Tensile Mean Stress Research Articles

Damage mechanisms of Ti60 under different uniaxial/multiaxial thermo-mechanical loading modes

The fatigue experiments for titanium alloy Ti60 under different uniaxial/multiaxial thermo-mechanical loading modes found that the combined action of high temperature and tensile stress can cause the debonding of the second phase strengthening particles between grain boundary, reducing the ability to resist deformation of Ti60, which leads to a decrease in the fatigue life of the material. In addition, mean tensile stress increases the ability of cracks to break through intergranular barriers and the non-proportional additional hardening caused by multiaxial loading exacerbates the formation of microcracks. Both will increase the fatigue damage of the material. The fatigue damage mechanism identified in this investigation can reasonably explain the fatigue life law under multiaxial loading at high temperature, uniaxial and multiaxial thermo-mechanical fatigue loadings.

In-plane biaxial fatigue life prediction model for high-cycle fatigue under synchronous sinusoidal loading

The unique advantage of in-plane biaxial loading is no rotation of the maximum principal stress during cyclic loading, which has a distinct effect on fatigue life. This study aims to propose a life prediction model for in-plane biaxial fatigue encompassing both in-phase and out-of-phase conditions. For synchronous sinusoidal loadings, an equivalent stress expression is derived using the integral method, accounting for the influences of shear and normal stresses across all planes. The equivalent stress is then compared to a reversed uniaxial constant amplitude loading to predict fatigue life. To validate and compare the model, in-phase and out-of-phase in-plane biaxial fatigue experiments were conducted using 24 nickel-based superalloy cruciform specimens at temperatures of 420℃, 550℃, and 600℃. The results show that the proposed model is superior to conventional stress-invariant based models, with most results staying within the ± 2 error bands. Using the proposed model, the effects of mean tensile stress, biaxiality and phase shift are discussed. Additionally, a novel non-proportional factor is introduced to enhance multiaxial fatigue life prediction by distinctly separating the effects of principal stress and its directional variations.

Effect of strain ratio and pre-strain on the low-cycle fatigue behavior of 4130X steel at different strain amplitudes

This study investigates the impacts of strain ratio and pre-strain on the low-cycle fatigue properties and microscopic damage mechanisms of 4130X steel across varying strain amplitudes. Under symmetric loading, initial cycles at low strain amplitudes demonstrate clear peak/valley stress hardening followed by cyclic softening in later stages of fatigue. In contrast, the hardening behavior vanishes at higher strain amplitudes. Increasing strain ratio and pre-strain cause the initial hardening behavior at low strain amplitudes to gradually disappear. Additionally, at lower strain amplitudes, fatigue life decreases as strain ratio and pre-strain rise, attributed to substantial tensile mean stress. Microscopic examination reveals that symmetric cyclic loading at low strain amplitudes releases stress concentrations caused by quenched and tempered processing and reduces both dislocation density and localized plastic strain. Conversely, at higher strain ratios and pre-strains, increased tensile mean stresses not only intensify dislocation multiplication, resulting in high dislocation density, but also activate multi-slip system, leading to dislocation cross-slip. Moreover, at a high strain amplitude of 0.45 %, pre-strain aids in martensite recovery and promotes dislocation annihilation during recovery, thus inducing cyclic softening. Finally, the fatigue lives under varied loading conditions are compared with the fatigue design curve prescribed by ASME VIII-II code.

Mean Stress Correction in Low Cycle Fatigue Life of High Strength Steels

Fatigue strength of welded joints varies depending on the shape, filler metal, welding procedure, and post-treatment method. In addition, mean stress affects the fatigue behavior in terms of stress ratio. Typically, it is well known that tensile mean stress tends to decrease fatigue life while compressive mean stress increase fatigue life. There are various methods to incorporate the mean stress effect in fatigue strength, but there are relatively few correction methods in compressive mean stress, especially in low cycle fatigue regime.</br>In this study, a load-based fatigue test was conducted to evaluate the effect of mean stress on the welded joints of High Yield strength steel(HY Steel) with T-joint shape. The effect of the mean stress on the welded part of HY Steel with a T-joint shape was investigated using stress-based mean stress correction methods and strain-based mean stress correction methods. When the effective mean stress approach, which can correct compressive mean stress and tensile mean stress, is applied to HY Steel with a T-joint shape, it shows accurate correction result than stress-based mean stress correction method and strain-based mean stress correction method. Sensitivity parameters to consider mean stress for HY steel are presented.

