Smith-Watson-Topper Parameter Research Articles

Smith–Watson–Topper Parameter in Partial Slip Bimodal Oscillations of Axisymmetric Elastic Contacts of Similar Materials: Influence of Load Protocol and Profile Geometry

Based on a very fast numerical procedure for the determination of the subsurface stress field beneath frictional contacts of axisymmetric elastic bodies under arbitrary 2D oblique loading, the contact mechanical influences of loading parameters and contact profile geometry on the Smith–Watson–Topper (SWT) fatigue crack initiation parameter in elastic fretting contacts with superimposed normal and tangential oscillations are studied in detail. The efficiency of the stress calculation allows for a comprehensive physical analysis of the multi-dimensional parameter space of influencing variables. It is found that a superimposed normal oscillation of the contact can significantly increase or decrease the SWT parameter, depending on the initial phase difference and frequency ratio between the normal and tangential oscillation. Written in proper non-dimensional variables, the rounded flat punch always exhibits smaller values of the SWT parameter, compared to a full paraboloid with the same curvature, while the truncated paraboloid exhibits larger values. A small superimposed profile waviness also significantly increased or decreased the SWT parameter, depending on the amplitude and wave length of the waviness. While both the load protocol and the profile geometry can significantly alter the SWT parameter, the coupling between both influencing factors is weak.

An equivalent strain energy density model for fatigue life prediction under large compressive mean stress

In this work, a modified Smith-Watson-Topper (SWT) model is proposed for the consideration of large compressive and tensile mean stresses. Firstly, the maximum normal stress in the original SWT model is replaced with equivalent stress amplitude, and the SWT parameter is thereafter interpreted as equivalent strain energy density (ESED). The newly proposed ESED model gives improved prediction results in fatigue life, especially under conditions with large compressive mean stress. Secondly, the applications of different mean stress correction (MSC) models are investigated with their limitations carefully examined. In order to improve the ESED model with higher accuracy, a new exponential MSC model is proposed. Moreover, an additional parameter concerning the dependency of material on mean stress is proposed. With the exponential MSC model incorporated, the ESED model is validated with experimental data from several different materials, and shows obviously improved prediction results compared with SWT model and some recent life prediction models.

Effects of Mean Stress and Multiaxial Loading on the Fatigue Life of Springs

In this paper, the effects of mean stress and damage accumulation on the fatigue life of springs are theoretically studied. The study examines the fatigue life of homogeneously stressed material subjected to cyclic loading. The mean stress of a load cycle is non-zero. Goodman and Haigh diagrams are commonly used for estimating fatigue life in engineering applications. Alternatively, conventional hypotheses by Smith–Watson–Topper, Walker and Bergmann have been successfully used to describe uniaxial cyclic fatigue with non-zero mean value over the whole range of the fatigue life. However, the physical characteristics of the mean stress sensitivities in these hypotheses are different. The mean stress sensitivity according to Smith–Watson–Topper is identical for all materials and stress levels. This weakness reduces the applicability of the Smith–Watson–Topper parameter. At first glance, the mean stress sensitivities according to Walker and Bergmann are diverse. The mean stress sensitivities depend upon two different additional correction parameters, namely the Bergmann parameter and the Walker exponent. The possibility of fitting the mean stress sensitivity in these hypotheses overcomes the significant drawback of the Smith–Watson–Topper schema. The principal task of this actual study is to reveal the dependence between the Bergmann parameter and the Walker exponent, which leads to a certain mean stress sensitivity. The manuscript establishes the simple relationship between both fitting parameters, which causes the equivalent mean stress sensitivity for the Bergmann and Walker criteria. As known from the state of the technology, fabrication and operation yield several impacts with a significant influence on the fatigue life of springs. One effect deals with the sequence of low and high stress amplitudes and amplitude-dependent damage accumulation. Particularly, during the load cycle a certain microscopical creep occurs. This creep causes damage. The accumulation hypothesis for creep damage is introduced. The hypothesis can be verified experimentally.

Using the Smith-Watson-Topper Parameter and Its Modifications to Calculate the Fatigue Life of Metals: The State-of-the-Art.

The Smith-Watson-Topper parameter (SWT) in its original form was designed to estimate the fatigue life of metal materials in a uniaxial load state (tension–compression) in the range up to fatigue crack initiation, with non-zero mean values. This parameter is based on the analysis of both stress and strain. Therefore, the stress–strain criterion is the focus, rather than the energy criterion. This paper presents the original SWT model and its numerous modifications. The first part presents different versions of this parameter defined by the normal parameters. Then, it presents versions defined through the tangent parameter and the most promising parameter defined through the tangent and normal parameters. It was noted that the final form of the equivalent value is defined either by stress or by an energy parameter. Therefore, the possible characteristics from which the fatigue life can be determined are also presented.

