Multiaxial Fatigue Loading Research Articles

On the notch sensitivity of cast iron under multi-axial fatigue loading

This work deals with the notch sensitivity of sharp notches under multi-axial fatigue loading. The main discussion concerns the differences in notch sensitivity at high cycle fatigue regime, between tensile, torsional and combined loading. For this comparison, this paper considers a large set of fatigue experimental tests and several computing simulations analyzed with several notch theories for predicting fatigue life of a component. The considered experimental data, taken from literature, deal with the fatigue behavior of cast iron circumferentially V-notched specimens under tension, torsion, and combined loading mode. This paper tries to apply several techniques for theoretical strength assessment and to compare different procedures. The examined procedures need the computation of many parameters, focusing on the importance of using the tensile resistance to set these parameters or using both tensile and torsion resistances. However, the improvements obtained by means of the more complex procedures are not noteworthy, compared to the overall scatter. In author’s opinion, the differences in notch sensitivity under tensile and torsional loading remain questionable.

The Research Development of the Mechanism of Fatigue Crack Initiation Based on Microstructure for Offshore Platform

In the capricious marine environment, the offshore platform structure is exposed to the multiaxial fatigue loading in which damage would be formed in different directions and planes. Evolution of the structural damage physical mechanism caused by marine environment load is more complicated. Based on the analysis of a large number of literatures, this paper reviews the research status of the fatigue crack mechanism in China and abroad, and predicts the development direction in the future.

Some analytical remarks on the influence of phase angle on stress fields ahead of sharp V-notches under tension and torsion loads

The effect of out-of-phase loadings in multiaxial fatigue is still an open problem which is of interest for engineers and researchers engaged with design against fatigue. In the present contribution, the effect of the phase angle on sharp V-notches subjected to multiaxial fatigue loading is theoretically studied with an analytical frame based on the maximum shear stress averaged over an entire fatigue cycle. The formulation is applicable as it stands to varying V-notch opening angles, biaxiality ratios and phase angles.The proposed frame has in common with critical plane approaches, which in principle cannot be straightforwardly applied to sharp V-notches, the consideration of the shear stress as critical parameter but uses the notch stress intensity factors to describe the asymptotic stress distributions in the highly stressed region surrounding the V-notch tip. Based on linear elastic stress fields, the frame does not take into account the non-linear effects related to cyclic plasticity. Some considerations on the effect of the phase angle can be drawn on the basis of the obtained results. The main conclusion is that the phase angle plays a non-negligible effect on the fatigue strength of pointed notches. This effect is strongly influenced by the biaxiality ratio.

On the use of the Prismatic Hull method in a critical plane-based multiaxial fatigue criterion

In the present paper, the modified Carpinteri–Spagnoli (C–S) criterion is combined with the Prismatic Hull (PH) method proposed by Mamiya, Araújo et al. [15] to evaluate an equivalent shear stress amplitude for multiaxial fatigue loading. More precisely, the PH method, originally formulated for synchronous loading and successively extended to asynchronous loading, is here adopted to compute the shear stress amplitude acting on the critical plane, used in the modified C–S criterion. By comparing some experimental data available in the literature with the theoretical estimations, the multiaxial fatigue strength evaluations derived through the modified C–S criterion are shown to be improved if the shear stress amplitude is determined by applying the PH method instead of the Minimum Circumscribed Circle (MCC) method, especially for particular shear stress paths as is here discussed.

Influence of complex defect on cast AS7G06-T6 under multiaxial fatigue loading

AS7G06-T6 cast aluminum alloy is tested under tension, torsion and tension–torsion fatigue loading for two load ratios. Basquin’s law and step loading method are used to obtain the fatigue limit under multiaxial loading. Crossland criterion and principal stress criterion considering Goodman idea are compared to evaluate the multiaxial behavior. The influence of complex defects on fatigue limit is analyzed under multiaxial loadings. Several artificial defects are machined on fatigue specimen with different distance between edges. A new definition of the equivalent defect size considering the distance between defect edges is proposed. For both tension and tension–torsion fatigue, the competition between single natural defect and complex artificial defects is observed and analyzed.