Mean Stress Correction of S45C Carbon Steel Based on Crack Growth Concept (Proposal of Non-Closure Model)

Abstract Influence of the tensile mean stress on fatigue life and fatigue limit was investigated for carbon steel. Uni-axial fatigue tests were conducted under stress and strain-controlled conditions at room temperature. The fatigue life and fatigue limit were reduced by applying the mean stress for the same stress amplitude. The fatigue life exhibited a better correlation with the strain range than with the stress amplitude. Increase in strain range caused by applying the mean stress correlated well with the decrease in the fatigue life. It was proposed that the mean stress effect on the fatigue life was brought about by the change in crack growth rate caused by applying the mean stress. The mean stress enhanced crack opening and accelerated the crack growth. The reduction in the fatigue limit was also brought about by the same effect. It was shown that the effective strain range considering crack closure effect gave good prediction of fatigue life and fatigue limit with and without the mean stress.

High-cycle and very-high-cycle fatigue of an additively manufactured aluminium alloy under axial cycling at ultrasonic and conventional frequencies

Along the building direction, the fatigue behavior of an additively manufactured (AM) aluminium (AlSi10Mg) alloy was investigated in high-cycle and very-high-cycle regimes by using conventionally electromagnetic resonance and ultrasonic vibration with axial loading frequencies of ∼110 Hz and ∼20 k ± 500 Hz, respectively. No frequency effect was observed on the resulted fatigue strength and the fractography up to 108 cycles at stress ratio R = –1. All cracks initiated at AM pores and the dominating one prefers shifting from specimen surface to subsurface with growing very-high-cycle fatigue (VHCF) lives. As the tensile mean stress increases, fatigue strength sharply drops in high value regime of R ≥ 0.5 with annihilating VHCF occurrence, and the fatigue limits degrade on a Gerber relation beyond 109 cycles. At last, a fatigue failure map was proposed to directly describe the panorama of specimen lives under different external loads.

Study on crack resistance of self-healing microcapsules in asphalt pavement by multi-scale method.

Self-healing microcapsules in the asphalt pavement must be kept intact under vehicle load to ensure there is enough rejuvenator in capsules when cracks appear in asphalt pavement. In this paper, the crack resistance of self-healing microcapsules in asphalt pavement was evaluated. Firstly, an expanding multi-scale analysis was conducted based on proposed mesoscopic mechanical models with the aim to determine the mechanical parameters for the following contracting multi-scale analysis. Secondly, the periodic boundary condition was introduced for the contracting multi-scale analysis and the stress field of the capsule wall was obtained. Finally, the effects of the design parameters of the microcapsule on its crack resistance in asphalt pavement were investigated. The results showed that the incorporation of microcapsules has almost no effect on the elastic constants of the asphalt mixture. The core could be simplified as an approximately incompressible solid with the elastic constants determined by the proposed mesoscopic mechanical model. With the increase of the modulus of the capsule wall, the mean maximum tensile stress of the capsule wall increased from 0.372 MPa to 0.465 MPa, while with the decrease of the relative radius of the capsule core, the mean maximum tensile stress of the capsule wall increased from 0.349 MPa to 0.461 MPa. The change in the mean maximum tensile stress of the capsule wall caused by the change of capsule diameter was within 5%. The relative radius of the capsule core and the elastic modulus of capsule wall were two key parameters in capsule design. Besides, the microcapsules with the wall made of resin would not crack under the vehicle load before microcracks occurred in asphalt pavement.

Fatigue Studies of Welded Stainless Steel 304L: Effect of Manufacturability and Weld Type, Choice of Fatigue Model, and Comparison to Pristine Material

Abstract This study investigates fatigue life and fracture in welded stainless steel 304L (SS 304L) resulting from load-controlled fatigue. This was done for specimens from two welding manufacturers. Mechanical testing was carried out using a MTS test frame in uniaxial tension. Specimens fabricated in 3 weld configurations (butt, lap, butt-with-backer) were cycled at stress ratio R = 0.1, frequency f = 5 Hz, and experienced varying mean tensile stress. A comparison of the fatigue life of welded and unwelded (or pristine) specimens determined that the fatigue life of welded specimens is considerably shorter. The microstructure in the parent material (PM), heat affected (HAZ) and fusion zones (FZ) was analyzed using SEM, and results suggest that, for a limited number of specimens (backer welds), fracture in the (FZ) was primarily the result of Zener-Stroh cracks. Most welded specimens fractured at the weld-HAZ interface (weld toe), and we postulate that stress concentrations primarily due to abrupt geometrical change at the weld interface led to crack initiation there. Additional stress concentrations at welding induced defects (resulting from high temperature) such as second phase particles, fatigue induced defects, and pre-existing impurities are responsible for crack initiation, crack growth, and eventual fracture. Comparison of unwelded and welded SN curve data using numerical curve fitting methods reveal that the fatigue life of pristine SS 304L follows the expected sigmoid shape found in literature (specifically the Chandran fatigue model), while that of welded SS 304L deviates considerably in low cycle fatigue (LCF) and follows the Basquin power law equation.

