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.     

Effect of steady torsion on fatigue crack initiation and propagation under rotating bending: Multiaxial fatigue and mixed-mode cracking

Axles and shafts are of prime importance concerning safety in transportation industry and railway in particular. Knowledge of fatigue crack growth under typical loading conditions of axles and shafts with rotating bending and steady torsion is therefore essential for design and maintenance purposes. The effect of a steady torsion on both small and long crack growth under rotating bending is focused in this paper. For small crack growth, a modified effective strain-based intensity factor range is proposed as the parameter that correlates small fatigue crack growth data under proportional or non-proportional multiaxial loading conditions. Results show that this parameter is appropriate for determining fatigue crack growth of small cracks on rotating bending with an imposed steady torsion.     

Use of a load non-proportionality measure in fatigue under out-of-phase combined bending and torsion

A load non‐proportionality measure has been developed for use with an existing critical plane fatigue criterion for the case of fatigue under out‐of‐phase bending and torsion. Use of this measure shows improved agreement with test data in the literature for this loading condition.     

Area and point approaches in fatigue life evaluation under combined bending and torsion loading

We present a new nonlocal approach to nonuniform stress distribution, consisting in reduction of stresses to representative local ones in the critical plane for fatigue life calculation. The shear and normal stresses are averaged in two overlapping areas of different sizes on the critical plane. The proposed method is compared with the point (in critical distance) method and both are verified by fatigue tests under combined bending and torsion. Verification is done for the experimental and calculated fatigue lives with use of two multiaxial fatigue failure criteria. __________ Translated from Problemy Prochnosti, No. 1, pp. 69–72, January–February, 2008.     

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.     

Selection of the critical plane orientation in two-parameter multiaxial fatigue failure criterion under combined bending and torsion

The present paper is focused on engineering application of the algorithm of fatigue life calculation under multiaxial fatigue loading. For that reason, simple two-parameter multiaxial fatigue failure criterion is proposed. The criterion is based on the normal and shear stresses on the critical plane. Experimental results obtained under multiaxial proportional, non-proportional cyclic loading and variable-amplitude bending and torsion were used to verify the proposed two-parameter criterion and other well-known multiaxial fatigue criteria. Elastic–plastic behaviour of the bulk material was taken into account in calculation of the stress/strain distribution across the specimen cross-section. It is shown that the proposed two-parameter multiaxial fatigue failure criterion gives the best correlation between the experimental and calculated fatigue lives.     

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.     

Impact strength of thin-walled composite structures under combined bending and torsion

The effect of bending and torsional stresses on the fracture characteristics of thin-walled square, rectangular and circular cylindrical structures has been investigated under static and impact loadings by use of the apparatus capable of applying bending and torsional moments in various proportions. The thin-walled structures were fabricated from glass-fiber strand, chopped strand mat and unsaturated polyester resin. Comparisons between experimentally determined strength and theoretical predictions using the failure criteria are presented. As a result of this investigation, the existence of the relation between the fracture mode and the strength was recognized and the failure criteria examined could be used successfully to predict the combined impact bending and torsional strength of thin-walled composite structures.     

Comparison of the fatigue characteristics for some selected structural materials under bending and torsion

A survey of the multiaxial fatigue criteria including the ratio of normal and shear stresses is presented. We also discuss the fatigue characteristics of some selected structural materials in bending and torsion. The ratio of normal stresses to shear stresses is determined for a given number of cycles N _f within the range 5∙10⁴ −2∙10⁶ . Moreover, it follows from the performed analysis of the fatigue equations and the relative difference R that the materials can be split into groups for which it is possible or impossible to apply a constant value of the considered ratio in the criteria including this ratio.     

Multiaxial fatigue behaviour of A356‐T6

Aluminum alloy A356‐T6 was subjected to fully reversed cyclic loading under tension, torsion and combined loading. Results indicate that endurance limits are governed by maximum principal stress. Fractography demonstrates long shear mode III propagation with multiple initiation sites under torsion. Under other loadings, fracture surfaces show unique initiation sites coincidental to defects and mode I crack propagation. Using the replica technique, it has been shown that the initiation life is negligible for fatigue lives close to 10⁶ cycles for combined loading. The natural crack growth rate has also been shown to be comparable to long cracks in similar materials.     

Multiaxial fatigue life prediction method based on path‐dependent cycle counting under tension/torsion random loading

A path‐dependent cycle counting method is proposed by applying the distance formula between two points on the tension‐shear equivalent strain plane for the identified half‐cycles first. The Shang–Wang multiaxial fatigue damage model for an identified half‐cycle and Miner's linear accumulation damage rule are used to calculate cumulative fatigue damage. Therefore, a multiaxial fatigue life prediction procedure is presented to predict conveniently fatigue life under a given tension and torsion random loading time history. The proposed method is evaluated by experimental data from tests on cylindrical thin‐walled tubes specimens of En15R steel subjected to combined tension/torsion random loading, and the prediction results of the proposed method are compared with those of the Wang–Brown method. The results showed that both methods provided satisfactory prediction.     

Multiaxial fatigue of welded joints under constant and variable amplitude loadings

Flange-tube joints from fine grained steel StE 460 with unmachined welds were investigated under biaxial constant and variable amplitude loading (bending and torsion) in the range of 10³ to 5 × 10⁶ cycles to crack initiation and break-through, respectively. In order not to interfere with residual stresses they were relieved by a heat treatment. In-phase loading can be treated fairly well using the conventional hypotheses (von Mises or Tresca) on the basis of nominal, structural or local strains or stresses. But the influence of out-of-phase loading on fatigue life is severely overestimated if conventional hypotheses are used. However, the hypothesis of the effective equivalent stress that is introduced leads to fairly good predictions for constant as well as for random variable amplitude loads. Therefore, the knowledge of local strains or stresses is necessary. They are determined by boundary element analyses that are dependent on weld geometry. This hypothesis considers the fatigue-life-reducing influence of out-of-phase loading by taking into account the interaction of local shear stresses acting in different surface planes of the material. Further, size effects resulting from weld geometry and loading mode were included. Damage accumulation under a Gaussian spectrum can be assessed for in- and out-of-phase combined bending and torsion using an allowable damage sum of 0.35.     

Multiaxial fatigue of a railway wheel steel under non-proportional loading

The results of an experimental investigation of the multiaxial fatigue behaviour of the R7T steel are presented. The R7T steel is currently employed in the production of solid high-speed railway wheels. Wheel failures due to rolling contact fatigue may occur and, on some occasions, fatigue cracks nucleate in the sub-surface region under the contact area between wheel and rail. Here, the stress field is multiaxial and the loading path is non-proportional. Specimens extracted from the rim of railway wheels were subjected to combined out-of-phase alternating torsion and pulsating compressive axial loads, a non-proportional stress state which is similar to that observed under the contact area in the wheel rim. The tests results are discussed in the light of some multiaxial fatigue theories, chosen among those based on the critical plane concept and those implementing an integral approach, with the aim of selecting a fatigue criterion suitable for the sub-surface fatigue assessment of railway wheels.