Effect Of Crack Depth Research Articles

Effect of crack depth on the initiation and propagation of crack-induced sliding in a paleosol area on a loess slope: Three-dimensional investigation based on model testing and laser scanning

On the Chinese Loess Plateau (CLP), crack-induced sliding in paleosols triggers retrogressive slope collapse, compromising the long-term stability of loess slopes. Establishing a quantitative relationship between crack depth and slide size is key to elucidating the progressive evolution of crack-induced sliding in paleosols; however, research on this topic is scarce. In this study, a model test was conducted on a paleosol slope subjected to five drying–rainfall cycles. Three-dimensional (3D) laser scanning technology was employed to accurately quantify the variations in crack depth and slide size, and water content sensors were embedded to monitor the preferential flow changes induced by these cracks. Results reveal that crack depth plays a pivotal role in initiating and controlling the propagation of crack-induced sliding in paleosols by influencing the preferential flow capacity through cracks. In the slide initiation stage, a critical crack depth capable of triggering sliding by inducing a sufficiently significant preferential flow and large saturation zones was identified. The depth at which sliding occurs can be expressed as a variable dependent on crack depth based on the single triggering effect of cracking on sliding. Once a crack-induced slide is initiated, the combined action of prior sliding events and current crack propagation accelerates the subsequent sliding in terms of increased size and varying spatial locations by influencing the preferential flow capacity and sliding force values. A comprehensive empirical formula was established to characterize the depth of crack-induced slides, considering the dominant influence of crack depth and slope gradient on sliding development at this stage of slide evolution. Our findings emphasize the pivotal role of crack depth in triggering progressive crack-induced sliding in paleosols, thereby providing valuable insights for soil conservation in paleosol areas on loess slopes on the CLP.

Phase field thermal shock analysis of rotating porous cracked pretwisted FGM microblade using exact shear correction factor

The present work is an attempt to develop a simple and accurate finite element formulation for the thermal shock analysis of the rotating porous cracked pretwisted functionally graded material (FGM) microblade using modified coupled stress theory in conjunction with phase-field and first-order shear deformation theory (FSDT). The physical neural surface is taken as the reference plane and the exact value of the shear correction factor is calculated from the shear stiffness. The elastic properties are assumed to be temperature-dependent and the upper ceramic layer is subjected to a high thermal shock whereas the bottom metallic layer is maintained at room temperature or is thermally insulated. The governing differential equation for the present analysis is derived using Hamilton’s principle and Newmark average acceleration method is used to obtain the transient response of the rotating porous cracked pretwisted FGM microblade subjected to thermal shock. The results obtained from the present finite element formulation are first validated with several benchmark examples available in the literature. New results are presented investigating the effect of crack depth, crack location, crack angle, rotational velocity and material scale ratio on the transient response of the cracked rotating porous pretwisted FGM microblade subjected to thermal shock. It is shown here that the parameters like crack depth, crack location and crack angle have a significant influence on the transient response of the rotating porous cracked pretwisted FGM microblade.

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.

XFEM based study on fatigue performance of rib-to-diaphragm welded joints considering initial defects

Orthotropic steel bridge decks (OSBDs) have been widely used in the field of bridges. However, their service life is significantly limited by fatigue issues. This study presents an analysis of the fatigue performance at the structural details of the rib-to-diaphragm joint, taking into account the impact of initial defects. A numerical segment model employing shell-solid coupling is established to determine the influence surface range and the most unfavorable working condition of the fatigue details, using fatigue standard vehicle loading. The accuracy of the local full-scale model is validated. A local model test of the rib-to-deck welded joint is carried out to deduce the parameter selection for the numerical simulation, based on the test results. Additionally, the crack propagation process in rib-to-diaphragm joints is simulated using XFEM. The simulation results of crack propagation demonstrate good agreement with the actual bridge crack path and shape. The crack propagation model can effectively evaluate the fatigue life, crack development stage, and shape of fatigue details. The study determines the effects of crack depth, crack length, and crack angle on fatigue performance. This study provides a basis for studying the residual fatigue life and crack propagation behavior of rib-to-diaphragm welded joints with initial defects. It is of great significance for understanding the crack propagation mechanism, formulating repair measures, and determining repair time.