Fatigue strength evaluation of scale railway axle with surface defect considering mean stress effect

In order to evaluate the notch fatigue strength of transition groove in railway axle, a series of fatigue tests were conducted on small specimens and press-fitted axles containing surface defects. Based on the experimental and finite element (FE) analyses, a novel method considering mean stress effect was proposed to evaluate the fatigue strength of scale railway axle with surface defect. It is found that press-fitted axles exhibit significantly lower notch fatigue strength than small specimens. Furthermore, the theory of critical distance (TCD) provides a good correlation between the notch fatigue strength of small specimens and experimental results. FE analyses revealed that the press-fitting reduces the fatigue strength of the transition groove through increasing stress concentration and introducing a mean tensile stress that decreases with an increase in the applied loading. To account for the mean stress effect, the axial stress at the groove is corrected as an equivalent stress amplitude at R = -1 based on Goodman relation. Through the combination of TCD and Goodman relation, an estimated fatigue strength with an error of less than 11 % can be achieved for the scale railway axle with surface defect.

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.

Influence of pre‐strain and bake hardening on the static and fatigue strength of a DP600 steel sheet

AbstractThe influence of pre‐strain on the tensile and fatigue properties of a dual phase DP600 steel was studied. The material was pre‐strained by uni‐axial tension in rolling and transverse direction. Thereafter, specimens were cut from the deformed plates in parallel or orthogonal to pre‐strain direction. It was found that pre‐strain increases yield and tensile strength. Results suggested that strain path change primarily affects the elastic‐plastic transition during early stage of reloading. Pre‐strained specimens showed an increase in high cycle regimes as a consequence of yield strength increment, irrespective of imposed pre‐straining direction. A modified stress life equation that accounts for pre‐strain was proposed and showed good agreement with experimental data. Bake hardening enhanced both tensile and high cycle fatigue resistance. Walker equation was successfully fitted to account for tensile mean stress. In low cycle fatigue, negligible influence of pre‐strain was observed due to cyclic softening and residual stress relaxation.

Life prediction method based on damage mechanism for titanium alloy TC4 under multiaxial thermo-mechanical fatigue loading

In this paper, a life prediction method based on damage mechanism for titanium alloy TC4 under multiaxial thermo-mechanical fatigue loading is proposed. Temperature and time dependent influence factors are proposed and introduced into the strain amplitude-life curve method to consider the temperature and time dependence of damage, respectively. The increase in fatigue and oxidation damages caused by tensile mean stress and non-proportional additional hardening is expressed by the mean stress in Macaulay brackets and by using a multiaxial damage parameter, respectively. A fast cracking influence factor is proposed to consider the influence of fast cracking of materials caused by the combined action of high temperature, tensile stress and shear stress on damage behavior. The material constants are identified by test data under uniaxial and proportional loadings, and are further used for prediction under non-proportional loading. The failure life results of uniaxial isothermal fatigue tests with and without dwell time, uniaxial and multiaxial thermo-mechanical fatigue tests are used to verify the proposed method. The value of the scatter band of life prediction result is less than ± 2, as well as the maximum and mean relative errors between predicted and experimental strain amplitudes are 18.49% and 6.54%, respectively.

