Crack Tip Stress Research Articles

Stress interaction and crack penetration mechanism between slit charge blasting holes in high in-situ stress rock mass

Abstract The research primarily focuses on the stress interaction between boreholes in slit charge blasting and the crack penetration mechanism. It thoroughly explores the impact of these stress interaction on crack propagation and analyzes the blasting stress wave evolution between boreholes and characteristics crack propagation characteristics. First, numerical simulation was run to look into the inter-borehole stress interaction mechanisms. Results indicate that stress wave interaction between boreholes promotes the formation and extension of radial directional cracks. However, interactions between the stress fields at crack tips and the stress wave from adjacent boreholes, as well as between crack tip stress fields themselves, negatively affect the connectivity of radial cracks between boreholes. Furthermore, the study also examines how in-situ stress and borehole spacing affect crack connectivity between boreholes. Simulation findings indicate that in-situ stress weakens hoop tensile stress between boreholes, hindering crack connectivity and suppressing the slit charge's directed blasting impact. Reducing borehole spacing can improve crack connectivity between boreholes. However, reducing spacing can negatively impact the directional blasting effect, potentially compromising surrounding rock stability. Finally, Response Surface Methodology (RSM) was used to analyze the effects of borehole spacing and in-situ stress on crack penetration, and a predictive model was constructed. Based on this, the study provides a theoretical foundation and scientific reference for the optimization of slit charge blasting parameters under high in-situ stress conditions.

The role of the second non-vanishing terms in the material failure curve on APL 5L steel

PurposeIt is now well-known in the fracture-mechanics community that a single fracture parameter alone may not be adequate to describe crack-tip condition. To address this problem, there has been a recent surge of interest in crack-growth behaviour under conditions of low crack-tip stress triaxiality. This paper exploited the K-A3 crack approach, which was derived from a rigorous asymptotic solution and has been developed for a two-parameter fracture.Design/methodology/approachThe material failure curve or master curve, has been established as a result of the notched specimen tests. It was shown that the notch fracture toughness is a linear decreasing function of the stress. The use of the material failure curve to predict fracture conditions was demonstrated on gas pipes with the longitudinal surface notch.FindingsNo finding.Originality/valueThis approach requires that the constraint in the test specimen approximate that of the structure to provide an “effective” toughness for use in a structural integrity assessment. The appropriate constraint is achieved by matching thickness and crack depth between the specimen and structure.

Simulating hydrogen-controlled crack growth kinetics in Al-alloys using a coupled chemo-mechanical phase-field damage model

Environmentally Assisted Cracking (EAC) of 7xxx series aluminium alloys involves interactions between multiple physical phenomena, which ultimately influence the in-service life of critical components. In this work, we present a new model to study EAC in 7xxx series alloys, which is implemented in the multiphysics simulation framework, DAMASK. The chemo-mechanical model couples crack tip hydrogen generation, resulting from surface oxidation, and transport, with crystal-plasticity-governed intergranular crack propagation, through the microstructural trapping of hydrogen at dislocations, grain boundaries (GB), and crack tip stress fields. Large-scale simulations with realistic grain structures have been performed to provide novel insight into the dominant rate-controlling processes associated with intergranular EAC in 7xxx series aluminium alloys. The model was able to reproduce experimentally measured crack velocities under different loading conditions. Parametric studies indicate that, in addition to the GB network morphology, the crack growth rate was controlled by hydrogen generation at the crack tip with long-range diffusion having negligible influence. Additionally, the total hydrogen generated through crack tip oxidation appears to be more significant than the peak generation rate.

The regulation of dislocation and precipitated phase improving hydrogen embrittlement resistance of pipeline steel in high pressure hydrogen environment

In this study, the hydrogen embrittlement behavior of quenched pipeline steel tempered at 550 °C to 650 °C in a high-pressure hydrogen environment was analyzed. Hydrogen permeation tests and microstructural analyses indicated that the dislocation density of the steel decreases with increasing tempering temperature, while precipitates gradually nucleate and grow. These hydrogen traps interact with hydrogen atoms, resulting in significantly higher diffusible hydrogen content in steel tempered at 550 °C compared to that tempered at 600 °C and 650 °C. Fatigue crack growth (FCG) test results show that steel tempered at 600 °C and 650 °C exhibits significantly better hydrogen embrittlement resistance than steel tempered at 550 °C. This is primarily due to the combined effect of the high hydrogen concentration, high dislocation density and low nano carbide content in the steel tempered at 550 °C, which inhibits dislocation slip and emission, leading to high crack tip stress and rapid crack propagation. In contrast, the low dislocation density and and dispersed nano carbides in steel tempered at 600 °C and 650 °C facilitate some dislocation slip and emission, result in crack tip stress relaxation and reduced crack propagation rate. Properly controlling the initial dislocation density and increasing the density of irreversible hydrogen traps can enhance the strength of materials while improving their resistance to hydrogen embrittlement.

