Influence Of Crack Depth Research Articles

Research of energy characteristics and fault position detection for cracked rotor system

Early crack faults will introduce subtle local changes in the whole rotor system, which may bring difficulties to the fault detection process due to external disturbing factors. Meanwhile, judging the damaged position of rotor systems might be tough only through displacement or velocity. To overcome these issues, the harmonic balance-energy power flow analysis (HB-EPFA) is presented to investigate the rotor system with a transverse crack. Besides, a novel indicator (Time-averaged power flow) is proposed to evaluate the crack faults. For the energy characteristic analysis, the cracked rotor appears a special amplitude-jumping phenomenon, even in the case of shallow crack depth. The influence of crack depth on power flow values under different rotating speeds is obtained. Furthermore, the existence of cracks will lead to the rotation shaft presenting an abrupt energy-changing zone, which can be used to detect crack position. Relevant experiments are applied to validate the proposed detection method, and the experimental results agree with the theoretical analysis. The conclusions achieved in this paper can provide a reference for fault diagnosis of rotor systems in engineering practice.

Double-Probe Ultrasonic Detection Method for Cracks in Steel Structure

To investigate the feasibility analysis of ultrasonic detection methods applied in the fatigue crack characteristics of steel structures, the double-probe ultrasonic detection method was applied to the prefabricated crack specimens fabricated from of flat steel plate. The test features including length, width, depth, angle, and crack location were considered. Based on the calculation of geometric relationship and experimental results, a method for judging the crack tip position was developed. The formulae for determining the depth and angle of crack were not only established but also analyzed the detection accuracy of the double-probe penetration method. The feasibility of this method in weld crack detection was verified by a combination of the finite-element simulation and actual experiment. The results showed that the ratio of crack tip wave height to crack free wave height ωK is related to the K value (K value is one of the parameters of the angle probe, which is defined as the tangent value of angle β between the incident wave and an interface normal line), but the influence of crack depth and width can be ignored. Due to higher detection accuracy for crack depth and angle, a double-probe penetrating method could improve the detection accuracy for crack angle by nearly 5% more than the single probe pulse reflection method. Therefore, application of the double-probe penetrating method had a significant impact on accurate crack detection of rib-to-deck weld in the practical issue.

Molecular dynamics simulations of silica aerogel nanocomposites reinforced by glass fibers, graphene sheets and carbon nanotubes: A comparison study on mechanical properties

Silica aerogel is a brittle as well as a low-tensile strength highly porous solid. Therefore, the primary goal of the present work is to incorporate glass fibers, graphene sheets and carbon nanotubes into the silica aerogel matrix using molecular dynamics (MD) simulations to improve not only the mechanical properties, e.g., tensile strength, elastic modulus, and toughness, but also the deformation characteristics due to the pre-existing cracks. This work investigates and compares the mechanical properties obtained from tension and compression tests of native silica aerogels and their nanocomposites. The results show that the axial and lateral direction mechanical properties of carbon-based nanocomposites are significantly higher than the native and glass fibers reinforced silica aerogels. For example, in the axial loading, the elastic modulus of the proposed glass fibers, graphene sheets, and carbon nanotubes reinforced nanocomposites were ∼3.5, ∼9.5 and ∼11.5 times higher than the native silica aerogels, respectively. Moreover, the influence of crack depth has been studied in the tensile fracture simulations, and we found that in nanocomposites, the tensile load bearing candidates are mainly reinforced materials. The outcome of this work is a vital step in the process of designing advanced nanocomposites.