Uniform fatigue damage tolerance assessment for additively manufactured and cast Al-Si alloys: An elastic-plastic fracture mechanical approach

• Influence of additively manufacturing and casting on microstructure and porosity characteristics as well as quasi-static and cyclic stress-strain behavior of Al-Si alloys. • Evaluation of Murakami-Noguchi approach and Shiozawa approach for fatigue limit and lifetime estimation, however, both approaches are not sufficient for AM Al-Si alloys. • Linking J integral (elastic-plastic fracture mechanics) including cyclic stress-strain curve by means of morrow parameter (K’, n’), defect size and position, stress amplitude and stress ratio. • New approach enables a uniform fatigue damage tolerance assessment of fatigue lifetime and limit for additively manufactured alsi10mg alloy as well as die-cast and sand-cast alsi7mg alloy. Lightweight Al-Si alloys are used in the automotive and railway industry due to their excellent strength-to-weight ratio and near-net-shape manufacturing. In additive manufacturing and casting, the near-net-shape manufacturing results in a non-homogenous solidification and cooling of the parts, leading to significant local gradient in microstructural and defect features as well as deformation behavior. In this paper, a uniform damage tolerance assessment was developed based on fracture mechanical approaches of Murakami (√area) and Shiozawa for a reliable defect-based mechanical design of fatigue-loaded structures. The linear-elastic fracture mechanical (LEFM) approaches of Murakami and Shiozawa were used to calculate defect-based lifetime curves, where the cyclic stress intensity factor (ΔK) at the failure-initiating defect (√area) was used to describe the local stress concentration conditions, called K-N curves, instead of nominal stress-based S-N curves. The LEFM-based K-N curves did not allow to describe the fatigue behavior in terms of a unified fatigue design of AM and casting material. Therefore, the cyclic stress-strain (CSS) behavior was used for a plasticity-modification of the LEFM approach by calculating the effective cyclic J integral (ΔJ eff ) to plot J-based K-N curves, called Kj-N curves. This elastic-plastic fracture mechanical (EPFM) approach allowed a uniform fatigue damage tolerance (FDT) assessment of AM and cast Al-Si alloys for the HCF regime by FDT law and fatigue limit by FDT limit. Exemplarily, the FDT limit could be used to predict synthetic Haigh diagrams for specific AM and cast batches and derive process- and service-relevant knowledge on the effect of tensile or compressive mean stress.

Combining welding-induced residual stress with thermal and mechanical stress in continuous welded rail

Continuously welded rail (CWR) with flash-butt welded joints has become standard practice for railway construction around the world. The welding process during rail installation or repair forms a residual stress field in the weldment altering locally the distribution and amplitude of the total stress that develops when the rail is in service. This paper presents a computer simulation approach to study the combined residual, thermal, and mechanical stress caused by the fastener system that develops in rail during the in-track welding and installation. The proposed approach simulates within a Finite Element Analysis framework the rail welding and installation sequence using detailed thermal and mechanical models of the weldment formation, and in-track installation. The model is validated with experimental measurements reported in the literature. It is implemented in a study that demonstrates the combined effects of such stresses with stress that develops in the rail during a daily solar-induced thermal cycle. A non-trivial stress gradient is observed where the mean tensile stress in the weldment is elevated relative to the rail at large. The higher mean stress warrants further investigations in view of fatigue performance under wheel loading. The proposed computer simulation approach is a tool that will enable future investigations focusing on more detailed examinations of weldment behavior, particularly concerning fatigue failures and track configurations, as well as in optimizing welding parameters to control the development of residual stresses.

Stress shielding in laser melting multilayered nickel-base superalloys under monotonic and cyclic loadings

In the present work, the mechanical properties and fatigue performance of laser melted mismatching nickel-base superalloys were investigated by multiscale experiments and computations. It confirmed that the local strength degradation does not affect the macroscopic stress–strain responses and overall low-cycle fatigue performance due to the stress shielding in the remelting material. The stress shielding mechanism was quantitatively illuminated and the critical shielding criterion was established. Accumulation of cyclic plastic deformations stimulates the cyclic stress softening and complete tensile mean stress relaxation in the remelting material, which significantly decreases the fatigue driving force of the mismatching material.

Probabilistic stress and strain-life fatigue crack initiation models with mean stress effects and life-dependent scatter considering runouts

