Fatigue Crack Growth Calculations Research Articles

Defects in Electron Beam Melted Ti-6Al-4V: Fatigue Life Prediction Using Experimental Data and Extreme Value Statistics

Electron beam melting is a powder bed fusion (PBF) additive manufacturing (AM) method for metals offering opportunities for the reduction of material waste and freedom of design, but unfortunately also suffering from material defects from production. The stochastic nature of defect formation leads to a scatter in the fatigue performance of the material, preventing wider use of this production method for fatigue critical components. In this work, fatigue test data from electron beam melted Ti-6Al-4V specimens machined from as-built material are compared to deterministic fatigue crack growth calculations and probabilistically modeled fatigue life. X-ray computed tomography (XCT) data evaluated using extreme value statistics are used as the model input. Results show that the probabilistic model is able to provide a good conservative life estimate, as well as accurate predictive scatter bands. It is also shown that the use of XCT-data as the model input is feasible, requiring little investigated material volume for model calibration.

Consistent and coherent treatment of uncertainties and dependencies in fatigue crack growth calculations using multi-level Bayesian models

Engineers perform fatigue assessments to support structural integrity management. Given that the purpose of these calculations is linked to problems of decision making under various sources of uncertainty, probabilistic methods are often more useful than deterministic alternatives. Guidance on the direct probabilistic application of procedures in existing industrial standards is currently limited and dependencies between marginal probabilistic models are generally not considered, despite their potential significance being acknowledged. This paper proposes the use of Bayesian data analysis as a flexible and intuitive approach to coherently and consistently account for uncertainty and dependency in fatigue crack growth rate models. Various Bayesian models are established and presented, based on the same data as the existing models in BS 7910 (a widely used industrial standard). The models are compared in terms of their out of sample predictive accuracy, using methods with a basis in information theory and cross-validation. The Bayesian models exhibit an improved performance, with the most accurate predictions resulting from multi-level (hierarchical) models, which account for variation between constituent test datasets and partially pool information.

LCF behaviour and a comprehensive life prediction model for AlSi10Mg obtained by SLM

The full potential of additive manufacturing (AM) components is today yet to be reached. Space and aerospace industries are still conservative in the use of AM parts for safety–critical applications, mostly because of the uncertainties and low reproducibility that are often associated with the process. One of the most challenging issues is the fatigue resistance. The rough surface condition and the presence of manufacturing defects can cause significant scatter, leading to the adoption of large conservative safety factors. To robustly model the fatigue resistance of defected AM materials, there is a need to implement defect-tolerant designs and deal with these uncertainties. The present research activity aims at developing a model for fatigue life estimation in a large range of loading conditions, from high cycle fatigue to low cycle fatigue. This is achieved by adopting a fracture mechanics approach, through elastic–plastic fatigue crack growth calculations based on the known defect population inside the material. The model has been applied to AlSi10Mg produced by three slightly different selective laser melting processes, showing a robust estimation of fatigue life and scatter with limited experimental effort. The life predictions performed are then summarised in design maps where the allowable stress (or strain) depends on the defect size and on the HCF/LCF design upon the number of cycles selected.

Fatigue crack propagation prediction for marine structures based on a spectral method

A method based on spectrum analysis is proposed for predicting fatigue crack propagation (FCP) of a crack in marine structures. The stress intensity factors (SIF) for a crack can be different under different load cases, such as loading conditions, heading angles and wave frequencies, even at the same level of nominal or hotspot stress. Therefore, the load spectrum obtained from the stress transfer function and wave spectrum may be failing to calculate the FCP accurately. In current study, SIF transfer functions were evaluated through detailed structural analysis for different crack sizes, and the short term SIF distribution obtained from the SIF transfer function. FCP life could then be calculated from numerous short term SIF distribution and the improved Paris formula. A sub-model technique was integrated, facilitating SIF re-analysis due to crack growth, and an Improved Euler method was adopted to reduce the computational steps. FCP of a semi elliptical surface crack at the weld toe between hatch coaming and forward bulkhead of a container ship superstructure was used to demonstrate the application of the proposed spectral method. This paper offers a way of combining the spectral analysis and fracture mechanics in fatigue crack growth calculation for marine structures.