Interfacial stress of carbon fiber patch bonded to transverse cracked steel plate reinforcement

A three-dimensional elastic-plastic finite element model was established in finite element software ANSYS to investigate the interfacial stress of carbon fiber patch bonded to transverse cracked steel plate reinforcement. The patch and adhesive were modeled as linear elastic. The steel plate was modeled as elastic-plastic. The load-deflection curve of the steel was obtained by bending test. The influence of crack depth, adhesive thickness, patch thickness and patch length on reinforcing efficiency was studied. The results show that the peel stress of the adhesive was distributed symmetrically along the center line, mainly concentrated on the crack center, near the crack and the patch ends. The peel stress at the crack center was always greater than the near crack. The shear stress is anti-symmetric along the center line, and the shear stress at the crack center is zero, mainly concentrated near the crack and plate end. The debonding may be initiated from the vicinity of the crack. Increasing the crack depth can significantly increase the peel stress and shear stress at the crack, but has little effect on the stresses at the end. Increasing the thickness of the adhesive can reduce the peel stress and shear stress at the crack center and near the crack, and the shear stress at the ends, but has little effect on the peel stress at the ends. Increasing the patch thickness can reduce the stress at the crack but increase the stress at the end. Increasing the patch length cannot reduce the stress at the crack, but significantly reduce the stress at the end.

Analytical approach to coupled bending-torsional vibrations of cracked Timoshenko beam

The explicit expressions of steady-state responses of a coupled bending-torsional Timoshenko beam with cracks and damping effect subjected to external harmonic loadings are presented in this paper. The Green's functions method is employed to obtain the analytical solutions. The beam is split to several segments due to the existence of cracks. General Green's functions of each segment with unknown boundary constants are given by using Laplace transform method. A mixture line-spring is introduced to obtain the compatibility conditions of the cracked cross-section between the segments. Based on the transfer matrix method, those constants in the Green's functions for each segment are determined with those matching conditions, as well as boundary relationships and end boundary conditions. Then, the solutions of the whole cracked beam with one or multiple cracks can be expressed in terms of the piecewise functions. The solutions of the multi-cracked beam cover those of the beam with only one crack and the uncracked beam. The theory developed can be used for the beam with classical boundary conditions, but for illustration, results for a cantilever cracked beam with T shape cross-section are illustrated, emphasizing the effect of cracks on the solutions. Comparisons between results in the published literature and those obtained from the developed method show a good agreement, which confirms the validity and accuracy of the proposed approach. The influences of crack depth, location and number on the natural frequencies are discussed. The changes of the steady-state responses of beam are investigated due to the existence of crack. Moreover, the symmetric property of the Green's functions and damping effect on the amplitude of steady-state responses of the cracked beam are studied particularly.

Critical Stresses in Materials with Cracks

The fracture mechanics concepts, as well as the concepts introduced on the basis of principle of critical energy, correlated with strength of materials with cracks is analysed. The equivalent stress method of strength was applied to cracked materials, by using the concept of local critical stress. This one depends on the material behavior and the deterioration due to crack. Experimental results have been obtained with specimens of OL304 steel with different cracks. The influence of crack depth and crack width is put into evidence.

A nonlinearity measure-based damage location method for beam-like structures

In our previous work, nonlinearity measure was proposed for assessment of nonlinearity severity of distributed parameter systems (DPSs). However, its engineering applications are restricted due to the high-dimensional optimization procedure in the nonlinear quantification. In this paper, we employ proper orthogonal decomposition (POD) to remove this restriction and apply this viewpoint to establish a damage location method for beam-like structures. The targeted structure was first divided into the sections by designated characteristic points, and the POD was used to obtain an optimized approximation of nonlinear systems’ trajectory. When comparing the nonlinearity degrees of the characteristic points in undamaged and damaged structures, the location was identifiable by finding positions of maximal change. Additional experiments were conducted to demonstrate the method’s effectiveness and applicability by determining the crack location and the influence of crack depth. Given our findings, we hope that this method can be extended to other vibrating structures with underlying nonlinearities.

