Multiaxial Fatigue Experiments Research Articles

Fatigue behavior analysis and life evaluation method of building steel under the influence of multiple factors

The paper aims to analyze the stress–strain response of building steel under low-cycle multiaxial fatigue and to accurately evaluate the fatigue life of specimens by selecting the more important relevant factors that affect fatigue behavior. Based on this, low-cycle multiaxial fatigue experiments of Q355D notched specimens under different multiaxial loading are carried out. Firstly, the fatigue behavior of notched specimens under different loadings and the relationship between the biaxial strain amplitude ratio and fatigue life are analyzed. Secondly, Grey correlation analysis, Pearson correlation analysis, and Random Forest importance analysis are used to screen out the important factors affecting fatigue life. Finally, the grey MGM (1, N) model is used to predict the fatigue life of notched specimens, and the results show that the predicted life based on Random Forest importance analysis is in good agreement with the experimental life. In this paper, the multiaxial fatigue problem is decoupled into two sub-problems, i.e. screening out related factors and life prediction based on the related factors, which can be used as a reference for life prediction in structural design.

Effect of Loading Frequency Ratio on Multiaxial Asynchronous Fatigue Failure of 30CrMnSiA Steel.

Multiaxial asynchronous fatigue experiments were carried out on 30CrMnSiA steel to investigate the influence of frequency ratio on fatigue crack initiation and propagation. Test results show that the surface cracks initiate on the maximum shear stress amplitude planes with larger normal stress, propagate approximately tens of microns, and then propagate along the maximum normal stress planes. The frequency ratio has an obvious effect on the fatigue life. The variation of normal and shear stress amplitudes on the maximum normal stress plane induces the crack retardation, and results in that the crack growth length is longer for the constant amplitude loading than that for the asynchronous loading under the same fatigue life ratio. A few fatigue life prediction models were employed and compared. Results show that the fatigue life predicted by the model of Bannantine-Socie cycle counting method, section critical plane criterion and Palmgren-Miner’s cumulative damage rule were more applicable.

Multiaxial fatigue experiments for elastomers based on true strain invariants

For decades, multiaxial fatigue tests have been proposed in order to derive models for fatigue life prediction of elastomers. Nevertheless, the importance of quantifying the multiaxiality has not sufficiently been discussed. In this paper, a new method is proposed to handle the multiaxiality in elastomers fatigue testing. It is based on the pair $$(K_2,K_3)$$ , two invariants of the Hencky (true) strain tensor. Thanks to the example of the simultaneous uniaxial tension-torsion fatigue of a Styrene Butadiene Rubber, we demonstrate that it is possible to prescribe a constant multiaxiality level throughout different tests. The method consists in fixing the multiaxiality indicator $$K_3$$ , and then varying the strain level with the intensity of distorsion indicator $$K_2$$ . Results show that the fatigue lives seem to unify with $$K_2$$ regardless of the value of $$K_3$$ . They also demonstrate that the initiation crack angle depends on the multiaxiality indicator $$K_3$$ but not on $$K_2$$ . Finally, the relevance of the approach is acknowledged by comparing the pair $$(K_2,K_3)$$ to the classical largest principal stretch ratio and biaxiality factor.

Multiaxial fatigue life prediction of polychloroprene rubber (CR) reinforced with tungsten nano-particles based on semi-empirical and machine learning models

In this paper, multiaxial fatigue experiments on a hyperelastic rubber-like material made of polychloroprene rubber (CR) reinforced with tungsten nano-particles have been carried out on notched specimens and hourglass specimens, utilized for limiting dome height fatigue tests. Based on the uniaxial (Choi et al., 2020) and multiaxial fatigue experiments, a semi-empirical ε-N fatigue model is proposed, allows accounting for both material anisotropy and complex stress states, showing an average error of 20.7%. Furthermore, six machine learning models have been employed for the fatigue life prediction and shown that the Deep Neural Network is the most accurate, with an average error equal to 14.3%.

A novel energy-based model for predicting the fatigue life of the automobile sealant adhesively bonded butt joints

The evolution of dissipation energy of the uniaxial and multiaxial fatigue experiments on the automobile sealant adhesively bonded butt joints was investigated by the method of fatigue dissipation energy analysis and fatigue failure identification. The results demonstrated that the dissipation energy increased and the fatigue life decreased with the increase of stress amplitude, mean stress, and the decrease of cycle time. Meanwhile, the non-proportional loading path resulted in greater dissipation energy and shorter fatigue life than that of uniaxial and proportional loading path. Moreover, the existing energy-based model using the energy dissipated in different cyclic loading stages as the fatigue parameters were adopted to predict the fatigue life of the automobile sealant adhesively bonded butt joints, respectively. The practical limitations of the prediction model using the total dissipation energy as the fatigue parameter were evaluated. Therefore, a novel energy-based fatigue life prediction model was proposed which using the partial steady stage of dissipation energy curves as the parameters. The predicted results of the novel model and the comparison with that of the existing energy-based model indicated that the novel model had an excellent ability to predict the fatigue life, and was more practical in engineering application for the automobile sealant adhesively bonded butt joints.

