Influence Of Crack Length Research Articles

A characteristic model for the relationship between cracking and bearing performance of reinforced concrete

Cracks are the most common disease in reinforced concrete structures, which seriously affects the stability of the structure. At present, the evaluation criteria for the degree of crack danger are relatively vague, and there are significant shortcomings in the quantitative evaluation of the stability of concrete structures containing cracks. This article comprehensively utilizes numerical simulation, numerical fitting, and fractal theory to establish a quantitative calculation method for structural bearing performance based on crack characteristic parameters. The main research conclusions are as follows: the influence of crack length, direction, and depth characteristic parameters on the bearing performance of reinforced concrete structures is determined through numerical simulation; A quantitative calculation method for structural bearing performance was established using a step-by-step fitting method, which comprehensively considers crack characteristic parameters. On this basis, the fractal theory was used to describe the complexity of cracks and the calculation results of the combined crack-bearing performance were corrected. Compared with numerical simulation and model experiment results, the average error in calculating the structural bearing coefficient was 5%. The research results have improved the accuracy of crack evaluation and can provide an important reference for the safety analysis of cracks in concrete structures.

Simplified analytical method for predicting the large deformation of stiffened plates with initial cracks under repeated impacts

The impact resistance capacity of structures can be affected by the formation of cracks. To address the issue of repeated impacts on structures with initial cracks, a relationship was established between cracks and the energy dissipation of stiffened plates based on rigid–plastic theory. A simplified analytical method was proposed to predict the large plastic deformation of stiffened plates with initial cracks. To verify the accuracy of the analytical method, repeated impact experiments and numerical simulations were conducted. The influences of crack length and position on the dynamic responses of stiffened plates were explored. The experimental, numerical, and analytical results were in good agreement. The research results showed that the permanent deformations of stiffened plates increases approximately linearly with increasing crack length on the outer plate. However, the influence of stiffener cracks on the permanent deformation of stiffened plates depends on whether the stiffener fractures. The influence of cracks on the load-carrying capacity of the structure is more pronounced when the crack is located in the stiffener.

Stress-driven nonlocal integral model with discontinuity for size-dependent buckling and bending of cracked nanobeams using Laplace transform

Due to the frequent occurrence of cracks as structures age, examining the size-dependent responses of cracked micro/nanobeams is critical for safely designing and optimizing high-tech devices such as those used in MEMS/NEMS. With this understanding, we present the size-dependent bending and buckling studies of cracked nanobeams with different boundary edges adopting the well-posed stress-driven nonlocal integral model with discontinuity. Since the presence of a crack, the beam is divided into two segments connected by a rotary spring and a linear spring, whose elastic coefficients can be determined through compliance calibration methods. We propose an efficient method to solve the original integral model directly by converting the integral form of the nonlocal constitutive equation into a general equation through the Laplace transform technique, equipped with three extra constraint conditions. Subsequently, the governing equations of two beam segments are solved by considering the standard boundary and compatibility conditions as well as the extra constraint conditions, while the bending deformation and buckling loads of various bounded nanobeams are presented analytically in the presence of a crack. After verifying the derived formulation, the influence of crack length and location as well as nonlocality on the beam deflections and buckling loads of the first several modes are investigated in detail. Communicated by Rossana Dimitri.

A Numerical Study of the Dynamic Crack Behavior of Brittle Material Induced by Blast Waves.

Blast stress waves profoundly impact engineering structures, exciting and affecting the rupture process in brittle construction materials. A novel numerical model was introduced to investigate the initiation and propagation of cracks subjected to blast stress waves within the borehole-crack configuration. Twelve models were established with different crack lengths to simulate sandstone samples. The influence of crack length on crack initiation and propagation was investigated using those models. The linear equation of state was used to express the relationship between the pressure and density of the material. The major principal stress failure criterion was used to evaluate the failure of elements. A triangular pressure curve was adopted to produce the blast stress wave. The results indicated that the pre-crack length critically influenced the crack initiation and propagation mechanism by analyzing the stress history at the crack tip, crack propagation velocity, and distance. The inducement of a P-wave and S-wave is paramount in models with a short pre-crack. For long pre-crack models, Rayleigh waves significantly contribute to crack propagation.

Fracture Toughness Testing of Brittle Laminated Geomaterials Using Hollow Double-Wing Slotted Specimens.

