Crack Depth Ratio Research Articles

A hybrid approach to detect crack parameters using measured natural frequencies in thin walled angle section steel beams

Present study outlines a hybrid approach using Finite Element Method (FEM)–Response Surface Method (RSM)–Genetic Algorithm (GA) to predict the crack parameters, namely crack position and crack depth ratio with the help of only the measured natural frequencies of cracked thin walled beams. Numerical experimental trials of cracked beams have been conducted based on design of experiment (DOE) approach using an improved Finite element model. The improvement has been achieved by consideration of warping stiffness in cracked angle section beam. Thereafter, regression analysis has been conducted to construct Response Surface Function (RSF). Optimum crack parameters were then calculated using GA by minimizing an objective function which has been formed as the root mean square (RMS) of the residuals between RSFs and measured frequencies. Results of the study indicate that, the proposed approach performs with excellent accuracy and it does not require the response of an uncracked beam as benchmark information.

WES 2808 for Brittle Fracture Assessment of Steel Components under Seismic Conditions – Part V: Equivalent CTOD ratio for correction of constraint loss in beam-to-column connections

Crack-tip plastic constraint in beam-to-column connections with a surface crack 1) at the bottom of a conventional type of weld access hole and 2) at weld start/end points of butt welds to connect beam flange and diaphragm subjected to bending moment were analyzed by FEM. The equivalent CTOD ratio β used for engineering toughness correction for constraint loss for the beam-to-column connections are compared with those for the wide plate components with the same size of a crack subjected to tension load. Then, the analyses of β by means of the wide plate component, CSCP and ESCP, are conducted, and the crack depth effect on β is formulated with focusing on crack depth ratio a/t.

Influence of different sizes of concrete and roller compacted concrete on double-K fracture parameters

Affected by physical properties of various components, characteristics and stress states of junction surface and other multiple factors, concrete, as a kind of multi-phase composite material, has complicated failure mechanism, thus making its fracture mechanism research difficult. But concrete has been widely used in engineering construction, so research on concrete fracture theory is of important realistic significance and construction value. This study discusses influence rule of specimen size and crack-depth ratio (?0/h) on doubleK fracture parameters (initial fracture toughness ini ICK and unstable fracture toughness un ICK ) and its size effects by using fracture test. Different sizes of concretes and roller compacted concrete (RCC) specimens are adopted to explore influence of specimen size on concrete double-K fracture parameters. Results reveal that initial fracture toughness ini ICK and unstable fracture toughness un ICK increase as specimen size enlarges, showing a size effect; besides, subcritical crack extends with the increase of specimen size. With regard to specimens with different crack-depth ratios, its unstable fracture toughness un ICK is unrelated to initial crack-depth ratio when crack-depth ratio is more than or equal to 0.4, while initial fracture toughness ini ICK is correlated with initial crack-depth ratio, which indicate that double-K fracture parameters can be considered as material constants describing concrete initial fracture, stable expansion and whole process of stability failure.

Transverse Vibrations of Mixed-Mode Cracked Nanobeams With Surface Effect

Slant edge cracked effect considering the inherent relation between surface energy and mixed-mode crack propagations on the free transverse vibrations of nanobeams with surface effect is investigated. First, the slant edge cracked effect, which considers residual surface stress effect on the crack tip fields of a mode-I and mode-II surface edge crack, is developed and the corresponding stress intensity factors (SIFs) and local flexibility coefficients are derived. Moreover, a refined continuum model of slant cracked nanobeams is established by considering both slant edge cracked effect and surface effect. The effects of fracture angles, crack depth, surface elasticity, surface stress, and surface density on the local flexibility and free transverse vibration characteristics of cracked nanobeams are, respectively, analyzed. The results show that the flexibility coefficients distribute symmetrically about residual surface stress. Fracture angles have a profound influence on both the symmetries of the mode shapes and the natural frequencies of nanobeams, and the influence becomes more pronounced as crack depth ratios increase. Furthermore, the natural frequencies will first decrease and then increase with fracture angles when the slant edge cracked effect is considered. The results demonstrate that the inherent relation between surface energy and crack propagations should be considered for both the stress distributions at the crack tip and the dynamic behavior of cracked nanobeams.

