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• We present a DIC approach to measure J-R curve of M(T) specimens. • The proposed approach covers both monotonic and reversed loading conditions. • We validate the accuracy of the DIC approach in numerical and experimental studies. • We demonstrate the crack-tip re-sharpening caused by reversed loadings in DIC. This paper proposes a digital image correlation (DIC) based method to measure the fracture resistance curve and quantify the reversed loading effects in middle tension, M(T) specimens. The proposed method employs free-surface DIC measurement to derive J and utilizes the deformation profile to determine the crack size with enhanced accuracy than the conventional compliance-based approach. This study observes the re-sharpening of the crack-tip field during the reversed cycle through DIC, which facilitates the crack propagation and decreases the fracture resistance. The comparison between monotonic and reverse-loaded M(T) specimens demonstrates the decrease of the fracture resistance under reversed loadings. [ABSTRACT FROM AUTHOR]

Grinding damage of hard and brittle materials has a direct impact on part strength and subsequent polishing efficiency. Damage suppression is one of the key research issues in hard and brittle material processing. Due to the uncertain damage evolution law, there is still a lack of optimization methods for the multi-step grinding process under given damage constraints. In this paper, the extended finite element method is used to establish a model between the prefabricated crack depth and final crack depth, which reveals the influence of various existing subsurface damages on crack propagation. It is found that only when the prefabricated crack depth is close to the indentation crack depth on the perfect surface, the final crack depth will be affected to some extent. To optimize the grinding process to achieve low damage, a semi-empirical model for predicting grinding damage is proposed which is suitable for process optimization and does not rely on some difficult-to-obtain parameters. Finally, based on the damage evolution law and prediction model, the core content of this paper is proposed, that is, a multi-step grinding process optimization method with variable grinding depth. This method can minimize the damage while ensuring the same processing efficiency, the damage depth is reduced by 25 %. The effectiveness of the optimization method and the correctness of the damage evolution law are proved by experiments. This method is suitable for engineering applications and has practical significance for understanding the damage evolution mechanism, which is helpful for the suppression of grinding damage and the optimization of the grinding process. • Reveal the evolution mechanism of various existing subsurface damage on crack propagation by XFEM. • Propose a semi-empirical model for grinding damage prediction suitable for process optimization. • Propose a multi-step grinding process optimization method for hard brittle materials with variable grinding depth. • Prove the effectiveness of the optimization method and the evolutionary model through experiments. [ABSTRACT FROM AUTHOR]

Hydrogen significantly influences the fatigue crack growth (FCG) of pipeline steel, while traditional semi-empirical models sometimes fail to accurately describe the fatigue crack growth rate (FCGR) at which hydrogen assisted. Traditional machine learning methods also struggle to analyze the physical correlations between model outputs, parameters, and data. In this paper, a two-stage equation for hydrogen-assisted FCG is proposed using Balanced Iterative Reducing and Clustering Using Hierarchies (BIRCH) clustering and domain knowledge-guided symbol regression. The segmentation of crack growth data is achieved through the BIRCH algorithm and outputs the transitive stress intensity factor K t , while domain knowledge is obtained by analyzing the symbol regression (SR) trees of six existing semi-empirical models. By constraining the symbol regression search space with variable subtrees including Δ K , Δ K t h , R, K I H , and K I C , a SR model is developed based on the ×60-5.5 MPa-R0.5 test data. The applicability of the equation under different conditions was validated using test data from X60-5.5 MPa-R0.1, X60-21 MPa-R0.1, X60-21 MPa-R0.5, X42-6.9 MPa-R0.1, and X42-6.9 MPa-R0.8. The results indicate that our model outperforms the other six semi-empirical crack propagation rate models, achieving higher prediction accuracy with a minimum R 2 value of 0.968912 and a maximum RMSE value of 0.000003. Therefore, this two-stage model accurately captures the hydrogen-assisted FCGR and enhances the predictive capability of fatigue life in a hydrogen environment, providing valuable references for hydrogen-related pipeline design and operational safety. [Display omitted] • Adaptive segmentation of hydrogen crack growth data based on BIRCH clustering algorithm. • Physical knowledge of six semi-empirical models guides the process of symbolic regression search equations. • A two-stage equation describing the hydrogen-assisted crack growth rate is proposed. • The proposed equation is applicable to experimental data with different materials, hydrogen pressures, and stress ratios. • Comparison with existing semi-empirical models proves the superiority of the proposed equation. [ABSTRACT FROM AUTHOR]

Carbon/carbon (C/C) composites impress with their excellent high-temperature mechanical properties. In this paper, in order to simulate the complex service conditions of aerocraft thermal protection systems, an experimental platform for simultaneous ablation and tension was designed. The mechanical and ablation properties of the C/C composites were tested under an oxyacetylene flame at heat flux of 2185 kW/m2. Meanwhile, the mechanism of mutual influence of ablation and tensile loading was revealed by microstructural characterisation. By comparing the tension-only and ablation-only conditions, the results show that the strength of the C/C composites under ablation conditions decreased by 52.0%, which was associated with the crack propagation and porosity increase caused by flame. The tensile loading increased the linear and mass ablation rates by 21.8% and 82.9%, respectively, which was due to the interfacial damage caused by tensile stresses provides more channels for flame to enter the material interior, thus accelerating oxidative ablation. [ABSTRACT FROM AUTHOR]

The AlN/BN composite ceramic, fabricated via hot-press sintering, exhibits obvious anisotropy due to the establishment of directional alignment of h-BN. However, the variation and influence mechanisms of bending strength (σ) and thermal conductivity (λ) are remain unclear in different directions, which greatly limit the application of AlN/BN composite ceramics. In this paper, the effects of h-BN content on phase composition, microstructure and anisotropy of AlN/BN composite ceramics are discussed in detail. The results reveal that AlN/BN composite ceramics have three directions: perpendicular (⊥), longitudinal parallel (∥), and lateral parallel (≡) to the hot-pressing direction. The content of h-BN is a crucial factor affecting the anisotropy of AlN/BN composite ceramics. h-BN enhances the thermal conductivity in the ∥ and hinders the thermal conductivity in the ⊥. With the increase in h-BN amount, λ ∥ rises gradually, while λ ⊥ gradually falls. When the mass percentage of h-BN and AlN is 25 % (AB25), the λ ∥ is as high as 90 W m−1 K−1, which is about 2.25 times that of λ ⊥. In terms of mechanical properties, σ ≡ and σ ⊥ first increase and then decrease, while σ ∥ only decreases. This is attributable to h-BN being effective in enhancing mechanical properties by inhibiting crack propagation in the ⊥ and ≡ direction, while the promotion of crack propagation leads to a decrease in mechanical properties in the ∥ direction. σ ≡ reaches the highest values (σ ≡ = 460.2 MPa) at an h-BN amount of 10 % (AB10), which is about 1.19 and 2.04 times that of σ ⊥ and σ ∥ , respectively, and 22.1 % higher than that of AB0. [ABSTRACT FROM AUTHOR]

Accurate prediction of crack extension is crucial for ensuring the structural integrity of metal components exposed to diverse loads. While the Gurson model and its extensions are widely accepted for delineating ductile fracture stages, especially in porous materials with a rigid-perfectly plastic matrix, their efficacy diminishes in the presence of strain-hardening matrices. To address this limitation, our study introduces a robust numerical implementation and assessment of Perrin's model. In contrast to Gurson's approach, Perrin's model incorporates two distinct strain-hardening parameters derived from an intricate analysis of a strain-hardening hollow sphere subjected to axisymmetric loading. Moving beyond theoretical discussions, this paper actively engages in the rigorous evaluation of Perrin's model under various scenarios, encompassing isotropic, kinematic, and mixed isotropic-kinematic hardening conditions. The model's effectiveness is convincingly demonstrated through meticulous comparisons between numerical simulations and real-world experimental observations conducted on pre-cracked specimens. Facing challenges related to achieving global elastic-plastic convergence in large-scale simulations, our research introduces a sophisticated approach. Leveraging stiffness tangent moduli ensure the maintenance of quadratic convergence in global Newton method iterations. This not only enhances the reliability of our simulations but also underscores the practical applicability of our findings. The study also focuses on the necking and crack propagation of a cylindrical specimen through meticulous computational modeling. Our mesh captures intricate details and addresses stress gradients, revealing coplanar crack propagation contrary to prior beliefs. The confirmation of the cup-cone fracture effect challenges previous interpretations, emphasizing the critical role of void nucleation. This reinforces the credibility and applicability of our approach in advancing the understanding of material fracture behavior. In summary, this study significantly contributes to existing knowledge in fracture prediction models, offering a robust framework for predicting ductile fracture under substantial deformations. The presented findings pave the way for advancements in structural engineering, providing invaluable insights for optimizing the performance and resilience of metal structures in real-world applications. • We present a numerical implementation and assessment of a model for ductile fracture, considering three hardening scenarios. • We discuss the numerical implementation of the model and address the projection problem algorithm for three hardenings • We introduce a numerical integration strategy for handling significant deformations and rotations in complex structures. • We demonstrate the model effectiveness by comparing numerical simulations and experiments in pre-cracked specimens. [ABSTRACT FROM AUTHOR]

