A GENERALIZED FATIGUE LIMIT CRITERION AND A UNIFIED THEORY OF LOW-CYCLE FATIGUE DAMAGE

Abstract— A generalized fatigue limit criterion for multiaxial stress state conditions of isotropic materials is presented. This criterion includes four material parameters and uses two invariants of stress amplitudes and furthermore two invariants of mean stresses. It is shown that the fatigue criteria of Sines and Crossland are particular cases of the formulated criterion. Practical recommendations for the use of different fatigue limit criteria are established. Theoretical predictions are compared with experimental data. Finally a continuum damage mechanics theory for low cycle fatigue of isotropic materials is proposed. This theory describes simultaneously the influence of the stress amplitude and the mean stress on the fatigue damage suffered by materials. The proposed theory is based on four material parameters. Special damage theories with a smaller number of material parameters are obtained. Practical recommendations for the use of these fatigue damage theories are presented.     

Lebensdauerermittlung bei mehrachsigen wechselnden Beanspruchungen im niedrigen und hohen Temperaturbereich

Life time assessment on multiaxial cyclic loadings at low and high temperatures For the calculation of fatigue strength of components made out of ductile materials under complex cyclic load different assessments are present. As typical representatives of stress theories the shear stress intensity hypothesis (SIH) as well as the method of critical plane approach (MKS) are considered and compared for rigid and non rigid principle stress directions. Furthermore for synchronous loads the calculation methods are compared with Bach's method. The calculation method becomes more complex, if time dependent material properties at corresponding high temperatures have to be taken into account. In this case the application of viscoplastic material models is necessary, which allows the consideration of combination of creep and fatigue. As an example a modified material model by Chaboche / Nouailhas is used in order to present the calculation of multiaxial creep fatigue tests.     

Prediction methods of fatigue critical point for notched components under multiaxial fatigue loading

Two methods based on local stress responses are proposed to locate fatigue critical point of metallic notched components under non‐proportional loading. The points on the notch edge maintain a state of uniaxial stress even when the far‐field fatigue loading is multiaxial. The point bearing the maximum stress amplitude is recognized as fatigue critical point under the condition of non‐mean stress; otherwise, the Goodman's empirical formula is adopted to amend mean stress effect prior to the determination of fatigue critical point. Furthermore, the uniaxial stress state can be treated as a special multiaxial stress state. The Susmel's fatigue damage parameter is employed to evaluate the fatigue damage of these points on the notch edge. Multiaxial fatigue tests on thin‐walled round tube notched specimens made of GH4169 nickel‐base alloy and 2297 aluminium‐lithium alloy are carried out to verify the two methods. The prediction results show that both the stress amplitude method and the Susmel's parameter method can accurately locate the fatigue critical point of metallic notched components under multiaxial fatigue loading.     

Fatigue strength CAE system for three-dimensional welded structures

ABSTRACT Fatigue strength assessment methods are applied to practical arc-welded structural features that have complex three-dimensional geometry. Two methods are investigated in the present research. The criterion of the first method is cyclic plastic zone size, which is calculated from stress singularity parameters. The criterion of the second method is hot spot stress. These fatigue strength criteria are proved to be applicable to the fatigue strength assessment of practical arc-welded structural features. These criteria enable a critical point at which fatigue cracks are most likely to initiate to be specified for each type of welded joint and load. Consequently, the critical point simplifies the classification of various welded joints. Furthermore, a fatigue strength computer-aided engineering system, which includes functional engines for the evaluation of the fatigue strength of a designed shape, is proposed.     

Stress-life fatigue assessment of pipelines with plain dents

This paper presents a new algorithm for assessing the fatigue life of dented pipelines. The proposed methodology was conceived according to the current stress-life fatigue theory and design practice: it employs S–N curves inferred from tensile test material properties and uses well established methodologies to deal with the stress concentration, the mean stress and the multi-axial stress state that characterizes a dented pipe. Finite element analyses are carried out to model the denting process and to determine the stress concentration factors of several pipe-dent geometries. Using dimensional analysis over the numerical results, a non-dimensional number to characterize the pipe-dent geometry is determined and linear interpolation expressions for the stress concentration factors of dented pipelines are developed. Fatigue tests are conducted with the application of cyclic internal pressure on small-scale dented steel pipe models. In view of the fatigue test results, the more appropriate S–N curve and mean stress criteria are selected.     

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.     