Effects of multiple reflected P waves on crack-tip stress and crack propagation in directional fracturing blasting

Directional fracturing blasting is effective for rock engineering, but it is inevitably disturbed by multiple reflected waves from different directions in natural rock mass due to discontinuous boundaries. Reflected waves affect both crack-tip stress and crack propagation, hence affect the results of directional fracturing blasting. In this paper, with the aid of high-speed photography, an optical caustics method is used to study effects of multiple reflected P waves on a directional blast-induced crack in a polymethyl methacrylate (PMMA) plate, specifically on crack path, crack fracturing mode, crack-tip stress and crack velocity. Crack-tip stress field is indicated by the shape of caustics pattern. Before the loading of reflected P waves, the mode I directional crack driven by blast-induced gases propagates in a straight path; crack-tip stress field is K-dominated, and crack-tip caustics pattern is consistent with classical caustics theory. On the contrary, under the loading of reflected P waves, the directional crack changes to be mixed-mode I + II and propagates in a curved path; Crack-tip stress field is non-K-dominated due to transient stress superposition of reflected P waves, and crack-tip caustics pattern is consistent with modified caustics theory. Transient stress superposition is not obvious for reflected P waves with a longer reflection distance. The tension loading of reflected P waves plays a more important role than the compression loading, which increases crack-tip stress intensity factors and crack velocity. This study provides a comprehensive understanding of effects of multiple reflected P waves from different directions on directional fracturing blasting.

Crack Growth Analytical Model Considering the Crack Growth Resistance Parameter Due to the Unloading Process

Crack growth analysis is essential for probabilistic damage tolerance assessment of aeroengine life-limited parts. Traditional crack growth models directly establish the stress ratio–crack growth rate or crack opening stress relationship and focus less on changes in the crack tip stress field and its influence, so the resolution and accuracy of maneuvering flight load spectral analysis are limited. To improve the accuracy and convenience of analysis, a parameter considering the effect of unloading amount on crack propagation resistance is proposed, and the corresponding analytical model is established. The corresponding process for acquiring the model parameters through the constant amplitude test data of a Ti-6AL-4V compact tension specimen is presented. Six kinds of flight load spectra with inserted load pairs with different stress ratios and repetition times are tested to verify the accuracy of the proposed model. All the deviations between the proposed model and test life results are less than 10%, which demonstrates the superiority of the proposed model over the crack closure and Walker-based models in addressing relevant loading spectra. The proposed analytical model provides new insights for the safety of aeroengine life-limited parts.

Very high cycle fatigue behavior of TC4 titanium alloy: Faceting cracking mechanism and life prediction based on dislocation characterization

This research analyzes the very-high-cycle-fatigue behavior of TC4 titanium alloy through fatigue tests at R = −1, −0.3, and 0.1. The results show that the S-N curves are all bilinear and exhibit three failure modes as surface slip failure, surface cleavage failure and interior cleavage failure. Transmission electron microscopy analysis reveals the dislocation structure in interior cleavage failure and suggests that the deformation mechanism of faceting cracking involves both anti-phase boundary shearing and stacking fault shearing mechanisms. It concludes that interior failure results from cleavage fracture of α grains due to dislocation slip. Based on the stress intensity factor of the maximum defect, a slip-cleavage competitive failure model was developed by considering factors such as control volume, defect size, external loading, and grain content, with good predictive results. Additionally, on the basis of the failure mechanism and crack propagation rate model, considering the coupled effects of crack tip blunting, stress ratio, Vickers hardness, and material fracture toughness on crack propagation, the crack propagation life prediction model is constructed. The life prediction model is further modified to be more conservative and accurate in predicting life by consideration the maximum defect size, providing important theoretical support and practical guidance for engineering applications.

