Smith–Watson–Topper Model Research Articles

Thermo-mechanical fatigue behavior and microstructure evolution of 4Cr5Mo3V hot work die steel

Thermo-mechanical fatigue (TMF) testing was used to study the fatigue behavior of 4Cr5Mo3V hot work die steel to reflect the in-service conditions. The synergistic effect of cyclic temperature and mechanical load was investigated using a strain-controlled method. Our results confirmed that the cyclic softening degree of 4Cr5Mo3V steel increased as the mechanical strain amplitude get bigger, leading to a reduction of the fatigue life. The microstructure evolution was studied before and after the TMF testing, and it was found the maximum texture strength in as-received steel decreased from 7.22 to 2.34 when the strain amplitudes was set as ± 1.1 %. Experimental evidence showed that martensite decomposition, oxidation, dislocation density reduction and carbide segregation all contributed to the final TMF failure. Severe deformation existed in the vicinity of the newly precipitated M2C carbide during the TMF process, acting as fatigue crack initiation sources due to stress concentration. Four different models were interrogated including Basquin-Coffin-Manson model, Smith-Watson-Topper (SWT) model, Ostergren model and 3SE energy model; and it was found that SWT model yielded the best fatigue life description. Nevertheless, all the four models showed reasonable fitting capability within the 2x scatter band, which proved the reliability of the experiments established in this study.

Multiaxial fatigue behavior and crack orientation prediction for steel and cast iron

This study investigates multiaxial fatigue behavior of ductile construction steel S355 and cast iron EN-GJS-500-14. Fatigue lives and crack initiation orientations are measured. Three critical plane models are evaluated for predicting fatigue life and crack initiation angles. While all models achieve decent accuracy in predicting fatigue life, crack initiation angle predictions are less satisfactory. Weak correlation is observed between the quality of fatigue life and crack orientation prediction, particularly for the Smith–Watson–Topper (SWT) and Fatemi-Socie (FS) models. The SWT model performs better in predicting fatigue life and crack angles for cast iron, while the FS model shows higher accuracy for S355. The short-crack model (SC) provides the best overall fatigue life prediction but crack orientation estimation is not superior.

Ratcheting Effect of 304 Stainless Steel Manufactured by Laser Metal Deposition Under Uniaxial Cyclic Stress

Laser metal deposition (LMD) is an advanced manufacturing technology which has become increasingly popular in recent years. The cyclic tests of 304 austenitic stainless steel (SS304) manufactured by LMD are conducted under symmetrical and asymmetrical cyclic stress. In the results, it is shown that SS304 manufactured by LMD exhibits cyclic softening/hardening and ratcheting effect under symmetrical cyclic stress. The ratcheting strain and ratcheting strain rate of the smooth specimen both increase as the cyclic stress amplitude under the asymmetric cyclic stress. The ratcheting strain and ratcheting strain rate of the smooth specimen change non‐monotonously as the mean stress increases. As the stress amplitude increases, the area of fatigue fracture becomes smaller until no fatigue crack initiation zone can be observed. In this case, only the characteristic of plastic fracture is significant. Park et al.'s model has the worst predicted accuracy. Modified Goodman equation and Smith–Watson–Topper model have the similar predicted accuracy.

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.

A physics‐informed generative adversarial network framework for multiaxial fatigue life prediction

AbstractDeep learning has achieved great success in multiaxial fatigue life prediction. However, when data‐driven models are used to describe data from physical processes, the relationship between inputs and outputs is agnostic. This paper proposes a deep learning framework combining generative adversarial networks and physical models to predict multiaxial fatigue life. This framework incorporates three life prediction equations in the loss function of generator, respectively. The results show that models with suitable physical constraints outperform neural networks in predicting results. Introducing the Smith–Watson–Topper model as a physical loss degrades the predictive performance of the physics‐informed network. On the contrary, introducing Fatemi–Socie and Shang–Wang model as physical loss improves the predictive performance of physics‐informed network. Learning using physics knowledge can lead to the ability of model to generate data that satisfy the governing equations of physics.

