Goodman Diagram Research Articles

Fatigue limit estimation for carburized steels with surface compressive residual stress considering residual stress relaxation

The mechanism of residual stress relaxation for carburized steels was elucidated and their fatigue limit was estimated. The compressive residual stress in the carburized steel after rotating bending fatigue tests is mainly influenced by the relaxation during the compressive loading phase, although it increases at the early stage. The fatigue limit of carburized steels can be estimated according to the modified Goodman diagram considering the residual stress relaxation. The proposed equation shows the maximum value of the fatigue limit (1013 MPa) of carburized steel and the maximum value of the compressive residual stress contributing to the increased fatigue limit.

Finite element analysis of newly developed hip prosthesis

AbstractThe present study focuses on the design and finite element analysis of a novel hip prosthesis comprising truss structures intended to equally distribute the stress along the prosthesis. The prosthesis is designed to suit three different inclination angles of 20°, 40° and 60°. The three designs were subjected to loading conditions that emulate walking, jogging, and cycling activities via finite element simulations. Using the von Mises yield criterion and Goodman relation for fatigue, it is found that the safety factor and the life cycle of the proposed prosthesis design was within the acceptable range. Furthermore, the truss structures incorporated in the prosthesis appear to reduce the stress levels in the femur.

Mean stress sensitivity of sintered iron and steel

Abstract There is a well-based correlation between the pulsating amplitude σ A(R = 0) and the alternating amplitude σ A(R = – 1) in fatigue testing of sintered iron and steel which permits to predict the mean stress sensitivity and the pulsating amplitude if the alternating endurance limit σ A(R = – 1) has been measured. Without loss of precision the relationship can be extended from smooth unnotched specimen geometries to notched geometries if only the stress concentration factor is known. The coefficients of the predictive equation depend on the brittleness of the material, a systematic approach to take the brittleness into account is still missing. In Haigh diagrams, the slope of the σ A–σ m diagram with tensile mean stresses can be linearly extrapolated also into the compressive mean stress range σ m < 0.

On the Effect of the Stress Ratio on Fatigue Properties of Ti-6Al-4V Produced by Laser Powder Bed Fusion

Fatigue life estimation of Ti-6Al-4V parts produced by additive manufacturing (AM) technologies has received increasing interest during the last decade. Recent studies focused mostly on the fatigue performance of Ti-6Al-4V considering a fixed stress ratio ( R ), usually 0.1 or −1. However, in order to properly design structural components subjected to variable loads, the effect of different stress ratios on the fatigue performance has to be carefully investigated. This research studies the stress ratio influence on the fatigue properties of Ti-6Al-4V specimens produced by laser powder bed fusion (L-PBF). Miniaturized Ti-6Al-4V samples were tested with the step procedure for different R values. A constant life Haigh's diagram ( 2 · 1 0 6 cycles) was generated for L-PBF Ti-6Al-4V in as-built, electro-polished, and machined surface condition. The results present for the first time the relations between alternating and mean stresses for L-PBF Ti-6Al-4V with a fine α + β microstructure when different surface posttreatments are used to enhance the coupons’ final surface quality.

Fatigue life prediction of needled ceramic matrix composite under variable amplitude loading

The fatigue loading parameter-life (S-N) curve of the needled composite was proposed by constant amplitude fatigue tests first, and then the variable amplitude fatigue tests of needled C/SiC ceramic matrix composite were completed. Combined with the rainflow counting method, the Goodman line, the constant amplitude S-N curve and the linear damage accumulation rule, the fatigue life of the needled C/SiC composite was predicted under tensile variable amplitude block loading. According to the ratio of the width containing needled fiber bundle to the specimen width, the influence of needled fiber bundle on the fatigue life dispersion was quantitatively analyzed for the specimens with different fatigue lives.

