Simulate Fatigue Crack Research Articles

Numerical Simulation of Fatigue Crack Growth and Fracture in Welded Joints Using XFEM-A Review of Case Studies.

Numerical simulation of fatigue crack growth in welded joints is not well represented in the literature, especially from the point of view of material heterogeneity in a welded joint. Thus, several case studies are presented here, including some focusing on fracture, presented by two case studies of mismatched high-strength low-alloyed (HSLA) steel welded joints, with cracks in the heat affected zone (HAZ) or in weld metal (WM). For fatigue crack growth, the extended finite element method FEM (XFEM) was used, built in ABAQUS and ANSYS R19.2, as presented by four case studies, two of them without modelling different properties of the welded joint (WJ). In the first one, fatigue crack growth (FCG) in integral (welded) wing spar was simulated by XFEM to show that its path is partly along welded joints and provides a significantly longer fatigue life than riveted spars of the same geometry. In the second one, an integral skin-stringer panel, produced by means of laser beam welding (LBW), was analysed by XFEM in its usual form with stringers and additional welded clips. It was shown that the effect of the welded joint is not significant. In the remaining two papers, different zones in welded joints (base metal-BM, WM, and HAZ) were represented by different coefficients of the Paris law to simulate different resistances to FCG in the two cases; one welded joint was made of high-strength low-alloyed steel (P460NL1) and the other one of armour steel (Protac 500). Since neither ABAQUS nor ANSYS provide an option for defining different fatigue properties in different zones of the WJ, an innovative procedure was introduced and applied to simulate fatigue crack growth through different zones of the WJ and evaluate fatigue life more precisely than if the WJ is treated as a homogeneous material.

An improved phase-field model for fatigue crack growth considering constraint effects

The phase field model is a promising method for simulating fatigue crack growth (FCG) behavior. However, the conventional phase field (PF) model may not adequately account for constraint effects, where fracture toughness is affected by geometries. Therefore, stress triaxiality is incorporated into the PF model by modifying the fracture energy release rates to consider constraint effects. The model successfully simulates the FCG behavior of different geometries, such as CT, SENB, and MT specimens, as well as the mixed-mode FCG behavior of CTS specimens and other complex geometries. All simulations agree well with experiments, proving that our model is capable to capture the constraint effects in FCG behavior. These findings indicate that stress triaxiality is important to capture the constraint effects.

A crystal plasticity phase-field model for microstructure sensitive fatigue crack growth in a superalloy

In this work, a dislocation density-based crystal plasticity phase-field model (CP-PFM) is developed to simulate fatigue crack growth in nickel-based superalloys. Through normalization validation, the plastic dissipation work and crystallographic work are shown to be consistent with the fatigue indicator factors (FIPs), cumulative equivalent plastic strain and cumulative shear strain, and the two energies are computed as the main driving forces of the phase field. Both driving force models are able to obtain fatigue crack growth in close approximation to the experimental rate. However, the model with crystallographic work as the main driving force obtains crack growth paths that are in better agreement with electron backscattering pattern (EBSD) observations, which is attributed to its greater ability to characterize the microstructural susceptibility of fatigue crack growth. Specifically, the model is able to capture the tendency of cracks to crack along the close-packed planes and the hindering effect of grains with large misorientation angles on fatigue crack growth, which together contribute to the curved morphology of fatigue cracks. The combination of large grains or grains with small misorientation angles favors persistent slip band (PSB) formation and leads to softening of the crack tip, which results in lower fatigue crack growth rates.

Effect of shot peening equivalent impact force on fatigue crack growth behavior and fatigue life prediction of train brake discs

Brake discs, vital rail components, are subjected to intense friction and thermal cycling during braking, leading to surface cracking and fatigue failure. To address these issues, a novel equivalent impact force model for shot peening is proposed in this paper, with the aim of measuring the efficacy of shot peening and predicting the fatigue crack propagation life of brake discs with the assistance of an enhanced SSO algorithm. A finite element model of a cast steel brake disc simulated fatigue crack propagation under sinusoidal cyclic loading. The validity of the multiple projectile random impact model was experimentally confirmed by introducing a residual stress field into the disc surface using equivalent impact forces of 0.3, 0.4 and 0.5 MPa. This stress field was incorporated into the cyclic fatigue crack propagation model and compared with the FCGR results. Shot peening produced a compressive residual stress layer which increased in thickness with increasing impact force. The fatigue crack propagation rate was highly sensitive to the equivalent impact force, decreasing between 0.3 and 0.4 MPa and increasing from 0.4 to 0.5 MPa. Optimal crack propagation inhibition was at 0.4 MPa, which increased fatigue life by 457 % compared to non-peened discs. The improved SSO algorithm also achieved a 6 % increase in prediction accuracy.

