Scatter Band Research Articles

Fatigue life prediction of cold expansion hole using physics-enhanced data-driven method

Cold expansion (CE) serves as a practical surface enhancement to improve the fatigue life of hole structures by improving surface integrity in both macro-scale and micro-scale. Due to the inaccessibility and high cost of experimental measurements, the physical relation between surface integrity and fatigue life are always implicit, serving as the major challenge for accurate life prediction. To address this issue, a novel method is proposed by introducing physical information to traditional data-driven method, where surface integrity enriched by multi-scale simulation is mapped to fatigue life via machine learning (ML) mechanism. As integrated to four typical ML algorithms, the proposed physics-enhanced data-driven method exhibit outstanding capability for accuracy improvement, decreasing the scatter band by amplitude between 27.3 % and 71.4 %. The proposed method offers a promising option for fatigue life prediction on surface treated structures with limited physical information.

A novel LCF lifetime model for PM superalloys considering crack energy differences induced by surface underconstraint

The mechanism behind why internal defects are less competitive than surface roughness in low cycle fatigue (LCF) failure is still an issue for inclusion-containing powder metallurgy (PM) superalloys. Differentiating the differences in applied energy and fatigue resistance at various failure sites is crucial to addressing this issue. This study first captures the dependence of failure site on applied loading from the fractographic observations to quantify the characteristics such as surface roughness, internal defects, and sub-surface facets. Subsequently, an LCF lifetime model is developed based on fracture mechanics principles, considering the difference in applied energy and cracking energy requirements due to underconstraint degree at different sites. A representative volume element (RVE) with similar grain characteristic is then established, and different boundary conditions are applied to describe the energy differences around internal and surface. By comparing the energy at different failure sites, the model predicts the tendency of failure sites under varying loading conditions. The developed LCF lifetime model distinguishes energy input and fatigue resistance differences at surface, sub-surface, and interior of the specimen, which reduces the lifetime prediction error from a scatter band of 9 times to within 3 times.

Crystal plasticity-driven evaluation of notch fatigue behavior in IN718

The aim of this study was to establish a method for evaluating notch fatigue behavior through crystal plasticity finite element (CPFE) simulations based on the actual microstructure of the nickel-based alloy Inconel 718 (IN718). Initially, the equivalent plastic strain, εeps, which reflects the comprehensive slip at the grain scale, was employed to analyze the fatigue crack initiation mechanism of IN718, revealing that twinning and triple junctions of grain boundaries were high-risk locations for fatigue crack initiation. Next, fatigue simulations were performed on notched specimens using the CPFE model, with a material-level CPFE model particularly employed at the notch root. The increment of εeps, Δεeps, in a stable cycle was used as the fatigue damage control parameter and correlated with the fatigue life, Nf, revealing that the Δεeps-Nf relationship at material-level satisfied the form of the Mason-Coffin model. Finally, fatigue life prediction of IN718 notched specimens was carried out based on the Δεeps-Nf relationship, with the predicted results falling within the 2-fold scatter band, demonstrating good prediction accuracy.

Determination of equivalent crack length for voids in metallic alloys based on continuum damage mechanics modeling

Metals contain different kinds of spatial defects significantly reducing the fatigue performance. Accurate defect-based life prediction methods are required to improve structural integrity analysis and life design reliability. The present work developed a method to determine the equivalent crack length for defects based on continuum damage mechanics. The spatial effects of defects in the calculation of the equivalent crack were quantified and verified by fatigue tests. It is confirmed that the equivalent crack length of both slit and elliptic defects is affected not only by the defect geometry but also by the applied load. Based on the equivalent crack and combined with Paris’ law, the predicted fatigue lives of various slit holes under different loading orientations are within the double scatter band and are much more accurate than the conventional projection method.

A modified critical distance method for estimating fretting fatigue life of dovetail joints

AbstractIn this paper, a modified theory of critical distance (TCD) method (i.e., Gradient‐TCD method) is proposed, which combines fatigue parameter gradient and the TCD, to estimate fretting fatigue life of dovetail joints. The advantage of Gradient‐TCD method lies in utilizing the gradient parameters to effectively characterize the local effect zone caused by fretting, thereby enabling the determination of a suitable critical distance length independent of material fatigue parameters. The reliability and predictive capability of the method is validated through experimental results. Furthermore, this method demonstrates insensitivity to mesh size, resulting in an 83.6% reduction in computational time while maintaining the predictions within the two‐times scatter band. The novel Gradient‐TCD method may provide an efficient and reliable approach for fretting fatigue life prediction, which holds promise for evaluating complex full‐scale fretting problems.

