Fatigue Life Calculation Methods Research Articles

Use of non-destructive testing methods in a new one-specimen test strategy for the estimation of fatigue data

The comprehensive characterisation of the change in the metallic materials’ microstructure due to an applied load is of prime importance for the understanding of basic fatigue mechanisms or more general damage evolution processes. If they are fully understood, advanced fatigue life calculation methods, which are far away from linear damage accumulation models, can be realised providing even more than only “classic fatigue data”.Within the scope of this paper, it is shown how the potential of non-destructive testing methods, the digitalisation of the measurement techniques as well as signal processing can be combined with a new one-specimen test strategy in order to achieve a gain in information concerning the fatigue behaviour with a simultaneous reduction of experimental effort and costs. The result is therefore not only a considerable advantage with respect to conventional determined Woehler- or S-N-data, but also to established short-term procedures, due to the possibility to separate several material effects by means of data analysis and to use this for fatigue life calculations based on the results of one single specimen.The SteBLife (step-bar fatigue life) approach is a new short-time calculation method developed at the Chair of Non-Destructive Testing and Quality Assurance at Saarland University, which allows to provide S-N-data on the basis of a small number of fatigue tests.For the first investigations in accordance to the new SteBLife approach, temperature measurements by means of an infrared camera were used. The change in temperature is directly related to deformation-induced changes of the microstructure in the bulk material and is considered to represent the actual fatigue state. Within the framework of this paper, the SteBLife procedure was validated on specimens from normalised SAE1045 steel.

Effect of mean shear stress on the fatigue strength of notched components under multiaxial stress state

The effect of a static and intermittent shear stress on the HCF strength of two quenched and tempered steel grades used to produce shafts in crane industry was studied on notched specimens (Kt,bending=1.7 and 2.7) for being representative of critical areas. Three main loading configurations were considered: C1=rotative bending (RB), C2=RB and static torsion and C3=RB and mean torsion fluctuating in blocks to simulated start and stop cycles. In this last case the first investigated mean shear stress, τm, was equal to the material yield stress in pure shear, τy. Additional C3 variants were investigated too where τm was equal to 0.3τy and 0.7τy. It has been shown that τm has little effect on the rotating bending HCF strength at 3×106 cycles. For both steel grades and notch geometries studied, the results of the fatigue tests confirm that the influence of a static torsion on the rotating bending HCF strength is negligible even when the static torsion level is equivalent to the yield strength of the material in torsion. However, in intermittent service conditions (C3), it has been shown that torsion cycles can affect significantly the HCF strength in RB, depending on the notch acuity and torsion level. Elastic-plastic cyclic finite element analysis has been done for the two specimen geometries to assess the stabilized stress-strain state at the notch root and then compute the fatigue life by using the multiaxial HCF models proposed by: Fatemi-Socie, Smith-Watson-Topper, and Wang-Brown. The Palmgreen-Miner hypothesis was used to cumulate damage mainly because of its simplicity for design purposes. According to our simulations and with the chosen cumulative damage rule, none of the tested fatigue life calculation methods give good results for all the load cases. The efficiency of the tested methods is very dependent on both the material and the load cases. However, the Smith-Watson-Topper approach gives the best results whereas the Fatemi-Socie model leads to the more conservative ones except in one load configuration.

