Goodman Diagram Research Articles

Dynamic strain distribution monitoring and fatigue damage analysis on a 100 kW wind turbine blade based on field aerodynamic measurements

Abstract Operation and maintenance (O&M) costs can account for 10%–20% of the total costs of electricity for a wind project. Structural health monitoring method is a form of preventive maintenance consisting of regular monitoring of the wind turbine components to detect potential faults. The strain measurements on the blades are typically used for load monitoring and damage detection, but only obtain a small amount of concentrated load information. In this work, a strain distribution monitoring method was proposed and validated based on aerodynamic measurements in the field. Then the contribution and evolution of the strain distribution from the aerodynamic load, gravity load, inertial load, and centrifugal load in the complex start-up process of the wind turbine were analyzed. The results shows that the mean value of the synthetic strain is mainly determined by the aerodynamic load and the centrifugal load, while the fluctuation amplitude is mainly determined by the gravity and the aerodynamic load. Furthermore, the fatigue damage of the blade root was evaluated based on strain extrapolation, rainflow cycle-counting algorithm, Goodman diagram and Miner’s linear superposition principle. It is found that the fatigue damage is generally greatest near the pressure side and suction side, and least near the leading edge and trailing edge. The strain distribution monitoring method can capture the location of maximum stress and the most severe fatigue damage on the blade, which are helpful for damage detection and load control, and further reduces O&M costs.

Effect of peening with fine iron-sulfide particles on the rotating bending fatigue properties of low alloy steel and formation of iron-sulfide layer

Low alloy steels were subjected to peening with fine iron sulfide particles (FeS-peening) under ambient conditions to transfer a layer of such particles, which can improve seizure resistance and sliding properties, and thus enhance the fatigue characteristics of the steel. This process was performed without the use of aqueous Na2S2O3 and the specimens were assessed using electron probe microanalysis and rotating bending fatigue tests. Treated specimens exhibited higher fatigue limits as a result of high degree of compressive residual stress generated on the steel surface. The effects of residual stress on the fatigue limit were quantitatively investigated using a modified Goodman diagram. Sample cross-sections were observed using electron backscattered diffraction, which confirmed that FeS-peening formed fine surface grains. Grain refinement was determined to be at least partly responsible for the improved fatigue properties of the steel following FeS-peening.

Titanium Alloy Materials with Very High Cycle Fatigue: A Review.

As the reliability and lifespan requirements of modern equipment continues to escalate, the problems with very high cycle fatigue (VHCF) has obtained increasingly widespread attention, becoming a hot topic in fatigue research. Titanium alloys, which are the most extensively used metal materials in the modern aerospace industry, are particularly prone to VHCF issues. The present study systematically reviewed and summarized the latest (since 2010) developments in VHCF research on titanium alloy, with special focus on the (i) experimental methods, (ii) macroscopic and microscopic characteristics of the fatigue fractures, and (iii) construction of fatigue fracture models. More specifically, the review addresses the technological approaches that were used, mechanisms of fatigue crack initiation, features of the S-N curves and Goodman diagrams, and impact of various factors (such as processing, temperature, and corrosion). In addition, it elucidates the damage mechanisms, evolution, and modeling of VHCF in titanium alloys, thereby improving the understanding of VHCF patterns in titanium alloys and highlighting the current challenges in VHCF research.

Temperature effects on the lifetime reinforcement due to strain-induced crystallization in carbon black filled natural rubber under non-relaxing torsion: comparison with non-relaxing tensile loadings

This paper investigates the lifetime reinforcement at different temperatures of carbon black filled natural rubber under non-relaxing torsion. Torsion fatigue tests with different angle ratios have been carried out with axisymmetric-shaped specimens. Finite element analysis was used to predict the local mechanical state by taking into account temperature effects and stress softening heterogeneities. It has been shown that when the temperature of the test is increased, the mechanical response does no longer stabilize, contrary to what is observed when the test is carried out at ambient temperature. A strategy has been proposed to evaluate an equivalent loading ratio, in order to compute the minimum loading as the Cauchy stress normal to the crack plane for the minimum torsion angle applied and to represent the results in the Haigh diagram. It was found that the lifetime reinforcement under torsion loading decreases when the temperature is increased to 90 °C, but is still observed. The lifetime reinforcement under torsion at 90 °C was of the same amplitude as the one obtained with the same material under uniaxial tension at the same temperature. The study has been completed by post-mortem analysis at the macro- and the microscale in order to characterize damage mechanisms at 90 °C.