Advances in low cycle fatigue probabilistic modeling

New advances in the probabilistic S-N model proposed by Castillo and Canteli are presented. The requirements for a S-N model derivation to be valid are emphasized, in particular, that of the compatibility between the statistical distributions of lifetime and stress reference variable. The definition of the generalized reference variable (GRV) in the S-N field, as GRV=ψ·σM, where ψ is a non-dimensional factor derived from the σ-ε law of the material, allows the former model to be applied to LCF data. The new model ensures the incontrovertible and unitary definition of the scatter band in the S-N field and the justification of an asymptotic lower limit of the lifetime, N0. As a result, the stress- and strain-based approaches can be envisaged as a unique probabilistic ψσM-N approach applicable in the three conventional, i.e., LCF, HCF and VHCF domains. An extension as the ψσM-R-N model that includes the stress ratio effect is presented. The utility of the model is confirmed with the assessment of LCF data from different external experimental campaigns.

Multiaxial fatigue behavior and life estimation of Al‐Li alloy 2099 under strain‐controlled loading

AbstractAluminum‐lithium alloys are a class of advanced materials designed to reduce weight and improve performance in aerospace and other high‐tech applications. This paper presents a research investigation on the in‐phase and out‐of‐phase multiaxial fatigue behaviors of the third‐generation AW2099‐T83 aluminum‐lithium alloy that have not been addressed before. Additional hardening was observed under nonproportional loading condition at high strain amplitudes. Fatigue lives were estimated using von Mises equivalent strain and two critical plane models: the Fatemi‐Socie (FS) and the Smith‐Watson‐Topper (SWT). In addition, a supervised machine‐learning model (support vector machine—SVM) was employed to predict the fatigue life under the above‐mentioned loading conditions. The FS criterion was found to yield better fatigue life predictions than SWT. The estimations of FS model mostly fall within ±3× scatter bands with some data falling within the conservative and non‐conservative regions. The SVM model resulted in excellent predictions within ±2× scatter bands.

Fretting fatigue life prediction of full-scale dovetail joints using the theory of critical distances with mesh control

The fretting fatigue life of full-scale dovetail joints in two contact configurations was estimated using the theory of critical distance with the area method (TCD-AM) and the mesh control method (TCD-MC). The TCD-MC method demonstrated prediction accuracy comparable to the traditional TCD-AM method, while improving computational efficiency by 85 %. By incorporating a calibration strategy with the TCD-MC method, the predicted fatigue life was within the scatter band of factor 3 when compared with the experimental data, indicating its reliability. The proposed parameter-fitting method for TCD-MC yielded results nearly identical to the conventional method, while reducing the workload by 75 %. The TCD-MC method is expected to provide a potentially novel and convenient approach for fretting fatigue life prediction in full-scale specimen.

Fatigue Behaviour and Life Prediction of YSZ Thermal Barrier Coatings at Elevated Temperature under Cyclic Loads

The concentration of interfacial normal stress at the free edges of thermal barrier coatings (TBCs) can result in coating spallation. Fatigue cracking is one of the main reasons for creating free edges under complex loads. It is crucial to investigate the fatigue cracking of coatings under cyclic loads to assess potential coating failure. To address this issue, a novel model was proposed to predict the fatigue life of the YSZ topcoat under stress parallel to the interface. Firstly, this study conducted uniaxial and tensile-torsional fatigue tests at elevated temperatures on specimens with atmospheric plasma-sprayed TBCs. The test results revealed that fatigue cracks appeared in the topcoat under cyclic loads, but these cracks did not propagate into the bondcoat or substrate immediately. The number of cycles before the topcoat cracked was found to be associated with the magnitude of the cyclic load. Secondly, this study analyzed the test conditions using the finite element method. Simulations indicated that the crack direction in the topcoat under complex loading conditions was aligned with the first principal stress direction. Finally, the fatigue life prediction model of the topcoat was established based on experiments and simulations. The predicted results fell within a fourfold scatter band.

