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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]

• 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]

High fatigue load, which exists widely in steel building structures, likely leads to brittle failure at the joints, supports, and so on. This can lead to the partial or total damage of the structure and even to cause the collapse of the whole structure. This article aims to provide a method to simulate high-cycle crack propagation in tubular joints, which is one of the most common types occurring in steel structures. Firstly, sixteen T-shaped tubular joint models under different load conditions and initial crack dimensions were built through the coordinate mapping method. Secondly, based on the extended finite element method (XFEM), an algorithm was developed by combining the secondary development in Abaqus and a quasistatic simulation method to simulate high-cycle crack growth in tubular joints under a constant amplitude. The results of the simulations were compared with experimental data. The study found that the surface stress calculated from the tubular joint models using the coordinate mapping method was close to the experimental data. Through the comparison of the crack propagation rate and the crack growth process between the simulation and experiment results, the simulation method was validated. When a crack penetrated the tube wall, the difference in the load cycles between the simulations and the experiment was 9.5%. The initial crack dimension had an impact on the crack propagation, with the decrease in the a/c and KII generally becoming the dominant factor with respect to the crack growth, while the fatigue life of the joints tended to increase. [ABSTRACT FROM AUTHOR]

• The surface corrosion methods affect the fatigue cracking modes of Inconel 617 at high temperature. • The small fatigue cracking behavior at 700 °C was estimated based on grain-scale strain field. • Small grains will lead to greater crack deflection and increase crack propagation resistance. • The small fatigue crack propagation path was predicted by CPFEM-XFEM model. • A prediction model of small fatigue crack growth rate and lifetime of Inconel 617 was proposed. Small fatigue crack initiation and propagation behavior of Inconel 617 was studied by in-situ SEM observation, electron back-scattered diffraction (EBSD), digital image correlation (DIC), crystal plasticity finite element method (CPFEM) and extended finite element method (XFEM) in this paper. The experimental results indicated that different surface corrosion methods used to display surface microstructure will affect the small fatigue cracking mode of Inconel 617. The local micro-scale strain field of Inconel 617 near the notch and crack tip was quantitatively measured by a new grain scale DIC method. The CPFEM-XFEM simulation model of small fatigue crack initiation and propagation characteristics of Inconel 617 was established. A new framework for small fatigue crack path and lifetime prediction at the polycrystalline scale was constructed, which includes the influences of slip system and grain boundary on small fatigue crack initiation and growth rate. [ABSTRACT FROM AUTHOR]