The fracture toughness of shale is a key parameter guiding hydraulic fracturing design and optimization. The hollow double-wing slotted (HDWS) specimen is a typical specimen configuration for measuring the mode I fracture toughness of rock. The calibration of the shape factor (f) is the basis for accurately obtaining the fracture toughness of rocks. In this study, the influences of crack length, hole size, and the anisotropy of elastic parameters on f for specimens with three typical bedding orientations-arrester (A), divider (D), and short-transverse (ST) orientations-are systematically investigated using finite element software. The numerical simulation results support the following findings. The mode I f increases monotonically with an increase in hole size. The influence of crack length on f varies depending on hole sizes. Under different bedding orientations, significant anisotropy in f was observed. In addition, the degree of anisotropy in Young's modulus has a major impact on f, which is related to the bedding orientation of the specimen. The apparent shear modulus ratio has relatively little influence on f. As the hole size and crack length increase, the influence of the anisotropy of elastic parameters on f increases. Based on numerical calculations, hydraulic fracturing experiments were conducted on HDWS specimens of Longmaxi shale with three bedding orientations, and the results showed that the peak pressure and fracture toughness of the samples in the ST direction were the lowest, while those in the A direction were the highest.

Mesoscopic modeling and simulation of tensile properties of cracked concrete using cohesive model

A random aggregate (RA) model consisting of mortar, aggregate, and the interfacial transition zone (ITZ) was established to investigate the effect of existing cracks on the tensile properties of concrete. Based on this, a method for establishing a geometric model of cracked concrete was proposed by inserting 0-depth cohesive elements into the RA model. The influence of crack length, width, and area on the tensile properties of concrete were studied using the established cracked concrete model. In addition, the key parameters of bond strength and fracture energy of the mortar and ITZ regions were tested. The cement is ordinary Portland cement with a strength grade of 42.5, and the sand is medium sand. The fracture energy tests were conducted using a displacement-controlled loading model with a loading rate of 0.4 mm/min, while the tensile strength tests were conducted using a stress-controlled loading method with a loading rate of 0.06 MPa/s. The feasibility and accuracy of the numerical method used were verified by comparing the results with those of a finite compression simulation. The numerical results show that as the crack length increases, the tensile strength and elastic modulus of concrete gradually decrease, but if the crack length is 0.47 h, the elastic modulus of concrete shows an abnormal increase. The range of the crack's influence on the tensile performance of concrete is between 50 mm and 100 mm. If the crack width is less than 0.55 mm, the tensile strength of concrete gradually decreases with the increase of crack width, and when the crack width is greater than 0.55 mm, the tensile strength stabilizes.

An analytical method to calculate the time-varying mesh stiffness of spiral bevel gears with cracks

Time-varying mesh stiffness (TVMS) is one of the main dynamic excitation sources of gear transmission systems. The accurate calculation of TVMS is the foundation to comprehensively investigate the vibration of powertrain. Compared with the spur gear, the meshing process of spiral bevel gear is spatially time-varying, which makes the analytical calculation of TVMS more difficult. In this paper, the meshing relationship of spiral bevel gears is first established by extending the slice method of spur and helical gears to spiral bevel gear. Secondly, the analytical models of perfect and cracked spiral bevel gears are presented to evaluate TVMS. Meanwhile, the effects of crack length and depth on mesh stiffness are investigated. Thirdly, the influence of crack length and depth on the dynamic response are simulated based on the 8-DOF dynamic model of spiral bevel gear. Finally, the experiments are conducted to verify the effectiveness of the analytical model. Experimental results demonstrate that the existence of tooth crack fault makes the response characterized by periodic impact with the rotating frequency of cracked pinion.

Vibration characteristics of gear system with a cracked-gear tooth: modeling and experiments

Gear tooth crack failure is a cruel problem in the gear transmission system. The research on the simulation and experiment is the hotpots in the field. The theoretical and experimental investigations on the vibration characteristics of a gear system with a cracked gear tooth are carried out in this study. A finite element (FE) model is built to predict the crack propagation path in a gear tooth and determine the time-varying mesh stiffness (TVMS) of gear pairs. A dynamic model of the gear system is developed using the lumped-mass model. The established models are validated by comparing the computing results with experimental ones. The influences of crack length on TVMS and vibration characteristics of the gear system are analyzed in detail. The proposed methods can provide useful guidance for fault diagnosis and dynamic performance evolution prediction of a gear system.

