Crack Shape Factor Research Articles

Effect of repair welding on the fatigue behavior of AA6082-T6 T-joints in marine structures based on FFS and experiments

In this study, the effect of repair welding on the fatigue behavior of AA6082-T6 welded T-joints in marine structures was investigated based on experiments and the fitness-for-service (FFS) assessment in BS7910. Repair welding led to an increase in residual stress and a decline in fatigue life according to fatigue tests and FEA. Meanwhile, repair welding changed the crack initiation site (CIS) and crack shape factor (CSF, the ratio of crack depth a to length 2c; i.e., a/2c), as indicated by fatigue fractography. In addition, when FFS assessment was performed, two methods for characterizing the CSF under different repair welding lengths during fatigue crack growth were presented: fixed and non-fixed a/2c. The results showed that repair welding led to a transition from ductile fracture to brittle fracture. For a fixed CSF, the critical crack depth and crack opening area of T-joints with repair welding lengths of 30 mm were greatly reduced by 63–66% and 86–89%, respectively, compared to T-joints without repair welding. However, the corresponding reductions for the non-fixed a/2c method were approximately 40% and 90%. The comparison indicated the results obtained with a non-fixed CSF were more consistent with the experiments, with a deviation below 15%.

Dynamic Behavior Analysis of a Rotating Shaft with an Elliptical Breathing Surface Crack

PurposeIn this paper, dynamic behavior of a rotor system with an elliptical breathing crack that simulates the real shape of the crack front is investigated.MethodsA finite element model of the cracked rotor system is developed. The crack breathing mechanism is modelled based on an improved breathing model which considers the inclination of the neutral axis of the cracked element cross-section during shaft rotation. Harmonic balance method is used to solve the equations of motion of the rotor system for steady-state response characteristics. The effect of some parameters such as crack depth, crack shape factor and the spinning speed is investigated.Results and conclusionsThe results show that the unique whirl orbits behavior during passage through the subcritical speeds serve as a key indicator of crack presence in the shaft. The effects of the crack front curvature and the breathing model are revealed. The value of shape factor affects the whirl orbit characteristics such as size of the inner or outer loops and the amount by which the orbits rotate while crossing the subcritical speeds. The presented model considering the real crack front shape may contribute towards improved modelling of cracked rotors and better interpretation of measured vibration response.

Modeling electrode-level crack and quantifying its effect on battery performance and impedance

Electrode-level cracks in a Li ion battery significantly impact its performance. We build a crack-containing electrochemical model to reveal the mechanism and quantify the effect of crack geometrical characteristics on specific energy, specific capacity and cell impedance. An elliptical-shaped crack is introduced into the electrode, which represents various configurations by changing the semi-axis ratio, crack angle and crack position. We show that lithium ion transport, electrochemical intercalation and the overall cell impedance are sensitive to the crack characteristics and electrotype absorption on crack surfaces. A longer crack more parallel to the current collector reduces the specific energy and specific capacity more significantly, especially when the current density is high. By contrast, a crack perpendicular to the current collector has little impact. The dependence on a series of crack orientation is quantified. The study of crack position shows that a crack closer to the separator has a stronger negative impact, dramatically reducing capacity. Electrochemical impedance spectroscopy simulations show that the crack shape factors such as semi-axis ratio, crack angle and electrolyte wetting ratio primarily affect the ohmic resistance. A longer crack more parallel to the current collector increases the ohmic resistance, while more crack wetting reduces the ohmic resistance. By contrast, crack position significantly affects the charge transfer resistance but with little impact on the ohmic resistance. A crack closer to the separator increases the charge transfer resistance. The effect of connected cracks into an open or closed ring shape is also considered, which can partially isolate active materials from the electrode depending on the size and orientation of the opening. This work provides a comprehensive and fundamental understanding of how various crack geometrical parameters affect the electrochemical behavior, which can assist in evaluating the significance of cracking, allow comparison with other degradation mechanisms to identify the limiting factor, and provide guidance on battery design and application strategy.

Effect of shape factor on structural reliability analysis of a surface cracked pipeline-parametric study

The variation of crack shape factor (a/c) during propagation has an important role on calculation of the stress intensity factor (SIF), where imprecise estimation of this latter can lead us to an inaccurate prediction of failure probabilities. For the case of external cracked surface pipeline carried oil and gas products, such estimation can results undesired fault decisions like excessive repairs action or inspection planning. In this paper, the structural integrity analysis of pipeline with semi elliptical crack on the external surface is evaluated. Reliability calculations expressed in term of reliability index β are carried out based on Monte Carlo simulation and First Order reliability Method (FORM). The crack shape factors are varied to cover a variety of geometries from shallow to deep cracks while fatigue crack growth is assumed in depth direction. For SIF estimation, surface and deep point are considered. Results of the analysis indicate that for a constant crack depth a/t, the reliability index is strongly affected by a/c ratio and the trend is not similar in deep and surface point for different crack shapes.

