Initial Crack Angle Research Articles

Investigation on the dynamic characteristics of gears considering spatial crack propagation

Abstract Considering the failure of gear space cracks caused by uneven load distribution, local material defects and installation errors, the effect of gear crack space propagation path on dynamic characteristics was investigated based on the extended finite element model and gear dynamics model. The effect of the initial crack location and angle on the extent of crack expansion and the dynamic characteristics of the gear was discussed, and experimental verification was conducted. The results demonstrated that with the expansion of the spatial crack, the time-varying meshing stiffness TVMS gradually decreases, which leads to the periodic impact response of the dynamic meshing force and dynamic transmission error, and sidebands appear around the meshing frequency and harmonic components. Furthermore, the location and angle of the initial crack lead to different crack propagation paths in space, which in turn lead to different variations of gear dynamic characteristics.

Fatigue Crack Propagation Analysis of Rail Surface Under Mixed Initial Crack Patterns

Prolonged rolling contact fatigue between wheels and rails results in the formation of surface cracks on the rail and accurately analyzing the crack expansion behavior is essential to ensuring the safe operation of the train. Drawing upon the principles of fracture mechanics and finite element theory, this study establishes a finite element model of wheel–rail rolling contact that incorporates the presence of cracks. The method utilizes an interaction integral to calculate the stress intensity factors at the leading edge of the crack; then, the Paris formula is used to solve the crack spreading rate. It systematically examines the effects of the initial crack angle, the coefficient of friction of wheels to rails, and crack size on the behavior of fatigue crack propagation. The results indicate that the cracks primarily extend in the depth direction of the rail, transforming the semi-circular surface cracks into elliptical cracks with the major axis oriented along the rail’s width. Crack propagation is primarily driven by model II and III composite crack propagation, with their expansion rates influenced by operating conditions. In contrast, mode-I expansion is less sensitive to these conditions. Under single-variable loading conditions, a smaller initial crack angle results in a faster crack growth rate. Increasing crack length accelerates crack growth, while a higher friction coefficient inhibits it.

Parameter analysis and prediction of crack propagation for thermoplastic composite pipes under lateral pressure

ABSTRACT The research investigates the process of crack propagation in thermoplastic composite pipes (TCPs) with initial racks subjected to lateral pressure, through a combination of numerical simulations and experimental studies. In the numerical analysis, a TCP is subjected to lateral pressure, considering parameters such as initial crack length, initial crack angle, and lateral displacement. This analysis employs the extended finite element method (XFEM). The results reveal that crack propagation predominantly occurs perpendicular to the fibre winding angle. Moreover, it is observed that longer initial cracks result in lower crack initiation loads, while the final extent of crack propagation increases with the initial crack length. The experimental study considers three distinct initial crack angles and verifies the conclusions drawn from the numerical simulations. Furthermore, a crack propagation prediction model is developed that combines particle swarm optimization (PSO) with backpropagation (BP) neural networks. The predictive results demonstrate a high level of accuracy.

Strength Model for Prestressed Concrete Beams Subjected to Pure Torsion

A torsional strength model for prestressed concrete beams was proposed considering the initial crack angle, principal stress angle, and longitudinal strain, which are affected by the axial stress induced by the effective prestress. The use of the torsional effective thickness was also proposed to calculate the torsional strength of prestressed concrete beams by considering the effect of prestress. The shear element in the torsional member was simplified under the assumption that the principal tensile stress and principal compressive strain were negligible in the ultimate state. The torsional strength was determined when the principal compressive stress or shear stress at the crack surface in the shear element reached the failure criterion according to the multipotential capacity model, which considers concrete crushing and aggregate interlocking as the main resistances to the applied load. The proposed strength model was verified using test specimens collected from existing experimental studies. The proposed model accurately evaluated the torsional strength of prestressed concrete beam specimens, regardless of the key variables of the prestressed concrete specimens, where the mean value of the tested results to the calculated torsional strengths was 1.123, and the corresponding coefficient of variation was 17.7% for 104 prestressed concrete beam specimens, while the ACI 318-19 torsional design method gave the mean and coefficient of variation of 0.880 and 24.3%, respectively.

