Non-local Fatigue Research Articles

Non-local fatigue criterion based on standard deviation for notches and defects in Ti-6Al-4V

The aim of this study is to propose a non local multiaxial fatigue criterion in order to assess the fatigue limit of stress concentrator such as notches or defects in Ti-6Al-4V. This criterion is based on the standard deviation of the stresses integrated over a given volume around the hot spot point. Up to now, the standard deviation has never been tested as an indicator of stress heterogeneity to assess fatigue life of notch components. Four parameters are necessary to identify the criterion. The criterion is first validated on notched samples based on literature results and shows very good results. A set of experimental tests is conducted on natural and artificial defects including clustering defects and demonstrates the flexibility and accuracy of the criterion.

Non-local muscle fatigue is mediated at spinal and supraspinal levels.

The objective was to measure the corticospinal excitability and motoneuron responsiveness of the right and left Biceps Brachii (BB), and left Abductor Digiti Minimi (ADM) muscles in response to submaximal isotonic fatiguing contractions performed by the right BB muscle. With the familiarization session, ten young moderately active male subjects came to the lab on seven occasions. Three sets of 3min seated elbow curls at 25% of one-repetition maximum (1RM) separated by a 1-min rest performed by the right BB muscle were used as the fatiguing protocol. The motor evoked potential (MEP), cervicomedullary motor evoked potential (CMEP), and compound muscle action potential (Mmax) of the right BB muscle (baseline and after each set of the fatiguing task), the left BB and ADM muscles (baseline, post-fatigue, post-10, and post-20min) were measured. MEP and CMEP were then normalized to Mmax for statistical analysis. The results showed that in the right BB muscle, there was a significant reduction in the MEP after performing the fatiguing task (p= 0.03), while no significant effect of time was seen in the CMEP (p= 0.07). In the left BB muscle, the MEP significantly decreased from pre-fatigue to post-fatigue (p= 0.01) and post-10 (p= 0.001), while there was a significant decline in the CMEP post-fatigue (p= 0.03). In the left ADM muscle, MEP significantly decreased post-fatigue (p= 0.03) and no changes were seen in the CMEP (p= 0.12). These results not only confirm the incidence of non-local muscle fatigue (NLMF) in response to performing submaximal isotonic fatiguing contractions but also as a new finding, imply that both spinal and supraspinal modulations account for the NLMF response.

The utility of laser scanning welds for improving fatigue assessment

Welded joints are a common source of fatigue failures. Traditional fatigue assessment approaches usually describe the weld with an idealized geometry defined by the weld flank angle and the weld toe radius. By doing so, the actual stress concentrations are not considered in such fatigue life predictions. 3D laser scanning technology offers an opportunity to more accurately represent the weld geometry, and accordingly perform fatigue assessment on more accurate representations of weld geometry. This manuscript explores the benefit of incorporating scanned weld geometries into linear elastic stress analysis for fatigue life prediction. Additionally, the capabilities to explain experimental scatter of six different fatigue indicator parameters have been quantified. Using experimental data from 28 tests across three geometries, a total of 60 deterministic and probabilistic fatigue models were assessed using both scanned and idealized weld geometries. The use of scanned weld geometries is found to substantially improve fatigue prediction when using local fatigue indicator parameters. However, if nonlocal fatigue indicator parameters are employed, the use of scanned weld geometries does not display a benefit. In total, the use of nonlocal fatigue indicator parameters with idealized weld geometry offer the greatest accuracy across the three cases examined. Thus, for linear elastic fatigue life assessment, the use of a nonlocal parameter in the fatigue life model is more motivated than utilizing 3D scanned weld geometry. Regardless of how the weld geometry is included, the signed von Mises equivalent stress led to the most reliable fatigue life predictions overall for the specimens considered in this work.

Transcutaneous electrical nerve stimulation improves fatigue performance of the treated and contralateral knee extensors.

