Fatigue Crack Growth Analysis Research Articles

Fatigue analysis using the singular ES-FEM

A novel procedure of singular edge-based smoothed finite element method (singular ES-FEM) has been customized for the fatigue crack growth analysis. For this method, a layer of crack-tip elements with special shape functions was adopted to capture the theoretical singularity of the stress field. In addition, a ‘strain smoothing technique’ on the smoothing domains associated with the elements’ edges was implemented that significantly improves the accuracy of results compared to the existing finite element method. A comparison of results with the experimental observations reported by others reveals an excellent agreement between them implying that singular ES-FEM accurately simulates the fatigue behavior.

Finite element fatigue propagation of induced cracks by stiffeners in repaired panels with composite patches

Fatigue crack growth analyses of aluminum panels with stiffeners repaired by composite patches have been rarely investigated. Generally, cracks may occur around the rivets which are capable to propagate under cyclic loadings. A composite patch can be used to stop or retard the crack growth rate. In this investigation, finite element method is used for the crack propagation analyses of stiffened aluminum panels repaired with composite patches. In these analyses, the crack-front can propagate in 3-D general mixed-mode conditions. The incremental 3-D crack growth of the repaired panels is automatically handled by a developed ANSYS Parametric Design Language (APDL) code. Effects of rivets distances and their diameters on the crack growth life of repaired panels are investigated. Moreover, the obtained crack-front shapes at various crack growth steps, crack trajectories, and life of the unrepaired and repaired panels with various glass/epoxy patch lay-ups and various patch thicknesses are discussed.

OS0801 Ni基合金溶接金属のBWR環境中疲労き裂進展特性の検討

Structural integrity assessment for nuclear power components is one of the most important policies for improvement of safety and reliability of nuclear power plants. When the flaws are detected by in-service inspection, fatigue crack growth analysis shall be performed as a part of structural integrity assessment for the technical judgment on continuous service based on the Rules on Fitness-for-Service for Nuclear Power Plants of the Japan Society of Mechanical Engineers Code (JSME FFS Code). However, fatigue crack growth analysis for BWR components consisted of Ni-base alloy is not able to be performed since the fatigue crack growth rate curve for Ni-base alloy in BWR water environment is not specified yet in the JSME FFS Code. In this study, fatigue crack growth tests in BWR water environment were performed for Ni-base alloy weld metal. Based on the test data, effects of stress ratio and rising time of cyclic loading on the fatigue crack growth behavior were evaluated. Furthermore, reference curves of fatigue crack growth were formulated with consideration for the scatter of data. And the values of ΔK_<th> were quantified.

Structural integrity analyses for preemptive weld overlay on the dissimilar metal weld of a pressurizer nozzle

This paper presents structural integrity analyses for preemptive weld overlay on the dissimilar metal weld (DMW) of a pressurizer nozzle in a pressurized water reactor (PWR). Based on MRP-169 and ASME Code Case N-504-2, weld overlay sizing calculation, residual stress improvement, shrinkage evaluation, fatigue crack growth and fatigue usage analysis are performed. The weld overlay procedure has to be confirmed to improve the residual stresses around the inside surface of DMW. The residual compressive stress distribution is thus addressed to be resistant to subsequent primary water stress corrosion cracking (PWSCC) initiation and further crack growth. To ensure the structural integrity of the original attached piping system, the measured displacement is transformed to temperature gradient to simulate the shrinkage after overlay and is used to determine the post weld distortion and stress situation. Further, the conservative postulated surface cracks are assumed in the DMW for fatigue crack growth analysis with system design cycles. The stress limits and cumulative fatigue usages of the pressurizer nozzle with overlay are also evaluated to meet ASME Code, Section III. Based on the present results, the structural integrity of the pressurizer nozzle with preemptive weld overlay is shown.

New Method for Concurrent Dynamic Analysis and Fatigue Damage Prognosis of Bridges

A new methodology for concurrent dynamic analysis and structural fatigue prognosis is proposed in this paper. The proposed methodology is on the basis of a novel small time scale formulation of material fatigue crack growth that calculates the incremental crack growth at any arbitrary time within a loading cycle. It defines the fatigue crack kinetics on the basis of the geometric relationship between the crack tip opening displacement and the instantaneous crack growth rate. The proposed crack growth model can be expressed as a set of first-order differential equations. The structural dynamics analysis and fatigue crack growth model can be expressed as a coupled hierarchical state-space model. The dynamic response (structural level) and the fatigue crack growth (material level) can be solved simultaneously. Several numerical problems with single degree-of-freedom and multiple degree-of-freedom cases are used to show the proposed methodology. Model predictions are validated using coupon testing data from open literature. Following this, the methodology is demonstrated using a steel-girder bridge. The proposed methodology shows that the concurrent structural dynamics and material fatigue crack growth analysis can be achieved. The cycle-counting method in the conventional fatigue analysis can be avoided. Comparison with experimental data for structural steels and aluminum alloy shows a satisfactory accuracy using the proposed coupled state-space model.

