Crack Depth Ratio Research Articles

Fatigue cracking characteristics of components stiffened with vertical ribs under eccentric loading in steel bridge deck

The components in orthotropic steel decks are generally in an eccentrically loaded state for the nonuniformly distributed wheel loads. By conducting numerical simulation and fatigue tests of components stiffened by the vertical rib (CVR) with single butt weld, the propagation law of CVR cracks under eccentric loading were analyzed. By comparing with components stiffened by U-ribs (CUR), the difference of crack-growth characteristics between components with single and multi butt welds under eccentric loading was explored. The results show that CVR cracks will initiate at the eccentrically loaded side of the weld and propagate obliquely, but still perform the bilateral cracking mode as that under symmetric loading. The CUR and CVR cracks present the same three-stage characteristics of fast-slow-rapid growth and components will accelerate to failure in the third stage, which shall be avoided. The section-damage rate of CUR will be greatly relieved for the unilateral cracking under eccentric loading compared with that of bilateral cracking under symmetric loading, which delays the crack to enter the rapid-growth stage. Since there’s little effect of eccentric loading on the demarcations of crack-growth stages in CVR, it is reasonable to take the demarcation 80 mm between the second and third crack-growth stages as the warning length for maintenance. The semi-elliptical CVR cracks will quickly penetrate base metal after extending to 75 % of thickness with the average ratio of crack depth to length being 0.09, which can be treated as the operation timing of maintenance methods for non-penetrating 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.

Simulation of Surface Crack Interaction of Marine Solid Shaft

In the marine industry, an engine transmits power through a marine shaft, also called a propeller shaft, to a propeller drive. Almost all naval architects construct this shaft as a solid cylinder. When a crack shows up in the hub of a shaft, it is essential to take preventative measures. When solid cylinders are exposed to various mechanical stresses, cracking or fracturing is a typical failure, and most of the crack exists in single and multiple cracks. Owing to the possible interactions between fractures, they are likely to play a significant role in how the structure collapses. Consequently, this study is being conducted to address issues emerging from the interaction of multiple cracks during particular loading conditions. This paper will highlight the research conducted on various cracks interacting with parallel configurations on the cylinder's surface. Finite Element Software, AnsysTM has been employed through modelling and simulation to calculate the stress intensity factor (SIF) for various crack geometry features and separation distances under various types of loading. The dimension for length and diameter of the cylinder has been set as 200 mm and 50 mm, respectively. The values of crack depth ratio used is ranged from 0.1 to 0.4 with the increment of 0.1, while for crack aspect ratio is 0.6. The results from the SIFs are normalized for generalization to determine the interaction factor and the relationship between two cracks and a single crack.

Fracture analysis-based mode-I stress intensity factors of crack under fracture grouting in elastic–plastic soils

For the interaction of crack on the soil–grout interface under fracture grouting, an approximate method to determine the stress intensity factor (SIF) of crack on the soil–grout interface was proposed based on the conservation J2-integral. With this method, the energy release rate of crack propagation under fracture grouting can be defined by the parameters of elastic–plastic soils and the grouting pressure. In order to study the change of strain energy near the crack of elastic–plastic soil under fracture grouting, a mechanical model of elastic–plastic soil with crack was established based on non-associated Mohr–Coulomb criterion model, and the SIF of crack with spring boundary was investigated. The influence of the crack depth ratio and crack aspect ratio on the SIF of cracks under the spring boundary were analyzed, and revealed the rule of crack growth under fracture grouting in elastic–plastic soils. The results showed that the variation of the crack depth ratio and crack aspect ratio had an effect on the change of the SIF of cracks. Increasing the crack depth ratio and crack aspect ratio caused an increase in the SIF of the crack. The results can provide the reference for foundation reinforcement in elastic–plastic soils.

