A three-scale Generalized Finite Element Method (GFEM 3 ) is proposed for the simulation of three-dimensional crack propagation in domains where the characteristic crack size is substantially smaller than the structural dimensions. The approach integrates the Generalized Finite Element Method (GFEM) with global-local enrichments (GFEM gl ) and classical submodeling. Within this framework, the GFEM gl decomposes the problem into two scales and provides boundary conditions for a set of submodels created along the crack front. These submodels are solved in parallel to recover high-fidelity displacement fields, enabling accurate computation of stress intensity factors (SIFs). The SIFs obtained along the crack front are assembled into a continuous profile that drives the crack propagation. Three numerical studies of increasing complexity demonstrate that the GFEM 3 achieves SIF accuracy comparable to single-scale GFEM, offers a reduction in computational cost relative to two-scale GFEM gl analyses, and enables the simulation of three-dimensional crack propagation problems that are beyond the practical reach of both single-scale GFEM and two-scale GFEM gl . Overall, the method provides a robust and scalable framework for multiscale modeling of three-dimensional fracture where crack features are small compared to the overall structure.

Numerical investigation of stress intensity and geometry correction factors in welded cover plate details

A damage-tolerant approach for fatigue in cold-formed profiles combining numerical modelling and machine learning

Intelligent prediction of crack stress intensity factors for nuclear-grade pressure vessels based on XFEM-PSONN collaboration

This study employed a low-speed drop-hammer-impact test combined with the digital image correlation technique to investigate the dynamic failure performance of bamboo fiber/high-density polyethylene (BPE) composites and to explore the mechanism of fiber content's influence on it. Results indicated that with the increasing of BF content, the density, acoustic velocity, and Poisson's ratio of BPE gradually decreased, while the elastic modulus initially decreased and then increased. Although the introduction of Bamboo Fiber (BF) enhanced the rigidity of BPE, allowing the materials to withstand greater impact forces during initial fracture stages, it reduced the toughness of BPE. BPE with 80% BF content showed a higher crack propagation rate and a shorter fracture process compared to composites with lower BF content. However, according to the stress intensity factor (SIF) history, the introduction of BF could enhance the resistance of crack propagation, which depends on the dispersibility of BF and the interfacial bonding properties between BF and high-density polyethylene (HDPE). Overall, BF could increase the rigidity of BPE and restrict the crack propagation at the initial fracture stages. As an eco-friendly and sustainable material, the dynamic fracture toughness of BPE can contribute to the application and promotion of biomass fiber-filled composites.

ABSTRACT Cement sheath fracture is a critical integrity concern in CO2 injection wells under cyclic thermal and pressure loading. This study presents a coupled transient thermal – static structural finite element model of a CO2 injection well with a pre-existing semi-elliptical fracture in the cement sheath, applied to the Waseca Formation in Lloydminster, Saskatchewan. Fractures aligned with the minimum horizontal stress produced the highest Mode I stress intensity factor (≈0.096 MPa·√m), about 90% below the cement fracture toughness (1 MPa·√m), indicating unstable fracture propagation is unlikely under the investigated conditions. Sensitivity analyses show that increasing Young’s modulus from 5 to 25 GPa raises K I by ~1289%, while increasing Poisson’s ratio from 0.20 to 0.40 raises it by ~45%, suggesting that moderately stiff cement may be optimal for minimising crack-tip driving forces under the investigated conditions. Injection temperature has the strongest influence, with K I decreasing from 0.17 MPa√m at −20°C to near zero at +20°C, consistent with crack-face closure as the thermal differential decreases. In contrast, injection pressure (4.0–5.5 MPa) changes K I by less than 0.3%. No plastic strain accumulated after five 30-day injection – shut-in cycles. A normalised risk classification is proposed for the Waseca formation to guide cement design and fracture monitoring.

