Goodman Diagram Research Articles

Evaluation of high cycle fatigue behaviour of alloy 617M at 973 K: Haigh diagram and associated mechanisms

Combined influence of mean stress and alternating stress on the high cycle fatigue (HCF) behaviour of Alloy 617 M at 973 K is discussed in the present study. Constant life Haigh diagrams have been generated using different combinations of alternating stress (σa) and mean stress (σm). The alloy exhibited dynamic strain aging (DSA) which is found to strongly influence the cyclic life as well as the fatigue limit. Apart from DSA, presence of annealing twins and carbide precipitation at high temperature during fatigue deformation is also found to positively influence the fatigue life of the alloy.

Influence of the Realistic Artery Geometry Parameters on a Coronary Stent Fatigue Life

The stents’ adaptability and safety in realistic and idealized stenotic coronary model were compared to investigate the influence of artery geometry parameter on stent fatigue life. The stents’ fatigue resistance ability was calculated using Goodman diagram, and the cycle to failure, the fatigue life, and the fatigue safety factor (FSF) were analyzed. Although the peak top of the von Mises stress was located at the bending area of crowns, the stress distributions were different in the two models. Considering the safety and accuracy, it is necessary to use a realistic geometric model to calculate the stent fatigue performance.

Enhanced Pre-Strain Application for Goodman Data Generated with Vibration-Based Testing

Imparting residual stress is an essential step in the generation of Goodman data via Air Force Research Laboratory’s vibration-based fatigue test. Conventional Goodman data is constructed through uniaxial fatigue testing at a rate of 40 Hz, while the vibration-based testing excites stresses at 1,600 Hz in a stress state similar to those of gas turbine engine (GTE) airfoils in service. Fully reversed oscillating fatigue loads are combined with a steady residual stress imparted by a preliminary plastic straining procedure, and a finite element model (FEM) is used to predict the residual stress distribution at the fatigue zone of the sample. The goal of this work is enhancing the Pre-strain procedure that imparts residual stresses to develop a less conservative design approach that captures GTE phenomena on a modified Goodman line. Improvements were made to the FEM by more effectively incorporating empirical tensile stress-strain behavior, in addition to more accurately representing the pressures and forces acting on the specimen during monotonic loading. Results are demonstrated on Aluminum 6061-T6 by comparing strain field results from digital image correlation to FEM analysis. The converged FEM solution had a standard deviation in eyy of 2,557 microstrain and predicted a residual σyy of 73.91 MPa, while the optimized solution had a standard deviation in eyy of 495.2 microstrain (akin to the experimental variation of 376.1 microstrain) and predicted a residual σyy of 31.03 MPa.

The effect of mean axial and torsional stresses on the fatigue strength of 34CrNiMo6 high strength steel

The present study consists of a theoretical, experimental and fractographic investigation of the effect of superimposed static axial and shear stresses on the high cycle fatigue behavior of a 34CrNiMo6 high strength steel in quenched and tempered condition (UTS = 1210 MPa), commonly employed in highly stressed mechanical components. The Haigh diagrams for the axial and torsional cases under different values of mean stress were obtained. In both cases, experimental results showed that increasing the mean stress gradually reduces the stress amplitude that the material can withstand without failure. The results of the present tests are compared with the theoretical predictions from Findley, based on the maximum damage critical plane; and the methods of Marin and Froustey, which are energetic based criterions. Froustey’s method shows the best agreement with experimental results for torsional fatigue with mean shear stresses, showing a non-conservative behaviour for the axial fatigue loading case. Macro-analyses and micro-analyses of specimen fracture appearance were conducted in order to obtain the fracture characteristics for different mean shear stress values under torsion fatigue loading.