Influence of Wear Profile Geometry on Critical Plane Fatigue Crack Initiation Criteria in Plane and Axisymmetric Elastic Fretting Contacts

The subsurface elastic stress fields in plane and axisymmetric contacts with friction under oscillating tangential loading are calculated via a very robust, high-precision method, which operates with appropriate superpositions of analytic solutions for the respective Hertzian contact problems. Based on the stress fields, two critical plane fatigue crack initiation criteria—the Smith-Watson-Topper (SWT) parameter and the Findley parameter—are evaluated for three types of contact profile geometries: (unworn) parabolic contact, the partial slip limiting wear profile of an initially parabolic contact, and truncated parabolic contact. Appropriate scaling laws are introduced to formulate a general solution in terms of non-dimensional variables. The crack initiation criteria are determined in the full subsurface loading plane. It is found that the truncated profile—which may originate from sliding wear—has practically the same local distribution of crack initiation criteria as the unworn profile, despite the (weak) stress singularity at the edge of the flat face. The partial slip limiting wear profile, on the other hand, exhibits a strong edge stress singularity at the boundary of the permanent stick zone, the crack initiation criteria are drastically increased (and theoretically infinite). Also, while for the unworn and truncated profiles high values of the crack initiation criteria are extremely localized around “hotspots” at the surface, for the partial slip limiting wear profile they reach much deeper into the subsurface material. This offers a new explanation for the dominance of fatigue failure in the partial slip regime of fretting. The differences between plane and axisymmetric cases are generally small. The SWT parameter is generally more localized than the Findley parameter.

Modeling detrimental effects of high surface roughness on the fatigue behavior of additively manufactured Ti-6Al-4V alloys

This article presents a fatigue model that can robustly capture the effect of high surface roughness on the fatigue crack initiation of additively manufactured Ti6Al4V (AM Ti64) alloys in the moderate cycle fatigue regime based on nonlinear finite element (FE) analyses and the theory of critical distances. We propose two methods to use surface measurements of AM components to create FE models, viz., surface topography of the component is explicitly represented in the FE models or a simplified geometrical model, which has only a single sinusoidal-shaped notch, is proposed to replace the surface topography in the FE models. The geometrical parameters of the simplified model are derived based on the MOTIF method (ISO 12085) and its parameters are determined by using the leave-one-out cross-validation method. In the moderate cycle fatigue regime, the stress applied to components is below the yield stress, but the high surface roughness acts as a stress raiser and causes local plasticity at surface valleys. Thus, a nonlinear hardening elasto-plasticity model is employed in the FE models to capture the cyclic mechanical behavior of AM Ti64 alloys. Afterward, the fatigue analyses are performed by employing our in-house C++ software within which fatigue indicator parameters (FIPs) are computed by post-processing the finite element results. In the present work, the Smith-Watson-Topper (SWT) parameter is used as an FIP and is computed at every element in the FE mesh, i.e., the local FIP. Subsequently, to account for the stress gradient effect in the proposed fatigue model, the SWT parameter is averaged over a so-called critical area to compute a nonlocal FIP. The physical fidelity of the proposed fatigue model is shown by a good agreement between the predicted fatigue life cycles based on the nonlocal FIP and the corresponding experimental data. Moreover, the predicted fatigue cycles obtained from the simplified geometrical model also yield good accordance to the experimental data, thus we can model the effect of the surface roughness on the fatigue properties of AM Ti64 in an efficient way.

A coupled 3D wear and fatigue numerical procedure: Application to fretting problems in ultra-high strength steel wires

This work presents a coupled 3D wear and fatigue numerical procedure for fretting problems in ultra-high strength steel wires that combines Archard’s wear equation with the Smith–Watson–Topper parameter to predict crack nucleation. For total life prediction, a mode I crack propagation based on the weight function method was used. To assess fretting fatigue lifetime, several experimental campaigns were run. The numerical results were in good agreement with the fretting fatigue experimental results. Thus, this study provides a 3D numerical methodology to study the combined effects of wear and fatigue in fretting with a case study in ultra-high strength steel wires.

