Fatigue Scatter Research Articles

A Multi-Scale Model for Predicting Physically Short Crack and Long Crack Behavior in Metals.

The fatigue behavior of metal specimens is influenced by defects, material properties, and loading. This study aims to establish a multi-scale fatigue crack growth model that describes physically short crack (PSC) and long crack (LC) behavior. The model allows the calculation of crack growth rates for uniaxial loading at different stress ratios based on the material properties and specimen geometry. Furthermore, the model integrates the Gaussian distribution theory to consider material heterogeneity and the experimental measurement errors that cause fatigue scatter. The crack growth rate and fatigue life of metal specimens with different notch geometry were predicted. The curves generated by the multi-scale model were mainly consistent with the test data from the published literature at the PSC and LC stages.

Effect of chemical etching time on the fatigue behavior of Ti‐6Al‐4V produced by laser powder bed fusion

AbstractThis study focuses on the evolution of the fatigue strength of Laser Powder Bed Fusion (L‐PBF) produced Ti‐6Al‐4V as a function of the chemical etching finishing process. The aim is to identify the critical fatigue crack initiation mechanisms and the transitions between them in terms of the evolution of the surface micro‐geometry. This is done using three different geometries and six different surface states. The evolution of the crack initiation mechanisms is then used to explain the evolutions of the fatigue strength and the fatigue scatter. Chemical etching affects the fatigue life via a polishing effect, which directly influences both the finite and the high cycle fatigue domains. It is shown that chemical etching makes it possible to obtain fatigue strengths that are almost similar to those of the machined surface. However, it is also observed that etching cannot fully counteract the effects of large surface cavities caused by surface connected porosities.

Stochastic or deterministic: Duality of fatigue behaviour of 3D-printed meta-biomaterials

The two deformation modes of meta-biomaterials during cyclic loading have been revealed: stochastic and deterministic strut failure processes. Biomimetic Voronoi structures with a range of strut thicknesses and number of cells per unit volume are printed. We show that when the strut thickness is 200 μm or above, the fatigue fracture process of the lattice is deterministic and the fatigue scatters are below 15%. As the strut is thinned to 150 μm, the local failures occur randomly within the structure, which may lead to a high fatigue scatter (>30%). The two distinct behaviours result from the processing limit of the laser powder bed fusion technique. We demonstrate that the fatigue scatter and the location of the failure process within the lattice are related to the probability that a cluster of unconnected struts larger than a critical value can exist within the lattice. Unlike solid parts, porosity hardly triggers any damage in metallic lattices during cyclic deformation. The discovery of the Janus-like failure process opens up our understanding of meta-biomaterials and defines the pathway towards the design of mechanically durable intricate implants.

Combined effect of random porosity and surface defect on fatigue lifetime of additively manufactured micro-sized Ti6Al4V components: An investigation based on numerical analysis and machine learning approach

Surface defects and internal porosities resulting from the additive manufacturing process contribute to a scatter in fatigue lifetime, increasing uncertainty in applications such as aerospace engineering. This study proposes a combined approach of machine learning and finite element modelling to explore the interaction between random porosity distribution and high surface roughness on the fatigue lifetime of micro-sized additively manufactured parts. To achieve this, a high-fidelity finite element model is constructed with randomly distributed porosities and surface defects. A fatigue lifetime estimation model, developed using a combination of continuum damage mechanics and the theory of critical distance, is then applied to predict lifetime using effective stress extracted from simulations. A total of 1200 simulations are conducted using these models to examine the interaction effects of subsurface porosity and surface defects on localized stress distribution and fatigue lifetime. Subsequently, two machine learning algorithms, Support Vector Regression and Kernel Ridge Regression, are employed to estimate fatigue lifetime, accounting for the effects of randomly distributed subsurface porosities and surface defects. Eighty percent of the developed finite element models are employed to construct an input dataset, incorporating geometrical features of pores, and to train the algorithms, while the remaining 20% are reserved for verification purposes. The observed results demonstrate that the combined effect of random porosity and surface defects increases fatigue scatter behaviour, leading to greater uncertainty in lifetime prediction. Furthermore, the machine learning algorithms exhibit promising prediction performance.