A Computational Framework for Structural and Fatigue Analysis of a 5MW Wind Turbine Blade Under Wind Loads

With the pressing requirement of wind energy capacity, the wind turbine blade size has been getting larger and larger in recent decades. For such a large-size blade, it is of prime importance to accurately evaluate the mechanical response under various wind loading conditions. In this work, we present a computational framework to achieve this end. Firstly, a finite element model for a 5MW blade is established according to the well-known NREL report. A composite laminated element is adopted to describe the blade structure. The effectiveness of this model is validated by means of eigenfrequency analysis. Secondly, a one-way partitioned FSI coupling algorithm is developed to consider the wind loading condition applied on the blade surface. The coupling algorithm facilitates the use of two parallel open source codes, e.g., FrontFlow/blue and ADVENTURE. Finally, an empirical approach is adopted to estimate the fatigue life of the blade under wind loads. This approach uses the so-called rainflow counting algorithm to reduce a spectrum of varying stress to equivalent stress cycles with constant amplitude. The remaining service life of the blade is then estimated by means of the Goodman diagram and the Miner’s damage accumulation law. Several numerical cases are carried out, which validates the capacity of the proposed computational framework for structural and fatigue analysis of wind turbine blades under various wind loads.

Finite Element Analysis of Fatigue Behavior of Stent in Tapered Arteries

In order to open up the blocked lumen and remodel the blood environment, vascular stents were usually used to transplant into narrowed blood vessels. Due to its minimally invasive and highly efficiency, stenting has achieved great success in the treatment of cardiovascular diseases. However, failure of stents due to its fatigue will damage the arterial wall, leading to adverse reactions such as thrombosis and in-stent restenosis (ISR), which severely limited its long-term outcome. Therefore, it was very important to predict the service life of stents, especially in tapered arteries. FEA was adopted to study the effects of arterial tapering and stent material on the fatigue life of stents. Balloon-stent-plaque-vessel coupling systems were established to simulate the working environment of stents in vivo. Five different tapered vessel models were established to study the vessel tapering level on the fatigue life of stents. Besides, the fatigue life of 316L stainless steel stent and L605 cobalt-chromium (Co-Cr) alloy stent deployed into a 0.43° tapered vessel were analyzed and compared. The Goodman diagram method was adopted to evaluate the fatigue resistance of stents. Results showed that the stress concentration was found on the inner crown of the strut when the stent was subjected to pulsating blood pressure. It was similar to the stress distribution on the stent after expansion. This also indicated that the crown of the strut played a decisive role in the long-term efficacy of the stent. The maximum average stress of Co-Cr alloy stent was higher than 316L stainless stent. However, the fatigue resistance of stents was improved by simply changing stent material from 316L stainless to L605 cobalt-chromium alloy. So the L605 Co-Cr alloy stent can withstand greater stress without fatigue. In addition, the tapering of the vessel will also affect the fatigue performance of the stent. The stent implantation in tapered vessels could lead to greater residual stress and shorter fatigue life of the stent. With the tapering level gradually increased, the minimum fatigue safety factor of the stent decreased, which indicated the stent was more likely to fatigue. Compared to a straight vessel, the fatigue life of the stent was shortened by 9.8%, when it was deployed in a 1.13° tapered vessel. The obtained results showed that finite element analysis was an effective tool to predict stent fatigue life. The method that predicted stent fatigue life in tapered vessels can help clinicians select stents that are more suitable for tapered vessels and help stent engineers design stents that are more resistant to fatigue.

An Experimental Method to Evaluate the Effect of Welding Residual Stress on Corrosion Fatigue Properties of Structural Steel in Synthetic Seawater

Tensile residual stress can cause a reduction in the fatigue strength of steel not only in air but also in corrosive environments. In air, for example, the effect of residual stress on fatigue strength can be estimated by using relations between fatigue strength and mean stress such as the modified Goodman diagram. However, it is not clear whether a sort of fatigue strength estimation can be applicable to corrosion fatigue properties. This paper presents an experimental method to evaluate the effect of welding residual stress on corrosion fatigue properties quantitatively, where corrosion fatigue tests were conducted in synthetic seawater by using characteristic fatigue specimens that have two parts, a tensile residual stress part and the other supporting part. Bead-on-plate welding was performed for applying welding residual stress in the tensile residual stress part. Residual stress relaxation was measured using the X-ray diffraction method in the midst of fatigue testing. Effects of tensile residual stress on corrosion pit growth and S-N curves were discussed.