Multiaxial fatigue of forged Inconel 718 at room and high temperature

This work investigates the effects of high temperature on the fatigue behavior of forged Inconel 718 under axial/torsional loading conditions. To this end, strain-controlled tension, torsion, and proportional fatigue tests were performed at 20 °C and 450 °C on thin-walled tubular specimens extracted from an as-forged turbine disk. All tests were conducted with axial and shear strain ratios equal to zero, and the applied equivalent von Mises strain amplitude was such to result in fatigue lives within the range of 104 to 106 cycles, which is the typical fatigue life of the component of interest in this study. It was observed that for a given loading condition and prescribed equivalent strain amplitude, the fatigue lives of tests at 450 °C were longer than the room temperature tests. Moreover, the longest lives were observed in the torsion tests, followed by the proportional and tension tests in all temperature and prescribed equivalent strain amplitude tested. The capability of the cyclic plasticity model proposed by Chaboche in describing the cyclic response of Inconel 718 was also addressed. This model successfully simulated the stress–strain behavior of this material under all loading conditions, and for both temperatures investigated. In addition, the cracking behavior of the material was examined. For both temperatures, the tension tests failed by Mode I tensile cracks, while Mode II shear cracks were observed in the torsion and proportional tests. After a scanning electron microscope analysis, it was concluded that the transgranular propagation mode was the predominant failure mechanism of all tested conditions. The fatigue life of Inconel 718 was predicted by the Fatemi–Socie (FS) and the multiaxial version of the Smith–Watson–Topper (SWT) fatigue models, resulting in estimations within a factor-of-two and a factor-of-four, respectively. Moreover, crack directions were also determined by the critical plane models and compared with the orientation of the observed cracks. The SWT model correctly predicted the crack direction of the tension tests, while the FS model was more accurate in determining the orientation of the cracks seen in the torsion tests. None of the two models was able to correctly predict the angles of the critical plane in all tested loading conditions.

Study of the notch fatigue behaviour under biaxial conditions of maraging steel produced by selective laser melting

The current work aims to characterise the fatigue behaviour of an additively manufactured maraging steel, AISI 18Ni300. This is a class of high-strength steel widely used in biomedical, aircraft, aerospace, offshore, and military industries thanks to its good performance in terms of strength, toughness, ductility, dimensional stability, and weldability. Laser-beam powder bed fusion (additive manufacturing) is used to fabricate this type of steel and endows it with properties that make it an excellent candidate for producing prosthetic parts, thereby facilitating a reduction in manufacturing material consumption, labour, and machining time. Given the wide range of loads biomedical components are often subjected to, the current study focused on the multiaxial behaviour of this type of steel. To this end, Fatemi–Socie (FS) and Smith–Watson–Topper (SWT) critical plane methods combined with the theory of critical distances were applied to predict the fatigue life and cracking orientation of this material, with and without notches, under three biaxial loading scenarios. Cylindrical specimens were used and these were fabricated on the base plate in the vertical orientation using a linear printing system equipped with a Nd:YAG fibre laser. The building strategy involved the deposition of 40 μm thick layers at a scan speed of 800 mm/s. The two critical plane models returned good results at low life cycle fatigue but the FS model obtained better results at high life cycle fatigue. Regarding the crack angles, SWT model produced the best predictions.