EXAMINATION OF SHORT-CRACK MEASUREMENT AND MODELLING UNDER CYCLIC INELASTIC CONDITIONS

The opening and closure behaviour of short fatigue cracks is seen as one of the important phenomena which control fatigue life of components where a major part of life consists of the growth of short cracks. Therefore attempts are undertaken to experimentally assess and to model the behaviour of short cracks with respect to opening and closure. In this paper crack opening results obtained by Sunder et al. through SEM evaluation of striation patterns of 2000 series aluminium alloys are examined and compared to predictions using a model recently developed for fatigue life prediction based on fracture mechanics of short cracks. Sunder's technique for crack opening measurements involves particular load sequences with increasing and decreasing load ranges applied to notched specimens with naturally nucleated surface cracks where crack opening levels are identified by steady-state striation widths for increasing load ranges. A detailed review of Sunder's results, however, indicates a number of inconsistencies and contradictions which are discussed. Opening and closure behaviour of short fatigue cracks, in particular for inelastic conditions, is compared to predictions obtained with the above-mentioned model which incorporates a constant strain opening and closure assumption. For inelastic conditions that may develop at notches this assumption means that cracks would close at considerably lower stress levels as compared to the opening stress which becomes important when effective (local) stress-strain ranges are to be determined for fatigue life prediction under spectrum loading. The constant strain assumption is supported by a number of experimental observations from the literature as discussed in the paper. The approximative nature of this assumption and further details of the model are pointed out which show a need for further developments.     

Structural optimization procedure of a composite wind turbine blade for reducing both material cost and blade weight

A composite blade structure for a 2 MW horizontal axis wind turbine is optimally designed. Design requirements are simultaneously minimizing material cost and blade weight while satisfying the constraints on stress ratio, tip deflection, fatigue life and laminate layup requirements. The stress ratio and tip deflection under extreme gust loads and the fatigue life under a stochastic normal wind load are evaluated. A blade element wind load model is proposed to explain the wind pressure difference due to blade height change during rotor rotation. For fatigue life evaluation, the stress result of an implicit nonlinear dynamic analysis under a time-varying fluctuating wind is converted to the histograms of mean and amplitude of maximum stress ratio using the rainflow counting algorithm Miner's rule is employed to predict the fatigue life. After integrating and automating the whole analysis procedure an evolutionary algorithm is used to solve the discrete optimization problem.     

Schadensakkumulationshypothesen zur Lebensdauervorhersage bei schwingender Beanspruchung. Teil 1. – Ein kritischer Überblick—

Cumulative Damage Theories for the Prediction of Fatigue Life . Most fatigue data are determined in constant stress amplitude tests. Therefore they are not applicable directly for the prediction of fatigue life under service loads: A ?cumulative damage theory”? is necessary. For about 350 program test series (blocked 8 stress level tests) the cumulative damage sum Σ n_i/N_i at failure is calculated. The mean value of this ratio is near 1,0 and thus agrees with Miner's rule; however the scatter is extremely high. Tests in bending give significantly lower damage sums than tests under axial loads. Furthermore about 130 random and flight by flight tests are analysed. Next, modified linear damage theories are discussed and it shows that only theories which take residual stresses into account will improve the accuracy. A relative fatigue life estimation is proposed, where one test under service conditions is the basis and Miner's rule is used as a transfer function.     

Fatigue failure transition analysis in load‐carrying cruciform welded joints based on strain energy density approach

This paper details a study of the application of notch stress intensity theory to the fatigue failure mode analysis of the transition in load‐carrying cruciform welded joints. The weldment fatigue crack initiation point is difficult to predict precisely because it usually occurs in the vicinity of the weld toe or weld root. To investigate the relationship between fatigue failure location and the geometry of the weldments, we analysed the weld toe and root asymptotic notch stress fields were analysed using the notch stress intensity factors on the basis of the Williams' solution in Linear Elastic Fracture Mechanics (LEFM). Numerous configurations of cruciform joints of various plate thicknesses, transverse plate thickness, weld sizes and incomplete penetration size were used to investigate the location of the fatigue failure. The strain energy density (SED) surrounding the notch tip was introduced to unify the scalar quantity and preclude the inconsistency of the dimensionality of the notch stress intensity factors for various notch opening angles. The results of the investigation showed that the SED approach can be used to determine the transition zone for a variety of joint geometries. The validity of the SED criteria was verified by comparing the experimental results of this study with the complied results for load‐carrying cruciform welded joints reported in literature.     

The effect of overloading sequences on landing gear fatigue damage

In service, landing gear can be subject to unexpected hard landing load, which is beyond the design domain. The consequences due to overload can affect the design life of a landing gear to some extent. In this paper, the effect of overload and different loading sequences in random spectra on fatigue damage are investigated, using strain–life based fatigue analysis methods. The discussions are emphasised on the effect of loading sequences on residual stress and mean stress, especially the effect of overload on the fatigue damage of subsequent cycles. In addition, different fatigue analysis techniques in commercial fatigue analysis packages are reviewed and compared. The analysis indicates that the overload effect is stress state dependent and dominated by local residual and mean stress. A ‘Begin’ overload in a load spectrum would cause more damage in the local compressive yield area and an ‘End’ overload within a spectrum will worsen the tensile yielding area. It is suggested that the load sequence effect should be considered in common fatigue analysis if local yielding would exist before or after overloading.     