High-cycle fatigue life prediction of L-PBF AlSi10Mg alloys: a domain knowledge-guided symbolic regression approach.

The large scatter in high-cycle fatigue (HCF) life poses significant challenges to safe and reliable in-service assessment of additively manufactured metal components. Previous investigations have indicated that inherent manufacturing defects are a critical factor affecting the fatigue performance of the components, and the HCF life is significantly influenced by the geometric parameters of the critical defects inducing crack nucleation. Therefore, it is highly important to elucidate the correlation of the HCF life with the geometric parameters of critical defects. This study proposes a new fatigue life prediction model for laser additively manufactured AlSi10Mg alloys by including the combined effects of loading stress and defect geometries (size, location and morphology) in terms of domain knowledge-guided symbolic regression (SR). Domain knowledge is extracted from the semi-empirical Murakami, Z-parameter and X-parameter fatigue life models to establish the variable subtrees. The results show that compared with these semi-empirical models, the domain knowledge integration-based SR model has higher prediction accuracy and generalization ability. Moreover, compared with traditional 'black box' machine learning models, SR excels at balancing prediction accuracy and model interpretability, which provides useful insights into the relationship between fatigue life and defect geometries. This article is part of the theme issue 'Physics-informed machine learning and its structural integrity applications (Part 2)'.

Defect driven physics-informed neural network framework for fatigue life prediction of additively manufactured materials.

Additive manufacturing (AM) has attracted many attentions because of its design freedom and rapid manufacturing; however, it is still limited in actual application due to the existing defects. In particular, various defect features have been proved to affect the fatigue performance of components and lead to fatigue scatter. In order to properly assess the influences of these defect features, a defect driven physics-informed neural network (PiNN) is developed. By embedding the critical defects information into loss functions, the defect driven PiNN is enhanced to capture physical information during training progress. The results of fatigue life prediction for different AM materials show that the proposed PiNN effectively improves the generalization ability under small samples condition. Compared with the fracture mechanics-based PiNN, the proposed PiNN provides physically consistent and higher accuracy without depending on the choice of fracture mechanics-based model. Moreover, this work provides a scalable framework being able to integrate more prior knowledge into the proposed PiNN. This article is part of the theme issue 'Physics-informed machine learning and its structural integrity applications (Part 1)'.

Rolling contact fatigue performance of M50 steel: A combined experimental and analytical approach to determine life

This article presents an experimental and analytical investigation into the rolling contact fatigue (RCF) performance of AISI M50 bearing steel across a range of Hertzian contact pressures (Ph=2.6GPa to 3.4GPa). RCF experiments were conducted using a ball-on-rod test rig at three contact pressures to experimentally establish the relationship between contact pressure (contact stress) and the RCF life of M50. Simultaneously, a previously developed continuum damage mechanics finite element (CDM-FE) model, employing the Fatemi-Socie critical plane approach as the failure criteria, was utilized to provide analytical predictions of RCF life. The CDM-FE model’s damage rate equation was calibrated using open literature AISI M50 bearing steel torsion stress life (SN) data. The CDM-FE model incorporated Voronoi tessellations to represent the material microstructure and capture the material topological effect on fatigue scatter. RCF simulations were conducted at seven contact pressures ranging from 1.0 GPa to 3.4 GPa in 0.4 GPa increments. Similar to the experimental results, the analytical RCF life data set yielded a relationship between contact pressure and simulation life for M50. Good corroboration is observed between the contact pressure – life relationships from the experimental and analytical RCF life data sets. This is significant as it supports the use of a hybrid approach combining experimental tools (e.g. torsion fatigue and ball-on-rod) and a CDM-FE computational model to efficiently assess the RCF performance of bearing materials.

