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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]

In this paper, Composite Repair System (CRS) is applied to repair the circumferential internal surface cracked steel pipes subjected to bending. The Stress Intensity Factor (SIF) is quantitatively analysed by means of numerical simulations, and the crack growth rate is predicted by using the Paris' law. First, the three-dimensional finite element (FE) model is developed, and its reliability of evaluating SIF of internal surface crack in CRS reinforced pipe is validated. Then based on the FE method and combined with Paris' law, a case study is deployed to predict the internal surface crack growth in steel pipes reinforced with CRS. The results show that CRS have significantly reduced the SIF of the internal surface crack and decrease the crack growth rate, while unchanging the variation trend of the crack aspect ratio. Afterwards, a parametric study is performed in order to guide the optimisation design of CRS reinforcement. [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 paper deals with an optimization problem related to axisymmetric membrane shells made of homogeneous, linear and isotropic materials and subject to a cyclic internal pressure. The optimization problem considers the possible crack growth in the shell as a structural constraint, which is accounted for by the well-known Paris law, and hence obeys the Linear Elastic Fracture Mechanics (LEFM) principles. The design variables are the meridian shape and the thickness distribution along the axis of the shell. After recalling the general background on the mechanics of thin-walled shells, the optimization problem is stated, formulated and solved in closed form by means of Pontryagin's Principle, showing two LEFM-based design criteria capable to help the designer in selecting the desired elastic performance through which the shell undergoes. It is shown that the derived optimal solutions are ellipsoids with variable thicknesses, whose distributions depend on the mass constraint and the applied pressure. Nevertheless, the optimal shapes guarantee the uniformity of either the meridian or the hoop stress, and such uniformity has been verified within a numerical example by an accurate finite element analysis. • The maximum volume problem for axisymmetric membrane shells is formulated. • The shells are subject to cyclic pressure and mass constraints. • The membrane theory of shells and Paris law are taken into consideration. • Optimal shapes are derived analytically by means of Pontryagin's Principle. • Two design criteria are given for uniform meridian and hoop membrane stresses. • The finite element method confirms the theoretical stress behavior. [ABSTRACT FROM AUTHOR]

• Implementation of slow growth design strategy for bonded joints/patch repairs for primary aircraft structures, consistent with FAA guidance. • Static and fatigue testing of a novel specimen configuration to identify the entire disbond crack growth process. • Indication of slow growth management approach feasible for bonded joints/patch repairs if the doubler/patch is designed to be sufficiently long. • Establishment of modified Paris law for predicting allowable fatigue life and determining inspection interval, in accordance with FAA guidance. • Potential solution for maintenance cost reduction for primary aircraft structures. The applicability of a damage slow growth management strategy to bonded joints/patch repairs of primary aircraft structures was evaluated through an experimental and computational study. Fatigue tests were conducted to investigate the entire process of disbond growth from initiation up to joint ultimate failure. The residual static strength of the joint as a function of disbond length was established using finite element modelling, in which the mesh size was calibrated using the static strength of the specimens measured in room temperature and dry (RD) and hot-wet (HW) conditions, based on the characteristic distance approach. A virtual crack close technique (VCCT) approach was utilised to assess the strain energy release rates (SERRs) as a function of disbond crack length. The measured disbond growth rates were correlated with the SERRs using a modified Paris law that enabled prediction of joint fatigue life. The fatigue test results indicated that for a joint having a sufficient static strength safety margin under a typical fatigue loading that would propagate disbond, the disbond growth would be stable in a particular length range. Thus, the slow growth approach would be feasible for a bonded joint/patch repairs if the patch is designed to be sufficiently large to allow extended damage propagation (whilst in the case when patch size must be limited, safe-life design for the patch termination region in critical repairs must be considered. Should disbond growth occur in this case, the joint must be repaired or replaced). The work presented in this paper validated the framework/procedure proposed previously by the authors (Tanulia et al., 2020) for managing damage slow growth in bonded joints/patch repairs. In the last part of this paper the planned follow-on research is briefly described. [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]

The 7075 aluminum alloy is a promising material for the aerospace industry due to its combination of light weight and high strength. This study proposed a method for predicting fatigue crack initiation of the 7075 aluminum alloy by crystal plasticity finite element analysis considering microstructures. In order to accurately predict the total fatigue life, it is necessary to calculate the number of cycles for fatigue crack initiation, small crack growth, and long crack growth. The long crack growth life can be estimated by the Paris law, but fatigue crack initiation and small crack growth are sensitive to the microstructures and have been difficult to predict. In this work, the microstructure of 7075 aluminum alloy was reconstructed based on experimental observations in the literature and crystal plasticity simulations were performed to calculate the elasto-plastic deformation behavior in the reconstructed polycrystalline model under cyclic deformation. The calculated local plastic strain was introduced into the crack initiation criterion (Tanaka and Mura, 1981) to predict fatigue crack initiation life. The predicted crack initiation life and crack morphology were in good agreement with the experimental results, indicating that the proposed method is effective in predicting fatigue crack initiation in aluminum alloys. From the obtained results, future issues regarding the prediction of fatigue crack initiation were discussed. [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]

