An investigation of the fatigue of CK45 steel in the as‐received state and after pre‐fatigue deformation

Fatigue failure, ratcheting behaviour and influence of pre‐fatigue on fatigue behaviour were investigated under uniaxial cyclic loading for CK45 steel at room temperature. The fatigue life was recorded for various stress ratios, and then, three mean stress models were considered. The Walker model showed an acceptable accuracy in comparison with Smith–Watson–Topper and Park et al. models. The ratcheting strains were measured for various loading conditions in order to evaluate the impact of mean stress, stress amplitude and stress ratio on ratcheting behaviour. The experimental results showed that the ratcheting strain increased with increasing mean stress, stress amplitude and stress ratio. In addition, the results of the post‐ratcheting‐fatigue tests showed that although the fatigue life decreased with increasing pre‐ratcheting strain (the ratcheting strain that is accumulated in pre‐fatigue), the loading condition that pre‐fatigue experiments were conducted has a significant effect on subsequent fatigue behaviour.     

Fatigue behaviour and modelling of talc‐filled and short glass fibre reinforced thermoplastics,including temperature and mean stress effects

Effects of temperature and mean stress on fatigue behaviour of talc‐filled polypropylene (PP‐T) and short glass fibre reinforced polypropylene (PP‐G), polyamide‐66 (PA66), and a blend of polyphenylene ether and polystyrene (PPE/PS) were investigated. Load‐controlled fatigue tests were conducted under positive stress ratios (R = 0.1 and 0.3) and at several temperatures (T = 23, 85 and 120 °C). Larson–Miller parameter was used and a shift factor of Arrhenius type was developed to correlate fatigue data at various temperatures. Effect of mean stress on fatigue life was significant for some of the studied materials; however, for the PPE/PS blend no effect of mean stress was observed. Modified Goodman and Walker mean stress equations were evaluated for their ability to correlate mean stress data. A general fatigue life prediction model was also used to account for the effects of mean stress, temperature, anisotropy and frequency.     

Einfluss der Porosität auf die Schwingfestigkeit von Proben und Bauteilen aus Aluminiumdruckguss

Influence of Porosity on Fatigue Strength of Aluminium Die‐Cast Specimens and Components Aluminium die‐casting is widely used in the automotive industry. Brackets, engine blocks, wheels and suspension arms etc. are typical applications. Due to the gases contained in the melt, more or less spherical pores arise in the cast components during the cooling procedure, usually with a higher concentration in the middle. The distribution of the pores depends both on the casting condition and on the form of the components and is stochastic. In the past, the simple way is often chosen for the fatigue life estimation of aluminium die‐casting: The fatigue strengths of the material, e.g. in the form of S‐N curves, are determined by an unnotched specimen which are then used in the fatigue calculation. However, the application of these data to real components with notches leads in many cases to fatigue life estimations which are by far too conservative. In the present paper a simple geometrical model of pores is presented. Using this model, the notch stress caused by a pore can be estimated. The behaviour of pores in a real component with notches will be treated. It will be shown that the mentioned conservative nature of the fatigue life prediction and the apparent notch insensitivity of aluminium die‐casting can be explained by the facts that the stress distribution in a real component, contrary to an unnotched specimen, is inhomogeneous and that the porosity density on the surface is often low.     

Lebensdauerberechnung gekerbter Bauteile auf Basis der elastisch‐plastischen Schwingbruchmechanik

Fatigue life calculation of notched components based on the elastic‐plastic fatigue fracture mechanics The life of notched components is subdivided into the pre‐crack, or crack‐initiation, and crack propagation phases within and outside notch area. It is known that a major factor governing the service life of notched components under cyclic loading is fatigue crack growth in notches. Therefore a uniform elastic‐plastic crack growth model, based on the J‐Integral, was developed which especially considers the crack opening and closure behaviour and the effect of residual stresses for the determination of crack initiation and propagation lives for cracks in notches under constant and variable‐amplitude loading. The crack growth model will be introduced and verified by experiments.     

Effect of mean stress on fretting fatigue of Ti-6Al-4V on Ti-6Al-4V

Fretting fatigue tests of Ti‐6Al‐4V on Ti‐6Al‐4V have been conducted to determine the influence of stress amplitude and mean stress on life. The stress ratio was varied from R=−1 to 0.8. Both flat and cylindrical contacts were studied using a bridge‐type fretting fatigue test apparatus operating either in the partial slip or mixed fretting regimes. The fretting fatigue lives were correlated to a Walker equivalent stress relation. The influence of mean stress on fretting fatigue crack initiation, characterized by the value of the Walker exponent, is smaller compared with plain fatigue. The fretting fatigue knockdown factor based on the Walker equivalent stress is 4. Formation of fretting cracks is primarily associated with the tangential force amplitude at the contact interface. A simple fretting fatigue crack initiation metric that is based on the strength of the singular stress field at the edge of contact is evaluated. The metric has the advantage in that it is neither dependent on the coefficient of friction nor the location of the stick/slip boundary, both of which are often difficult to define with certainty a priori.     