Transcutaneous electrical nerve stimulation (TENS) can reduce acute and chronic pain. Unilateral fatigue can produce discomfort in the affected limb and force and activation deficits in contralateral non-exercised muscles. TENS-induced local pain analgesia effects on non-local fatigue performance are unknown. Hence, the aim of the study was to determine if TENS-induced pain suppression would augment force output during a fatiguing protocol in the treated and contralateral muscles. Three experiments were integrated for this article. Following pre-tests, each experiment involved 20min of TENS, sham, or a control condition on the dominant quadriceps. Then either the TENS-treated quadriceps (TENS_Treated) or the contralateral quadriceps (TENS_Contra) was tested. In a third experiment, the TENS and sham conditions involved two\; 100-s isometric maximal voluntary contractions (MVC) (30-s recovery) followed by testing of the contralateral quadriceps (TENS_Contra-Fatigue). Testing involved single knee extensors (KE) MVCs (pre- and post-test) and a post-test 30% MVC to task failure. The TENS-treated study induced greater (p = 0.03; 11.0%) time to KE (treated leg) failure versus control. The TENS_Contra-Fatigue induced significant (p = 0.04; 11.7%) and near-significant (p = 0.1; 7.1%) greater time to contralateral KE failure versus sham and control, respectively. There was a 14.5% (p = 0.02) higher fatigue index with the TENS (36.2 ± 10.1%) versus sham (31.6 ± 10.6%) conditions in the second fatigue intervention set (treated leg). There was no significant post-fatigue KE fatigue interaction with the TENS_Contra. Unilateral TENS application to the dominant KE prolonged time to failure in the treated and contralateral KE suggesting a global pain modulatory response.

Numerical investigation of the influence of twinning/detwinning on fatigue crack initiation in AZ31 magnesium alloy

An analysis of the fatigue behavior of rolled AZ31 magnesium alloy through numerical simulations of polycrystalline aggregates using the crystal plasticity finite element method is presented. A phenomenological pseudo-slip model including twinning, detwinning and subsequent slip in the twinned region was considered in this study. It was calibrated against uniaxial monotonic and cyclic experiments on rolled AZ31 Mg alloy. Multiple periodic two-dimensional synthetic microstructures were generated based on morphological and crystallographic data obtained from electron backscattering diffraction (EBSD) measurements. Fatigue simulations were conducted at different stress amplitudes and mesoscopic non-local fatigue criteria for slip-induced and twin-induced crack initiation were investigated. It was observed that basal slip and twinning-detwinning are the main deformation mechanisms taking place during cyclic loading but that these deformation modes generally occur in different grains. The comparison of the investigated criteria with experimental data also revealed that the twin-induced criterion exhibit better trends in terms of mean behavior, relative dispersion and stress amplitude sensitivity compared with the slip-induced criterion. Finally, the predictive capabilities and limitations of the current modeling approach are discussed.

Numerical modelling of surface roughness effect on the fatigue behavior of Ti-6Al-4V obtained by additive manufacturing

Selective Laser Melting (SLM) is a powder bed fusion process which allows to build-up parts by successive addition of layers using 3D-CAD models. Among the advantages, the high degree of freedom for part design and the small loss of material explain the increasing number of Ti-6Al-4V parts obtained by this process. However, right after additive manufacturing, these parts contain defects (surface roughness, porosity, residual stresses) which significantly decrease the High Cycle Fatigue (HCF) life. In order to minimize the porosity and residual stresses, post-processing treatments like Hot Isostatic Pressing (HIP) and Stress Relieving (SR) are often conducted. But the reduction of the surface roughness by machining is very costly and not always possible, especially for parts with complex geometry. The aim of this work is to evaluate the effect of the surface roughness of Ti-6Al-4V parts produced by SLM on the HCF behavior and to propose a methodology to estimate this effect. Three sets of specimens were tested in tension-compression: Hot-Rolled (reference); SLM HIP machined; SLM HIP as-built. For each condition, microstructure characterization, observation of the fracture surface of broken specimens, surface analysis and volume analysis were carried out respectively by Optical Microscope (OM), Scanning Electron Microscope (SEM), 3D optical profilometer and 3D X-ray tomograph. Results of fatigue testing show a significant decrease of the HCF life mainly due to the surface roughness. Along with experimental testing, numerical simulations using FEM were conducted using the surface scans obtained by profilometry and tomography. Based on extreme values statistics of a non-local fatigue indicator parameter (FIP), a methodology is proposed to take into account the effect of the surface roughness on the HCF life.

