Goodman Diagram Research Articles

Fatigue strength evaluation of a bogie frame for urban maglev train with fatigue test on full-scale test rig

This study evaluated experimentally static strength for bogie frame of an urban maglev train including performing fatigue analysis, cumulative damage and fatigue test based on a developed fatigue load and as a final outcome, aimed to propose a fatigue strength evaluation method for the bogie frame of urban maglev. The results of FEM analysis adopting load combinations showed that all data was under a fatigue limit of the butt welded joint made of A6005 in Goodman diagram. The cumulative fatigue damage was calculated at the highest level from a bolt connecting area of electromagnetic pole in casting block but the total sum was evaluated as D=0.808 based on 1×107 cycles, which indicates it did not exceed the failure criteria. In addition, as the results of fatigue test, there was no crack on the any position of the bogie frame with the outcomes that corresponded to the results of fatigue test.

저비중 SMC 외장패널의 피로특성 평가

A research for application of LDSMC(Low Density Sheet Molding Compound) composite is in progress for lightening the weight. This paper has performed fatigue test and simulation of external panel for Korean commercial vehicle. Before the fatigue test, static test was carried out. From the test, the structural safety was investigated using Goodman diagram. After the static test performance, the fatigue test was conducted at a range of load frequency 5Hz, a stress ratio(R) of 0.05 and an endurance limit of <TEX>$10^6$</TEX> to obtain the S-N curve. The S-N curve is applied to the fatigue analysis of the external panel assembly. The result of FEM analysis was in accord with the experimental result within 83% confidence. It showed that the process to set up the safety range of allowable error is required in process of the design and simulation verification.

Mechanical properties of SPCC low carbon steel joints prepared by metal inert gas welding

To better understand the fatigue and tensile properties of SPCC steels welded by metal inert gas welding, the mechanical properties of the welded component in several localized regions, e.g., weld metal, heat affected zone (HAZ) and base metal, were investigated. The tensile and fatigue properties of the weld metals were high compared to the other areas (base metal and HAZ) due to the precipitated Ti containing oxide inclusions in acicular ferrite (bainite). Two typical microstructures were mainly observed in the heat affected zones (HAZ): (i) bainite in a ferrite matrix (HAZ-B) and (ii) a ferrite phase with low internal stress (HAZ-A). The hardness of HAZ-B was higher than HAZ-A because of the partially formed bainite structure and precipitated Ti containing oxide inclusions. The mechanical properties of the weld sample were further investigated using test specimens that included all regions, i.e., weld metal, HAZ and base metal (BHW). The tensile and fatigue properties of the BHW sample were found to be lower than those in all other regions, which was influenced by the high internal stress. The mechanical properties were analyzed using microstructural and crystal characteristics, as examined by TEM and EBSD analysis. In addition, the fatigue strength can be precisely evaluated using a modified Goodman diagram.

Fatigue design of lattice materials via computational mechanics: Application to lattices with smooth transitions in cell geometry

A numerical method based on asymptotic homogenization theory is presented for the design of lattice materials against fatigue failure. The method is applied to study the effect of unit cell shape on the fatigue strength of hexagonal and square lattices. Cell shapes with regular and optimized geometry are examined. A unit cell is considered to possess a regular shape if the geometric primitives defining its inner boundaries are joined with an arc fillet, whose radius is 1% of the cell length. An optimized cell shape, on the other hand, is obtained by minimizing the curvature of its interior borders, which are conceived as continuous in curvature to smooth stress localization.For a given multi-axial cyclic loading, failure surfaces of metallic hexagonal and square lattices are provided along with their modified Goodman diagrams to assess the effect of mean and alternating stresses on the fatigue strength. In good agreement with the experimental data available in literature, the numerical results show that the shape of the unit cell has a major impact on the fatigue performance of the lattice material. For example under fully reversible tension, the fatigue strength of optimized square lattices of 10% relative density is shown to be 54% higher than that of their conventional counterparts with regular cell geometry.

Application Research on Haigh Diagram in the Wind Turbine Fatigue Analysis

The influence of mean stress on fatigue has to be considered by means of Haigh diagram, the actual stress range is modified to damage-equivalent range. There are three main methods for creating Haigh diagram, such as experiment and empirical relationships and six points, which has the different application field. The creating and application of Haigh diagram in GL certification for wind turbines is studied, and the solving method for the mean stress sensitivity is given.