Advanced Evaluation of Fatigue Phenomena Using Non-Destructive Testing Methods

The comprehensive characterization of the change in metallic materials’ microstructure due to an applied load is of prime importance for the understanding of basic fatigue mechanisms or more general damage evolution processes. If those mechanisms and processes are to be understood to a much greater extent, advanced fatigue life calculation methods being far away from linear damage accumulation models, have to be realized providing more than “classic fatigue data” only. Among others the PHYBAL (physically based fatigue life calculation) method including current enhancements and a thereon-based development named SteBLife (step-bar fatigue life approach) have been developed over the last 10 years. These methods allow the efforts in experimentation to be reduced by more than 90 % and therefore offer the possibility to take further fatigue relevant parameters into account. This therefore allows a variety of S,N-curves dependent on those fatigue relevant parameters to be generated with those methods easily establishing a multidimensional dataset. To just name a few examples of those parameters such as the influence of temperature, loading conditions, geometry as well as thermal and mechanical ageing processes on the fatigue behavior can now be calculated in accordance to a process being straightforward leading to an important step with regard to improving the efficiency of assessing structural components. Consequently, safety factors can be defined more in accordance to structural needs, being of highest interest with respect to the increasing number of ageing infrastructure such as highways, bridges or others. A lot of this ageing infrastructure has a strong need to be managed with respect to its structural integrity and the engineering community therefore tries the residual life of this infrastructure to be determined as appropriate as possible. In that context non-destructive testing parameters are increasingly considered to characterize a metallic material’s microstructure allowing more precise information to be obtained regarding the actual damage condition and the integrity of a component. The paper will address the high capability of non-destructive testing techniques for the evaluation of damage evolution processes also with respect to mechanism based fatigue as well as residual life calculations according to PHYBAL and SteBLife.

Relative fatigue life prediction of high-speed and heavy-load ball bearing based on surface texture

In this paper, a new calculation method of relative fatigue life considering surface texture on high-speed and heavy-load ball bearing is presented. Rolling bearing quasi-dynamics, micro-TEHL analysis, non-Gaussian surface simulating technique and stress analysis with FEM are combined to obtain the relative fatigue life. The maximum subsurface stress with the new method are compared with data in inference, the relative error is 3.9%, which caused by decreasing surface stress under high speed. The non-Gaussian surface textures effect on surface pressure and shear stress are studied, which show transverse texture perpendicular to entrainment direction is helpful to form film because of the increasing hydrodynamic effect, and decrease the pressure and shear stress, but longitudinal texture has an opposite effect. Non-Gaussian parameters effects on relative fatigue life are researched, which display relative fatigue life increase with the increase of transverse texture, and decrease with the increasing longitudinal texture. The increasing skewness and curtosis can bring the decrease of relative fatigue life, but the relative fatigue life is beneficial as skewness is negative and curtosis is small, which is helpful for bearing life. Finally, the whole relative fatigue life of inner race and balls are given.

Frequency-domain fatigue life estimation with mean stress correction

Two frequency-domain fatigue life calculation methods are presented which take into account the impact of the mean stress effect. The emphasis is set on the algorithm for fatigue life assessment of the method proposed by the authors. It is supplemented with a mean stress effect correction. Correction method is based on the direct transformation of the zero mean stress Power Spectral Density (PSD) due to mean stress. The method is verified on the basis of own results for the S355JR steel. The authors analyze five models for the designation of the probability density function used in the calculation process. The results are presented in the form of probability distributions after PSD transformation and the calculated fatigue life is being compared with the experimental life in fatigue comparison graphs. An analysis of the choice of a mean stress correction model is also widely discussed and a fatigue life estimation is also performed. The method proposed by the authors is being compared with the Kihl–Sarkani method for mean stress correction in frequency domain.

Cyclic deformation behaviour, microstructural evolution and fatigue life of duplex steel AISI 329 LN

This paper summarises fatigue results obtained on the duplex steel AISI 329 LN (German designation 1.4462). For the characterisation of the fatigue behaviour, the mechanical stress–strain hysteresis loops, the temperature change and the evolution of the electrical resistance were monitored. Transmission electron microscopy was performed to investigate the microstructural changes caused by the fatigue loading. The data were used to apply the fatigue life calculation method “PHYBALLIT”. This procedure requires only one load increase test and two constant amplitude tests for a timesaving and material-efficient assessment of S–N (Woehler) curves. The method has already been successfully applied to different carbon and austenitic steels as well as lightweight materials. The results show an excellent agreement between the conventionally determined and the calculated fatigue lifetimes. This agreement is rationalized on a microstructural basis.

Mean Stress Effect Correction in Frequency-domain Methods for Fatigue Life Assessment

Two fatigue life calculation methods are presented. One defined in the time domain and the second one defined in the frequency domain – both supplemented with a mean stress effect correction. The method is verified on the basis of own results for the S355JR steel. The authors analyze six models for the designation of the probability density function (PDF) of stress amplitudes used in the calculation process. The results are presented in the form of probability distributions before and after PSD transformation and the calculated fatigue life's are being compared with the experimental ones in fatigue comparison graphs.