Effects of mean stress and stress concentration on fatigue behavior of short fiber reinforced polymer composites

An experimental study was conducted to evaluate the effect of mean stress on fatigue behavior of two short glass fiber reinforced thermoplastic composites and the effect of stress concentration on fatigue behavior of an unreinforced and a short glass fiber reinforced thermoplastic. Load‐controlled fatigue tests were conducted on unnotched (smooth) specimens at R ratios of ?1, 0.1, and 0.3 in different mold flow directions or fiber orientations and at a range of temperatures between ?40 and 125 °C. Effect of mean stress on fatigue life was found to be significant at all temperatures. Several mean stress parameters including modified Goodman, Walker, and Smith–Watson–Topper were evaluated for their ability to correlate mean stress data. A general fatigue life prediction model was also used to account for the effect of mean stress, temperature, and fiber orientation. Notched fatigue tests of an unreinforced polymer and a short glass fiber thermoplastic composite were also conducted using plate type specimens with a central circular hole and with or without the presence of mean stress. Effect of stress concentration was found to be considerable, with or without mean stress and in both the longitudinal and transverse directions. The commonly used Neuber's rule for metallic materials, nonlinear finite element analysis, as well as critical distance approaches were utilized for notch deformation and fatigue life analyses.     

Analyse der Wirkung von Kerben,Mittel‐ und Eigenspannungen auf die Schwingfestigkeit des hochumgeformten Werkstoffbereichs von Spaltprofilen

Analysis of the effect of notches, mean and residual stresses on the fatigue strength of severely deformed material areas of linear flow split profiles The results of fatigue experiments on specimens extracted from the highly deformed area of linear flow split profiles are presented. The Focus is on the effect of mean stresses and notches, which is influenced by the previous forming process. The residual stress state inside a component as well as inside specimens is described. By numerical analyses considering residual stresses their effect on fatigue life can be analysed. Using Weibulls Weakest‐Link Appoach parameters, which were derived by testing smooth specimen are transferred to notched ones.     

Deterministic Processing of Complex Multiaxial Fatigue Load Data on a Tubular Specimen with Hole

A study of the use of deterministic fatigue life prediction methods for a set of multiaxial experimental data on broad‐band random loading applied to a tubular specimen with a hole is presented. There is a discussion of the applicability of stress‐based predictions and strain‐based predictions based on the linear cumulative rule under current conditions. The only feasible criteria finally chosen for the application are strain‐based methods for analysing the fatigue life until fatigue crack initiation. Several methods differing in the damage parameter and application of the mean stress effect (MSE) are evaluated. The MSE is optimised so that a comparison of the predicted and experimental data have the least scatter and similar mean values. The results are presented, and the most promising method (by Erdogan and Roberts) has been selected. The positive properties of Walker mean stress correction and the failure of SWT and Landgraf methods are commented on.     

A stress-based method to predict lifetime under multiaxial fatigue loadings

This paper extends to low/medium‐cycle fatigue a stress‐based method recently proposed by the same authors for high‐cycle multiaxial fatigue assessments. By considering the plane of maximum shear stress amplitude coincident with the microcrack initiation plane, the method requires the calculation both of the maximum shear stress amplitude and the maximum normal stress relative to the same plane. Multiaxial fatigue life estimates are made by means of bi‐parametric modified Wöhler curves, which take into account the mean stress effect, the influence of the out‐of‐phase angle and the presence of notches by using a generalization to multiaxial fatigue of the fatigue strength reduction factor K_f. Approximately 700 experimental data taken from the literature are used to demonstrate that the method is a useful tool to summarize fatigue strength data of both smooth and notched components, subjected to either in‐phase or out‐of‐phase loads. Finally, a simple practical rule for the calculation of the multiaxial fatigue strength reduction factor is proposed.     