A unified approach to model the effect of porosity and high surface roughness on the fatigue properties of additively manufactured Ti6-Al4-V alloys

In this article, we propose a model that can account for the effect of porosity and high surface roughness on the fatigue crack initiation of AM Ti6Al4V alloys in moderate and high cycle fatigue regimes. Within these fatigue regimes, the applied force to the component is below the yield stress, however, defective features, viz., porosity and high surface roughness, can act as stress raisers. As a consequence, local plasticity can occur. To capture this phenomenon, a nonlinear isotropic kinematic hardening elasto-plasticity model is employed in our finite element (FE) model. For creating the geometry of the FE models, inputs from fractography analyses and surface roughness measurements are needed. From fractography analyses, the shape of pores formed by gas bubbles during manufacture appears quite regular. Thus, these pores are modeled as circles in FE models. The size of these pores and their distance to a free surface of the tested specimens are extracted from Scanning Electron Microscope images. Moreover, it has been mentioned in the literature that statistical parameters of surface roughness cannot fully describe the detrimental effect of this type of defect to the fatigue life of the associated component. Thus, in our FE model, the surface topography, which was measured using stylus-based profilometer, is explicitly modeled. The finite element results are then post-processed by our in-house software to extract the Smith–Watson–Topper (SWT) fatigue indicator parameter (FIP). The SWT parameter is calculated at each element centroid of the FE mesh, i.e., the local indicator. Afterward, an average value of the SWT parameter over a so-called critical area whose center is located at the considered centroid is also calculated, i.e., the average indicator. The results show that the local SWT indicator is too conservative in predicting the fatigue life of the AM Ti64 alloys while the average SWT one can provide good results.

Investigation of crack initiation path in AA7050-T7451 under fretting conditions

Abstract Early crack orientation in 7050-T7451 aluminum alloy was investigated under fretting conditions. New tests were performed in the partial slip regime to observe the influence of the tangential load amplitude, mean bulk stress, and pad radius on the crack orientation. Three critical plane fatigue parameters were combined with different stress averaging methods to estimate the crack initiation direction. The normal stress-based Smith–Watson–Topper parameter provided better crack orientation estimates than the shear stress-based parameters. The experimental observations indicated a small increase in the early crack angle when the tangential load amplitude was raised.

Applications of Neuber’s and Glinka’s notch plasticity correction rules to asymmetric magnesium alloys under cyclic load

The asymmetric cyclic behaviour of rolled ZEK100-F magnesium alloy has been considered, while approximating its notch stress-strain response through applying Neuber’s and Glinka’s rules. To this end, a numerical procedure has been developed and scripted in Matlab that makes use of a hysteresis regeneration model in association with plane stress/strain notch approximate rules as well as Smith-Watson-Topper (SWT) fatigue model. Output from the Matlab routine in terms of notch root strain estimations are validated using constant and variable amplitude load-controlled cyclic experimental results, obtained via digital image correlation (DIC) technique, on ZEK100-F plate specimens with a central circular hole. Glinka’s rule is shown to give comparatively closer approximations. Applying Glinka’s rule, further validation of modelled notch response is adequately done by estimating fatigue life based on SWT parameter and comparing it with DIC-measured crack initiation life.

Study on the Effect of Laser Quenching on Fretting Fatigue Life

Laser quenching hardening is one of the most used surface treated technologies. In order to study the effect of laser quenching on the fretting fatigue life, fretting fatigue experiments of TC11 (Ti-6.5Al-1.5Zr-3.5Mo-0.3Si) titanium alloy specimens with different surface conditions were carried out on a special hydraulic servo fatigue test system. The experimental results showed that laser quenching hardening has a good performance in increasing the fretting fatigue lives of the TC11 alloy. However, the effects of laser quenching on fretting fatigue are more obviously at low stress level than at high stress level, the fretting fatigue life was increased by 110.78% at low stress level and 17.56% at high stress level, respectively. Based on the critical plane approach, the traditional SWT (Smith–Watson–Topper) parameter was modified and used to describe the fretting fatigue life of the TC11 alloy after hardening by the consideration of the variations of the hardening layer’s elastic modulus. Compared with the experimental results, all the errors of the predicted results lied in the error band of two.

A low cycle fatigue life model for a shot peened gas turbine disc alloy

Turbine disks in gas turbines are subjected to cyclic load at high temperature, making, especially the fir tree type blade attachments, susceptible to fatigue. Shot peening of the fir tree attachments may be used to increase the fatigue life by introducing compressive residual stresses. In the current study, both polished and shot peened notched specimens made from alloy 718 were subjected to low cycle fatigue at 450–550 °C. The shot peening generally increased the fatigue life, although the effect diminished for high loads. It was shown that the effect of shot peening could be handled as mean stress effects in a life model based on a Smith–Watson–Topper (SWT) type parameter, σmaxΔε/2. A material model which captured the mean stress was set up to get the SWT parameter at the notch root. It was shown that thermal relaxation of residual stresses and initial strain hardening from cold work could be excluded from the finite element analysis used to establish the mean stress; this since the plasticity in the first cycle dominated the plastic deformation of the specimen. Overall, the SWT-based life model worked satisfactorily. However, the prediction of correct mean stresses at 550 °C proved somewhat difficult as the degree of mean stress relaxation at this temperature varies widely in available literature data.