Low cost estimation of Wöhler and Goodman–Haigh curves of Ti‐6Al‐4V samples by considering the stress ratio effect

AbstractThe stress ratio effect on the fatigue life of materials is a topic which have been studied by two different approaches. On the one hand, several experiments, performed under different stress ratios are necessary to estimate the corresponding Wöhler curves. Afterwards, these curves are considered to estimate the fatigue life under a particular stress range. On the other hand, fatigue failure criteria for fluctuating stress like the Goodman–Haigh relationship, are applied to estimate the stress amplitude for a constant fatigue life. Based on the Stüssi function, this paper presents a low cost model to estimate Wöhler curves and constant fatigue Goodman–Haigh diagrams. This procedure requires a set of tests performed under a particular stress ratio from LCF to HCF, and data from minimum two additional stress ranges for each subsequent stress ratio. An application on data from Ti‐6Al‐4V samples manufactured by selective laser melting (SLM) is presented.

Probabilistic Approach for the Fatigue Strength Prediction of Polymers

One of the dominating factors in the fatigue of structures made from fiber-reinforced polymers, for example, wind turbine blades, is the polymer matrix. Traditionally, experimental stress–life data of polymers are approximated via a linear double-log Basquin model. Recently, the nonlinear stress–life formulation by Stüssi was found to provide a better fit of the experimental data with a substantially reduced standard deviation. Moreover, a nonlinear constant–life formulation, as proposed by Boerstra, can enhance the representation of the mean stress effect compared with state-of-the-art linear models given by the modified Goodman relation. To this end, Stüssi’s model was incorporated into the Boerstra relation to take account of the mean stress effects of an epoxy. This stress–life formulation was then enhanced with the Weibull probability function. The probabilistic–stress–life model provided a good approximation of the fatigue performance as a function of the stress ratio on the basis of an experimental data set. Finally, a stepwise engineering approach was suggested to derive the permissible stress–life with a view to practical design purposes. The procedure increased the reliability of the fatigue design evaluation compared with the state-of-the-art methodologies.

Numerical and experimental justification of transcatheter aortic valve prosthesis design

Objective: to justify the design of a self-expanding transcatheter aortic valve prosthesis based on a biomaterial stabilized with ethylene glycol diglycidyl ether using numerical simulation and a series of field experiments with working prototypes to determine the consistency of the proposed design solutions.Material and methods. Numerical computer models of a developed aortic valve prosthesis intended for transcatheter implantation, as well as prototypes of the most promising concepts for a series of field tests, were used in the work. Computer 3D models were subjected to numerical analysis in the Abaqus/CAE environment (Dassault Systemes, France) based on the finite element method with iterative design optimization and repeated numerical experiments. Physical prototypes of the transcatheter prosthesis were subjected to a series of mechanical tests for axial and radial compression, as well as tests on a Vivitro hydrodynamic stand (Vivitro Labs, Canada) under simulated normal flow. All studies were carried out in a comparative aspect with a similar transcatheter aortic valve prosthesis (control), the CoreValve™ bioprosthesis (Medtronic, Inc., USA).Results. Computer simulation demonstrates the stress-strain state values that do not significantly exceed the critical levels (628 and 756 MPa versus the threshold value 1080 MPa) for two basic concepts of support frames. The fatigue strength based on the calculation of the mean and alternating stresses corresponding to normo- and hypertensive states based on the Goodman diagrams, did not reveal any evidence that the threshold values (destruction area after 200 million cycles) were exceeded. The hydrodynamic characteristics of working prototypes made on the basis of computer models correspond to the testing data of CoreValve™ clinical bioprosthesis: the effective orifice area was 1.97 cm2, the mean transprosthetic gradient was 8.9 mm Hg, the regurgitant volume was 2.2–4.1 mL per cycle depending on the prototype model.Conclusion. Generally, experiments carried out showed the consistency of the concepts, including from the point of view of implementation of the leaflet apparatus based on xenogeneic tissues treated with ethylene glycol diglycidyl ether.

