A statistical model for scatter representation in stress life curves

Fatigue life reliability often is accounted for through minimal material data. To provide this information within structural calculation, experimental data from specimen testing needs to be processed with statistical methods. The results are either mean or worst case material data. However, in a robust design environment, scatter itself must be numerically available. In this paper, fatigue test results of a nickel‐based super alloy at two temperatures are taken from literature. These data are processed according to ASTM standard E739 to identify median and standard deviation, based on a stress life curve (S—N curve) in double logarithmic coordinates first proposed by Basquin. In addition, a new method for non‐constant standard deviation is applied to the dataset. The S—N curve parameters are treated with a statistical distribution to account for scatter in the material data. The basic parameter set is perturbed by Monte Carlo simulation to generate pseudo‐scatter in the life result, which can be plotted as a Wöhler field. This pseudo‐scatter is analysed and compared to the ASTM constant standard deviation regression. Statistical methods are used to show that a realistic prediction of fatigue life is feasible using the Perturbation approach. Both models represent the literature fatigue data very well, whereas the Perturbation approach provides more flexibility. It is especially recommended for black box Monte Carlo studies of structural lifing. The Perturbation approach is additionally capable of including runouts and using other life curves than such of S—N type.     

Dauerschwingfestigkeit bei nichtsynchroner mehrachsiger Beanspruchung

Fatigue Strength under Nonsynchronous Multiaxial Stresses In [1] various multiaxial criteria for synchronous stresses as well as for combined and alternating stresses have been reviewed. This paper discusses various criteria for nonsynchronous stresses, e. g. out-of-phase stresses, nonsinusoidal stress time functions and different frequencies between stress components. The criteria aim at the predictions of high cycle fatigue only. Two groups of multiaxial criteria are considered:

• — critical plane criteria that means fatigue failure is governed by stresses on certain critical planes and
• — criteria of integral straining (Anstrengung) that means the stresses in all interference planes of a volume element effect the fatigue behaviour.

Only the last groups, i. e. Effective Shear Stress Criteria [8, 32], Shear Stress Intensity Hypothesis (SIH) [10] allow a reliable fatigue evaluation both for constant and changing direction of principal stresses. An extensive comparison between test results (phase difference, different frequencies, complex stress time functions) and prediction, according to the SIH, shows good agreement.     

SOME CREEP/FATIGUE PROPERTIES OF TYPE 316 STEEL AT 625°C

Abstract— Strain controlled continuous cycling fatigue tests are reported on three casts of Type 316 steel; the results obtained are shown to be consistent with published data. Strain controlled creep/fatigue tests are reported involving a hold period per cycle of between 0·2 and 168 h on one batch of Type 316 steel. An empirical extrapolation of the data and one involving a linear damage summation suggest that the existing Code Case N47 creep/fatigue design curve and rules are over-conservative. A stress relaxation/fatigue endurance correlation shows some promise for predictive purposes. Although many of the mechanical test and metallurgical features observed are consistent with a fundamental crack growth extrapolation approach, further consideration of detailed aspects are necessary before it can be used with confidence. It is concluded that there are no entirely reliable methods of extrapolation currently available for Type 316 steel and longer term tests are therefore essential to reduce the extrapolation uncertainties.     

Über den Sinn und Unsinn von Schwingfestigkeits-Datenbanken und -Expertensystemen

The Use and Abuse of Fatigue-Data Banks and -Expert Systems The following definitions will apply in this paper:

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Berechnung der Schwingfestigkeit festgewalzter Kurbelwellen

Predicting the fatigue strength of fillet-rolled crankshafts Since three years Darmstadt University of Technology uses finite element method for simulation of fillet rolling process. Now, together with Daimler-Benz AG, a fracture mechanics based concept has been successfully applied predicting the fatigue strength of fillet-rolled crankshafts. For these parts conventional assessment of fatigue behaviour shows several disadvantages. The new concept reduces time and costs for development and design. It consists of three parts:

• calculation of residual stresses induced by fillet rolling and affected by crankshaft and roller geometry, rolling load and work hardening data of material
• simulation of residual stress redistribution due to cyclic load
• assessment of fatigue cracks starting from notch root and propagating under compressive residual stresses by means of linearelastic fracture mechanics.