Influence of Crack Depth on Dynamic Characteristics of Spur Gear System

Root crack is relatively common failure scenarios in spur gear system, and its dynamic characteristics and crack identification theory are addressed by many scholars. However, cracked spur gear identification model, especially related to its signal propagation characteristics, requires in-depth research due to the limited published works. Therefore, a bending–torsional coupling nonlinear vibration model of six degrees of freedom (DOF) is established through lumped mass method. Besides, the influence of tooth root crack on the measuring point signal is considered in the model. The system response is solved by Runge–Kutta numerical integration method. The change of different tooth-root crack depth on the response amplitude of measuring points is studied. It is found that with the increase of crack length, meshing stiffness of single-tooth mashing area and double-tooth meshing area are reduced. In addition, precision reduces slightly, but the overall precision calculated by 6-order ARX identification model is greater than 99.40%. The research provides a theoretical basis for the system testing and measuring point’s parameter identification.

Study of Multi-Cracked Cantilever Composite Beams Subjected to External Moving Load

The behaviour of multiple cracked cantilever composite beams is studied when subjected to moving periodic force. In this investigation a new model of multiple cracked composite beams under periodic moving load is solved. Three cracks are considered at different position of the beam for numerical solution. The results from experimental work compared to numerical solution. The multiple cracks are identified easily from the deflection graphs at different force speed. Influences of crack depth at different load speed are investigated

Vibratory characteristics of cracked non-uniform beams with different boundary conditions

Non-uniform beams with bending moment of inertia and mass per unit length varying as I(x) = α1(1+βx)λ+4 and m(x) = α2(1+βx)λ are widely used in various engineering fields, such as the civil and mechanical engineering etc. This paper presents an exact method to investigate the free vibration of cracked non-uniform beams with different conditions. Firstly, the closed form solution for the mode shape functions of the non-uniform beam is obtained based on the Euler-Bernoulli beam theory. Secondly, the beam is divided into several segments according to the different variable form, and each segment is further divided into many sub-segments by cracks. Four undetermined coefficients could represent the mode shape function of each sub-segment by simulating crack with the massless rotational spring. The undetermined transfer relationship in the same segment is obtained based on the principle of the transfer matrix method. The fourorder undetermined coefficient matrix is obtained by using continuity and equilibrium conditions between adjacent segments, and then the characteristic equation of the entire cracked beam is obtained after that. Finally, the results obtained from the finite element method and published papers are used to validate the correctness and reliability of the proposed method. The influences of crack depth, location and boundary conditions on natural frequencies of cracked non-uniform beams are discussed.

Influence of crack depth on the stress intensity coefficient in notched and smooth plates

The paper presents an analysis of variations in the stress intensity coefficient (SIC) in plates with different sizes of the cross-section, with and without concentrators. We also analyze the dependence of the SIC maximal value on the size of the smallest section of a plate with stress concentrator. SIC of smooth specimens and specimens with stress concentrator in the form of a semicircular notch are calculated using the ANSYS finite- element analysis program system. The static elastic problem is solved, with the strained state taken to be biaxial. The material of the plate is considered to be isotropic. The plates under consideration with a concentrator in the initial area of the crack size increase show maximum stress intensity coefficient. In plates without concentrator the SIC changes smoothly over the whole area of the crack size increase. It is established that the crack size is equal to 0.02 of the plate smallest size at the maximal value of the stress intensity coefficient. The study conducted confirms the feasibility of using the criterion of average integral residual stresses to calculate the increase of the endurance limit of surface- hardened specimens and parts with concentrators due to compressive residual stresses.

Dynamic analysis for cracked fiber-metal laminated beams carrying moving loads and its application for wavelet based crack detection

The present study considered the free and forced vibration of cracked fiber metal laminated (FML) beams with a damper subjected to a moving load, and the detection of the cracks by using continuous wavelet transform (CWT). The beam is regarded as multi segments which are assumed to obey the Euler-Bernoulli beam hypothesis and the crack is modeled as rotational spring with sectional flexibility. The modal expansion theory and Newmark method are employed to solve the dynamic responses of FML beam numerically. Two classes of boundary conditions are considered and the dynamic responses at the tip of a FML cantilever beam with a single crack are obtained for various load velocity, and the outcome results have been compared to the results obtained by literature. The influences of crack depth, crack location, ply angle of the fiber layer, stiffness coefficient of the damper and velocity of the moving load on free vibration and forced vibration of FML cantilever beams are investigated. Numerical results indicate that the above-mentioned effects play a very important role on both free vibration and dynamic responses of the beam. In the end of the numerical examples, continuous wavelet transform is used to detect the location of the cracks of a clamped-clamped FML beam.