This paper discusses the effect of reversed austenite (RA) on hydrogen embrittlement (HE) behavior of a high-strength multi-alloyed steel. Three heat treated samples were fabricated by quenching-lamellarization-tempering (QLT) treatment with varying the features of RA. The experimental results revealed that the existence of reversed austenite could reduce the effective diffusion coefficient and HE susceptibility. QLT specimens exhibited the optimization of the strength and HE resistance with 6.7% filmy and stable reversed austenite, which could hinder the hydrogen diffusion, reduce local hydrogen concentration, delay the crack initiation and further arrest the crack propagation. Moreover, a 23% reduction in hydrogen embrittlement susceptibility of QLT specimens was achieved by comparing with quenching-tempering (QT)specimens. However, the interface of RA and matrix was a preferred site for crack initiation. • The role of "lamellarization" on the hydrogen embrittlement was investigated. • Both fraction and stability of revered austenite affected the HE behavior. • The interface of revered austenite and matrix is a preferred site for crack initiation. • The role of RA on the crack propagation was discussed. [ABSTRACT FROM AUTHOR]

One of the main challenges for spaceflight safety is preventing crack growth. These defects can occur both in the skin of spacecraft and during the combustion of solid fuels. An important problem is the propagation of cracks at high temperatures. This paper proposes a study of a single polygonal crack under a constant load perpendicular to the crack plane. The solution is constructed numerically using the boundary element method. The main goal of the work is to calculate the stress intensity factors in the vicinity of the crack. The first intensity coefficient was calculated, and calculations were carried out for various crack parameters. • A symmetrical and asymmetrical polygonal cracks were studied. • An asymmetrical crack is more resistant to growth than a symmetrical one. • For a symmetrical crack the stress intensity factor increases in proportion to the size of the crack. • For an asymmetric crack, the stress intensity factor does not change on increasing one shoulder. [ABSTRACT FROM AUTHOR]

• The GDH-PD is proposed to address size-dependent effects and fracture problems. • The lower- and higher-order micro-modulus states of GDH-PD are firstly derived. • GDH-PD eliminates zero-energy modes of traditional higher-order peridynamics. • HOBCs are applied by constructing quadratic functional on the boundary points. • Nonlocal effects, size effects, strain gradient effects and damage are considered. In this paper, we propose the implicit stabilized dual-horizon peridynamics-based strain gradient damage model (GDH-PD) to describe the cross-scale fracture behavior of materials. To this end, firstly, the strain energy density function of GDH-PD is reformulated by considering the energy compensation to eliminate zero-energy modes of the traditional higher-order peridynamics. And then, the constitutive force state of GDH-PD is derived and explicitly expressed with the help of the proposed special dimension reduction of the nonlocal higher-order tensors. To solve the steady-state crack propagation problems, the implicit GDH-PD is developed by deriving the lower- and higher-order micro-modulus double state, such that the linearization of the equilibrium equation of GDH-PD is established. At last, the bond length-dependent energy-based failure criterion is used to characterize the cross-scale fracture in the form of bond breakage. The effectiveness of GDH-PD to characterize microstructure size effects and macrostructure strain gradient effects are investigated by numerical simulations. The numerical results are in good agreement with the analytical solutions or the available experimental results. We believe that the proposed GDH-PD may pave the way to an increased application of peridynamics to be used in the cross-scale fracture predictions for the advanced material. [ABSTRACT FROM AUTHOR]

In this paper, the damage progression and fracture behavior in notched cross-ply SiC/SiC composites were investigated using the in situ digital image correlation (DIC) and acoustic emission (AE) techniques. Under tensile loading, the mechanical properties of composite's elastic modulus, proportional limit stress (PLS), ultimate tensile strength (UTS), and fracture strain were obtained for non-notched, single-hole, double-holes, and four-holes samples. Based on the analysis of composite's tangent modulus, the nonlinear tensile stress-strain curves were divided into three main domains, relating with internal multiple damage mechanisms observed using the in situ DIC and AE. Effects of the number and location of the circular holes on the full-filed composite's damage and strain evolution, AE energy and ring-down count were investigated. After tensile fracture, the composite's macro fracture morphology and micro damage mechanisms were observed under the scanning electronic microscopy (SEM). Numerical modeling of tensile damage and fracture process of different notched samples were conducted using the extend finite element method (XFEM). Relationships between the notch types, tensile mechanical properties, macro strain evolution, and micro damage mechanisms were established. [ABSTRACT FROM AUTHOR]

• This paper presents a numerical method for predicting the nucleation and propagation of multiple cracks based on XFEM. • The proposed competitive criterion can accurately judge the sequence of new-crack nucleation and existing-crack propagation. • The implementation of modified XFEM is introduced and verified to be effective. In practical engineering, structures will inevitably suffer from multiple cracks and require accurate numerical methods to calculate the structural behavior. Regarding the multi-crack problems, the nucleation of new cracks and the development of existing cracks will affect the subsequent structural responses. Therefore, the criterion for calculating crack nucleation and development is a critical factor influencing the numerical results. This paper presents a modified Extended Finite Element Method (XFEM) to predict the nucleation and development of multiple cracks in plane members focusing on the interaction of multiple cracks. In the proposed method, the crack competition criterion is based on the minimum total energy principle, which can ensure that the nucleation and development of cracks can achieve a maximum energy dissipation per unit length. The effectiveness and robustness of the presented method are verified by comparing the numerical results with experimental and/or other numerical simulations. The result shows that the proposed competition criterion can accurately judge the sequence of new-crack nucleation and existing-crack propagation. [ABSTRACT FROM AUTHOR]

For the assessment of existing riveted railway bridges, the German railway provides guideline 805 for estimating residual lifetimes and calculating safe inspection intervals. Safe inspection intervals are calculated using tonnage factor diagrams. Crack propagation calculations determine these tonnage factors within the framework of linear elastic fracture mechanics under various input configurations. These calculations are based on an assumed or measured crack and future traffic. The recent revision of the guideline, aimed at harmonization with the Eurocodes, also included a recalculation of these tonnage factors. This paper presents the methodology employed in determining tonnage factors, along with the assumed input parameters. Crack propagation calculations and two subsequent regression analyses lead to the tonnage factors and, finally, to the determination of model limitations. Resulting diagrams of tonnage factors for different fracture mechanics models and traffic compositions are presented, including curves for heavy traffic not covered by the guideline. Generally, heavier traffic yields lower tonnage factors, implying shorter safe inspection intervals. However, exceptions are noted for certain span lengths in the upper range investigated. Additionally, the assumed dynamic factors and load distribution by the rail are discussed in detail, providing comparative insights through calculations deviating from guideline 805. In summary, the revised results in this paper enable users of guideline 805 to determine safe inspection intervals without fracture mechanics knowledge, thus ensuring that potential crack growth does not lead to component failure between two inspections. • Riveted railway bridges are assessed according to the revised guideline 805. • Safe inspection intervals are determined based on crack propagation calculations. • Tonnage factor diagrams allow easy application for railway bridge assessment. • Traffic composition clearly impacts safe inspection intervals in guideline 805. • The effect of load distribution by the rail and dynamic factors are discussed. [ABSTRACT FROM AUTHOR]

This paper presents an efficient approach for modeling beams with crack propagation and discontinuities. The proposed approach relies on a globally enriched element within the framework of eXtended/Generalized Finite Element method (XFEM/GFEM), utilizing the principle of partition of unity to incorporate analytical global equations that mimic the beam's deformation in the longitudinal direction. This enables a substantial reduction in the number of elements required along the beam's length, resulting in a decreased computational burden of the model. A typical Euler–Bernoulli beam free-vibration problem is utilized to derive enrichment functions that enhance the approximation space in each strip of a complex cross-section beam. This problem provides an infinite number of vibration modes of the beam, depending on its end boundary conditions. Thus, one can also employ high-order modes to enhance the approximation of the solution. Previous works have demonstrated the method's effectiveness for homogeneous uncracked thin-walled beams. In this paper, the method is extended to address crack propagation problems. A convergence study is presented, assessing the effectiveness of the enrichment functions for various crack lengths and orientations where the cracks are modeled using the double nodes approach. Additionally, the crack propagation is modeled using cohesive zone elements for two and three-dimensional beams. The results demonstrate that our approach produces accurate results even with a small number of elements in the longitudinal direction. Furthermore, it is shown that including the higher deformation modes significantly improves the convergence when evaluating these problems. • A new approach for modeling cracked extruded beams is proposed. • The method relies on enhancing the approximation field with global enrichment functions derived from beams' free vibration. • The results show that the high vibration modes significantly improve the approximation of cracked elements. • The convergence of the method is investigated for various crack lengths and orientations. • The method is implemented for crack propagation utilizing cohesive zone elements. [ABSTRACT FROM AUTHOR]