A Comparison Study of Machine Learning Based Algorithms for Fatigue Crack Growth Calculation.

The relationships between the fatigue crack growth rate and stress intensity factor range are not always linear even in the Paris region. The stress ratio effects on fatigue crack growth rate are diverse in different materials. However, most existing fatigue crack growth models cannot handle these nonlinearities appropriately. The machine learning method provides a flexible approach to the modeling of fatigue crack growth because of its excellent nonlinear approximation and multivariable learning ability. In this paper, a fatigue crack growth calculation method is proposed based on three different machine learning algorithms (MLAs): extreme learning machine (ELM), radial basis function network (RBFN) and genetic algorithms optimized back propagation network (GABP). The MLA based method is validated using testing data of different materials. The three MLAs are compared with each other as well as the classical two-parameter model ( approach). The results show that the predictions of MLAs are superior to those of approach in accuracy and effectiveness, and the ELM based algorithms show overall the best agreement with the experimental data out of the three MLAs, for its global optimization and extrapolation ability.

Failure analysis of a pull rod actuator of an ATOX raw mill used in the cement production process

Abstract A failure analysis of a forged and machined pull rod made of a quenched and tempered high strength steel – namely DIN 34CrNiMo6 – is presented in this paper. The pull rod under study is one of the three rods that connect the three existing hydraulic cylinders to the roller mill and it is used to exert grinding pressure on the roller in an ATOX raw mill. The study of the failure involved the mechanical system's simulation, as well as the fatigue damage assessment based on the application of the Rainflow Method and Fracture Mechanics principles. The pull rod's stress state was determined from in situ strain gages rosettes measurements, and system's simulation showed that the pull rod was designed to support axial loadings only. To ensure this stress state, a proper functioning of the plain bearings and a good condition of the elastomers of the horizontal rod buffer are required. According to the stress-life approach given in the FKM guideline, the current design solution should provide a useful life of 50 years to the pull rod. However, fatigue crack growth calculations made with the strain spectra registered demonstrated that the presence of an initial surface crack is extremely harsh to the lifespan of the rod, which will reach a critical value in a much shorter period of time. Surface finish, corrosion protection and maintenance actions to ensure the correct functioning of the plain bearings, could be important to ensure the desired longevity of the pull rod.

Fatigue crack growth calculations for two adjacent surface cracks using combination rules in fitness-for-service codes

If multiple discrete cracks are detected in structural components, the combination rules provided in fitness-for-service (FFS) codes are employed to estimate the remaining lives of the components by fatigue crack growth (FCG) calculations. However, the specific criteria for combination rules prescribed by various FFS codes are different. This paper presents FCG calculations for two adjacent surface cracks in a flat plate using different combination criteria. Three different crack aspect ratios of 0.05, 0.15 and 0.5, and a nominal distance of 5 mm between the two cracks are investigated in the calculations. The results show that the FCG behaviors obtained by various codes are significantly different. In addition, the combination process of the two cracks is found to affect the crack shape development remarkably.

Analysis on Crack Fatigue Growth Calculation for Nuclear Power Plant In-service Inspection

Fatigue is the common failure mode for nuclear mechanical components during operation which could induce crack initiation and growth. In order to predict the behaviour of fatigue crack propagating, fatigue calculation is introduced. A new method of crack fatigue growth calculation has been presented in this paper according to French RSE-M Rules. Regarding this method, detail analysis on key formulas selecting, essential calculation factors of occurrences combination, K-value calculation and mechanic modelling, characterization interval option has been performed. One fatigue crack growth calculation example of dissimilar weld of Reactor Pressure Vessel outlet nozzle to the safe end has been taken and the result demonstrates a good expectation.