Defect sensitivity in additively manufactured aluminium alloys: contribution of CAD artificial defects

The prediction of the fatigue resistance of additively manufactured parts is a current issue for the materials and process qualification in aerospace industry. Despite a continuous improvement of AM process, the presence of defects cannot yet be completely avoided, and the latter are still one of the main causes of fatigue damage in AM materials. In this framework, the present work focused on the influence of defects on the uniaxial fatigue behavior of AlSi7Mg0.6 alloy produced by Selective Laser Melting (SLM). Uniaxial fatigue tests have been performed. Fatigue specimens were subjected to a T6 treatment, and then machined in order to avoid the influence of surface roughness. Besides, for some specimens, artificial defects were directly introduced through CAD. The introduction of artificial defects, whose sizes and positions are precisely controlled, aims to provide a proper assessment of defect sensitivity. X-ray tomography was used to characterize both natural and artificial defects. Finite-element calculations of the local stress fields in the vicinity of defects were conducted, accounting for the real defect geometries obtained with CT scans. The application of a non-local multiaxial fatigue criterion then allowed to analyze defect criticity.

Defect size map for cast A357-T6 component under multiaxial fatigue loading using the Defect Stress Gradient (DSG) criterion

Experimental fatigue tests have been performed on structural components casted in A357-T6 aluminum alloy. A non-local fatigue criterion based on the stress gradient has been used in order to simulate the Wöhler diagram of the components. The criterion is accurate and shows that the stress gradient at the scale of the structure leads to good estimation of fatigue life whereas a local criterion gives results 100% below the experimental one. A critical defect size map based on a model of the whole component using the DSG (Defect Stress Gradient) criterion is provided. Simulation results have been compared with experimental results obtained on components with artificial surface defects: the DSG criterion provides good estimation of crack initiation sites.

Probabilistic Model of Fatigue Damage Accumulation in Rubberlike Materials

The paper presents a mathematical model of the non-localized fatigue damage accumulation process in rubberlike materials. A relation for the determination of the constants of the corresponding equation with allowance for known fatigue curve characteristics, in particular for their random spread, is proposed. Computational relationships for the determination of the probabilistic characteristics of damage have been derived. Experimental data for the determination of realization of the fatigue accumulation process in rubber specimens, which are in good agreement with theoretical results, are considered.

Conditions for the Transition from Nonlocalized to Localized Damage in Metals and Alloys. Part 3. Determination of the Transition Conditions by the Analysis of Crack Propagation Kinetics

Special features of initiation and growth of short cracks under stresses above the fatigue limit are studied for a wide range of metals and alloys. The authors analyze the growth kinetics of short fatigue cracks, which is assessed by the dependence of crack length or crack growth rate on the number of loading cycles. The transition from the stage of short crack propagation (nonlocalized fatigue damage) to the stage of a main crack propagation (localized fatigue damage) is shown to be characterized by a more intensive increase of the crack growth rate. A procedure for determination of the main crack sizes corresponding to the transition from nonlocalized to localized fatigue damage has been substantiated. It has been found out that the fatigue crack sizes corresponding to this transition at stresses above the fatigue limit decrease with increasing stresses and remain smaller than those at stresses equal to the fatigue limit.