• The enhanced PINNs specifically for solving crack problems are proposed. • An automatic crack growth simulation method is developed based on PINNs. • The algorithm based on PINNs for fatigue life considering overload is developed. • The stress intensity factors are accurately calculated based on enhanced PINNs. • The mixed-mode crack paths and overload fatigue life are accurately predicted. The fatigue crack growth simulation and life prediction of structures are implemented in this paper based on the physics-informed neural networks (PINNs). Firstly, the enhanced PINNs are proposed by introducing the crack tip asymptotic displacement fields, so that the crack tip stress intensity factors can be calculated accurately even when the number of collocation points is small and the distribution grid is regular. The enhanced PINNs essentially transform the solution of elastic body containing crack into the optimization of minimizing the constructed loss functions, and can invert the fracture parameters. Then, an automatic crack propagation simulation method is developed based on the enhanced PINNs. The network architecture and the overall node distribution can be unchanged during the crack propagation process, and only new crack surfaces need to be processed and corresponding loss functions need to be modified. Because the nodal refinement around crack-tip is not required, this simulation method is convenient and can accurately predict the mixed-mode crack propagation path. Finally, the fatigue crack growth life algorithm considering overload is developed, where the effect of each overload can be captured by the cycle-by-cycle method. Based on this algorithm, the retardation behavior can be characterized and the fatigue life of structure under the load spectrum with periodic overloads can be accurately predicted. The sufficient examples are given to verify the feasibility and accuracy of the method proposed in this paper. [ABSTRACT FROM AUTHOR]

In this paper, the anchorage mechanism and bearing capacity of the special type of pawl bolt anchored in concrete under uplift load were studied. Static tests were carried out on two typical pawl bolts, namely 135° and 180° pawl bolts, and the effects of anchorage depth and pawl type on their failure modes were studied. The experimental results show that the uplift bearing capacity of pawl bolt is improved more effectively than that of smooth bolt. The two typical failure modes of pawl bolts under uplift load are concrete breakout failure and bolt yield failure. The concrete breakout failure exclusively occurs with anchorage depth of 5 d , while the failure mode could change from concrete breakout failure to bolt yield failure with the increase of anchorage depth. The finite element model was established to elucidate the failure mechanism of anchorage bolt and concrete. The crack propagation and diffusion angle distribution of anchorage concrete can be directly judged by concrete tensile damage and stress vector in simulation analysis. Additionally, a calculation method to accurately predict the uplift bearing capacity of pawl bolt was proposed, which considered the effect of diffusion angle θ i on the uplift bearing capacity and further discusses the change law of cone diffusion angle θ i and concrete crack propagation. The calculated results exhibited a concordance with the experimental and numerical results, which shows that the formula presented in this paper can be considered reliable and can guide the practical engineering design. ● Studied design params' impact on pawl bolts force transfer mechanism and concrete cone diffusion angle. ● Examined concrete crack behavior under uplift load for pawl bolts. ● Proposed spatial angle-variation elliptic concrete cone calculation model for pawl bolts based on cone diffusion angle. [ABSTRACT FROM AUTHOR]

Low cycle fatigue cropping technology is a new type of cropping technology with advantages such as no chip waste and low load need. Numerous studies have shown that increasing the fatigue frequency or increasing the displacement load can improve the cropping efficiency, but at the same time, it will reduce the quality of the cross-section and cannot achieve a balance between high efficiency and high quality of cross-section. In response to this issue, this paper found the phenomenon of transition of fracture modes (from fatigue mode to tensile fracture mode) of 6061Al material in LCFC process, and proposed the Active Load Reducing Optimization Strategy for 6061Al in LCFC, which achieves a significant improvement in quality of cross-section with a slight loss of cropping efficiency. Firstly, this paper studied the crack fracture mechanism of 6061Al bar under different displacement loads in the LCFC process. It was found that the transition of crack propagation mode in 6061Al- LCFC process was the main reason for the increase in cross-section roughness. The crack propagation mode changed from fatigue propagation to tensile fracture propagation during the LCFC process, and the roughness of the area significantly increased under the tensile fracture propagation mode. Further research has found that the fundamental reason for the contradiction between the cropping efficiency and section quality of 6061Al is the change in time of crack propagation mode transition and tensile fracture zone area under different displacement loads. Finally, the LCFC process was modeled in a time dimension using acoustic emission(AE) technology, and it was divided into three stages according to the AE signals and the fracture mechanism. As a result, an active load reducing optimization strategy for LCFC process was developed to delay the occurrence of tensile fracture propagation modes. Experiments have shown that compared to the traditional LCFC cropping strategy using constant displacement loads, the active load reducing strategy proposed in this paper can reduce the proportion of tensile fracture area, achieve a significant improvement in quality of cross-section with a slight loss of cropping efficiency, thus achieving a balance between efficiency and section quality to some extent. At the same time, an LCFC process section quality efficiency evaluation index with dual weights of efficiency and section quality has been proposed, which can assist in selecting LCFC active load reducing strategy parameters with consideration of efficiency and section quality weights. [ABSTRACT FROM AUTHOR]

• For superconductor REBa 2 Cu 3 O 7-x (REBCO, RE = rare earth) tapes. • A randomly distributed multi-edge crack model was established based on the H -formulation and the J-integral method. • The interaction effect of multiple edge cracks was investigated by the comparison of various edge crack models. • Numerical results indicate that geometrical parameter randomness is essential for the fracture damage of REBCO tapes. It is often necessary to narrow wide tapes through a slitting process in applications of the second-generation high-temperature superconductor REBa 2 Cu 3 O 7-x (REBCO, RE = rare earth) tapes. However, this results in some random length edge cracks appearing on the slit edge and extending at certain angles towards the center of the tape. In this paper, we proposed a randomly distributed multiple-edge crack model to investigate the fracture mechanism of the superconducting tape under electromagnetic force due to high magnetic fields and current density (∼10 T and ∼ 1010A/m2). The electromagnetic body force distributions within the superconducting tape, incorporating multiple edge cracks, are simulated based on the H-formulation. Then a fracture analysis is conducted under the combined loading of tensile and electromagnetic forces, with the numerical calculation of stress intensity factors (SIFs) using the J-integral method. To validate the model's accuracy, we compare the body force distribution caused by an edge crack and the SIFs of edge cracks under uniform tension with existing results. Detailed analyses are undertaken to explore the impacts of electromagnetic body force non-uniformity, interactions between neighboring cracks, and the stochastic nature of geometrical parameters (length, angle, and spacing) on the fracture behavior under an alternating magnetic field. Numerical results indicate that non-uniform electromagnetic body forces arising from defects are a critical factor in crack propagation. Furthermore, the randomness of the geometrical parameters amplifies the interactions between some of the neighboring cracks, causing the tendency of the tape containing random edge cracks to fracture. Therefore, it is advisable to avoid random cracks with substantial length, angle, and spacing during the mechanical slitting process. [ABSTRACT FROM AUTHOR]

This paper presents an adaptive multi-patch isogeometric phase-field model based on Nitsche's method for simulating dynamic brittle fracture. Complex structures are accurately represented with multiple patches, and Nitsche's method is used to link two adjacent patches to ensure the compatibility and continuity of physical quantities (such as displacements, stresses, phase-field variables) on the coupling edge. LR NURBS with the local refinement ability are used for spatial discretization, while a generalized- α method is used for temporal discretization. The staggered algorithm and hybrid PFM formulation are adopted to enhance the solution efficiency of multi-field coupled system. In addition, the local refinement is executed utilising the phase-field threshold. Several dynamic fracture examples are used to validate the proposed approach's accuracy and effectiveness. The proposed approach can effectively model dynamic fracture propagation, and numerical results demonstrate that the adaptive analysis may significantly lower the computing cost. • An adaptive dynamic multi-patch isogeometric phase-field model is developed. • Complex structure is represented with multiple patches. • Nitsche's method is employed to link two patches. • A prescribed threshold of phase-field variable is used as a refinement indicator. • Numerical results demonstrate the accuracy and effectiveness of the approach. [ABSTRACT FROM AUTHOR]