Multiple-crack identification in a channel section steel beam using a combined response surface methodology and genetic algorithm

Summary The present study outlines a sequentially integrated finite-element method (FEM)–response surface method (RSM)–genetic algorithm (GA) framework and implements this to predict the crack parameters, namely, crack location and crack depth ratio. A central composite face centered response surface design of the RSM technique is used to establish the direct relationships between the input parameters (crack location and crack depth ratio) and responses (natural frequencies) to build the response surface function (RSF). Multiple edge cracks are considered, which exist on the top flange of a thin-walled channel section cantilever beam and modeled as line spring elements. In order to obtain RSFs of the first five natural frequencies in terms of process factors such as crack position and crack depth ratio, a number of numerical experiments based on FEM are conducted by using the design-of-experiment approach. An objective function obtained as the square of the difference between RSF and experimentally measured natural frequency has been minimized using GA to find out the optimum crack parameters. Twenty-four steel channel beam specimens have been tested in the laboratory to extract the crack parameters from measured natural frequencies using the proposed approach. The results of the study indicate that the proposed approach performs remarkably, yielding crack parameters with great precision. Copyright © 2015 John Wiley & Sons, Ltd.

Effect of large crack–depth ratio on three-point bending concrete beam with single edge notch

There are three stages in the crack propagation process of concrete. They are crack initiation, crack stable propagation and crack unstable fracture. Double-K fracture model describes the three stages quantitatively. The crack–depth ratio is mainly set at 0·2–0·6 in existing studies of double-K fracture parameters. In this paper, combined with test verification, the extended finite element method is adopted to study the variation of three-point bending concrete beam with the crack–depth ratio from 0·2 to 0·85. The results shows that when the crack–depth ratio α0 > 0.6, variation of concrete beam fracture parameters is different from that with small crack–depth ratio, and the double-K fracture parameters cannot be considered as constant any more. The fracture energy, fracture toughness decrease sharply; the concrete beam has the best toughness when 0.6 ≤ α0 ≤ 0.7; and concrete beam becomes completely brittle when α0 > 0.8.

Stress Intensity Factor Solution for a Naturally Emanating Crack Out of a V-Notched Round Bar

During the estimation of Stress Intensity Factor (SIF) of a notched round bar, standard crack geometries such as elliptical, semi-circular, and straight crack fronts are commonly considered at the notch root region. In the present work, the SIF solution for a naturally initiating crack out of a V-notched round bar has been estimated experimentally and the results are compared with data obtained from 3D finite element analysis. The fractographic investigation of the fractured surface suggested a non-symmetric crack propagation and the strong influence of stress concentration factor on SIF, especially in the early stages of crack growth (up to a/d ratio of 0.15, where “a’” is crack length and “d” is notch root diameter). Four aspect ratios (a/c = 0.4, 0.5, 0.75, and 0.85, where “c” is semi-major axis of elliptical crack) and seven crack depth (a/d) ratios in the radial directions were considered with and without offset of surface crack origin to match experimental observations. It was noted that a naturally formed crack had an elliptic shape with aspect ratio of 0.75, with its center offset by 0.5 mm in an upward direction from the notch root region.

STRESS INTENSITY FACTORS OF A SEMI-ELLIPTICAL CRACK IN A HOLLOW CYLINDER

In this investigation, the weight function method was employed to calculate stress intensity factors for semi-elliptical surface crack in a hollow cylinder. A uniform stress and a linear stress distribution were used as the two references to determine the weight functions. These two factors were obtained by a three-dimensional finite element method which employed singular elements along the crack front and regular elements elsewhere. The weight functions were then applied to a wide range of semi-elliptical surface crack subjected to non-linear loadings. The results were validated against finite element data and compared with other analyses. In the parametric study, the effects of the ratio of the surface crack depth to length ranged from 0.2 to 1.0 and the ratio of the crack depth to the wall thickness ranged from 0.2 to 0.8 on stress intensity factors were investigated.

