Fatigue and Fracture Reliability of Articulated Tower Joint Under Random Loading

2009 ◽  
Author(s):  
Mohd Moonis Zaheer ◽  
Nazrul Islam
Keyword(s):  
Fracture Mechanics ◽  
Fatigue Damage ◽  
Offshore Structures ◽  
Probability Of Failure ◽  
Random Wave ◽  
Shear Stresses ◽  
Random Loading ◽  
Sea Bed ◽  
Fatigue Damage Accumulation ◽  
Reliability Method

An articulated tower is one of the compliant offshore structures connected to the sea bed through a universal joint. In the random sea environment, this joint is subjected to reversal of shear stresses, which makes it susceptible to fatigue damage. In this study, fatigue damage accumulation in articulated joint under random loading is studied. The dynamic analysis of the tower has been carried out for twelve simulated sea states under random wave alone and random wave with wind. Nonlinearities due variable submergence, instantaneous position of the tower and hydrodynamic loading have been taken into account in the derivation of equation of motion. Fatigue life of the joint has been determined by S-N curve and fracture mechanics (F-M) approaches. Advanced First Order Reliability Method (FORM) and Monte Carlo Simulation method have been used for the reliability estimation. The results of the analyses are presented in terms of probability of failure and reliability indices. Sensitivity analysis is carried out to study the effect and participation of various random variables on the joint reliability. Most probable point (MPP) or design points have been located on the failure surface. Important parametric studies have been carried out which yield important information for reliability based design. The results of the study indicate that Miner’s rule, which is generally used in the design against fatigue in steel structures, yields a conservative estimate of probability of failure as compared to the fracture mechanics approach.

Seismic Analysis of a Double-Hinged Articulated Offshore Tower

2008 ◽  
Author(s):  
Syed Danish Hasan ◽  
Nazrul Islam ◽  
Khalid Moin
Keyword(s):  
Seismic Analysis ◽  
Offshore Structures ◽  
Random Wave ◽  
Wave Forces ◽  
Offshore Structure ◽  
Concentrated Mass ◽  
Energy Principle ◽  
Rotational Angle ◽  
Sea Bed ◽  
Time Histories

The response of offshore structures under seismic excitation in deep water conditions is an extremely complex phenomenon. Under such harsh environmental conditions, special offshore structures called articulated structures are feasible owing to reduced structural weight. Whereas, conventional offshore structure requires huge physical dimensions to meet the desired strength and stability criteria, therefore, are uneconomical. Articulated offshore towers are among the compliant offshore structures. These structures consist of a ballast chamber near the bottom hinge and a buoyancy chamber just below the mean sea level, imparting controlled movement against the environmental loads (wave, currents, and wind/earthquake). The present study deals with the seismic compliance of a double-hinged articulated offshore tower to three real earthquakes by solving the governing equations of motion in time domain using Newmark’s-β technique. For this purpose Elcentro 1940, Taft 1952 and Northridge 1994 earthquake time histories are considered. The tower is modeled as an upright flexible pendulum supported to the sea-bed by a mass-less rotational spring of zero stiffness while the top of it rigidly supports a deck in the air (a concentrated mass above water level). The computation of seismic and hydrodynamic loads are performed by dividing the tower into finite elements with masses lumped at the nodes. The earthquake response is carried out by random vibration analysis, in which, seismic excitations are assumed to be a broadband stationary process. Effects of horizontal ground motions are considered in the present study. Monte Carlo simulation technique is used to model long crested random wave forces. Effect of sea-bed shaking on hydrodynamic modeling is considered. The dynamic equation of motion is formulated using Lagrangian approach, which is based on energy principle. Nonlinearities due to variable submergence and buoyancy, added mass associated with the geometrical non-linearities of the system are considered. The results are expressed in the form of time-histories and PSDFs of deck displacement, rotational angle, base and hinge shear, and the bending moment. The outcome of the response establishes that seismic sea environment is an important design consideration for successful performance of hinges, particularly, if these structures are situated in seismically active zones of the world’s ocean.