Schadensakkumulationshypothesen zur Lebensdauervorhersage bei schwingender Beanspruchung. Teil 2. – Ein kritischer Überblick—

Cumulative Damage Theories for the Prediction of Fatigue Life . Most fatigue data are determined in constant stress amplitude tests. Therefore they are not applicable directly for the prediction of fatigue life under service loads: A “cumulative damage theory” is necessary. For about 350 program test series (blocked 8 stress level tests) the cumulative damage sum Σ n_i/N_i at failure is calculated. The mean value of this ratio is near 1,0 and thus agrees with Miner's rule; however the scatter is extremely high. Tests in bending give significantly lower damage sums than tests under axial loads. Furthermore about 130 random and flight by flight tests are analysed. Next, modified linear damage theories are discussed and it shows that only theories which take residual stresses into account will improve the accuracy. A relative fatigue life estimation is proposed, where one test under service conditions is the basis and Miner's rule is used as a transfer function.     

An improved fatigue life model for mechanical components considering load strengthening characteristics

The small load has fuzziness on the strengthening and damage of the component under the action of random fatigue load. This paper introduces the two-dimensional membership function in fuzzy mathematics to characterize the relationship between stress amplitude, mean value, and damage below the fatigue limit. An exponential function is used to describe the strengthening effect. Under the two-dimensional load spectrum, the influence of various levels on the component's life is comprehensively considered, and the fatigue life prediction model under random load is proposed. Through the small sample experiment of the car swing support rod, the relevant parameters of the model are obtained. The difference between the modified two-dimensional and the two-dimensional load spectrum is compared in fatigue life prediction results. The rules of membership function selection and parameter setting are summarized, and it makes the estimation of component load spectrum life more reasonable.     

Theoretical framework for estimating a product's reliability using a variable‐amplitude loading spectrum and a stress‐based approach

An innovative approach for predicting the reliability of a structure that is subject to a variable‐amplitude dynamic load is presented. In this approach, a Gassner durability curve with its scatter is modelled using a 2‐parametric Weibull's probability density function (PDF). The trend of the Gassner durability curve is modelled with a general hyperbola equation in a log‐log scale. The hyperbola equation is applied to represent the durability curve for the 63.2% probability of fatigue failure that describes the dependency of the Weibull's scale parameter on the loading spectrum's maximum stress. Equations are derived to link the parameters of the hyperbola curve to the material's S‐N curve and the loading spectrum. The Weibull's shape parameter is estimated from the scatter of the material's S‐N curve. The proposed Gassner‐curve model is applied to calculate the fatigue reliability from the PDF of the loading spectrum's maximum stress and the PDF of the durability‐curve's amplitude stress for the selected number of loading‐cycles‐to‐failure.     

Environmental effects on fracture resistant and biaxial fatigue design of aircraft structures

This paper discusses the two interrelated fields of crack initiation and crack propagation by presenting analytical techniques for calculating fatigue damage in biaxially stressed structures along with determining safe inspection intervals for contained crack growth.The equivalent stress concept is used to derive a set of uniaxial stresses that produce the same amount of fatigue damage as the biaxial stress exposure. The distortion energy concept serves as the basis for combining alternating principal stresses by translating the uniaxial SN curves for zero mean stress into a family of concentric ellipses. The major axis bisects the principal stress axes for isotropic materials with invariant directional fatigue performance. The intercept of these ellipses with the maximum alternating principal stress axis defines the equivalent alternating stress at various cyclic lives.Empirical procedures are given for treating problems with varying principal stress directions and areas with directional dependent fatigue performance.The Goodman diagram relates alternating stresses and mean stresses at any constant cyclic life. If two uniaxial Goodman diagrams are constructed on each reference axis, a three-dimensional body can be visualized which intercepts the zero alternating stress plane in a shape identical to that described by the applicable static load criterion. The equivalent mean stress concept is based on the existence of a similarly shaped closed surface at any value of alternating stress. The intercept of this surface boundary with the maximum mean stress axis is the equivalent mean stress.Crack growth rates and residual strength of structure are important items since it is necessary to consider the possible existence of cracks. Static failsafety consists of contained crack growth for reasonable lengths of time and back-up structure providing alternate load paths. The stress intensity factor $\text{K}$, reflecting the distribution of stress in cracked structure, is the basis for computing crack growth. Baseline crack growth data for several material toughnesses and environmental exposures is required for fracture analysis. The method employed consists of calculating stress intensities for various crack lengths in the structure, these primarily being a function of geometry and applied stress distribution. The crack growth curves are constructed by integrating the baseline data for the appropriate corrosive exposure with additional factors applied to allow for scatter in growth rates and load magnitudes.     