A Creep Constitutive Model, Based on Deformation Mechanisms and Its Application to Creep Crack Growth

In this paper, a constitutive model, based on the creep deformation mechanism in P91 steel, under a wide range of stress levels, was established and embedded into finite element software. The accuracy and reliability of the model was verified by comparing the simulation of uniaxial creep tensile test results and the experimental data under different stress levels for P91 steel at 600 °C. The creep crack growth behavior of P91 steel, under a wide range of stress levels was simulated using a ductility-exhaustion-based damage model, combined with the stress-dependent creep ductility model, and the predicted creep crack growth (CCG) rates were compared with the experimental data. Finally, the established model was used to predict the CCG behavior for the pressurized pipes with axial surface cracks. The results show that the constitutive model, established on the basis of the creep deformation mechanism, agrees better with the experimental data than other constitutive models. The CCG rate varies at different direction angles θ for the axial surface cracks. The direction angle θ corresponding to the maximum creep crack length is about 33°, when the internal pressure exceeds 10 MPa. The initial crack shape (a0/c0) = 1, and it does not change with different initial crack depth ratios (a0/t). The established constitutive model can be well used in CCG life analyses and designs of high-temperature structures.

Localized Damage Identification in the Last Stage Low-Pressure Steam Turbine Blade Using Dynamic Parameter Measurements

Abstract Steam turbine blades are the important components in power system shaft lines subjected to severe temperatures, leading to low/high cycle fatigue failures. The transient conditions occurring during startup and shutdown events generate alternative stresses causing the fracture at the blade roots. The present work deals with the effect of localized damage on the vibration characteristics and damage identification study in the last stage low-pressure (LP) steam turbine blade. Initially, free vibration studies and transient analysis of the last row LP blade section are conducted using the finite element model. A crack near the root region is modeled by a torsional spring, whose stiffness is expressed in terms of crack depth ratio. Effects of crack depth ratio and location near the roots on the natural frequencies and transient response amplitudes are studied in detail. The relationship between the damage parameters and blade frequencies is established through the backpropagation neural network model.

Experimental Study on Fracture Properties of Hydraulic Concrete with Different Crack-Depth Ratios Based on Acoustic Emission and DIC Techniques

In order to study the fracture behavior of hydraulic concrete, wedge splitting tests are performed on notched cubic concrete specimens with different crack-depth ratios (0.3, 0.4, and 0.5). Meanwhile, acoustic emission and the digital image correlation method were used to monitor the crack propagation. Test results show that the initiation toughness of the hydraulic concrete specimen is independent of the crack-depth ratio. As the crack-depth ratio increases, the fracture toughness, the fracture energy, and the critical crack length decrease. The AE cumulative counts and hits can reflect not only the four-stages fracture process of hydraulic concrete but also the boundary effect of hydraulic concrete. The acoustic emission b value can reflect the two stages of postpeak damage of the hydraulic concrete. The length of fictitious crack, the propagation velocity of macrocrack and effective crack length decrease with the increase of the initial notch depth ratio. The effective crack length increases with the increase in the maximum aggregate size, and the growth time increases with the maximum aggregate size and an effective height of the specimen.

Stress intensity factors and weight functions for semi-elliptical cracks at weld toes in U-rib-to-deck joints

The weight function (WF) has unique advantages when calculating the stress intensity factor (SIF) and evaluating the fatigue performance of cracked components. However, exiting WFs are common for simple geometries, but cannot accurately calculate the SIFs for surface cracks in U-rib-to-deck joints. Here, WFs are derived for semi-elliptical surface cracks in U-rib-to-deck joints. Firstly, the finite element method (FEM) is used to calculate the SIF for semi-elliptical surface cracks at weld toes in U-rib-to-deck joints. The effect of different crack configurations, such as the weld angle (θ), aspect ratio (a/c), crack depth ratio (a/T), and deck-to-rib thickness ratio (T/t), on SIFs is discussed. Then new WFs are developed and validated based on different stress distributions, and the effects of different crack geometric characteristics are considered. Finally, using the derived WFs, the SIFs for surface crack in a U-rib-to-deck joint are calculated accounting for the welding residual stresses. Comparisons were made with predictions from the existing WFs for T-plate joints, and the FEM. The proposed WFs comprehensively account for the effects of the crack geometry characteristics of U-rib-to-deck joints and accurately calculate the SIFs for surface cracks at weld toes.