Research on Buckling Load of Cylindrical Shell with an Inclined through Crack under External Pressure and Its Solution

In order to evaluate the reliability of cracked cylindrical shell effectively and reasonably, study the load capacity of cracked structures and understand the failure modes of cracked structures, in this paper the finite element method is adopted for cylindrical shells with mixed mode crack. The finite element models of cylindrical shell with an inclined through crack under external pressure were established by finite element method, the elastic and elastic-plastic buckling loads were calculated. The influences of crack length (c), crack angle (θ), cylindrical shell length-radius ratio (L/R), radius-thickness ratio (R/T), boundary conditions on buckling load were explored. The analysis of cracked cylindrical shells with simple support on buckling load shows that the load bearing capacity of cracked cylindrical shells decreases with the increase of length- radius ratio, radius-thickness ratio and crack inclination angle. The increase of crack length can weaken the bearing capacity of cylindrical shell. The variation of elastic-plastic buckling load is consistent with that of elastic buckling load. Under the clamped support, the variation of buckling load is consistent with the buckling load of cracked cylindrical shell with simple support, and the buckling load of cracked cylindrical shell with clamped support is evidently higher than that of simple support. The post-buckling analysis further shows that the changes of crack inclination angle and crack length do not affect the variation modes of pre-buckling and post-buckling deformation of cracked cylindrical shells, but affect the load capacity. The relationship between buckling load of different boundary conditions (simply supported and clamp-supported) and geometrical parameters (length-radius ratio, radius-thickness ratio, crack length and crack Angle) was obtained by nonlinear regression. The results of solution can predict the buckling load of cylindrical shell with an inclined through crack.

AE Characteristic and Mechanical Behaviors of Red Sandstone with Two Prefabricated Close-Collinear-Equal Length Cracks under Compression.

Preexisting cracks are of great significance for the stability of rocks, they can influence the growth and propagation pattern of cracks. For revealing the failure characteristics of rocks with prefabricated cracks, the mechanical behaviors of red sandstone with two close-collinear-equal length cracks were studied by acoustic emission (AE) monitoring experiment. The results indicated that the stress of red sandstone specimens showed an obvious stepwise growth phenomenon, and AE ring counts can better characterize the growth of microcracks of rocks. Moreover, AE events were mainly distributed near the prefabricated cracks of rocks. Then, a novel modified Kachanov method for analyzing collinear-close cracks was proposed. The influences of crack length and crack spacing on the interaction force of cracks were discussed. Then, it can be found that this modified method had a good applicability for two close-collinear-equal length cracks of rocks under compression.

Fracture Process and Failure Mode of Brazilian Discs with Cracks of Different Angles: A Numerical Study

In order to determine the effect of internal cracks on the tensile failure of materials, a hybrid finite–discrete element method was used to analyze the Brazilian disc test with cracks of different angles. When the pre-crack angle is between 0° and 60°, the wing crack is initiated from the pre-crack end. When the pre-crack is 90°, the crack initiated from the pre-crack center. When the pre-crack angle is between 0° and 60°, the maximum principal stress and plastic strain are concentrated at the pre-crack end. When the pre-crack angle is 90°, the maximum principal stress and plastic strain are concentrated in the pre-crack center. As the crack angle increased from 0° to 90°, the failure mode of Brazilian discs with cracks transits from splitting into two parts to splitting into four parts. The influence of crack length is further studied. When the crack length is less than 5 mm, the crack angle has little influence on the disc failure mode; Brazilian discs with cracks of different angles undergoes splitting failure along the loading axis. When the crack length is larger than 5 mm, the crack angle has a great effect on the disc failure mode.

Vibration characteristics of cracked FG-GRC plates in thermal environments based on phase field theory and meshless method

Stiffness degradation resulting from matrix cracking has a great impact on the vibrational behaviors of composite laminates. However, the vibration frequencies of functionally graded graphene-reinforced composite (FG-GRC) plates with crack defects remain largely unexplored. In this paper, the variational phase field theory is implemented to investigate the vibration characteristics of cracked FG-GRC plates subjected to thermal conditions. The effective elastic constants depending on the temperature of FG-GRC plates are characterized by the extended Halpin-Tsai model. The first-order shear deformation theory (FSDT) is employed to describe the displacement fields of the cracked FG-GRC plates. The meshfree kernel particle method is engaged to discretize governing equations over the computational domain and then the obtained governing eigen-equations are calculated using the Ritz methodology. The numerical results illustrate the influences of crack length, crack number, the strength of foundations, graphene distribution, temperature variation and geometric values on the vibration fundamental frequencies of the FG-GRC plates. The present work not only provides an alternative and feasible approach for solving the interaction problems between cracking and vibration, but also makes significant advances to characterize the vibrational behaviors of cracked functionally graded materials for engineering applications.