The Life Prediction of Transmission Tower Based on Multi-Scale Analysis

In order to study the residual fatigue life of 500 kv transmission tower under load conditions, a multi-scale finite element model of transmission tower is established. By simulating time course of wind load, using Miner fatigue cumulative damage theory and linear S-N curve, the calculation method of transmission towers fatigue life is established. The research shows that the multi-scale model can better simulate the stress and strain state of the transmission tower, and can predict the remaining service life of the transmission tower .The research has important significance and application value for the safe operation of the transmission lines.

Fatigue life prediction of a rubber material based on dynamic crack growth considering shear effect

This paper suggests a fatigue life calculation method (A fatigue life calculation method is suggested) for rubber components based on the dynamic crack growth considering shear effect. Dynamic tearing tests were carried out, and the crack length was measured using an optical microscope to calculate the dynamic crack growth rate which characterizes and determines the fatigue life. The algorithm was numerically implemented in finite element code, ABAQUS standard, by using the user subroutine and applied to several rubber components. In the finite element analysis, deformation mode of an element was classified into tension and shear, and a weighting factor was multiplied to a strain energy density according to the degree of shear strain. Tension and compression of an elliptic dumbbell specimen was simulated in order to verify the material parameters of the suggested fatigue life prediction equation and to enhance the reliability of the algorithm. Finally, the fatigue life of a vehicle suspension bushing was calculated and compared with test. There were good agreements in the failure location and the magnitude of the fatigue life.

Investigation on the Fatigue Characteristic in Support Structure of HL-2M Tokamak

In order to obtain enhanced plasma parameters a complete new tokamak HL-2M is now under construction in Southwestern Institute of Physics. To assure the structural safety of the device for the entire operation cycle, one of the most important issues is the lifetime-limiting effects due to the pulsed operation mode. Fatigue is one of the major failure modes to be considered in mechanical design, and pulsed operation imposes stress with significant alternating components on the support structure (SS). Therefore, the reliability of the whole device is strongly affected by the stress and fatigue characteristic of the SS as the interface structure. This article introduces the SS design and details the fatigue life calculation methods based on the different characteristics of the sub-structures. The fatigue life in hazardous areas of the toroidal field coils anti-torque structure (TFCs-ATs) has been determined by non-linear analysis results. And with the stress-time history data of the vacuum vessel & poloidal field coils support structure (VV&PFCs SS), the fatigue analysis of the hot spots has been completed based on rain-flow counting method and linear cumulative damage method. The calculated minimum fatigue life on TFCs-ATs and VV&PFCs SS is 4.743E+05 and 1.805E+06 cycles, respectively. And the calculated fatigue life on sub-structures can meet the required life for HL-2M tokamak: 1.0E+05 cycles.

Non-local energy based fatigue life calculation method under multiaxial variable amplitude loadings

Reliable design of industrial components against high cycle multiaxial fatigue requires a model capable of predicting both stress gradient and load type effects. Indeed, taking into account gradient effects is of prior importance for the applicability of fatigue models to real structures. In this paper, a fatigue life assessment method is proposed for proportional and non-proportional multiaxial variable amplitude loadings in the range 104–107 cycles. This method derives from the fatigue criterion initially proposed by Palin-Luc and Lasserre (1998) [2] and revisited by Banvillet et al. (2003) [16] for multiaxial constant amplitude loading. The new proposal consists of a complete reformulation and extension of the previously cited energy based fatigue strength criteria. It includes two major improvements of the existing criteria. The first one consists in a fatigue criterion for multiaxial variable amplitude loadings while only constant amplitude loadings were considered in the above cited works. The second one is an extension to an incremental fatigue life assessment method for proportional and non-proportional multiaxial variable amplitude loadings. No cycle counting technique is needed whatever the variable amplitude loadings type considered (uniaxial or multiaxial). The predictions of the method for constant and variable amplitude multiaxial loadings are compared with experimental results on specimens from literature and from new experiments on a ferrito-perlitic steel. The above mentioned method has been implemented as a post-processor of a finite element software. An application to a railway wheel is finally presented.