Analysis of fatigue crack growth in an attachment lug based on the weight function technique and the UniGrow fatigue crack growth model

A generalised step-by-step procedure for fatigue crack growth analysis of structural components subjected to variable amplitude loading spectra has been presented. The method has been illustrated by analysing fatigue growth of planar corner crack in an attachment lug made of Al7050-T7451 alloy.Stress intensity factors required for the fatigue crack growth analysis were calculated using the weight function method. In addition, so-called “load-shedding” effect was accounted for in order to determine appropriate magnitudes of the applied stress intensity factors. The rate of the load shedding was determined with the help of the finite element (FE) method by finding the amount of the load transferred through the cracked ligament. The UniGrow fatigue crack growth model, based on the material stress–strain behaviour near the crack tip, has been used to simulate the fatigue crack growth under two variable amplitude loading spectra. The comparison between theoretical predictions and experimental data proved the ability of the UniGrow model to correctly predict fatigue crack growth behaviour of two-dimensional planar cracks under complex stress field and subjected to arbitrary variable amplitude loading.

Modelling Fatigue Crack Growth near an Open Hole under Spectrum Loading Using a New Method for Elastic-Plastic Stress Calculation

To date the analysis of fatigue crack growth from an open hole subjected to contained cyclic plastic deformation is problematic due to considerable computational effort involved. This paper presents the integration of a new efficient method for calculating the elastic-plastic notch stress field under cyclic loading into a crack growth analysis tool. The anticipated crack path is defined along a line emanating from an open hole, and the line is discretized into a series of elements on which the elastic-plastic stress distribution is solved for the uncracked body. This solution is then used in conjunction with a weight function approach to determine the stress intensity factors used in the crack growth analysis. This technique has been incorporated into a Defence Science and Technology Organisation proprietary crack growth analysis tool based on plasticity-induced crack closure. Results are presented for cases involving service load spectra from F/A-18 and F-111 aircraft and are compared to those obtained from a commonly used crack growth code that does not account for the effect of contained notch plasticity. It is hoped that this generic approach will lead to improved predictions for crack growth in plasticity-affected zones.

An Analysis of Fatigue Strength of Notched Components

Geometrical discontinuities in the engineering components, such as holes, fillets, grooves, and keyways, are unavoidable in design. In essence, they act as a stress-raiser that causes the fatigue cracks. Accordingly, the geometrical discontinuities trigger a significant amount of reduction for the fatigue strength. It is well known that the fatigue limit of the notched components is governed by either the initiation or propagation of a small crack at the root of a notch. Since the elastoplastic behaviors and the crack closure effect should be properly taken into consideration, the behavior of such a small crack cannot be characterized solely by linear elastic fracture mechanics. To overcome the difficulty mentioned above, in this study, a novel method is proposed to investigate the notch effect by making use of the McEvily method, which has been widely used for the analysis of small fatigue crack growth. Further, to modify the McEvily method, the plastic zone size of a crack is calculated based on the Dugdale model to incorporate the effect of the plastic yielding near the crack tip. Finally, the predictive capability of the proposed method is demonstrated by comparing our theoretical predictions with the available experimental data.

Stress Analysis and Fatigue of welded structures

Fatigue analyses of weldments require detailed knowledge of the stress fields in critical regions. The stress information is subsequently used for finding high local stresses where fatigue cracks may initiate and for calculating stress intensity factors and fatigue crack growth. The method proposed enables the determination of the stress concentration and the stress distribution in the weld toe region using a special shell finite element modelling technique. The procedure consists of a set of rules concerning the development of the finite element mesh necessary to capture the bending and membrane structural stresses. The structural stress data obtained from the shell finite element analysis and relevant stress concentration factors are subsequently used to determine the peak stress and the non-linear through-thickness stress distributions. The peak stress at the weld toe is subsequently used for the determination of fatigue crack initiation life. The stress distribution and the weight function method are used for the determination of stress intensity factors and for the analysis of subsequent fatigue crack growth.

Numerical and experimental analyses of the plasticity-induced fatigue crack growth in high-strength steels

Numerical analyses of plasticity-induced fatigue crack growth (FCG) were performed for high-strength steels. FCG proceeds by large crack tip deformations promoting transfer of material from the tip apex to the crack flanks, thus rendering plastic crack growth based on plastic deformations without bond breaking or material splitting at the crack tip (Laird–Smith mechanism of FCG by blunting and re-sharpening). Plastic FCG rates (d a/d N) p were obtained and numerical results were fitted with a Paris-like equation (d a/d N) p = CΔ K m . An experimental validation of the simulations was performed by comparing the numerical Paris-like equation with real (experimental) Paris equations in the steels.