Influence of Loading History on Delamination in Multilayered Beam with Creep

The present paper deals with an analytical study of the time-dependent delamination in a multilayered inhomogeneous cantilever beam with considering of the loading history. The multilayered beam exhibits creep behaviour that is treated by using a non-linear stress-strain-time relationship. The material properties are continuously distributed along the thickness and length of the layers. The external loading is applied in steps in order to describe the loading history. The analysis reveals that during each step of the loading, the strain energy release rate increases with time. The influences of crack length and location on the time-dependent strain energy release rate are also investigated.

Influence of Different Crack Factors on Acoustic Wave Signals Using Orthogonal Analysis

The existence of cracks in key components of engineering equipment is a huge threat to the safe operation of the equipment. The influence of four factors (length, location, orientation, and width of the crack) on the attenuation characteristic of signal propagation is studied through simulation and experiment. The orthogonal experimental design is applied to design the simulation scheme, and the signal affected by the four factors is simulated by the finite-difference time-domain method. The degree of influence of the different factors is evaluated by conducting an analysis of range and an analysis of variance. The results show that the influence of crack length and location on signal relative attenuation is more remarkable according to the significance level α = 0.05, followed by crack orientation and crack width. The attenuation trend in the experimental results is similar to the simulation. Therefore, the longer the crack length is, the easier it is to be detected by the acoustic wave technique, while the effect of crack orientation and crack width on identifying cracks is limited. The study successfully establishes the relationship between signal parameters and crack factors and offers a theoretical foundation for evaluating the status of cracks in key components.

Effect of edge and internal cracks in 8YSZ thermal barrier coatings subjected to mechanical loading: An numerical approach

Abstract The paper presents fracture parameters for edge and internal cracks subjected to mechanical load by the finite element method. The influence of crack length and crack position on edge and internal crack in TBCs on the strain energy release rate (SERR) and stress intensity factor (SIF) are discussed in detail. The numerical results show that the edge crack near the top surface results in high SERR and SIF mode I. In edge crack, the decreasing trend in the SERR was observed with a decrease in crack length and crack position change towards the TC/BC interface. About 60.06% reduction in the SERR was observed for 100 µm edge crack positioned near the top surface when shifted towards TC/BC interface. Similarly, 60 µm and 80 µm edge crack show a 30% and 56% reduction in SERR. Whereas, 20 µm and 40 µm edge crack shows 1.76 and 1.48 times more value of SERR. The internal crack shows a small value of SERR and SIF mode I irrespective of crack length and position compared to edge crack. For internal crack, as the crack length was increased from 20 µm to 100 µm, the reduction in SERR value increases from 59.23% to 90.23%. Similarly, the edge crack shows high SIF mode I compared to internal cracks irrespective of crack length and position. The edge crack appears to be more unstable than the internal crack and propagates early to cause the failure. The crack length and position strongly influence the crack initiation and propagation, resulting in the failure mechanism.

Influence of crack length and anatomical location on the fracture toughness of annulus fibrosus

Fracture toughness (Jc) of a soft biological tissue is an important mechanical property that characterizes its resistance to crack or tear extension. To date, no information is available on fracture toughness of annulus fibrosus (AF); therefore, its defect tolerance is not known. The present study modified a previously introduced method to determine Jc of ovine AF. Then, the effect of the notch length on the failure pattern and Jc was investigated. Also, the test samples of anterior and lateral regions were collected to determine the effect of the location on Jc. Results showed that for a notch length of less than 45% of total width, no crack extension occurred, but for a notch length above 45% of the width, crack propagation and ultimately the failure of the AF were observed. However, statistical analysis indicated no significant difference on Jc (p = 0.5) for the initial notch length of 50% and 70% of total width. The fracture toughness was significantly higher for the samples extracted from the lateral site than those from the anterior site (p < 0.05). Dissimilar failure patterns were observed for different initial notch lengths. Among the parameters studied, the defect tolerance of AF was dependent on the initial tear size.