Toughness Enhancement of Airfield Concrete Pavement by Using Short Fiber

Few efforts have been made to understand the progressive failure of concrete pavements, especially the crack propagation in the concrete materials. More detailed information about concrete material, such as its fracture properties, is required along with the strength to better quantify crack propagation rates of varying concrete mixture proportions and constituents. The susceptibility of concrete pavements to crack growth may be eliminated by adding short steel or glass fibers. Therefore, an experimental study was carried out to investigate the effect of adding short fiber, steel or glass, in controlling the fracture energy of concrete. The analysis was conducted for a constant fiber length of 25 mm. The flexure test of single edge notched as well as unnotched specimens was performed using three-point bending configuration. Four different values of crack-depth ratios were considered, namely 0, 0.1, 0.25, and 0.4. For the same crackdepth ratio, results show that the maximum value of crack mouth opening displacement, and value of curvature in steel-fiber-reinforced concrete (SFRC) were greater than those in glass-fiber-reinforced concrete (GFRC). However, the beam-carrying capacities of GFRC are higher than those of the SFRC for all crack-depth ratios. In general, the fracture energy of the SFRC is greater than that of the GFRC. It is noteworthy that the last portion of moment-curvature curve of the GFRC is steeper than the SFRC curve, thereby indicating that the SFRC is relatively more ductile. The fracture energy depends on the fiber type and crack-depth ratio. Moreover, the fracture energy calculated from notched beam with high crack-depth ratios was found to be more stable and reliable.

Evolution of crack paths and compliance in round bars under cyclic tension and bending

The aim of this paper is to calculate how the surface crack front and the dimensionless compliance evolve in cylindrical bars containing a transverse edge crack subjected to cyclic tension or bending with different initial crack geometries (crack depths and aspect ratios). A Java computer program was developed and implemented to obtain the crack path evolution (changes of crack depth and aspect ratio), as well as the progress of mechanical compliance, by discretizing the crack front (characterized with elliptical shape) and calculating the crack front changes on the basis of the Paris law, and using a three-parameter stress intensity factor (SIF). The results show that in fatigue crack propagation, relative crack depth influences more on dimensionless compliance than the aspect ratio, because the crack front tends to converge when the crack propagates from different initial geometries, showing greater values of dimensionless compliance for tension than for bending. Furthermore, during fatigue crack growth, materials with higher values of the exponent of the Paris law produce slightly greater dimensionless compliance and a better convergence between the results for straight-fronted and circular initial cracks.

A toughness based deformation limit for fatigue-cracked X-joints under in-plane bending

This study reports a deformation limit for the initiation of ductile fracture failure in fatigue-cracked circular hollow section (CHS) X-joints subjected to brace in-plane bending. The proposed approach sets the deformation limit as the calculated crack driving force in a fatigue crack at the hot-spot location in the tubular joint reaches the material fracture toughness measured from standard fracture specimens. The calibration of the proposed approach and the numerical procedure utilizes two large-scale X-joint specimens with fatigue generated surface cracks. The subsequent numerical investigation covers X-joints with two different brace-to-chord intersection angles, a wide range of geometric parameters and a practical range of material parameters. The development of the deformation limit includes a non-dimensional material toughness, which covers both the geometric parameters and material properties. The lower-bound deformation limit thus developed exhibits a linear relationship with respect to the crack depth ratio and indicates consistent values among X-joints with different brace-to-chord intersection angles.

Research on the Influences of Crack-Depth Ratio on Fracture Energy of Ultra-High Performance Cementitious Composites

For the study of fracture characteristics of ultra-high performance cementitious composites(ECC),16 different sizes of three-point bending beams were made and ultimate load, ultimate deflection and crack mouth opening displacement ,the curve andcurve of ECC were contructed,with the method of fracture work recommendedby RILEM , the external work was respectively calculated by the curve ofand, which determined the fracture energy of ECC.Results show that two kinds of calculation result are roughly equal;The influence of size effect on fracture character was: fracture energy increased with the increasing of the crack-depth ratio, the fracture energy of concrete specimen is the maximum when the crack-depth ratio is 0.4 ; is proportional to the initial crack-depth of the specimen, but there is no relationship betweenand crack-depth ratio. This paper would have great significance for the study of fracture characteristics of ECC.

