Crack Growth Algorithm Research Articles

Fatigue crack propagation direction under different loading conditions using MTS and MSS criteria

Fatigue Crack Growth plays a major role on structural integrity. When mixed mode fatigue crack propagation is introduced by complex geometry or loading conditions, numerical methods are essential for fatigue life determination. This paper explores the differences between two crack propagation models. Using an automatic fatigue crack growth algorithm and the finite element method, crack propagation on CTS and four-point bending specimens was simulated. Both specimens allow for pure mode I, mixed mode and pure mode II loading conditions. According to the maximum tangential stress criteria, fatigue crack propagation occurs along the direction where tangential stress is maximized. Comparing crack propagation results with literature, it was possible to conclude that this criterion can be used under pure mode I or mixed mode loading conditions. The maximum tangential stress criterion was also compared to the maximum shear stress criterion, where crack propagation occurs along the direction that maximizes shear stress. Crack propagation directions between these criteria were compared and it was possible to conclude that the maximum shear stress criterion should be used for pure mode II loading conditions. Overall, this methodology allows for fatigue crack growth simulations under complex loading conditions.

Structural fatigue investigation of transverse surface crack growth in rail steels and thermite welds subjected to in-plane and out-of-plane loading

Abstract This study investigates the structural fatigue crack growth behavior of observed transverse surface cracks in rail steel and thermite weld subjected to in-plane and out-of-plane loading. Stress Intensity Factor (SIFs) solutions were derived from finite element model analysis for transverse surface cracks located at five different crack initiation locations in the cross-section of rail steel and thermite weld. The SIFs were presented by the conventional geometry factor Y and weld magnification factor M k solutions for rail steel and thermite weld. Fracture toughness and fatigue crack growth rate tests were conducted to determine the mechanical properties of thermite weld materials and are compared with reported data for rail steels (R260 and R350HT). Fatigue crack growth prediction algorithm was developed using the coupled root mean square integration approach and was compared with the conventional uncoupled two-degree of freedom approach for semi-elliptical surface crack growth in the depth and surface directions respectively. The fatigue crack growth algorithm and propagation life prediction provide valuable observations on the crack shape evolution. It proves that out-of-plane bending loading is a more significant failure mode as compared to in-plane bending loading for thermite weld joints at curve tracks. Fatigue crack propagation results provide fatigue stress range-life curves for weld-toe surface cracks initiated at the head-to-web region of thermite welded joint structure.

A finite element-based adaptive energy response function method for 2D curvilinear progressive fracture

An adaptive arbitrary-order curvilinear progressive 2D crack growth algorithm is presented. The method is automated such that the full crack path from inception to failure is computed with multiple finite element analyses. During each simulation step, a hypercomplex finite element method (ZFEM) program computes arbitrary order derivatives of strain energy with respect to self-similar and perpendicular crack extensions. These derivatives are used to construct a family of surrogate models as trial functions, each of which is a Taylor series function of strain energy versus crack growth direction. An adaptive algorithm automatically selects the trial function that most accurately models the existing crack path to extrapolate a forward progressing curvilinear crack path. The length of each crack growth increment is limited to maintain the advancing path and its consequential strain energy increase within desired tolerances. Numerical examples up to sixth order are presented and compared against experiments. The high-order simulations complete the crack growth analysis with fewer, longer progressive fracture steps than traditional first-order simulations of similar accuracy.

An algorithm for fatigue crack growth applied to mixed and biaxial mode loadings

Abstract Fatigue is still one of the main concerns when dealing with mechanical components failure. While it is fundamental to experimentally determine the fatigue material behavior using standard specimens, testing large and complex component geometries can be complicated. In these cases, the Finite Element Method can be a cost-effective solution but developing fatigue crack growth models is still a complicated task. In order to solve this problem, an algorithm for automatic crack propagation was developed. Using three different modules, the algorithm can generate a complex Finite Element Method model including a fatigue crack; solve this model considering complex loading conditions, by applying the superposition method; and calculate the fatigue crack propagation rate, using it to update the original model. In order to benchmark this solution two different problems were analyzed, a modified compact tension specimen and a cruciform specimen. By modifying the compact tension specimen hole location and simulating an initial crack, it was possible to understand how mixed mode conditions influence the fatigue crack path. Different load ratios and initial crack directions on the cruciform specimen were analyzed. Increasing the load ratio will increase the crack deflecting angle. The obtain solutions were compared with experimental results, showing good agreement. Therefore the developed algorithm can be used to predict the fatigue crack growth behavior on complex geometries and when different types of loads are applied to the component.