Dynamic analysis on rotor-bearing system with coupling faults of crack and rub-impact

Rub-impact and fatigue crack are two important rotor faults. Based on the crack theory, an improved switching crack model is presented. Dynamic characteristics of a rotor-bearing system with imbalance, rub-impact and transverse crack are attempted. Various nonlinear dynamic phenomena are analyzed using numerical method. The results reveal that unstable form of the rotor system with coupling faults is extremely complex as the rotating speed increases and there are some low frequencies with large amplitude. The influence of crack depth and angle on the dynamic behavior of a cracked rotor is important insomuch as the quasi-periodical and chaotic motions in system response will occur along with different parameters. It is indicated that this study can contribute to a further understanding of the nonlinear dynamics of such a rotor system with coupling faults of crack and rub-impact.

Interaction of the Shear Horizontal Bend Guided Mode (SHB) with Transverse Cracks

Recent research by the authors has revealed the presence of shear horizontal-type of feature-guided (SHB) waves in plates with 90˚ transverse bends. The SHB mode is non-dispersive and has low attenuation over a range of higher frequencies (500kHz – 1MHz). This mode is attractive for Non-destructive Evaluation (NDE) of bends in practical structures such as aerospace spar joints. Here the interaction of the SHB mode with transverse small-width notches (cracks) running across bends in plates is studied using 3D finite element simulations and validated by experiments. For through-thickness cracks, the influence of transverse crack length on SHB mode reflection is studied. For part-depth but long cracks (transverse length greater than operating wavelength), influence of crack depth on mode reflection is studied. The results demonstrate the potential of the SHB mode for NDE of bent plate structures.

Influence of Crack Depth on Chloride Transport of Cracked Self-Compacting Concrete under Non-Steady State Migration Test

From a physical and mechanical point of view, concrete cracking is hard to avoid. So, it is meaningful to study the influence of crack depths on chloride transport in cracked self-compacting concrete. Following the NT BUILD 492 chloride migration test method, water soluble chloride conetnt, acid soluble chloride content and penetration depth were determined on cracked concrete samples which were prepared by artificial crack method. Afterwards, the migration coefficients were obtained by curve fitting on water soluble chloride contents and penetration depths seperately. The results show that the influence of crack depth on chloride concentration of concrete is significant for the concrete zone deeper than 20 mm from the surface. Secondly, the influential zone caused by the crack is limited to a distance of 10 mm at both sides from the crack. Thirdly, the existing equation of chloride transport is not applicable to concrete with different crack depths.

Abnormality monitoring model of cracks in concrete dams

The abnormality monitoring model (AMM) of cracks in concrete dams is established through integrating safety monitoring theories with abnormality diagnosis methods of cracks. In addition, emphasis is placed on the influence of crack depth on crack mouth opening displacement (CMOD). A linear hypothesis is proposed for the propagation process of cracks in concrete based on the fictitious crack model (FCM). Abnormality points are detected through testing methods of dynamical structure mutation and statistical model mutation. The solution of AMM is transformed into a global optimization problem, which is solved by the particle swarm optimization (PSO) method. Therefore, the AMM of cracks in concrete dams is established and solved completely. In the end of the paper, the proposed model is validated by a typical crack at the 105 m elevation of a concrete gravity arch dam.