Fatigue life evaluation model for high-strength steel wire considering different levels of corrosion

This article studies the quantitative influences of corrosion on the fatigue life of high-strength steel wires, considering a wide variation in the degree of corrosion. A multiparameter Weibull model for corrosion-stress-life (C-S-N) is proposed, and the Goodman relation is employed to deal with the dependences of stress ranges on positive stress ratios. Fatigue data are collected from the literature for three groups with different ultimate tensile strengths and the degree of corrosion ranging from 0.18% to 18.67%. This data is then used to estimate the parameters of the Weibull model; subsequently, quantitative influences of corrosion on fatigue life for steel wires with a wide range in the degree of corrosion are illustrated and discussed. The results indicate that the influence of ultimate tensile strengths on fatigue life for corroded steel wire can be ignored, because corrosion causes crack nucleation faster, especially at lower stress ranges. The fatigue life decreases sharply as the corrosion increases, and reduction is much pronounced under a lower stress range. Negative correlation of fatigue life and corrosion increases as the stress range decreases, which further confirms that corrosion has a higher influence at lower stress ranges. The proposed model can provide quantitative evaluation on the fatigue life of steel wires at specified survival probabilities, considering a wide range in the degree of corrosion; these results can be used by engineering designers to ensure the safety for cable-supported bridges during their lifetime.

High Cycle Fatigue Appearance of 10wt% cr steel and Dissimilar Metal Weld

The present study deals with the high cycle fatigue (HCF) behavior of a ten wt% Cr steel at ambient also as high temperatures (300–853 K). S–N curves were created at unlike temperatures using an R-ratio of −1. Outcome of mean stress was established over and done with Haigh diagram at 853 K using different R-values. Fatigue life was found to decrease with upsurge in test temperature and stress amplitude. Fatigue life was attempted using Basquin equation. Detailed fracture surface analysis was performed to study the crack initiation and propagation modes towards empathetic the mechanisms of failure at different temperatures.

High Temperature, High Cycle Fatigue Demeanor of 10wt% cr Steel and Unlike Metal Weld

The present study primarily focuses on understanding the high cycle fatigue behavior (HCF) of alloy 10wt%Cr Ferritic Steel and Dissimilar metal weld (DMW) joint between 617M and 10wt%Cr Ferritic Steel. For assessing the HCF behavior, tests were conducted under stress controlled cycling, by employing dissimilar stress ratios (R) and wide range of temperatures (300 K – 853 K). The S-N curves plotted at R= -1 and temperatures (300 K,673 K,853 K) for 10wt%Cr Ferritic Steel shows that fatigue life decreased with increase in stress amplitude. It is also observed that fatigue life of 10wt%Cr Ferritic Steel falls with increase in the temperature regardless of the stress amplitude, clearly showing the strong dependence of fatigue life on the temperature. An effort has been made to find out the fatigue parameters at 300 K and 853 K using Basquin equation. These fatigue parameters were used for life prediction, showed that predicted life is in good agreement with experimental life with in a scatter band of 2. At 853 K, Goodman diagram shows that limiting alternating stress decreases with increase in the mean stress. The results were linked with the detailed scanning electron microscope investigation where it is analyzed that at 300 K, the fatigue failure was by trans-granular mode, characterized by striations while at 673 K and 853 K, intergranular mode and strong oxidation is seen, thus lowering the life at said temperatures. The standard S-N behavior for DMW at R= -1 and at temperature of 853 K showed that the welding reduces the number of cycles to failure. Vicker’s hardness measurements show that there is softening in the 10wt%Cr side & hardening in the butter layer resulting in failure of all non-defective samples on the 10wt%Cr side. HCF test was also showed on damaged samples at 230 MPa and 200 MPa, found, that crack initiates & propagates near the damage at 230 MPa while at 200MPa crack initiates and propagates in the 10wt%Cr side irrespective of the damage.