• Fracture behaviors of ductile adhesive with T-peel test are studied experimentally. • Fracture toughness and adhesive toughness of T-peel test are sensitive to pre-notch or pre-crack lengths. • Deep length pre-crack T-peel samples are easy to realize steady state debonding. • Trapezoidal shape CZM is better to simulate T-peel test than that of exponential shape CZM. • Factors lead to the discrepancy between pre-notch and pre-crack T-peel samples are discussed. T-peel test of ductile adhesive is always an interesting and important topic in peeling mechanics and fracture mechanics. In this paper, the pre-notch and pre-crack effect on the T-peel test with a ductile adhesive layer is studied. Based on the experimental test of SAC 305 adhesive and copper adherent T-peel tests, it is found that the peak loads, fracture toughness, resistance curve, and adhesive toughness are sensitive to pre-crack or pre-notch lengths. Short pre-notch or pre-crack trigger unsteady state debonding frequently, and deep pre-notch or pre-crack conditions achieve steady state debonding more easily. Different data reduction schemes such as simple beam theory (SBT), corrected beam theory (CBT), and compliance-based beam method (CBBM) will lead to variations of fracture toughness extractions for T-peel tests. Trapezoidal shape cohesive zone model (CZM) is found to be easier matching T-peel tests conducted in this paper. However, T-peel samples with shorter pre-notch or pre-crack lengths are hard to simulate with the CZM method due to the unstable crack propagation. The reasons, which may lead to the discrepancy between pre-notch and pre-crack T-peel samples, are also presented and discussed. The selection of different pre-notch or pre-crack lengths is a very important factor that needs to be considered in the T-peel test. [ABSTRACT FROM AUTHOR]

• Paper explores loading mode and temperature impact on fatigue in two polyurethanes. • PU's hard segment strongly influences fatigue sensitivity at elevated temperatures. • Mode I component is more temperature-sensitive than mode II in mixed mode loading. The paper investigates mixed-mode fatigue crack growth in ductile polyurethane adhesives, emphasizing mode decoupling to distinguish the impact of each loading mode component on crack propagation. It also explores the temperature sensitivity of fatigue crack growth rates for each loading mode. Individual scrutiny of the role of each loading mode in tests is accompanied by an analysis of fatigue fracture surfaces to clarify failure mechanisms. The findings indicate differential sensitivity to ambient temperature between the mode I and mode II components in a mixed mode fatigue test. Notably, the fatigue response of the mode I component exhibited higher sensitivity to temperature than the mode II component in mixed mode fatigue fracture of the tested polyurethanes. The polyurethane adhesives' composition, particularly the hard segment ratio, emerged as a pivotal factor influencing their sensitivity to fatigue loading at elevated temperatures. Temperature effects led to a significant reduction (63%) in the mode I component of mixed mode fatigue for one of the tested adhesives, while the other exhibited a noteworthy increase (154%). This trend which was attributed to the hard segment ratio of the adhesives was also persisted in the shear mode of the mixed mode fatigue results. [ABSTRACT FROM AUTHOR]

• Local splitting of bridge girders due to prestressing needs to be always addressed. • Strategy of comprehensive analysis of bridge global and local response is proposed. • Efficiency of the Concrete Damage Plasticity law is confirmed. • Importance of local analyzes of post-tensioned bridges is strongly emphasized. The cracking of a post-tensioned T-beam superstructure, which was built using the incremental launching method, is analyzed in the paper. The problem is studied in detail, as specific damage was observed in the form of longitudinal cracks, especially in the mid-height zone of the girder at the interface of two assembly sections. The paper is a case study. A detailed inspection is done and non-destructive testing results of the girders are briefly discussed. The attention is especially focused on advanced and comprehensive numerical simulations of the bridge mechanical behavior. Linear and nonlinear static calculations are performed employing the Finite Element Method at global and local levels of precision, enabling deep insight into the bridge response during all the stages of bridge construction and after it is opened to traffic. The crack propagation process in local analyses is described by the application of the Concrete Damage Plasticity law, the parameters of which were carefully chosen. The predicted damage patterns closely resemble those observed at the site. The results reveal, that the girder damage process was initiated when centric prestressing was applied, because vertical reinforcement of the assembly section front-end surface was not designed. However, the damage did not compromise the safety of the bridge. Finally, the repair methods employed are described and also a discussion is presented on how to prevent the occurrence of such cracking. [ABSTRACT FROM AUTHOR]

• A 3D peridynamic model is presented to examine fractures in steel welded connections. • The 3D peridynamic model is well-validated with experimental results. • New cases of steel beam-column welded connections are considered. • The role of welding efficiency in the integrity of steel welded connections is studied. The integrity of steel structures depends primarily on the strength of beam-column connections. The paper presents a new and novel three-dimensional (3D) peridynamic model to study the fracture behavior of steel beam-column welded connections. The mesh-free nature of the peridynamic method enables simulating the excessive deformation and fractures in steel elements. The 3D peridynamic model is validated by comparing its fracture and deformation results with experimental data from several beam-column welded connections. According to the proposed model, there are two conditions for the failure of steel beam-column welded connections as follows: 1) crack propagation in the steel elements (beam or column) or bonds' breakage in the welding zone (welding defects); 2) sudden drop of the load value in the load–displacement curve. The study emphasizes its originality by presenting an efficient tool for researchers and engineers to examine fracture responses in steel beam-column welded connections under various conditions. The inclusion of different steel section profiles adds versatility to the study. The paper also explores the performance of new steel beam-column welded connection cases. Moreover, the paper examines the effects of welding defects in the fracture mechanism of steel beam-column welded connections. This study demonstrates that welding defects can determine the failure source and mechanism. Moreover, the load capacity of steel beam-column welded connections decreases due to the welding defects. This finding underscores the importance of welding quality in maintaining the structural integrity of these connections. [ABSTRACT FROM AUTHOR]

• This paper investigates the dynamic evolution of the fractal dimension (FD) of surface cracks on polypropylene fiber-reinforced geopolymer (PFRG) during flexural process. • Cracks FD can be accurately extracted based on the image system and the deep-learning network. • Crack FD at the peak load and the fracture failure load could be used as indicators of deflection hardening behavior. • Crack development can be divided into four stages based on load, FD, CMOD, and energy capacity with time: elastic segment, internal crack development segment, surface crack extension segment, and crack destabilization segment. FD shows an obvious exponential increase in the surface crack extension segment and crack destabilization segment, and the changing trend is basically parallel with the load in the surface crack extension segment. Crack mouth opening displacement (CMOD) is the most widely used parameter to evaluate the crack width changing process in concrete fracture research. However, it is difficult to accurately and comprehensively describe the multi-crack cracking characteristics of high-toughness concrete with only crack width. This paper investigates the dynamic evolution of the fractal dimension (FD) of surface cracks on polypropylene fiber-reinforced geopolymer (PFRG) during flexural process. The box counting method was used to calculate the FD of cracks in the segmentation images that were generated by deep learning. Crack FD at the peak load and the fracture failure load could be used as indicators of deflection hardening behavior, with threshold values of 0.83 and 0.86, respectively. Crack development can be divided into four stages based on load, FD, CMOD, and energy capacity with time: elastic segment, internal crack development segment, surface crack extension segment, and crack destabilization segment. FD shows an obvious exponential increase in the surface crack extension segment and crack destabilization segment, and the changing trend is basically parallel with the load in the surface crack extension segment. The FD of peak load and fracture failure load showed a trend of increasing and then decreasing as the fiber factor was increased. The FD value peaks at 585 when W/B = 0.35 and at 252 when W/B = 0.38. To achieve the best stress diffusion and crack propagation process and achieve the toughening objective, it is necessary to reasonably match the fiber factor and matrix strength. [ABSTRACT FROM AUTHOR]

• A novel visual omnidirectional measurement method has been proposed to measure In-situ residual fracture opening after hydraulic fracturing experiment. • Using Canny operator to correct the width of tortuous hydraulic fractures, the accuracy is improved by 33.4%. • The quantitative relationship between "acidizing effect" and "acid etching efficiency" in acid fracturing experiments is discovered. The laboratory fracturing simulation experiment is an important basis for the design and optimization of the on-site hydraulic fracturing process, and the fracture width is a key parameter for evaluating the fracturing effect. However, it is very difficult to directly obtain the in-situ residual fracture opening of the fracturing experiment. The reason is that the specimen is subjected to hydraulic action or other external forces to form a penetrating fracture surface, which displaces the original position of the fracture to be dislocated. This paper focuses on the characterization of the original residual fracture opening after the laboratory fracturing experiment and proposes a visual measurement method for the in-situ fracture width based on 3D digital image scanning technology. Hydraulic and acid fracturing studies confirmed its applicability, and residual fracture holes from the two conventional fracturing experiments were measured at the "mm" level. With the help of the Canny operator, the calculation method of zigzag residual fracture opening is revised, and the measurement accuracy of residual fracture opening is improved by 33.4%. In the meantime, by comparing and analyzing the fracture propagation characteristics of the "severe acid corrosion area" and "slight acid corrosion area" of 10%, 15%, and 20% gelling acid, the relationship between the gradient of the residual fracture opening and the "acidizing effect" and "acid etching efficiency" was obtained. This paper mainly solves the problem that in-situ residual fracture opening cannot be obtained in fracturing experiments and can provide parameter guidance for quantitative evaluation of fracturing effects and estimation of fracturing productivity. [ABSTRACT FROM AUTHOR]

