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Paris' power law is commonly used to describe transverse thermal cracking propagation in asphalt concrete (AC) pavements. In its most common format, it relates the rate of change in the crack length per cycle to changes in either the stress intensity factor K or the energy release. The parameters defining this relationship for ACs can be obtained using the Texas cyclic Overlay Test (OTR). This paper describes two numerical approaches for simulating the OTR using the extended finite element method (XFEM). The first uses the direct low-cyclic fatigue (LCF) approach and the second uses the virtual crack closure technique (VCCT). Comparisons of the model predictions to laboratory OTR measurements for six mixtures suggest that the XFEM model coupled with VCCT is better suited for simulating the OTR. The model output includes the crack length and the energy release rate ERR (i.e. ${\rm \Delta }J_R$ Δ J R ) as cracks propagate. This data was used to fit the modified Paris' law parameters ${A}^{\prime}$ A ′ and ${n}^{\prime}$ n ′ as a function ${\rm \Delta }J_R$ Δ J R . Subsequently, the traditional A and n Paris' power law parameters were fitted by estimating the corresponding ΔK. Using this model, it was possible to efficiently estimate the AC cracking parameters using as input only the tensile modulus and the critical ERR. [ABSTRACT FROM AUTHOR]

• Mode II fatigue crack growth is characterized at the steel-to-composite interface. • Displacement and load controlled ENF and 4ENF test methods are compared. • Novel method is proposed to determine crack growth by shear strains from DIC. • Friction and geometrical non-linearity is considered by finite element models. In this paper, mode II fatigue crack growth properties of the composite-to-steel interface are characterised through different test configurations, namely ENF and 4ENF tests. Different loading types including force control and displacement control methods are compared. An innovative shear strain based method is proposed for monitoring the mode II crack growth at the bi-material interface through Digital Image Correlation (DIC). A 3D finite element model with Virtual Crack Closure Technique (VCCT) is built and used for obtaining the strain energy release rate (SERR) to investigate the effect of geometrical nonlinearity, friction at the interface and steel yielding, as well as to verify the mode mixity. The results show that the standard 3-point bending ENF specimen can be unstable under force control and sweeps narrow SERR range by a single test under displacement control. The 4-point bending 4ENF test shows stable crack propagation and clear SERR developing trend. More pronounced geometrical nonlinearity and friction effect exist for 4ENF test which can be considered when interpreting the Paris curves by a nonlinear finite element model. [ABSTRACT FROM AUTHOR]

• The CRTS Ⅲ slab track model with prefabricated cracks is established by extended finite element method. • The stress intensity factors (SIFs) at the tips of cracks on the track slab under train load are solved. • The effects of the crack length and depth on the SIFs of three types of cracks are discussed. • The variations of crack growth rate calculated by Paris' semi-empirical during service are analyzed. Microcracks may occur in Chinese Railway Track System type III (CRTS III) ballastless track slabs during service, and it is necessary to investigate their potential propagation under train load, which could lead to slab deterioration and affect the durability of the track structure. In this paper, based on the fracture mechanics theory, the stress intensity factors (SIFs) at the tips of transverse crack, longitudinal crack and vertical crack on the CRTS III track slabs under train load are solved by the extended finite element method (XFEM) in Abaqus software. The changes of SIFs at the crack tips during the passage of the train are analyzed, and the effects of the crack length and depth on the SIFs of the three types of cracks are discussed under train load. Crack growth rate is calculated using Paris' semi-empirical law to estimate slab life. The results show that the train load contributes to the propagation of transverse and vertical cracks in the vertical direction and inhibits the longitudinal cracks. When the middle of the sixth vehicle is above the crack, the SIFs at the tips of the crack reach their maximum values. The SIF of vertical cracks exceeds the fracture toughness at a certain depth. The fatigue load cycles calculated by Paris' semi-empirical law suggest that maintenance will not be required due to insufficient propagation under train load during service. [ABSTRACT FROM AUTHOR]