A general life estimation method for overhead conductors based on fretting fatigue behavior of wires

This work proposes a new methodology to assess the fatigue life of overhead conductors. The approach relies on (i) a global stress analysis of a multistranded conductor using a 3D finite element (FE) beam-to-beam contact model and (ii) a local fatigue damage analysis of the wires that exploits the similitude concept of the S-N method. The methodology can be applied to general conductor-clamp assemblies and provide predictions about the fatigue life and the critical regions of failure of conductors. The effectiveness of the methodology is demonstrated using experimental data of an AAAC 900 MCM conductor obtained in a resonant fatigue testing bench. Different levels of tension loads and bending displacement amplitudes were considered in the assessment. Experimental strain measurements show that the conductor-clamp FE model can compute the stress distribution along the critical region of failure of the conductor with satisfactory accuracy. New fretting fatigue data together with literature data of AA6201-T81 wires are used to demonstrate that the stress-based version of the Smith–Watson–Topper model can reasonably describe the fatigue behavior of these aluminum wires and hence is used as fatigue parameter to predict the fatigue behavior of the AAAC 900 MCM. The predicted critical regions of failure and fatigue lives of the conductor-clamp assembly were in good agreement with the experimental observations. The level of accuracy obtained is acceptable for engineering calculations, indicating that the methodology can be a promising fatigue analysis tool for overhead conductors.

Fatigue life prediction and effects of cerium oxide‐filled vulcanized natural rubber on fatigue life under multiaxial loading

AbstractIn this study, a rubber dumbbell cylindrical tube specimen is used as an example to study the effect of cerium oxide on the multiaxial fatigue life of vulcanized natural rubber (rb) under different strain amplitudes and different loading paths. The cracking energy density (CED), strain energy density (SED), Smith–Watson–Topper (SWT), Chen–Xu–Huang (CXH), and Fatemi–Socie fatigue life prediction models were used to evaluate the experimental data. The results show that the multiaxial fatigue life of the specimen increases with decreasing strain amplitude, the loading path has a significant influence on the life of rb, the SWT model and the CXH model have good prediction results for both materials, and the filling of cerium oxide can improve the fatigue resistance of vulcanized natural rubber.

Multiaxial low cycle fatigue of notched 10CrNi3MoV steel and its undermatched welds

It is a fundamental step to quantify the multiaxial fatigue damage considering the complex service conditions for notched components or welded structures. In our study, multiaxial Low Cycle Fatigue (LCF) tests of notched specimens were conducted on 10CrNi3MoV high strength steel and related undermatched welds under proportional and non-proportional cyclic loadings. The characteristic states of normal/shear stress, strain and energy around notch roots are analyzed considering the elasto-plastic material behavior under low cyclic loadings by the cyclic plasticity model. The predicted fatigue life curves of the test data were constructed by five strain-based and energy-based parameters combining with the critical plane approach and notch Theory of Critical Distance (TCD). According to Smith-Watson-Topper (SWT) damage parameters definitions, the paper proposed a simplified SWT model incorporating the effect of non-proportional loading, notch energy concentration characteristics and cyclic hardening behaviors for the LCF assessment of notch specimens. The proposed model shows good agreements between predictions and test data by comparing different multiaxial fatigue damage models for notch specimens.

Fatigue reliability and hazard assessment of road load strain data for determining the fatigue life characteristics

This paper aims to assess the fatigue reliability associated for determining the fatigue life characteristics under random strain loads from various road load conditions. Fatigue failure for automotive components is mainly due to the random loads during the operating condition. However, there are still limited studies to associate fatigue reliability from fatigue life data for random loads, especially in the automotive industry. Experimentally measured random road load strain data at a sampling rate of 500 Hz in 60 s were captured from three different road conditions. The time history of the road load strain data illustrated low amplitude and high-frequency events on uneven surface roads. Fatigue life is assessed using the Coffin–Manson, Morrow and Smith–Watson–Topper models based on the Rainflow cycle counting technique. The fatigue life was estimated to be within a range of 3.21 × 102 to 1.08 × 105 cycles/block with a mean cycle to failure of 3.36 × 104 to 1.20 × 105 cycles/block. The Gumbel distribution is identified as the suitable distribution for the predicted fatigue lives data to model the reliability, hazard rate and mean cycle to failure. Hence, the distribution of reliability, cycle to failure and hazard rate is modelled and proposed for determining fatigue life characteristics under random road load strain data.