Combining phase field method and critical distance theory for predicting fatigue life of notched specimens

Notch features, widely used in engineering components, have negative effect on the fatigue life of structural parts due to the stress concentration caused by their geometry. This highlights the importance of numerical methods to help assessing the adverse effect of geometrical discontinuities like notch on the fatigue properties of structural components. In this study, a new phase field fatigue formulation was proposed to predict the fatigue behavior of metallic notched specimens, suggesting a dimensionless parameter based on the critical distance theory to capture the notch effect. The slope of S-N curve was regarded as a function of the effective stress ratio obtained from different critical distances, and the fatigue damage threshold was varied with the slope of the S-N curve. Two S-N curves of smooth and notched specimens were used to calibrate the fatigue model parameters for each material. Numerical examples validated by experimental data of various configurations in terms of geometry, stress ratio and loading mode indicated the validity of the proposed model and its ability to accurately predict the fatigue life of notched specimens with different notch geometries and materials, as the predicted fatigue lives mostly fell within the ± 2 scatter band. The results indicated that compared with the traditional TCD method the proposed model eliminates the requirement to recalculate the critical distance at different fatigue lives, and the stress ratio effect can be naturally captured without recalibrating the critical distance.

Predicting fatigue life with the IMWCW under complex loading

The Integration Modified Wöhler Curve Method (IMWCW), a novel approach for predicting fatigue life under complex strain-based non-proportional loading paths is introduced in this research. This method integrates concepts from the Modified Wöhler Curve Method (MWCW) with the principle of damage incremental integration to provide a more nuanced prediction of material fatigue. Besides two established E-N curves (strain-number of cycles) for uniaxial tension and torsion, a new fundamental E-N curve that characterizes the strain-life relationship under complete non-proportional loading paths is introduced. A novel strain path decomposition technique is presented, which dissects an infinite number of instantaneous micro-elements along any loading path into components parallel and perpendicular to the proportional loading direction. It is assumed that each instant will cause fatigue damage to the material. A concurrent model for the incremental integration of damage is formulated, allowing for the calculation of cumulative damage. The model is further expanded to provide analytical expressions for proportional loading and non-proportional loading, linking them to three fundamental E-N curve, so as to calibrate the parameters required for the integration model. The empirical validity of the model is confirmed through experimental testing on 7 different metallic materials under 20 loading conditions, with 391 data points analyzed. The results demonstrate that 91% of the model's predictions fall within a scatter band of 2, confirming its robustness and reliability in forecasting fatigue life in complex, real-world scenarios.

Experimental study of the fatigue failure behavior of aluminum alloy 2024-T351 under multiaxial loading

Multiaxial fatigue has been drawing much attention because it is more applicable to engineering practice. In this paper, an experimental study of aluminum alloy (AA) 2024-T351 was carried out under multiaxial loading with an aim to assess the damage evolution process and failure mechanism under in-phase and out-of-phase loadings. Firstly, fatigue life and stress response under multiaxial cyclic loads were obtained, and it found that although there is non-proportional hardening, the fatigue life subjected to proportional loading is significantly shorter than that of under a nonproportional loading, which was tried to be explained by the ductility of the material. Secondly, a detailed analysis of the damage evolution process based on the degradation of the elastic modulus and the fatigue failure process based on the digital image correlation (DIC) method was provided. Next, a micro-analysis of the specimens’ fracture appearance was conducted to obtain the fracture characteristics and found that AA2024-T351 presents a dominant shear fracture mode under proportional loading and a mixed mode of tensile and shear fracture under non-proportional loading. Last but not least, The Fatemi-Socie criterion was modified by considering the material’s ductility and the interaction between normal stress and shear stress acting on the critical plane. The multiaxial life prediction results of the modified FS model for AA2024-T351 in this paper were all within the scatter bands of 3 on life.

A modified SWT model for very high cycle fatigue life prediction of L-PBF Ti-6Al-4V alloy based on Single Defect: Effect of building orientation

The ultrasonic fatigue tests on laser-powder bed fused (L-PBF) Ti-6Al-4V specimens manufactured at 0°, 45°, and 90° building orientations were conducted. It is found that the very high cycle fatigue (VHCF) lives decrease with the building orientation from 0°, 45°, to 90°. All the fatigue cracks initiate from internal pores or Lack of Fusion defects. Mode Ι cracks grow perpendicular to the direction of the maximum opening stress, regardless of the building orientation. The maximum prospective defect evaluated by the extreme value statistics (EVS) method is used as the typical defect for VHCF life prediction. A modified Smith-Waston-Topper (SWT) model was proposed and combined with the Critical Distance Method to predict ultra-high cycle fatigue life. The life prediction accuracy was validated by using both experimental data obtained from the experiments conducted in this paper and experimental data taken from the literature. The results show that 84% of the predicted fatigue lives are within a scatter band of 2 standard deviation, and 16% of the predicted lives are outside a scatter band of 2 standard deviation and within a scatter band of 3 standard deviation.