• The Johnson-cook damage model, traction separation and Paris law equations are incorporated in the XFEM model to predict the formation of spalling, crack propagation and fatigue life for the spur gear respectively. • 3D finite element analysis was performed to determine the fatigue life of the spur gear using with and without spall using different crack lengths and backup ratio. • Numerical modeling of spur gear developed and results showed that the increase in backup ratio from 0.3 to 3.3, an exponential increase in the fatigue life with and without spall. • The spalling depth obtained on the spur gears with backup ratio 0.3, 0.5, 1.0, and 3.3 are within the range of 20–100 μm. Spur gears are most commonly used to transmit power, and speed variation from one shaft to another shaft. Spalling more frequently occurs surface fault in the gears and sometimes it causes severe damage to the gear tooth. This paper focuses on the effect of spalling on the fatigue life of spur gear. The simulation study is conducted in two parts. In the first part, the Johnson-Cook Damage model is used for the spall generation on the tooth surface. After that, the spalling results are imported as input into the crack initiation /crack propagation model and calculated the rate of crack growth of fatigue crack is based on Paris law implemented in user-defined subroutine Abaqus software. User-defined subroutine code is also validated with the comparison of the numerical and experimental results available in the literature. Cracks with different initial lengths are placed in the deeper cavities of spalling and the crack propagation analysis is conducted using XFEM. The study is conducted for four different backup ratios with cracks of three different initial lengths. The fatigue crack growth life of spur gears is investigated using different crack lengths and backup ratios. Further, a comparison has been made between the fatigue life of a spur having a spalling fault with the fatigue life of spur gear that does not have spalling fault present on its surface. It has also been found in this study that spur gear having cracks originating from the spall region have a less fatigue life as compared to the spur gear without spalling. With the increase in backup ratio from 0.3 to 3.3, an exponential increase in fatigue life is observed. However, the fatigue life of spur gear without the presence of spalling fault has higher fatigue for all backup ratios. [ABSTRACT FROM AUTHOR]

Highlights • A fatigue analysis of a type of fillet welded joint is presented. • Four welded joint series for evaluating the fatigue performance were produced. • The fatigue behaviour combines an experimental campaign and numerical analysis. • In this fatigue analysis two main numerical tools – FEM and XFEM – were used. • Fatigue predictions based on crack initiation and propagation phases were made. Abstract This paper presents a fatigue analysis of a type of fillet welded joint representative of one main joint of the steel box girder of the Alcácer do Sal railway bridge. From previous studies, it was found that the welded joint between the box girder diagonal and the central hanger gusset is one of the most stressed details of the bridge. This welded joint was not fully manufactured according to current construction procedures, as regards the fillet weld end configuration. In order to assess the fatigue behaviour of such welded joint, the present study combines an experimental campaign and numerical analysis. A total of four welded joint series were produced in order to allow the comparison of the fatigue performance of similar type of welded joint of the Alcácer do Sal bridge with welded joints produced according to existing recommendations, such as EC3. Since scale-down specimens were considered, two different thicknesses were included in this study for each joint configuration, to allow the verification of any thickness effect. Concerning the numerical analyses, two main numerical tools were used: the standard Finite Element Method (FEM) with ANSYS and the eXtended Finite Element Method (XFEM) with ABAQUS. Fatigue life predictions were performed including both fatigue crack initiation and fatigue crack propagation phases. The number of cycles to initiate a fatigue crack was computed using local notch strain-life approaches, and the number of cycles for fatigue crack propagation was computed by integrating the Paris fatigue crack growth law with stress intensity factors computed with ANSYS (virtual crack closure technique) and ABAQUS (contour integral method, 3D XFEM model). Experimental tests demonstrated little influence of fillet weld end geometry on fatigue behaviour of welded joints and plate thickness effects were also reduced as also confirmed by the similar fatigue crack propagation rates. Both numerical simulations provided very accurate predictions of the experimental S-N curves, however the XFEM modelling opens new possibilities for mix-mode fatigue crack propagation simulations. [ABSTRACT FROM AUTHOR]