An analytical solution of direction evolution of crack growth during progressive failure in brittle rocks

AbstractMicrocrack growth during progressive compressive failure in brittle rocks strongly influences the safety of deep underground engineering. The external shear stress τxy on brittle rocks greatly affects microcrack growth and progressive failure. However, the theoretical mechanism of the growth direction evolution of the newly generated wing crack during progressive failure has rarely been studied. A novel analytical method is proposed to evaluate the shear stress effect on the progressive compressive failure and microcrack growth direction in brittle rocks. This model consists of the wing crack growth model under the principal compressive stresses, the direction correlation of the general stress, the principal stress and the initial microcrack inclination, and the relationship between the wing crack length and strain. The shear stress effect on the relationship between y‐direction stress and wing crack growth and the relationship between y‐direction stress and y‐direction strain are analyzed. The shear stress effect on the wing crack growth direction during the progressive compressive failure is determined. The initial crack angle effect on the y‐direction peak stress and the wing crack growth direction during the progressive compressive failure considering shear stress is also discussed. A crucial conclusion is that the direction of wing crack growth has a U‐shaped variation with the growth of the wing crack. The rationality of the analytical results is verified by an experiment and from numerical results. The study results provide theoretical support for the evaluation of the safety and stability of surrounding rocks in deep underground engineering.

A micro-macro mechanism of hydraulic fracturing with initial stress state effect of brittle rock

The external initial stress state seriously affects the hydraulic fracturing process of rocks. However, the external initial stress effect on the mechanical relationship between the hydraulic pressure and the internal microcrack extension in brittle rocks is rarely studied. This paper proposes a micro-macro mechanical model for predicting the hydraulic fracturing process of brittle rock under compressive stress. Based on the correlation of the stress intensity factor at the tip of the extended micro-cracks, the hydraulic pressure, and the force characteristics of the cracks inside the brittle rock, the evolution law of the hydraulic pressure with the wing crack length is determined. The effects of confining pressure, axial pressure, stress difference, initial crack angle, initial crack length, initial crack density and rock fracture toughness on the hydraulic initiation stress and peak stress are discussed. The rationality of hydraulic fracturing models is verified by experimental comparison. With the increase of axial pressure, stress difference, fracture toughness, initial crack length and initial crack density, the hydraulic initiation and peak stress of rock decrease, and with the increase of confining pressure and fracture toughness, the hydraulic initiation stress and peak stress of rock increase. The study results optimize the parameters such as pre-crack angle, pre-crack length, and external loading conditions based on rock characteristics. It helps to grasp the progress of hydraulic fracturing according to the nature of rock and the degree of hydraulic pressure change, improve the efficiency of hydraulic fracturing, and enhance economic benefits.

Investigation of Crack Propagation and Failure of Liquid-Filled Cylindrical Shells Damaged in High-Pressure Environments

Cylindrical shell structures have excellent structural properties and load-bearing capacities in fields such as aerospace, marine engineering, and nuclear power. However, under high-pressure conditions, cylindrical shells are prone to cracking due to impact, corrosion, and fatigue, leading to a reduction in structural strength or failure. This paper proposes a static modeling method for damaged liquid-filled cylindrical shells based on the extended finite element method (XFEM). It investigated the impact of different initial crack angles on the crack propagation path and failure process of liquid-filled cylindrical shells, overcoming the difficulties of accurately simulating stress concentration at crack tips and discontinuities in the propagation path encountered in traditional finite element methods. Additionally, based on fluid-structure interaction theory, a dynamic model for damaged liquid-filled cylindrical shells was established, analyzing the changes in pressure and flow state of the fluid during crack propagation. Experimental results showed that although the initial crack angle had a slight effect on the crack propagation path, the crack ultimately extended along both sides of the main axis of the cylindrical shell. When the initial crack angle was 0°, the crack propagation path was more likely to form a through-crack, with the highest penetration rate, whereas when the initial crack angle was 75°, the crack propagation speed was slower. After fluid entered the cylindrical shell, it spurted along the crack propagation path, forming a wave crest at the initial ejection position.

Experimental and numerical failure mechanism evaluation of anisotropic rocks using extended finite element method

Rocks often show an anisotropic behavior due to microcracks, mineral-based structure, and unequal in-situ stresses. The crack tip's stress intensity factors (SIFs) that control rock failure heavily depend on anisotropy. Given the significance of extensive research to identify the effects of anisotropy on the mechanical behavior and strength of rocks, numerical modeling is considered an essential method in designing structures and analyzing their stability. This study experimentally and numerically evaluated the effects of the bedding angle, initial crack angle with the loading axis, crack length, and anisotropy ratio on the stress intensity factor of transversely isotropic rocks via the extended finite element method (XFEM). Cracked chevron-notched Brazilian disks (CCNBDs) were fabricated from phyllite under the International Society for Rock Mechanics (ISRM) standards and tested at different initial crack lengths and angles for validation. The XFEM approach was then used to predict toughness and crack propagation path in the tested and new specimens with varying ratios of anisotropy and bedding angles (ψ = 0, 30, 45, 60, and 90°). The results demonstrated that with the increase of the anisotropy ratio, in equal crack length and initial angle, the absolute value of the SIFs have larger values. In addition, with the increase of crack length, the first and second modes of SIF increased, which indicates the failure of the specimen at lower loads. Also, bedding angle is effective on the stress intensity factors and this effect becomes more intense as the crack length increases. Finally, the anisotropy properties not only affect the values of SIFs, but also can change the angle at which the specimen experiences pure mode I or mode II.