Analisis Konstruksi Pipa Pompa Suction 112-JB

The 101-JTC condenser tank has excess steam condensate due to the addition of admission steam from 101-JT. Therefore, it is necessary to design a piping system that connects 101-JTC condenser tank with the 112-JB pump to drain the condensed excess steam. The designed piping system will encounter a dynamic response caused by fluid flow fluctuation over the time. This dynamic response causes the pipe to experience stress. To find out the resulting voltage which will not cause damage or failure, it is necessary to estimate the safety factor in a piping system that has been given static and dynamic loading. This research uses the fluid structure interaction or FSI method with the help of ANSYS software as a simulation tool. The results of this study are, the flow in the pipe causes an impact load which makes the structure vibrate freely damped. The resulting dynamic response describes, the structure displacement amplitude decreases with increasing time. This indicates a stable vibration. Finally, when viewed from the value of stress against time, the fatigue that occurs in the pipe structure induce a stress below the stress limit on Goodman diagram. It can be estimated that the structure has no service life limit. The fatigue safety factor is 7.1.

Transformative Use of Additive Technology in Design and Manufacture of Hydraulic Actuator for Fly-by-Wire System

In this paper, the results of research on additively manufactured aerospace parts made of maraging steel are presented. This state-of-the-art technology seems to have the highest potential for practical use in the field of ultra-light and high-performance aerospace hydraulic parts. The strength properties of representative specimens made with steel 1.2709 were investigated. The researchers conducted static tensile testing, fatigue tensile testing, and pressure impulse testing. A Goodman diagram was plotted to visualize the impact of the building orientation vs. load character on the fatigue strength of the additive manufacturing (AM) specimens. Based on the research carried out on the strength of the AM samples, an aircraft flight control actuator was designed to achieve the highest level of safety integrity along with the greatest simplicity and lowest weight relative to hydraulic actuators manufactured using classical methods. The entire design process was integrated with the manufacturing process to achieve this target.

Fatigue of crystallizable rubber: Generation of a Haigh diagram over a wide range of positive load ratios

A Haigh diagram is built for a carbon black filled rubber blend that exhibits Strain Induced Crystallization (SIC) for a wide range of positive displacement ratios. A strategy for the initiation detection, which becomes difficult for high displacement ratios, is proposed and validated thanks to regular visual follow-up. Some experimental cautions are taken to avoid any temperature and strain rate effects on the results, more specifically on the strain induced crystallization phenomenon. It is found that a reinforcement related to strain induced crystallization is present for load ratios (up to displacement load ratio of 0.35). For higher load ratios, the reinforcement effect reduces leading to a Haigh diagram that looks like a bell, as already shown by Cadwell et al. (S. Cadwell, R. Merrill, C. Sloman, F. Yost, Dynamic fatigue life of rubber, Industrial and Engineering Chemistry 12 (1940) 19–23).

A re-visit to the Haigh diagram with the effect of creep damage on the high cycle fatigue behavior of alloy 617M

The present work is aimed at a re-evaluation of the Haigh diagram incorporating the effect of creep on HCF. HCF testing was carried out at 973 K with varying mean stress (σm) and alternating stress (σa) to generate the Haigh diagram. The influence of creep on HCF was investigated by imposing periodic holds at σm during the course of HCF cycling. Under such HCF-creep interaction tests, specimens were found to fail for certain σa-σm combinations that resulted in run-outs in the absence of superimposed creep holds, leading to a deviation in the Haigh diagram. Such deviation was more prominent with an increase in the σm (increase in R) and the hold time. The test results obtained are correlated with microscopic and fracture surface analysis to understand the mechanism of crack initiation and propagation, as well as the role of precipitation under HCF-creep interaction.