Corrosion and crack defects often exist at the same time in pipelines. The interaction impact between these defects could potentially affect the growth of the fatigue crack. In this paper, a crack propagation method is proposed for pipelines with interacting corrosion and crack defects. The finite element models are built to obtain the Stress Intensity Factors (SIFs) for fatigue crack. SIF interaction impact ratio is introduced to describe the interaction effect of corrosion on fatigue crack. Two approaches based on extreme gradient boosting (XGBoost) are proposed in this paper to predict the SIF interaction impact ratio at the deepest point of the crack defect for pipelines with interacting corrosion and crack defects. Crack size, corrosion size and the axial distance between these two defects are the factors that have an impact on the growth of the fatigue crack, and so they are considered as the input of XGBoost models. Based on the synthetic samples from finite element modeling, it has been proved that the proposed approaches can effectively predict the SIF interaction impact ratio with relatively high accuracy. The crack propagation models are built based on the proposed XGBoost models, Paris' law and corrosion growth model. Sensitivity analyses regarding corrosion initial depth and axial distance between defects are performed. The proposed method can support pipeline integrity management by linking the crack propagation model with corrosion size, crack size and the axial distance. The problem of how the interaction between corrosion and crack defects impacts crack defect growth is investigated. [ABSTRACT FROM AUTHOR]

This paper presents a novel method to construct a plate element enveloping crack tip in the extended finite element method (XFEM) frame for crack growth simulation. The element enveloping a crack tip is sub-partitioned into several triangular quarter-point singular elements around the crack tip. The sub-triangular singular element cut by the crack, like the ordinary elements separated by the crack in other regions, is enriched with the Heaviside function. As the sub-partition scheme retains the original boundary of the crack tip element and the discontinuity of the entire crack is reproduced by the Heaviside enrichment, the proposed method can model cracks independent of the background mesh. Using the singular elements instead of analytical asymptotic functions employed in the conventional XFEM allows to reflect the crack tip singularity for more fracture scenarios. The additional nodes created by the sub-partition act as internal nodes of the crack tip element, thus the classical and enriched degrees of freedom (DOFs) on these nodes can be eliminated through an element-level condensation, which could reduce the condition number of the system matrix. Crack growth in plates and shells under fatigue loading is described by using Paris' law. The performance of the proposed method is investigated through stress intensity factors (SIFs) prediction, convergence study, and fatigue crack growth analysis in several examples of cracked plates and cylindrical shells. • A novel method for constructing crack tip element is developed based on XFEM. • The crack tip element is sub-partitioned into several triangular singular elements. • The sub-triangular singular element cut by crack is enriched with the Heaviside function. • All the DOFs on the sub-partition-induced nodes are eliminated through element-level condensation. • Several examples including fatigue crack growth in cylindrical shells show effectiveness and accuracy of the method. [ABSTRACT FROM AUTHOR]

• Biaxial fatigue crack growth is modeled using CFEM with the cyclic damage. • Effects of loading conditions on fatigue crack growth are explored systematically. • Both transverse stress and tensile overload reduce fatigue crack growth rate. • Fatigue crack growth is faster under low-high loading than high-low one. • The mechanisms of fatigue crack growth are elaborated by plastic dissipation. During the operation of proton exchange membrane in fuel cells, cyclic mechanical loads are introduced due to the humidity cycles. The resulting fatigue crack is known to be the main source for its mechanical degradation. In this paper, we use a relation between damage evolution of the cohesive elements and Paris law to simulate the biaxial fatigue crack growth. The effects of various loading conditions are investigated. The predicted crack growth is in a good agreement with experimental studies. Both the transverse stress and the tensile overload have retardation effects. It is also found that the fatigue crack growth rate associated with a shorter pre-crack depends more on the load waveform. Moreover, fatigue crack grows faster under the low-high loading history than the high-low one. These simulation results have provided significant insights into the fatigue failure behavior of membranes during operation conditions and can help improve their durability. Image, graphical abstract [ABSTRACT FROM AUTHOR]