Two-dimensional weight function for the determination of stress intensity factors for semi-elliptical surface cracks in finite-thickness and finite-width plates

In this study, a new two-dimensional (2D) weight function of stress intensity factors (SIFs) for semi-elliptical surface cracks in finite-thickness and finite-width plates subjected to arbitrary stress distributions was proposed. To determine the unknown coefficients in the weight function, parametric three-dimensional finite element (FE) models were developed to obtain the solutions of SIFs. The analysis matrix covers wide ranges of relative crack-length ratios 0.1 ≤ c/W ≤ 0.9, to consider the finite width effect, as well as aspect ratios 0.2 ≤ a/c ≤ 1.0 and relative crack-depth ratios 0.025 ≤ a/T ≤ 0.8. The present weight function was verified against the FE results and the solutions available in the literature. The maximum differences were within 6% for both the surface and deepest points. The proposed 2D weight function can be applied to calculate SIFs and predict the fatigue life of engineering structural components involving surface flaws.

Online monitoring of crack depth in fiber reinforced composite beams using optimization Grey model GM(1,N)

The existing analytical and numerical simulation models are not able to estimate the crack depth when poor information available about the crack. The present study is aimed to develop an online monitoring system to estimate crack depth in composites. The online monitoring system is developed with optimization Grey model OGM(1,N) and support vector machine (SVM) separately and the crack depth is estimated in E-glass fiber reinforcement polymer composites. In this study, cracks are made artificially on the E-glass fiber reinforcement polymer at distance of 50, 100 and 150 mm from free end with crack depth ratios of 12.9%, 14.1%, 15.3%, 16.5%, 17.6% and 18.8%. Natural frequency is measured at three nodes for all the cracks. The proposed SVM and GN(1,N) models are trained with four samples for each position and tested for the remaining two samples. In the proposed OGM(1,N) model, training samples are updated by adding recent data sample and deleting old data. So that the OGM(1,N) model predicts the crack depth ratio more accurately than the SVM model with an error of 1.06%. The OGM (1, N) is simple and directly estimates the crack depth by taking into account online measured data of the vibration frequency. Based on the accuracy in prediction, the Grey online modeling and monitoring system is suggested to estimated crack depth in composites. Interaction effect of the crack position and crack depth ratio on the natural frequency at the three nodes is studied.

Stress Intensity Factors for Radial Crack on Inner Surface of Interface in Multi-Layer Rotating Thick-Walled Cylinder

Cracks often appear on the inner surface of metal thick-walled cylinders with multiple interference fits. Considering that no relatively accurate model exists for the cracks on the interface of multi-layered, rotating, thick-walled cylinders, in this paper, the stress intensity factor is established for a radial penetrating crack on the interface of a multi-layered, rotating, thick-walled cylinder. The parameters included in the equation are the rotation speed, the wall thickness ratio, and the interference. First, finite element software is used to calculate the stress intensity factors of two thick-walled cylinders under an interference fit with a crack on the interface. Then, the equation of the stress intensity factor is fitted with the parameters of contact pressure, crack depth, and wall thickness ratio. Next, the weight function is used to calculate the stress intensity factor for radial penetrating cracks on the inner surface of the cylinder’s interface. Finally, 2D finite element models of the four-layer cylinder with a crack are established to verify the equation.

Using a continuous mathematical model to investigate the effect of a symmetric circumferential crack on the free vibrations of a simply supported Euler–Bernoulli beam

This paper investigates the influence of a circumferential crack on a simply supported beam’s free vibration behavior analytically and numerically. The beam is modeled by Euler–Bernoulli beam theory with a circular cross-section. The circumferential crack is modeled by considering a continuous effect in the displacement field. An exponential function is considered in the displacement field with an exponential decay rate parameter which characterizes the influence of crack on its surroundings. The exponential function of crack depth ratio was proposed for the exponential decay rate of symmetric circumferential open cracks using a comparative method based on finite element simulation for the first time. The equation of motion is derived using Hamilton’s principle and solved by a Galerkin method, and natural frequencies are obtained. The crack depth and position influence on the natural frequency are analytically clarified and compared with a symmetric and single-edge crack. The possibility of identifying the location and relative depth of the crack has been investigated. Whatever the crack is, closer to the maximum amplitude vibration in each mode, the frequency ratio is more dropped, making it more detectible. Also, the circumferential crack is more affected on vibration behavior than the symmetric and single-edge crack. The analytical results have excellent conformity with the finite element results obtained by the ABAQUS 3-dimensional model. Also, some experimental results have been obtained to validate the finite element model. The finite element model has an excellent agreement with experimental results. The results can be used to identify circumferential cracks.