Physics-guided machine learning frameworks for fatigue life prediction of AM materials

Introducing random defects is a type of the dominant causes of fatigue scatter of additive manufacturing (AM) materials. The fracture mechanics-based models oversimplify the fatigue damage process and ignore the key influencing factors. Given data-driven nature of machine learning (ML), sufficient samples are required to train, which generally cannot be met in practice. In view of this, this work develops two physics-guided machine learning frameworks which combine physics-based models and ML algorithms, for improving the prediction ability. In the proposed framework, ML models can consider those factors ignored by physics-based models and physics-based models can ensure the consistency with physical results. Finally, fatigue data of three AM materials are used for model evaluation and comparison. The results show that, physics-based models lack sufficient explanatory power for scatter of fatigue life. Moreover, compared with the purely data-driven methods, the proposed framework can maintain high accuracy and alleviate the over fitting phenomenon under insufficient fatigue data sources.

Anisotropic high cycle fatigue property estimation for laser additive manufactured Ti6Al4V alloy dependence on tomographic imaging of defect population

Improvement of fatigue properties of additive manufactured metals is subject to the regulation of process-induced microstructure and defect population. Here, the high cycle fatigue properties of the annealed Ti6Al4V alloy manufactured by two types of laser powder bed fusion (L-PBF) processes, in orthogonal sample orientations, were studied. The fatigue performance of this alloy was also estimated dependence on the investigation of microstructure and defects using optical microscopy, X-ray diffraction, scanning electron microscopy and micro computed tomography. The results demonstrated that the fatigue properties were degraded by the negative effect of prior-β columnar grain boundaries and defects, wherein the surface keyhole governed the pronounced fatigue scatter and anisotropy due to its geometrical parameters and anisotropy severity along the building direction. The projection size √area of keyholes was well applied in the fatigue property estimation. The theorical fatigue limits were estimated individually due to the keyhole anisotropy, and provided conservatively in the improved Kitagawa-Takahashi diagram based on the modified El-Haddad model and the extreme size of keyholes. A relation derived from Paris law was proposed for fatigue life prediction, and to well establish a linear fitting correlating fatigue life with the projection size of surface keyholes and stress amplitude range with the achievement of the alleviation of fatigue anisotropy and scatter. The research provides a reference for the non-destructive estimation of fatigue properties in terms of tomographic imaging of defect population.

Probabilistic and defect tolerant fatigue assessment of AM materials under size effect

Basic fatigue properties captured by laboratory testing of small specimens are usually applied to safety design of actual components. Nevertheless, their fatigue performances are significantly different due to size effect attributing a fault to possibility of large defects occur. Accordingly, extreme value statistics and weakest-link theory are applicable to defect tolerant fatigue assessment under size effect in this study. Firstly, the basic theory of extreme value statistics and weakest-link are explicated. Then, a probabilistic framework is developed to estimate the fatigue strength/life of Additive manufacturing (AM) material, wherein size effect and fatigue scatter from statistical viewpoint are illustrated and quantitative analysis. In particular, different types of size effect are simplified and unified as defect size variation, and the quantile of the critical defect derived by extreme value statistics is implemented to estimate the bounds of fatigue performance. Finally, three groups of additive manufactured specimens with different volume and processing parameters are utilized for method validation and comparison, which show great capability to estimate the fatigue scatter of AM material under size effect. The goal of this study is also to clarify the potential application of extreme value statistics and weakest-link theory from the probability and defect tolerant perspective.

