Fatigue analysis of unidirectional GFRP composites under combined bending and torsional loads

Fatigue behavior of unidirectional glass fiber reinforced polyester (GFRP) composites at room temperature under in-phase combined torsion/bending loading was investigated. All fatigue tests were carried out on constant-deflection fatigue machine with frequency of 25 Hz. A 30% reduction from the initial applied moments was taken as a failure criterion in the combined torsion/bending fatigue tests of the composite materials. A series of pure torsional fatigue tests were conducted to construct the failure contour of GFRP composites using different failure theories. The obtained S–N curves from combined torsion/bending tests were compared with both, pure torsion fatigue test results and published results of pure bending fatigue tests of GFRP rods. Pictures by scanning electron microscope were used to closely examine the failure mode of the tested specimens under combined torsion/bending loading.

The results showed that, the unidirectional glass fiber reinforced polyester composites have poor torsional fatigue strength compared with the published results of pure bending fatigue strength. Endurance limit value (calculated from S–N equation at N = 10⁷ cycles) of GFRP specimens tested under combined torsion/bending loading equals 8.5 times the endurance limit of pure torsion fatigue. On the other hand the endurance limit of combined torsion/bending fatigue strength approximately half the fatigue limit of pure bending fatigue strength. The predicted values of combined torsion/bending fatigue strength at different number of cycles, using the published failure theory are in good agreement with the experimental data. For the investigated range of fiber volume fractions (V_f) it was found that higher stress levels are needed to produce fatigue failure after the same number of cycles as V_f increases.     

Fatigue behaviour of tubular AlMgSi welded specimens subjected to bending–torsion loading

This paper is concerned with an experimental and numerical study of the fatigue behaviour of tubular AlMgSi welded specimens subjected to biaxial loading. In‐phase torsion–bending fatigue tests under constant amplitude loading were performed in a standard servo‐hydraulic machine with a suitable gripping system. Some tests in pure rotating bending with and without steady torsion were also performed. The influence of stress ratio R and bending–torsion stress ratio were analysed. Correlation of the fatigue lives was done using the distortion energy hypothesis (DEH), based on the local stresses and strains. The applicability of the local strain approach method to the prediction of the fatigue life of the welded tubular specimens was also investigated. Static torsion has only a slight detrimental influence on fatigue strength. The DEH (von Mises criterion) based on local stresses in the weld toes was shown to satisfactorily correlate fatigue lives for in‐phase multiaxial stress–strain states. The stress–strain field intensity predictions were shown to have less scatter and are in better agreement with the experimental results than the equivalent strain energy density approach.     

A multiaxial criterion for notch high-cycle fatigue using a critical-point method

In the present paper, a high-cycle critical plane-based multaxial fatigue criterion, recently proposed by the first two authors to determine the fatigue strength of smooth components, is extended to notched ones by using the so-called point method. Accordingly, once the location of the ‘hot spot’ (crack initiation point) on the notch surface is determined, the orientation of the critical plane (where to perform fatigue strength assessment) is assumed to be correlated with some averaged principal stress directions in the hot spot itself. Some experimental results related to round bars with a surface circular notch (an artificially drilled surface hole) submitted to three types of cyclic loading (bending, torsion and combined in-phase bending and torsion) are compared with the theoretical predictions of the criterion herein proposed. The comparison, which is instrumental in highlighting the notch size-effect (as the hole diameter varies) under uniaxial and biaxial far-field stress conditions, appears to be quite satisfactory.     

Development of a new device to perform torsional ultrasonic fatigue testing

The interest in gaining experimental knowledge on fatigue strength of materials over 10⁹ cycles is rapidly increasing as evidenced for the large amount of investigations on this subject presented at the last very high cycle fatigue meeting (VHCF-3), held on September 2004. Most of the fatigue results presented at this conference were obtained under tension-compression, rotating bending, flexion and bending cyclic loading (some attaining 10¹⁰ cycles), using ultrasonic devices whose design was based on the natural frequency principles. In general, very little literature concerning the metallic alloys behavior under torsion cyclic loading using ultrasonic is available; however, in order to perform an accurate component design under multi-axial loading and VHCF, the material behavior under torsion cyclic loading is required. This investigation presents the development of a new mechanical device for testing and characterizing metallic alloys in the range of 10⁹–10¹⁰ cycles in torsional cyclic loading and the first experimental results for medium carbon steel (38MnSV5S). The new device was designed to excite the components under testing with pure torsional vibration mode at a frequency of 20 kHz.     