Crack tip stress intensification in strain-induced crystallized elastomer

Natural rubber (NR) exhibits strain-induced crystallization (SIC), enhancing tearing strength and crack resistance. However, the reinforcement mechanism along with nonuniform strain around a crack tip remains unclear. We reveal the nonuniform stress field around a crack tip using the DIC-based deformation field data and a hyperelasticity approach. A hyperelastic strain energy density function (W) is derived to be able to replicate stress-strain data across various deformations, encompassing equal and unequal biaxial, uniaxial, and pure shear stretching. These data cover the full range and magnitude of deformations around the crack tip. SIC significantly impacts the singular behaviors of strain and stress near the crack tip, causing a pronounced stress increase and strain decrease within the SIC zone that extends up to approximately 100 μm away from the crack tip. This results in a distinct crossover in singularity power-law index between the SIC zone and the fully amorphous zone. With increasing crack opening, the stress upturn intensifies, and the crossover shifts away from the crack tip due to SIC zone enlargement and local crystallinity increase. These findings deepen our understanding of the physics of SIC near crack tips and its reinforcement mechanism in strain-induced crystallizable soft solid materials.

Mixed-mode crack-tip stress intensity factors measurements by caustics method: A comparison between low and high loading rate conditions

Mixed-mode crack-tip stress field is different in low and high loading rate conditions, resulting in different mixed-mode stress intensity factors (SIFs) measurements. How to correctly measure mixed-mode SIFs in different loading rate conditions is of critical importance. To this end, mixed-mode SIFs are measured and compared by optical caustics method with high-speed photography, specifically by the interpretation of crack-tip optical image, i.e., caustics pattern which reflects crack-tip stress field. Different mixed-mode caustics patterns in shape are observed in drop weight and blast loading conditions, indicating that corresponding crack-tip stress field and mixed-mode SIFs measurements are different. Under drop weight loading, mixed-mode caustics patterns are consistent with the classical caustics interpretation for SIFs measurements, while those under reflected P wave loading in blasts are not consistent. Therefore, a modified mixed-mode caustics interpretation is proposed and verified to be available for SIFs measurements in blast loading condition. Finally, underlying reasons for different mixed-mode SIFs measurements in low and high loading rate conditions are discussed, and it is concluded that in low loading rate condition, a longer loading time results in crack-tip K-dominated stress field which is suitable for the classical caustics interpretation, while in high loading rate condition, the loading time is too short to form K-dominated stress field in the crack tip, hence a modified caustics interpretation is necessary. This paper benefits correct applications of caustics method to mixed-mode SIFs measurements in different loading rate conditions.

Fatigue life prediction of cracked cross beam of mining linear vibrating screen under cyclic load

The cross beam of a mining linear vibrating screen is prone to cracking under long-term cyclic load. In order to accurately predict the fatigue life of the cracked cross beam, a coupled analysis method of vibration and crack propagation is proposed. A 2D dynamic model of the vibrating screen is established based on the finite element method, which is verified by the vibration test platform. The cracked Euler beam element is used to model the cracked cross beam. The effects of crack depth, amplitude of excitation force, frequency of excitation force, and crack location on the crack-tip stress intensity factor of the cracked cross beam are investigated in detail. In addition, an iterative method is proposed on the basis of the Paris model. The residual service life of the beam under different frequencies of excitation force, amplitudes of excitation force, spring stiffness, crack positions, and degrees of stiffness imbalance are discussed. The results demonstrate that the fatigue life of the beam increases as the frequency of excitation force and spring stiffness increase. The increase of the amplitude of excitation force and spring permanent deformation reduces the fatigue life. The conclusion obtained provide some theoretical guidance for the design and routine maintenance of mining linear vibrating screens.

Atomistic and continuum Ascertainment of The crack tip stress fields in anisotropic elastic cubic media

The article provides a comparative analysis of stresses associated with the crack tip in an anisotropic elastic medium with cubic crystalline symmetry of elastic properties under mixed loading conditions obtained by two fundamentally different approaches: atomistic simulations and continuum fracture mechanics methods. The atomistic modelling approach is premised on the application of the molecular dynamics (MD) method implemented in the open source code program Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). The continuum mechanics approach is based on the classical elasticity theory of anisotropic media, in which the mechanical fields associated with the crack tip are represented by the crack tip stress and displacement series expansions generalizing the well-known classical asymptotical presentation of M. Williams to the case of anisotropic media. Using the MD method, a large series of computations of the loading of monocrystalline copper and aluminum plates with a face-centered cubic crystal lattice weakened by a central crack applying the embedded atom potential (EAM) was implemented. MD modeling is aimed at determining the atomic stresses and strains near the crack tip. The computed atomic stresses were compared with the stress field determined by the continuum elasticity theory of anisotropic media for crystal lattices with cubic symmetry of elastic properties. A comparative analysis was carried out for the angular dependencies of the stress and strain tensor components at various selected distances from the crack tip for the entire range of mixed deformation forms starting from pure tensile loading and ending with forms close to pure transverse shear. It is ascertained that the crack tip fields determined on the basis of two fundamentally different approaches, precisely, discrete and continuum, are completely consistent with each other. It is established that mathematical methods of continuum fracture mechanics can be applied to describe stress, strain and displacement fields at the atomic level.