Constraints-related microscopic fatigue crack propagation behaviour of polycrystalline alloys

Based on the microscopic polycrystalline fatigue crack propagation (MPFCP) model, the MPFCP behaviours of GH4169 alloy under different micro-notch depths and lengths (constraints) were studied from aspects of MPFCP path, MPFCP rate and stress distribution. The influences of the initial crack angle on MPFCP behaviour were further explored. It was observed that the grain boundary, the grain size and the stress state were different during crack propagation under different constraints, resulting in different MPFCP paths. The MPFCP path was straighter under high constraints, and the MPFCP rate was related to the micro-notch size and the loading direction. The crack tip needed more stress accumulation at low constraints than under high constraints to ensure smooth MPFCP behaviour. The influence of the initial crack angle on the MPFCP path was mainly reflected in the grain interior where the initial crack was located. The initial crack angle had a greater influence on the MPFCP rate than on the MPFCP path.

Mesoscopic damage study of red sandstone considering initial defects under drying-wetting cycles

Abstract In order to study the mechanical properties and microscopic damage of red sandstone by dry and wet cycling, this paper establishes a 3-dimensional uniaxial compression model of red sandstone by using PFC3D software. On this basis, microscopic cracks were introduced to analyze the influence of different cracks on the mesoscopic cracking of the model. The results show that the error between the simulation results and the test results is less than 10% for the model established by PFC3D software. Based on the discrete element model, displacement and velocity maps were obtained, and the values are larger at the contact with the load and smaller at the distance from the load. With the increase of the initial crack angle, the peak stress gradually increases, and with the decrease of the crack size, the peak stress gradually decreases, and the contact force also decreases.

A Meso-Macro Method of Evaluating Water Content Effect on Direct Tensile Fracture in Brittle Rocks

Tensile stress is one of the primary forms of loading triggering the fracture in brittle rocks. Water content strongly affects the fracture process induced by meso-crack extension under the direct tensile loading of brittle rocks. Due to limitation of current equipments, the experiment of direct tensile fracture considering water content effect of brittle rocks is hardly implemented. Furthermore, the meso-macro model simultaneously considering the influence of water content and tensile loading on fracture behaviours of brittle rocks is also rarely studied. This paper proposes a meso-macro mechanical model to evaluate the water content effect on the fracture process under direct tensile loading of brittle rocks. This model is developed by combining the suggested model of meso-crack extension under direct tensile loading, the correlation of macroscopic strain and meso-crack extension, and considering the effect of water content on fracture toughness KIC and initial damage D0. This meso-macro model is linking the development process of meso-crack initiation, extension and coalescence to macroscopic fracture. The axial stress-strain curves during progressive tensile fracture under different water contents were studied, and the rationality of the suggested theoretical model was validated by the test results. The influences of water content on the relation between wing crack length and axial stress, the relation between wing crack length and stress intensity factor KI, crack initiation stress, peak stress, and elastic modulus were analyzed. The influences of the model parameter β and the initial crack angle φ on the peak stress and crack initiation stress under the different water contents are also discussed.

Numerical Investigation of Fatigue Crack Propagation Behaviour of 550E High-Performance Steel

The fatigue crack propagation behaviour of Q550E high-performance steel (HPS) is studied in this paper. Static tensile testing and fatigue crack propagation testing were carried out, and the results were compared with those of Q235. Finite element models were developed and verified against the experimental results. The impacts of the initial crack angle, crack depth ratio, stress ratio, thickness, and corrosion pitting on the fatigue crack propagation behaviour of the HPS were analysed. The results show that the fatigue life of Q550 was reduced by 18% due to the corrosion pitting, but it did not change the crack propagation path. When the stress intensity factor is higher than a certain value, the fatigue performance of Q235 is better than that of Q550E. The initial crack angle of 52.5° is the critical angle of the crack stress intensity factor. The steel tends to fracture as the crack depth ratio increases, and more attention should be paid to the effective crack length in engineering practice. An increasing stress ratio leads to a smaller stress intensity factor, and the thickness affects the stress intensity factor in the later stage. The crack stress intensity factor around the corrosion pits gradually decreases along the thickness direction, and the crack tips around the corrosion pits tend to reach the yield state initially, accelerating the fatigue fracture of the specimen and ultimately leading to a decrease in fatigue life.