     

A Parametric Lifetime Model for the Prediction of High-Cycle Fatigue Based on Stress Level and Amplitude

The goal of this paper is to present a general parametric lifetime model for predicting fatigue behaviour at any stress level and amplitude (for example, at any combination of σ_max and σ_min pair) in the high‐cycle fatigue regime. The problem of the design of the experimental laboratory test required for such a prediction is dealt with. The surprising and relevant result is that running two groups of tests for two different constant stress levels of σ_max or σ_min is sufficient to predict the whole collection of Wöhler fields for any possible stress level. However, some combinations of tests, such as one for a fixed value of σ_max and one for a fixed value of σ_min, are shown to be insufficient. Closed formulas for obtaining any Wöhler field from the results of the experiments corresponding to the two different fixed values of σ_max or σ_min are given. Together the proposed model and lab tests allow any fatigue analysis to be performed in the current investigation. One example of application illustrates the proposed method.     

Probabilistic analysis of the uncertainty in the fatigue capacity of welded joints

This paper presents the results of a study of the uncertainty in the fatigue capacity (constant amplitude fatigue life) of welded steel joints, due to uncertainties related to geometrical and material parameters.An efficient method of probabilistic fracture mechanics analysis is described and applied. A linearelastic fracture mechanics model and the Paris-Erdogan law of crack propagation were adopted. Stressintensity factors were evaluated by employing an influence function method, which is very cost-effective. The main parameters were treated as stochastic variables. Data for weld and crack geometry of the non-load carrying fillet weld cruciform joint selected as the example joint in the study, were recorded from specimens. Other data were compiled from the literature. The uncertainties associated with the basic variables were transformed into a measure of uncertainty of the fatigue capacity by employing the Monte Carlo simulation technique. The relative contributions to the uncertainty in the fatigue capacity from the various factors were also compared.The $\text{S-N}$ data established analytically compared fairly well with test data obtained with 42 specimens. The probabilistic fracture mechanics analysis provided a sufficient sample of data to allow a test of analytical probability distributions to the fatigue life. The fit of two- and three-parameter lognormal and Weibull distributions was examined. Only the three-parameter lognormal pdf passed the chi-square test on the 5% confidence level.     

Derzeitiger Stand der Lebensdauervorhersage für Bauteile

The State of the Art in the Fatigue Live Evaluation of Components For fatigue life estimations of components many compromises must be entered in the utilization of available fatigue design data. The parameters of the chosen design data which do not fit the component to be evaluated are in most cases taken into consideration by very global factors. These factors and the inaccuracies of Miner's Rule provide only a rough estimate of the fatigue life of a component. When the component is allready available, these uncertainties can be reduced by performing a fatigue test with service like load-time histories and a relative Miner's Calculation. For the same reason the total knowledge about the service fatigue behaviour of similar components should be taken into account in the life estimation.     

Crack growth behavior and fatigue-life prediction based on worst-case near-threshold data of a large crack for 9310 steel

ABSTRACT Both experimental and analytical investigations were conducted to study crack initiation and growth of small cracks, near‐threshold growth behavior of large cracks at constant R‐ratio/decreasing ΔK and constant K_max/decreasing ΔK, respectively, for 9310 steel. The results showed that a pronounced small‐crack effect was not observed even at R = ?1, small cracks initiated by a slip mechanism at strong slip sites. Worst‐case near‐threshold testing results for large cracks under several K_max values showed that an effect of K_max on the near‐threshold behavior does not exist in the present investigation. A worst‐case near‐threshold test for a large crack, i.e. constant K_max/decreasing ΔK test, can give a conservative prediction of growth behavior of naturally initiated small cracks. Using the worst‐case near‐threshold data for a large crack and crack‐tip constraint factor equations defined in the paper, Newman's total fatigue‐life prediction method was improved. The fatigue lives predicted by the improved method were in reasonable agreement with the experiments. A three‐dimensional (3D) weight function method was used to calculate stress‐intensity factors for a surface crack at a notch of the present SENT specimen (with r/w = 1/8) by using a finite‐element reference solution. The results were verified by limited finite‐element solutions, and agreed well with those calculated by Newman's stress‐intensity factor equations when the stress concentration factor of the present specimen was used in the equations.     

Fatigue performance of Friction Stir Welded titanium structural joints

The Friction Stir Welding process for producing corner and T-joints out of 6 mm Ti–6Al–4V was developed in this effort using previous work on butt weld joints as a starting point. A limited number of corner joints were also subjected to a bending fatigue test to preliminarily assess the applicability of the process in producing fatigue critical structures. These results were also compared to predictions made by applying stress concentration factors to previously generated uniaxial butt joint test data. While additional testing is still required to obtain a higher degree of confidence in the conclusions of this study, it was found that the performance of these corner joints in fatigue could be compared to butt joint data when a geometrically based stress concentration factor is applied. Furthermore, these welded joints possessed equivalent fatigue performance relative to identical test specimens machined from wrought product forms, both bar and extrusion. Thus, from the perspective of fatigue design, this study has shown that Friction Stir Welding is able to produce structures with the same performance as currently made from wrought materials.     