Different Fatigue Dynamics Under Statistically and Spectrally Similar Deterministic and Stochastic Excitations

2013 ◽  
Vol 81 (4) ◽  
Author(s):  
Son Hai Nguyen ◽  
Mike Falco ◽  
Ming Liu ◽  
David Chelidze
Keyword(s):  
Crack Growth ◽  
Fatigue Damage ◽  
Damage Accumulation ◽  
Growth Dynamics ◽  
Experimental System ◽  
Counting Method ◽  
Random Loading ◽  
Stochastic Excitations ◽  
Fatigue Damage Accumulation ◽  
System Coupling

Estimating and tracking crack growth dynamics is essential for fatigue failure prediction. A new experimental system—coupling structural and crack growth dynamics—was used to show fatigue damage accumulation is different under chaotic (i.e., deterministic) and stochastic (i.e., random) loading, even when both excitations possess the same spectral and statistical signatures. Furthermore, the conventional rain-flow counting method considerably overestimates damage in case of chaotic forcing. Important nonlinear loading characteristics, which can explain the observed discrepancies, are identified and suggested to be included as loading parameters in new macroscopic fatigue models.

Advanced Probabilistic Fracture Mechanics Using the R6 Procedure

2010 ◽  
Author(s):  
David W. Beardsmore ◽  
Karen Stone ◽  
Huaguo Teng
Keyword(s):  
Fracture Toughness ◽  
Monte Carlo ◽  
Fracture Mechanics ◽  
Monte Carlo Methods ◽  
Probability Of Failure ◽  
Defect Size ◽  
Probabilistic Fracture Mechanics ◽  
Safety Margins ◽  
Reliability Method ◽  
Failure Assessment

Deterministic Fracture Mechanics (DFM) assessments of structural components (e.g. pressure vessels and piping used in the nuclear industry) containing defects can usually be carried out using the R6 procedure. The aim of such an assessment is to demonstrate that there are sufficient safety margins on the applied loads, defect size and fracture toughness for the safe continual operation of the component. To ensure a conservative assessment is made, a lower-bound fracture toughness, and upper-bound defect sizes and applied loads are used. In some cases, this approach will be too conservative and will provide insufficient safety margins. Probabilistic Fracture Mechanics (PFM) allow a way forward in such cases by allowing for the inherent scatter in material properties, defect size and applied loads explicitly. Basic Monte Carlo Methods (MCM) allow an estimate of the probability of failure to be calculated by carrying out a large number of fracture mechanics assessments, each using a random sample of the different random variables (loads, defect size, fracture toughness etc). The probability of failure is obtained by counting the proportion of simulations which lead to assessment points that lie outside the R6 failure assessment curve. This approach can give good results for probabilities greater than 10−5. However, for smaller probabilities, the calculation may be inefficient and a very large number of assessments may be necessary to obtain an accurate result, which may be prohibitive. Engineering Reliability Methods (ERM), such as the First Order Reliability method (FORM) and the Second Order Reliability Method (SORM), can be used to estimate the probability of failure in such cases, but these methods can be difficult to implement, do not always give the correct result, and are not always robust enough for general use. Advanced Monte Carlo Methods (AMCM) combine the two approaches to provide an accurate and efficient calculation of probability of failure in all cases. These methods aim to carry out Importance Sampling so that only assessment points that lie close to or outside the failure assessment curve are calculated. Two methods are described in this paper: (1) orthogonal sampling, and (2) spherical sampling. The power behind these methods is demonstrated by carrying out calculations of probability of failure for semi-elliptical, surface breaking, circumferential cracks in the inside of a pressure vessel. The results are compared with the results of Basic Monte Carlo and Engineering Reliability calculations. The calculations use the R6 assessment procedure.

Reliability-Based Fatigue Design for Piping Using Spectrum Characteristics

2012 ◽  
Author(s):  
Shinsuke Sakai ◽  
Jyunki Maeda ◽  
Masahiro Takanashi ◽  
Izumi Satoshi
Keyword(s):  
Fatigue Damage ◽  
Limit State ◽  
Equivalent Stress ◽  
Random Wave ◽  
State Function ◽  
Counting Method ◽  
Random Loading ◽  
Analytical Treatment ◽  
Fatigue Design ◽  
Spectrum Characteristics