Application of an energy model for fatigue life prediction of construction steels under bending, torsion and synchronous bending and torsion

The paper contains a mathematical model of the material’s behaviour under cyclic loading taking into account the dynamics of the fatigue process, including the number of cycles to failure, induced by the mean stress value. The coefficients in the proposed model have been obtained from experimental tests under symmetrical and nonsymmetrical loading (with the stress ratio R=0). The proposed model has been used in order to modify an energy criterion with the aim of accounting for the influence of the mean stress on the fatigue life. The fatigue tests have been performed for structural steels 10HNAP and 18G2A subjected to cyclic bending, torsion and synchronous bending with torsion, by considering different values of the mean stress. A good agreement between the calculated and experimental results has been obtained.     

A NEW CRITERION OF FATIGUE STRENGTH OF A ROUND BAR SUBJECTED TO COMBINED STATIC AND REPEATED BENDING AND TORSION

Abstract Criteria of fatigue strength of a round bar subjected to combined static and repeated bending and torsion have already been published by Findley and Sines together with empirical formulas by Gough. However, it is only Sines'criterion, by which the fatigue limit under combined bending and torsion is calculated, when completely reversed and pulsating fatigue limits and mean stresses are known. The authors show that Sines'criterion does not conform strictly with experimental results and they correct Sines'criterion so that fatigue failure occurs when the octahedral shearing stress amplitude attains a material constant value which decreases not only in proportion to the octahedral normal mean stress, but also in proportion to the octahedral normal stress amplitude. Applying the authors'criterion to combined repeated bending and torsion, plus coexistent static bending and torsion, a design formula was derived. The formula was compared with experimental results of Gough.     

Schwingfestigkeit von Kehlnähten mit und ohne Fugenöffnung

Fatigue strength of the fillet welds with and without joint preparation Does the thick sheet metal welding with and without joint preparation have a dominating influence on the operating strength? In the literature there is not sufficient work to find over the influence of the weld shapes on the operating strength. The minimization of the seam cross section as well as without the joint preparation affect crucially the production costs of the welded joint constructions and at the same time, can be saved enormous time, material and energy. In this work the operating strength behavior of the fillet weld joints with and without joint preparation under bending and subjections to torsion is examined. The test results are represented and commentated in diagrams and tables. As most important test results it can be determined that the weld shape does not have dominating influence on the structural durability in the pure bending und torsion loading. The life time lines run for both weld shapes (HV‐ and HY. fillet welds) nearly identically.     

Fatigue life estimation for 2017A-T4 and 6082-T6 aluminium alloys subjected to bending-torsion with mean stress

This paper proposes a model for estimating fatigue life under multiaxial stress states, based on critical plane concepts, taking into account the effect of mean shear stress. The fatigue life test results, calculated on the basis of the proposed model, are compared to the experimental ones related to 2017A-T4 and 6082-T6 aluminium alloy specimens under constant-amplitude bending, torsion and proportional combinations of bending and torsion. For the results obtained a statistical analysis is performed by comparing the calculation results with experimental data.     

Energy approach to fatigue under combined cyclic bending with torsion of smooth and notched specimens

We present the results of fatigue tests of smooth and notched round specimens made of 10HNAP steel under the combined action of cyclic bending and torsion. The experimental results are analyzed by using the well-known energy models proposed by Neuber and Molski-Glinka and a new model proposed by the authors and based on the analysis of the amplitude of the strain-energy density. The accumulation of fatigue damage in the stage of crack initiation was observed only in the active part of the cross section of the specimen where the level of stresses is higher than the fatigue limit. The proposed model enables one to determine the fatigue life of smooth and notched specimens under the combined action of cyclic bending and torsion by using standard characteristics of uniaxial fatigue and the relationship between cyclic stresses and strains. Department of Mechanics and Machine Design, Technical University of Opole, Opole, Poland. Published in Fizyko-Khimichna Mekhanika Materialiv, Vol. 34, No. 5, pp. 34–42, September–October, 1998.     