Considerations on the Necessity of Determining Principal Stresses and Directions for Analysis of Material Durability under Multiaxial Fatigue

A special situation arises when multiaxial fatigue loadings are present, given not only the time-dependency of extreme principal stress values, but also the fact that principal plane positions change during one load cycle (non-proportional loading). Thus, the analysis of principal stress and principal direction variation becomes a very important step, necessary to be carried out before starting any multiaxial fatigue testing. Based on the above, the authors present a generalized method for computing principal stresses and determining principal plane positions, applicable for cyclic tension-torsion loadings with zero mean stresses but with different phase shifts and amplitude ratios. Based on original experimental data and data collected from the literature, the authors point out in the final part of the paper that the maximum principal shear stress can be considered as the main parameter for plotting Wöhler curves.

New cycle counting method for multiaxial fatigue

Multiaxial fatigue is a very important physical phenomenon in several mechanical components. Fatigue life study under cyclic stresses is of utmost importance to avoid unexpected failure of equipments, vehicles or structures. Among several fatigue characterization tools, a correct definition of a loading cycle under multiaxial fatigue loading conditions shows to be crucial to estimate multiaxial fatigue life.The aim of this work is to achieve a correct definition for a multiaxial fatigue loading cycle and accomplish a multiaxial fatigue model to estimate block’s fatigue life under multiaxial loading conditions. To reach this goal, several loading paths were carried out using the 42CrMo4 low alloy steel under different loading conditions. Sequential, proportional, non-proportional and asynchronous loading effects were modulated through eleven loading blocks. Furthermore, two models were proposed: a cycle counting method and a fatigue life evaluation criterion. The results from the proposed models were correlated with the fatigue data and compared with two well known cycle counting models: the Bannantine and Socie and the Wang and Brown criteria. The proposed models were successfully validated by experimental data. Results show that the new proposals lead to an improved multiaxial fatigue characterization under complex loading conditions.

Effect of the Ratio between Tension and Bending Vibration Loads on the Fatigue Behavior and Failure Mode of Titanium Alloy TA11

This paper studied the effect of the ratio between the axial tensile force and the transversal vibration loads on the fatigue behavior and failure mode of the near alpha titanium alloy TA11, to simulate the service stress state applied on the engine blades, where a large centrifugal force is superimposed with bending vibration loads. The plate-like specimens were used in the fatigue tests by a special testing device which was designed and fabricated in the present research,where the vibration loads were applied by the electro-magnetic exciters. By experiments under various multi-axial fatigue loading cases with different ratios between the axial tensile force and the transversal vibration loads, the fatigue behavior and failure modes were observed and compared. Then, the energy based fatigue criteria were applied for correlation of the test results. The fatigue properties of titanium alloy TA11 under the specialized loading conditions are characterized and discussed. In addition, the experimental observations on the vibration behavior superimposed with different magnitude of axial tensile force are also helpful for understanding the real working conditions of the engine blades.

Dissipated energy-based fatigue lifetime calculation under multiaxial plastic thermo-mechanical loading

The paper concerns the metallic material lifetime calculation under arbitrary multiaxial thermo-mechanical fatigue loading. An energy-based damage operator approach ([Formula: see text]) is introduced. In such an approach, fatigue lifetime is continuously computed by the Prandtl type damage operator. The dissipated energy of plastic deformation is applied as a damage parameter that is obtained at any moment by the recently developed multiaxial energy operator approach. Strain-life curves are transformed into energy-cycle damage curves in order to associate the damage parameter with the fatigue lifetime. The present approach is validated on turbocharger housing. A satisfactory evaluation of the fatigue lifetime is obtained even though visco-plasticity and mean stress correction are not addressed yet.