Energy density zone model and fatigue life prediction considering microscopic effects

An energy density zone (EDZ) model is developed for the prediction of fatigue life. The microscopic effects can be involved in the EDZ model. Three scale transitional functions in the model are utilized to describe the trans‐scale behaviours of fatigue failure from micro‐scale to macro‐scale. Fatigue failure behaviours of a low‐alloy and ultra‐high‐strength steel material (i.e. 40CrNi2Si2MoVA steel) is investigated. Two fatigue parameters in the model are determined from the experimental S–N curves for the smooth cylinder specimens (the stress concentration factor, SCF, K_t = 1). Then, fatigue lives of notched specimens with SCFs K_t = 2 and K_t = 3 are predicted respectively by the proposed model. The predicted S–N curves are satisfactory in comparison with the experimental results. Scatter of the fatigue test data can be depicted when the microscopic effects are considered. Influences of microscopic effects on the fatigue behaviours are explored by means of numerical simulations.     

Reliability-based robust multi-objective optimization applied to engineering system design

ABSTRACT

Probabilistic and non-probabilistic methods have been proposed to deal with design problems under uncertainties. Reliability-based design and robust design are probabilistic strategies traditionally used for this purpose. In the present contribution, reliability-based robust design optimization (RBRDO) is formulated as a multi-objective problem considering the interaction of both approaches. The proposed methodology is based on the differential evolution algorithm associated with two strategies to deal with reliability and robustness, respectively, namely inverse reliability analysis and the effective mean concept. This multi-objective optimization problem considers the maximization of reliability and robustness coefficients as additional objective functions. The effectiveness of the methodology is illustrated by two classical test cases and a rotor-dynamics application. The results demonstrate that the proposed methodology is an alternative method to solve RBRDO problems.     

Simplified procedure for pavement fatigue analyses

It is commonly understood that fatigue is often a major contributory cause of pavement cracking. How the subject of pavement fatigue should be treated in highway design and analysis has been of continuing concern to highway planners. A suitable methodology for considering pavement fatigue has been elusive due to the very large number of variables in regard to pavement composition which can be encountered in practice. The simplified approach proposed here enables the computation of fatigue factors for a given mixture by comparison with previous fatigue tests on dissimilar compositions. The fatigue factors for each variable are then combined, using the uniaxial ultimate tensile strain of the given mixture, to determine the theoretical fatigue tests on dissimilar compositions. The fatigue factors for each variable are then combined, using the uniaxial ultimate tensile strain of the given mixture, to determine the theoretical fatigue life in years. A simplified illustrative example is given to show how the procedures might be utilized. The given procedures are now of limited applicability for obtaining quantitative results because of insufficient pavement fatigue data available in the literature. The procedures and data given will however enable qualitative results to be calculated.     

On the determination of the bending fatigue strength in and above the very high cycle fatigue regime of shot-peened gears

Demands on modern gearboxes are constantly increasing, for example to comply with lightweight design goals or new CO₂ thresholds. Normally, to increase performance requires making gearboxes and powertrains more robust. However, this increases the weight of a standard gearbox. The two trends therefore seem contradictory. To satisfy both of these goals, gears in gearboxes can be shot-peened to introduce high compressive residual stresses and improve their bending fatigue strength. To determine a gear’s tooth root bending fatigue strength, experiments are conducted up to a defined number of load cycles in the high cycle fatigue range. However, investigations of shot-peened gears have revealed tooth root fracture damage initiated at non-metallic inclusions in and above the very high cycle fatigue range. This means that a further reduction in bending load carrying capacity has to be expected at higher load cycles, something which is not covered under current standard testing conditions. The question is whether there is a significant decrease in the bending load carrying capacity and, also, if pulsating tests conducted at higher load cycles—or even tests on the FZG back-to-back test rig—are necessary to determine a proper endurance fatigue limit for shot-peened gears. This paper examines these questions.