Dependence of Critical Stress Intensity Factor on Crack Depth From the Loading Boundary of Crystalline Silicon

Abstract In the present work, an atomistic scale investigation is done on crystalline silicon to understand the effect of crack depth from the loading (pulling) boundary on the critical near-tip state of stress. For various depths of embedded cracks, the near-tip stress field has been calculated at the critical state just before the crack propagation initiation. This atomistically calculated stress field is found to be quite close to those found using continuum linear elasticity. Thereafter, the critical stress intensity factor (SIF) is calculated for all cases by fitting the atomistically calculated normal stress over inverse square-rooted distance from the crack tip. It has been found that the closer the crack is located to the loading boundary (i.e., lesser depth), the lower is the (locally calculated) critical SIF. This implies that it is easier to initiate crack propagation when the crack is located closer to the loading boundary. The claim is also strengthened by a similar observation of (globally calculated) boundary stresses at the critical state just before crack propagation initiation.

Numerical study on damped nonlinear dynamics of cracked FG-GNPRC dielectric beam with active tuning

Functionally graded (FG) graphene nanoplatelets (GNPs) reinforced composite (FG-GNPRC) is widely used in various engineering fields due to its high-performance and multifunctional features. Cracks generated in complex environments have a significant impact on the structural behavior of FG-GNPRC structures. This paper studies the damped nonlinear dynamics of cracked FG-GNPRC dielectric beam subjected to mechanical excitation and electrical field. The effective material properties of the composites are determined by the effective medium theory (EMT). Based on Timoshenko beam theory and nonlinear von Kármán strain–displacement relationship, the governing equations which incorporate damping and dielectric properties are derived by using energy method. Stress intensity factor (SIF) of cracked FG-GNPRC beam at the crack tip is calculated via finite element method. Differential quadrature (DQ) and incremental harmonic balance (IHB) methods combined with arc-length algorithm are utilized to discretize and solve the nonlinear system. After validation of the model and solution, the effects of crack depth and location, damping, FG distribution and the attributes of GNP and the electric field on the dynamic response of the system are comprehensively investigated. The study indicates that when an electric field is applied, the amplitude ratio of cracked FG-GNPRC beam with profile V is the largest when the crack is close to the edge, whereas profile A exhibits the largest value when the crack is near the mid-span. In addition, the generated bending moment enables profiles A and V to transit into profile U at a certain voltage or GNP aspect ratio due to the existence of electrostatic stress.

Simulation study of crack parameters’ effects on the vibration characteristics of a bladed disk system

As a key component of the turbo machine rotor in harsh operating conditions, high cycle fatigue failure and even cracks are common in bladed disks. In this paper, modal analysis was carried out for a single cracked bladed disk system, the effects of crack depth, crack height and rotating speed on its vibration characteristics were studied by the method of both numerical simulation and orthogonal test, and the effects of crack distribution on the vibration characteristics of multi-crack bladed disk systems were also studied. Finally, some conclusions have been drawn, they provide a fundamental understanding of blade health monitoring and fault prediction, and are important to improve the reliability and safety of turbine operation.

Measurement and evaluation of time-varying meshing stiffness of faulty gears under different types

When operating under complex conditions, gear failure is inevitable, and gears are often accompanied by multiple failures. In view of this phenomenon, this paper establishes a pitting crack coupling failure model and sets four different fault levels, from healthy to severe. Time-varying meshing stiffness (TVMS) decreases with the occurrence of faults, such that it could be employed as a gauge to assess the level of failure. Firstly, considering that the base circle and the tooth root circle do not coincide, the improved potential energy method is used to solve the TVMS under different fault degrees. Secondly, the effects of crack depth, angle, pitting radius, depth and number on meshing stiffness are studied. Then, the result of the potential energy method is verified by the finite element method, and the consequence shows that the difference between the two is within 5%, which indicates the effectiveness of the proposed model. Finally, when the crack degree is certain, the influence of pitting evolution on the meshing stiffness of the coupling model is studied.

A unified fatigue life evaluation method for different failure modes of the repaired rib-to-deck joints in orthotropic steel decks

The rib-to-deck welded joints in orthotropic steel decks (OSDs) are prone to fatigue damage with different fatigue failure modes. The damage accumulation of the corresponding failure modes should be estimated in repair design. This study proposed a unified fatigue life evaluation method for different failure modes of rib-to-deck welded joints based on the structural stress method and linear damage accumulation theory. The method considers the effect of crack depth and crack propagation on life evaluation, validated by the tests of repaired rib-to-deck joints with interior repair welds. Damage accumulation before and after repairing corresponding to different failure modes was assessed. The dominant failure modes before and after repairing were analyzed. Finally, the damage accumulation law of welded joints after repair under standard traffic load was investigated based on the existing damage status of each failure mode of the rib-to-deck welded joint. The results indicate that the failure mode will transfer from root-deck to exterior toe-deck at the rib-to-deck joint after the interior repair welding. The dominant failure mode of the repaired joint is governed by the existing damage status and the repair method.