Fatigue design of lattice materials via computational mechanics: Application to lattices with smooth transitions in cell geometry

A numerical method based on asymptotic homogenization theory is presented for the design of lattice materials against fatigue failure. The method is applied to study the effect of unit cell shape on the fatigue strength of hexagonal and square lattices. Cell shapes with regular and optimized geometry are examined. A unit cell is considered to possess a regular shape if the geometric primitives defining its inner boundaries are joined with an arc fillet, whose radius is 1% of the cell length. An optimized cell shape, on the other hand, is obtained by minimizing the curvature of its interior borders, which are conceived as continuous in curvature to smooth stress localization.For a given multi-axial cyclic loading, failure surfaces of metallic hexagonal and square lattices are provided along with their modified Goodman diagrams to assess the effect of mean and alternating stresses on the fatigue strength. In good agreement with the experimental data available in literature, the numerical results show that the shape of the unit cell has a major impact on the fatigue performance of the lattice material. For example under fully reversible tension, the fatigue strength of optimized square lattices of 10% relative density is shown to be 54% higher than that of their conventional counterparts with regular cell geometry.     

Multiaxial fatigue behaviour of a short‐fibre reinforced polyamide – experiments and calculations

This paper deals with the fatigue behaviour of a short fibre reinforced thermoplastic under multi‐axial cyclic stress. Based on experimental results on notched and plain specimens, limits of existing methods for the fatigue life estimation in the design process of components exposed to complex multi‐axial loads were investigated. During the manufacturing process of short fibre reinforced thermoplastic components, a moderately anisotropic behaviour in stiffness and strength arises. Because of the material's anisotropy, classical failure hypotheses for the assessment of multiaxial load cases do not apply. In this study, a fatigue failure hypothesis was implemented that assesses the stress components in accordance with the correlating fatigue strengths in the material coordinate system, considering potential interaction between the stress components. Striving for a verified multi‐usable fatigue life assessment method, multiaxial load cases were examined experimentally. The experimental results on unnotched and notched specimens and the fatigue life estimation on the basis of the Tsai‐Wu‐failure hypothesis will be presented.     

A fatigue model developed by modification of Gough’s theory, for random non-proportional loading conditions and three-dimensional stress fields

As a first stage, fatigue damage models proposed by some well-known references and the corresponding assumptions are discussed and some enhancements are proposed. Generally, these models are suitable for bending–torsion fatigue problems with zero mean stress and are restricted to cases where the numbers of cycles of the stress components are identical. In the present paper, a general fatigue model for the HCF regime is proposed. This model overcomes most of the shortcomings of the previous theories and is suitable for life assessment in three-dimensional stress fields. Furthermore, a different critical plane concept is introduced and a different life assessment algorithm is presented. Since results of the previous fatigue theories are generally validated by experiments done on simple components with simple loading time histories, the discrepancies exist among the various theories have not been invoked appropriately. In the current paper, validity of these theories as well as the modified versions proposed in the current paper and the new criterion is examined for more general cases with non-proportional random loadings and complicated geometries. Finally, results of the various theories are compared with the experimental results. Experimental results are prepared for both proportional and non-proportional cases. Significant enhancements are observed due to employing the proposed modifications, especially for three-dimensional stress fields and random loadings.     

Fatigue life prediction of motor-generator rotor for pumped-storage plant

To predict the fatigue life of motor-generator rotor in a pumped-storage plant, the most dangerous position of the rotor under the highest applied load was found to be at the dovetail of magnetic pole and yoke after failure analysis and stress condition analysis. In this work, two types of steel sheets used to manufacture those parts were chosen to study the microstructures and mechanical properties, especially the fatigue properties. Based on those results, some methods including widely applied Forschungskuratorium Maschinenbau (FKM) method and modified one were used to predict fatigue life of the key parts. Considering possible influencing factors, based on the fatigue theories or methods to modify mean stress and predict fatigue life, a novel method, named key part life (KPL) method, was proposed briefly. The KPL method not only suits well for the motor-generator rotor, but also provides a new idea for life prediction of parts in engineering field.     

Fatigue analysis for crack initiation

For the prediction of life leading to fatigue crack initiation, a method for performing a cycle-by-cycle local stress analysis at the stress concentration area of a structural component was developed. Elastoplastic stress-strain values along the hysteresis loop are traced for each load reversal in making the life prediction calculations. In this manner, the load sequence effect and the residual stress due to local yielding are inherently included. Neuber's rule and a linear rule were used with this method and compared. The results of life prediction were compared with test results. The use of the linear rule provided more accurate predictions than using other alternatives, including Miner's rule.