A Fluid-Solid-Magnetic Coupling Algorithm of Internal Crack Growth in the Weld of Oil and Gas Pipelines

In order to characterize the dynamic process of the crack growth in the weld of oil and gas pipelines, a mathematical model of fluid-solid-magnetic multifield coupling was constructed in this paper. Based on this model, the bidirectional fluid-solid coupling and unidirectional magnetic structure coupling caused by the weld deformation were achieved by dynamic application of the fluid permeation pressure, calculating the internal crack growth in the pipe weld, reconstructing the computational grid near the internal crack, and discussing the characteristics of the magnetic leakage field in the process of the internal crack growth in pipe weld. Thus, a fluid-solid-magnetic coupling algorithm for the internal crack growth in pipe welds considering fluid permeation pressure is established. According to the characteristics of the internal crack opening distance, internal crack growth length, crack tip energy release rate, peak values of magnetic induction intensity level, and vertical component, the process of the internal crack growth is measured. The results show that the fluid osmotic pressure accelerates the process of the internal crack growth and this algorithm can solve the problem of the characterization and evaluation of crack growth in pipe welds under fluid-solid-magnetic coupling action.

An Integral Formulation of Two‐Parameter Fatigue Crack Growth Model

A two‐parameter fatigue crack growth algorithm in integral form is proposed, which can describe the continuous crack growth process over the time period. In this model, the fatigue crack propagation behavior is governed by the temporal crack‐tip state including the current applied load and the physical condition due to the previous load sequence. The plasticity‐induced crack closure, left by the historical loading sequence, controls the following fatigue crack growth behavior and typically leads to the interaction effects. In the proposed method, a modified crack closure model deriving from the local plastic deformation is employed to account for this load memory effect. In general, this model can simulate the fatigue crack growth under variable amplitude loading. Additionally, this model is established on the physical state of crack tip in the small spatial and temporal scale, and it is used to evaluate the macroscopic crack propagation and fatigue life under irregular tension‐tension loading. A special superimposed loading case is discussed to demonstrate the advantage of the proposed model, while the traditional two‐parameter approach is not proper functional. Moreover, the typical various load spectra are also employed to validate the method. Good agreements are observed.

Simulating fracture propagation in brittle materials using a meshless approach

In the present work, a meshless method is combined with a crack growth algorithm, considering a linear elastic model to simulate the propagation of cracks in brittle materials. The proposed methodology is automatic, which means that it does not require the user intervention. In this study, the meshless method used is the Natural Neighbour Radial Point Interpolation Method (NNRPIM), an efficient discrete numeric method. Being a truly meshless method, the NNRPIM only requires an unstructured nodal distribution to fully discretize the problem domain. With the coordinates of the nodes, the NNRPIM formulation is autonomously capable: to define the nodal connectivity; to build the background integration mesh; and to construct the shape functions. The crack propagation algorithm here proposed simulates the crack growth by displacing iteratively the crack tip. Updating the crack tip location requires a local remeshing, which does not represent a numeric difficulty for the NNRPIM. The updated position of the crack tip depends on the estimated stress field in the vicinity of the crack tip. Thus, in each iteration, the stress field in the vicinity of the crack tip is estimated, and then, the direction of the crack propagation is calculated using the maximum circumferential stress criterion.

The Natural Neighbor Radial Point Interpolation Method in Computational Fracture Mechanics: A 2D Preliminary Study

In this work, the natural neighbor radial point interpolation method (NNRPIM) is extended to the numeric analysis of crack propagation problems. Here, the advanced discretization meshless technique is combined with a linear elastic crack growth algorithm. The algorithm simulates the crack propagation by displacing iteratively the crack tip, which consequently requires a local remeshing. In each iteration, it is estimated the stress state in the crack tip and afterwards the direction of the crack propagation is obtained considering the maximum circumferential stress criterion.The required local remeshing does not represent a numeric difficulty for the NNRPIM. The main advantage of the NNRPIM is its capability to fully discretize the problem domain using only an unstructured nodal distribution. Being a truly meshless method, the NNRPIM is able to define autonomously the nodal connectivity and the background integration mesh.The classic NNRPIM formulation permits to enforce the nodal connectivity by means of two kind of influence-cells: first degree influence-cells or second degree influence-cells. This work investigates the influence of the nodal connectivity on the simulated crack propagation path. Thus, demanding benchmark crack propagation examples are studied and the obtained results are compared with reference solutions available in the literature.