A generalized cycle counting criterion for arbitrary multi-axial fatigue loading conditions

In this article, a generalized cycle counting criterion applicable for both uniaxial and arbitrary multi-axial loading conditions is presented. This criterion consists of two parts: (1) an effective fatigue damage parameter definition in either stress or strain space and (2) a fatigue cycle definition corresponding to maximum damage possibly attained by the fatigue damage parameter within a given loading history. After discussing its mathematical and mechanics basis, we first provide a rigorous proof that the proposed generalized cycle counting criterion yields exactly the same results as the rainflow counting method under uniaxial variable amplitude loading conditions. Then, its applications in multi-axial fatigue are demonstrated by presenting a series of closed-form solutions of both the fatigue damage parameter and number of cycles for a general harmonic loading history of three independent traction stress components on a crack plane. The validity of the new generalized cycle counting criterion is demonstrated by its ability to correlate available fatigue test data in the literature. These new developments also provide a more refined physical and mechanics basis for the recently proposed path length–based cycle counting method developed by the same authors for performing cycle counting of variable amplitude multi-axial loading histories.

On the multiaxial fatigue assessment of complex three-dimensional stress concentrators

This paper assesses and quantifies the detrimental effects of complex tri-dimensional notches subjected to uniaxial and multiaxial fatigue loading. A number of experimental results taken from the technical literature and generated by testing specimens containing complex geometrical features were reanalysed using a critical distance/plane method. The investigated notched samples were tested under uniaxial and multiaxial constant amplitude load histories, considering also the effects of non-zero mean stresses as well as non-proportional loading. The common feature of the considered notched geometries was that the position of the critical location changed as the degree of multiaxiality of the applied loading varied. The relevant linear-elastic stress fields in the vicinity of the crack initiation points were calculated by the Finite Element method and subsequently post-processed using the Modified Wöhler Curve Method in conjunction with the Theory of Critical Distances (the latter theory being applied in the form of the Point Method). This validation exercise confirms the accuracy and reliability of our multiaxial fatigue life assessment technique, which can be efficiently used in situations of practical interest by directly post-processing the relevant linear-elastic stress fields calculated with commercial Finite Element software packages.

Damage initiation and evolution in glass/epoxy tubes subjected to combined tension–torsion fatigue loading

The matrix-dominated behaviour of unidirectional composite laminae subjected to multiaxial fatigue loading was extensively investigated. Tubular specimens with three different lay-up ([90n], [0F/90U,3] and [0F/90U,3/0F]) were tested under combined tension/torsion loadings. Attention was focused on the initiation and propagation of cracks in the 90° layers, and fatigue data are presented in terms of S–N curves (for crack initiation) and Paris-like curves (for crack propagation) under several biaxiality ratios. Damage onset and evolution have been found to be strongly affected by the multiaxial loading condition, showing a particularly detrimental effect of the shear stress component. SEM investigations on the fracture surfaces confirmed a strong dependence also of the microscopic damage modes on the local multiaxial stress state.

Mean stress effect under Multi-Axial High Cycle Fatigue loading for cast A356-T6 alloy

Mechanical engineers are submitted to the antagonistic criteria when designing security components, such as, used in aeronautic, automotive and industrial components. They have to look for solutions leading to have as less as possible the weight, cost and in the same time as more as possible the security under complex and severe conditions of use. They consider fatigue to be the most common mechanism which causes components fail. In this context, cast A356-T6, which presents a good casting properties and mechanical strength resistance, will be studied in this paper.This work presents an experimental investigation to characterise the effect of mean stress on the Multiaxial High Cycle Fatigue (HCF) of cast A356-T6 alloy containing natural and artificial defects with various Secondary Dendrite Arming Spacing (SDAS). Traction, torsion and combined traction-torsion fatigue tests have been carried for two loading ratio R σ = 0 and R σ = −1. The fractured surfaces are analyzed through fractographic Scanning Electron Microscope (SEM) in order to determine the defect causing failure. To study the effect of the mean stress, the results are reported in kitagawa diagrams and Goodman diagrams for all the studied cases. In order to characterise qualitatively the effects of the defect size and SDAS, surface response method has been used. Interesting relationships and correlations have been obtained and introduced to improve the defect stress gradient (DSG) criterion for such defective material.The obtained results show clearly that: (i) the mean stress has detrimental, it is more significant in tension, lesser in tension-torsion case and slightly in torsion tests. (ii) The improved DSG criterion describes very well the trend of the fatigue limit as a function of defect size and SDAS.