Reproducibility and Scattering in Additive Manufacturing: Results from a Round Robin on PBF-LB/M AlSi10Mg Alloy

Abstract The round robin test investigated the reliability users can expect for AlSi10Mg additive manufactured specimens by laser powder bed fusion through examining powder quality, process parameter, microstructure defects, strength and fatigue. Besides for one outlier, expected static material properties could be found. Optical microstructure inspection was beneficial to determine true porosity and porosity types to explain the occurring scatter in properties. Fractographic analyses reveal that the fatigue crack propagation starts at the rough as-built surface for all specimens. Statistical analysis of the scatter in fatigue using statistical derived safety factors concludes that at a stress of 36.87 MPa the fatigue limit of 107 cycles could be reached for all specimen with a survival probability of 99.999 %.

Fatigue life estimation of additively manufactured Ti-6Al-4V: Sensitivity, scatter and defect description in Damage-tolerant models

Damage-tolerant models for fatigue life estimation rely on fracture mechanics principles to model fatigue crack initiation and growth. In Laser-Based Powder Bed Fusion (LPBF) produced Ti-6Al-4V defect populations present non-uniform in size, shape, and location within components. Considering defect populations in a statistical nature offers one method to characterise defects to be included in fatigue life modelling for AM parts. In this study a novel numerical fatigue life model is built upon which the sensitivity to input parameters, short crack growth mechanics, defect morphology and location for LPBF-produced Ti-6Al-4V is established. Furthermore, we introduce the potential for multiple crack initiation sites and crack interaction. Fatigue strength is shown to be more sensitive to selected threshold parameters and short crack growth mechanics. Furthermore, the introduction of multiple crack initiations and interaction results in distributions of fatigue strength estimates sensitive to defect number, illustrating the importance of its inclusion as a source of fatigue scatter in LPBF produced Ti-6Al-4V parts. Overall, this study establishes areas of nuance and criticality required in the design and modelling of fatigue life unique to AM produced components.

Defect tolerant fatigue assessment of AM materials: Size effect and probabilistic prospects

Despite the significant advantages such as rapid prototyping of complex structures, engineering application of Additive Manufacturing (AM) technique has been limited due to the weak fatigue performance and lacking of fatigue design rules of AM parts. Particularly, this application relies on the improvement of AM processing technique and integrity assessment of AM parts, the latter usually demands costly and time-consuming fatigue tests, especially for full-scale tests. Accordingly, the size effect and fatigue performance scatter in AM materials are explored on basis of defect data scanned by CT and experimental data in this work. Firstly, the distribution of maximum defects of AM materials under size effect is extrapolated via extreme value statistics theory; then a strength altering factor is proposed to characterize the effect of defects on fatigue scatter and size effect. From essential structure of fatigue curves, the relationship among defects, fatigue strength and fatigue curves are quantitatively analysed to extrapolate the probabilistic fatigue curves for AM materials; finally, three series of AlSi10Mg specimens with different processing parameters and gauge volumes prove the method effectiveness that the “location” and “scale” of fatigue curves is successfully predicted, and defect-tolerant assessment for AM parts is performed by employing the predicted fatigue curves.

Scatter and size effect in High Cycle Fatigue of cast aluminum-silicon alloys: A comprehensive experimental investigation

Cast Al-Si alloys have been widely used in automotive applications with regard to their low density and excellent thermal conductivity. Many components made of these alloys are subjected to cyclic loads which can lead to fatigue failure. For these materials, the well-known size effect in fatigue, whereby the fatigue strength is reduced when the size is increased, can be significant and needs to be properly evaluated. This paper analyses the role of casting defects on the fatigue scatter and size effect. A uniaxial fatigue testing campaign (R=0.1) has been conducted using two cast aluminum alloys, fabricated by different casting processes (gravity die casting and lost foam casting), associated with the T7 heat treatment, and with different degrees of porosity. The fatigue response of different specimens (smooth and notched) with different stressed volumes has been investigated. The first part of this article is about the experimental characterization of the size effect and scatter in both alloys via the concept of the Highly Stressed Volume. The second part investigates the effect of the Highly Stressed Volume on the critical defect size and the establishment of Kitagawa-Takahashi diagram. It is shown that the alloy B, with a population of defects of large size, shows a slight size effect and low scatter. In comparison, alloy A that exhibits a population of defects of relatively small size manifests significant size effect and high scatter.