Stochastic extended finite element implementation for fracture analysis of laminated composite plate with a central crack

Abstract A stochastic extended finite element method (SXFEM), developed previously by the first two authors, has been extended for the fracture analysis along with reliability analysis of the central cracked laminated composite plate subjected to uni-axial tension with random system properties. The implemented SXFEM approach is based on the M -integral interaction combined with second-order perturbation technique (SOPT) and independent Monte Carlo simulation (MCS) is performed for the evaluation of statistics of mixed mode stress intensity factors (MMSIFs). The random system properties such as material properties, crack length, crack angle, lamination angle, and uni-axial loading, are assumed as input uncorrelated Gaussian random variables. The effect of the different crack angles, crack lengths, lamination angles, and loading on the statistics of MMSIF in terms of mean, standard deviation (SD), probability density function (PDF) and safety factor of cracked laminated composite plate is examined along with the reliability analysis. The effect of crack propagation and its direction along with its effect on the MMSIFs is carried out through global tracking crack growth algorithm. The results obtained by present approach, are compared with an analytical solution and results available in various literature.

Crack Growth Resistance Characteristics Determination Algorithm for Creep-fatigue Interaction

Abstract A creep-fatigue crack growth rate interpretation method and algorithm and test results are described. The algorithm allows to obtain a crack growth rate diagram in terms of creep stress intensity factor. The proposed algorithm is realized on steel compact tension specimens (12Х1MF). Crack growth rate was determined on standard compact specimens under temperature 550°C. The waveforms for the loading and unloading portions were trapezoidal, and the loading/unloading times were held constant – 5 s. A hold time of predetermined duration, 60 s, was superimposed on the trapezoidal waveforms at maximum load. The potential drop and the unloading compliance methods were used to monitor crack length during the creep–fatigue tests. For the experimental crack paths in tested specimens the governing parameter for the 3D-fields of the stresses and strains at the crack tip in the form of In-integral was calculated by finite element analysis along crack front. The governing parameter of the stress-strain fields in form of I n -integral was used as the foundation of the creep stress intensity factor. The creep stress intensity factor approach was applied to the fatigue crack growth. The numerical and experimental results demonstrated that K cr is the most effective crack tip parameter in correlating the creep–fatigue crack growth rates in power plant materials and can be used reliably for practical purposes.

Quarter elliptical crack growth using three dimensional finite element method and crack closure technique

Shape evolution of a quarter-elliptical crack emanating from a hole is studied. Three dimensional elastic-plastic finite element analysis of the fatigue crack closure was considered and the stress intensity factor was calculated based on the duplicated elastic model at each crack tip node. The crack front node was advanced proportional to the imposed effective stress intensity factor. Remeshing was applied at each step of the crack growth and solution mapping algorithm was considered. Crack growth retardation at free surfaces was successfully observed. A MATLAB-ABAQUS interference code was developed for the first time to perform crack growth on the basis of crack closure. Simulation results indicated that crack shape is sensitive to the remeshing strategy. Predictions based on the proposed models were in good agreement with Carlson’s experiments results.

Reliability assessment of high cycle fatigue under variable amplitude loading: Review and solutions

In fatigue reliability assessments, the random load process is commonly represented by its marginal distribution (load spectrum) only. However, as shown in this paper, the correlation characteristics of the load process can have a strong influence on the fatigue reliability and should be accounted for. The paper reviews the modeling of random fatigue crack growth under variable amplitude loading for reliability analysis. Solutions for fatigue crack growth evaluation at different levels of detailing are described and a fatigue crack growth and failure evaluation algorithm, based on a discretization of the random stress process, is presented. As an alternative, a mean approximation is described. Finally, effective computational methods for assessing the fatigue reliability under variable amplitude loading are introduced and applied exemplarily to a case study. The solutions are based on the first-order reliability method FORM and the subset simulation. Using a Markov process model of the loads, the influence of different types of service histories is investigated, by varying the correlation length of the stress cycle process. The results show that the correlation length of the load process has significant influence on the resulting reliability; the resulting probability of failure can vary up to several orders of magnitude for the same marginal probability distribution of stress amplitudes. Based on the results of the case study, the influences of the stress process correlation and of the adopted failure criteria on the reliability are discussed. The mean approximation and the random variable model of the random load process are demonstrated to be applicable under specific conditions.