THE ENGINEERING FATIGUE PROPERTIES OF WROUGHT COPPER*†

The paper presents a comprehensive review, supplemented by original data, of the engineering fatigue behaviour of copper. Variations in manufacturing route and softening treatments are shown to have little effect on the fatigue of annealed copper but the high cycle fatigue strength is increased by cold work. The high strain fatigue behaviour is defined in terms of the plastic strain range and the cyclic stress-strain characteristics are documented. Fatigue behaviour in bending and torsion is defined by data and related to that in tension by simple design rules. Notches are found to reduce the laboratory measured fatigue strength of copper by ～ 30% and the effect of surface finish, surface distortion and surface residual stress is defined in the literature. Fatigue crack growth is defined in terms of stress intensity factor range ΔK by an upperbound law and, together with the conditions for non-growth (ΔK₀), shown to relate to the equivalent conditions for steels via the ratio of the respective elastic moduli. The effect of environment on the fatigue of copper has received scant attention in the literature, such results as exist suggesting little if any reduction in strength to be brought about by gaseous or aqueous environments. The most dramatic change is the improvement of about an order of magnitude which results when tests in vacuum are compared with equivalent tests in air. Results of fatigue tests on copper in ammoniacal environments are conspicuously absent from the literature. As the test temperature is reduced below room temperature there is a predictable increase in high cycle fatigue strength, a reduction in fatigue strength occurring above room temperature. High strain fatigue test results presented in terms of plastic strain range appear insensitive to temperature although at very low strain rates and high temperatures a reduction in fatigue strength occurs. A linear life fraction cumulative damage creep-fatigue law appears sometimes to be non-conservative but much more testing is needed to evaluate fatigue damage summation laws generally for copper. Numerical data are given in support of all the aspects of the engineering fatigue behaviour reviewed in the paper.     

“板—桁模型”计算预应力混凝土复合受力构件抗扭强度

弯、剪、扭复合受力下混凝土构件的受力特性非常复杂,准确计算构件的抗扭强度对构件的设计及工作性能的分析都非常重要。在钢筋混凝土构件的板-桁模型理论基础上,以预应力混凝土构件在复合受力下的板—桁模型理论为基础,以箱形截面预应力混凝土构件为例,由力及力矩的平衡、变形关系、材料本构关系及构件的破坏准则,建立了在小扭弯比情况下复合受力构件抗扭承载力的计算方法。所建立的计算模型及公式理论基础强、概念清晰,经试验值与理论计算值对比,符合情况较好,证实了板—桁模型理论分析复合受力构件抗扭性能的正确性。     

Strength of Cylindrical Specimens Subjected to Laser Hardening along the Generator and a Spiral Path

We have shown that the path of a continuous CO₂-laser beam over the cylindrical surface of specimens in the course of their hardening substantially affects the strength of steels in cyclic axial tension and bending with torsion. Hardening on a spiral path ensures higher mechanical parameters as compared with that along the generator of the cylindrical surface.     

Über die Eignung der Wechselbiegemaschine „WEBI”︁ zur Ermittlung von Ermüdungskennwerten

On Alternating Bending Machine WEBI's Suitability for Determination of Fatigue Characteristics Already in 1966, experimental investigations revealed that the flat bending torsion testing machine ?FLATO”? (Schenck, Darmstadt) doesn't keep constant its torsional moment amplitude in case of specimen's fatigue softening or hardening, respectively. Thus. conclusions concerning the material's fatigue characteristics drawn from such experimental results might therefore be seriously false. Furthermore, also the alternating bending testing machine ?WEBI”? (Schenck, Darmstadt) shows an equivalent behaviour concerning its bending moment amplitude. For this reason. the main findings of a comprehensive experimental study carried out on WEBI with an unalloyed steel C 45 (0.45 mass perccnl C) in different heat treatment conditions are reported in this paper.     

Fatigue crack growth of a welded tube–flange connection under bending and torsional loading

In this contribution the results of an experimental investigation into the fatigue crack growth of welded tube-to-plate specimens of steel StE 460 under bending, torsion, and combined in-phase and out-of-phase bending/torsion loading are presented. The tests were performed at stress ratios of R = −1 and R = 0. The residual stresses were reduced by thermal stress relief. The fatigue crack development is compared with the prediction on the crack growth rates of Paris. Individual stress intensity factors for the semielliptical surface cracks in the tube-flange specimens are approximated on a weight function analogy using the published solutions of other workers.     

Multiaxial fatigue behaviour of AA6068 and AA2017A aluminium alloys under in‐phase bending with torsion loading condition

This paper presents an analysis of the multiaxial fatigue properties of two selected aluminium alloys. Several experimental results were used to perform the analysis e.g. the latest experimental results done in Opole University of Technology on PA6 (2017 A), PA4 (6068) under bending, torsion, and combined bending with torsion. Analyses of the results were done to find similarities of the multiaxial fatigue behaviour of selected aluminium alloys. Based on the (σ_a – τ_a) curves, prepared for a fixed number of cycles, it was possible to show some tendencies of the multiaxial fatigue behaviour of selected material group. This is an important indicator while selecting proper multiaxial fatigue failure criterion suitable to perform fatigue life assessment of aluminium alloys.     

Methodological problems in the investigation of thin hardening films

We present the results of experimental and numerical-analytic investigations of thin hardening films and discuss some methodological problems encountered in this case. We propose the relations for the evaluation of fracture stresses under cyclic bending and residual stresses taking into account the specific features of thin coatings, as well as a computational model for the prediction of cyclic strength depending on the thickness and type of the coatings. The accumulated experimental data confirm the indicated dependences. __________ Translated from Problemy Prochnosti, No. 2, pp. 99–112, March–April, 2007.     

