables. The output randomness is represented by polynomial chaos expansion. Two-dimensional benchmark numerical examples are presented to demonstrate the benefits of the non-intrusive approach to study fracture characteristics. The influence of the randomness in the material properties on the peak load carrying capacity is considered as a primary quantity of interest in this study. A systematic parametric study is carried out to bring out the sensitivity of the input randomness on the stochastic output response using Sobol indices.

Carbon Fiber Reinforced Polymer Composites Doped with Graphene Oxide in Light of Spectroscopic Studies.

Carbon fiber reinforced polymer composites are a dynamically developing group of lightweight composites for applications in the automotive, wind energy, aerospace, and sports sectors. Interfacial connection is the weakest place in these materials. In this study, an attempt was made to improve adhesion between carbon fiber and epoxy resin. For this purpose, nanoparticles of graphene oxide were added to a polymer matrix. The results of the three-point bend test showed that the strength of samples with added graphene oxide increased. Improvement of adhesion between components, reduction of the pull-out effect and change in the method of crack propagation were observed. An attempt was made to explain this effect using spectroscopic methods, both IR and Raman. On the basis of the obtained results, chemical bonds between the individual components of the composites were identified.

On the Topology Update of the Numerical Manifold Method for Multiple Crack Propagation

Crack initiation and propagation are the two key issues of concern in the geotechnical engineering. In this study, the numerical manifold method (NMM) is applied to simulate crack propagation and the topology update of the NMM for multiple crack propagation is studied. The crack-tip asymptotic interpolation function is incorporated into the NMM to increase the accuracy of the crack-tip stress field. In addition, the Mohr-Coulomb criterion with tensile cut off is adopted to be the crack propagation criterion to judge the direction of crack initiation and propagation. Then a crack tip searching method is developed to automatically update the position of the crack tips. The inapplicability of the original loop search method in the NMM is also illustrated and a novel loop search method based on manifold elements is developed for physical loop updating. Moreover, methods for the manifold element updating and physical cover updating are provided. Based on the above study, the developed numerical method is capable to simulate multiple crack propagation. At last, typical rock rupture problems are numerically simulated to manifest the effectiveness of the developed numerical method.

A four-way enhanced numerical manifold method for crack propagation and failure analysis of rock slopes

A four-way enhanced numerical manifold method (NMM) is proposed in order to simulate crack propagation in rock media and progressive failure of jointed rock slopes. Specifically, the original NMM is improved in the following four aspects: (1) An “enriched local approximation” is employed to characterize singularity and discontinuity of the displacement/stress fields near the crack tip. (2) A “modified generalized Duffy transformation” is proposed to improve the accuracy of numerical integration associated with the 1/r and 1/r singularities. (3) A “critical length cracking criterion” is introduced to determine propagation length and direction for both tensile-shear and compressive-shear cracks in rock mass. (4) A “cone-complementary-based contact formulation” is incorporated to resolve the cohesive/frictional contact phenomena between discontinuous interfaces more accurately. Some examples demonstrate the performance and application prospect of the presented NMM in stability and failure analysis of the jointed rock slopes.

Study on prediction method of crack propagation in absorber weld by experiment and simulation

As an important equipment for purifying crude oil and natural gas in energy industry, absorber is subjected to harsh working environment of high stress and severe corrosion. Especially, weld is the weak region of the absorber, which faces significant risk of crack propagation due to residual stress caused by the welding process, working pressure and temperature. Meanwhile, crack propagation in absorbers with high pressure, high temperature and toxic media can often cause disastrous consequences. Therefore, to solve this problem, a systematic method considering welding, heat treatment and working process is presented in this paper to predict crack propagation completely in the weld. In the case, based on actual conditions, a finite element model (FEM) of welding process considering transient heat transfer and heat radiation for residual stress field analysis is established to obtain the far-field stress for cracks. Then, the detailed analysis of stress field and stress intensity factor (KI) under the obtained far-field stress at the crack tip is carried out through the method of integrating the strain energy density (SED) in the crack tip region. Finally, experiments of fracture toughness (KIC) of undamaged weld specimens and post-corrosion weld samples are carried out to compare with KI obtained by FEM and evaluate the safety of existing cracks. The method presented in this paper is a complete system that can provide a universal technological basis for crack propagation prediction and safety assessment of pressure vessel.