Fatigue Crack Growth and Coalescence Algorithm Starting from Multiple Surface Cracks

Fatigue crack growth and propagation analysis in welded joints have to deal with the complexity of modeling multiple weld toe surface cracks originating from weld toes. Fitness-For-Service (FFS) assessments for weld toe surface cracks employ a fracture mechanics and Paris Law approach to predict the fatigue crack propagation life of a semi-elliptical surface crack (SESC) to failure. A fatigue crack growth algorithm for assessing multiple surface crack growth, coalescence and propagation life was initially validated with previuously report crack growth data for a fillet shoulder specimen. Next a parametric study for single, double, and triple SESCs located along the weld toe line of a fillet weld was investigated with three starting crack depth sizes (0.1mm, 0.5mm, 1.0mm) coupled with three different crack aspect ratios (a/c = 1.0, a/c = 0.5 and 0.25) giving a total of 27 cases studied.

A New Progressive Curvilinear Strain Energy-Based Crack Growth Modeling Algorithm Using Multicomplex Variable Finite Elements

Arbitrary, non-planar progressive fracture analysis is of critical importance to the integrity of structures. While significant progress has been made in the last 25 years, there are still technical issues regarding computational expense, robustness, and accuracy. Based upon the recent significant enhancements available through the use of multicomplex finite element methods, a new high-order progressive strain energy based progressive crack growth algorithm is proposed.

扩展有限元法在准脆性混凝土结构断裂中的数值模拟

扩展有限元法是基于自适应离散裂纹方法进行的混凝土裂纹扩展仿真模拟。并采用接触边界模型，接触边界模型包括正向位移和切向位移，允许通过界面进行剪切应力的传递，在扩展有限元法的框架中，对一个有凝聚力的裂纹扩展的延伸方向的研究有不同准则。通过两个例子，对最大周向应力理论，最大能量释放率理论和最小势能理论的实验数据进行了比较并形成规范。采用XFEM方法在一般加载模式I型和混合型加载条件下进行的混凝土断裂扩展数值模拟的灵活性和有效性已经得到了证实。 In this paper, the extended finite element method (XFEM) is used for a discrete crack simulation of concrete using an adaptive crack growth algorithm. An interface model is proposed which includes normal and tangential displacements and allows the transfer of shear stresses through the interface. Different criteria for predicting the direction of the extension of a cohesive crack are conducted in the framework of the XFEM. On the basis of two examples, a comparison between the maximum circumferential stress criterion, the maximum energy release rate and the minimum potential energy criterion with experimental data has been carried out. The considered numerical simulations have confirmed the flexibility and effectiveness of the XFEM for the modelling of crack growth under general mode I and mixed-mode loading conditions.

Numerical Analysis of Hypervelocity Impact Problems with Large Deformations, High Strain Rates and Spall Fractures

In the study, a software program named “SUPER CE/SE” is developed for the simulation of hypervelocity impact problems with large deformations, high strain rates and spall fractures. In the software program, an Eulerian method consisting of an improved CE/SE (Space-time Conservation Element and Solution Element Method) scheme is used. A void growth model which takes the Bauschinger Effect (BE) into account and a newly proposed front tracking method are adopted in the simulation. The formation and propagation of a crack is described by a newly developed automatic crack growth algorithm. Numerical simulation of spall fracture in a plate when impacted by a spherical projectile at a velocity of 6.0 km/s is carried out. The numerical results are in qualitative agreement with the corresponding experimental data. It turns out that the BE has obvious influence on the length of the crack and better agreement with the experiment is obtained when the BE is considered. It is also validated that the newly proposed front tracking method is feasible and reliable for representing the cracks in the problems with large deformation and high strain rates. According to those research results, it is proved that the software program SUPER CE/SE is robust and effective in the simulation of hypervelocity impact problems.