A new approach to the Haigh diagram of sintered steels from unalloyed iron to heat treated conditions

ABSTRACT Systematic investigations on the fatigue strength of heat treated sintered steels with notched specimens are barely found in the literature, especially at stress ratios other than R = −1. For that reason a larger study was initiated with the aim to provide a base for safe estimates of fatigue strengths also for heat treated components. This work deals with one possibility to design a Haigh diagram for the positive mean stress range beyond R = −1. Starting point is a new approach to determine the mean stress sensitivity M. As all equations derived are based on averages, in extreme cases individual test results can deviate by more than 20% from the calculated value. Regularly, however, deviations around ±10% are observed.

Fatigue behaviour of a spring: a case study

A durability design case study concerning a U spring is presented. For a given geometry of the component, the question was to predict the maximum permissible displacement per cycle whilst ensuring a service life of at least 260 kcycles. The stiffness of the spring was evaluated using the finite elements software SolidWorks. As an approximation a linear model was used in the finite elements analysis, which was also compared with an analytical treatment based on Castigliano’s theorem. Using a given safety factor, a high cycle fatigue analysis was performed assuming the use of a steel with 650 MPa ultimate tensile strength. The spring is either loaded by an imposed displacement, or it is load free,i.e.load ratio (minimum load / maximum load per cycle), isR= -1. An algorithm based on finite fatigue life prediction techniques, the Basquin and Goodman diagrams, and the relationship between ultimate tensile strength and fatigue limit was used and will be briefly presented and discussed. Also, the stress analysis helped to highlight the need for some minor geometry changes. The outcome of the study was the evaluation of the maximum permissible displacement per cycle, as required in the real life case addressed.

Using surrogate models to predict nodal results for fatigue risk analysis

Fatigue life analysis and FEA require high computational costs for aerospace models. Goodman diagrams are useful tools for determining the fatigue life of a part, and depend on structural and modal FEA simulations. Surrogate models have been used in fatigue analysis to predict the steady stresses and alternating stresses FEA model for every par node enabling a dynamically-updated Goodman diagram that responds to design parameter changes in real time. This research analyzes a jet engine compressor blade, and compares the accuracy of these nodal surrogate methods to previous surrogate methods where only a single value is predicted for failure analysis. Quantitative data summarizing the error between the single value and full field models are presented for the transonic Purdue blade.

Mean and residual stress effects on fatigue behavior in a pre-strained corner of stainless steel sheet

There are many thin-walled corners in the components of automobiles, machines, and structures. It is essential to elucidate their fatigue properties and influence factors. Parameters for stress–strain behavior of ferritic stainless plane sheet and pre-strained sheet were obtained under tensile, bending, and cyclic bending loads using the Ramberg–Osgood model. The parameters were integrally used as the fundamental characteristics of bending fatigue behavior for obtaining the mean stress and crack initiation stress amplitude from the measured strains in the curved portion of corner specimens. Bending fatigue tests of pre-strained corner specimens were carried out, and the relationships between the crack initiation strain amplitudes and the mean strains were verified. The strain amplitude ratios of the curved inside to outside portion were analyzed. The residual stress and hardness were measured, and work hardening effect on the inside was higher than that on the outside for improving fatigue strength. The fatigue limit of the corner specimen with the radius ratio of 1.3 was 23% higher than the unworked plane sheet. The effects of mean stress and residual stress on the fatigue strength were analyzed using the fatigue limit–static stress relation equations, indicating that the Gerber parabola can be used for fatigue limit predictions in the stress ratio range of R < –0.5 and that the Goodman line can be used after the point of R = –0.5. The SWT function can be used to accurately predict the fatigue lives in various conditions of stress amplitudes combined with static stresses.

Research on Strength Test Technology of Bogie Frames

The bogie frames play a vital role in the reliable operation of rolling stocks. In order to more effectively test the performance of the bogie frames’ strength, a test plan of bogie frames’ static tests and fatigue tests is designed according to related standards which is carried out by calculating the load and applying the load spectrum and combined with Goodman diagram to evaluate the structural performance of bogie frames. The research on the strength test technology of bogie frames provides an important guarantee for the operation safety of the railway system.