Evaluating a strain energy fatigue method using cyclic plasticity models

For the development of constitutive equations that describe the behaviour of materials under cyclic plastic strains, different kinds of formulations can be adopted. Recently, an energy‐based fatigue damage parameter has been developed to present energy‐fatigue life curves using a calculation of the total strain energy. In this study, the damage criterion is examined by calculation of the plastic strain energy from stress–strain hysteresis loops in the cyclic plasticity models under condition of multi‐axial fatigue. These cyclic plasticity models are the Garud multi‐surface model and the Chaboche nonlinear kinematic hardening model. The models are briefly explained and the general features of their computational procedure are presented. Then, the hysteresis loops of these models will be obtained and the fatigue lives are predicted and compared to experimental data by the ratio of predicted life to experimental life. Consequently, a weighting factor on shear plastic work is presented to decrease the life factors.     

Mean stress and ratcheting corrections in fatigue life prediction of metals

Ratcheting occurs easily because of the presence of mean stress during the stress‐control fatigue of engineering components. For ductility exhaustion dominated fatigue failure, a new fatigue life prediction model is developed by introducing the mean ratcheting strain rate to incorporate the effects of ratcheting and mean stress on fatigue life. The prediction accuracy of the proposed model was compared with that of the generalised damage parameter, Xia–Kujawski–Ellyin, Walker and Goswami models. Specifically, the model predictions and tested lives were compared using nine sets of experimental data from the literature. In the statistical analysis of these five models, the proposed model provides the highest accuracy and robust life predictions with the lowest model prediction errors.     

A Walker exponent corrected model for estimating fatigue life of metallic materials in loading with mean stress

Mean stress significantly influence the fatigue life predictions of metallic materials. The Walker mean stress equation with its additional material parameter w provides good predictions for a wide range of materials. Unfortunately, additional tests are necessary to determine the Walker exponent w. In order to overcome this shortcoming, for aluminum alloys, the Walker exponent w was correlated linearly with the sum of ultimate tensile strength and true fracture strength. Then, a Walker exponent corrected effective strain energy density criterion was developed by incorporating the Walker mean stress equation into the strain life curve. The capability of fatigue life prediction for the developed model was checked against the tested data of 304 L stainless steel, SAE 1045 steel, 7075‐T651 aluminum alloy, and Incoloy 901 superalloy, and comparisons were also performed by using the Lv's Walker exponent corrected model. The developed model provides more satisfactory results, especially for the considered materials in loading with mean stress.     

Uniaxial ratcheting behavior and fatigue life models of commercial pure titanium

The uniaxial fatigue and ratcheting behavior of commercial pure titanium (CP‐Ti) was investigated by asymmetric cyclic stress‐controlled experiments at room temperature. The effects of mean stress, stress amplitude, stress ratio, and peak stress on ratcheting behavior and fatigue life were discussed. It was found that increasing mean stress, stress amplitude, and peak stress or decreasing stress ratio reduced fatigue life and promoted ratcheting behavior. The applicability of different fatigue life models was analyzed, and a new stress ratio‐related failure model was proposed based on the exponential increase of fatigue life with stress ratio. Among all the models investigated in this study, the exponential stress ratio‐related model has more advantage in fatigue life predictions for CP‐Ti under ratcheting‐fatigue interaction.     

Werkstoffauswahl für schlagartig und zyklisch belastete metallische Bauteile

Material Selection for Impact and Fatigue Loading The structural durability of components is dominated mainly by the geometry, i.e. notches. Compared with the impact resistance of forged components from ductile materials high impact values can be realized by an appropriate shaping also using less ductile cast materials. Creep deformations can be suppressed in presence of notches. The strength level of the base material remains for stress concentrations above K_t = 2.5 and for the welded state without influence on the fatigue behaviour. If sharp notches cannot be avoided by a new design, benefits from high‐strength materials can be taken only in connection with surface treatments which introduce high compressive residual stresses. Principally, advantages from high‐strength materials can be gained for unwelded components only by reduction of the stress‐concentration and in case of welded joints by smoothening or removal of the weld notches and in case of spot welds by transferring of the failure location outside of the nugget.     

Biaxial fatigue for proportional and non‐proportional loading paths

In order to study the use of a local approach to predict crack‐initiation life on notches in mechanical components under multiaxial fatigue conditions, the study of the local cyclic elasto‐plastic behaviour and the selection of an appropriate multiaxial fatigue model are essential steps in fatigue‐life prediction. The evolution of stress–strain fields from the initial state to the stabilized state depends on the material type, loading amplitude and loading paths. A series of biaxial tension–compression tests with static or cyclic torsion were carried out on a biaxial servo‐hydraulic testing machine. Specimens were made of an alloy steel 42CrMo4 quenched and tempered. The shear stress relaxations of the cyclic tension–compression with a steady torsion angle were observed for various loading levels. Finite element analyses were used to simulate the cyclic behaviour and good agreement was found. Based on the local stabilized cyclic elastic–plastic stress–strain responses, the strain‐based multiaxial fatigue damage parameters were applied and correlated with the experimentally obtained lives. As a comparison, a stress‐invariant‐based approach with the minimum circumscribed ellipse (MCE) approach for evaluating the effective shear stress amplitude was also applied for fatigue life prediction. The comparison showed that both the equivalent strain range and the stress‐invariant parameter with non‐proportional factors correlated well with the experimental results obtained in this study.     