Dynamic response of damaged rigid-frame bridges subjected to moving loads using analytical based formulations

PurposeThis study aims to perform dynamic response analysis of damaged rigid-frame bridges under multiple moving loads using analytical based transfer matrix method (TMM). The effects of crack depth, moving load velocity and damping on the dynamic response of the model are discussed. The dynamic amplifications are investigated for various damage scenarios in addition to displacement time-histories.Design/methodology/approachTimoshenko beam theory (TBT) and Rayleigh-Love bar theory (RLBT) are used for bending and axial vibrations, respectively. The cracks are modeled using rotational and extensional springs. The structure is simplified into an equivalent single degree of freedom (SDOF) system using exact mode shapes to perform forced vibration analysis according to moving load convoy.FindingsThe results are compared to experimental data from literature for different damaged beam under moving load scenarios where a good agreement is observed. The proposed approach is also verified using the results from previous studies for free vibration analysis of cracked frames as well as dynamic response of cracked beams subjected to moving load. The importance of using TBT and RLBT instead of Euler–Bernoulli beam theory (EBT) and classical bar theory (CBT) is revealed. The results show that peak dynamic response at mid-span of the beam is more sensitive to crack length when compared to moving load velocity and damping properties.Originality/valueThe combination of TMM and modal superposition is presented for dynamic response analysis of damaged rigid-frame bridges subjected to moving convoy loading. The effectiveness of transfer matrix formulations for the free vibration analysis of this model shows that proposed approach may be extended to free and forced vibration analysis of more complicated structures such as rigid-frame bridges supported by piles and having multiple cracks.

Three-Dimension Crack Propagation Behavior of Conical-Cylindrical Shell

The conical-cylindrical shell is prone to stress concentration in the convex cone position under the action of deep-sea pressures. This results in unidirectional or bidirectional positive tensile stresses on the surfaces of the shell. The conical-cylindrical shell is a large, welded structure. Welding residual stress was generated at the cone-column joint position, resulting in high-stress concentration at this location. Under both the residual stress of welding and seawater pressure, cracks easily form and propagate on the shell weld toe, leading to fatigue damage and even structural failure. In this paper, based on the seawater’s alternating load and the residual stress of welding, the three-dimensional crack propagation process was studied for the submarine conical-cylindrical shell. The effects of crack depth and shape ratio on crack propagation trend and fatigue life were analyzed. The results can provide references for predicting the crack propagation trend, assessing the remaining life and evaluating the structural safety of the submarine conical-cylindrical shell.

INFLUENCE OF SURFACE CRACKS ON THE STABILITY OF CRACKED SOIL SLOPE

The slope stability is a major concern to geotechnical engineers. Traditional methods of slope stability analysis have potentially ignored the influence of surface cracks. It is also known that seasonal rainfall and seepage through crack are closely related with slope failure. First, surface cracks provide special flow channels which increase the soil permeability and decrease the soil strength. Second, water-filled cracks apply an additional active force on the slope. Finally, cracks can create a part of the critical failure surface that has no shear strength. The objective of this paper is to investigate the influence of existing cracks on the stability of a cracked soil slope in different state. The effects of crack depth, slope angle and water-filled cracks on the stability of the cracked slope are explored. The analysis was conducted using the computer modelling programs Optum G2 to analysis of slope factor of safety. The results show that with increasing of slope angle the factor of safety decreases and this problem is significant in the slope with water filled cracks. Also, Factor of safety for all of slope angles in Dry and water filled cracks states with increasing the crack depth, decrease significantly.

S0 Lamb Mode Scattering Studies in Laminated Composite Plate Structures with Surface Breaking Cracks: Insights into Crack Opening Behavior

Ultrasonic-guided waves are attractive for rapid inspection of laminated composite structures, where cracks developed transverse to the loading direction are the severe type of damage. This paper presents studies of the interaction of fundamental symmetric S0 Lamb mode with vertical surface-breaking cracks in laminated composite plate structures. Finite element simulations and experimental investigations are used to study the effect of crack depth on S0 wave reflection behavior. Results show a monotonic rise of the reflection coefficient for different crack depths in a manner that is strongly dependent on the orientation of the plies and transverse ply location in the vicinity of the crack. Scattered wave packets in the reflection regime are captured using an in-plane laser. The S0 Lamb mode's sensitivity is numerically presented for the different crack depths in the long wavelength limit. We also observed that the reflected wave mode depicts the information of the corresponding broken interfaces. An attempt was made to show that this behavior relates to the crack-opening behavior in response to in-plane excitation. The reflection coefficient as a characteristic polynomial is proposed for various orientations. It was observed that the dispersion at receiver nodes makes the analysis challenging for distinguishing the signal from crack faces due to the smaller dimension. The study outcomes show its prospect as a promising NDE tool for crack damage detection in thin laminated plate structures.