A powerful probabilistic framework is proposed to account for life-dependent data scatter in fatigue crack initiation (FCI) predictions considering mean stress effects. It is applicable to any stress, strain, or energy-based fatigue damage parameter (DP), as long as the logarithm of DP for a given FCI life Nf can be assumed to follow a three-parameter Weibull (W3P) distribution. The proposed approach, named P-DP-N, does not require the assumption of any particular statistical distribution for Nf, thus it can fit the shape of virtually any equation correlating DP and Nf. Hence, it can deal simultaneously with LCF, HCF and VHCF FCI data, considering mean stress effects and runout statistics. The approach deals with heteroscedasticity through a user-defined life-dependent scedastic function of Nf, allowing the consideration of variable data scatter in log–log scales. The P-DP-N performance is evaluated using the Walker Equivalent Strain (WES) equation proposed by the authors, which is generalized to explicitly consider fatigue limits. Procedures are proposed to calibrate both stress and strain-based versions of the deterministic WES-life FCI model, as well as to optimize the W3P parameters from the resulting P-WES-N probabilistic model, considering runout data when available. A compact computational implementation of the calibration routines is presented as well. The W3P-based P-WES-N probabilistic model is evaluated for 31 metallic alloy data sets from the literature that include non-zero mean stresses and at least twenty specimens each, totaling 1,498 uniaxial fatigue specimens, including 141 runouts. This comprehensive evaluation shows that the proposed probabilistic model is able to account for tensile and compressive mean stress effects, as well as to calibrate the usually observed increase in experimental scatter for longer FCI lives.

Ratcheting Fatigue of Superalloy IN-617 Under Tensile Mean Stress at RT

Ratcheting Fatigue of Superalloy IN-617 Under Tensile Mean Stress at RT

Multiaxial thermo-mechanical fatigue damage mechanism of TC4 titanium alloy

In this paper, the experimental investigation was carried out on the TC4 titanium alloy to understand the cyclic deformation behavior and fatigue damage mechanism of materials under multiaxial thermo-mechanical loading. The results showed that the fast cracking mode of the material may be activated by the combined action of high temperature, tensile stress and shear stress, inducing a fast degradation in the axial mechanical properties of the material, which results in a drastic decrease in the failure life of the material. Moreover, it is also found that the non-proportional additional hardening and the tensile mean stress can increase the fatigue and oxidation damages of the material, and the material damage behavior is temperature dependent and time dependent. It should be pointed out that the damage mechanisms identified in this paper can reasonably explain the life law under uniaxial isothermal fatigue loading with and without dwell time, uniaxial and multiaxial thermo-mechanical fatigue loadings.

An improved strain-life model based on the Walker equation to describe tensile and compressive mean stress effects

Strain-life models that include Walker-like products can reproduce the higher mean stress effects in fatigue crack initiation observed in high-strength materials. These models are able to improve Smith-Watson-Topper’s strain-life predictions, at the cost of additional data-fitting exponents. This work reviews and compares several such models using 34 metallic alloy data sets from the literature that include non-zero mean stresses, totaling 1,355 uniaxial fatigue specimens. This comprehensive evaluation suggests that two different calibrations of Walker’s exponent are required to properly fit data measured under tensile and compressive mean stresses. Hence, an equivalent strain amplitude is proposed based on these two exponents, as well as on the ratio between the stress peak and amplitude. The new strain-life model resulting from this equivalent strain amplitude is able to describe uniaxial fatigue data under all stress ratios R < 1. Estimates for both exponents are provided as a function of the ultimate tensile strength of the material, which could be used in the absence of fatigue data under non-zero mean stresses, an asset for practical applications. A modified version of the proposed strain-life model, which considers mean stress effects only in the elastic damage term, is evaluated as well. Explicit equations are presented for the optimal calibration of all parameters from both models.

High Cycle Fatigue Life of Ti-6Al-4V Titanium Alloy Processed by Electron Beam Welding

Fatigue is the most important failure mode of welded structures in engineering applications. However, unlike steel and aluminum alloy welds, the fatigue design guideline of titanium-welded structures are still limited. In this study, Ti-6Al-4V titanium alloy welds with butt joint were produced by electron beam welding (EBW). We examined the suitability of related design codes and established an optimal fatigue-life analysis method for titanium structures. Fatigue tests with constant amplitude loading and variable amplitude loading were performed. Two mean stress correction methods usually adopted in high cycle fatigue analysis, Goodman and Gerber, were evaluated. The results showed that the fracture site of the EBW fatigue sample was located in the base metal. The EBW butt joints of the Ti-6Al-4V alloy apparently illustrated a higher fatigue strength compared to the corresponding fatigue design curve in the AWS D1.9 standard. Under constant amplitude loading with tensile mean stress, the experimental fatigue life fell between the Gerber and Goodman curves. The Miner rule combined with the Goodman mean stress correction approach was recommended to obtain a better fatigue life prediction in the case of variable amplitude loading with tensile or slightly compressive mean stress. All predicted fatigue lives fell within a three-fold change boundary for both SAE transmission and bracket histories.