Study on wake-induced fatigue on wind turbine blade based on elastic actuator line model and two-dimensional finite element model

Atmospheric and wake turbulence have a great and immediate impact on the fatigue life of wind turbine blades. Generally speaking, wake-induced fatigue accounts for 5%–15% increase of fatigue load on the wind turbine rotor, which definitely threats the safety and economy of the whole wind farm. However, this effect is difficult to simulate which involves multi-wake interaction and fluid structure interaction. To better simulate the wake-induced fatigue on wind turbine blades, a novel elastic actuator line model is employed in this study. The elastic actuator line is a two-way coupling model, consisting of traditional actuator line model and one-dimensional implicit or explicit finite difference method beam structural model, among which the beam model takes gravitational force, aerodynamic force and centrifugal force into consideration. Large eddy simulation method in the NREL SOWFA code is employed to model the turbulence effect, including wake-induced turbulence and atmospheric turbulence. For the fatigue analysis part, the fatigue life of an NREL 5MW turbine blade subjected to upstream wind turbine wake effects is studied using the elastic actuator line model and laminate data available from Sandia Laboratory in the United States. First, the strain and stress on different composite materials, such as uniaxial carbon fibre and biaxial composite material, are recovered by using the sectional force and moment obtained with the one-dimensional beam model and two-dimensional finite element method model, namely BECAS. Second, the stress-life method, rain-flow counting method, shifted Goodman diagram (constant life diagram) and Miners rule are employed to estimate the fatigue life for different composite materials. Noticeably, elastic actuator line largely reduces the computational efforts compared with a high-resolution computational fluid dynamics model, in which each wind turbine blade is fully resolved. Both the characteristics of different composite materials and airfoil geometries will be considered during fatigue analysis. As a result, the above procedure makes the fatigue life estimation more reliable and feasible. In the case studies, the moment time series predicted by elastic actuator line and FAST are compared. The fatigue damage of NREL 5MW wind turbine under turbulent neutral atmospheric boundary layer is calculated, and the fatigue critical section is determined to be at 10.25 m section from root. Finally, in the study of two in-line turbines, the fatigue damage increase by wake flow is 16%, which is close to the results from previous studies.

High cycle fatigue and ratcheting interaction of laser powder bed fusion stainless steel 316L: Fracture behaviour and stress-based modelling

Variations in the physical and mechanical properties of parts made by laser power bed fusion (L-PBF) could be affected by the choice of processing or post-processing strategies. This work examined the influence of build orientation and post-processing treatments (annealing or hot isostatic pressing) on the fatigue and fracture behaviours of L-PBF stainless steel 316L in the high cycle fatigue region, i.e. 104–106 cycles. Experimental results show that both factors introduce significant changes in the plastic deformation properties, which affect fatigue strength via the mechanism of fatigue-ratcheting interaction. Cyclic plasticity is characterised by hardening, which promotes mean stress insensitivity and improved fatigue resistance. Fatigue activities, involving the initiation of crack at defects and microstructural heterogeneities, are of greater relevance to the longer life region where the global deformation mode is elastic. As the simultaneous actions of ratcheting and fatigue generate complex nonlinear interactions between the alternating stress amplitude and mean stress, the fatigue properties could not be effectively predicted using traditional stress-based models. A modification to the Goodman relation was proposed to account for the added effects of cyclic plasticity and was demonstrated to produce good agreement with experimental results for both cyclic hardening and softening materials.

Structural safety evaluation of a subway bolster based on numerical simulation and experimental test

The structural safety of a subway bolster is studied by fatigue strength testing and numerical simulation. A novel approach is proposed to determine the loading scheme in the fatigue test. This method identifies the loads accurately and allows for efficient yet economical fatigue test. Full-scale fatigue test of the bolster is carried out up to 1 × 107 load cycles under normal atmospheric conditions. The finite element model is validated based on the stresses measured by strain gauges. The fatigue life of the bolster is evaluated by Goodman diagram and nondestructive test since it is modeled as a series system of weak points. The results demonstrate that this bolster satisfies the structural safety requirement and its fatigue life is more than 1 × 107 load cycles with 90% reliability.