Evaluation Method for Cohesive Crack Propagation in Fragile Locations of RCC Dam Using XFEM

Roller compacted concrete (RCC) dams own a large number of horizontal construction layers, which can easily lead to weak joints among layers and generate interlayer joints with different scales to reduce the dam bearing capacity. In this study, extended finite element method (XFEM) is used to simulate crack propagation, the finite element description is first taken on the strong discontinuity. Subsequently, the displacement function of the crack-tip in the quadrilateral element and the geometric determination method of the crack-tip strengthening region are established. Afterwards, the discrete form of the governing equation is derived and the XFEM increment discretization method of the cohesive crack with the crack-tip reinforcement is proposed using the virtual node method to represent the discontinuity of the fracture element. These methods are validated through simulating mixed-mode cracking of one-sided notched asymmetric four-point bending beam. Eventually, the proposed methods are applied to RCC gravity dam to study the development rule and propagation path of the interlayer joints, so as to evaluate the effect of different lengths of the interlayer joints on the dam structural performance. The estimated critical values of dam deformation are helpful to prevent the dam failure during long term operation.

Verification of a cohesive model‐based extended finite element method for ductile crack propagation

AbstractIn this study, an approach utilizing a conjunction of the extended finite element method (XFEM) and the Gurson‐Tvergaard‐Needleman (GTN) micromechanical damage model is proposed for predicting the ductile crack propagation of a mill‐annealed Ti‐6Al‐4V alloy. The cohesive model‐based XFEM approach is used to capture the continuous crack propagation process, and the GTN model is applied to describe the constitutive behaviour of the material. Simulations are conducted by using the standard finite element code ABAQUS following a Newton–Raphson algorithm solution with employing the user material subroutine of the GTN model. In comparison with the experimentalresults of the smooth, notched and cracked titanium specimens, this approach is shown to be an efficient method for simulating the ductile crack propagation process under different stress triaxialities.

A phase field numerical manifold method for crack propagation in quasi-brittle materials

In the present work, a phase field numerical manifold method (PFNMM) is proposed for crack growth in brittle materials. The advantages of the phase field method (PFM) in modeling crack initiation and crack branching, and those of the numerical manifold method (NMM) in discretizing the computational model are integrated together in the proposed numerical model. The proposed numerical model is very suitable for simulating multiple crack propagation problems. The implementation details of the proposed numerical model are well presented. Several benchmark examples are adopted to validate the proposed numerical approach. The results indicate that the crack propagation topologies and force-displacement curves obtained by the proposed numerical model are in good agreement with others, e.g. Miehe et al. (2010) and Molnar and Gravouil (2017) [3]. The convergence of numerical solution from the proposed numerical model is also investigated. The PFNMM deserves a further investigation.

Glass-cutting medical images via a mechanical image segmentation method based on crack propagation

Medical image segmentation is crucial in diagnosing and treating diseases, but automatic segmentation of complex images is very challenging. Here we present a method, called the crack propagation method (CPM), based on the principles of fracture mechanics. This unique method converts the image segmentation problem into a mechanical one, extracting the boundary information of the target area by tracing the crack propagation on a thin plate with grooves corresponding to the area edge. The greatest advantage of CPM is in segmenting images involving blurred or even discontinuous boundaries, a task difficult to achieve by existing auto-segmentation methods. The segmentation results for synthesized images and real medical images show that CPM has high accuracy in segmenting complex boundaries. With increasing demand for medical imaging in clinical practice and research, this method will show its unique potential.

A local-domain based phase field method for crack propagation

The phase field method transfers the crack surface area into a domain integral through a smeared damage parameter. As a result, the fracture energy release rate can be directly incorporated into the energy form without tracking of crack surface, and a minimization approach to optimize the crack shape becomes possible. This nonlocal damage approach requires a fine mesh discretization to capture the damage gradient in the smeared crack zone, which produces a significant degree of freedom problem to optimize over the entire domain. In this research, a local-domain based phase field method is proposed. This method considers only elements in critical regions for energy minimization, whose internal energy are dominant, thus significantly reducing the degree of freedom to be solved. A numerical verification is carried out to demonstrate the feasibility of this approach, and simulations are presented to verify the accuracy of the new method.

Extended Voronoi cell finite element method for multiple crack propagation in brittle materials

This paper introduces a new extended Voronoi cell finite-element method (X-VCFEM) for modelling the propagation of multiple cracks in brittle materials. The direction of the crack propagation is adaptively determined in terms of the maximum energy release rate near the crack tip, and we apply a remeshing strategy that a node at a last incremental crack tip in the crack advance process is replaced by a node pairs to realize the gradual crack propagation. In order to accurately capture crack-tip stress concentrations, some singular stress terms of Williams expansion in the vicinity of crack tips are introduced in the assumed stress hybrid formulation which also includes the polynomial terms and the reciprocal terms. Then several numerical examples are used to demonstrate the effectiveness and accuracy of X-VCFEM enriched by some singular stress terms of Williams expansion by comparing X-VCFEM results with those computed by the commercial finite element package ABAQUS or established results in the literature. At last, two numerical examples are given to simulate multiple crack propagation in brittle media. The effects of morphological distributions such as length, orientation and dispersion on the crack propagation are studied. It is obvious that the X-VCFEM has great advantage of analyzing large regions of the microstructure with multiple growing and interacting cracks.