Effect of stress ratio on fatigue life of GFRP composites for WT blade

Fatigue life of GFRP (glass-fiber reinforced plastic) composites used in wind turbine rotor blades has been evaluated considering the glass fiber orientations. Three different laminate composites with the respective laminating orientation of 0°, ±45°, and 0°±45° were prepared using vacuum infusion method. Tensile properties and S-N curves for these composites were experimentally determined at room temperature. From the tensile tests, it was found that tensile properties were greatly dependent upon the fiber orientation and the tensile strength of unidirectional composite was the largest and bidirectional (45°) composite was the weakest among three composites. The fatigue properties were determined under constant amplitude load control at different stress ratios, R, of 0.5, 0.1 and −0.2. The properties also show the dependency of stress ratios and fiber orientation. The fatigue life diagrams of these three composite were relatively well presented with the double logarithmic S-N curve. The linear slopes of the respective S-N curves for three composite were not greatly different. The fatigue limits for the composites were evaluated and predicted with linear Goodman and Gerber diagrams.

MULTIAXIAL FATIGUE CRITERIA APPLIED TO A POLYCHLOROPRENE RUBBER

Abstract Due to their interesting mechanical behavior and their diversity, rubber materials are more and more used in industry. Indeed, formulating a multiaxial fatigue criterion to predict fatigue lives of rubber components constitutes an important objective to conceive rubber products. An experimental campaign is developed here to study the multiaxial fatigue behavior of polychloroprene rubber. To reproduce multiaxial solicitations, combined tension–torsion tests were carried out on a dumbbell-type specimen (an axisymmetric rubber part bonded to metal parts with a reduced section at mid-height), with several values of phase angles between tension and torsion. A constitutive model is needed to calculate multiaxial fatigue criteria, and then analyze fatigue results. A large strain viscoelastic model, based on the tension–torsion kinematics, is then used to determine the material's stress–strain law. Dissipated energy density is introduced as a multiaxial fatigue criterion, and compared with those usually used in the literature. A multiaxial Haigh diagram is then built to observe the influence of Rd-ratio (ratio of the axial displacement's minimum to the axial displacement's maximum) on the multiaxial fatigue lives of polychloroprene rubber.

Durability evaluation of a composite bogie frame with bow-shaped side beams

In the current study, the static structural safety and durability of two composite bogie frame models were evaluated using a finite element analysis. Prior to evaluation, the in-plane and out-of-plane mechanical properties of the base material were measured. The fatigue property was also measured to evaluate the durability of two composite bogie frames. Based on material data, the static structural safety was examined using the Tsai-Wu failure criterion under ten different loading conditions. Stress combination data were used to evaluate durability of two composite bogie frames. Analysis results indicate that the maximum Tsai-Wu failure indices of the two composite bogie frames under a twisting load were 0.48 and 0.57. Based on the durability evaluation using Goodman diagrams, all combined stress data of the two models were within the endurance limit. In the bogie frames with a side beam height of 50 mm, the side beam bottom area was the most affected region. The joint center area revealed higher mean stress and stress amplitude values in the bogie frames with a side beam height of 150 mm.

Evaluation of tension-compression and tension-tension fatigue life of woven fabric glass/epoxy laminate composites used in railway vehicle

In this study, the fatigue characteristics and life of two types of woven fabric glass /epoxy laminate composites with WR580 glass fiber for carbody structures and GEP224 glass fiber for bogie frames were evaluated and compared with those of conventional metallic materials. Additionally, the laminate composite for carbody structures was reinforced with carbon plies to investigate the improvement of fatigue life. A fatigue test was conducted for tension-tension and tension-compression load with a stress ratio, R of 0.1 and -1, and up to endurance limit of 107 with frequency of 5Hz. In tension-compression fatigue test, the anti-buckling jig was designed to prevent buckling of specimen induced by compressive load. The Goodman diagrams were introduced to evaluate the fatigue life of laminate composites. The test results showed that the fatigue life of the GEP224 woven fabric glass/epoxy laminate composite with the stacking sequence of warp direction had a good performance in comparison with that of SM490A used to existing metal bogie frame. Also, the fatigue performance of WR580 woven fabric glass/epoxy laminate composite with the reinforcement of woven fabric carbon /epoxy ply had shown a significant improvement than that of a bare specimen without reinforcement.