• Evaluate the SIF of surface cracked steel plate reinforced with FRP under tension by FEM. • The FE model is validated by a experimental study. • By the validated FE model and Paris' law, surface crack growth rate is quantitatively predicted. • Reveal the mechanism of FRP reinforcement on the surface crack growth. • Indicate the key influential parameters of FRP reinforcement on surface crack growth. In this paper, we analyse the surface crack growth in the Fibre-Reinforced Polymer (FRP) reinforced steel plates subjected to tension by means of the finite element (FE) method. Following the experimental study, a three-dimensional FE model is developed to evaluate the Stress Intensity Factor (SIF) of the surface crack, and the crack growth rate is calculated by using the Paris' law. Then the FE model is validated by the experimental results. Afterwards, on account of the validated FE model, a parametric study is developed in order to guide the optimization design of FRP reinforcement accounting for different reinforcing schemes and multiple influential parameters. The results indicate that the single-side FRP reinforcement on the cracked surface is the most efficient method, owing to the generated out-of-plane bending moment. In addition, the optimum bond length and number of layers are indicated. Besides, surface crack growth is sensitive to the influential parameters including aspect ratio of the surface crack and crack dimension, while less sensitive to the Carbon-FRP (CFRP) tensile modulus, and the adhesive thickness. The analysis is of instructive value to facilitate the application of FRP reinforcement on the surface cracked metallic structure repairing domain. [ABSTRACT FROM AUTHOR]

• PFEM based on 12-fold branch functions is first proposed for interfacial cracks. • Wachspress shape functions for arbitrary polygonal elements are exploited. • Fatigue crack growth analysis of interfacial edge crack in bi-materials is performed. • Excellent performance of proposed approach is confirmed via numerical investigations. The fatigue crack growth analysis of an interfacial cracked structure plays an essential role in the design process as well as the safety assessment for various engineering fields in real life. This paper proposes a novel and effective computational approach based on polygonal meshes for crack growth simulation of interfacial crack problems. Polygonal meshes are fully exploited to provide greater flexibility in mesh generation for complicated domains as well as obtain more accuracy in terms of the numerical results. The twelve crack tip enrichment functions to capture the near-tip oscillating singular field are first implemented for polygonal meshes to improve the obtained results. The Wachspress shape function is applied for arbitrary polygonal elements. The strong discontinuities e.g. crack face, crack tip can be modeled, respectively, via Heaviside and asymptotic crack tip enrichment functions while the material interface discontinuities are defined by signed distance functions. The stress intensity factors (SIFs) of the interfacial crack problems can obtain by using the domain based interaction integral approach while the fatigue life is estimated via the Paris law. The accuracy and efficiency of the present approach are demonstrated through several numerical investigations regarding the crack growth problems in both homogeneous materials and bi-materials. The results which are generated from the proposed approach are compared with other earlier ones as well as the conventional XFEM solutions. [ABSTRACT FROM AUTHOR]

In this paper, interactions of double parallel cracks were studied by performing experiments and numerical simulations. Fatigue crack propagation tests were carried out to measure crack growth rates in the specimens with double parallel cracks or a single crack. Finite element method was adopted to calculate stress intensity factors at the crack tips. Results show that the double parallel cracks at different positions present a shielding effect or enhancement effect on crack growth rates and stress intensity factors. When the double parallel cracks are offset, crack interactions mostly behave as enhancement effects. Empirical formulas were obtained to calculate the stress intensity factor at the "dangerous" crack tip of the double parallel cracks. By modifying the material parameters in Paris equation of the single crack, the double parallel cracks are simplified into a single crack with the same crack growth rates. [ABSTRACT FROM AUTHOR]

• Corresponding relationship between heat diffusion equation and seepage diffusion equation. • An analogy method to compute fatigue fracture in steam turbine by using ABAQUS. • An analysis process for turboset to estimate the remaining thermal-fatigue life. • To supply a structural assessment and lifetime prediction for pressure vessels. 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. [ABSTRACT FROM AUTHOR]