Uncertainty quantification and model validation of fatigue crack growth prediction

This paper presents a methodology for uncertainty quantification and model validation in fatigue crack growth analysis. Several models – finite element model, crack growth model, surrogate model, etc. – are connected through a Bayes network that aids in model calibration, uncertainty quantification, and model validation. Three types of uncertainty are included in both uncertainty quantification and model validation: (1) natural variability in loading and material properties; (2) data uncertainty due to measurement errors, sparse data, and different inspection results (crack not detected, crack detected but size not measured, and crack detected with size measurement); and (3) modeling uncertainty and errors during crack growth analysis, numerical approximations, and finite element discretization. Global sensitivity analysis is used to quantify the contribution of each source of uncertainty to the overall prediction uncertainty and to identify the important parameters that need to be calibrated. Bayesian hypothesis testing is used for model validation and the Bayes factor metric is used to quantify the confidence in the model prediction. The proposed methodology is illustrated using a numerical example of surface cracking in a cylindrical component.

Numerical Modeling of Fatigue Crack Growth in Single Crystals Based on Microdamage Theory

Proper life-time prediction modeling of single crystalline components is of increasing importance due to their common use in turbine industry. Viscoplastic damage approaches are of great interest in that context. However, mechanical properties of single crystals are strongly anisotropic and nonlinear in service conditions, bringing certain complexity into constitutive and numerical modeling. The aim of this work is to develop a thermodynamically consistent constitutive model based on generalized continua in order to simulate fatigue crack initiation and growth in single crystals. For that purpose, a standard crystal plasticity model is taken as a basis and coupled with the continuous damage model developed by Marchal et al. (2006a) [Marchal, N., Forest, S., Remy, L. and Duvinage, S. (2006a). Simulation of Fatigue Crack Growth in Single Crystal Superalloys Using Local Approach to Fracture, In: Moinereau, D., Steglich, D. and Besson, J. (eds.), Local Approach to Fracture, 9th European Mechanics of Materials Conference, Euromech-Mechamat, Moret-Sur-Loing, France, Presses de l’Ecole des mines de Paris, pp. 353-358]. As a variant of micromorphic theory, microdamage approach is applied to the model in order to obtain a regularized continuum damage formulation which solves mesh dependency problem by introducing an intrinsic length scale. A detailed finite element implementation procedure and its validation for monotonic crack growth are-shown. Fatigue crack growth analyses have been performed on a single edge notched geometry and a comparison between numerical and experimental results is presented.

Fatigue crack growth model for assessing reliability of box-girders for cable-stayed bridge combining SHMS with strain data

Enhancement of the computer algorithm developed for the Runyang cable-stayed bridge (RYCB) in China is made by incorporating the fatigue crack growth analysis in contrast to the SN curve approach. Strain data obtained from the structural health monitoring system (SHMS) and finite element calculations are used. This provides the application of a deterministic method in addition to the probabilistic approach with the added feature of crack growth. The choice of selecting the two-parameter fatigue crack growth criterion was based on the definition of reliability index β such that the new results can be compared with those using the SN curves. A gradual drop of the reliability index β with time with an upper limit was obtained for the crack growth model in contrast to the linear time relation for the SN curve model that had no upper limit. This difference is significant and reveals the importance for selecting the fatigue failure criterion. Deterministic and probabilistic crack growth models are used to assess the differences. The results are based on the box-girder component strain history data of the Runyang Cable-stayed Bridge (RYCB) in China, stress history recorded by structural health monitoring system (SHMS) is analyzed using the monitored stress amplitude, mean stress and stress ratio. Finite element calculations are used to supplement data at locations not accessible for measurements. Additional improvement with reference to damage accumulation and the physical meaning of the reliability index will be studies in relation to the fatigue damage of box-girder of long cable-stayed bridges.

ERROR AND UNCERTAINTY QUANTIFICATION AND SENSITIVITY ANALYSIS IN MECHANICS COMPUTATIONAL MODELS

Multiple sources of errors and uncertainty arise in mechanics computational models and contribute to the uncertainty in the final model prediction. This paper develops a systematic error quantification methodology for computational models. Some types of errors are deterministic, and some are stochastic. Appropriate procedures are developed to either correct the model prediction for deterministic errors or to account for the stochastic errors through sampling. First, input error, discretization error in finite element analysis (FEA), surrogate model error, and output measurement error are considered. Next, uncertainty quantification error, which arises due to the use of sampling-based methods, is also investigated. Model form error is estimated based on the comparison of corrected model prediction against physical observations and after accounting for solution approximation errors, uncertainty quantification errors, and experimental errors (input and output). Both local and global sensitivity measures are investigated to estimate and rank the contribution of each source of error to the uncertainty in the final result. Two numerical examples are used to demonstrate the proposed methodology by considering mechanical stress analysis and fatigue crack growth analysis.