Analysis on the fatigue damage evolution of notched specimens with consideration of cyclic plasticity

This paper presents a damage mechanics method applied successfully to assess fatigue life of notched specimens with plastic deformation at the notch tip. A damage‐coupled elasto‐plastic constitutive model is employed in which nonlinear kinematic hardening is considered. The accumulated damage is described by a stress‐based damage model and a plastic strain‐based damage model, which depend on the cyclic stress and accumulated plastic strain, respectively. A three‐dimensional finite element implementation of these models is developed to predict the crack initiation life of notched specimens. Two cases, a notched plate under tension‐compression loadings and an SAE notched shaft under bending‐torsion loadings including non‐proportional loadings, are studied and the predicted results are compared with experimental data.     

J‐integral in the description of fatigue crack growth rate induced by different ratios of torsion to bending loading in AlCu4Mg1

The paper presents the results of tests on fatigue crack growth under proportional torsion with bending in AlCu4Mg1 aluminium alloy. Specimens with rectangular cross‐sections and stress concentrator in the form of external one‐sided sharp notch were used. The tests were performed under the different ratios of torsion to bending moments. The results of the experimental tests have been described by a nonlinear formula based on ΔJ‐integral range. The tests have shown that the change of ratio of torsion to bending moments from 0.58 to 1.73 caused an increase in crack growth rate. It has been shown that at the constant loading and the change of stress ratio (R) from ‐ 1 to 0, the fatigue crack growth rate also increases.     

A notch stress intensity approach to assess the multiaxial fatigue strength of welded tube-to-flange joints subjected to combined loadings

Full penetration T butt weld joints between a tube and its flange are considered, subjected to pure bending, pure torsion and a combination of these loading modes. The model treats the weld toe like a sharp V‐notch, in which mode I and mode III stress distributions are combined to give an equivalent notch stress intensity factor (N‐SIF) and assess the high cycle fatigue strength of the welded joints. The N‐SIF‐based approach is then extended to low/medium cycle fatigue, considering fatigue curves for pure bending and pure torsion having the same slope or, alternatively, different slopes. The expression for the equivalent N‐SIF is justified on the basis of the variation of the deviatoric strain energy in a small volume of material surrounding the weld toe. The energy is averaged in a critical volume of radius R_C and given in closed form as a function of the mode I and mode III N‐SIFs. The value of R_C is explicitly referred to high cycle fatigue conditions, the material being modelled as isotropic and linear elastic. R_C is thought of as a material property, independent in principle of the nominal load ratio. To validate the proposal, several experimental data taken from the literature are re‐analysed. Such data were obtained by testing under pure bending, pure torsion and combined bending and torsion, welded joints made of fine‐grained Fe E 460 steel and of age‐hardened AlSi1MgMn aluminium alloy. Under high cycle fatigue conditions the critical radius R_C was found to be close to 0.40 mm for welded joints made of Fe E 460 steel and close to 0.10 mm for those made of AlSi1MgMn alloy. Under low/medium cycle fatigue, the expression for energy has been modified by using directly the experimental slopes of the pure bending and pure torsion fatigue curves.     

EFFECT OF BIAXIAL MEAN STRESS ON CYCLIC STRESS-STRAIN RESPONSE AND BEHAVIOUR OF SHORT FATIGUE CRACKS IN A HIGH STRENGTH SPRING STEEL

Abstract— Biaxial fatigue tests were conducted on a high strength spring steel using hour-glass shaped smooth specimens. Four types of loading system were employed, i.e. (a) fully reversed cyclic torsion, (b) uniaxial push—pull, (c) fully reversed torsion with a superimposed axial static tension or compression stress, and (d) uniaxial push—pull with a superimposed static torque, to evaluate the effects of mean stress on the cyclic stress—strain response and short fatigue crack growth behaviour. Experimental results indicate that a biaxial mean stress has no apparent influence on the stress—strain response in torsion, however a superimposed tensile mean stress was detrimental to torsional fatigue strength. Similarly a superimposed static shear stress reduced the push—pull fatigue lifetime. A compressive mean stress was seen to be beneficial to torsion fatigue life. The role of mean stress on fatigue lifetime, under mixed mode loading, was investigated through experimental observations and theoretical analyses of short crack initiation and propagation. Using a plastic replication technique the effects of biaxial mean stress on both Stage I (mode II) and Stage II (mode I) short cracks were evaluated and analysed in detail. A two stage biaxial short fatigue crack growth model incorporating the influence of mean stress was subsequently developed and applied to correlate data of crack growth rate and fatigue life.