Fatigue behavior of copper thin films

In this study, to investigate the mean stress effect on fatigue life of a 12 μm thick copper thin film, fatigue tests were performed at four maximum stress levels for a wide range of stress ratios. Tensile and creep tests were also performed to obtain the reference mechanical properties of the copper thin film tested. The fatigue behavior of copper thin films depended on the regions of the stress ratio and the modified Goodman and Gerber equations could not describe the mean stress effect on fatigue life well. The Haigh diagram was constructed using stress vs. life curve data obtained in this study, and the constant life curve was approximated by three straight lines. The Haigh diagram for copper thin films can be classified into three regimes: fatigue, fatigue-creep, and creep, depending on the fracture mode. The fatigue life can be well described with the equivalent stress amplitude calculated from the constant life curve, regardless of stress ratio.

Practical fatigue strength diagrams for compression springs based on the FKM-Guideline “Analytic Strength Assessment for Springs“

Metal springs are used extensively in technical products. The mathematical relationships and Goodman diagrams contained in the DIN EN 13906–1 standard form the essential basis for the design and calculation of cylindrical helical compression springs. They are used not only nationally, but internationally in the spring industry and by spring users. However, the diagrams are more than 50 years old and no longer reflect the current status of modern spring materials and spring manufacturing technologies. This results in great uncertainty for users of the standard, which currently has to be compensated by costly fatigue tests.In order to overcome the problems, the research project IGF 19693 aimed to renew the Goodman diagrams of the DINEN13906–1 standard in accordance with the state of spring technology. Therefore, the FKM guideline “Analytic Strength Assessment for Springs and Spring Elements“ was used to calculate permissible fatigue strength values for standard springs. Additionally, an extensive experimental program was carried out with fatigue tests on cold-formed helical compression springs to validate the calculations. The main results of the project are presented in this manuscript, which strengthens SMEs in designing competitive springs, which they can offer in a shorter time and at a lower cost due to lower development costs.© 2024 The Authors. Published by Elsevier B.V.

Fatigue life reinforcement of carbon black filled natural rubber under non‐relaxing torsion loadings and comparison with non‐relaxing tension loadings

AbstractIn this paper, the effect of non‐relaxing torsion loadings on the fatigue lifetime reinforcement of carbon black filled natural rubber is fully addressed. Torsion fatigue tests with different loading ratios have been performed with highly notched axisymmetric‐shaped specimens. Finite element analysis is used to predict the mechanical state at any point in the specimens. The prediction is significantly improved by taking into account the heterogeneous accommodation. The first Haigh diagram under fatigue torsion is built and analyzed by calculating the minimum loading in terms of the Cauchy stress as the normal stress to the crack for the minimum angle prescribed during the cycle. A strong lifetime reinforcement has been observed, which is found to be of the same amplitude to the one obtained under uniaxial tension with the same material. This has been confirmed by specific tests that combined non‐relaxing torsion and non‐relaxing tension loadings. Post‐mortem analysis carried out at the macroscopic and the microscopic scales enabled us to identify damage mechanisms, especially in the cases where the lifetime reinforcement was observed.

Influence of mean stress and building orientation on the fatigue properties of sub-unital thin-strut miniaturized Ti6Al4V specimens additively manufactured via Laser-Powder Bed Fusion

Fatigue is a complex, localized phenomenon affecting lattice structures at the level of struts and junctions. This study examines the fatigue properties of Laser-Powder Bed Fusion (L-PBF) Ti6Al4V miniaturized strut-like specimens, printed in four distinct building orientations (0°, 15°, 45°, 90°), and subjected to four stress ratios (R = 0.1, R = −1, R = −4, R = 10). Experimental data, summarized in Haigh diagrams, align well with predictions from the SWT and Walker methods. Notably, the dependency on mean stress diminishes as the building angle increases, attributed to progressively lower surface roughness which primarily drive failure at R = 0.1 and R = −1. In contrast, vertical specimens at R = −4 display a pronounced susceptibility to sub-surface defects affecting their fatigue strength, a finding corroborated by CT scan analyses. Additionally, the influence of buckling on fatigue performance is investigated and incorporated into the Haigh diagrams. These findings can contribute to a more informed design of L-PBF Ti6Al4V lattice structures against fatigue.

The correlation between static strength and fatigue strength test and simulation

In the bogie, the frame plays a vital role. It is not only the installation foundation and direct bearing structure of other components but also can transmit the excitation load from all directions. Therefore, the rationality and reliability of the frame design are particularly critical. In this work, according to EN13749, UIC615-4, JIS E 4207, and JIS E 4208 standards, the load conditions are compiled, and the finite element analysis is carried out. The static strength and fatigue strength are tested on the test bench. The results show that the static strength results of the bogie frame are less than the allowable stress of the corresponding material. The fatigue assessment was carried out by Goodman diagram, and the data all fell within the envelope, which met the requirements of fatigue assessment. Finally, the test results are compared with the simulation results. Through the correlation analysis of the static strength test results and the finite element simulation results of the frame, the stress exceeds 10% of the material yield limit under the exceptional load condition, and the large stress points of the local hanger are compared. The results show that the frame strength test results and the finite element simulation results maintain a good correlation.