Phase field modelling of elastic-plastic fatigue fracture of oil and gas pipeline

This paper established a fatigue fracture phase-field model (PFM) to evaluate fatigue damage evolution and crack propagation in oil and gas pipeline. To address inaccuracies in damage evolution, a threshold of the elastic-plastic fracture energy was introduced in the proposed PFM. Using the finite element method, the PFM was applied to simulate fatigue crack growth. Results from compact tension (CT) specimen of the X56 gas pipeline steel demonstrated that the da/dN-ΔK curve from the current PFM, accounting for plasticity, aligned more closely with experimental results than the elastic PFM. The fatigue crack propagation and fatigue life of the X80 gas pipeline with different defects of the same depth were also analyzed. The results indicated that triangular defects significantly impacted the fatigue life of the X80 gas pipeline. Finally, a model of X60 pipeline with various initial defects was developed to validate the effectiveness of the proposed PFM for full-scale pipeline fatigue fracture by comparing it to experimental a-N curves. The simulation results indicated that the distance and angle between two initial defects in the pipeline significantly influenced the propagation of fatigue cracks and the pipeline’s service life. These findings of this paper can serve as a reference for estimating the service life of gas and oil pipelines.

Optimizing structural topology design through consideration of fatigue crack propagation

This paper presents an advanced approach for structural topology optimization by incorporating fatigue crack propagation analysis. The extended finite element method (X-FEM) is employed to model initial crack propagation, while the Paris model serves as the basis for simulating fatigue crack growth. The proposed methodology aims to optimize the structural design by minimizing compliance while considering volume and fatigue constraints. The proposed method employs the developed bi-directional evolutionary structural optimization (BESO) algorithm. The accuracy of the proposed technique is validated through the solution of benchmark problem and is further demonstrated in its effectiveness and robustness by examining several numerical examples. The optimization process considers various crack conditions, including the absence of cracks, horizontal and vertical cracks of different lengths. The optimized topologies obtained through the proposed algorithm clearly demonstrate the impact of crack presence, crack direction, and crack length on the material distribution. Furthermore, the convergence histories of the objective function, represented by mean compliance, highlight the influence of crack length on the stiffness and converged compliance of the structure. The results demonstrate its ability to adapt the material distribution based on fatigue cracks propagation conditions and achieve optimal topologies that balance structural integrity and performance.

Assessment of Crack Growth and Fatigue Life of an Axial Fan Blade Based on a Co-Simulation Approach

Abstract This paper presents static and dynamic stress analyses of an axial fan blade, which were carried out under real-life centrifugal and aerodynamic loading conditions using the Abaqus software. The location of the crack was identified on the pressure side of the blade at the conjunction between the blade and the blade root. It reveals a high agreement between the predicted location of stress distribution and the real origin of the crack location. Furthermore, a fracture mechanics criterion was adopted to simulate fatigue crack growth. This was performed using a fracture analysis FRANC3D code for three-dimensional problems. As a result, the calculated stress intensity factors (SIFs) were presented for the first steps, and the fatigue life of the fan blade was evaluated using the Forman de Koning model at different stress ratios.