Remaining Lives of Fatigue Crack Growths for Pipes With Subsurface Flaws and Subsurface-to-Surface Flaw Proximity Rules

If a subsurface flaw is located near a component surface, the subsurface flaw is transformed into a surface flaw in accordance with a subsurface-to-surface flaw proximity rule. The recharacterization process from subsurface to surface flaw is adopted in all fitness-for-service (FFS) codes. However, the specific criteria of the recharacterizations are different among the FFS codes. Recently, the authors have proposed a new subsurface-to-surface flaw proximity rule based on experimental data and equivalent fatigue crack growth rate calculations. In this study, fatigue crack growth calculations were carried out for pipes with subsurface flaws, using the proximity rule provided in the current ASME (American Society of Mechanical Engineers) Section XI and JSME (The Japan Society of Mechanical Engineers) codes and the proposed subsurface-to-surface flaw proximity rule. Different pipe sizes, flaw aspect ratios, and ligament distances from subsurface flaws to inner surface of pipes were taken into account. The results indicate the current proximity rule gives less conservative fatigue lives, when the aspect ratios of the subsurface flaws are small.

Consideration of the residual stress distributions in fatigue crack growth calculations for assessing welded steel joints

ABSTRACTTo better understand the crack closure and propagation, an analytical model is established. The residual stress effect on fatigue crack growth equations has been considered using the residual stress intensity factor (SIF) (Kres). The joint geometries, residual stress distributions (σres) and residual stress ratio (Rres) were considered also. Kres are calculated using the analytical weight function (WF) method and different residual stress distributions. It is to be emphasized that the current approach is little investigated. This is because the WF has already been developed to calculate SIF for an existing crack. The current approach calculates Kres for the crack that initiates and propagates until failure. Different stress distributions have been used, and Rres is defined. The validity of using the WF has been shown. SIF due to applied load (Kapp) and applied stress ratio (Rapp) have been considered. Fatigue crack growth rate was investigated in accordance with the current approach. The results have been verified and benchmarked.

Practical use of defect assessment procedures for industrial component integrity assessment

The practical use of defect assessment procedures for industrial component integrity assessment is described through two practical examples in this paper. In the first example, the procedure is used to perform low temperature fitness-for-service (FFS) analysis of a longitudinal seam welded vessel manufactured from a duplex stainless steel. The impact energy obtained from the Charpy impact test performed on the weld of the vessel was found lower than the value of the minimum impact energy criteria given by the British Standard BS 5500. Charpy impact energy and fracture toughness correlation and failure assessment diagram (FAD) methodology were used in this FFS analysis to determine the fracture resistance of the vessel. For the assumed defect size used in the assessment, the weld was found to meet the fracture resistance criteria and therefore would still be fit-for-purpose. The FAD analysis was, however, repeated using the J-values obtained from the CTOD test to gain better confidence as the Charpy impact test does not provide direct measurement of the fracture toughness. The FAD was later used to determine the critical surface crack length which was then represented as a function of crack depth. The Charpy impact energy correlation method was found to be more conservative than the method of evaluation using the CTOD J-values. The lack of side wall fusion (LOF) which is a typical defect in this type of vessel would usually be influenced by the size/diameter of the electrode wire used in the weld and the number of runs. In this case, the fracture resistance of the 15mm thick vessel with the longitudinal seam weld should be adequate if less than 5mm diameter of electrode wire is used.The second example illustrates defect assessment of a high temperature plant component. A defect was found in the high pressure final superheater header. A defect assessment incorporating FAD on the header showed that the defect was non-critical. This led to the need to perform creep and fatigue crack growth calculations and remaining life assessment in order to determine the mitigation plan for the engineers. The deterministic approach, which mainly considers the worst case scenario, suggested that the remaining life of the header was approximately 4.5 years. Probabilistic analysis showed that the component could still be fit for service up to 6 years. This will allow the engineers to mitigate a more efficient plan with a decision to either repair or replace the header and when. The use of probabilistic lifing methodologies and algorithms could consequently bring considerable financial benefits to the plant owners/operators e.g. by avoiding premature component repair or replacement. Nevertheless, it would be in the management’s interest to avoid a forced outage. The recommendation would be that the component could still be fit to use until their next minor outage (in 3 years). From then, the remedy option would be to grind down to a depth of suspected crack, excavate a small area/surrounding which might be affected, followed by correct and regular monitoring, or alternatively replace the component.