Four stress analysis strategies to use the Modified Wöhler Curve Method to perform the fatigue assessment of weldments subjected to constant and variable amplitude multiaxial fatigue loading

The present paper investigates the different ways of using the Modified Wöhler Curve Method (MWCM) to perform the fatigue assessment of steel and aluminium welded joints subjected to in-service variable amplitude (VA) multiaxial load histories. Thanks to its specific features, the above critical plane approach can efficiently be applied in terms of both nominal, hot-spot, and local quantities, that is, by using any of the stress analysis strategies suggested by the Design Recommendations of the International Institute of Welding (IIW). The MWCM can efficiently be used also along with the so-called Theory of Critical Distances applied in the form of the Point Method (PM). The accuracy of the different formalisations of the MWCM investigated in the present paper was systematically checked against a large number of experimental results taken from the literature and generated by testing, under VA biaxial nominal loading, welded samples having different geometries. Such a systematic validation exercise allowed us to prove that our multiaxial fatigue criterion is successful in designing welded joints against VA multiaxial fatigue, this holding true independently from both definition adopted to calculate the necessary stress quantities and complexity of the assessed load history.

Damage Mechanics and Critical Plane Approach to Multiaxial Fatigue

The mechanical behaviour of structural components subjected to multiaxial fatigue loading is very important in modern design. Several approaches have been introduced in recent decades to analyse this problem. The so-called critical plane approach, based on the stresses acting on the plane where the crack nucleation is expected to occur, is widely used. This criterion can give us a fatigue damage measurement, which can be used to evaluate fatigue life. On the other hand, fatigue life under general multiaxial stress histories can also be assessed by applying the damage accumulation method. In such a method, a scalar damage parameter is quantified through the damage increments which develop during the fatigue process up to the critical damage value corresponding to the final failure of the structures. The damage increment approach to fatigue has recently been discussed and connected to the classical crack propagation approach. In the present paper, the interpretation of the critical plane approach based on the continuum damage mechanics concepts is examined. In particular, the physical meaning of the critical plane approach is shown, that is, such an approach can be interpreted as a damage method which takes into account the scalar damage parameter evaluated along preferential directions. Finally, the fatigue behaviour of a metallic material under multiaxial cyclic load histories is analysed through the two above approaches.

Structural Integrity of a Shaft Subjected to Multiaxial Fatigue Loads in Presence of Short Crack

The behavior of short cracks, focusing on the study of small manufacturing flaws in a critical structure working under a high frequency load spectrum, is a complex and very current topic and its investigated in this study. The modeling and predicting of the effect of these flaws is a matter of interest also for industrial manufacturers with regards to the future design of high stressed components. Aeronautical components in general, but particularly helicopter components, are subjected to a high number of fatigue cycles that potentially cause the propagation of very small flaws and thus require careful analysis. The application of multi-axial loading conditions such as axial and torsional load complicate the assessment by provoking a multimode propagation. A high cycle multi-axial fatigue loading condition (torsional and axial) on a tube that is representative of a helicopter main transmission shaft has thus been investigated in this work. The presence of a small flaw has been artificially created on the surface of the tube and the behavior of the defect in terms of the threshold of the propagation of a crack emanating from it under high cycles fatigue due to axial and torsional stresses has been investigated by means of analytical and FE models. Experimental test have also been carried out to validate the results of the simulations.