Refined models for free vibration analysis of elastic plates with part-through surface cracks

In this paper, two refined models are proposed for the vibration analysis of isotropic and orthotropic thin plates with part-through surface cracks. The governing equations of cracked plates are formulated via the refined models. Like in the conventional model, crack terms are incorporated in the governing equations. All-over and finite-length cracks (i.e., central and edge cracks) can be directly handled by the new models and their modified forms, respectively. The matched interface and boundary method is then applied to formulate eigenvalue equations. A series of parametric studies for investigating the effects of crack depth and crack length are presented. Numerical results of the proposed models are compared with the existing and finite element solutions to validate their performance and accuracy. The salient feature of the refined models is to complement the deficiency of the conventional model for the analysis of crack depth problems. Several illustrative examples are provided to demonstrate the superior performance of the refined models over the conventional one. The present models are effective for predicting the natural frequencies of thin plates with part-through surface cracks.

Asphalt complex cracks' sensitivity to temperature and crack depth and adjustment of the composite stress intensity factor

This paper is based on the fracture mechanics K-criterion with the composite stress intensity factor solution formula. The influence of temperature and depth in developing complex crack instability and diffusion in asphalt pavements is investigated. The crack composite stress intensity factor and development pattern are analyzed. The finite element modeling analyzes the change in stress intensity factor values at different temperatures and cracks depths. The composite stress intensity factor's temperature effect factor (t*) and crack depth effect factor (d*) are derived, and the calculation formulae are optimized. The study results show that among the complex cracks in asphalt pavements, the type I crack tip stress intensity factor (KⅠ) is the most seriously affected by temperature and crack depth and is also the main controlling factor of crack development. Type II crack tip stress intensity factor (KⅡ) is not significantly influenced by temperature but tends to rise and fall as the crack depth increases. Type III crack tip stress intensity factor (KIII) is smaller than KⅠ and KⅡ. It has less influence on the development of complex cracks in asphalt pavements. t* and d* were introduced to derive the formula for the modified composite stress intensity factor (Keff*). The formula was verified to calculate the composite stress intensity factor at different temperatures and crack depths and to study the cracking pattern of asphalt pavements.

Solutions and applications of 3D elastic–plastic constraint parameters for clamped single edge notched tension (SENT) specimens

Single edge notched tension (SENT) specimen is a common fracture toughness test specimen now widely used in the pipeline and pressure vessels industries. In this paper, an extensive study has been conducted by three-dimensional (3D) finite element analyses (FEAs) to investigate the in-plane constraint parameters (namely A and QSSY) and out-of-plane constraint parameter, that is, Eε33 for clamped SENT specimens with side-grooves. A wide range of crack depth to specimen width ratios a/W = 0.2, 0.3, 0.4, 0.5, 0.6 and 0.7, specimen thickness to specimen width ratios B/W = 0.5, 1.0, 1.5, 2.0, 3.0 and 4.0 were included. The various strain hardening exponent (n = 4, 7, 10) and applied loading levels (from small-scale yielding to large-scale yielding) were also investigated. The results show that the effects of crack depth, specimen thickness, loading level and strain hardening index on the 3D constraint parameters show a significant coupling effect. With the increase of load level, A value increases monotonically, while QSSY and the normalized Eε33 (called V33) decrease, and the influence of specimen geometry on the constraint levels will become greater. The values of A and V33 obviously decrease with the increase of hardening exponent, but the change of QSSY is relatively small. Moreover, it can be observed that both A and QSSY can well describe the in-plane constraint effect, and V33 can better quantify the out-of-plane constraint effect under varying loading levels and n. In addition, elastic–plastic constraint parameters were also calculated for various experimental test specimens made of 16MND5 steel, with n = 9.2. It was demonstrated these constraint parameters can be applied to quantify and predict the J-R curves of 16MND5 steel with good agreements for specimens with different in-plane and out-of-plane constraint conditions.