• Finite element analysis on the surface crack growth in steel pipes reinforced with CRS. • The FE model is validated by the experimental results. • Based on the FE model and Paris' law, surface crack growth rate is quantitatively evaluated. • Revealing the mechanism of CRS reinforcement on the surface cracked steel pipes. • Indicating the key influential parameters of CRS reinforcement on surface cracked steel pipe. This paper conducts a numerical analysis on the external surface cracked steel pipes reinforced with Composite Repair System. A three-dimensional finite element (FE) model is developed to calculate the Stress Intensity Factor (SIF) of the surface crack, and the crack growth process is evaluated by the Paris' law. The effect of FRP-to-steel interfacial bond condition on the SIF evaluation has been considered by incorporating the cohesive zone modelling. Then the FE model is validated by the experimental results. Thereafter, major issues including "interfacial bond condition" and "reinforcement effectiveness and influential parameters" have been discussed. The results indicate the reinforcement effectiveness on reducing the SIF owes to the decreasing of stress magnitude and the crack-bridging effect. Because of the crack-bridging effect, composite reinforcement performs more efficiently on reducing the SIF at the surface point than at the deepest point of the surface crack. The negative influence of the FRP-to-steel bond condition on the surface crack growth is not as significant as on reinforcing through-thickness cracks. However, since the interfacial stiffness is sensitive to the adhesive thickness, choosing an ideal adhesive thickness to acquire a good reinforcement effectiveness and to avoid potential interfacial bond failures is recommended. [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]

• Fatigue analysis of valve bodies DN100 and DN50. • Crack initiation on a valve body according to Basquin-Coffin-Manson equation. • Stress intensity factor estimation with eXtended Finite Element Method (XFEM). • Cycles for crack growth across the valve body thickness. • The engineering and the true stress–strain diagrams and cycle fatigue behaviour of GP240GH steel. Global industry depends of the different type of valves, such as globe valves which are used for precise flow regulation. Since most of the power plants rely on performance of globe valves, it is necessary that valves function without interruption. In this paper, the main part of the globe valve, valve body, is investigated. Simulation of crack initiation and its growth in a wall of valve body is carried out. Required number of cycles for crack initiation is estimated according to Basquin-Coffin-Manson equation. Afterwards, stress intensity factor is estimated through eXtended Finite Element Method (XFEM) and required number of cycles for crack growth across the valve body thickness is calculated according to Paris' law. The aforementioned method is validated on the results from the available literature by employing relatively simple shapes such as steel pipe with integrated flaw. Subsequently, the method is used on a relatively complex geometry, as is the valve body. The obtained results indicate lack of brittle fracture in a valve body. In other words, the results imply occurrence of Leakage Before Brake (LBB). This is utterly important for power plant industries, since it ensures the proper reaction of the user and possibly avoids possible catastrophic consequences for personnel and the equipment located in the proximity of the valve. [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]

Analysis benchmarking is used to evaluate new algorithms for automated VCCT-based delamination growth analysis. First, existing benchmark cases based on the Single Leg Bending (SLB) specimen for crack propagation prediction under quasi-static loading are summarized. Second, the development of new SLB-based benchmark cases to assess the static and fatigue growth prediction capabilities under mixed-mode I/II conditions is discussed in detail. Additionally, a scheme is proposed to interpolate between known fatigue delamination growth rates to obtain values for mixed-mode ratios for which data has not been defined in the input. Further, a comparison is presented, in which the benchmark cases are used to assess new analysis tools in ABAQUS/Standard FD03. These recently implemented tools yield results that are in good agreement with the benchmark examples. The ability to assess the implementation of new methods in one finite element code illustrates the value of establishing benchmark solutions. [ABSTRACT FROM AUTHOR]

The mixed mode I‐II fatigue and fracture is briefly reviewed, addressing experimental and numerical modelling aspects, and focusing on planar specimens. One major challenge concerns the determination of equivalent stress intensity factor (Keq) in mixed mode situations. Several approaches were compared through the determination of Keq/KI over a wide range of values of KI/KII or KII/KI. Whereas all different approaches converge to the same value as KI/KII increases, the same does not happen for large KII/KI, where differences between values of Keq persist. In the regions of 0 < KI/KII < 2 and 0 < KII/KI < 2, no stable trend of results can be defined. Experimental fatigue crack growth results are presented for Al alloy AA6082‐T6. Compact tension specimens, modified with holes, and four‐point bending specimens under asymmetrical loading promoting mixed mode situations, were subjected to fatigue crack growth tests, where crack path and crack growth rate were measured. The presentation of the fatigue crack growth data was made using a Paris law based upon Keq. Differences in the Paris law constants were found for the different Keq criteria. Recent developments in numerical techniques, as the implementation of the extended finite element method (XFEM) in finite element software packages allows to determine accurately crack paths in mixed mode fracture. This article highlights concepts for mixed‐mode fatigue and fracture and supporting data, identifying challenges still to be overcome. [ABSTRACT FROM AUTHOR]

Summary: Structures are subjected to cyclic loads that can vary in direction and magnitude, causing constant amplitude mode I simulations to be too simplistic. This study presents a new approach for fatigue crack propagation in ductile materials that can capture mixed‐mode loading and overloading. The extended finite element method is used to deal with arbitrary crack paths. Furthermore, adaptive meshing is applied to minimize computation time. A fracture process zone ahead of the physical crack tip is represented by means of cohesive tractions from which the energy release rate, and thus the stress intensity factor can be extracted for an elastic‐plastic material. The approach is therefore compatible with the Paris equation, which is an empirical relation to compute the fatigue crack growth rate. Two different models to compute the cohesive tractions are compared. First, a cohesive zone model with a static cohesive law is used. The second model is based on the interfacial thick level set method in which tractions follow from a given damage profile. Both models show good agreement with a mode I analytical relation and a mixed‐mode experiment. Furthermore, it is shown that the presented models can capture crack growth retardation as a result of an overload. [ABSTRACT FROM AUTHOR]