Evaluation of Quasi-Static and Dynamic Fracture Toughness on the Low-Alloy Reactor Pressure Vessel Steel JRQ in the Transition Region

Three point bending and impact tests with sub-sized Charpy specimens were performed on the JRQ reference steel for reactor pressure vessels. Quasi-static and dynamic fracture toughness data were calculated and the fracture behavior in the ductile to brittle transition region was evaluated within the frame of the master curve method (ASTM E1921). Specimens with shallow and deep cracks were studied and the respective influence of crack length and loading rate on the reference transition temperature was determined. The force-time curves of specimens with shallow cracks presented significantly smaller oscillations with respect to the absolute force, making the fracture toughness evaluation more accurate.

Comprehensive study on the crack tip parameters of two types of disc specimens under combined confining pressure and diametric concentrated forces

Stress intensity factors and T-stress of centrally cracked circular disc (CCCD) and hollow central cracked disc (HCCD) specimens with different geometric parameters under the combined diametric concentrated forces and confining pressure were calculated using Finite Element Method. The influence of crack length, crack inclination angle, aperture ratios and confining pressure on the mixed mode SIFs, T-stress and biaxiality ratio of CCCD and HCCD specimens is investigated in this paper. Compared with the HCCD specimens, CCCD specimens can more easily transform pure mode I loading to pure mode II loading. The results obtained in this paper are helpful to understand the mechanical mechanism of rock fracture under combined confining pressure and diametric concentrated forces.

Prediction of RCF clustered cracks dimensions using an ACFM sensor and influence of crack length and vertical angle

ABSTRACTRolling contact fatigue (RCF) cracks are the predominant reason for rail grinding maintenance and replacement on all types of railway system, as they can potentially cause rail break if not removed. To avoid excessive material removal, accurate crack sizing is required. Alternating current field measurement has been used as an electromagnetic method for RCF crack sizing, incorporating with modelling results for single RCF cracks with large vertical angles (>30°). No study using this knowledge to size shallow angled crack clusters has yet been reported. A novel method, the pocket length compensation method, is proposed to determine the length and depth of RCF cracks with shallow vertical angles. For shallow crack clusters, vertical angle predictions are close to the measured values with a deviation of less than 13.6%. Errors in crack pocket length prediction are greatly reduced when the pocket length compensation was included. The predicted vertical depth using the approach developed for clustered angled cracks is accurate with errors <8.3%, which compares to errors of up to 60% if the single RCF crack approach is used and errors of up to 21.4% if a non-compensated prediction for crack clusters is used.

Estimation of the resource of a structure with the tensile crack on the basis of fuzzy simulation

Statement and solution of the problem. The problems of optimal design of structure, which is operated under the constraints of strength, stability and rigidity are considered. As an additional restriction, the possibility of the crack presence in a stretched element is considered. With a small, compared with the yield strength, destructive stress, the construction element is in critical condition. So that, the calculation of strength can be carried out according to the well-known Irwin criterion of a linear destructive mechanics. An algorithm for solving the optimal design problem using dynamic programming is proposed. A numerical-analytical solution is obtained in the form of recurrent formulas. In addition to the deterministic optimal design solution there is a situation where a tensile crack in the rod of the truss is considered. The size of the crack is not clearly defined. The influence of the fuzzy problem of the initial crack length on the number of load cycles during non-destruction for separate elements of the structure is estimated. The truss consists of four elements in a deterministic formulation. The effect of a predetermined accuracy of calculation on the convergence of the process, when the optimal design problem is solved with using dynamic programming, is estimated. For the case of sufficient predetermined accuracy for the truss, a search was made for the influence of the length of the crack on the cross-sectional area of the rods and the volume of the structure. Numerical experiments of the influence of the fuzzy problem of the crack length for different values of the modal value spread on the volume of the structure are carried out. Conclusion. Convergence of the solution starts when relative error is approximately equal 0.003. Influence of crack length on the volume of rod structure shows its growing after the value of 15 cm in deterministic problem. Investigation shows the principle possibility of the theory of fuzzy sets using in problems of optimal design of hinged-rod systems. As an example, the fuzzy numbers with triangular form of membership function were used in the procedure. The stages such as fuzzification, optimal design and defuzzification let us estimate the result of fuzzy problem. So, the result of the possible value of volume for situation, when modal value of crack length is 25 mm and deviation has different domain, is shown in the article.