Closed-Form Stress Intensity Factor Solutions for Circumferential and Axial Surface Cracks With Large Aspect Ratios in Pipes

Abstract The ASME Boiler and Pressure Vessel Code Section XI prescribes the stress intensity factor solutions at the surface and deepest points for a semi-elliptical crack. The ASME Code Section XI, however, provides no solutions for a crack with a large aspect ratio, that is a crack in which the crack depth a is larger than the half-length c. The difficulty in treating the crack with a large aspect ratio relates to the position of the maximum stress intensity factor, which appears at neither the surface point nor the deepest point. In this paper, we investigate the influence of the stress intensity factor at the maximum point for circumferential and axial inside surface cracks with a large aspect ratio in a cylinder. First, we obtain the influence coefficients Gi for the stress intensity factor at the surface point, the deepest point, and the maximum point by finite element analysis, and developed a series of closed-form Gi solutions. Three geometrical factors are considered as parameters affecting the influence coefficients Gi: aspect ratio (a/ℓ = 0.5, 1.0, 2.0, and 4.0), crack depth ratio (a/t = 0.01, 0.1, 0.2, 0.2, 0.4, 0.6, and 0.8), and radius to thickness ratio (Ri/t = 2, 5, 10, 20, 40, and 80). Finally, we propose methods for evaluating the stress intensity factor for a crack with a large aspect ratio in a manner that characterizes the influence of the solutions at the maximum point.

J estimation based on regression machine learning applied to circumferential surface clad pipes with V groove weld

A regression machine learning approach is applied to propose a new equation for J-integral estimation for circumferential surface clad pipelines. The training data is provided based on a large number of simulations accomplished using a parametric finite element model generator script. The analysis matrix includes several crack depth ratios a/t, crack aspect ratios c/a, pipe diameter ratios Dext/t, V-groove angle, and material strain hardening exponent, n. The clad layer thickness is considered fixed with 3 mm. A model generator based on the Python programming language is used to generate an extensive data set of models. Training and testing sets are formed for five features and one target to develop a machine learning model. This paper aims mainly to promote fracture assessments by presenting an easy-to-use regression model encompassing several geometrical and material parameters. This is for finding an initial conservative J-integral estimation for a fully plastic description of fracture behavior under considerable plastic strain to provide a numerical evaluation of the crack driving force. The validation of the proposed model is ensured by comparing the results herein with those from different approaches.

Free-vibration analysis of cracked beam with constant width and linearly varying thickness

This study carries out free-vibration analysis of a cracked tapered beam with a constant width and a linearly varying thickness. The finite-element and component mode synthesis methods are used to determine the dynamic behavior of the tapered cracked beam. In accordance with the Bernoulli–Euler beam theory, the stiffness and mass matrices are obtained to find the natural frequencies and mode shapes of the tapered beam. The beam containing a crack is divided into subcomponents from the crack section. A massless spring model is used to define the local flexibility caused by the crack in the beam. The spring stiffness is calculated by taking the inverse of the compliance matrix found by using proper stress intensity factors and strain energy release rates calculated from linear elastic fracture mechanics. Different boundary conditions are considered such as fixed–free and pinned–pinned ends. Variations of natural frequencies and mode shapes depending on the crack location, crack depth and taper ratio of the beam are found, presented in graphs and examined. The applicability, accuracy and validity of the present method are found to be compatible with the literature.

Dynamic responses of a damaged double Euler-Bernoulli beam traversed by a 'phantom' vehicle.

SummaryIn this paper, the dynamic response of a damaged double‐beam system traversed by a moving load is studied, including passive control using multiple tuned mass dampers. The double‐beam system is composed of two homogeneous isotropic Euler–Bernoulli beams connected by a viscoelastic layer. The damaged upper beam is simulated using a double‐sided open crack replaced by an equivalent rotational spring between two beam segments, and the lower primary beam is subjected to a moving load. The load is represented by a moving Dirac delta function and by a quarter car model, respectively. Road surface roughness (RSR) is classified as per ISO 8606:1995(E). The effect of vehicle speed of the moving oscillator and variable RSR profiles on the dynamics of this damaged double Euler–Bernoulli beam system for different crack‐depth ratios (CDRs) at various crack locations is studied. It is observed that coupling of two beams leads to a vehicular effect on the damaged beam, even when no vehicle on it is present. The effects of single and multiple tuned mass dampers to control the vibrational responses of the primary beam due to damage on the secondary beam is studied next. The performance of tuned mass dampers to reduce the transverse vibrations of the damaged double‐beam system and of the quarter car is investigated. The paper links the coupling between the two levels of double beam with the inertial coupling of the vehicle to the double‐beam system.