Abstract Quarter-circular corner cracks are typical flaws in three-dimensional (3D) structures. For curved 3D cracks, the application of a plane-strain fracture criterion often leads to inaccurate fracture predictions. To enhance prediction accuracy, a 3D fracture assessment method incorporating an equivalent thickness model based on the T z factor is employed to evaluate the fracture strength of a quarter-circular corner crack within a finite body. Analysis reveals that as the ratio of crack depth to plate width ( c/W ) increases, the plane of strongest T z constraint shifts away from the 45° plane normal to the crack front. Through systematic finite element analyses, a new equivalent thickness equation for quarter-circular corner cracks in finite bodies is derived. Additionally, a modified stress intensity factor equation is developed based on Newman’s original formulation, with the applicable upper limit of c/W extended from 0.2 to 0.95. To validate the proposed 3D fracture prediction method, a new fracture test involving a quarter-circular corner crack is conducted. Experimental results demonstrate that the 3D method provides significantly improved accuracy compared to traditional two-dimensional fracture criteria. For a specimen containing a quarter-circular corner crack under tensile loading, the prediction error is reduced from 35.3% to 2.2%.

Hydraulic concrete structures, such as high dams, operate under elevated water pressure and complex stress fields, where crack propagation at the dam heel is a critical determinant of load-bearing capacity. This study investigates the fracture behavior of the concrete-rock interface under varying water pressures (0-4MPa) through four-point shear tests, with mode mixity ratios ranging from 0.398 to 2.411. Digital image correlation was employed to characterize crack extension and morphology. The results demonstrate that high-pressure water significantly modifies crack propagation patterns. The influence of water pressure on fracture parameters intensifies as the mode mixity ratio increases; conversely, the impact of the mixity ratio on fracture behavior diminishes at higher water pressures. Based on these findings, empirical models were developed to predict fracture loads and deformations. Furthermore, prediction models for Mode I and Mode II stress intensity factors and an initial cracking fracture criterion are proposed, providing a robust theoretical framework for fracture mechanics analysis in extra-high dam heels.

Stress intensity factor – Life: Improving high cycle fatigue understanding of laser powder bed fusion 316L stainless steel by combining effects of stress, defect size, and defect shape

• Filling material type significantly affects PMMA joint crack propagation, with air-filled joints producing multi-cracks and silicone/epoxy-filled joints generating single cracks at different positions. • Quasi-static loading leads to more pre-crack energy accumulation and a higher initial stress intensity factor than dynamic loading, and silicone/epoxy-filled specimens show longer energy recovery time than air-filled ones. • Under dynamic loading, PMMA joint length positively correlates with crack initiation and propagation time, and material hardening parameter and fractal dimension also exert notable impacts on PMMA fracture. This study employed a dynamic caustics system integrated with a Hopkinson pressure bar, Schlieren optics, and a high-speed camera to investigate how joint span and shape affect crack initiation and propagation. First, crack penetration into joints with different spans (10 mm, 30 mm, 50 mm) and different shapes (“u” and “n”) was visualized. Then, crack-tip stress intensity factors and propagation velocity were measured by high-speed caustics patterns. Finally, fractal dimensions of crack trajectories were obtained to quantitatively evaluate the complexity of the crack layout. Based on loading time, the crack behavior is divided into 4 phases: first precrack initiation, propagation toward the joint, secondary initiation from the joint and final propagation toward the boundary. Since the phase 1 duration increases with span, crack initiation from precracks clearly depends on span length. In phases 2 and 3, reflected waves occur from the joint interface; furthermore, they are confirmed to be Rayleigh waves through wave velocity. Meanwhile, the reflected Rayleigh waves from the “n”-shaped joint have a significant effect on crack propagation in phase 2. In phase 4, crack trajectories initiating from joint ends are heavily influenced by joint span, which is associated with crack interaction. Furthermore, different opening orientations (“u” and “n”) of arc-shaped joints have different effects on crack behavior. The “u”-shaped joint exhibits crack behavior similar to that of same-span line-shaped joints. The “n”-shaped joint demonstrates a strong fracture resistance. This work advances the understanding of fracture resistance as influenced by joint span and shape variations.