Efficient probabilistic methods for real-time fatigue damage prognosis


 
 
 A general probabilistic fatigue crack growth prediction methodology for accurate and efficient damage prognosis is proposed in this paper. This methodology consists two major parts. First, the realistic random loading is transformed to an equivalent constant amplitude loading process based on a recently developed mechanism model. This transformation avoids the cycle-by-cycle calculation of fatigue crack growth under variable amplitude loading. Following this, an inverse first-order reliability method (IFORM) is used to evaluate the fatigue crack growth at an arbitrary reliability level. Inverse FORM method does not require a large number of function evaluations compared to the direct Monte Carlo simulation. Computational cost is significantly reduced and the proposed method is very suitable for real-time damage prognosis. Numerical examples are used to demonstrate the proposed method. Various experimental data under variable amplitude loading are collected and model predictions are compared with experimental data for model validation.
 
 

Evaluation of the fretting fatigue behaviour of commercially pure titanium

Fretting fatigue occurs when the contact surfaces of two components undergo small oscillatory movement while they are subjected to a clamping force. A cyclic external load gives rise to the early initiation of fatigue cracks, thus reducing their service life. In this paper, the fretting fatigue behaviour of commercially pure titanium flat samples (1.5mm thick) is evaluated. A fretting device composed of a frame, load cell, and two screw-mounted cylindrical fretting pads with convex extremities was built and set to a servo-hydraulic testing machine. The fatigue tests were conducted under load control at a frequency of 10 Hz and stress ratio R = 0.1, with various contact load values applied to the fretting pads. Additional tests under inert environment allowed assessing the role of oxidation on the wear debris formation. The fracture surfaces and fretting scars were analysed via scanning electron microscopy in order to evaluate the surface damage evolution and its effect on the fatigue crack features. The effect of the fretting condition on the S-N curve of the material in the range of 104-106 cycles is described. Fatigue crack growth calculations allowed estimating the crack initiation and propagation lives under fretting conditions. The effect of the fretting condition in fatigue life is stronger for the lower values of cyclic stress and does not seem to depend on the contact loading value.

Improved modeling of the effect of R-ratio on crack growth rate

Most engineering structures with crack-like defects experience varying crack-tip loading during their service. This variation may result from combinations of varying applied loads and displacements and/or varying body force including residual stress. It is known that crack growth rates differ according to the R-ratios when expressed via a single parameter, stress intensity factor range, Δ K. Many methods have been proposed to incorporate the effect of the R-ratio, including effective stress intensity factor range models based on crack closure and the two-parameter driving force model etc. However there are few clear statements about the choice of material constants for the calculation of crack growth lives under varying amplitude loading. This is a significant omission. In this paper, a simple crack growth rate equation has been proposed, which can condense the crack growth data under different R-ratios to the curve corresponding to R = 0. Fatigue crack growth rate data for several materials taken from the literature, were analyzed using a new formulation. These data then cluster around the R = 0 crack growth rate curve. The result implies that crack growth rates for fatigue life calculation under different R-ratios may be obtained directly from the constants corresponding to R = 0. Thus the most commonly tested crack growth rate constants corresponding to R = 0–0.1 are sufficient for fatigue crack growth calculation under different loading conditions.

Metallurgical Failure Analysis of a Rotating Blade in the Compressor Section of a Gas Turbine

A metallurgical failure analysis was performed for the stage 17 gas turbine rotating blade and stationary vane. Four pieces, including the failed rotating and stationary blades, were removed from the air-compressor section of a gas turbine. The damaged components were found during a borescope examination. The objectives were to determine the failure mechanism and to estimate an inspection interval. The measured chemical compositions of the rotating blade and stationary vane are consistent with that of 403 stainless steel. The failure mechanism for the rotating blade is fatigue based on the beach marks on the fracture surface and the transgranular cracking. The fatigue crack initiated at the trailing edge of the blade. The crack at the trailing edge is due to impact damage. The probable root cause of failure for the rotating blade is the loss of axial clearance between the stationary and rotating blades. Fatigue crack growth calculations were performed using the NASGRO computer program and the corner cracked plate geometry to estimate the inspection interval. The estimated inspection interval is of order of magnitude hours to days for failure by high-cycle fatigue crack growth.