Layered stacking structures, also known as laminations, are characteristic features of shale formations. These laminations with varying properties significantly influence the propagation path of hydraulic fractures. In this study, different laminations exhibit varying mechanical properties (mechanical contrasting). The interfaces between laminations are continuously stacked weak planes (lamination weak interfaces, or LWIs) with fracture toughness significantly lower than the rock matrix. The propagation mechanism of hydraulic fractures within laminated shale is not yet fully understood, particularly the complex propagation behavior crossing LWIs. This paper effectively predicts hydraulic fracture propagation patterns and paths based on He-Hutchinson's theory. Several typical mechanical behaviors during the interaction between the hydraulic fractures (HFs) and LWIs can be characterized. A fully coupled numerical solver to simulate the propagation of hydraulic fractures in laminated shales is developed based on the discrete fracture model and the extended finite element method (XFEM), which can accurately capture the local features of the physical field by using different enrichment functions. The study investigates the effects of varying elastic modulus and stress differences on the interaction between hydraulic fractures and LWIs. And two multi-lamination problems containing inclined laminations are studied, demonstrating the potential widespread application prospects of the method in this paper. [ABSTRACT FROM AUTHOR]

Characterizing the cracking behavior of epoxy adhesive material is of great importance for composite structures. Recently, the phase field model has emerged as the preferred method for predicting the crack propagation. This paper presents a length-free phase field model considering the characteristics of epoxy adhesive materials. The proposed model is formulated within a framework that decomposes the phase field fracture driving force, ensuring that it adequately considers the tension/compression asymmetry of the epoxy adhesive materials. The effects of hydrostatic pressure, deviational stress, and friction are incorporated into the model by employing a modified Drucker-Prager failure criterion. The failure criterion is included in the phase field model using the effective stress invariants. Furthermore, the internal length scale, previously considered to lack real physical meaning, is reformulated based on material strength. This model addresses the challenge of measuring the internal length of epoxy materials. It serves as a valuable reference for applying phase field models to epoxy materials. The accuracy of the model is validated through an L-shaped plate simulation, and an attempt using the model to predict the crack development in thick epoxy adhesive joints is undertaken. Several representative samples are simulated, including three double cantilever beams with different configurations. The numerical results demonstrate a good correlation with experimental data, highlighting the potential of the model in simulating the crack propagation in epoxy adhesive joints. [ABSTRACT FROM AUTHOR]

Many biological materials such as tendons and muscles contain helical fibers. In this paper, the fracture behavior of such chiral composites is investigated through a combination of theoretical analysis and finite element simulations. A mesoscopic fracture mechanics model of helical fiber-reinforced biological composites is presented, with the effects of interfacial damage and fiber breakage. A cohesive law is adopted to characterize the interfacial damage induced by the relative slipping between the fibers and the matrix. The theoretical model agrees well with the numerical results. The optimized fiber radius that can maximize the fracture toughness of the composites is determined. The effects of interfacial (e.g., bonding strength and energy dissipation) and material properties (e.g., strength and elastic modulus) on the resistance to crack propagation are revealed. Our results show that the composites reinforced by helical fibers exhibit comprehensively excellent mechanical properties, e.g., simultaneous high strength, stiffness, and fracture toughness. This work not only helps understand the structure–property interrelations of biological chiral composites, but also provides inspirations for designing high-performance engineering materials. [ABSTRACT FROM AUTHOR]

The mechanical performance of rock masses is significantly impacted by the existence of cracks. Distribution of the cracks may result in different mechanical or fracture behaviors of rock. To gain a preliminary understanding of such problems, a series of numerical tests of three-point bending (TPB) are designed and carried out with the consideration of single pre-notch and double pre-notches. The numerical method of grain-based model (GBM) approach is employed in this paper, with a validation implemented by comparing the results with previous experiments to demonstrate the reliability of this model. Afterward, a comprehensive investigation, including the mechanical behavior, strength characteristics, crack evolution and progressive failure mechanism of the above mentioned TPB tests are conducted. The conclusions are as follows: (1) During TPB tests, as the offset distance increases, the fracture mode of the single pre-notched specimens gradually transitions from Mode I to Mode II, with the peak fracture toughness occurring at a mixed Mode I-II fracture condition (2 p / s = 0.4). Moreover, the failure angle, notch open degree and expansion area all tend to rise regardless of specimens of single or double pre-notches. (2) A thorough exploration of crack evolution shows that the specimens primarily fracture during the crack propagation and failure stages. Shear failure predominates among these stages, with microcracks mostly occurring inside the rock mineral grains. (3) When offset distance increases to a certain degree (2 p / s = 0.8), the fracture of specimen ceases to be governed by the pre-notch; instead, it occurs directly from the middle of the beam specimen. This phenomenon can be attributed to the reduction of stress concentration at the notch tip, as inferred from analysis of the contact force chain. (4) In double pre-notched specimen, microcracks initiate at both pre-notches, but the final failure results from crack propagation at one notch tip. Compared to single pre-notched specimen, the presence of double pre-notches exhibits superior fracture resistance performance. [ABSTRACT FROM AUTHOR]

Stress intensity factors (SIFs), which represent the stress distribution of material crack tip, are crucial in the field of rock fracture mechanics. However, the existing photoelastic methods of calculating SIFs are inaccurate, and others are constrained by experimental data. In this study, the focus is on SIFs in brittle materials, such as rock. This paper proposes an enhanced five-parameter photoelastic method to calculate SIFs at the crack tip, building upon the existing three-parameter photoelastic method. Our photoelastic experiments involve semicircular rock-like specimens with asymmetrical inclined cracks subjected to three-point bending loading, and we acquire isochromatic fringe patterns around the crack tip. A numerical simulation is carried out to verify the accuracy of the five-parameter method. The results demonstrate good agreement between SIFs obtained via the photoelastic five-parameter method and numerical simulations. We find that the five-parameter method is more accurate than the photoelastic three-parameter method. Notably, our model identifies the maximum value of mode II SIF, a critical parameter for predicting crack propagation and the potential for structural failure. This work may be useful in advancing the calculation of SIFs in rock fracture mechanics. [ABSTRACT FROM AUTHOR]

In this paper, the fracture performance of nano-metakaolin (NMK) cement mortar during early hydration period was investigated. Different NMK contents (0 %, 3 %, 5 %, 7 %) were considered, and three-point bending tests were conducted. The digital image correlation technology and acoustic emission technology were utilized to analyze P -CMOD curves, initial fracture toughness, unstable fracture toughness, fracture energy, cumulative AE hits, and cumulative AE energy, AE source locations of cement mortar at early hydration stages. Furthermore, SEM experiments were utilized to analyze the mechanism by which NMK affects fracture performance of cement mortar. The results indicate that the incorporation of NMK enhances the fracture properties of cement mortar, with the most suitable NMK content being 5 %. The addition of NMK increases the cracking load, peak load, and the CMOD at the peak load of the cement mortar at 3 d, 7 d, and 14 d. The cracking load and fracture energy of the cement mortar with 5 % NMK increase by 22.5 % and 35.7 % respectively, compared to ordinary cement mortar at 14 d. NMK enhances the initial fracture toughness and unstable fracture toughness of the cement mortar, improving its crack propagation resistance. The unstable fracture toughness of the cement mortar is the largest when the NMK content is 5 % at 14 d, which is 31.6 % higher than that of ordinary cement mortar. Furthermore, NMK increases the cumulative AE energy and fracture energy of the cement mortar, increasing the cumulative ring counts and cumulative AE hits, causing the crack propagation path to deviate and resulting in improved crack resistance. The cumulative ring counts and AE hits for the cement mortar with 5 % NMK are 42.9 % and 66.2 % higher, respectively, than those for ordinary cement mortar at 14 d. NMK significantly modifies the cement matrix, thereby enhancing the fracture resistance of cement mortar. • NMK enhances the fracture resistance of cement mortar at early hydration age. • NMK causes the crack propagation path of cement mortar to deviate. • NMK increases the energy required for the fracture of cement mortar. • The propagation process of cracks in NMK cement mortar is investigated. [ABSTRACT FROM AUTHOR]