Very-high-cycle fatigue behavior of AlSi10Mg manufactured by selected laser melting: Crystal plasticity modeling

The high-cycle and very-high-cycle fatigue (VHCF) behaviors of AlSi10Mg alloy produced by additive manufacturing (AM) were studied. A crystal plasticity finite element model (CPFEM) with Voronoi tessellation was developed to simulate the cyclic plastic deformation considering defect effects. Morrow’s model and Smith-Watson-Topper (SWT) model were used to predict the fatigue life and the SWT model was in good agreement with the experimental life between 105 and 109. CPFEM simulation indicated that the accumulated cyclic plastic strain is significantly increased near a pore than that of an inclusion. The residual stress near an inclusion led to large plastic strain localization, which is harmful to fatigue performance.

Fatigue reliability assessment in time domain using stochastic-induced random stress loads due to limited experimental data

This study aims to determine the fatigue reliability of an automotive crankshaft by stochastically inducing random loads because of limited experimental data. Given the difficulties in capturing actual load–time history data from laboratory or field-testing and the lack of loading history data, the corresponding stochastic modellings are formulated. The maximum and minimum loads obtained from the automobile industry at various rotational speeds are stochastically induced to generate random loads for assessing fatigue reliability. Fatigue life is evaluated using the Coffin–Manson, Morrow and Smith–Watson–Topper models in the time domain using the rainflow cycle counting technique. Weibull distribution is identified as the best fit of the data for fatigue lives on the basis of Akaike’s information criterion and is used to model reliability and hazard rate. Reliability below 0.09 with a hazard rate of over 1.35 × 10−5 is proposed as the high-risk regions according to the mean number of cycles to failure obtained from the fatigue life models. Thus, stochastic-induced random loads can assess the hazard rate-reliability from fatigue life data to predict the durability and structural integrity of components.

Three-dimensional coupled thermo-mechanical analysis for fatigue failure of a heavy vehicle brake disk: Simulation of braking and cooling phases

In this paper, transient coupled thermo-mechanical finite element analysis of a three-dimensional model of braking pairs (brake disk and brake pads) is accomplished in order to estimate temperatures and stresses in brake disk during a braking cycle, including braking and cooling phases, and calculate fatigue life. A nonuniform distribution of temperatures is revealed on the surface of the brake disk, gradually generating surface hot spots and hot bands with temperatures up to 800 °C that lead to an uneven distribution of thermal stresses on the frictional surfaces. According to the simulations, variations in the circumferential stress, which is mainly responsible for the cracking of the brake disk, can reach up to 400 MPa in the hot spot areas, depending on the braking configurations. The numerical results are also used to estimate the fatigue life of brake disk using the Smith–Watson–Topper model. The numerical model demonstrates a high accuracy of fatigue life estimation when evaluated by prior experimental studies, signifying the effects of hot spots in reducing the service life of brake disk. Results of the fatigue life estimation show superiority to the analytical method both in the accuracy of calculation and detection of the failure location.

A Virtual-Strain-Energy-Density-Based Critical-Plane Criterion to Multiaxial Fatigue Life Prediction

The Smith–Watson–Topper (SWT) fatigue damage parameter has been discussed based on the critical-plane concept. It was found that the fatigue life prediction obtained by the SWT model tended to be unconservative during the non-proportional loading as only the tensile components on the plane of maximum principal strain range has been considered. To overcome this shortcoming, a virtual strain energy density model has been proposed using the von-Mises criterion, where the shear component on the plane of maximum principal strain range can be included during the non-proportional loading conditions. However, on the other hand, this model will be equivalent to the SWT model under the uniaxial and/or proportional loading conditions.