Fatigue damage assessment of orthotropic steel deck using dynamic Bayesian networks

Current health monitoring of orthotropic steel deck (OSD) subjected to fatigue damage mainly relies on deterministic physical models and the field measurements through inspections and monitoring. Nevertheless, various aleatory (random) and epistemic (lack of knowledge) uncertainties exist due to empirical justifications, model simplifications, inaccurate statistics of model parameter, measurement error, etc. The present study proposes a probabilistic model for fatigue damage diagnosis and prognosis of an OSD through integrating the physical model with field inspections while accounting for the associated uncertainties, using the dynamic Bayesian network (DBN). The DBN is suitable for representation and reasoning under uncertainty in various fields. The proposed framework aims to fulfill two interdependent tasks (1) diagnosis: track the time-dependent variable (i.e., the crack growth) and calibrate the time-independent variables (i.e., the geometric parameters and the multiplier for the crack shape factor); and (2) prognosis: predict the crack growth in the future. The particle filter (PF) is employed as the Bayesian inference algorithm for the established non-Gaussian DBN composed of continuous variables of various distribution types, as well as nonlinear conditional dependence between them. In addition, a Gaussian process (GP) surrogate model is established to relate the output stress response of the physical model (OSD) under the input truck load and model parameters, which is further implemented as the conditional probability distribution (CPD) in the DBN model. Finally, the proposed framework is illustrated by a numerical example of fatigue crack growth on the OSD subjected to truck load.

Analysis of the ground surface finish effect on the LCF life of a 304L austenitic stainless steel in air and in PWR environment

In this paper, the Low-Cycle Fatigue (LCF) resistance of an austenitic 304L stainless steel used in nuclear plant components is investigated. More precisely, a special attention is here paid to the respective role of surface finishing and environmental effects on the elementary damage stages, namely crack initiation and crack propagation. The objective is not only to assess the conservatism of design rules introducing corrections factors to account for the decay induced by these parameters, but also to get insights into the mechanisms controlling the fatigue life. With this aim, fatigue tests are performed under a controlled total strain amplitude Δεt/2 of 0.6% with a strain rate of 10−4s−1 on ground or polished cylindrical specimens, in air and in Pressurized Water Reactor (PWR) environment. A detailed analysis of surface damage and fracture surfaces is conducted to estimate the respective fraction of initiation and propagation in the total life according to the environment and surface finishing. It first comes out that, regardless of the considered condition, the initiation stage is negligible with respect to the propagation duration. Furthermore, it is shown that the propagation in ground specimen is affected, in both environments by the specific crack shape resulting from the initiation process and subsequent coalescence of multiple initiated cracks within the grinding scratches. Moreover, a detailed analysis of striations present on fracture surfaces indicates that while a good correlation between the striation spacing and the average crack growth rate is noticed in PWR environment, a discrepancy is observed in air. Nevertheless LCF crack growth laws have been identified is each environment by introducing the strain intensity factor ΔKε. It is then demonstrated that predictions of fatigue life carried out by accounting for the initial surface finishing through the crack shape factor and the environmental effect by means of the proper crack growth law present a good agreement with experimental data.

Influence of Fatigue Crack on Strains State Within Assembly Holes in a Web of Steel Bridge Girder

The paper presented an attempt to assess service life of steel girders in military bridges (or bypass temporary bridges) when fatigue cracks are detected in them. A function describing the geometry of fatigue cracks, the so-called crack shape factor Y, for two different, assumed calculated models, was presented. The function was used to plot sample graphs allowing assessing the remaining service life of such structural elements or engineering structures in a simple way. This method of analyzing can be used not only for the military bridges but also for other steel structures with existing cracks. The work also presented assessments of possible applications of two FEM calculated models using shell elements to test stress and deformation at the top part of a fatigue crack located in a web of a steel girder used in the military bridges. The results of the conducted numerical analyses were compared with the results obtained in experimental research conducted in laboratory conditions using extensometers.

Probabilistic analysis of stress intensity factor (SIF) and degree of bending (DoB) in axially loaded tubular K-joints of offshore structures

The stress intensity factor (SIF) and the degree of bending (DoB) are among the crucial parameters in evaluating the fatigue reliability of offshore tubular joints based on the fracture mechanics (FM) approach. The value of SIF is a function of the crack size, nominal stress, and two modifying coefficients known as the crack shape factor (Yc) and geometric factor (Yg). The value of the DoB is mainly determined by the joint geometry. These three parameters exhibit considerable scatter which calls for greater emphasis in accurate determination of their governing probability distributions. As far as the authors are aware, no comprehensive research has been carried out on the probability distribution of the DoB and geometric and crack shape factors in tubular joints. What has been used so far as the probability distribution of these factors in the FM-based reliability analysis of offshore structures is mainly based on assumptions and limited observations, especially in terms of distribution parameters. In the present paper, results of parametric equations available for the computation of the DoB, Yc, and Yg have been used to propose probability distribution models for these parameters in tubular K-joints under balanced axial loads. Based on a parametric study, a set of samples were prepared for the DoB, Yc, and Yg; and the density histograms were generated for these samples using Freedman-Diaconis method. Ten different probability density functions (PDFs) were fitted to these histograms. The maximum likelihood (ML) method was used to determine the parameters of fitted distributions. In each case, Kolmogorov-Smirnov test was used to evaluate the goodness of fit. Finally, after substituting the values of estimated parameters for each distribution, a set of fully defined PDFs were proposed for the DoB, crack shape factor (Yc), and geometric factor (Yg) in tubular K-joints subjected to balanced axial loads.