Fatigue life prediction of offshore tubular joints using fracture mechanics

ABSTRACT Fatigue crack growth calculations were performed on offshore tubular joints using the Paris crack growth law. The stress intensity factors required for such calculations were obtained from T‐butt solutions previously proposed by the authors. The applicability of the solutions to tubular joints was first demonstrated by comparing the fatigue life of a base case with that obtained from a mean S–N curve, and the influence on fatigue life of various factors including load shedding, the size of initial defects, weld geometry, etc. was investigated. The solutions were then used to predict the lives of tubular T‐joints from an experimental database. The results show that the solutions underestimate the fatigue life; this underestimation was shown to be primarily due to ignoring the combined effects of load shedding and the intersection stress distribution. In general, however, the trends in the predicted fatigue lives with joint geometry and other details were seen to be superior to predictions from the S–N approach, with the solutions significantly reducing the dependency on loading mode exhibited by the test data.

Estimation of stress intensity factor solutions for weld toe cracks in offshore tubular joints

This paper proposes an engineering methodology for estimating stress intensity factor ( K) solutions for semi-elliptical weld toe cracks in tubular joints. The methodology uses the T-butt solutions proposed previously by the authors in conjunction with the stress concentration factors and the degrees of bending in the uncracked tubular joints. The estimated K factors are then compared with those obtained from a well-validated finite element procedure and the validity of the proposed methodology is demonstrated. A more refined way of calculating the uncracked stress field parameters which leads to more accurate predictions is also proposed. Fatigue crack growth calculations on experimental joints indicate that the proposed methodology is conservative.

Fatigue crack growth calculations for a vessel internal corner crack under repeated thermal transients

A problem of current fundamental and industrial interest is the structural integrity of pressure vessels containing defects when subjected to repeated thermal shock at constant internal pressure. The component considered is a nozzle to a hemispherical pressure vessel intersection containing a defect at the internal corner. A range of 12 cases of thermal shock loads characterised in severity by two dimensionless parameters, the Biot ( B) and Fourier ( F) numbers, were applied. Estimation of remaining life for each case was carried out based on the PD6493 procedure. Numerical modelling of the crack growth from the quadrant shaped crack showed that more severe shocks accelerate crack growth while less severe shock leads to slow growth or eventual crack arrest. The effect of the Biot and Fourier parameters on the remaining life of the component was quantified. A methodology that comprises of heat transfer, thermal stress and fracture mechanics of defect assessment is applied to a problem of industrial interest.

An Approach to Account for Negative R-Ratio Effects in Fatigue Crack Growth Calculations for Pressure Vessels Based on Crack Closure Concepts

Current fatigue crack growth procedures in the commercial nuclear industry do not clearly specify how compressive loads are to be handled and, therefore, regulatory agencies usually recommend a conservative approach requiring full consideration of the loads. This paper demonstrates that a more realistic approach to account for compressive loads can be formulated using crack closure concepts. Several empirical plasticity-induced crack closure models were evaluated. An approach in the Section XI ASME Code for tensile loading only has been extended and evaluated for negative R-ratios. However, the paper shows this approach to be overly conservative. The approaches using crack closure models are shown to be more accurate. An analytically based crack closure model, while more complicated, is shown to give a theoretical basis to the empirically derived crack closure models. The paper concludes with a recommendation for modifying the current ASME Code practices consistent with the crack closure models and fatigue crack growth data from negative R-ratio tests.

Prediction of the fatigue behaviour of welded steel and aluminium structure with the fracture mechanics approach

Abstract The paper deals with the fracture mechanics approach to the fatigue life and crack growth of welded connections in steel and aluminium structures. This approach can be used as a design as well as a maintenance tool. The following aspects of fatigue calculations are highlighted: modelling of the geometry and stresses, crack schematisation and a fracture mechanics based model. Special attention is given to stress intensity factor solutions for welded joints and several crack growth laws. Examples of fatigue crack growth calculations are an important contribution to this paper. The effect on lifetime of the following parameters are demonstrated and compared with experimental results: thickness, weld toe grinding and weld dimensions. Additional attention will be given to an application for tubular joints.