Crack paths in multiaxial fatigue of C45 steel specimens and correlation of lifetime with the thermal energy dissipation

The work reports the observed fatigue damage of C45 steel specimens tested in a previous work under multiaxial loading conditions and its relationship with the thermal energy dissipation which has been used in the last decades to estimate the uniaxial fatigue behavior of metals. For this purpose, fatigue data relevant to thin-walled samples made of quenched and tempered C45 steel tested under completely reversed combined axial and torsional cyclic loadings with different biaxiality ratios and phase-shift angles have been analysed. The analyses of crack paths at the initiation point of failure were performed after a 50% stiffness loss that corresponded to a crack size ranging from 7 to 15 mm; afterwards, the characteristic crack paths of each loading condition were analysed by using a digital microscope to identify the orientation of the crack initiation plane. After having broken all fatigue tested specimens under static tensile loading, the fracture surfaces were inspected close to the crack initiation point using a digital microscope. Despite the stress states and fatigue damage mechanisms dependent on the load condition, the Q parameter applied to the present experimental results proved to correlate all multiaxial fatigue test results in a single fatigue scatter band.

A polygonal FEM and continuum damage mechanics based framework for stochastic simulation of fatigue life scatter in duplex microstructure titanium alloys

The scatter in the fatigue behavior of duplex microstructure titanium alloys occurs due to microstructural randomness. The presence of two phases in titanium alloy microstructure also contributes to the scatter in fatigue life data. In the literature, several mathematical frameworks have been developed to consider the effect of microstructural randomness on the prediction of fatigue scatter. However, no numerical study has been found that considers the effect of presence of two phases on the fatigue life scatter. Thus, in the present work, a mathematical framework based on continuum damage mechanics (CDM) and polygonal finite element method (PFEM) is developed to predict the fatigue life scatter in α+β titanium alloys. In this framework, PFEM is applied to perform the numerical simulations and CDM is used to explain the fatigue behavior of material. In PFEM, the Voronoi tessellation approach is used to generate the idealized microstructure models. The Waschpress shape functions are adopted to compute the shape functions over the arbitrary convex polygonal elements. In CDM, a fatigue damage model is adopted to consider the crack initiation and propagation under the cyclic loading conditions. The advantage of combined CDM-PFEM framework is that the numerical simulation can be performed at relatively coarser mesh which decreases the computational cost and increases the efficiency of the computational model.While predicting the fatigue life, it has been observed that micro cracks may initiate and propagate at several locations inside the microstructure. Thus, to track the nucleation and growth of micro cracks effectively, a machine learning based technique ‘cluster analysis’ is employed in the developed framework. The “cluster analysis” identifies the location and dimensions of the micro and dominant crack patterns in the domain. Furthermore, for an idealized representation of duplex microstructures, both phases of titanium alloy (i.e., primary α and β) are modeled using random distribution function. The effect of different sources of randomness in microstructures i.e., topology of microstructure, grain size, volume fraction of alpha phase, inhomogeneity in elastic modulus and internal voids, on the fatigue life is investigated. Several simulations are performed on the numerically generated microstructures at various loads. The statistical analysis of the predicted fatigue lives data is performed through normal and Weibull distribution fits. The simulation results highlight that the combined CDM-PFEM based framework is simple and an effective tool to predict the fatigue life scatter and can effectively analyze the mean fatigue life in titanium alloys under cyclic loading conditions.