Three-Dimensional Fracture Analysis of Large Opening Box Girder With Crack Damage Under Bending and Torsion Loads

Abstract This work aims to investigate the complex fracture behavior of a large opening box girder (LOBG) using three-dimensional (3D) finite element method (FEM). A numerical model is developed to simulate the fracture of LOBG under individually or jointly applied torsion and bending loads. The crack damage is introduced into the side plate and bottom plate of LOBG. The influencing factors such as crack angles, crack locations, and load types are emphatically discussed. Additionally, the crack growth angles are also predicted during the analysis. The results present that the large opening can generate significant effects on the crack growth of the side plate crack (SPC) and the bottom plate crack (BPC). Under the condition of torsion or hogging, SPC grows more easily than BPC, while BPC is relatively prone to grow under sagging condition. Compared with the torsion condition, the initial crack angle can significantly reduce the stress intensity factor (SIF) under the bending condition. Furthermore, the cracks that gradually approach transverse frames are also more likely to induce mode I fracture under torsion conditions. These findings from the present study can reveal insights for a better understanding of fracture behavior for LOBG.

Energy-based critical plane fatigue methods applied to additively manufactured 18Ni300 steel

In this work, the uniaxial and biaxial fatigue behaviour of maraging steel (18Ni300) obtained by additive manufacturing was studied. The material was evaluated using several biaxial load paths and different load levels. The predictive capacity of the fatigue life and crack initiation angle of the critical plane methods of Liu (I and II), and Chu, Conle, and Bonnen (CCB) were evaluated. The results obtained showed that normal stresses had a strong effect on the fatigue life. In general, the best estimates of the useful life and initial crack angle prediction were obtained with the CCB method.

Investigation on 3D fatigue crack propagation in pitch bearing raceway of offshore wind turbines

In complex marine environments, pitch bearings are more prone to crack initiation, propagation, and evolution, which leads to contact fatigue problems. Accurately identifying and predicting the evolution of early crack extensions in pitch bearings can effectively prevent major economic losses caused by failure. The two limitations of the current research on pitch bearing cracking are the low efficiency of the simulation and the fact that the contact fatigue models are mostly simplified to two-dimensional models. These models do not accurately reflect the influence of the raceway geometry parameters on the real situation. This study combined Bladed and MATLAB for an integrated life cycle simulation using Python and a cloud platform to reduce the simulation duration. A three-dimensional modelling method was proposed to calculate the crack propagation in pitch bearings throughout the full life cycle. The effects of different operating conditions, crack depths, and initial crack angles were investigated and analyzed. The results suggested that the maximum Hertz contact stress was 2961.4 MP. When the initial crack angle was greater than 0°, the crack generally propagated towards the core area. When the crack angle was less than 30°, the crack propagated gradually in depth and towards the surface. The fatigue life at an initial crack angle of 60° was 1.5 times that of an initial crack angle of 30°.

Experimental study on the influence of prefabricated fissure size on the directional propagation law of rock type-I crack

To investigate the influence of prefabricated fissure size on the directional propagation law of rock type-I cracks, a simple device for simulating rock crack directional propagation was developed. Subsequently, loading tests for white sandstone samples with different prefabricated fissure lengths and widths were performed. The evolution laws of the deformation field and acoustic emission (AE) were analyzed during the entire crack propagation process. Finally, the influence of fissure size on the crack directional propagation mechanism was elucidated. The obtained results indicate that: The initial crack angle was mainly influenced by the prefabricated fissure width. The initial crack angle increased with the increase in the prefabricated fissure width. The crack directional propagation process can be divided into four stages: local strain-band initiation, local strain-band development, crack initiation, and crack coalescence. The crack maximum relative strain increases with an increase in the prefabricated fissure length but decreases with an increase in the prefabricated fissure width. This phenomenon indicates that increasing the prefabricated fissure length is advantageous to crack propagation at the fissure tip. The AE evolution process includes quiet, slowly increasing, booming, and decreasing periods. When the prefabricated fissure length increased, the durations of the quiet and slowly increasing periods decreased, but the durations of booming and decreasing periods increased. However, the durations of quiet, slowly increasing, and booming periods decreased as the prefabricated fissure width increased. In other words, increasing the prefabricated fissure length can enhance the stability of crack directional propagation, but increasing the prefabricated fissure width leads to the instability of main crack propagation path. In underground engineering practice, increasing the prefabricated fissure length and decreasing the prefabricated fissure width may be excellent approaches to realizing the crack directional propagation of rock or coal fracturing.