Monotonic and low cycle fatigue behaviour of 2024‐T3 aluminium alloy between room temperature and 300 °C for designing VAWT components

In the present study, the results of the monotonic tension tests and low cycle fatigue tests performed on aluminium alloy EN AW‐2024‐T3 under various operating temperatures are presented in order to assess the fatigue behaviour of the aluminium alloy under evaluated temperatures. Monotonic tests were performed to determine the influence of temperature on mechanical properties of the material. The aim of cyclic tests was to acquire the parameters required for Manson–Coffin equation in order to plot strain–fatigue life curves. Moreover, stress–strain behaviour of the alloy and the cyclic hardening behaviour were evaluated using Ramberg–Osgood equation. Finally, P_SWT‐damage parameters for each temperature have been calculated for further investigation of the effects of the temperature on fatigue life using acquired data while taking the account of mean stress effect into calculations. Variations in the experimental data due to various test temperatures are presented for both monotonic and cyclic tests.     

Multiaxial fatigue criterion for a high‐density polyethylene thermoplastic

The multiaxial fatigue behaviour of a high‐density polyethylene was investigated at room temperature and constant frequency. As a consequence of the mode of failure, an end‐of‐life criterion for fatigue tests is discussed in the first part of the work, in order to define the number of cycles to failure. Based on force controlled fatigue tests under tension, compression and torsion at two stress ratio, a multiaxial fatigue criterion including the stress‐ratio effect is proposed for the fatigue design of this polymer. This criterion is based on the maximum and mean values of the second invariant of the stress tensor.     

Requirements for stress gradient‐based fatigue assessment of notched structures according to theory of critical distance

Notches, local stress raisers within structural components, are one of the most important locations for fatigue crack initiation. It is well known that fatigue is governed by the effective stresses in the vicinity of notches. Within this study, differences in prediction accuracy between different types of theory of critical distance methods, that is, point and line methods, are systematically investigated in conjunction with a sensitivity study regarding mesh refinement, assumed strength hypothesis and material behaviour. For this purpose, a finite element analysis parameter study on notched structures is performed and recommendations for the application of stress gradient methods are presented. Difference in effective stress of up to 30%, and hence a significant difference in fatigue life (e.g., 185% for a slope of S‐N curve of k = 4), is found for typical notch shapes, for example, in welded joints.     

A high-cycle fatigue life model for variable amplitude multiaxial loading

A high‐cycle fatigue life model for structures subjected to variable amplitude multiaxial loading is presented in this paper. It treats any kind of repeated blocks of variable amplitude multiaxial loading without using a cycle counting method. This model based on a mesoscopic approach is characterized by the following features: (i) the choice of a damage factor related to the accumulated mesoscopic plastic strain per stabilised cycle; (ii) the use of a mesoscopic mechanical behaviour taking into account the fatigue mechanisms such as plasticity and void growth. This behaviour is a von Mises elastoplastic model with linear kinematic hardening and hydrostatic stress dependent yield stress. The fatigue life model has six parameters identified with one SN curve and two fatigue limits. In‐phase and out‐of‐phase experimental tests from the literature are simulated. The predicted fatigue lives are compared to experimental ones.     

Fatigue life prediction for stainless steel welded plate CCT geometry based on Lawrence''s local-stress approach

In the present study, the effect of welding process and procedure on fatigue crack initiation from notches and fatigue crack propagation in AISI 304L stainless steel welds was experimentally investigated. Full penetration, double-vee butt welds have been fabricated and CCT type specimens were used. Lawrence's local-stress approach (a two-stage model) is used to predict the fatigue life. The notch-root stress method was applied to calculate the fatigue crack initiation life, while the fatigue crack propagation life was estimated using fracture mechanics concepts. The fatigue notch factor is calculated using Lawrence's approach. Constant amplitude fatigue tests with stress ratio, R=0 were carried out using 100 kN servo-hydraulic DARTEC universal testing machine with a frequency of 30 Hz. The predicted lives were compared with the experimental values. A good agreement has been reached. It is found that the weld procedure has a stronger effect on lives to initiation than on propagation lives.