Rapid stress intensity factor evaluation in cracked welded joints

Determination of stress intensity factor from crack opening profile in notched components

ABSTRACT In this paper, an attempt is made to analyze and correlate load ratio effects on fatigue crack growth (FCG) when multiple mechanisms are involved. To identify different mechanisms, a plot of normalized stress intensity factor (SIF) range as a function of the load ratio (R) at a given constant fatigue crack growth (FCG) rate is used. The proposed analysis is validated and compared with FCG data reported in the literature.

Welded joints are widely recognized as the most critical point in structures made of armour steels due to pronounced thermal effects, microstructural heterogeneity, and the degradation of mechanical and fatigue properties. This study investigates the mechanical properties and fatigue crack growth resistance of a welded joint produced on SA 500 armour steel, with the aim of preserving the properties of the base material as much as possible. To achieve this, a welding procedure incorporating a high-strength filler wire and optimized welding parameters was applied. Hardness and tensile testing was conducted to evaluate the extent of property degradation caused by welding. The results demonstrate that the applied welding process effectively limited the reduction in hardness and tensile strength, achieving values reasonably close to those of the base material. In addition, fatigue crack growth behaviour was investigated in accordance with ASTM E647, using both the Paris law and the McEvily law. The obtained fatigue crack growth curves and threshold stress intensity factor (ΔKth) values indicate the nearly identical fatigue behaviour of the base material and the heat-affected zone, confirming the successful preservation of base material fatigue behaviour in the thermally affected zone. Moreover, the weld metal exhibited superior resistance to fatigue crack initiation and growth. Overall, the results confirm that the proposed welding approach provides favourable mechanical and fatigue performance for welded joints in armour steel applications.

The fatigue crack growth (FCG) of 690 MPa grade offshore steel has been investigated. The characteristic acoustic emission (AE) parameters of EH690 steel compact tensile (CT) specimens during FCG were measured, and the FCG response was quantified in terms of AE count (CNTS). The energy entropy of each wavelet ( E S ) was calculated to establish the relationship between the AE wavelet energy entropy rate (d E S /d N ) and the stress intensity factor range(Δ K ) during the crack stable growth stage. The results indicate: (1) A linear correlation between AE cumulative count and cycle number ( N ) across stress ratios ( R = 0.05, 0.1, 0.3, and 0.5), e.g., the N to grow from 21 to 32 mm crack length the base metal (BM) is less than the weld metaland the heat‐affected zone. (2) The AE CNTS exhibits greater dispersion with respect to the N , which is beneficial for the characterization of plastic deformation in the crack tip region. (3) Log–log plots of d E S /d N versus Δ K are linear correlated with the slope of the fitted line increasing from 2.81 ( R = 0.05) to 5.26 ( R = 0.5) for BM. (4) E S is highly concentrated with respect to the N , serving as an effective parameter for characterizing crack growth.

ABSTRACT A detailed linear‐elastic stress state analysis around the vertex of an axisymmetric V‐notch depends on the understanding of stress singularity orders, eigenangular functions, and generalized stress intensity factors. This study introduces a numerical method for determining the stress singularity state of an axisymmetric V‐notch. The displacement field near the axisymmetric V‐notch tip is expanded asymptotically and substituted into the equilibrium equations of the axisymmetric structure, yielding a system of characteristic singularity equations that govern the stress singularity orders. The interpolating matrix method is introduced for solving the established characteristic equations, which simultaneously determine the stress singularity orders and their associated eigenangular functions under different radial boundary conditions. Generalized stress intensity factors of axisymmetric V‐notches are computed using the finite element method by postprocessing the stress results. The effects of material properties and notch geometry on singularity orders and generalized stress intensity factors are discussed in detail.