A fracture toughness model for brittle coating on ductile substrate under indentation loading

This paper presents an analytical fracture toughness model for brittle coating/ductile substrate systems. The model considers a well-developed radial/median crack of semi-elliptical shape in proximity of the coating/substrate interface. It incorporates three critical factors to correct Lawn et al.’s formalism for monolithic materials: (i) an elliptical crack shape factor introduced by adopting Borodachev’s solution for an elliptical crack under a concentrated force at the crack center, which represents the residual plastic component due to expansion of the plastic zone under indentation; (ii) an interface correction factor obtained by analyzing Noda et al.’s results for an elliptical crack near a bi-material interface, which expresses explicitly its dependence on the distance ratio, h/a, and Young’s modulus ratio, Es/Ec, and (iii) the composite system hardness incorporated in the formula to take into account the influence of the substrate material. Overall, the model shows a non-linear relationship between the radial crack length, c3/2, and indentation load, P, for brittle coating on ductile substrate systems. A series of indentation experiments have been carried out on a WC/10Co/4Cr coating/1080 low carbon steel substrate system to validate the model.

The sub-critical indentation fracture process in soda-lime-silica glass

The sub-critical propagation of indentation cracks in soda-lime silicate glass was investigated. Vickers indentations were produced using a force of 9.8 N, and both as-indented and annealed samples were studied. Indented bars were subjected to various flexural loading and unloading cycles in a water environment. Fractographical analysis revealed that the radial crack propagation process could be divided into two successive stages. Initially, the radial crack growth is strongly influenced by interaction with the lateral crack, which obstructs crack growth. This “pinning” effect of the lateral crack leads to bowing of the radial crack front into a complex shape. In the second stage, the radial cracks escape from the lateral cracks interaction and assume a semi-elliptical shape. Measurement of radial crack speed from the markings left on the fracture surface allowed the crack shape factor, ψ and the indentation-residual stress factor, χ, to be calibrated as a function of the crack size, c. The shape factor was found to be a decreasing function of c during the first stage of propagation, then it abruptly increases when radial cracks escape from lateral crack interaction. For further crack extension, ψ decreases again, assuming absolute values larger than those measured during the first stage. Conversely, the residual stress factor is constant during the first phase of radial crack growth while it suddenly decreases and becomes zero for larger c. The implications of the trend in ψ( c) and ψ( c) on the stable growth and on the time-to-failure predictions in static fatigue tests are discussed.

Models and time constants for permeability evolution

Permeability of crystalline rocks results mainly of cracks. Using percolation theory and a statistical approach, Dienes has recently derived a model which appears to be very adequate to describe and calculate permeability in such rocks at a scale which is larger than the scale of the cracks. Using this model, we show that three microstructural parameters are of primary importance : the crack shape factor A, the mean crack length and the average crack spacing Although the third one, is frequently presented as the most important parameter, we suggest that A and are indeed as much important. Percolation transition depends on and but high permeabilities are obtained if either A or are large. Using these results we discuss time constants for permeability evolution by taking into account slow crack growth processes. We suggest that slow crack growth could result in large increases of permeability with or without developing a macroscopic fracture. Such effects are of interest for seismogenesis, underground repositories and other problems concerned with fluid flow in the crust.

Fracture Mechanics Analysis of the Effects of Residual Stress on Fatigue Life

Abstract In this paper it is reemphasized that the effect of residual stress in fatigue is analogous to but not the same as the mean stress effect from applied loads. By including a residual stress term in the stress intensity factor range of the fatigue crack propagation rate equation, one is permitted to include the residual stress in calculations of fatigue life estimates. Using crack shape factors calculated for given aspect ratios of surface flaws and integrating the fatigue crack growth rate da/dN, one obtains an equation for the applied stress-cycles to failure S-N curve that includes the residual stress effect on fatigue performance. In this process of calculation that fact that compressive residual stress has a much stronger influence on fatigue life than tensile residual stress is revealed, mainly because the former decreases the stress intensity factor range and increases the critical crack size while the latter only decreases the critical crack size. A numerical solution of an example illustrates an application of these concepts.

Crack-front shape effects in the double torsion test

The conventional use of the double torsion test to measure the rate dependence of crack growth is here subjected to a critical re-examination. Following from a series of such tests on polyesters, this examination was motivated by misgivings on the role of crack front curvature in undermining the geometry-independence of the results. Working through a successful prediction of the crack shape from simple (but experimentally justified) geometric considerations, an analysis leads to a general relation describing the distortion of the measured fracture toughness versus crack speed characteristics in terms of a single, measurable crack shape factor.