Conditions for the Transition from Nonlocalized to Localized Damage in Metals and Alloys. Part 1. Crack Sizes at Fatigue Limit

The paper addresses special features of nonlocalized and localized fatigue damage in metals and alloys. The sizes of maximum fatigue cracks at a fatigue limit in metals and alloys of various grain sizes and strengths are analyzed. The authors discuss the linear and nonlinear fracture mechanics criteria that relate the fatigue crack sizes and the fatigue limits. The experimental values of the fatigue crack size are compared to those calculated by different criteria. Special features of initiation of nonpropagating fatigue cracks in the presence of stress concentrators are studied.

Knee extension fatigue attenuates repeated force production of the elbow flexors

Non-local muscle fatigue has been demonstrated with unilateral activities, where fatiguing one limb alters opposite limb forces. Fewer studies have examined if non-local fatigue occurs with unrelated muscles. The purpose of this study was to investigate if knee extensors fatigue alters elbow flexors force and electromyography (EMG) activity. Eighteen males completed a control and fatiguing session (randomised). Blood lactate was initially sampled followed by three maximal voluntary contractions (MVC) with the elbow flexors and two with the knee extensors. Thereafter, subjects either sat (control) or performed five sets of bilateral dynamic knee extensions to exhaustion using a load equal to the dominant limb MVC (1-min rest between sets). Immediately afterwards, subjects were assessed for blood lactate and unilateral knee extensors MVC, and after 1 min performed a single unilateral elbow flexor MVC. Two minutes later, subjects performed 12 unilateral elbow flexor MVCs (5 s contraction/10 s rest) followed by a third blood lactate test. Compared to control, knee extensor force dropped by 35% (p < 0.001; ES = 1.6) and blood lactate increased by 18% (p < 0.001; ES = 2.8). Elbow flexor forces were lower after the fatiguing protocol only during the last five MVCs (p < 0.05; ES = ∼0.58; ∼5%). No changes occurred between conditions in EMG. Elbow flexor forces significantly decreased after knee extensors fatigue. The effect was revealed during the later stages of the repeated MVCs protocol, demonstrating that non-local fatigue may have a stronger effect on repeated rather than on single attempts of maximal force production.

Fatigue life estimation of notched elements with use of non-local volumetric method

The work presents non-local fatigue computations method together with volumetric approach, in which energy parameter has been used. Proposed model has been used for simulation computations, based on experimental testing of unnotched (smooth) and notched specimens subjected to two types of loads, i.e. tensile – compressive and oscillatory bending. Computations of energy parameter value have been done based on results of FEM elastic–plastic analysis for cyclic properties of a material. Averaging operation was performed for assumed constant threshold value, resulting in averaged value of energy parameter, on the grounds of which fatigue life has been read off from characteristics of unnotched specimens. The threshold value assumed depends on load type, and the volume within which averaging is performed depends on load level.

From uni- to multi-axial fretting-fatigue crack nucleation: Development of a stress-gradient-dependent critical distance approach

Fretting fatigue is characterized by combined high stress gradients induced by contact loading and more homogeneous stress gradients induced by bulk fatigue stressing. The stress gradients computed at the “hot-spot” located on the surface at the trailing contact border are very high, usually above 10GPa/mm. For such uncommon stressing conditions, prediction of cracking risk becomes very complex and non-local fatigue approaches must be adopted. The purpose of the present study was to investigate how non-local strategies, such as “critical distance”, developed for medium stress gradient conditions such as “notch” configurations, were transposed to predict fretting cracking risk. Elastic crack nucleation conditions of a 35 Ni Cr Mo 16 low alloyed steel at 10E6 cycles have been identified for various cylinder pad radius, contact pressure and fatigue stress conditions. The experimental crack nucleation conditions were then compared to predictions from analytical simulations coupling uni-axial and Crossland’s multiaxial fatigue descriptions. The local “hot-spot” analysis systematically overestimated cracking risk and induced more than 30% error with respect to the experimental values. The non-local “critical distance method” based on a constant length scale value still displayed more than 10% dispersion suggesting that a non-constant “critical distance” approach must be considered. By expressing the critical distance evolution as a function of the hydrostatic stress gradient operating next to the stress hot-spot, dispersion was reduced below 5%. Established for the Crossland’s stress invariant formulation, this tendency is confirmed by comparing McDiarmid and MWCM critical plane fatigue approaches.