Crack Detection in Bearing Plate of Prestressed Anchorage Using Electromechanical Impedance Technique: A Numerical Investigation

The bearing plate is an important part of a tendon–anchorage subsystem; however, its function and safety can be compromised by factors such as fatigue and corrosion. This paper explores the feasibility of the electromechanical impedance (EMI) technique for fatigue crack detection in the bearing plate of a prestressed anchorage. Firstly, the theory of the EMI technique is presented. Next, a well-established prestressed anchorage in the literature is selected as the target structure. Thirdly, a 3D finite element model of the PZT transducer–target anchorage subsystem is simulated, consisting of a concrete segment, a steel anchor head, and a steel bearing plate instrumented with a PZT transducer. The prestress load is applied to the anchorage via the anchor head. The EMI response of the target structure is numerically obtained under different simulated fatigue cracks in the bearing plate using the linear impedance analysis in the frequency domain. Finally, the resulting EMI response was quantified using two damage metrics: root-mean-square deviation and correlation coefficient deviation. These metrics are then compared with a threshold to identify the presence of cracks in the bearing plate. The results show that the simulated cracks in the bearing plate are successfully detected by tracking the shifts in the damage metrics. The numerical investigation demonstrates the potential of the EMI technique as a non-destructive testing method for assessing the structural integrity of prestressed structures.

Fatigue Repair of Cracked Steel Plates Using Small-Patch Ultrahigh-Modulus CFRP Governed by Bond Failure

This study evaluates the effectiveness of externally bonded small-patch ultrahigh-modulus (UHM) carbon fiber–reinforced polymer (CFRP) plates of 460 GPa modulus in extending fatigue life and slowing crack propagation in steel plates with simulated fatigue cracks. The study investigates a range of very short bond lengths for applications where bonding space may be limited or accessibility restricted, together with the effect of single- versus double-sided application, on fatigue performance. It also compares short UHM CFRP plates with similar length normal modulus (NM) (165 GPa) CFRP plates with regard to extending fatigue life and reducing stress concentration at the crack tip. Distributed fiber-optic sensors (DFOS) and digital-image correlation (DIC) are used to capture the full strain field and track crack growth. Results showed that fatigue life was increased by up to 2.0 and 2.34 times for single- and double-sided UHM CFRP repairs. As bond length increased from 25 to 100 mm, fatigue life increased from 1.36 to 2.0. UHM CFRP more effectively reduced stress concentration at the crack tip, by 60% compared with 37% for NM CFRP, indicating that it has the potential for superior fatigue life gains, relative to NM CFRP if the necessary bond length to prevent or delay debonding is provided. As debonding failure governed in this study, NM CFRP plates achieved comparable fatigue life extension. DIC tracking of crack growth matched the traditional “beach marking” technique with less than 6% difference.

Numerical calculation of [formula omitted] to simulate fatigue crack growth under large scale viscoplastic deformations

Crack propagation under low cycle fatigue and thermomechanical fatigue is characterized by high plastic and creep strains that extend over large regions around the crack, so that concepts of linear-elastic fracture mechanics cannot be applied. In these cases, the cyclic crack tip opening displacement ΔCTOD is a promising loading parameter to quantify crack growth. In this work, suitable definitions and Finite Element techniques are investigated and compared for an accurate calculation of ΔCTOD under cyclic mechanical and/or thermal loading. A viscoplastic temperature dependent material model of Chaboche-type is used along with large strain settings, specified for the austenitic cast iron Ni-resist. Extensive two-dimensional analyses of Single Edge Notch Tension specimens revealed that collapsed special crack tip elements are superior compared with commonly used regular quadrilateral 8-node elements. At the same level of accuracy of ΔCTOD, they require an about ten times coarser mesh and show less sensitivity w.r.t. element size for both stationary and propagating cracks. In order to simulate fatigue crack growth, an efficient, fully automated FE-technique is developed for an incremental crack propagation by successive remeshing, whereby the deformations and internal state variables are mapped from the old mesh onto the new one. Recommendations are made regarding important numerical control parameters like optimal size of crack tip elements, length of crack growth increment in relation to plastic zone size and ΔCTOD value.

A peridynamic approach to simulating fatigue crack propagation in composite materials.

In this article, a numerical tool is proposed in the framework of bond-based peridynamics to simulate fatigue crack propagation in composite materials and structures. The cycle-dependent damage-cumulative model derived from Peerlings' law and applied to a bilinear constitutive law is used to evaluate the fatigue degradation of the bond stiffness. Several benchmark cases are studied to validate the proposed approach. Finally, static and fatigue crack propagations in composite systems with single or multi-inclusions are simulated to illustrate the capabilities and characteristics of the developed approach. This article is part of the theme issue 'Ageing and durability of composite materials'.