Generalized Irwin plastic zone correction of a sub-interface Zener–Stroh crack in a coating-substrate system

Elastic–plastic stress analysis of a Zener–Stroh crack paralleling to the interface of a coating-substrate system has been carried out in this work. The sum of the Burgers vectors of the climb and the glide dislocations along the crack line accounts for the stress field around its blunt tip where dislocation enters, and the sharp tip where crack propagates. Firstly, Gauss–Chebyshev quadrature technique is applied to solve the governing equation of dislocation density functions constrained by load-free crack faces. When taking plasticity into account at both crack tips where stresses are high, the generalized Irwin plastic zone correction is recommended. Plastic zone size (PZS) for both tips, crack tip opening displacement (CTOD) and effective stress intensity factors for the sharp tip are then obtained. The effects of coating thickness, crack depth, material mismatch and displacement loads ratio onto PZSs and CTOD have been analyzed in detail.

Experimental Study of the Effect of RCC Specimen Size and Crack Depth Ratio on Double-K Fracture Parameters

Abstract When the height of roller compacted concrete (RCC) specimen is less than 400 mm, the specimen size and crack depth ratio will affect the double-K fracture parameters. In this paper, two groups of RCC specimens with different specimen size and crack depth ratio were investigated and the wedge splitting method was employed. Double-K fracture parameters were calculated employing the double-K fracture theory of concrete. It is indicated that when the crack depth ratio, α, increased from 0.4 to 0.6, the unstable fracture toughness, KICun, increases, while the initial fracture toughness, KICini, decreases. The crack depth ratio, α, has a continuous effect on KICini, however the effect on KICun decreases with the increase of α. When the height of the specimen, h, is less than 300 mm, the effect of specimen size on KICun is significant, but it decreases when h is greater than 300 mm and less than 500 mm.

Determination of the Stress Intensity Factor of an elliptical breathing crack in a rotating shaft

The failures due to the propagation of fatigue cracks are one of the most frequent problems in rotating machines. Those failures sometimes are catastrophic and are sufficient to provoke the loss of the complete machine with high risks for people and other equipments. When a cracked shaft rotates, the breathing mechanism appears. The crack passes from an open state to a close state with a transition in which a partial opening or closing of the crack is produced. In this work, a new general expression that gives the Stress Intensity Factor (SIF) along the crack front of an elliptical crack in a rotating shaft in terms of the crack depth ratio, the crack aspect ratio, the relative position on the front and the angle of rotation has been developed for linear elastic materials. By the moment, no expressions of the SIF in term of these variables have been found in the literature. To this end, a quasi-static 3D numerical model of a cracked shaft with straight and elliptical cracks subjected to rotary bending using the Finite Element Method (FEM) has been made. To simulate the rotation of the shaft, different angular positions have been considered. The SIF in mode I along the crack front has been calculated for each angular position of the cracked shaft and for different crack geometries. The expression results have been compared with solutions obtained from the literature. It has been found that they are in good agreement. The model has been applied to other crack geometries with good results. The obtained SIF expression allows studying the dynamic behavior of cracked shafts and can be used to analyze the crack propagation.

Study on Roller Compacted Concrete’s Nominal Fracture Toughness Based on Crack-Depth Ratio

The roller compacted concrete (RCC) has been widely used, and the practical concrete crack usually has different crack-depth ratios, but the researches about the fracture toughness formula for RCC rarely consider crack-depth ratio. Here the wedge-splitting fracture test was carried on the RCC specimens with different crack-depth ratios(0.4, 0.5, 0.6). At the same time, the theoretical nominal fracture toughness formula based on the crack-depth ratio was also studied. At the end, the modified and suitable RCC' formula based on crack-depth ratio was gotten by combining the RCC test results with theoretical formula.