The structural strain method for fatigue evaluation of welded components: Analytical treatment of reversed plasticity

The traction structural stress method has been adopted by various industry sectors, in addition to ASME Boiler and Pressure Code (B&PV), for fatigue life evaluation and assessment of welded components, especially for high-cycle fatigue applications. Its effectiveness has been validated and demonstrated by showing good data correlation in the form of the master S–N curve scatter band. For low cycle fatigue with the involvement of elastic-plastic deformation, the structural strain method has been recently developed by simply extending the current elastic-deformation-based structural stress method to more general elastic-plastic deformation. Closed-form structural strain solutions for elastic-perfectly plastic materials and numerical solutions for nonlinear strain hardening materials have been obtained under simple load-controlled loading and unloading cycling conditions. In this paper, the equations of nonlinear cyclic structural stress-strain curves under fully-reversed fatigue loading are analytically derived for the first time with a 3-bar model, which consists of three elastic-perfectly plastic bars. The general trends and patterns of the loading paths of the constructed cyclic structural stress-strain curves with the 3-bar model are validated with finite element analysis (FEA). Based on the insights gained from the 3-bar model and the FEA results, a simple procedure for constructing cyclic structural stress-strain curves from their corresponding monotonic loading curves are developed for both elastic-perfectly plastic model and the modified Ramberg-Osgood nonlinear strain hardening model. The effectiveness of this procedure is demonstrated by correlating low-cycle fatigue data of welded structures under pulsating and fully-reversed loading conditions.

Fracture mechanism of Ti60 alloy at high temperature in very high cycle fatigue regime and fatigue life prediction

AbstractThis study aimed to investigate the failure mechanism of Ti60 titanium alloy in the high cycle fatigue (HCF) and very high cycle fatigue (VHCF) at 500°C. Ti60 specimens were characterized before and after the 500°C VHCF test, and the fracture surfaces were observed. The results show that there are three different fatigue failure mechanisms at 500°C: (i) equiaxed primary α phase (αp) cleavage, forming small unsmooth facets and rough fracture area (RA), and fusion of non‐adjacent facets to grow into the main crack. (ii) αp grains gather into large grain with triple junction, and large grain slip to form large fusion facet. (iii) Oxide shedding and then cracks form. A dynamic recurrent neural network model is used to predict the fatigue life of Ti60 alloy, 91% of the overall predictions were within the scatter band of 3.0, and 100% were within the scatter band of 5.0.

Fatigue Life Data Fusion Method of Different Stress Ratios Based on Strain Energy Density.

To accurately evaluate the probabilistic characteristics of the fatigue properties of materials with small sample data under different stress ratios, a data fusion method for torsional fatigue life under different stress ratios is proposed based on the energy method. A finite element numerical modeling method is used to calculate the fatigue strain energy density during fatigue damage. Torsional fatigue tests under different stresses and stress ratios are carried out to obtain a database for research. Based on the test data, the Wt-Nf curves under a single stress ratio and different stress ratios are calculated. The reliability of the models is illustrated by the scatter band diagram. More than 85% of points are within ±2 scatter bands, indicating that the fatigue life under different stress ratios can be represented by the same Wt-Nf curve. Furthermore, P-Wt-Nf prediction models are established to consider the probability characteristics. According to the homogeneity of the Wt-Nf model under different stress ratios, we can fuse the fatigue life data under different stress ratios and different strain energy densities. This data fusion method can expand the small sample test data and reduce the dispersion of the test data between different stress ratios. Compared with the pre-fusion data, the standard deviations of the post-fusion data are reduced by a maximum of 21.5% for the smooth specimens and 38.5% for the notched specimens. And more accurate P-Wt-Nf curves can be obtained to respond to the probabilistic properties of the data.

Fatigue Analysis of Composite Bolted Joints under Random and Constant Amplitude Fatigue Loadings.

This paper attempts to analyze the random fatigue life and failure modes of joints using two calculation methods. Three kinds of tests were carried out, which were the static test, constant amplitude fatigue test and the random fatigue test, and four kinds of joints were designed. After the static test, the joint was subjected to a constant amplitude fatigue test by selecting different percentages of load according to the static strength. In order to predict the random fatigue life more precisely, two calculation methods were carried out, which were the linear cumulative damage method and the equivalent loading finite element method. Based on the linear cumulative damage hypothesis, the fatigue life of the joint was established as a function of the load amplitude, and then, the random life prediction was calculated by the amplitude distribution of the random loading. Another method was the equivalent loading method, which was to obtain the equivalent constant amplitude fatigue loading of the random loading spectrum. The finite element model was established based on the stiffness and strength degradation rule. The equivalent random life and fatigue failure modes of the joint were modeled. The two life prediction methods show good agreement with the fatigue experimental result, and all prediction results were included in a scatter band of the factor of 2.