THE EFFECT OF NOTCHES ON THE FATIGUE LIFE OF A NICKEL-BASE GAS TURBINE DISK MATERIAL

Gas turbine disks carry significant load under high temperatures and may be subject to fatigue failure. Disks contain several notches in the form of the fir tree blade attachments. Low cycle fatigue tests were performed on blunt notch compact tension specimens made from alloy 718. The results indicated that notch support needed to be incorporated not to cause an overly conservative life prediction. The notch support diminished as the plastic strain range decreased, indicating that notch support is only present in the low cycle fatigue regime. A critical distance approach was applied to account for the notch support. An equation relating the critical distance to the notch root stress was derived. The chosen life model was formulated in terms of a variation on the Smith–Watson–Topper (SWT) parameter. The modified SWT parameter taken at the critical distance was used in a life model calibrated for smooth specimens to successfully predict the fatigue life of notched specimens.

Fretting fatigue optimization of piston skirt top surface of marine diesel engine

Composite pistons are often used in highly rated marine diesel engines. Fretting usually occurs on the mating surfaces of piston crown and skirt due to alternating loads. A finite element contact model is introduced to calculate the temperature and stress distribution in the composite piston of a marine diesel engine. The Archard model and Smith–Watson–Topper parameter (a prediction parameter of fretting fatigue, also called SWT parameter for short), which is used as fretting wear and fatigue criteria, are calculated according to the stress and strain variation and relative slip on the contact surface. The model has been validated by previous cylindrical–flat contact experiments. The effects of shape of contact face and pretension of bolts on fretting performance have been analyzed. To reduce the possibility of fretting failure of the composite piston, the expression of the generating line of the piston skirt contact surface has been designed by Theory of elasticity. The parameters of the generating line have been optimized with nonlinear sequential quadratic programming and finite element mesh updating method. The optimization results show that the fretting fatigue parameter SWT on the optimized contact surface can be reduced by more than 35.6%, which means the longer fatigue life of the pistons. Some suggestions for designing contact surfaces have also been proposed. In the end, the design was proved by durability tests of the engine.

Prediction of fatigue crack initiation under biaxial loading

This investigation revisits biaxial fatigue experiments carried out with the nickel-based superalloy termed Waspaloy. Recently, yield criteria extended to multiaxial fatigue and stress based approaches were analysed and their performance to correlate the biaxial test data was evaluated. It was concluded that despite their reliable results, the parameters did not properly represent the physical behaviour of the material. In this context, an extension of this study was executed considering the strain based critical plane approaches proposed by Fatemi-Socie (FS) and Smith- Watson-Topper (SWT). The first parameter presented overly conservative predictions with large scatter of results. In contrast, more accurate predictions were obtained with the SWT parameter.

Fretting fatigue life estimation using fatigue damage gradient correction factor in various contact configurations

A fretting fatigue life estimation method that takes into account the stress gradient effect was developed by the authors [Journal of Mechanical Science and Technology, 28 (2014) 2153-2159]. In the developed method, fatigue damage value at the cracking location is corrected with fatigue damage gradient and the corrected value is compared directly with the plain fatigue data for life estimation. In other words, the correction factor is the ratio of plain fatigue damage to fretting fatigue damage at the same life and a function of fatigue damage gradient. Since reliability of the method was verified only for cylinder-on-flat contact configuration in the previous study, the present study extends application of the method to flat-on-flat contact configurations by developing the correction factor for both the contact configuration. Fretting fatigue experiments were conducted to obtain fatigue life data for various fretting pads. Finite element analyses were conducted to evaluate the Smith-Watson-Topper (SWT) fatigue damage parameter in the cracking region. It is revealed that the SWT parameter in fat-on-flat contact configuration decreases exponentially away from the surface as in cylinder-on-flat contact configuration, and thus the SWT gradient at the surface can be evaluated reliably. Moreover, it is found that decrease in the SWT parameter around the cracking location can be expressed by piecewise exponential curves. If the gradient of SWT at the surface is used as a representative value of SWT gradient, it is impossible to establish functional relationship between the SWT gradient and the correction factor for both the contact configurations although it was possible for cylinder-on-flat contact configuration. However, if weighted average of the SWT gradient values obtained from each exponential curve in the piecewise exponential curve is used as a representative value, the correction factor for both the contact configurations becomes a function of the SWT gradient, and thus fretting fatigue life in both the contact configurations can be estimated with a single correction function.