ABSTRACT This study evaluates the effectiveness of adhesively bonded glass fiber‐reinforced polymer (GFRP) patches in repairing cracked aluminum specimens under Mode I (opening), Mode II (in‐plane shear), and mixed‐mode I/II loading conditions. Performance was assessed using critical load and absorbed energy measured from load–displacement responses. The focus is on the influence of fiber orientation—unidirectional (UD) 0°, UD 90°, and woven—on fracture behavior and load‐bearing capacity. Composite patches were bonded to aluminum plates using Araldite 2011 adhesive, and tests were performed using an Arcan fixture. Results show that fiber orientation plays a critical role in repair performance. Under Mode I loading, the GFRP‐UD‐0° patch achieved the highest critical load, while the woven patch demonstrated superior absorbed energy. In Mode II, the woven patch increased critical fracture load by approximately 350% compared to the unrepaired specimen. For mixed‐mode loading, the UD‐0° configuration provided the highest critical fracture load and absorbed energy. Overall, considering performance across all loading modes, the woven patch delivered the most balanced improvement in both load capacity and energy absorption. Finite element analysis confirmed that fiber orientation strongly influences stress intensity factors. Under Mode I loading, the UD‐0° patch exhibited the highest critical stress intensity factor, followed by the woven patch. In contrast, woven patches yielded the highest stress intensity factors under mixed‐mode and Mode II loading. Scanning electron microscope analysis revealed mixed adhesive–cohesive failure, with woven patches enhancing load transfer and energy dissipation. All patched specimens outperformed the unrepaired samples, confirming the effectiveness of patch repairs.

Numerical simulation of adhesively bonded joints is a demanding challenge in engineering, especially in mixed-mode fracture applications, due to the intricate stress fields and complex interface treatment. A wide variety of numerical techniques are available, yet, meshless methods allow the discretization of the problem domain uniquely in a set of unstructured field nodes, allowing to expedite the local remeshing algorithm, reduce stress concentration inaccuracies, and increase nodal connectivity established by influence domains. Hereby, we present the application of a meshless technique to predict fracture propagation in Single Lap Joints (SLJ) and Double Lap Joints (DLJ). Stress Intensity Factors (SIF) are calculated using the Interaction Integral within a contour around the crack tip. Energy release rates can then be obtained, allowing the implementation of a mixed-mode energy criterion. The meshless analyses results are compared with experimental data of SLJ and DLJ tests, in addition to conventional Finite Element Analyses (FEA), defining the suitability of the proposed meshless crack propagation algorithm to predict fracture propagation in adhesive joints.

Accurate prediction of corrosion-fatigue crack growth rate in aluminum alloys is critical for the safety assessment of aerospace structures. Conventional empirical fracture-mechanic models often struggle to capture multiphysics coupling effects, whereas purely data-driven machine-learning models may lack physical interpretability and generalize poorly beyond the training distribution. To address this challenge, this study proposes a physics-guided knowledge-based XGBoost (KBXGB) model. Based on a comprehensive dataset comprising 2786 experimental records, Permutation Feature Importance was utilized to identify 11 key features, including the stress intensity factor range, stress ratio, frequency, and environmental parameters. The KBXGB framework learns the residual between physics-based empirical models (e.g., the Paris and Walker laws) and measured experimental data, recasting the complex nonlinear mapping into a correction of the systematic deviations of the physical models, thereby achieving deep integration of domain knowledge and data-driven learning. Test results demonstrate that the KBXGB model achieves a coefficient of determination (R2) of 0.9545 and a reduced Mean Relative Error (MRE) of 1.61% on the test set, outperforming standard XGBoost and traditional regression models. Crucially, in independent extrapolation validation, the standard XGBoost model failed (R2 = 0.2858) with non-physical staircase artifacts, whereas the KBXGB model maintained high predictive fidelity (R2 = 0.8646) and successfully reproduced physical crack growth trends. The proposed approach effectively mitigates the “black-box” limitations of machine learning in sparse data regions, offering a high-precision and physically robust tool for corrosion fatigue-life prediction under complex service conditions.

Deposition and cavitation erosion behaviour of HVOF sprayed CeO2-modified multimodal WC-10Co4Cr coatings on 316 stainless steel