     

Fatigue life prediction and failure analysis of a gas turbine disc using the finite-element method

A numerical prediction of the life of a gas turbine model disc by means of the finite‐element technique is presented and the solution is compared with an experimental rim‐spinning test. The finite‐element method was used to obtain the K solution for a disc with two types of cracks, both at the notch root of the blade insert and located in the corner and in the centre. A crack aspect ratio of (a/c) = 1 was assumed. The fracture mechanics parameters J‐integral and K were used in the assessment, which were computed with linear elastic and elastic–plastic material behaviour. Using a crack propagation program with appropriate fatigue‐creep crack growth‐rate data, previously obtained in specimens for the nickel‐based superalloy IN718 at 600 °C, fatigue life predictions were made. The predicted life results were checked against experimental data obtained in real model discs. The numerical method, based on experimental fatigue data obtained in small laboratory specimens, shows great potential for development, and may be able to reduce the enormous costs involved in the testing of model and full‐size components.     

An approach for determining an appropriate assumed distribution of fatigue life under limited data

The case of limited data implies that some unknown uncertainties may be involved in fatigue reliability analysis. For the sake of statistical convenience, for consistency with the relevant physical arguments and, most importantly, to ensure the safety in design evaluation, an approach is developed to determine an appropriate distribution, from four possible assumed distributions—three-parameter Weibull, two-parameter Weibull, lognormal and extreme maximum-value distributions. The approach makes allowance for consistency with the fatigue physics and checking tail fit effects. An application to nine groups of fatigue life data of 16Mn steel (Chinese steel) welded plate specimens shows that the lognormal distribution and the extreme maximum-value distribution may be the appropriate distributions of the fatigue life under limited data.     

Corrosive fatigue of structures with dimple holes under spectrum loading

ABSTRACT Experimental investigation and life prediction are made for structures with straight holes and dimple holes in both laboratory ambient conditions and 3.5% NaCl solution under spectrum loading. With the aid of acoustic emission, label loading and fractography technique, the crack‐growth data are obtained in both environments. Stress‐intensity factors for the corner crack emanated from the dimple hole are evaluated by three‐dimensional (3D) finite element (FE) method. Life prediction of the tested structures is made by using the modified FASTRAN‐II code on the basis of corresponding fatigue crack‐growth rate curves. It is shown that once the initial defect size a₀ is determined by one set of test data, it can be used together with the 3D crack‐growth method in order to provide accurate life prediction in alternative structure and loading condition. By comparison, life prediction by the traditional local strain method is also made which is shown to be less reliable than the 3D crack‐growth method.     

A Resource Allocation Framework for Experiment-Based Validation of Numerical Models

In experiment-based validation, uncertainties and systematic biases in model predictions are reduced by either increasing the amount of experimental evidence available for model calibration—thereby mitigating prediction uncertainty—or increasing the rigor in the definition of physics and/or engineering principles—thereby mitigating prediction bias. Hence, decision makers must regularly choose between either allocating resources for experimentation or further code development. The authors propose a decision-making framework to assist in resource allocation strictly from the perspective of predictive maturity and demonstrate the application of this framework on a nontrivial problem of predicting the plastic deformation of polycrystals.     

Packaging information system

The Packaging Information System is a basic module concerned with the creation of the expert system Risk-Engineering. The structure of this expert system was briefly described in Copenhagen at the IAPRI'92 symposium. It provides information about transport, handling and warehousing needs. The databank of this information system has the following components

• —general regulations
• —specific packaging data
• —specific goods data
• —goods and packaging testing methods

and is used to solve demanding problems, allowing the planner to concentrate on other important assignments. In combination with other modules of the expert system Risk-Engineering, it has at its disposal a range of experience and knowledge of various specialist resources.     

Statistische Auswertung von Dauerschwingversuchen an Schraubenverbindungen

Fatigue Tests on Threaded Fasteners By conducting fatigue tests on threaded fasteners the size of the transition range in the Wöhler-diagramme and the kind of distribution of failure and non-failure in this transition range was determined as a function of the stress-amplitude. On this basis it was attempted to find a suitable statistical evaluation method for the procedure and evaluation of fatigue tests on threaded fasteners regarding to the following criterions:

• Number of screws to be tested,
• reliability and precision of the achieved values,
• wasting of time at the testing machine,
• capability of extrapolation to load-levels which had not been considered during the test procedure and
• expenditure in evaluation of the test results.

The results show that the function of distribution within the transition range can be sufficiently described with the Gaussian-Normal-distribution. They show furthermore that the Boundary Technique is superior to the other two tested evaluation methods (stair-case-method and arc sin method) as far as the above mentioned criterions are concerned.