Consistent element-free Galerkin method for three-dimensional crack propagation based on a phase-field model

Element-free Galerkin (EFG) method for three-dimensional phase-field model of cracks is described. Quadratic moving least-squares (MLS) approximation is constructed for both the phase field and the displacement. The quadratically consistent 4-point (QC4) integration scheme using background tetrahedral elements (cells) is employed to efficiently compute the domain integrals in weak forms. As cracks propagate, adaptive refinement of the approximation nodes around crack fronts is implemented with the use of background integration cells. The refinement is triggered by the maximum residual strain energy history. New approximation nodes are inserted at the midpoints of the element edges. Several benchmark examples are investigated. Numerical results show that three-dimensional crack propagation is successfully modeled by the proposed method and correct crack paths and load-displacement responses are obtained. Due to the implemented h-adaptivity, lots of approximation nodes are saved and the computational scale is significantly reduced. Improved accuracy of the proposed method in stress distribution and crack width is also demonstrated.

Numerical modeling of crack propagation with dynamic insertion of cohesive elements

One of the most challenging issues in computational fracture mechanics is the propagation of a crack through a finite element mesh for arbitrary crack paths. In this work, this problem is approached by means of an advanced remeshing technique that propagates a crack using cohesive elements. The crack direction is computed using the maximal energy release rate criterion which is implemented using finite elements and the Gθ method. The remeshing procedure used here is composed of two stages. In the first step, a conforming mesh is obtained in the computed crack direction, ensuring that edges are placed over the sought direction. In the second stage, cohesive elements are dynamically inserted at the conforming edges previously remeshed. The combination of this remeshing technique with dynamic insertion of cohesive elements, leads to a mesh-independent crack propagation method. The effects of different numerical and physical parameters regarding the crack path and fracture energy is investigated.

Development of analogy method for thermal-fatigue crack propagation in pressurized cylinder by using permeation diffusion-fracture model

Natural crack propagation analysis in thermal-fatigue fracture problem is a challenging problem. Reliable predictions for the crack path and residual live of structure provide essential information for the structural integrity assessment and repairment. Various conventional predictive fatigue models have been proposed to evaluate the remaining life, but most of them can’t build an explicit relation between damage degree and fatigue life. In recent years, the advanced techniques on crack propagation analyses were proposed, which were used to simulate the fatigue crack growth, but no coupling thermal-fracture function existed in the commercial finite element codes. Fortunately, the extended finite element method (XFEM) in ABAQUS has the coupling permeation diffusion-fracture model. In this paper, an analogy method from coupling permeation diffusion-fracture to coupling thermal-fatigue is proposed to compute fatigue fracture, which is applied for predicting the fatigue life in a specific steam turbine by directly using ABAQUS. Typical fatigue experiments by compact specimens of cast iron are carried out for the fatigue parameters measurement. By using analogy method and Paris’ Law, an entire analysis process for the turbine units is built to estimate the thermal-fatigue life. The simulation results predicting remaining life and analyzing fatigue crack growth for the pressurized cylinder are agreed well with the measured engineering data.

Comparative Study on the Fatigue Assessment Concepts for Horizontal Butt Welds of Wind Turbine Towers

ABSTRACTThis paper presents a comparative study on the fatigue life prediction of different fatigue assessment methods. The nominal stress concept, the local stress concept and a two‐stage‐model, which consists of the strain‐life approach and the crack propagation method are applied to compute the fatigue life of horizontal butt welds and to assess the methods capability to provide adequate prognosis of fatigue life of wind turbine towers. The comparative study shows the impact of weld imperfections on the fatigue life according to the local stress concept and the strain‐life approach. The later approach even considers the influence of actual geometry and imperfection on the total damage sum. The approach has a great potential to accurately predict the fatigue life of butt welds and notch details of wind turbine structures with precise manufacturing, sophisticated processes and high‐quality control.

Extended finite element method and anisotropic damage plasticity for modelling crack propagation in concrete

In this article, a new algorithm is developed for predicting crack initiation and growth direction in 3D solid concrete. The algorithm combines the anisotropic damage-plasticity model used for simulation of concrete material degradation (crack) and irreversible plastic deformation and the eXtended Finite Element Method (X-FEM). The Voyiadjis local anisotropic damage-plasticity model is expressed in a non-local form to prevent strain and damage localization in damaged points. Also, a new crack propagation direction criterion based on second order damage tensor of anisotropic damage, containing different material degradation components in different directions is proposed for 3D problems. Computational algorithms with an elastic predictor and plastic and damage corrector returning map are also developed. Finally, three numerical examples are solved and results of crack propagation paths predicted by the proposed algorithm are compared with available experimental data and those of other numerical simulations. It is shown that the results from the proposed method are in better agreement with experimental data compared to other reported numerical methods.