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

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

Effect of multifunction cavitation on rotating bending fatigue properties of steel rods and its fatigue limit estimation

The effect of multifunction cavitation (MFC) on the rotating bending fatigue properties of low-alloy steel rods was examined. MFC generates compressive residual stress on the surface of steel rods, in contrast to conventional water jet peening, which improves the fatigue limit of steel rods. The fatigue limit of MFC-treated steel rods can be estimated using a modified Goodman diagram. The proposed equation gives the maximum value of the fatigue limit of MFC-treated steel rods (227.7 MPa) and the maximum value of the compressive residual stress contributing to the increased fatigue limit (-117.9 MPa).

Effects of Mean Stress and Multiaxial Loading on the Fatigue Life of Springs

In this paper, the effects of mean stress and damage accumulation on the fatigue life of springs are theoretically studied. The study examines the fatigue life of homogeneously stressed material subjected to cyclic loading. The mean stress of a load cycle is non-zero. Goodman and Haigh diagrams are commonly used for estimating fatigue life in engineering applications. Alternatively, conventional hypotheses by Smith–Watson–Topper, Walker and Bergmann have been successfully used to describe uniaxial cyclic fatigue with non-zero mean value over the whole range of the fatigue life. However, the physical characteristics of the mean stress sensitivities in these hypotheses are different. The mean stress sensitivity according to Smith–Watson–Topper is identical for all materials and stress levels. This weakness reduces the applicability of the Smith–Watson–Topper parameter. At first glance, the mean stress sensitivities according to Walker and Bergmann are diverse. The mean stress sensitivities depend upon two different additional correction parameters, namely the Bergmann parameter and the Walker exponent. The possibility of fitting the mean stress sensitivity in these hypotheses overcomes the significant drawback of the Smith–Watson–Topper schema. The principal task of this actual study is to reveal the dependence between the Bergmann parameter and the Walker exponent, which leads to a certain mean stress sensitivity. The manuscript establishes the simple relationship between both fitting parameters, which causes the equivalent mean stress sensitivity for the Bergmann and Walker criteria. As known from the state of the technology, fabrication and operation yield several impacts with a significant influence on the fatigue life of springs. One effect deals with the sequence of low and high stress amplitudes and amplitude-dependent damage accumulation. Particularly, during the load cycle a certain microscopical creep occurs. This creep causes damage. The accumulation hypothesis for creep damage is introduced. The hypothesis can be verified experimentally.

Effects of non‐proportionality and tension–compression asymmetry on the fatigue life prediction of equivalent stress criteria

AbstractBiaxial tension/compression–torsion fatigue tests with varying levels of non‐proportionality were performed employing a structural adhesive designed for wind turbine rotor blades. The cycles to failure were found to be independent of the level of non‐proportionality. It is demonstrated that numerical fatigue life predictions via rainflow‐counted equivalent stress histories are not able to replicate these experimental observations and overestimate the fatigue life up to a hundredfold. The tension–compression asymmetry of the adhesive resulted in significant damage prediction differences depending on the stress space representation of the Haigh diagram. If not properly taken care of, the asymmetry will also lead to non‐conservative results. While demonstrated with a short fiber‐reinforced adhesive, the results can be transferred to other materials.

Very High Cycle Fatigue Behavior of Austenitic Stainless Steel in Annealed and Predeformed Condition

Abstract Engineering components in service nowadays are designed for a large number of loading cycles (∼109), which makes fatigue behavior in this cycle range (designated as very high cycle fatigue [VHCF]) a topic of significant interest. The present study aims to investigate the high cycle fatigue (HCF) and VHCF behavior in type 304 stainless steel in two different conditions (annealed and with a martensite volume fraction of ∼45 %) through low cycle fatigue predeformation at a subzero temperature. A fatigue diagram in the form of an S–N curve extending up to the VHCF range is generated, which shows different HCF and VHCF behaviors for the annealed and predeformed conditions. Further tests are carried out at different R ratios to generate constant-life Haigh diagrams for both conditions. Although no failure is observed in the VHCF range under the annealed condition, an internal crack initiation mode is observed under the predeformed condition (Type II behavior), which is attributed to the enhanced notch sensitivity under VHCF cycling induced by a significant extent of strain-induced martensite formed during predeformation. To address the influence of varying load history under service, specimens were prefatigued in HCF, followed by VHCF cycling. The HCF–VHCF boundary is found to be significantly impacted by the prior HCF damage, with lowering of the fatigue limit under VHCF.