Fatigue life-based reliability assessment of a heavy vehicle leaf spring

Purpose This study aims to determine the reliability assessment based on the predicted fatigue life of leaf spring under random strain loading. Design/methodology/approach Random loading data were extracted from three various road conditions at 200 Hz using a strain gauge for a duration of 100 s. The fatigue life was predicted using strain-life approaches of Coffin–Manson, Morrow and Smith–Watson–Topper (SWT) models. Findings The leaf spring had the highest fatigue life of 1,544 cycle/block under highway data compared uphill (1,299 cycle/block) and downhill (1,008 cycle/block) data. Besides that, the statistical properties of kurtosis showed that uphill data were the highest at 3.81 resulted in the presence of high amplitude in the strain loading data. For fatigue life-based reliability assessment, the SWT model provided a narrower shape compared to the Coffin–Manson and Morrow models using the Gumbel distribution. The SWT model had the lowest mean cycle to failure of 1,250 cycle/block followed by Morrow model (1,317 cycle/block) and the Coffin–Manson model (1,429 cycle/block). The SWT model considers the mean stress effects by interpreting the strain energy density that will influence the reliability assessment. Research limitations/implications The reliability assessment based on fatigue life prediction is conducted using the Gumbel distribution to investigate the behaviour of fatigue random loading, where most previous studies had concentrated on a Weibull distribution on random data. Originality/value Thus, this study proposes that the Gumbel distribution is suitable for analysing the reliability of random loading data in assessing with the fatigue life prediction of a heavy vehicle leaf spring.

Reliability-based fatigue life of vehicle spring under random loading

Purpose The purpose of this paper is to analyse fatigue-life prediction based on a reliability assessment for coil springs of vehicle suspension systems using different road excitations under random loading. Design/methodology/approach In this study, a reliability assessment was conducted to predict the fatigue life of an automobile coil spring during different road data surfaces. Campus, urban and highway road surfaces were considered to capture fatigue load strain histories using a data acquisition system. Random loadings are applied on top of a coil spring where coil is fixed from down. Fatigue reliability was established as a system of correlated events during the service life to predict the probability of fatigue life using Coffin–Manson, Morrow and Smith–Watson–Topper (SWT) models. Findings Fatigue-life prediction based on a reliability assessment revealed that the Morrow model can predict a safe region of a life data point for the three road surfaces. Highway road data indicated the highest rate of reliability at 0.8 for approximately 1.69 × 105 cycles for the SWT model. Originality/value Reliability assessment of the fatigue life of vehicle coil springs is vital for safe operation. The reliability analysis of a coil spring under random loading excitations can be used for fatigue-life prediction.