A probabilistic approach for high cycle fatigue of Wire and Arc Additive Manufactured parts taking into account process-induced pores

Wire and Arc Additive Manufacturing (WAAM) is a direct-energy deposition technique (unlike SLM or EBM) that builds up a part in a layer-by-layer fashion, each layer being constituted of interlaced weld beads. It is the best suited Additive Manufacturing (AM) technique for large structures thanks to its high deposition rate (5 kg/h). The resulting material shows a rough surface, strong residual stress induced by its complex thermal history, a heterogeneous microstructure marked by the different weld passes as well as defects formed by gas pockets. Despite their rarity, pores are found to have a first-order influence on the fatigue life of machined specimens. The discrepancy in their size (> 100 μm) and position is responsible for a considerable scatter that makes classical fatigue tests ineffective. The aim of this study is to propose a novel approach to take into account the effect of rare WAAM-induced defects in high cycle fatigue. To achieve this, numerical porous structures are generated from the knowledge of the real pore population determined by tomography. Their fatigue performances are predicted via a two-scale probabilistic model identified on experimental self-heating results, on which pores have no influence. In that sense, the probabilistic model describes the behavior of a virtually healthy material. Then, by computing a database of representative pore cases, the whole bundle of Wöhler curves for each numerical porous structure is determined. Finally, the numerical fatigue scatter is in close agreement with experimental data, and it is shown that the ranking in pore criticality according to the model matches the fractography observations.

Probabilistic modeling of the size effect and scatter in High Cycle Fatigue using a Monte-Carlo approach: Role of the defect population in cast aluminum alloys

In this study, a probabilistic model based on Monte-Carlo theory is applied to predict the fatigue behavior of cast aluminum alloys. The objective of the proposed approach is to investigate the effect of porosity (i.e. the defect size distribution and spatial density) on the fatigue strength and its associated scatter for uniaxial fatigue loads with the load ratio R = 0.1. The proposed model is applied to two cast aluminum alloys with very different defect characteristics. The results for these two alloys confirm that the model can be used to predict the average fatigue strength with a relative error <5%. It also accurately reproduces the experimentally observed trends concerning the scatter in fatigue strength. The scatter is underestimated but is of the same order of magnitude as the experimental values. It is believed that this is because the proposed model considers that the porosity is the only source of scatter. It is demonstrated that the model is well adapted for the prediction of the volume or scale effect in fatigue. This approach can also be used to estimate the Representative Volume Element in Fatigue for cast aluminum alloys.

Fatigue behavior of a Ti-based metallic glass: Effect of sampling location in association with free volume

The large scatter of fatigue property severely hinders the application of metallic glasses (MGs). The sampling location may be one important reason for the fatigue scatter, however the related studies are few. Here we confirmed that, the fatigue property and mechanism of a Ti-based MG were influenced by the sampling location from casting MG plate. The differential scanning calorimetry (DSC) result indicates that the free volume contents decrease from outside to inside along the thickness direction of casting plate, which is probably due to varying cooling rates in this direction during solidification. It is found that the shear-band features after fatigue fracture depend on the sampling location, that is, for the specimens containing smaller near-surface volume, the small amount of the initial free volume contents and increased free volume contents induced by cyclic loading suppress the formation of shear band. The fatigue endurance limit, fatigue ratio and fatigue life of the specimens containing smaller near-surface volume are obviously higher. The superior fatigue property can be well explained by the shear band-mediated fatigue cracking mechanism. These results enhance the understanding on the relation between the free volume, shear band and fatigue property under cyclic loading and provide the instruction how to regulate the fatigue resistance of MG by controlling where the specimens are cut from casting MG plates based on the microstructural state.

Fatigue strength of aluminium welded joints by a non-local approach

In this paper, the numerical implicit gradient approach already validated for steel welded joints is also used for aluminium joints. Some peculiarities of aluminium joints are discussed and a general fatigue scatter band for arc welded joints has been proposed. The analysed experimental data taken from the literature range from the simple butt-welded joints with a thickness of 2 mm up to the extruded I-beam with a length of about 2 m. The obtained SN behaviour has an inverse slope of 3.7 and, at high cycle fatigue, the strength is about half that of steel joints.