Multi-objective optimization, shrinkage and fracture properties of unsaturated polyester resin modified concrete for bridge deck pavement based on system theory

For the purpose of fabricating unsaturated polyester modified concrete (UPMC) with excellent shrinkage and fracture properties for bridge deck pavement, the optimization design of mix proportion and enhancement mechanism analysis were implemented based on system theory. Firstly, for unsaturated polyester resin (UPR) subsystem, the viscosity, mechanical properties and droplet-size distribution were analyzed to determine the types and dosage of auxiliary additives after emulsification treatment; Next, for UPMC mortar slave-system, the optimization design was implemented through the combination of experimental analysis and hybrid multi-attribute ellipsoidal decision of grey-target (HMEDG) model; Subsequently, for UPMC main-system, the optimal proportion was determined utilizing orthogonal design test. Finally, the variation law and enhancement mechanism on fracture properties and shrinkage characteristics of UPMC was analyzed by combining macroscopic test, thermogravimetry (TG) and X-ray diffraction (XRD). The results demonstrated that 2.0 wt%BPO+1.0 wt%DMA and meta-benzene types UPR were utilized as auxiliary additives for UPMC based on the results of HMEDG models. The demulsified and cured WUP might supplement the interior moisture losses based on humidity compensation, and substantially constrain the evaporation loss inside the matrix, upgrading the hydration degree and facilitating the generation of hydration products. The introduction of 3 %-6 % waterborne-UPR (WUP) would improve 28d-fracture toughness within approximately 23.33 %-49.32 %, and reduce the shrinkage deformation by roughly 28–43 % through inducing the crack tip stress redistribution against the initiation and propagation of interior microcracks and enhancing the homogenization and densification.

The toughening effect of twins on fracture in nanotwinned Cu during cyclic loading

Extensive studies have been focused on improving the fatigue performance of materials, as fatigue fracture is a primary mode of failure in material applications for structural components. The introduction of high-density twins emerges as a novel strategy for enhancing fracture toughness; however, the mechanisms driving this enhancement during fatigue remain elusive. In this work, the impact of twins on fracture toughness in nanotwinned Cu was investigated with correlated transmission electron microscopy under cyclic loading. The results revealed three toughening mechanisms, i.e., bridging, bending of twin lamellae and ductile cracking along twin boundaries. The occurrence of the three toughening mechanisms strongly depends on twin thickness and cracking orientations, as different dislocation modes are activated in varying scenarios. Specifically, bridging and ductile cracking along twin boundaries are facilitated by the pile-up and continuous emission of hard mode I dislocations, respectively, while the bending of twin lamellae is governed by the accumulation of same-signed soft mode dislocations triggered by crack-tip stress. These findings unveil the underlying toughening mechanisms of twins in nanotwinned metals during cyclic loading and offer valuable guidance for the design of high-toughness nanolayered materials.

On the loci of exactness for truncated Williams crack-tip stress expansions

On the loci of exactness for truncated Williams crack-tip stress expansions

Numerical Simulation and ANN Prediction of Crack Problems within Corrosion Defects.

Buried pipelines are widely used, so it is necessary to analyze and study their fracture characteristics. The locations of corrosion defects on the pipe are more susceptible to fracture under the influence of internal pressure generated during material transportation. In the open literature, a large number of studies have been conducted on the failure pressure or residual strength of corroded pipelines. On this basis, this study conducts a fracture analysis on buried pipelines with corrosion areas under seismic loads. The extended finite element method was used to model and analyze the buried pipeline under seismic load, and it was found that the stress value at the crack tip was maximum when the circumferential angle of the crack was near 5° in the corrosion area. The changes in the stress field at the crack tip in the corrosion zone of the pipeline under different loads were compared. Based on the BP algorithm, a neural network model that can predict the stress field at the pipe crack tip is established. The neural network is trained using numerical model data, and a prediction model with a prediction error of less than 10% is constructed. The crack tip characteristics were further studied using the BP neural network model, and it was determined that the tip stress fluctuation range is between 450 MPa and 500 MPa. The neural network model is optimized based on the GA algorithm, which solves the problem of convergence difficulties and improves the prediction accuracy. According to the prediction results, it is found that when the internal pressure increases, the corrosion depth will significantly affect the crack tip stress field. The maximum error of the optimized neural network is 5.32%. The calculation data of the optimized neural network model were compared with the calculation data of other models, and it was determined that GA-BPNN has better adaptability in this research problem.