Variable amplitude fatigue crack growth in a mild steel for railway axles: Experiments and predictive models

Railway axles, though designed for infinite life, are subject to failure due to various types of surface damage (ballast hits, corrosion) that might occur during their very long service life (30 years or 10 7 km). This problem is dealt with by regular axle examinations in the form of nondestructive testing inspections, whose periodicity is calculated on the basis of the propagation lifetime of a given initial defect. The key point is therefore a reliable estimation of propagation lifetime under service loads. This paper discusses the application of predictive crack growth algorithms to the propagations of cracks in A1N steel axles. In particular, constant amplitude crack propagation tests on small-scale and “companion specimens” were carried out together with experiments on full-scale axles. Variable amplitude tests on companion specimens were performed and the results were then analysed using a simple “no-interaction” algorithm. Then, variable amplitude tests on companion specimens and the analysis of results with a simple “no-interaction” algorithm and the Strip-Yield model were dealt with. The results showed a negligible load-interaction effect on “companion specimens” and a significant retardation on full-scale axles. The consequences resulting from the application of predictive models to a full-scale axle under service spectrum were then analysed.

Numerical Simulation of Quasi-Brittle Fracture in Concrete Structures with Extended Finite Element Method

In this paper, the extended finite element method (XFEM) is used for a discrete crack simulation of concrete using an adaptive crack growth algorithm. An interface model is proposed which includes normal and tangential displacements and allows the transfer of shear stresses through the interface. Different criteria for predicting the direction of the extension of a cohesive crack are conducted in the framework of the XFEM. On the basis of two examples, a comparison between the maximum circumferential stress criterion, the maximum energy release rate and the minimum potential energy criterion with experimental data has been carried out. The considered numerical simulations have confirmed the flexibility and effectiveness of the XFEM for the modelling of crack growth under general mode I and mixed-mode loading conditions.

Meshfree simulations of plugging failures in high-speed impacts

A meshfree method and (the related) a specified crack growth algorithm are used to simulate plugging fracture during high-speed impacts. In particular, we are simulating ballistic penetration of a steel plate, which is a ductile failure process involving projectile and target collision, contact, and subsequent projectile penetration companied plugging fracture inside steel plate. We have developed and implemented an explicit meshfree Galerkin formulation, which is capable of capturing ductile fractures during finite inelastic deformation. The developed meshfree computational procedure has the following features: (1) it has an effective dynamic meshfree contact algorithm that is suitable for high-speed impact; (2) it can deal with thermal–mechanical couplings, and the stability of coupled thermal–mechanical motion is guaranteed by an adiabatic split algorithm that integrates adiabatic heating and heat diffusion separately; (3) it has an automatic crack growth algorithm that can simulate the whole lifespan of crack growth including crack nucleation, propagation and arrest; (4) to compute the rate-dependent material responses, a modified forward Euler tangent algorithm is adopted in constitutive update process for the nonlinear thermal–mechanical inelastic constitutive relation that takes into account damage evolution. Results of a numerical simulation of plugging fracture due to projectile/target impact are presented, and they compare well with experimental data.

An approximation for the cyclic state of stress ahead of cracks and its implications under fatigue crack growth

Abstract Numerical methods are mostly used in the field of fatigue to derive the stress intensity factor (SIF) or J -integral solutions to be employed in damage tolerance analysis of cracked components. In this frame, simple assumptions about material properties are taken into account. More refined approaches try to describe the plasticity-induced crack closure in order to account for retardation effects under variable amplitude loading. In these approaches, the cyclic plasticity is used and cyclic finite element analyses are carried out. In the present work, a novel strategy is presented for the calculation of the relevant parameters to the fatigue crack growth, based on the evaluation of local field parameters ( J -integral, T -stress) and cyclic material properties. It is demonstrated that, in case of mild steels and under the assumption of a stress ratio R = −1, the global constraint factor α g widely employed in fatigue crack growth algorithms such as the strip-yield model, can be calculated in a closed-form on the basis of the expression of the crack-tip fields. Moreover, α g provides a reasonable explanation of the fatigue crack growth behaviour of the A1N steel for different geometrical and loading configurations. Further investigations carried out on different medium and high strength steel grades show that the plastic radius ahead of small and long cracks at their fatigue limits can be considered as a constant for the material.