The influence of microstructure on short fatigue crack growth rates in Zircaloy-4: Crystal plasticity modelling and experiment

Rates of fatigue crack growth in Zircaloy-4 are highly microstructurally sensitive and dependent upon texture. Crystal plasticity finite element modelling with the eXtended Finite Element Method and a stored energy density fracture criterion are used to simulate crack propagation in single crystals and polycrystalline microstructures for comparison with experimental crack growth rate data. Results demonstrate that growth rate fluctuations at microstructural features are driven primarily by elastic anisotropy and yield stress mismatch. Additionally, reduced rate of growth in soft hexagonal close packed grains (relative to the remote loading direction) can be linked with crack path tortuosity, which is shown to be controlled by the cyclic development of an in-plane shear back stress. Most importantly, stored energy density is shown to accurately capture major microstructure-driven differences in crack growth rate. Comparison of simulated fatigue crack growth rates with experimental data enables estimation of the critical stored energy density for crack propagation in Zircaloy-4 to be 250 J/m2.

Residual stress influence on fatigue crack propagation of CFRP strengthened welded joints

In order to take into account the influence of welding residual stresses on fatigue crack growth, thermo-elastic-plastic finite element models of steel cruciform welded joints were developed by the ABAQUS software. The distribution and magnitude of longitudinal and transverse residual stresses were obtained in consideration of different welding currents and speeds. Uniaxial tensile fatigue tests on cracked cruciform joints strengthened with carbon fiber reinforced polymer were conducted. The coupling actions of residual stresses and fatigue loads were applied to subsequently simulate fatigue crack propagation via using the Extended Finite Element Method. Good agreement between the simulated and theoretical transverse residual stresses at the weld toe along the plate thickness direction verifies the accuracy of numerical results. The welding speed has a greater impact on residual stresses than the welding current. The stiffness ratio of carbon fiber reinforced polymer and steel plate is larger, and a better reinforcement effect will be achieved. Whether specimens repaired or not, it significantly decreases the fatigue life of cracked welded joints in the presence of residual stresses, but the fatigue crack growth trajectory is almost unchanged.

Damage identification for nonlinear fatigue crack of cantilever beam under harmonic excitation

In order to accurately simulate structural fatigue crack damage, the non-linear contact model was selected and verified to be suitable for the fatigue crack simulation in cantilever beam. The influence of damage severity and location on harmonic vibration responses were revealed. Moreover, the damage identification indexes based on harmonic excitation response were constructed, and the effectiveness used to identify fatigue crack damage was validated. The results reveal that contact model is effective in simulating fatigue crack and sensitive to nonlinear fatigue crack through the comparative analysis of harmonic vibration response of intact structure and damaged one. For the vibration responses of beam with different damage severities and locations, the greater the damage severity is, and the closer the damage location is to the fixed end, the more obvious the non-linear vibration characteristics presents. Two damage indicators including distortion value of phase spectrum (h∆) and proportion of super/sub-harmonic amplitudes (Dd) are applied, which can effectively characterize the change of fatigue crack with different damage location and severity. Furthermore, contact model presents stronger non-linear information compared with bilinear model, which is more suitable for fatigue damage simulation.

An inverse method to reconstruct crack-tip cohesive zone laws for fatigue by numerical field projection

Cohesive zone failure models are widely used to simulate fatigue crack propagation under cyclic loadings, but the functional form of such phenomenological models does not have a strong micromechanical basis. While numerical techniques have been developed to extract the crack-tip cohesive zone law for monotonic fracture from experimental strain information, elucidating the unloading-reloading hysteresis representing accumulated and irreversible damage under fatigue cycling is still challenging. Here, we introduce a novel field projection method (FPM) to reconstruct the cohesive zone laws for steady-state fatigue crack growth from elastic strain field information at various loading and unloading stages within a single steady-state fatigue cycle. The method is based on the Maxwell-Betti’s reciprocal theorem, which considers the material response to be linear elastic during loading and unloading, albeit with a reciprocity gap to account for the inhomogeneous residual elastic strain accumulated at the end of each fatigue cycle. Through numerical experiments, we demonstrate that this FPM is capable of accurately extracting the crack-tip cohesive tractions and separations, along with the elusive unloading-reloading hysteresis, which constitute the cohesive zone law for fatigue crack growth. We discuss the errors and uncertainties associated with this inverse approach.