Gearbox Damage Diagnosis usingWavelet Transform Technique

Vibration-based schemes are founded on the assumption that vibration signals from gearboxes measured using accelerometers reflect their condition accurately. A large number of vibration based techniques are used to make this reflection. They include various spectral analyses such as traditional Fourier transform, short-time Fourier transform, amplitude phase modulation and time synchronous averaging and non-parametric special estimation. Recently, Wavelet Transform (WT) has been proven to be more suitable for analysis of vibration signals, since most of the time-vibration signals have instantaneous impulse trains and exhibit a transient (non-stationary) nature. This paper uses an adaptive wavelet filter, based on the Morlet wavelet, applied on the torsional vibration data measured from a single-stage gearbox with artificially induced cracks in the gear. This is done to extract some parameters and check their diagnostic behavior in an effort to search for those with the most potential and appropriateness for future health monitoring schemes. The results demonstrate that the adaptive wavelet filter is found to be very effective in detection of symptoms from vibration signals of a gearbox with early tooth cracks. Moreover the influence of crack depth, speed, and load on the wavelet entropy are interduced. Multi-hour tests were conducted and recordings were acquired using torsional vibration monitoring. The transitions in the wavelet entropy values with the recording time were highlighted suggesting critical changes in the operation of the gearbox.

The Behavior of Shallow Cracks in a Pipeline Steel Operating in a Sour Environment

Setting conditions for the avoidance of in-service crack growth in aggressive corroding environments has long been a major challenge due to the number of variables that have a significant effect on material behavior. One area where both experimental data and a validated assessment methodology are lacking is the behavior of shallow cracks. This paper describes the early results of an ongoing research program aimed at addressing the shortfall in experimental data to characterize material behavior in the shallow-crack regime, with the long-term aim of improving the understanding and assessment of the early stages of environment assisted cracking. There is an industry need for a better understanding of material behavior under these conditions and for the development of a more robust assessment methodology. API 5L X65 pipeline steel parent material was tested in a sour environment with initial flaw sizes in the range 1–2 mm. Fatigue crack growth rate tests have been performed to investigate the influence of crack depth on crack growth rate (da/dN). Initial results suggest that crack growth rates for deep flaws can increase by a factor of 5–100 compared with air depending on the applied stress intensity factor range (ΔK). Shallow cracks have been shown to grow up to 130 times faster in a sour environment than in air and up to an order of magnitude faster than deep cracks in a sour environment at the same value of ΔK. Constant load tests have also been performed to investigate the influence of crack depth on the threshold stress intensity factor for stress corrosion cracking (KISCC). Preliminary results suggest that in this case there is no crack depth dependence in the range of flaw sizes tested. While further experimental work is required, the results obtained to date highlight the potential nonconservatism associated with extrapolating deep-crack data. Guidance is therefore provided on how to generate appropriate experimental data to ensure that subsequent fitness for service assessments are conservative.

Influence of Crack Depth and Attached Masses on Beam Natural Frequencies

A mathematical model describing the lateral free vibration of a clamped—clamped cracked beam carrying concentrated masses is derived. The masses are assumed small relative to the beam mass; also, the beam is assumed continuous with uniformly distributed properties. The attached masses are modelled as point masses with negligible rotary inertia, and the crack is simulated by a torsional spring. The Lagrangian dynamics, in conjunction with the assumed mode method are used in deriving the equation of motion.The effect of the locations of the attached masses and depth of the crack on the system frequency change is investigated along with the interaction between the attached masses and the crack depth. This interaction appears as a nonlinear coupling term in the natural frequency equation of the system. It is found that the coupling term may be used as an indicator of the error in relating system frequency change to crack only. Verification is carried out using three-dimensional finite element analysis.

Thermoelastic state of a half space containing a thermally active elliptic crack perpendicular to its boundary

By the method of boundary integral equations, we solve the problem of stationary heat conduction and thermoelasticity for a semiinfinite body containing an elliptic crack perpendicular to its boundary in the case where the crack surfaces are kept at a certain temperature. The boundary of the body is unloaded and either thermally insulated or kept at temperature equal to zero. We study the influence of crack depth and its location on the stress intensity factor at a given constant temperature.