A reliability-based approach can play an important role in avoiding excessive conservative design for piping. We showed a formulation for applying the limit state function method to reliability-based fatigue design at the previous PVP conference. Using this method, the reliability can be expressed by two dominant parameters: the distribution of equivalent stress and the distribution of fatigue life. If the equivalent stress under stationary random loading can be related to some specific spectrum parameters, it is expected that reliability-based fatigue design can be achieved under random loading. Fatigue damage under random loading is usually estimated using Miner’s law together with the SN diagram. In applying Miner’s law, the random wave is decomposed to the fatigue range using some counting method. The rainflow cycle counting (RFC) method is widely used as a counting method. In view of design application, however, the estimation of fatigue damage from spectrum characteristics is important, and the RFC method is not necessarily suitable for this purpose because it is rather difficult to use in the analytical treatment. Fortunately, it has been shown that the level crossing counting (LCC) method provides a more conservative estimation when compared with the RFC method and the analytical treatment for the evaluation is available. In this paper, we will show a procedure for reliability-based fatigue design which evaluates fatigue damage using the LCC method, spectrum characteristics and Miner’s law.

A Life-Cycle Approach to the Assessment of Pipeline Dents

2016 ◽  
Author(s):  
Michael Turnquist ◽  
Ian Smith
Keyword(s):  
Life Cycle Assessment ◽  
Life Cycle ◽  
Fatigue Damage ◽  
Probability Of Failure ◽  
Life Cycle Approach ◽  
Remaining Life ◽  
Pressure Cycling ◽  
Damage Rate ◽  
Fatigue Damage Accumulation ◽  
Pressure Cycle

The application of in-line inspection (ILI) to assess pipelines for various anomalies is standard practice in the pipeline industry. When ILI data identifies the presence of anomalies such as denting or ovalization, current convention is to perform either a depth-based or strain-based assessment to assess the severity. Although a strain-based methodology is generally accepted in the pipeline industry, this approach does not address all of the primary damage mechanisms associated with pipeline dents. Assessment based upon either depth or strain alone may not only provide non-conservative results but also fail to properly rank dents in order of their true severity. A life-cycle assessment approach that considers the damage caused by the dent formation, the stress intensification effect of the dent profile, and the severity of future pressure cycling provides an improved understanding of the probability of failure, allowing for more informed integrity management decision making. Strain-based assessment of dents in pipelines is typically performed by calculating the local curvatures in the dent geometry as measured by ILI. Local strains are then calculated based on these local curvatures. However, this approach does not address that once a dent has been formed, continued pressure cycling at that location is what will ultimately cause a failure. The current strain-based methodology does not account for the severity of the pressure cycling at the dent. A new and innovative methodology has been developed which takes a life-cycle approach to the assessment of pipeline dents. This approach estimates the remaining life of a dent based on fatigue damage accumulation. Finite element analysis (FEA) is used to calculate various stress concentration factors (SCFs) based on the geometry of the dent. These SCFs are used to calculate an equivalent alternating stress for a unit pressure cycle event. Past representative pressure cycling data is gathered using a rainflow counting approach. The amount of damage accumulated during each pressure cycle is calculated using stress or strain based (S-N) fatigue curves; this allows for a damage rate to be calculated based on past operational history. A remaining life can be estimated based on this damage rate and an estimation of the initial fatigue damage accumulated during formation of the dent. This estimation is made based on previous elastic-plastic FEA of various scenarios which simulate the formation and shakedown of a pipeline dent. Case studies which explore the use of different assessment methods to analyze dents will be presented. A comparison of different assessment methodologies will illustrate the improved understanding of the probability of failure of dents based upon the life-cycle assessment.

Spectral Fatigue and Stress Based Reliability Assessment of Offshore Steel Structures

2008 ◽  
Author(s):  
H. Karadeniz
Keyword(s):  
Spectral Analysis ◽  
Limit State ◽  
Steel Structures ◽  
Offshore Structures ◽  
Statistical Characteristics ◽  
Random Wave ◽  
State Function ◽  
Efficient Computation ◽  
Reliability Method ◽  
Stress Spectrum

Having summarized briefly uncertainties in spectral fatigue damages of offshore structures, this paper presents the formulation and procedure of an efficient computation of reliability estimates on basis of fatigue damages and stresses. Most of uncertainties are embedded in response characteristics of the stress process and the damage-model used. Uncertainties in stress statistical characteristics are associated with the modeling of structures, random wave environment, wave loading and the analysis used. In the fatigue damage, additional uncertainties arise from the modeling of damage-mechanism. These uncertainties are due to experimental fatigue data and structural joint configurations. All these uncertainties can be classified into the categories as a) those naturally inherent (aleatory) and b) those due to lack of knowledge (epistemic). The second part of the paper is devoted to a fast and efficient computation of the fatigue reliability. This algorithm prevents repetitive execution of spectral analysis procedure during the reliability iteration. In this technique, a suitable formulation of the stress spectrum is used with a model uncertainty parameter representing most of uncertainties in the stress spectrum. The failure function of the reliability analysis is expressed independently of the spectral analysis. For the stress based reliability calculation the mean stress-amplitude of the stochastic stress variation is used to define a limit state function. The related uncertainties are the same as those aforementioned. The advanced FORM reliability method is used to calculate the reliability index and to identify important uncertainty parameters. The procedure is demonstrated by an example jacket structure. The third part of the paper explains the inverse reliability method to determine some parameters, which may be deterministic or probabilistic, under required reliability constraints.