Multiaxial cyclic behaviour of extruded and forged AZ80 Mg alloy

The quasi-static and cyclic response of as-extruded and closed-die extruded-forged AZ80 Mg alloy forged at 250 °C and 20 mm/sec was investigated. Servo hydraulic, fully reversed, strain controlled uniaxial “push-pull”, pure torsion, and biaxial fatigue testing were also conducted on the closed-die forged alloy. Two uniaxial loading paths (pure axial and pure shear) and three different biaxial loading paths were investigated (proportional loading, and non-proportional loading at phase angles of 45° and 90°). After forging of the as-extruded billet, the yield stress in the axial direction increased by 46%, the failure elongation by 35% and the ultimate strength by 13%. The spatial variation in both the local texture, microstructure and superficial hardness throughout the cross section of the forging was investigated and discussed. The web region in the center of the forged billet exhibited a virtually fully recrystallized and refined microstructure with intense basal texture, whereas the rib regions on each side exhibited a partially recrystallized and coarser microstructure with less intense texture. The fatigue life of the forged material in the axial direction showed dramatic improvement relative to the as-extruded material at strain amplitudes which were less than 0.35%. However, at higher strain amplitudes, there are significantly higher cyclic stresses (and associated fatigue damage) in the forged material (relative to the as-extruded), resulting in a decrease in life under fully reversed strain controlled fatigue loading. For the pure axial strain path, the total amount of strain energy density (SED) observed in the stabilized response was a function of number of cycles only, and was insensitive to material condition (as-extruded or forged). However, for the forged material, of all the strain paths investigated, only the pure shear path demonstrated a significantly different relationship of total SED vs. life. Furthermore, the amount of total SED for a given number of cycles decreases when biaxial loading is introduced, though following the same general relationship as the pure axial strain path. The effect of a decrease in total SED for a given number of cycles occurred in all biaxial strain paths, with proportional being the least prominent, then 45° and 90° out of phase being progressively more pronounced respectively. Both the Smith Watson Topper (SWT) and Jahed-Varvani (JV) models were utilized to predict the fatigue life of the uniaxial and biaxial cyclic tests. Calibration of each models intrinsic parameters were done using both of the uniaxial loading paths individually, then these same parameters were used in combination with one another to predict the life in the biaxial cases. Both the SWT and JV models are capable of giving an acceptable prediction, however the JV model’s prediction is more reliable, especially when the cyclic response has pronounced asymmetry. The biaxial fatigue response is somewhat dominated by the axial component for two significant reasons; firstly, the shape of the hysteresis in the shear direction dramatically changes based on phase angle and axial strain amplitude, whereas the axial hysteresis loop remains somewhat invariant to the presence or modulation of the other loading axis. Secondly, the initial crack propagation mode is predominantly transverse to the axial direction in all strain paths except for pure shear (which exhibits longitudinal cracking). Tensile cracking dominating the biaxial failure mode provides qualitative justification of a modification factor to an existing energy based biaxial fatigue life prediction model, enabling it to predict the life of extruded and forged AZ80 Mg reliably for a variety of different biaxial strain paths.

Effect of Precompression Deformation on the Strain-Controlled Low-Cycle Fatigue Behavior of Extruded AZ31 Magnesium Alloy

In this work, the effect of precompression along the extrusion direction on the strain-controlled low-cycle fatigue behavior of an extruded AZ31 magnesium alloy was investigated. After precompression deformation occurred, the tensile yield strength decreased, whereas the tensile yield strength and ultimate tensile strength increased gradually as precompression deformation increased. The shape of the stress–strain hysteresis of a specimen with 5% precompression deformation changed from asymmetrical to symmetrical compared with that of the as-extruded specimen. Hence, the whole process was likely dominated by twinning–detwinning behavior. Fractographic analysis revealed that the crack propagation region of the specimen with 5% precompression deformation was flatter than that of the as-extruded specimen because of the compressive mean stress and finer grains in the specimen with 5% precompression deformation. The fatigue lives of the as-extruded and precompression specimens were predicted by the Coffin–Manson model, the Ellyin energy model, the Smith–Watson–Topper model, the Fatemi–Socie model, and the Jiang model, respectively. The life predicted by the Ellyin energy model and the Jiang model was consistent with the experimental data.

A Novel Energy-Critical Multiaxial Fatigue Life Prediction for Low Cycle Fatigue under Mixed-Mode Loading

Fatigue failure evolution is a process of damage accumulation under continued stresses and forces. The mechanical component is always subjected to various loadings and the lifespan is mainly governed by fatigue. The low cycle fatigue (LCF) is a key failure mode of many components. In order to estimate the LCF life under multiaxial loadings in practical design, a modified model is proposed, based on the Fatemi-Socie (FS) and Smith-Watson-Topper (SWT) models, which considers the effects of shear and tensile behaviours. Then a novel judgment criterion is presented to distinguish the mixed-mode loadings and the procedures to employ the proposed model are also presented. Furthermore, two types of materials (TC4 and GH4169) and comparisons with the FS, Wang-Brown (WB) and redefined SWT (Re-SWT) models are employed to verify the accuracy and effectiveness of the proposed model, which has shown more reasonable predictions than the other models.