• The crack damage behavior of concrete is inversely analyzed. • The mechanical results and cracking area are taken as targets. • An inverse method of cohesive zone model is proposed. • The applicable parameter range of control factors is obtained. An accurate description of concrete crack propagation is essential to practical engineering. In this paper, the cohesive zone model (CZM) is used to investigate the macroscopic mechanical properties and the microscopic crack damage behavior of concrete beams in the three-point bending test. Five key factors controlling the cracking of cohesive elements, namely mode I fracture energy, mode II fracture energy, shear strength, tensile strength, and elastic modulus (stiffness), are subjected to parametric examinations. Based on macro-mechanical properties and micro-cracking, the test results and parametric models of specimens are inversely analyzed. The applicable parameter range of control factors in the three-point bending simulation is obtained. Considering the quantitative aggregate information of specimens with different mix proportions, three computation models with different aggregate areas are established. The quantitative results of crack propagation are derived by applying the parameter range. Finally, the accuracy of the parameter range is validated based on the simulated and experimental mechanical properties and quantitative results of cracks. [ABSTRACT FROM AUTHOR]

High-fidelity simulations are increasingly called-upon to resolve the nucleation of instabilities such as crack initiation and propagation and fluid mixing. While multiscale modeling capabilities have progressed rapidly over recent decades, associated simulations still present a computational burden, thus often preempting a systematic statistical analysis of related problems. Given the paucity of data that relate micro-structure to macroscale behavior, and the unavoidable modeling errors at both scales, the lack of a probabilistic characterization significantly limits the value of highly-resolved numerical simulators. The goal of the present research is to develop a probabilistic model that encodes pathwise relationships between micro and macro scales. Specifically, we develop a switching diffusion model to relate damage evolution, characterized at the microscale, to system performance identified with a macroscale property. Microscale behavior is modeled as a Markov switching process with a finite state space while the macroscale counterpart is modeled as a continuous-state diffusion process. The interaction between macro and micro scales is captured by coupling these two processes. Calibrated by data, the switching diffusion model can generate, with minimal computational effort, sample paths with prescribed statistics. The proposed model contributes new capabilities and perspectives at the interface of multiscale simulation, uncertainty quantification, and stochastic modeling. • The paper proposed a new stochastic model for interactions between subscale damage evolution and coarse scale stress–strain behavior. • The model is based on hybrid switching diffusions where damage accumulation is described as a finite state Markov process while stress and strain are described as a vector diffusion process. • The model is calibrated using high-fidelity simulations. [ABSTRACT FROM AUTHOR]

• Mixed-mode loading significantly influences fatigue crack growth in SAPH440 material. • CTS specimen and multi-level loading technique were used to study mixed-mode fatigue. • Mode II loading increases threshold stress intensity factor in mixed-mode conditions. • Fatigue crack propagation rate depends on applied load angles in multi-level loading. In this study, the effect of mixed-mode loading on fatigue crack growth under varying applied loads for SAPH440 material was experimentally investigated. Previous research has either examined the effect of mixed-mode loading at a fixed angle or its effect on slanted cracks. This paper uses a CTS specimen and a loading device to apply varying angles of load during Mode I loading conditions. Initially, a numerical analysis was performed to validate existing equations for the stress intensity factor, which quantifies the crack driving force in the experiments. In the crack initiation region, load shedding techniques and load increasing techniques were used to confirm fatigue cracking considering mixed-mode effects. The change in the threshold value according to the loading angle was also evaluated. In the crack propagation region, a multi-level loading technique was employed to assess the mixed-mode effects under varying loading angles. This process verified the mixed-mode effect under conditions where the applied load angle varies. The fatigue crack fracture surfaces were examined using digital camera capture and SEM. It was found that when mixed-mode loading occurs during Mode I loading, the fatigue crack propagation rate varies depending on the mixed-mode loading angle. [ABSTRACT FROM AUTHOR]

Digital image correlation is a widely used technique in the field of experimental mechanics. In fracture mechanics, determining the precise location of the crack tip is crucial. In this paper, we introduce a novel crack tip detection algorithm based on displacement and strain fields obtained by digital image correlation. Iterative crack tip correction formulas are discovered by applying deep symbolic regression guided by physical unit constraints to a dataset of simulated cracks under mode I, II and mixed-mode conditions with variable T-stress. For the training dataset, we fit the Williams series expansion with super-singular terms to the simulated displacement fields at randomly chosen origins around the actual crack tip. We analyse the discovered formulas and apply the most promising one to digital image correlation data obtained from uniaxial and biaxial fatigue crack growth experiments of AA2024-T3 sheet material. Throughout the experiments, the crack tip positions are reliably detected leading to improved stability of the crack propagation curves. • Crack tip correction formulas learned from FE simulations with physical deep symbolic regression. • Distinct correction formulas based on Williams coefficients for mode I, mode II, and mixed mode load cases. • Application to uniaxial and biaxial fatigue crack growth experiments accompanied by full-field and high-resolution DIC. [ABSTRACT FROM AUTHOR]

• Two incidences of failures of collective control rods of a particular type of helicopter were investigated. • In both the cases, the failure occurred at the threaded region of Al-alloy tube by fatigue mechanism. • Reasons for the two failures were different; manufacturing deficiency in one and assembly error in the other. This paper presents two incidences of failures of collective control rods which resulted in accidents to a particular type of helicopter. The control rods were made of 2024 Al-alloy tubes fitted with fork at one end and a spherical bearing at the other end (eye-end). In terms of physical appearance, the two failures in the control rods were identical to each other wherein there was fracture in the Al-alloy tube at the eye-end. Fractography study confirmed that in both the cases, multiple fatigue cracks had initiated over a sector at the internal thread roots on the Al-alloy tubes corresponding to 1st/2nd thread on the eye-end stud. After initiation, the cracks had propagated progressively into the tube-wall and then along the circumferential direction. As the crack propagation progressed, the load bearing capacity of the tubes diminished resulting in final overload fracture under the operational load at the time of accidents. Although failures in both the control rods looked alike in terms of failure location, fracture pattern and fracture mechanism, the primary reasons of failures were found to be different. Investigation revealed that premature fatigue crack initiation was due to non-uniform stress distribution on the internal threads of the control tube with increased level of stress over a sector. In one case, the non-uniform stress distribution resulted from thread manufacturing deficiency, and in the other case, it was due to incorrect assembly at the eye-end. [ABSTRACT FROM AUTHOR]

• We proposes a multiscale extension finite element method to simulate the fatigue crack propagation behavior of steel bridge RF details. • The crack propagation behavior of OSD longitudinal rib weld toes, transverse diaphragm weld toes, and transverse diaphragm arc notches was discussed. • The influence of fatigue crack length and angle on the initial crack stress intensity factor (SIF) of adjacent details was analyzed. In recent years, it has been found that multiple cracks coexist in the existing steel bridge orthotropic steel decks (OSDs) longitudinal rib-to-floorbeam (RF) details. The synergistic expansion mechanism of multiple cracks in the orthotropic steel bridge deck panel is still unclear. This paper proposes a multiscale extension finite element method based on ABAQUS and FRANC 3D interactive technology to simulate the fatigue crack propagation behavior of steel bridge RF details under dynamic vehicle loading. The effectiveness of this method is verified by comparing experimental data. The crack propagation behavior of longitudinal rib weld toes, transverse diaphragm weld toes, and transverse diaphragm arc notches is studied, and the influence of fatigue crack length and angle on the initial crack stress intensity factor (SIF) of adjacent details is discussed. [ABSTRACT FROM AUTHOR]

• Crack propagation has a significant impact on flight safety. • It is difficult to predict crack propagation accurately. • A novel method called AK-TCN (Attention-based Kernel TCN) is proposed for crack prediction. • The AK-TCN includes theoretical information assistance, multi-dimension feature fusion, and adaptive multi-scale convolution. • Compared with SOTA models and ablation models, the proposed AK-TCN achieves the best prediction accuracy. The crack propagation of wing rivet holes has a significant impact on flight safety. However, accurate crack prediction is difficult. On the one hand, the calculated values based on traditional mechanics theory are conservative and have a large safety margin. On the other hand, the predicted values of deep learning do not match the mechanical theory, and the significant role of peak load in crack propagation has not been fully reflected. Therefore, this paper proposes a novel AK-TCN model for the crack prediction, considering the theoretical information constraints. Firstly, the "theoretical information assistance" technology is adopted. The calculated values (strength, life) based on mechanical theory and the measured values (stress) based on sensors are jointly used as inputs, enabling the AK-TCN model to fully extract valuable information. Secondly, the "multi-dimension feature fusion" technology is adopted. The theoretical information and measured information are mixed, and the importance of different information is adaptively adjusted, enabling the AK-TCN model to balance the foundational nature of theoretical information and the time-varying nature of measured information. Then, the "adaptive multi-scale convolution" technique is adopted. The temporal features in different periods are perceived by multi-scale convolution, and weights of them are assigned by attention mechanisms, so that the AK-TCN model can focus on certain key features that have a significant impact on crack propagation. Finally, the accuracy, effectiveness, and robustness of the proposed AK-TCN are verified by comparative experiments, ablation experiments, and noise experiments. [ABSTRACT FROM AUTHOR]