Comparative analysis of fatigue life calculation methods of C45 steel in conditions of variable amplitude loads in the low- and high-cycle fatigue ranges

ABSTRACT In the paper [1] assumptions for fatigue life calculations in the low- and high- cycle fatigue ranges of metal alloys, have been formulated. Three calculation methods: that expressed in stresses, strains and a mixed (stress-strain) one, have been there presented. In this paper results of fatigue life calculations of C45 steel performed in line with the above mentioned methods have been described, and their comparative analysis has been made. The calculations have been carried out for two-level and multi-level load programs of the varying parameters: maximum load within a load program and different values of spectrum filling factor. The comparative analysis of the results of fatigue life calculations in compliance with the above mentioned methods makes it possible to assess differences in the results and depenendence of the differences on values of load program parameters.

Physically Based Fatigue Assessment of the Nodular Cast Iron ASTM 80‐55‐06 (EN‐GJS‐600) at Different Testing Frequencies

AbstractFor the fatigue assessment of the nodular cast iron ASTM 80‐55‐06 (EN‐GJS‐600) stress‐controlled fatigue tests were performed at testing frequencies of f = 5 and 150 Hz. Mechanical (f = 5 Hz), temperature, electrical resistance, and frequency (f = 150 Hz) measurements during cyclic loading provide the possibility to get detailed information about fatigue processes like cyclic hardening or graphite‐matrix debonding. Temperature measurements are well suitable to evaluate the influence of the testing frequency on the cyclic deformation behavior. Increasing testing frequencies result in higher values of the change in temperature caused by the increasing heat dissipation per second. On the basis of the measured data from only three fatigue tests the fatigue life calculation method “PHYBALLIT” (Load Increase Tests) can be applied on the investigated cast iron. Woehler (S–N) curves calculated for testing frequencies of 5 and 150 Hz yield an excellent accordance with conventionally determined ones. The application of this short‐time procedure leads to enormous scientific and economic advantages.

A Calculation Method of Vibration Fatigue Life with Coupling Effect

There are different modes of damage in any engineering structures, and most of them are cracks. In order to study the influence of coupling effect on the fatigue life, a calculation method of structure vibration fatigue life with crack propagation is proposed. In analysis, a series of finite element model with crack of different length is built to simulate the crack propagation, and Paris equation is employed to calculate the vibration fatigue life by stepwise method. The crack initiation life is got based on the change law of natural frequency from test results, and the total life is calculated in the end. Results indicate that the simulation results identical with the experimental results well.

Fatigue Life of Main Shaft Bearing of Direct Drive Wind Turbine

A calculation method of fatigue life for main shaft bearing of direct drive wind turbine was proposed. The statics models of the bearing were established and a set of equilibrium equations were obtained. By solving the equilibrium equations, the displacements of the inner ring were obtained, and the rolling element loads were calculated further. Based on the load distribution of the rollers, the fatigue life of the bearing was calculated and the influences of the clearances on it were researched. Results show that the clearances of the bearing can influence its service life distinctly. Zero axial clearance is recommended for the bearing.

Manufacturing influences on the fatigue properties of quenched and tempered SAE 4140 specimens

To analyse interactions between the manufacturing process chains, its design, variations in material properties, especially the microstructure and the resulting component properties, specimens with tension screw geometry were machined with specific varying process chains. According to the specific process chain the surface integrity and consequently the fatigue behaviour of the specimens is influenced in a characteristic manner. The cyclic deformation behaviour of these components can be benchmarked with conventional strain measurements as well as with high-precision temperature and electrical resistance measurements. The development of temperature-values provides substantial information. Furthermore, electrical resistance measurements enable the monitoring of proceeding fatigue damage during scheduled maintenances without any mechanical load. The physically based fatigue life calculation method “PHYBAL” was modified to calculate the lifetime.