Analysis of blade tip timing data from fan blades with synchronous and non-synchronous vibration

Blade tip timing (BTT) as an alternative method is capable of directly measuring the blade tip displacement and inferring the vibration characteristics of rotating blades. Its use is growing in popularity due to its ease of application and the ability to deliver information concerning all blades in a rotor. Although the interpretation of the collected data remains an issue, this paper puts forward a process of using such data to analyse the vibrational characteristics of fan blades under different operating conditions and find the blade endurance margin combined with finite element analysis (FEA).A test system with eight casing-mounted optical probes and one OPR (once per revolution) sensor is built to collect the blades’ arrival time of an axial fan. Results indicate that flutter occurs at engine order (EO) 1.5 with a combination of three nodal diameters (2, 3, 4), however, nodal diameter 2 is dominant. A noticeable response (EO≈0.5) is considered as stall. Because every blade vibrates with a frequency lower than its natural frequency (eigenfrequency), and all of them undergo a similar vibration form, continuously rising and falling, which caused by the rotating stall cells. The 1st flex mode – EO2 crossing is found at 48% rotor speed and it’s consistent with the results of FEA. Finally, the blade endurance in Goodman diagram demonstrates that flutter poses a higher risk in comparison with the synchronous vibration.

A new model for predicting the gigacycle fatigue strength of high-strength steels

Three models for predicting the gigacycle fatigue strength of high-strength steels were investigated in this study: the Tanaka-Akiniwa model, the Murakami equation and a newly-formulated model. The Tanaka-Akiniwa model proved to have the drawback of overestimating the inclusion size effects. In the Murakami equation, the calculated ODA growth curve was imaginary. Our results demonstrated that the new model generated the most accurate predictions. Predictions were then derived, with each constant calculated by fitting the experimental data to each steel grade. The derived predictions were therefore not universal but different for each steel grade. The accuracy of the derived predictions varied according to the grade of steel. The worst accuracy was for JIS-S40C, the second worst was for JIS-SUJ2 and the third worst was for JIS-SCM440 under R = –1. Other than these three predictions, though, the accuracy was excellent. During the fitting of the experimental data, the existence of new fatigue limits was suggested in the gigacycle regions: these were revealed by fatigue testing up to 1011 cycles. The derived predictions indicated only minor differences between steel grades for gigacycle fatigue strength. With increasing inclusion size, the drop in gigacycle fatigue strength became less steep, and looked at in terms of the mean stress effect, a modified Goodman line could safely be used for high-strength steel.

Fatigue of natural rubber under different temperatures

Natural rubbers have extraordinary physical properties, typically the ability to crystallize under tension that is assumed to be responsible for their high fatigue resistance. Strain-induced crystallization (SIC) is a high thermo-sensitive phenomenon. Better understanding how SIC reinforces fatigue life and how temperature affects this property is therefore a key point to improve the durability of rubbers. The present study investigates temperature effects on the fatigue life reinforcement due to SIC for non-relaxing loadings. After a brief state of the art that highlights a lack of experimental results in this field, a fatigue test campaign has been defined and was carried out. Results obtained at 23 °C were first described at the macroscopic scale. Both damage modes and number of cycles at crack initiation were mapped in the Haigh diagram. Fatigue damage mechanisms were then investigated at the microscopic scale, where the signature of SIC reinforcement in the crack growth mechanisms has been identified. Typically, fatigue striations, wrenchings and cones peopled the fracture surfaces obtained under non-relaxing loading conditions. At 90 °C, fatigue life reinforcement was still observed. It is lower than at 23 °C. Only one damage mode was observed at the macroscopic scale. At the microscopic scale, fracture surfaces looked like the ones of non-crystallizable rubbers. At 110 °C, the fatigue life reinforcement totally disappeared.