Life Prediction Techniques for Variable Amplitude Multiaxial Fatigue—Part 1: Theories

1996 ◽  
Vol 118 (3) ◽  
pp. 367-370 ◽  
Author(s):  
C. H. Wang ◽  
M. W. Brown
Keyword(s):  
Fatigue Damage ◽  
Life Prediction ◽  
Local Strain ◽  
Multiaxial Fatigue ◽  
Critical Plane ◽  
Random Loading ◽  
Variable Amplitude ◽  
Fatigue Damage Accumulation ◽  
Prediction Techniques ◽  
Searching Method

Fatigue life prediction under multiaxis random loading is an extremely complex and intractable topic; only a few methods have been proposed in the literature. In addition, experimental results under multiaxis random loading are also scarce. In part one of this two-part paper, a multiaxial non-proportional cycle counting method and fatigue damage calculation procedure are proposed, which is compared with one published damage-searching method. Both theories are based on critical plane concepts, one being an extension of the local strain approach for uniaxial variable amplitude loading and the other employing a new counting algorithm for multiaxis random loading. In principle, these two methods can be considered as bounding solutions for fatigue damage accumulation under multiaxis random loading.

Loading Sequence Effects on Fatigue Damage Accumulation of Offshore Structures: A Deterministic Approach

2017 ◽  
Author(s):  
Dimitrios G. Pavlou
Keyword(s):  
Crack Initiation ◽  
Crack Propagation ◽  
Crack Growth ◽  
Fatigue Damage ◽  
Mixed Mode ◽  
Fatigue Crack Initiation ◽  
Offshore Structures ◽  
Fatigue Damage Accumulation ◽  
Miner’S Rule ◽  
Miner's Rule

Offshore structures are subjected to irregular loading spectra due to their exposure to waves and wind. The environmental loads cause variable amplitude stress histories on critical spots of the structures. The existing engineering methodology (adopted by most of the national standards) to estimate the accumulated fatigue damage is based on Miner’s rule for crack initiation. Paris rule and its modifications are used for crack propagation prediction. However, Miner’s rule is a linear model and does not take into account the sequence effect of loading blocks with different stress amplitude. On the other hand, the widely used Paris rule does not take into account the load interaction effects (e.g. overload-induced crack growth retardations). The prediction of the crack growth rate and the crack growth direction of mixed mode cracks is an important issue as well. Aim of the present paper is the analysis of the weaknesses of the engineering tools for fatigue analysis, and the demonstration of the advantages of non-linear damage functions and crack propagation models. A review of models for fatigue crack initiation and growth (for mode I or mixed mode loading) developed by the author is presented. Representative results are discussed and commented.

Nonlinear Fatigue Damage Accumulation Under Random Loading

1996 ◽  
Vol 118 (2) ◽  
pp. 168-173 ◽  
Author(s):  
W. Q. Zhu ◽  
M. X. Jiang
Keyword(s):  
Fatigue Damage ◽  
Damage Accumulation ◽  
Stochastic Theory ◽  
Reliability Function ◽  
Random Loading ◽  
Fatigue Damage Accumulation ◽  
Probability Densities ◽  
Cumulative Fatigue Damage ◽  
Analytical Expressions ◽  
Damage Rule

The analytical expressions for the probability densities of the cumulative fatigue damage and fatigue life and for the reliability function are obtained for a mechanical or structural component subject to stationary random stress process on the basis of a stochastic theory of fatigue damage accumulation proposed by the first author and his co-worker and the Morrow’s nonlinear damage rule. The comparison between the results from Morrow’s and Palmgren-Miner’s damage rules for the case when the stress is a narrow-band stationary Gaussian process with zero mean is made and some important conclusions are drawn.

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