Structural Crack Identification Based on the Variational Mode Decomposition

In order to enrich the method of bridge damage detection and further improve the accuracy of bridge damage identification, a detection method of simply supported beam with crack under dynamic load is proposed, which is not based on the complete finite element model. Under the premise of not blocking traffic, the method only needs to analyze and deal with the acceleration response of simply supported beam span, which reduces the loading, unloading and maintenance of sensors in practical engineering. At the same time, based on the model, an analytical formula of acceleration in the mid-span of simply supported cracked beam is derived. Supported by theoretical derivation, instantaneous energy and mean energy difference are constructed by using variational mode decomposition and Hilbert transformation, which can effectively identify small cracks with 5% crack depth. Based on this, the influences of different wheel load, environmental noise and damage degree on detection results are studied. The results show that: ① The instantaneous frequency has a better recognition effect on crack location; ② The mean energy difference is sensitive to different crack depth ratio δ and wheel load; ③ This method has strong noise robustness.

Three-dimensional mixed-mode stress intensity factors for deflected external surface cracks in thin and midsize-thick-walled spherical pressure vessels

Normalized three-dimensional mixed-mode stress intensity factor (SIF) distributions are presented for deflected external surface cracks in thin- and midsize-thick-walled spherical pressure vessels. With an aim to build a library of SIF solutions, values of the governing parameters of the problem, namely crack deflection angle, normalized crack depth and crack shape aspect ratio, are changed within their practical ranges. The obtained results show that for a given case, increasing the deflection angle yields a decrease in mode-I SIFs and increases in mode-II and mode-III SIFs. It is also observed that as the normalized crack depth increases, SIFs generally increase along the crack front. The results also show that magnitudes of the normalized mixed mode stress intensity factors at the depth location for midsize-thick-walled vessels are lower than those of thin-walled spherical vessels. The crack deflection angle has the highest effect among all parameters, emphasizing the importance of this study. It is concluded that the presented SIF solutions can be used to assess damage tolerance of a spherical vessel with a deflected external surface crack.

Behavior of cracked Euler–Bernoulli beam and inverse problem for assessing crack severity

In this present study, natural frequencies of the first two modes of bending vibration for the cracked simply supported Euler–Bernoulli beam is determined using finite element analysis (FEA). FEA natural frequencies for the cracked beam are used to investigate the behavior of the cracked beam and also used in the inverse problem of crack depth detection. Dynamic behavior of the cracked simply supported beam is observed, and it is found that normalized mode shape at crack location has great effect on amount of decreasing of natural frequencies. When normalized mode shape at crack location is increased, then natural frequencies decrease. In this study, pattern of mode shape played a vital role in decreasing or increasing natural frequencies. At the midpoint of the beam, there is largest bending moment in first bending mode and there is nodal point in second bending mode. Harmonic analysis for the cracked simply supported beam is carried out to find von Mises stress responses and appearance of peaks at frequency of first bending mode is noticed in graphs of von Mises stress response, expressing high values of von Mises stress at crack tip. Inverse problem of assessing the crack depth is performed using results of FEA first mode frequency ratio and published experimental results and the method showed good results in case of high crack depth ratios.

Ductile crack initiation and growth on a plasticized Polyvinylchloride during air bag deployment

With the goal of ensuring the security of passengers for automotive industry, the present work addresses the ductile fracture process of plasticized PVC. Dedicated clamped single edge notch bending (SENB) specimens were used to characterize the mechanisms of crack initiation and propagation for the studied material. The exploitation of the experimental database associated with finite element simulation of the crack propagation allowed, on the one hand, the calibration factor η<sub>p</sub> of this specific SENB specimen to be established, as a function of the crack depth ratio. On the other hand, the fracture toughness of the studied plasticized PVC was estimated to be 10.8 kJ/m<sup>2</sup>, value which was close to that reported in the literature for modified PVC. By using this fracture toughness value, a methodology aiming at the prediction of ductile crack initiation of the PVC skin integrated into a real dashboard (full scale test) was proposed.