Effect of Plaque Composition on Biomechanical Performance of a Carotid Stent: Computational Study

Clinical application of bare metal stents is constrained by the occurrence of instent restenosis, mainly due to the complex biomechanical environment in the body. Numerical simulation method was used to evaluate the effect of plaque composition on stent performance in a carotid artery. CT angiography (CTA) data were used as a reference, and zero-load state of the carotid artery was used to establish a 3D stenotic artery model. Different plaque compositions, calcified and hypo-cellular were defined in Model 1 and Model 2, respectively. Interactions between the stents and arterial tissues within the stent crimping-expansion process were analyzed to explore the effects of plaque composition on the mechanical parameters of carotid stents. Goodman diagram and fatigue safety factor (FSF) were analyzed to explore the effects of plaque composition on fatigue performance of a carotid stent in the stent service process. In the stent crimping-expansion process, the von Mises stress in the stent and the dog-boning ratio in Model 1 were higher than that in Model 2. The calcified plaque prevented the stent from expanding the stenotic vessel to a pre-set diameter. Thus, the risk of rupture in the calcified plaque was higher than that in the hypo-cellular plaque. Plaque also affected the stress/strain in the vessel wall, which was observed to be lower in Model 1 than in Model 2. This indicated that calcified plaque could decrease the stress-induced injury of arterial tissues. Within the stent service process, the stents used in these two models were predicted to not fail under fatigue rupture as calculated by the Goodman diagram. Additionally, the points closer to the fatigue limit were generally observed at the inner bend of the stent crowns. The FSF of the stent in Model 1 was lower than that in Model 2. The stent operating in the presence of calcified plaques suffered high risk of fractures. Reliability and fatigue performance of the stent were found to be associated with plaque composition. Hence, this study may provide stent designers an approach toward enhancing the mechanical reliability of a stent.

How to evaluate the fatigue life of textile composite structures by the numerical analysis and the experimental data with scatter

The fatigue test data and Goodman diagram have employed in order to evaluate the safety for a long period of time. Since the discrepancies exist in the fatigue test data, a modified Goodman diagram with a failure probability and a confidence level has been proposed in this paper. The confidence level is a function of total number of test data. The proposed procedure has an advantage which can be applied to a small number of specimens. As a numerical example, a hydrogen gas tank for automobile made of CFRP has been picked up. FEM has been applied to obtain the stress under a pressure in the tank. The in and out of gas to tank is considered as a fatigue phenomenon. The safety of tank for repeated use has been evaluated by the comparison of maximum stress generated in the tank and the modified Goodman diagram with a probability of failure. It is recognized that the proposed procedure is a useful and reasonable method for safety evaluation.

Fatigue damage assessment of wind turbine composite blades using corrected blade element momentum theory

This paper presents a method for estimating the fatigue life of composite blades of horizontal axis wind turbines, and a real blade example of the NREL 5 MW reference wind turbine is employed to verify this proposed method. First, the distributions of aerodynamic loads are analysed by new corrected blade element momentum theory, and then the aerodynamic performance of the blade under various wind speeds is assessed. The time-history of the wind speed is generated by using the Weibull distribution based on the offshore wind parameters available. The maximum stress caused by the aerodynamic loads due to wind is then calculated through the finite element analyses. The fatigue cycle during the certain time period is estimated by fast Fourier transform for the load spectrum, which converts the time-stress spectrum to stress cycles. The fatigue damage and remaining service life of wind turbine composite blades are estimated by the Goodman diagram and S-N curve for stress cycles during the service time. Finally, the remaining service life is predicted by utilising the Miner's law for linear fatigue damage accumulation. The results of the real wind turbine composite blade show that the proposed approach can provide an effective tool for evaluating the fatigue damage and assessing the structural performance of the wind turbine composite blades during the service life.