Evaluation of fatigue life prediction models and investigation of fracture mechanisms of mild steel

Fatigue is one of the dilemmas of coiled tubing (CT) in oil and gas engineering. This study investigated the fatigue behavior of CT employing mild steel, which is commonly utilized in the CT110. Two fatigue life prediction methods based on cyclic strain-life principles, the Manson–Coffin and Landgraf models, as well as the Smith and Ellyin models based on energy-life principles, were evaluated. The Ellyin model demonstrated superior accuracy in predicting the low-cycle fatigue life of CT110, displaying dispersion within the 1.5 scatter band. This research integrated mechanical property analysis and microscopic deformation assessments for CT110. Fatigue mechanics studies show cyclic softening behavior in the CT110 of mild steel. The results of the microscopic analysis show that the fatigue fracture of CT110 has typical fatigue striations and equiaxial dimples as a plastic fracture. Combined with TEM and EBSD analysis, fatigue deformation increases grain deformation and dislocation density. In addition, the increase in dislocation density results from the combination of cycles and strain amplitude. The results of in situ EBSD further support this view. At 8% strain amplitude, the dislocation density increases to 0.196B when the cycle increases from 0 number to 10 number. Furthermore, the ferrite grain slip becomes accessible, but the 〈111〉 // Z0 direction is still the main texture. These are fundamental reasons for the cyclic softening of the CT110 mild steel, supported by a decrease in stress amplitude.

Energy-Based Unified Models for Predicting the Fatigue Life Behaviors of Austenitic Steels and Welded Joints in Ultra-Supercritical Power Plants.

The development of a cost-effective and accurate model for predicting the fatigue life of materials is essential for designing thermal power plants and assessing their structural reliability under operational conditions. This paper reports a novel energy-based approach for developing unified models that predict the fatigue life of boiler tube materials in ultra-supercritical (USC) power plants. The proposed method combines the Masing behavior with a cyclic stress-strain relationship and existing stress-based or strain-based fatigue life prediction models. Notably, the developed models conform to the structure of the modified Morrow model, which incorporates material toughness (a temperature compensation parameter) into the Morrow model to account for the effects of temperature. A significant advantage of this approach is that it eliminates the need for tensile tests, which are otherwise essential for assessing material toughness in the modified Morrow model. Instead, all material constants in our models are derived solely from fatigue test results. We validate our models using fatigue data from three promising USC boiler tube materials-Super304H, TP310HCbN, and TP347H-and their welded joints at operating temperatures of 500, 600, and 700 °C. The results demonstrate that approximately 91% of the fatigue data for all six materials fall within a 2.5× scatter band of the model's predictions, indicating a high level of accuracy and broad applicability across various USC boiler tube materials and their welded joints, which is equivalent to the performance of the modified Morrow model.

Investigation of ratcheting fatigue behavior and failure mechanism of 1Cr18Ni10Ti pressure pipe under different force amplitudes and internal fluid pressure

This work reports on the development of an improved testing system to examine the effects of force amplitude and internal fluid pressure on ratcheting behavior and failure mechanism of 1Cr18Ni10Ti aero-engine pipe. Experimental results indicate that the ratcheting displacement and its rate during steady stage increase with the increasing force amplitude or internal fluid pressure, exhibiting a reverse tendency to fatigue life. Continuous cyclic softening response until fatigue fracture was observed in all conditions. Furthermore, microstructural evolution was characterized by SEM, EDS, XRD, and EBSD. The critical force amplitude to trigger noticeable dislocation accumulation and transition from austenite to ferrite phase was evaluated to be around 1900 N. The results highlight the decreased high-angle grain boundary (HAGB) and increased dislocation density causing the sample with a higher force amplitude to be more inclined to fracture. The initiation of fatigue crack was accelerated by the accumulation of dislocation within ferrite phase grains. Similar fatigue fracture morphology with ovalization phenomenon was observed in all conditions. To predict the ratcheting fatigue life of aero-engine thin wall pipes, a validated fatigue life estimation model considering steady ratcheting displacement rate based on a finite element analysis (FEA) model was conducted, and all of the fatigue data are contained in a 1.1X scatter band.