Refined cyclic R-curve determination through residual crack tip stress reduction by annealing

The accurate determination of the cyclic R-curve of the threshold of stress intensity factor range is a demanding experimental task. The main challenge concerns the introduction of a pre-crack that is open under tension loading and free of residual stresses. When pre-cracks are generated by cyclic compression-compression loading, a zone of tensile residual stresses up to the material yield strength is generated ahead of the pre-crack tip. These stresses may affect crack propagation at the beginning of fatigue crack growth and should consequently be removed especially for high-strength materials. However, subsequent stress-relief annealing is impractical for numerous metallic material classes due to undesired microstructural alterations at the temperatures required for stress relief. In the present contribution, the above-described issue is addressed for a high speed steel using single-edge notched bending specimens pre-cracked at various stages of a typical high speed steel heat treatment process. It is shown that stress-relieving via a heat treatment route is a significant improvement compared to the conventional compression pre-cracking procedures to measure material-specific cyclic R-curves.

Crack-tip constraint analysis of bending specimens for considering higher order terms in asymptotic solution

In this research, a higher-order asymptotic J-A2-A4 solution was introduced for studying the effect of the bending moment on the crack-tip constraint of a specimen. The solution was applied to TPB and SENB specimens with varying bending moment loads, and compared to other methods such as FEA, HRR solution, J-A2 solution and J-A2-M solution. The results were analyzed and compared with the FEA, J-A2 theory and J-A2-M theory solutions obtained from references. The impact of global bending on the calculation of crack-tip opening stress was also investigated. The findings showed that the J-A2-A4 solution closely matched the FEA numerical results, and better accounted for the influence of global bending compared to the J-A2 method. Therefore, there is no need to modify the J-A2 method by adding a bending moment term, as suggested in the J-A2-M theory.

Influence of Interaction between Microcracks and Macrocracks on Crack Propagation of Asphalt Concrete.

This paper aims to reveal the interaction relationship between microcracks and macrocracks and the influence of the interaction on the crack propagation behavior. A theoretical model of asphalt concrete was established for the interaction between microcracks with different crack densities and a macrocrack. And a meso-structure model of AC-13 dense-graded asphalt concrete was established by combining the Talyor medium method and the DEM (discrete element method). Macro and micro parameters, such as the stress-strain characteristics, crack evolution parameters, and crack tip stress field, were obtained through a semi-circular bend virtual test and used to study the characteristics of crack propagation under the interaction between microcracks and the macrocrack. The results indicate that the interaction has an effect throughout the process of asphalt concrete damage, and shows shielding and acceleration effects as the microcrack density changes. When the microcrack density is low (f3 ≤ 0.8), the crack propagation process, which is affected by the interaction effect, exhibits significant differences, and the interaction effect shows the shielding effect. When the microcrack density is high (f3 > 0.8), the fracture stage is mainly affected by the interaction effect, which shows the acceleration effect. The results provide a predictive theoretical and numerical model for low-temperature cracking of asphalt pavement, and theoretical support for the design, maintenance, and upkeep of long-life pavement.

Crack-tip plastic zone and initiation mechanism of rock based on Eshelby stress

The crack initiation and propagation mechanism of rock is significantly related to characteristics of the crack-tip plastic zone due to energy dissipation. In this paper, conservation integral and configurational stress/force is derived by the Noether’s method. The crack-tip configurational stress field is then deduced and analyzed. Additionally, the Drucker–Prager yield criterion of configurational stress is derived and it is used to predict the crack-tip plastic zone of rock. The fracture criteria of rock are also developed based on the critical area and minimum polar radius of the crack-tip plastic zone. Subsequently, the effects of bedding dip angles and porosity on rock mixed mode fracture are investigated, and the fracture resistance of rock is assessed using the resistivity and wave velocity. It is shown that the configurational force as the crack driving force is induced by the invariant transformation of an action integral with respect to translation of a defect. It is also found that the crack-tip plastic zone assessed by Drucker–Prager yield criterion of Cauchy stress is discontinuous at the crack surface while that predicted by yield criterion of configurational stress is continuous. The present fracture criteria take into account the internal friction angle, and the predicted initiation angles and fracture loads are in good agreement with those determined by the maximum tensile stress (MTS) fracture criterion and experiments. The fracture loading envelope decreases with the porosity, bedding dip angles and resistivities of rock, but increases with wave velocity.

Crack propagation simulation and overload fatigue life prediction via enhanced physics-informed neural networks

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.