Stress gradient effect on the crack nucleation process of a Ti–6Al–4V titanium alloy under fretting loading: Comparison between non-local fatigue approaches

This study focuses on the stress gradient effect regarding the crack nucleation of a cylinder/plane Ti–6Al–4V titanium alloy contact under low cycle fatigue (LCF) fretting loading. Several local and non-local analytical approaches were compared to predict experimental results. The first part of the study presents fretting nucleation boundaries for three different cylinder radii in the partial slip regime. In the next part, the Crossland and Papadopoulos multi-axial fatigue criteria are computed and compared. Finally, local and non-local fatigue approaches are compared. Square constant volume, critical distance and weighted function approaches have been compared.The methodology used covers a large range of stress gradients. The impact of varying the stress gradients is that the larger the stress gradient, the larger the difference between experiments and local stress fatigue predictions. A Crossland local form was applied to confirm that a local stress fatigue analysis cannot predict the fretting cracking risk. Three non-local approaches were carried out, and the results allowed the proper prediction of the empirical thresholds with a 3–5% margin of error. The positive results obtained helped to select a multi-axial fatigue criterion and a non-local approach which take into account the gradient effect of contact fretting behavior.

Effect of annealing twins on crack initiation under high cycle fatigue conditions

Several experimental studies have shown that fatigue cracks in Ni-based superalloys preferentially form in the vicinity of favorably oriented annealing twin boundaries. However, this increase in the probability of crack nucleation has not been quantified in detail since 3 material modeling has not typically considered twins. The present work employs finite element simulations and a continuum crystal plasticity constitutive model for RR1000 Ni-based superalloy to assess the potential enhancement of nonlocal fatigue indicator parameters (FIPs) incurred by the presence of Σ3 twins. Two cases are analyzed: single crystals with twins of different widths subjected to single slip cyclic shear deformation aligned with the twin plane and polycrystals with 20 % of the grains half-twinned. Simulations with and without twins are compared in both cases. The results demonstrate the detrimental effect of twins in shifting the upper tail of the FIP distribution to higher values; this shift is more pronounced with an increase of twin thickness.

Microstructure-sensitive extreme-value probabilities of high-cycle fatigue for surface vs. subsurface crack formation in duplex Ti–6Al–4V

The distributions of the extreme-value driving force(s) for surface vs. subsurface fatigue crack formation (nucleation and early growth) in high-cycle fatigue are evaluated for a microstructure variant of duplex Ti–6Al–4V. In polycrystalline metals, previous work has explored estimation of the driving force(s) for fatigue crack formation at the scale of the grains by computing non-local fatigue indicator parameters (FIPs) based on the cyclic plastic strain averaged over domains on the length scale of the grains. Instantiated statistical volume elements (SVEs), which sample the distributed microstructure attributes of interest for a given material system, can be simulated via the finite element method with embedded polycrystalline plasticity models to estimate the distributed plasticity and resulting FIPs. This strategy of simulating multiple SVEs is in contrast to the simulation of a single representative volume element which is typically untenably large for extreme-value distributions of microstructure attributes or response variables. In this work, multiple SVEs are instantiated with both traction-free (i.e. surface) boundary conditions and fully periodic (i.e. subsurface) boundary conditions. In addition to estimating the extreme-value distributions of the FIPs, newly introduced extreme-value marked correlation functions are applied to characterize the coupled crystallographic microstructure attributes (e.g. grain size, grain orientation, grain misorientation) that most influence the extreme-value distributions of the FIPs. It is shown that there is overlap in the distributions of the driving forces for surface vs. subsurface crack formation in the low to moderate range of failure probability based on FIPs; however, at higher failure probability levels, the driving forces are highest for surface crack formation. The overlap in the distributions of the driving forces for fatigue crack formation in the low to moderate probability range may assist in describing the competing surface vs. subsurface failure modes that are observed experimentally.