Combining interlocking structures and gradient design, this paper proposes a 2D biomimetic nacreous composite material with a gradient interlocked structure. Experimental and numerical simulation methods are employed to investigate the initiation and propagation behavior of cracks in the regular interlocking and gradient interlocked biomimetic nacreous composite materials. Samples of biomimetic nacreous composite materials with pre-existing cracks are manufactured using 3D printing technology, and uniaxial tensile tests are conducted to explore their crack propagation behavior. For biomimetic nacreous composite materials with periodic interlocking structures, the interlocking angle is found to play an important role in the toughening mechanism of composites. In biomimetic composite materials with large interlocking angles, crack inhibition effects are achieved through structural gradient design, effectively preventing catastrophic failure. Within the numerical analysis framework, a cohesive zone modeling approach is employed to represent the softer phase of the material, and the numerical simulation are validated by direct comparison with experimental results. In addition, a comprehensive numerical analysis is carried out to comprehend how the structural gradient affects the spread of cracks in these nacreous composites. This research not only illuminate the underlying deformation and toughening mechanisms intrinsic to interlocking nacreous composites but also pave the way for innovative strategies in the design of biomimetic materials through the incorporation of structural gradients. [ABSTRACT FROM AUTHOR]

• A nonlocal energy-informed neural network is proposed to address the crack propagation. • Minimizing the peridynamic potential energy is considered as loss function. • Transfer learning is introduced to enhance efficiency and effectiveness. Discontinuities, such as joints, faults and pores, are prevalent in rock formations, significantly impacting the fracture behavior of rocks. This paper proposes an energy-driven machine learning framework to address crack initiation and propagation in rock-like materials by considering long-range interactions. By leveraging the minimization energy principle, the displacement of physical system is determined by minimizing the peridynamic potential energy instead of directly solving the equilibrium equation, which serves as the neural network's loss function. An incremental form loss function and transfer learning technique are developed to account for the cumulative effects of all preceding loading steps. Furthermore, the critical strain energy density criterion is established from an energy perspective. A key advantage of the proposed neural network lies in evaluating peridynamic strain energy through spatial integration rather than spatial derivatives, thus bypassing the limitations of automatic differentiation encountered in original physics-informed neural networks at crack surfaces. Notably, the proposed approach inherits the ability of peridynamics to simulate spontaneous damage evolution and crack propagation without necessitating special crack treatment techniques. Finally, the accuracy and effectiveness of the proposed approach is verified via comparison with analytical solutions, experimental observations, or classical numerical methods in fracture analysis of rock-like materials subjected to various quasi-static loading conditions. [ABSTRACT FROM AUTHOR]

• The multiscale scheme incorporates the strain rate effect in composites. • The microscale RVE accurately captures the off-axis damage process in composites. • Shear enhancement greatly affects the dynamic behavior of 3D braided composites. In this paper, a dynamic multiscale model is proposed for three-dimensional four-directional (3D4D) braided composites, considering the effects of strain rate and shear enhanced failure mechanism. The strain rate-dependent constitutive models are established for both resin and yarns. The accuracy of the yarn model is validated by comparing the simulated stress-strain curves with the experimental results obtained from the Split Hopkinson Pressure Bar (SHPB) tests with various strain rates. The shear enhancement coefficient of the yarn is determined from the failure envelopes with a discussion of crack propagation angles. The results show that, based on the calculated microscale properties, the mesoscale model accurately predicts both the longitudinal and transverse compressive strain-stress behavior of 3D4D braided composites at different strain rates. A comparative analysis reveals that the shear-enhanced failure model achieves a better prediction compared with other counterparts, such as Hashin-Rotem and Tsai-Wu Models. The proposed dynamic multiscale scheme for 3D braided composites is an efficient and accurate tool to characterize their multiscale features and strain rate-dependent behavior. [ABSTRACT FROM AUTHOR]

• Matrix, strain rate and temperature affect the mechanical property of the alloy. • High strain rate and temperature led to the fracture in the model, and the crack path is located in the matrix- γ Phase. • Lomer-Cottrell lock and stacking fault tetrahedron affect the strength of alloy. Nickel (Ni)-based single-crystal superalloys are of great importance in the aircraft industry due to their excellent mechanical properties, and cracks as unavoidable defects may affect the mechanical performances of materials dramatically. In this paper, large scale molecular dynamics (MD) simulations are carried out to understand the deformation mechanisms of Ni-based single crystal with a central crack under tension. Here, the effects of matrixes (γ, γ′ and γ/γ′), strain rates (1 × 109 s−1 ∼ 3 × 109 s−1) and temperatures (300 K∼900 K) on the role of crack propagation are considered. It is observed that dislocations and slip systems in the γ′ model are concentrated near the crack, resulting in the rapid expansion of dislocation, which leads to the fastest crack growth speed and early fracture. While the crack propagation rate of γ and γ/γ′ models are relatively slow, due to the combined action of the Lomer-Cottrell lock and stacking fault tetrahedron structure and Stair-rod dislocation, which hinders crack propagation. In addition, deformation at increased strain rates and/or reduced temperatures, lead to superior yield stress and Young′s modulus for models with a central crack at γ/γ′ interface. On the other hand, high temperature and high strain rate will promote crack propagation in the γ phase, and the higher the strain rate and/or temperature, the faster the crack propagation speed will be. These results will enrich our understanding on the crack propagation and evolution mechanisms in Ni-based single crystal superalloy. [ABSTRACT FROM AUTHOR]

For the practical use of cryogenic propellant tanks made of CFRP laminates, experimental elucidation of the laminates' microstructural damage propagation behavior at cryogenic temperatures is important. This paper presents a newly developed tensile test rig that enables in-situ observation of microscopic damage using an optical microscope at cryogenic temperatures using a Gifford–McMahon refrigerator. In-situ observations of microscopic damage under uniaxial tensile loading were done at room temperature (290 K, 17 °C) and at 30 K (−243 °C) on cross-ply thin-ply CFRP specimens of three kinds with different 90° layer thicknesses. The results demonstrated that the crack propagation behavior is independent of temperature, that the matrix crack density is higher, and that the onset of matrix crack initiation strain is lower at 30 K than at 290 K. Furthermore, the thermal strain within 90° layer at 30 K and at 290 K was estimated using finite element analyses (FEA). The FEA results suggest that the decrease in onset strain of matrix crack initiation at 30 K is mainly attributed to the increase in the thermal strains within the 90° layer. [Display omitted] [ABSTRACT FROM AUTHOR]

This paper presented a novel method to characterize the fracture toughness and cohesive law of laminated composites under combined compression and shear at high loading rate. Compact compression specimens with off-axis fibres which introduce the in-plane shear stresses were conducted on the uniaxial bidirectional electromagnetic Hopkinson bar system and the displacement field and strain field were recorded by the high-speed camera for the digital image correlation analysis and J-integral calculation. The results reveal that the in-plane shear stresses bring the increase of fracture toughness at crack initiation and propagation and advance the damage initiation of the specimens. The fracture surfaces indicate that the shear stresses cause the fibre bundles' shear failure during the formation of the kink band, accompanied by more energy dissipation with the increase of off-axis angle. [Display omitted] • Fibre kinking fracture toughness and cohesive law of laminated composites at high loading rate was investigated using compact compression specimens with different off-axis angles. • The in-plane shear stresses bring the increase of fracture toughness at crack initiation and propagation and advance the damage initiation of the specimens. • The in-plane shear stresses cause the fibre bundles shear failure at high loading rate during the formation of the kink band, accompanied with more energy dissipation. [ABSTRACT FROM AUTHOR]

• The BM specimen's lifetime at unstable crack growth is over twice that of the as-welded specimen. • The crack lengths of as-welded and BM specimens are similar at the onset of unstable crack growth. • ΔKCJP based on the CJP model is used for FCG assessment of welded joints. • The CJP model's description of the plastic zone at the fatigue crack tip in welded joints is validated. The fatigue crack growth behavior in welds is difficult to evaluate due to complex internal stresses and microstructural differences. This paper uses the CJP model based on displacement field variations to describe the fatigue crack growth behavior and the size of the crack tip plastic zone in welds. First, fatigue crack growth rate tests were conducted on base metal and as-welded specimens. The digital image correlation technique was used to capture the speckle pattern variations on the specimen surface during crack growth, obtaining the crack tip displacement field required by the CJP model. Based on this, by calculating the stress intensity factor ranges Δ K and Δ K CJP , two d a /d N –Δ K (Δ K CJP) curves defined by the traditional and CJP models were obtained, proving the model's applicability for describing fatigue crack growth behavior in welded joints. Finally, the CJP model was used to calculate and compare the crack tip plastic zones of base metal and as-welded specimens. It was found that the maximum error for the as-welded specimen was 37.84%, occurring at the initial stage of crack propagation and gradually decreasing with the fatigue process. [ABSTRACT FROM AUTHOR]