Determining the Walker exponent and developing a modified Smith-Watson-Topper parameter model

Mean stress effects significantly influence the fatigue life of components. In general, tensile mean stresses are known to reduce the fatigue life of components, whereas compressive mean stresses are known to increase it. To date, various methods that account for mean stress effects have been studied. In this research, considering the high accuracy of mean stress correction and the difficulty in obtaining the material parameter of the Walker method, a practical method is proposed to describe the material parameter of this method. The test data of various materials are then used to verify the proposed practical method. Furthermore, by applying the Walker material parameter and the Smith-Watson-Topper (SWT) parameter, a modified strain-life model is developed to consider sensitivity to mean stress of materials. In addition, three sets of experimental fatigue data from super alloy GH4133, aluminum alloy 7075-T651, and carbon steel are used to estimate the accuracy of the proposed model. A comparison is also made between the SWT parameter method and the proposed strainlife model. The proposed strain-life model provides more accurate life prediction results than the SWT parameter method.

Comparison of the cracking energy density and the Smith–Watson–Topper parameters in predicting fretting fatigue lifetime of a steel/aluminum alloy contact

ABSTRACTMany multiaxial fatigue parameters are available to estimate the onset of the crack initiation in mechanical components subjected to fretting fatigue conditions. This study focuses on the ability of the cracking energy density parameter to predict the fretting fatigue life. To estimate this, obtained predictions are compared with those given by another commonly used parameter, namely the Smith–Watson–Topper parameter. First, fretting fatigue experiments were achieved using a new designed setup with a mono‐contact configuration (aluminum/steel). A finite element model was used to compute the stress/strain fields around the contact zone. Because of the high stress gradient in the contact zone, the estimates of the two fatigue parameters, when using the mechanical quantities on the most loaded material point, lead to too conservative predicted values. It was therefore necessary to define a kind of process zone in which crack nucleation takes place. Using an averaging method to compute stress and strain in this zone, the obtained results show a quite good agreement between the estimated fatigue life and experimental data, whatever the used fatigue indicator. The size of this zone was then compared with the material microstructure and seems to be in the same magnitude that the average grain size.

Fracture and fatigue in osteocytes

Fatigue is a common mode of mechanical failure which occurs when a material is subjected to repeated cycles at a strain level less than that needed for monotonic fracture. Fatigue has been observed and measured in many different materials but, until recently, not in cells. We devised a novel experiment which allowed us to create both monotonic failure and fatigue in the cellular processes of osteocytes within samples of bone (Dooley et al., European Cells and Materials 2014). In the present paper, we describe the results of further experiments and a computer simulation, which has allowed us to estimate the strain history of each sample tested and thus present, for the first time, strain/life data for cells. Failure occurred during the first cycle at strains of 0.1–0.2; at lower strains failure occurred after a number of cycles which depended inversely on the applied strain range. Scatter in the strain/life data was reduced when we allowed for the effects of mean stress using the Smith–Watson–Topper parameter. We confirmed that aspects of our experimental method (the types of microcrack used and the testing of fresh versus frozen samples) did not affect the results. Such information is useful because many cell types, including the cellular processes of osteocytes, experience cyclic strain in vivo.

On deviatoric interpretation of Neuber’s rule and the SWT parameter

In this paper a deviatoric interpretation of Neuber’s rule and Smith–Watson–Topper (SWT) parameter is presented and discussed. It is found that the deviatoric formulation of Neuber’s rule results in inelastic strains at notch-root that are between estimations obtained from traditional Neuber’s rule and the equivalent strain energy density method of Molski and Glinka. Based on an energy interpretation and some analogy with the Neuber’s rule a deviatoric interpretation of the SWT parameter called SWTD is discussed. It is found that for positive mean stresses and moderate negative mean stresses the traditional SWT parameter and the proposed SWTD parameter yield similar results. On the other hand, for large compressive mean stresses with a stress ratio R<−2 the proposed SWTD parameter demonstrates a fairly good correlation while the original SWT parameter results in wide scatter. It can be noted that results obtain with both the deviatoric Neuber’s rule and the SWTD parameter do not involve or require any additional constants or fitting parameters.