Fatigue Crack Growth Analysis of Lap Joints in Deck Plates of Single-Deck Floating Roofs

Fatigue Crack Growth Analysis of Lap Joints in Deck Plates of Single-Deck Floating Roofs

Crack initiation and crack growth assessment of a high pressure steam chest

Extensive cracking had occurred in a number of high pressure steam chests. An assessment was undertaken based on the R5 British Energy methodology to assess the components for both creep–fatigue damage initiation and crack growth analysis to determine fitness for purpose. The analysis determined that the remaining base rupture endurance life of the component was greater then 1 million hours, however, due to the start-up and shutdown ramp rates, creep–fatigue damage greater then unity has occurred leading to crack initiation in a number of locations. These cracks were confirmed during internal inspection of the steam chest. A subsequent crack growth analysis determined that the component could safely be returned to service for the expected future life of the station.

Confidence Assessment in Fatigue Damage Prognosis

This paper presents a methodology for assessing the confidence and the predictive capability of prognosis models, using the application of fatigue crack growth analysis. Structures with complicated geometry and multi-axial variable amplitude loading conditions are considered. Several models –finite element model, crack growth model, retardation model, surrogate model, etc. – are efficiently connected through a Bayes network and the parameters of these models are calibrated after collecting inspection data. The results of the calibration are then used to develop a Bayesian confidence metric to assess the confidence of the models used in fatigue crack growth analysis. Three types of uncertainty are included in analysis: (1) natural variability in loading and material properties; (2) data uncertainty, due to crack detection uncertainty, measurement errors, and sparse data; (3) modeling uncertainty and errors in crack growth analysis, and finite element analysis. The proposed methodology is illustrated using a numerical example of surface cracking in a cylindrical structure.

Concurrent fatigue crack growth simulation using extended finite element method

In this paper, a concurrent simulation framework for fatigue crack growth analysis is proposed using a novel small time scale model for fatigue mechanism analysis and the extended finite element method (X-FEM) for fatigue crack growth simulation. The proposed small time scale fatigue model does not require the cycle counting as those using the classical fatigue analysis methods and can be performed concurrently with structural/mechanical analysis. The X-FEM greatly facilitates crack growth simulation without remeshing requirements ahead of the crack tip as in the classical finite element method. The basic concept and theory of X-FEM was briefly introduced and numerical predictions of stress intensity factors are verified with reference solutions under both uniaxial and multiaxial loadings. The small time scale fatigue model is integrated into the numerical simulation algorithm for concurrent fatigue crack growth analysis. Model predictions are compared with available experimental observations for model validation.

Fractographic analysis of fatigue crack growth in lightweight integral stiffened panels

PurposeThe purpose of this paper is to complement available macroscopic fatigue crack growth measurements in flat stiffened panels with scanning electron microscopy (SEM) measurements of striation spacing.Design/methodology/approachThe paper's approach is fatigue testing of two‐stiffener flat panels manufactured using three different processes, with a central initial crack perpendicular to the stiffeners and load, in order to identify striation spacing during crack growth up to final fracture, using SEM.FindingsAn increase of striation spacing as cracks grow was quantified. Although when cracks approach the stiffeners the stress intensity factor decreases, there is no clear decrease of striation spacing in that region. Striation spacing is roughly similar to macroscopic crack‐propagation rate da/dN measured in the panels testing. This observation is no longer valid once the stiffeners are reached; this stage is characterized by fast acceleration of the cracking process until final complete rupture is verified, and macroscopic crack growth measurements are made difficult because of the “T” geometry in that region.Originality/valueA complete picture of the striation spacing during the fatigue crack growth up to final fracture of a two‐stiffener flat panel is provided for three different manufacturing processes: high‐speed machining, laser beam welding and friction stir welding.

Inference of equivalent initial flaw size under multiple sources of uncertainty

A probabilistic methodology is proposed in this paper to estimate the equivalent initial flaw size (EIFS) distribution accounting for various sources of variability, uncertainty and error, for mechanical components with complicated geometry and multi-axial variable amplitude loading conditions. A Bayesian approach is used to calibrate the distribution of EIFS, where the likelihood function is constructed from model-based fatigue crack growth analysis and inspection results. The variability, uncertainties and errors in the above procedures are quantified, and the distribution of EIFS is calibrated by explicitly accounting for the various sources of uncertainty. Three types of uncertainty are considered: (1) natural variability in loading and material properties; (2) data uncertainty, due to crack detection uncertainty, measurement errors, and sparse data; (3) modeling uncertainty and errors during crack growth analysis, numerical approximations, and finite element discretization. A Monte Carlo simulation-based approach is developed for uncertainty quantification in the crack growth analysis and for constructing the likelihood function of EIFS. The proposed methodology is illustrated by a numerical example.