A Yoffe-type moving crack means that it propagates with a constant speed, healing at the rear tip, and remains an unchanged crack length during its crack propagation. Different from the traditional mode-III moving crack, this paper studies a Yoffe-type anti-plane shear crack subjected to couple tractions, not force tractions, on the crack faces. The governing equation is first deduced. Employing the Fourier transform, one derives two hypersingular integral equations for prescribed bending and twisting couple stresses on the crack surfaces, respectively. With the help of the Chebyshev series expansion, each hypersingular integral equation is converted to a system of linear algebraic equations. The strain and couple/force stress intensity factors are numerically calculated. Based on the numerical results, the couple/force stress field as well as the strain energy density is derived for each case. The obtained results indicate the size-dependent mechanical behavior. Moreover, the velocity and flexure–torsion effect may cause a redistribution of the couple/force stress field. The crack velocity and flexure–torsion effect also play an important role in assessing the crack bifurcation angle. • Yoffe-type mode-III crack subjected to bending and twisting couple tractions is studied. • Hypersingular integral equation is derived and solved via Chebyshev expansion method. • The singularities of r − 1 / 2 and r − 3 / 2 of the couple- and force-stresses are found. • Crack velocity and the couple stress parameter affect the crack bifurcation angle. • The size-dependent strain energy density factor is shown. [ABSTRACT FROM AUTHOR]

Delamination damage is a common failure mode of carbon fiber reinforced polymer (CFRP) laminates, which severely limits their application. This paper proposes a novel interlaminar toughening structure based on intrinsic and extrinsic multiscale toughening mechanisms using nanoscale multi-walled carbon nanotubes (MWCNTs) and microscale core-shell rubber (CSR). The resin sample M-0.5/C-8, containing 0.5 wt% MWCNTs and 8 wt% CSR, exhibited significant improvements in fracture toughness, with increases of 183.3 % in the mode-I critical stress intensity factor (K IC, Resin) and 412.0 % in the critical energy release rate of resin (G IC, Resin). However, its flexural strength and modulus decreased by 3.1 % and 3.3 %, respectively. Introducing MWCNTs and CSR into the interlayers of the CFRP, the interleaved toughened CFRP laminate exhibited a 123.3 % improvement in the mode-I critical energy release rate (G IC, Comp) and a 79.6 % increase in the mode-II critical energy release rate (G IIC, Comp) during the crack propagation stage, without sacrificing flexural performance. This remarkable enhancement in interlaminar fracture toughness results from the simultaneous triggering of nanoscale extrinsic toughening and microscale intrinsic toughening during crack growth. The flexural properties and fracture toughness of Epoxy/MWCNTs/CSR composites were also investigated to understand the properties transformation from resin matrix to CFRP. Morphological characterization and numerical analysis were used to analyze the synergies and constraints between two energy dissipation behaviors. [Display omitted] • Toughening strategies for engineering applications of CFRP. • CFRP toughening mechanism:multiscale intrinsic and extrinsic toughening. • Improving CFRP interlaminar fracture toughness without losing in-plane properties. • Mechanisms of intrinsic-extrinsic synergistic toughening. [ABSTRACT FROM AUTHOR]

[Display omitted] • First ever recommendations for the design of steel microstructures including second-phase retained austenite to resist fatigue crack propagation. • Short fatigue cracks grow towards second-phase retained austenite which transforms into martensite inside the plastic zone associated with the crack. • Retained austenite retards short fatigue crack growth by inducing crack deflection, branching and roughness-induced crack closure. • Large retained austenite grains with high aspect ratio and major axis parallel to the principal tensile stress promote fatigue toughness. Previous research has consistently found that introducing metastable retained austenite (RA) as a second phase retards the failure of steel under fatigue. However, the reasons for this benefit are not understood. Accordingly, the properties of RA most advantageous to resist fatigue are not known. Within this context, this paper examines the interaction between second-phase RA and short fatigue crack growth in a steel processed via quenching and partitioning, using quasi in situ electron backscatter diffraction experiments. Results show that most RA transforms into martensite under the plastic strain surrounding the crack. They also reveal various mechanisms whereby RA transformation delays short fatigue crack propagation; transformation-induced crack closure (TICC), crack deflection and branching, and roughness-induced crack closure (RICC). Crack deflection and branching are driven by a tendency of cracks to propagate towards transformed RA, which is against the previous assumptions in the literature. Furthermore, the impact of crack deflection/branching on retardation is more powerful than that of TICC acting alone. Microstructures including second-phase RA should avoid RA-lean areas and promote elongated RA grains, with relatively large size, and major axis normal to the preferential crack growth direction. Untransformed RA within the plastic zone (i.e. overstabilized) does not contribute to crack retardation. [ABSTRACT FROM AUTHOR]

Rubber-metal bonding interface prone to adhesive failure. Cohesive zone model (CZM) is widely used in numerical simulation analysis of fracture of interfacial mechanics. In this paper, the traction-separation curve of the bonding surface of vulcanized rubber-metal specimen was obtained by tensile shear test and dumbbell rubber uniaxial tensile test. Then, the influence of shear strain of rubber itself was removed by numerical simulation of tensile shear of rubber, so as to identify the CZM parameters of rubber-metal interface.On this basis, a numerical model of the cohesive force of vulcanized rubber-metal was established, and the stress distribution, variation and damage evolution of the interface along the shear direction were analyzed microscopically. The initiation and propagation of cracks are explained and compared with the failure process and phenomenon of the test interface. The traction-displacement relationship curve was analyzed macroscopically, which was consistent with the traction-displacement relationship curve obtained by the experiment, and the error is less than 5 %. The CZM could accurately express the interface mechanical relationship of the experimental specimen. In addition, the influence of the width and length of the bonding interface on the mechanical properties of the bonding is also analyzed. With the increase of the width or length of the bonding interface, the maximum traction force increases linearly, but the relative displacement value of the initial bonding failure remains unchanged, and the length of the bonding interface has a more significant effect on the maximum traction force. The results show that the cohesive zone model can accurately and effectively analyze the shear failure of the vulcanized rubber-metal bonding surface, which provides a reference for the study of the failure of the bonding surface of other elastic composites. [ABSTRACT FROM AUTHOR]

• The LCF tests of notched specimens under three temperatures after different degrees of initial overload treatment was conducted. • The initial overloads could significantly improve the crack initiation life, but could also introduce damage near the notch surface, especially for large overload situations. • The LCF life model considering the sensitivity of overload induced residual stress can give a more accurate prediction. • A recommendation to improve the fatigue life of GH4169 alloy by initial overload was given through comprehensive experimental results and finite element model analysis. In this paper, the effect of initial overload on the low cycle fatigue life of GH4169 alloy at different temperatures was studied. The plate specimen with a central hole was designed to perform low cycle fatigue tests at 20 °C, 500 °C and 650 °C with variable initial overloads. Results showed that the subsequent crack propagation rate depended on both overload ratio and following test temperature, and excessive overload treatment would also damage the surface or internal grains of the specimens through fracture characteristics under SEM. A finite element model was adopted to analyze the residual stress and stress-strain field at the edge of the central hole. Then, the stress and strain data were input to three strain-based model to predict the fatigue life of GH4169 alloy considering residual and mean stresses. Based on the combination of the experimental results and model prediction, the suggestion to improve the fatigue life of GH4169 alloy by initial overload can be put forward as following: a single initial overload makes the maximum local stress reach 90 %–93.5 % of the true ultimate stress of the material, so as to maximize its fatigue life. [ABSTRACT FROM AUTHOR]

This paper presents a numerical simulation method employing a quasi-adaptive optimization approach in the multi-scale modeling process. By integrating 3DEC with the Neper algorithm, the study develops a 3DEC-GBM model that surpasses traditional DEM in describing intra-grain damage. Focusing on the optimization of critical fracture areas, this method improves simulation accuracy while avoiding unnecessary model complexity. Validated through Brazilian splitting and uniaxial compression tests, the approach significantly enhances simulation fidelity and computational efficiency. It accurately identifies and refines primary fracture surfaces, which are essential for capturing crack initiation and propagation. [ABSTRACT FROM AUTHOR]