Free Vibration Analysis for Cracked FGM Beams by Means of a Continuous Beam Model

Based on Euler-Bernoulli beam theory and a continuous stiffness beam model, the free vibration of rectangular-section beams made of functionally graded materials (FGMs) containing open edge cracks is studied. Assuming the material gradients follow exponential distribution along beam thickness direction, the conversion relation between the vibration governing equations of a FGM beam and that of an isotropic homogenous beam is deduced. A continuous function is used to characterize the bending stiffness of an edge cracked FGM beam. Thus, the cracked FGM beam is treated as an intact beam with continuously varying bending stiffness along its longitudinal direction. The characteristic equations of beams with different boundary conditions are obtained by transfer matrix method. To verify the validity of the proposed method, natural frequencies for intact and cracked FGM beams are calculated and compared with those obtained by three-dimensional finite element method (3D FEM) and available data in the literature. After that, further discussions are carried out to analyze the influences of crack depth, crack location, material property, and slenderness ratio on the natural frequencies of the cracked FGM beams.

A deformation limit based on failure assessment diagram for fatigue-cracked X-joints under in-plane bending

This study develops a deformation limit based on the failure assessment diagram (FAD) for fatigue-cracked circular hollow section (CHS) X-joints subjected to brace in-plane bending. The proposed approach calibrates against two reported experimental tests on CHS X-joints. The subsequent numerical study considers CHS X-joints with two different brace-to-chord intersection angles. The parametric study focuses on both the material toughness level and the geometric parameters. The proposed, dimensionless deformation limit covers a wide range of material fracture-toughness and geometric parameters. The option 1 and option 3 failure assessment curves provide consistent deformation limits compared to the toughness-based deformation limits proposed in a previous study. The lower bound deformation limit exhibits an approximately linear relationship with respect to the crack-depth ratio for X-joints with different brace-to-chord intersection angles. The extrapolated deformation level at a zero crack-depth ratio represents a conservative estimation on the deformation level for intact joints.

Application of the Maximum Undamaged Defect Size (d max) Concept in Fiber-Reinforced Concrete Pavements

Many fiber types are used in fiber-reinforced concrete (FRC) pavements. The maximum undamaged defect size (d max) concept has been applied to predict notch-based fracture in different types of concrete. The present paper applies this concept to different types of FRC pavement, namely, glass fiber-reinforced concrete pavement and steel fiber-reinforced concrete pavement. Due to the quasi-brittle manner of concrete, various fracture models have been developed to study the crack propagation in the pavement structures. The fracture energy was determined based on the recommendation of the RILEM Committee 50-FMC. An experimental study was carried out to investigate the effect of adding short fiber, steel or glass, in controlling the fracture energy of concrete. The analysis was invoked for constant fiber length of 25mm. The flexure test of single-edge notched and unnotched specimens was performed using three-point bending configuration. Four different values of crack-depth ratios were considered, mainly, 0.00, 0.10, 0.25, and 0.40. Experimental results showed that the calculated d max based on RILEM Committee 50-FMC is greater than the maximum aggregate size (MAZ). This means that there is no compatibility between the flexural strength of FRC and its fracture energy calculated based on RILEM Committee 50-FMC. Therefore, a modified calculation of the area of load-deflection curve was suggested to improve the reliability of fracture energy measured based on RILEM Committee 50-FMC. It is found based on this modification that d max is less than 0.7 MAZ.

Experimental study of the crack depth ratio threshold to analyze the slow crack growth by creep of high density polyethylene pipes

To assess the durability of drinking water connection pipes subjected to oxidation and slow crack growth, a comprehensive database was constructed on a novel specimen geometry: the pre-cracked NOL ring.135 tests were carried out consisting of initial crack depth ratio ranging from 0.08 to 0.6; single or double longitudinal cracks: tensile with steady strain rate and creep loading. A threshold value of the crack depth ratio of 0.2, induced by the oxidation was determined by analyzing several mechanical parameters. This threshold value was shown to be independent on the strain rate effects, single or double crack configuration and the kind of loading: tensile or creep. Creep test results with crack depth ratio larger than 0.2 were then utilized to establish a failure assessment diagram. A methodology allowing the prediction of residual lifetime of in-service pipes was proposed, using this diagram.