Simulated microstructure-sensitive extreme value probabilities for high cycle fatigue of duplex Ti–6Al–4V

A newly developed microstructure-sensitive extreme value probabilistic framework to characterize the performance/variability for damage evolution processes is exercised to compare the driving forces for fatigue crack formation (nucleation and early growth) at room temperature for four different microstructure variants of a duplex Ti–6Al–4V alloy. The aforementioned probabilistic framework links certain extreme value fatigue response parameters with microstructure attributes at fatigue critical sites through the use of marked correlation functions. By applying this framework to study the driving forces for fatigue crack formation in these microstructure variants of Ti–6Al–4V, these microstructures can be ranked in terms of relative high cycle fatigue (HCF) performance and the correlated microstructure attributes that have the most influence on the predicted fatigue response can be identified. Nonlocal fatigue indicator parameters (FIPs) based on the cyclic plastic strain averaged over domains on the length scale of the microstructure attributes (e.g., grains, phases) are used to estimate the driving force(s) for fatigue crack formation at the grain scale. By simulating multiple statistical volume elements (SVEs) using crystal plasticity constitutive relations, extreme value distributions of the predicted driving forces for fatigue crack formation are estimated using these FIPs. This strategy of using multiple SVEs contrasts with simulation based on a single representative volume element (RVE), which is often untenably large when considering extreme value responses. The simulations demonstrate that microstructures with smaller relative primary α grain sizes and lower volume fractions of the primary α grains tend to exhibit less variability and smaller magnitudes of the driving forces for fatigue crack formation. The extreme value FIPs are predicted to most likely occur at clusters of primary α grains oriented for easy basal slip. Additionally, surrounding grains/phases with soft orientation shed load to less favorably oriented primary α grains, producing extreme value FIPs.

A non-local fatigue approach to quantify Ti–10V–2Fe–3Al fretting cracking process: Application to grinding and shot peening

This paper presents an experimental study on the tribological behaviour and cracking response of a Ti–10V–2Fe–3Al titanium alloy under fretting loading with a cylinder on plane configuration. Three types of surfaces were investigated: a polished one considered as the reference, a ground one and a shot peened surface. Surfaces were compared with respect to residual stress, hardness and roughness. The first step of this study was to determine sliding conditions and coefficient of friction of the three contact types. Next, fretting tests under stabilized partial slip regime were carried out to investigate crack nucleation and propagation. Results show that whatever surface roughness or residual stress in the material, tribological behaviour is the same. These latter confirm that sliding condition and coefficient of friction in partial slip regime is due to material effect and not to roughness or surface hardness. Then, residual stress induced by grinding or shot peening have no influence on the crack nucleation threshold under fretting solicitation because crack nucleation is only induced by a sufficient tangential loading. The crack nucleation threshold is formalized by applying the Crossland criterion taking into account the stress gradient and the ensuing “size effect”. As expected, cracks propagation is influenced by residual stress under the surface. Compared to the reference case, for a same loading parameters set, residual stress induced by grinding is not sufficient to decrease the crack length reached whereas effects of shot peening decrease highly these latter. So, there is a threshold of residual stress from which residual stresses are useful against cracking.

A fatigue endurance criterion in two stages with application to fretting contact

In this paper we propose a fatigue endurance criterion suitable for mechanical components under high stress gradients. It is composed of two stages in order to predict both short and long crack arrest. In the first stage, a non-local multiaxial fatigue criterion measures the potential for crack initiation/short crack arrest. In the second stage, linear elastic fracture mechanics is used to evaluate the possibility of long crack arrest. The predictions of the fatigue criterion are compared with available experimental data obtained with cylinder-flat contacts under partial slip, fretting wear conditions. The results show that the proposed criterion can describe the endurance mechanisms observed in the experimental data.