Strength of notched Ti-6Al-4V specimens not subjected to solution treatment and over-aging under cyclic loading

Ti-6Al-4V alloy is a popular titanium alloy due to its high strength / density ratio, high toughness, superior corrosion resistance and good biocompatibility. After forming operations, Ti-6Al-4V is typically subjected to Solution Treatment and Over-Aging (STOA). Fatigue is one of the most frequent causes of failure in mechanical components. The prediction and optimization of the strength of structural components under cyclic loads therefore plays a strategic role and must take into consideration the presence of defects. The aim of the work is to investigate the axial fatigue behaviour of Ti-6Al-4V alloy not subjected to STOA in inert environment in the presence of notches. The experimental results agree well with the results obtained using the Haigh diagram.

SUCKER RODS STRING DESIGN – RODS FATIGUE BEHAVIOR INTERPRETATION USING GOODMAN DIAGRAM

"During the standard pumping of an oil well, the sucker rods are subjective to alternative stress (tensile and compression). Certain steel grades have different behavior, taking into consideration their mechanical properties, like tensile strength. While most operators consider that, the higher the ultimate tensile strength (UTS) of a material is, it will behave better when subjected to loads. This paperwork shows that, comparing three different steel grades, they may have different results on the Goodman diagram, than expected. We are going to show that, even the steel grades have the same tensile strength (115 ksi), when calculating the %Goodman, the steel have different behavior, and this results from the manipulation of coefficients “A” and “b” involved in the formula, that each sucker rods manufacturer validates. "

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

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

Combined effect of surface morphology and residual stress induced by fine particle and shot peening on the fatigue limit for carburized steels

The combined effect of surface morphology and residual stress induced by peening on the fatigue limit of carburized steels were quantitatively elucidated to precisely estimate the fatigue limit. The fatigue limit of carburized steels treated with peening increased with decreasing the size of surface dents induced by peening, and the effect of residual stress on the fatigue limit was enhanced with a decrease in their size. Additionally, the maximum fatigue limit (1157 MPa) of carburized steels without surface dents, which is higher than those of steels treated with peening, could be estimated according to the modified Goodman diagram.

Flexural cracking behavior of reinforced UHPC overlay in composite bridge deck with orthotropic steel deck under static and fatigue loads

Ultra-high performance concrete (UHPC) has been used to enhance the fatigue resistance of orthotropic steel decks, but the enhancement effect is compromised by UHPC cracks in negative moment regions. This research investigates the flexural cracking behavior of reinforced UHPC (R-UHPC) overlay in composite bridge deck under static and fatigue loads. The investigated behavior included the load-carrying capacity of composite deck, and the cracking process, pattern and resistance of the R-UHPC overlay. Ten composite specimens were tested, including five slabs for the transverse behavior and five beams for the longitudinal behavior. Static tests investigated the load-carrying capacity, strain distribution and nominal cracking strength. Fatigue tests investigated the cracking process and fatigue resistance of R-UHPC overlay. The fatigue process included an internal force redistribution stage (less than10% of fatigue life) and a stable stage (greater than90% of fatigue life). The fatigue resistance of R-UHPC overlay was evaluated with a modified Goodman diagram.

Primary suspension failure analysis in FIAT type LHB bogies and life estimation

Multiple cases of failure in the primary suspension system of LHB coaches were reported in specific light-weight passenger coaches recently. Frequent failure in suspension systems led to increased downtime and maintenance costs. Failure was associated to fatigue in primary helical springs and was found to be preceded by failure of hydraulic dampers. We present a study on analysis of these failures and suggest design modifications for enhancing fatigue life. A flexible finite element model of the bogie, with suspension system involving flexible helical springs, is developed and simulated for typical load and vehicle speed parameters. Conditions of damper failure are incorporated and the exact location of failure and the observed fatigue life of spring are validated. Loading on the bogie involves tare weight and rail-wheel contact forces. Rail-wheel contact forces are computed through multibody dynamic model for typical track irregularity data. Linear static analysis is done to obtain stresses under steady loads. This is followed by pre-stressed modal analysis and harmonic response simulation of the flexible model of the bogie. Fatigue life computation under combined static and alternating load conditions is done by employing the Modified Goodman diagram. Iterative modifications in design of the primary suspension springs are carried out. Minimal changes, which do not require change in the designs of associated components or change in the manufacturing set-up, are suggested. Modifications are validated through comparative fatigue life estimation.