Fatigue–Strength Surface: basis for structural analysis under dynamic loads

The relation between fatigue strength and number of load cycles to failure is usually represented by Wohler curves. The four-parametric Weibull function shows a good relation between the static and dynamic strength in the low- and high-cycle fatigue range for a constant stress ratio R (minimum stress/maximum stress) (see Jarosch and Stepan in Fatigue properties and test procedures of glass reinforced plastic rotorblades. American Helicopter Society, 25th Annual National Forum, Paper No. 370, 1969; Och in Fatigue strength, AGARDograph No. 292, helicopter fatigue design guide, 1983; Bansemir and Emmerling in Fatigue substantiation and damage tolerance evaluation of fiber composite helicopter components, applied vehicle technology panel: applications of damage tolerance principles for improved airworthiness of rotorcraft, Corfu, Greece, 1999). However, in addition to the number of load cycles to the failure, fatigue strength also depends on the stress ratio R as well. In predicting the lifetime of a component, a more proper way for the presentation of fatigue life test data is the Goodman approach. This often used method affords the user to predict lifetime at any stress ratio, but does not represent the real material behaviour fully. The Goodman diagram does not take into account the combined effect of low-cycle fatigue and high-cycle fatigue. One better way to build an accurate relation between the fatigue strength, number of load cycles to failure and the stress ratio is to add the third dimension. The result is a three-dimensional view of the fatigue strength as a function of number of load cycles to failure and stress ratio R. Hence, the mathematical description of the fatigue strength as a kind of a surface function depending on the number of load cycles to the failure and the stress ratio is of high interest and indeed the focus of this study. The surface function represents the real material behaviour in low-cycle fatigue range as well as in high-cycle fatigue range more accurate compared to basic Goodman approach. For the determination of the Fatigue–Strength Surface, a so-called F–S Surface, test points with different stress ratios are necessary. The surface function can be adapted to the test points using a nonlinear regression analysis based on least square method. Therefore, it is advisable to use either the three-dimensional Weibull function or a surface function which consists of Tschebyscheff Polynomials. To enhance the regular two-dimensional Weibull function to a three-dimensional model, the four Weibull parameters are described as functions of the stress ratio. This method can be used to analyse the material behaviour based on the results of coupon or component tests. In case of coupon tests, this method is applied and validated as described in the paper. Furthermore, the use of material F–S Surface is compared with Goodman approach. For this purpose, mean surfaces of coupon test specimens with a survival probability of 50% are used. Especially in high-cycle fatigue range and for the stress ratios greater than zero, Goodman approach shows a slight deviation from the actual fatigue strength. In order to consider such effects, lifetime calculations are performed in Eurocopter Deutschland GmbH by using the reduced, so-called working S–N curves which are based on component test results. It has been found that the F–S Surface tends to describe the real fatigue strength in a more accurate way. This may lead to a longer lifetime of components and the possibility to extend the margins of components. This paper is developed from the Diploma thesis “Prediction of the dynamic strength behaviour of structural elements based on S–N–R surfaces created by nonlinear regression analysis of experimental data” (see Weinert in Prediction of the dynamic strength behaviour of structural elements based on S–N–R-surfaces created by nonlinear regression analysis of experimental data Technische Universitat Dresden 2011).

경량 복합재 대차프레임의 피로수명 및 강도 평가

본 논문은 4-매 주자직 유리섬유/에폭시 적층 복합재가 적용된 철도차량 경량 대차프레임의 피로 수명 및 강도 평가에 대해 기술한다. 대차프레임 경량화 재질로 적용된 유리섬유/에폭시 4-매 주자직 적층 복합재료의 피로특성 평가를 위하여 경사, 위사 그리고 0°/90° 방향으로 적층된 시험편에 대하여 인장-압축 피로시험을 수행하였다. 유리섬유/에폭시 4-매 주자직 적층 복합재료의 피로시험은 5Hz의 주파수, -1의 응력비(R), 107의 피로수명을 갖도록 하였다. 또한, JIS E 4207의 하중조건에 따른 대차프레임의 피로강도 평가를 Goodman 선도를 통하여 수행하였다. 유리섬유/에폭시 적층 복합재 경량 대차프레임의 피로수명 및 강도 평가기준을 만족하였으며, 무게를 고려할 경우 기존 대차프레임 재질인 SM490A 금속재에 비하여 우수한 피로특성을 갖는다.

Fatigue Behavior of Thin Sheets of DP590 Dual-Phase Steel

Fatigue properties of 1.6 mm thick dual-phase steel (DP590) sheet have been determined by carrying out axial fatigue tests in load controlled mode at different stress ratios for both smooth specimens and specimens with hole at center. The presence of hole at center of the specimen significantly reduces the fatigue strength. When the fatigue data points are plotted in the Haig-Soderberg diagram, they follow a parabolic relationship for smooth specimens represented by Gerber line and a straight line relationship for the specimens with holes at its center represented by Goodman line. Master Diagram which acts as a guide for the fatigue design is also drawn for both smooth specimens and specimens with holes.