Analysis of free vibration of tapered cracked double nanobeams using Maclaurin series

In the study, the Maclaurin series technique is presented to analyse the vibration of cracked tapered double nanobeams. The equation of motion is derived from the Euler–Bernoulli beam theory based on the Hamiltonian principle and Eringen’s nonlocal theory of elasticity. The double-nanobeam system consists of two parallel nanobeams attached by a Winkler elastic layer. Both beams are identical and their widths vary along the x-axis. A single crack is considered at the upper beam of the system. The mechanical behaviour of cracked cross-sections is simulated by the local stiffness model. According to the model, the cracked double-beam system is divided into two intact segments. A numerical investigation is carried out to scrutinize the effects of nonlocal parameters, crack severity, taper ratio, and spring constant on the vibration of the double nanobeam. The results reveal that the effects of crack depth, crack location, nonlocal parameters, taper ratio, and spring constant influence the natural frequency and dynamic response of the system significantly. This study highlights that a crack at the upper beam influences the mode shape of the upper beam as well as the intact lower beam. Numerical results have been examined with the previously published works and found a good agreement with them.

Vibrational power flow analysis of Timoshenko microbeams with a crack

In this paper, an analytical model based on the modified couple stress theory and Timoshenko beam theory is developed to study the vibrational power flow of a microbeam with a crack. The open edge crack on the microbeam is modeled as a rotational spring, which connects the two segments of the microbeam separated by the crack location. The governing equations of the cracked microbeam are derived from Hamilton's principle. By introducing the differential operator method, the differential equations are transformed into algebraic equations, and the governing equations are decoupled. The wave propagation method is applied to solve the vibrational problem of a cracked microbeam under a transverse harmonic excitation. Both the input power flow and the transmitted power flow in the cracked microbeam are computed and analyzed. The size effect of the cracked microbeam in terms of material length scale is firstly analyzed. Subsequently, the effects of crack depth and crack location on the input and transmitted power flows are investigated. It is found that the existence of crack significantly changes the transmission characteristics of the power flow.

Investigation of Rotating Eddy Current Testing Simulation Using Simplified Model

To reduce the time of simulation for rotating Eddy current testing (RECT) technique, a simplified model without modeling probe was proposed previously. However, the applicability of the simplified simulation model was unknown. In this paper, the applicability of the simplified model for the RECT technique was investigated. The application condition of the simplified model was provided by comparing it with the results of the traditional simulation model. The simplified model was suitable for the study of cracks shorter than 70% size of the uniform Eddy current induced by the probe in a traditional model or experiment. The experiment was conducted to validate the simplified model. Moreover, using the simplified model, the effects of crack depth, orientation, and exciting frequency were studied. The deeper the crack depth was, the greater peak value of [Formula: see text] signal was. The crack angle was linear with the phase of signal. The exciting frequency affected the amplitude and phase of the signal at the same time.

A Numerical Investigation of an Abnormal Phenomenon of Stress Intensity Factor (SIF) in a Cracked T-Butt Joint Accounting for Welding Effect

Industry design standards such as BS 7910 deployed some empirical formulas for the prediction of stress intensity factor (SIF) based on simulation results from traditional finite element method (FEM). However, such FEM simulation occasionally failed to convince people due to the large discrepancies compared with engineering practice. As a consequence, inaccuracy predictions via such formulas in engineering standards inevitably occur, which will compromise the safety of structures. In our previous research work, an abnormal phenomenon of SIF in a cracked T-butt joint accounting for welding effect has been observed. Compared with BS 7910, the calculation results of SIF at the surface points of welded specimens cannot be well predicted, with a large discrepancy appearing. In order to explore such problem with an abnormal increase at the surface points of cracked welded specimens, a numerical investigation in terms of SIF among BS 7910, XFEM, and FEM is performed in this paper. Numerical models on both a simple cracked plate without welding effect and a cracked T-butt joint with welding effect are developed through ABAQUS. Parametric studies in terms of the effects of varied crack depth to thickness ratio (a/T) and the effects of crack depth to crack half-length ratio (a/c) are carried out. Empirical solutions from BS 7910 are used for comparison. It is found that the XFEM can provide predictions of SIF at both the crack deepest point and crack surface point of a simple cracked plate as accurate as FEM. For a T-butt joint with a transverse stiffener, a large discrepancy in terms of the weld magnification factors (Mk) occurs at the crack surface point compared with empirical predictions. An exceptional increase of von Mises stress gradient in regions close to the weld-toe is found through the simulation of FEM, whereas a constant stress gradient is obtained through XFEM. The comparison results indicate an inappropriate prediction of SIF by the utilization of the empirical formulas in BS 7910. A more reasonable prediction of the SIF at the surface point of a crack is obtained by the XFEM. Therefore, further updating of the empirical solutions in BS 7910 for SIF accounting for welding effect is recommended.