Analysis of the fatigue performance of elastic rail clip

Abstract As a critical component of railway fastening system, the elastic rail clip (e-clip) maintains the rail position using its specified toe load. To understand its fatigue failure during service, the fatigue experiment, finite element analysis (FEA) and failure analysis were performed on e-clip. Under normal wheel load, e-clips with high, normal, and low toe loads were run-out at 5 × 106 cycles. Under the contribution of impact on wheel load, the fatigue lives were reduced to 5468 cycles and 16,839 cycles for e-clips with high and normal toe loads, respectively. For low toe load, the e-clip under the contribution of impact could withstand >5 × 106 cycles. The stress distribution on e-clip was numerically evaluated using FEA, which was in good agreement with that of experiment. Goodman diagram could be used for the fatigue evaluation of e-clip. The mean stresses and stress amplitudes of run-out e-clips were under the line of Goodman equation, while those of failed e-clips were on and above the line of Goodman equation. The fatigue crack was found to nucleate at the location of highest stress. The severity at fatigue crack front increased with the crack length until the overload fracture.

Effects of Stress Ratio and Microstructure on Fatigue Failure Behavior of Polycrystalline Nickel Superalloy

The effects of microstructure and stress ratio on high cycle fatigue of nickel superalloy Nimonic 80A were investigated. The stress ratios of 0.1, 0.5 and 0.8 were chosen to perform fatigue tests in a frequency of 110 Hz. Cleavage failure was observed, and three competing failure crack initiation modes were discovered by a scanning electron microscope, which were classified as surface without facets, surface with facets and subsurface with facets. With increasing the stress ratio from 0.1 to 0.8, the occurrence probability of surface and subsurface with facets also increased and reached the maximum value at R = 0.5, meanwhile the probability of surface initiation without facets decreased. The effect of microstructure on the fatigue fracture behavior at different stress ratios was also observed and discussed. Based on the Goodman diagram, it was concluded that the fatigue strength of 50% probability of failure at R = 0.1, 0.5 and 0.8 is lower than the modified Goodman line.

Mean Stress Effect on the Axial Fatigue Strength of DIN 34CrNiMo6 Quenched and Tempered Steel

The present study consists of a theoretical and experimental investigation of the effect of axial mean stresses on the high cycle fatigue behaviour of DIN 34CrNiMo6 high strength steel in quenched and tempered conditions. The axial S-N curves under 4 different stresses ratios were obtained. Experimental results show that increasing the value of the tension mean stresses gradually reduces the axial stress amplitude the material can withstand without failure. Moreover, the compressive mean stresses show a beneficial effect in terms of the axial fatigue strength, resulting in a non-symmetrical Haigh diagram. A historic review of the axial mean stress effect is presented, showing the shape of the Haigh diagrams for ductile metals and presenting the most-known empirical and physical theories. The results for this steel are compared with the physical theories of Findley based on the critical plane; the Froustey’s and Marin’s methods, based on energetic theories; and the Crossland invariants method based on the Gough’s theory of fatigue damage. Taking into account the experimental results, a physical fatigue function based on energetic considerations is proposed. Its application to the fatigue case with mean stresses can be interpreted in terms of a balance of elastic energies of distortion and volume change. Macro-analyses of specimen fracture appearance were conducted in order to obtain the fracture characteristics for different mean stress values.

Fatigue life of additively manufactured Ti6Al4V scaffolds under tension-tension, tension-compression and compression-compression fatigue load

Mechanical performance of additively manufactured (AM) Ti6Al4V scaffolds has mostly been studied in uniaxial compression. However, in real-life applications, more complex load conditions occur. To address this, a novel sample geometry was designed, tested and analyzed in this work. The new scaffold geometry, with porosity gradient between the solid ends and scaffold middle, was successfully used for quasi-static tension, tension-tension (R = 0.1), tension-compression (R = −1) and compression-compression (R = 10) fatigue tests. Results show that global loading in tension-tension leads to a decreased fatigue performance compared to global loading in compression-compression. This difference in fatigue life can be understood fairly well by approximating the local tensile stress amplitudes in the struts near the nodes. Local stress based Haigh diagrams were constructed to provide more insight in the fatigue behavior. When fatigue life is interpreted in terms of local stresses, the behavior of single struts is shown to be qualitatively the same as bulk Ti6Al4V. Compression-compression and tension-tension fatigue regimes lead to a shorter fatigue life than fully reversed loading due to the presence of a mean local tensile stress. Fractographic analysis showed that most fracture sites were located close to the nodes, where the highest tensile stresses are located.