Computational Investigation on Cracking Behaviors of AerMet 100

AerMet 100 exhibits excellent mechanical properties, proven in previous studies; however, defects may greatly influence the mechanical behavior during the service of the material, which serves as one of the major challenges in the wider application of the material. To quantify the crack evolution process, the in-plane type I crack propagation behavior is comprehensively investigated based on the extended finite element method (XFEM). The crack growth is characterized in terms of the extracted crack propagation angle, stress intensity factor (SIF) in the crack tip, and stress field profiles during the crack propagation process. An extrapolation method is adopted to calculate the SIF, followed by a series of parametric studies on the influence of the governing factors, i.e., initial crack length, initial crack location, initial crack angle, and the crack number through numerical investigation. It is found that the crack propagation angle enlarges monotonously with the increase of the initial crack location, the initial crack length, and the crack number, increases slowly with the growth of initial crack angle, and rapidly enlarges in reverse at about 45°. The SIF in Mode I, KId, gradually decreases with the increase of the initial crack location and the crack number, and nearly keeps steady when the initial crack length and initial crack angle varies. Results provide further understanding of the failure and fracture behavior of AerMet 100 and guide the future application and design of the structures.

Effect of Heterogeneity on the Failure of Rock with an Initial Crack under Uniaxial Compressions: A Numerical Study

Abstract Failure mechanisms of rock are intrinsically intertwined with heterogeneity and natural fracture. However, the effects of heterogeneity on the failure of rock with natural cracks are still far from clear. By simultaneously considering rock heterogeneity and natural fractures, this paper investigated the effects of heterogeneity on the failure of rock with a single initial crack under uniaxial compressions. The RFPA method with consideration of materials properties heterogeneity was employed, and numerical models with different crack angles were developed. The stress-strain curve, crack development, failure pattern, and AE characteristics were obtained. The numerical results were also compared with experimental results. Further, the effects of initial crack angle and heterogeneity on the strength, failure pattern, and acoustic emission (AE) characteristics were investigated by parametric studies. It has been found that, for a small homogeneity, rock failure is dominated by numerous microcracks within the crack bands that are smeared from the initial crack tips to the loading ends. Rock failure is dominated by macrocracks propagated from the initial crack tips to the loading ends for a large homogeneity. A logarithmic function is proposed to describe the relationship between the uniaxial compressive strength and the homogeneity. The AE characteristics and overall damage evolution are also significantly affected by the heterogeneity.

Effects of biaxial residual stress components on mixed-mode fatigue crack propagation behavior in friction stir welded 7075-T6 aluminium alloy panel

Residual stress in friction stir weld (FSW) joint significantly affects fatigue performance. It can often combine critically with the applied load cause premature fatigue failure. Research on the residual stress effects on fatigue behavior is required to assess the damage tolerance issues in FSW joints. In this study, the effect of biaxial residual stress components (longitudinal residual stress and transverse residual stress) on mixed-mode crack propagation behavior in FSWed 7075-T6 fuselage panel was studied. Residual stress profiles across the welded plate were measured by X-ray diffraction technique. Fatigue crack propagation for mode mixity angles of 30°, 45° and 60° were carried out. The stress intensity factors (SIFs) at the crack tip were evaluated by finite element method and used to study the effect of biaxial residual stress and the individual component on mixed-mode crack behaviors. The results show that the variation of crack path is strongly linked with the residual stress component as well as the initial oblique crack angle. SIF components are affected by the individual residual stress component. Both two components are required to study the mixed-mode crack propagation in FSWs.

Crack Propagation on the Surface of the Bottleneck of a Pressure Vessel Considering the Initial Crack Angle

In order to solve the impact on the accuracy of a life prediction model when the initial crack angle of the curved surface is not 0°, the traditional stress intensity factor model is revised by the non-linear regression analysis method, and an optimized crack growth model is established. This paper takes the surface of the bottle neck of the pressure vessel as the research object, and uses the finite element method to establish a simulation model with an initial crack angle of not 0°. By analyzing the stress intensity factors of different starting angles, the relationship between the correction factor F and the pressure vessel wall thickness h, the radius of curvature R of the joint surface between the bottle neck and the bottle body, the initial crack length L and the initial angle α are calculated. The modified stress intensity factor is used to optimize the crack growth model of the pressure vessel. The experiment proves that the accuracy of the pressure vessel life prediction model is improved.