Biaxial fatigue behavior of a polychloroprene rubber

Understanding phenomenon induced by complex fatigue loadings is an important issue for the conception of industrial components. Rubber materials, thanks to their abilities to withstand high deformations, are more and more used in industry. In an ongoing study, an experimental investigation is being carried out to study the effect of multiaxial loadings on the fatigue life of polychloroprene rubber. This material is used for pulleys. Specimen used is a dumbbell type, axisymetric geometry with a reduced section at mid-height. The experimental results indicate that under uniaxial tensile loading a kink in the conventional Haigh diagrams is observed leading to high lives at high R-ratio loading as compared to low R-ratios. Fractographic studies indicate the presence of crystallographic tongues under high R-ratio loading. To reproduce multiaxial conditions on this specimen, combined axial displacements and torsion rotation fatigue tests are performed, according to three different paths, depending on the phase angle between the two axes. Different multiaxial fatigue criteria are used to analyze experimental results.

Fatigue Life Analysis of Small Composite Sandwich Wind Tuebine Blades

The present fatigue life analysis of the small composite sandwich wind turbine blades (SCSWTBs) can be certified by IEC 61400-2:Wind Turbines - Part2: Design requirements of small wind turbines (IEC 61400-2 2006). The paper will establish an analytical method for the fatigue life analysis of SCSWTBs. Microsoft Office EXCEL is used to calculate the maximum stress, minimum stress, and stress ratio of the SCSWTBs under the fatigue loading. With the above stress data, the Goodman diagram (GD) can be constructed by the Autodesk AutoCAD. Finally, we can easilyestimate the fatigue life of the SCSWTBs.

A study on fatiguelife and strength of a GFRP composite bogie frame for urban subway trains

The objective of this study is to evaluate the fatigue life and strength of a GFRP bogie frame for urban subway train. The bogie frame was made of a GEP224 glass fiber/epoxy 4-harness satin woven composite. In order to obtain the S-N curve for a composite material applied to composite bogie frame, the tension-compression fatigue test was done with different stacking sequence of warp-direction, fill-direction, and 0°/90°-direction, respectively. The fatigue test was conducted with stress ratio (R) of -1, frequency of 5Hz and endurance limit of 107. The fatigue strength of bogie frame was evaluated by Goodman diagram according to the JIS E 4207. The results show that fatigue life and strength of a GFRP composite bogie have satisfied the requirements of JIS E 4207. Also, the GFRP composite bogie frame had a good fatigue performance in comparison with conventional metal bogie frame based on SM490A, considering its weight.

Development of Fatigue Test System for Small Composite Wind Turbine Blades

The research was to develop a small blade fatigue test system which met the criterion of the IEC (TR 61400-23) for the small composite wind turbine blades (SCWTBs). The fatigue test machine consisted of the servo motor, linear guide, transmission, controlling system and clamping apparatuses. These components were used to balance the weights loaded on the blades. Weights were added to change the different mass at each saddle for the loading tests. Amplitude of fatigue can be manipulated by rotating the eccentric holes of the flywheel. The kinetic power of the SCWTBs was translated from the circular motion to linear motion. The fatigue test system was able to test 1m-3m SCWTBs with single or multiple samples tested simultaneously. Because vibration frequency of the fatigue test system was limited to 3-6Hz, this research also tested the repaired samples after breaking them intentionally for the tests. Finally, the paper drew the linear formulation of the Goodman diagram. The experimentally determined S-N curve for R=–1 was used to define the intercepts of the constant life curves of the vertical axis of the SCWTBs.

J191053 Alloy718鍛造材の高サイクル疲労特性に及ぼす応力比の影響([J19105]構造・材料の高度化に向けた宇宙工学と材料力学の展開(5))

Efect of stress ratio on fatigue properties was investigated for Ni base super alloy 718 forging. Fatigue tests were conducted under stress ratios of R = -1, 0.01, 0.5 and under the condition fixing the maximum stress at 0.2% proof stress (6,,, =Co2 test). The internal fracture occurred in all test condition. The fracture sites of the internal fracture revealed the carbide inclusion and several facets. The fatigue limits determined at 107 cycles were below a modified Goodman line under R=0.01, although they were above under around R=0.5 and 0.7.