“PHYBAL” a Short‐Time Procedure for a Reliable Fatigue Life Calculation

AbstractThe reliable calculation of the fatigue life of high‐strength steels and components requires the systematic investigation of the cyclic deformation behaviour and the comprehensive evaluation of proceeding fatigue damage. Besides mechanical stress‐strain hysteresis measurements, temperature and electrical resistance measurements were used for the detailed characterisation of the fatigue behaviour of the steel SAE 4140 in one quenched and tempered, one normalised, one bainitic and one martensitic condition. To guarantee optimal operation conditions the new fatigue life calculation method “PHYBAL” on the basis of generalised Morrow and Basquin equations was developed. It is a short‐time procedure which requires the data of only three fatigue tests for a rapid and nevertheless precise determination of S‐N (Woehler) curves. Consequently, “PHYBAL” provides the opportunity to reduce significantly experimental time and costs compared to conventional test methods.

Fatigue behaviour and lifetime calculation of the cast irons EN-GJL-250, EN-GJS-600 and EN-GJV-400

The current paper focuses on the cast irons EN-GJL-250 (ASTM A48 35B), EN-GJS-600 (ASTM 80-55-06) and EN-GJV-400, which are often used as structural materials for internal combustion engines and components of the wheel suspension and in the wind energy industry, e.g. for rotor hubs. Light and scanning electron microscopic investigations were done to characterise the individual microstructure, e.g. different graphite precipitates, in particular lamellar graphite (EN-GJL-250), nodular graphite (EN-GJS-600) and compacted graphite (EN-GJV-400). In stress-controlled load increase and constant amplitude tests at ambient temperature, mechanical stress-strain hysteresis, temperature and electrical resistance measurements were performed to characterise the fatigue behaviour of the investigated materials. All measured data depend on microstructural changes due to plastic deformation processes in the bulk of the specimens and the interfaces between matrix and graphite. This data represent the actual fatigue state. The cyclic deformation behaviour is dominated by cyclic hardening processes and graphite-matrix debonding.The physically based fatigue life calculation method “PHYBAL” was modified to the specific requirements of more inhomogeneous materials like cast irons. On the basis of fatigue data determined in only nine fatigue tests, the enhanced method “PHYBALSB” allows the calculation of Woehler (S-N) curves for different probabilities of failure (Scatter-Bands). This shorttime procedure results in a reduction in experimental time up to 90% and leads to enormous scientific and economic advantages.

Influences of the manufacturing processes on the surface integrity and the resulting fatigue behavior of quenched and tempered SAE 4140

To analyze interactions between single steps of process chains, variations in material properties, especially the near-surface microstructure and the resulting mechanical properties, specimens with tension screw geometry were machined with five different typical process chains. The resulting microstructures were characterized with light optical and scanning electron microscopy, microhardness measurements as well as X-rays. The different process chains and their parameters lead to different developments of the microstructure and the resulting residual stresses. The particular process chain influences the surface integrity and consequently the fatigue behavior in a characteristic manner.The plastic strain amplitude as well as high precision temperature and electrical resistance measurements can be used to evaluate the fatigue properties of specimens with tension screw geometry. The development of the temperature provides substantial information with respect to cyclic load dependent changes in the microstructure. The load- and cycle-dependent change of the electrical resistance is a function of the specific electrical resistance, which is directly influenced by the defect structure and defect density of the material. Areas and process chains critical in respect to fatigue can be reliably identified. The measured values can be used as input data for the physically based fatigue life calculation method “PHYBAL” with a very limited number of specimens. Even though the geometry is more complex than a standard fatigue specimen, the calculated lifetimes are in a very good accordance with the conventionally determined S-N curves.

A fatigue life calculation method for structural elements made of D16CzATW aluminium alloy

A fatigue life calculation method for structural elements made of D16CzATW aluminium alloyIn the calculating of fatigue life of structural elements the methods based on hypotheses of fatigue damage summation are commonly applied. In using the methods, apart from choice of an appropriate hypothesis, it is necessary to know a loading spectrum which usually constitutes a set of sinusoidal cycles of variable parameters (Sa, Sm), as well as fatigue characteristics in the form of Wöhler fatigue diagram, as a rule. Knowledge of the above mentioned data is low during structural design process as designed material objects and possibility of performing measurements are lacking.Hence in this work a calculation method of fatigue life of structural elements, based on the relations between fatigue life diagrams determined in constant-amplitude conditions (Wöhler diagrams) and those obtained under programmed or random loads, is described. The proposed method was experimentally verified by using results of fatigue tests on structural elements made of D16CzATW aluminium alloy.