A Multiaxial Notch Fatigue Methodology to Estimate In-Service Lifetime of Corroded Cast Iron Water Pipes

The present paper summarises an attempt of using the so-called Modified Wöhler Curve Method (MWCM) to estimate fatigue damage in pitted cast iron water pipes subjected to in-service variable amplitude multiaxial fatigue loading. In this setting, pits are treated as hemispherical/hyperbolic notches whose depth increases over time due to conventional corrosion processes taking places in buried cast-iron pipes. The validity of such an approach is proven by showing, through a case study, that, under particular circumstances, the combined effect of corrosion and fatigue can remarkably shorten the in-service lifetime of cast-iron pipes as observed in the case study.

Life Prediction and Verification under Multiaxial Fatigue Loading

The strain change characteristics of multiaxial fatigue are analyzed under the condition of the combined tension and torsion loading for thin-tube specimen. Based on the principle of multiaxial critical plane approach, a multiaxial fatigue damage parameter is established, which takes account of the effect of not only the maximum shear strain amplitude and normal strain amplitude on the critical plane but also the parameter of non-proportionality. The non-proportionality is the function of loading parameters which is closely contact with the strain change characteristics of multiaxial fatigue and it can indicate the whole material damage. The experiments under the tension-torsion proportional and non-proportional loading were conducted to verify the multiaxial fatigue life model proposed in this paper. The life prediction has a good correlation with the experimental results.

On the estimation of the material fatigue properties required to perform the multiaxial fatigue assessment

ABSTRACTTo accurately perform the fatigue assessment of engineering components subjected to in‐service multiaxial fatigue loading, the adopted design criterion must properly be calibrated, the used information usually being the fatigue strength under both pure uniaxial and pure torsional fatigue loading. Because of the complex fatigue response of metallic materials to multiaxial loading paths, the only reliable way to generate the necessary pieces of calibration information is by running appropriate experiments. Unfortunately, because of a lack of both time and resources, very often, structural engineers are requested to perform the multiaxial fatigue assessment by guessing the necessary fatigue properties. In this complex scenario, initially, the available empirical rules suitable for estimating fatigue strength under both pure axial and pure torsional fatigue loading are reviewed in detail. Subsequently, several experimental results taken from the literature and generated by testing metallic materials under a variety of proportional and non‐proportional multiaxial loading paths are used to investigate the way such empirical rules affect the accuracy in estimating fatigue strength, the damage extent being evaluated according to the modified Wöhler curve method. Such a systematic validation exercise allowed us to prove that under proportional loading (with both zero and non‐zero mean stresses), an adequate margin of safety can be reached even when the necessary calibration information is directly estimated from the material ultimate tensile strength. On the contrary, in the presence of non‐proportional loading, the use of the empirical rules reviewed in the present paper can result, under particular circumstances, in a non‐conservative fatigue design.

Multiaxial fatigue criteria versus experiments for small crack under rolling contact fatigue

Rolling contact fatigue (RCF) is traditionally a very critical loading condition for fatigue and, moreover, material defects (as inclusions and inhomogeneities) play a significant role in determination of the service life of materials exposed to out-of-phase stresses, which typically occur at the interface and below the surface of contacting bodies.In this paper we summarize the results previously obtained for two different hard steels (that is, a bearing and a gear steel), together with a new set of experimental data for a mild railway wheel steel, that have been subjected to out-of-phase multiaxial fatigue loading, simulating RCF conditions in presence of small shallow pre-cracks.Then, the experimental results obtained have been discussed by employing the Dang Van and Liu–Mahadevan criteria, which are criteria extensively applied in the case of RCF problems.The results show that the Liu–Mahadevan criterion is close enough to experimental RCF tests, while the Dang Van criterion needs a substantial modification for the load cases when a negative hydrostatic stress component is present.