J191054 Ti-6AI-4V ELI合金鍛造材の低温高サイクル疲労特性に及ぼす応力比の影響([J19105]構造・材料の高度化に向けた宇宙工学と材料力学の展開(5))

The effect of mean stress or the stress ratio, R, (ratio of minimum stress to maximum stress) on the high-cycle fatigue properties of Ti-6A1-4V extra-low interstitial (ELI) forging was investigated at 293 K and 77 K. Fatigue tests were carried out for up to 107 cycles at stress ratios of R=-1, 0.01 and 0.5, and also under the condition where the maximum stress was fixed at 0.2% proof stress ( Crmax = cr02 test). The high-cycle fatigue strength at 107 cycles decreased at each temperature as the stress ratio increased, when the fatigue strength was evaluated in terms of stress amplitude (aa). In the R=0.01 and 0.5 tests, however, the high-cycle fatigue strength at 107 cycles exhibited deviations of aa below the modified Goodman line at both temperatures, indicating that this alloy exhibited an anomalous mean stress dependency. In particular, the amounts of negative deviations from the modified Goodman line at 77 K were larger than those at 293 K. Thus, it is concluded that the anomalous mean stress dependency of this alloy becomes remarkable at low temperatures.

Weight Reduction in an Indian Railway CASNUB Bogie Bolster Considering Fatigue Strength

Weight and strength are critical measures in the design of a railway bogie. The present work deals with the design of CASNUB bogie bolster of freight rolling stock in Indian Railways. The bogie is modelled using NX3, UGS software. Finite element analysis of the model is performed using MSC Patran/Nastran. Natural frequencies obtained from free vibration analysis are compared with those obtained experimentally using a Rap-Test. Effort has been made to reduce the weight of bogie bolster considering fatigue strength. Bogie loading includes vertical forces, longitudinal emergency brake force and vertical as well as lateral track excitations. Transient analysis of bogie is performed to identify the critical areas and surfaces relevant for weight reduction. Thicknesses of the bolster top, bottom and side surfaces are subsequently identified as design variables. These parameters are optimized using artificial neural network and genetic algorithm techniques. Such optimization has resulted in approximately 7.6% reduction in weight of the bolster. The optimal bogie bolster has been verified for its fatigue strength using Goodman diagram.

철도차량 대차 적용 유리섬유/에폭시 4-매 주자직 적층 복합재의 인장-압축 피로특성 평가 연구

본 논문은 철도차량 경량화 재질로 적용된 유리섬유/에폭시 4-매 주자직 적층 복합재료의 인장-압축 피로특성을 평가하였다. 유리섬유/에폭시 4-매 주자직 적층 복합재료의 인장-압축 피로시험은 경사, 위사 그리고 <TEX>${\pm}45^{\circ}$</TEX> 방향으로 적층된 시험편에 대하여 수행하였다. 인장-압축 피로시험은 5Hz의 주파수를 갖으며, 응력비(R)는 -1로 수행하였다. 인장-압축 피로시험 수행 시 압축하중에 의한 시험편의 좌굴을 방지하기 위하여 좌굴방지지그를 설계하고 이를 시험에 적용하였다. 또한, Goodman 선도는 유리섬유/에폭시 4-매 주자직 적층 복합재의 피로특성과 수명을 평가하기 위해 사용하였다. 유리섬유/에폭시 4-매 주자직 적층 복합재료의 인장-압축 피로시험결과 경사방향 적층 복합재의 피로특성이 기존 금속재 대차에 적용되는 SM490에 비하여 우수한 것으로 나타났다. This paper describes the evaluations of tension-compression fatigue characteristics and life for glass fiber/epoxy laminate composite applied to railway bogie to reduce weight. Test samples of tension-compression fatigue were composed of glass fiber/epoxy 4-harness woven laminate composites with different stacking sequence of warp-direction, fill-direction and <TEX>${\pm}45^{\circ}$</TEX>-direction. The tension-compression fatigue test was conducted with stress ratio (R) of -1 and frequency of 5Hz. Goodman diagram were used to evaluate the fatigue characteristics and life of glass fiber/epoxy 4-harness satin woven laminate composite. Anti-buckling jig was designed to prevent buckling of specimen under compression load. The test results showed that the fatigue characteristics of glass fiber/epoxy 4-harness satin woven laminate composite with stacking sequence of warp-direction had a good performance in comparison with that of SM490 used to conventional metal railway bogie.