Investigation of crack path near cold expanded hole

In a structure, holes are concentrators of stresses. When the structure is subjected to a cyclic load, the holes should be carefully designed to prevent the occurrence of fatigue cracks. The now well-accepted technique of cold expanding holes mitigates the effect of stress concentration by introducing an area of compressive stress near the hole surface. The resulting compressive residual stress is balanced by an area of tensile stress, which is detrimental from a fatigue standpoint. In this study, we do not focus on the formation of fatigue cracks at the surface of the cold expanded hole, but investigate the path of the fatigue crack approaching a region with such a hole. Using a special algorithm to simulate fatigue crack growth, we show that the cold expanded hole attracts the growing crack. This insight sheds new light on the beneficial effects of cold expanded holes.

Development of higher-order displacement discontinuity method to simulate fatigue crack growth in brittle materials

The 2D displacement discontinuity method (2D. DDM) is an indirect boundary element technique in which the stresses and displacements are expressed through normal and shear displacement discontinuities. The governing equations of fatigue crack growth are mostly power equations that depend on the stress intensity factor range. Accurate calculation of displacement discontinuity has importance in fatigue analysis of DDM. Therefore, in this study, DDM is extended using cubic variations of displacement discontinuity for ordinary and crack tip elements. This method also uses an appropriate algorithm based on the linear elastic fracture mechanics (LEFM) principle to analyze crack growth under cyclic fatigue loading. This process is accomplished by assuming the homogeneity of brittle material and the small plastic zone of the crack tip compared to the crack dimension. The condition of applying constant and stationary variable amplitude loading was provided. The algorithm is designed based on an iterative process, and the new incremental elements gradually are added to the crack tip until the failure criteria are reached; The size of these elements at each step of growth depends on the crack growth rate in the previous step. Therefore, the fatigue modeling of the structures with multiple cracks and different growth rates is enabled. Virtual crack criteria were employed to improve the accuracy and speed of analysis, which involves crack tips with a slower growth rate. Moreover, the direction of crack propagation is evaluated using the maximum circumferential stress criterion. Examples of simple and multi-fractured structures under constant and variable amplitude load are considered. Comparison of results with literature data shows excellent agreement with high accuracy.

An analytical-based approach for simulating fatigue crack growth in round bars

An analytical-based approach for simulating fatigue crack growth in round bars

2D fracture mechanics analysis of HFMI treatment effects on the fatigue behaviour of structural steel welds

The purpose of this paper is to present the extension of a previously developed strain-based fracture mechanics (SBFM) model from one to two dimensions for simulating fatigue crack growth in steel arc welds. The one-dimensional (1D) SBFM model is first briefly reviewed. Steps for extending it to simulate 2D growth of a semi-elliptical surface crack in a weld are then described. An application of the new model is lastly presented, which consists of analysing the behaviour of structural steel weld specimens from a previously published fatigue test program, in which the fatigue performance of weld specimens was enhanced by high frequency mechanical impact (HFMI) treatment. In this application, the effect of the treatment-induced compressive residual stress on the crack shape is simulated, and it is shown how the extended 2D SBFM model can be used to establish probabilistic design stress-life (S-N) curves for various loading conditions.

A cohesive XFEM model for simulating fatigue crack growth under various load conditions

This study presents calibration and validation of a cohesive extended finite element model for fatigue crack propagation in ductile materials. The approach relies on a separation between plasticity around the crack tip and fatigue crack growth at the crack tip such that the influence of plasticity on fatigue driving forces is predicted. This implies that characterization of crack growth requires effective Paris parameters. It is shown that the calibrated model can capture fatigue crack growth behaviour in ductile materials for in-phase and out-of-phase biaxial fatigue loading as well as in-phase biaxial loading with an overload.