Analysis of dissipation energy and ratchetting behaviors on multiaxial fatigue of adhesively bonded joints

The multiaxial fatigue experiments were conducted on the adhesive bonded hollow cylinder butt-joints under the stress-controlled mode. The effect of loading path, equivalent stress amplitude, equivalent mean stress and period on the multiaxial fatigue behaviors were discussed. The multiaxial fatigue damages of adhesively bonded joints were also analyzed from the evolution of ratchetting and dissipative energy behavior. The results showed that the loading paths had a great influence on dissipated energy and ratchetting strain, and the effects of non-proportional loading path on the ratchetting strain and dissipation energy were greater than that of the proportional loading path. Moreover, the equivalent stress amplitude, equivalent mean stress and period all had some influence on the dissipation energy and equivalent ratchetting strain. In addition, the dissipative energy and the ratchetting strain increased gradually with the number of cycle increase, which resulted in the fatigue life decreases with the increase of equivalent stress amplitude and mean stress, and the decreasing period. The effects of period on the multiaxial fatigue life under the elliptic loading path were insignificant for the adhesive bonding butt-joints.

Experimental investigation on multiaxial ratchetting behaviour and fatigue life of silicone seal adhesive bonding butt-joints

The multiaxial fatigue experiments were conducted on the silicone seal adhesive bonding hollow cylinder butt-joints under the stress-controlled mode at laboratory ambient temperature. The effect of loading path, equivalent stress amplitude, equivalent mean stress and cycle time on the multiaxial ratchetting behaviors and fatigue life were discussed. The experimental results showed that the effects of non-proportional loading path on the ratchetting strain were greater than that of the proportional loading path. Moreover, the effects of the normal stress on the ratchetting strain were relatively larger than that of the equivalent shear stress under the multiaxial loading paths. In addition, the ratchetting strain increases and fatigue life decreases with the increase of equivalent stress amplitude and mean stress, and the decreasing cycle time. The effects of cycle time on the multiaxial ratchetting strain and fatigue life under the elliptic loading path were insignificant for the silicone seal adhesive bonding butt-joints.

A new multiaxial fatigue life prediction model considering additional hardening effect

The established linear fatigue life prediction model based on the Miner rule has been widely applied to fatigue life prediction under constant amplitude uniaxial and multiaxial loading. Considering the physical significance of crack formation and propagation, a multiaxial equivalent linear fatigue life prediction model is put forward based on Miner rule and critical plane method under constant amplitude loading. The essence of this approach is that the equivalent strain, which consists of the shear strain and normal strain on the critical plane, replaces the relevant parameter of uniaxial nonlinear fatigue damage model. The principal axes of stress/strain rotate under non-proportional loading. Meanwhile, the microstructure of material and slip systems change, which lead to additional hardening effect. The ratio of cyclic yield stress to static yield stress is used to represent the cyclic hardening capacity of material, and the influence of phase difference and loading condition on the non-proportional hardening effect is considered. The multiaxial fatigue life is predicted using equivalent stain approach, maximum shear stain amplitude model, CXH model, and equivalent multiaxial liner model under proportional and/or non-proportional loading. The smooth and notched fatigue specimens of four kinds of materials (Q235B steel, titanium alloy TC4, Haynes 188, and Mod.9Cr-1Mo steel) are used in the multiaxial fatigue experiments to verify the proposed model. The predicted results of these materials are compared with the test results, and the results show that these four models can achieve good effect under proportional loading, but the proposed model performs better than the other three models under non-proportional loading. Meanwhile, it also verifies that the proposed enhancement factor can reflect the influence of phase difference and material properties on additional hardening.

Investigation on fatigue performance of adhesively bonded butt-joints and multiaxial life estimation using stress-based failure models

Uniaxial and multiaxial low-cycle fatigue experiments were conducted on the automobile sealant adhesive bonding hollow cylindrical butt-joints under stress-controlled mode, and the effects of equivalent stress amplitude, equivalent mean stress and loading frequency on the fatigue life of specimens were analyzed. The experimental results showed that the fatigue life of uniaxial tensile cycle was shorter than that one of uniaxial torsion cycle. The fatigue life of the automobile sealant adhesive bonding butt-joints decreased with the increase of equivalent stress amplitude, mean stress, loading frequency. The fatigue life of the non-proportional loading path was shorter than that of the proportional loading path. In addition, a modified stress-based fatigue life prediction model was proposed that collectively considered the effect of loading path, equivalent stress amplitude, equivalent mean stress and loading frequency on the multiaxial fatigue life. The comparisons of the predicted results and the experiment life indicated that the modified fatigue life prediction model had good prediction ability for the multiaxial fatigue life of the sealant adhesive bonding butt-joints.

Microstructure-sensitive computational multiaxial fatigue of Al 7075-T6 and duplex Ti-6Al-4V

Multiaxial fatigue experiments are expensive and typically require specialized equipment and specimens, but they are essential to support fatigue design of components that experience multiaxial stress states. To leverage limited experimental data, we pursue parametric simulations regarding the influence of multiaxial strain state on extreme value distributions (EVDs) of fatigue crack formation driving force in realistic microstructures. Ensembles of Statistical volume elements (SVEs) for both Al 7075-T6 and Ti-6Al-4V polycrystalline microstructures are subjected to multiaxial cyclic straining to compute EVDs of Fatigue Indicator Parameters (FIPs) that serve as computable surrogate measures of the driving force for fatigue crack formation.

Low-cycle multiaxial fatigue behavior and life prediction of Q235B steel welded material

Low-cycle torsional and multiaxial fatigue experiments are carried out for thin-walled Q235B steel welded specimens under both in-phase and 90° out-of-phase loading paths. A remarkable non-proportional additional hardening effect exists in the Q235B steel welded material under the 90° out-of-phase loading paths. A new energy-based fatigue parameter is proposed that incorporates the shear strain energy on the weighted critical plane and the normal strain energy on both the weighted critical plane and orthogonal plane. The proposed energy-based fatigue parameter provides a superior ability to make life prediction for the Q235B steel welded material under the torsional and multiaxial loading paths.

Notch size effect on in‐phase multiaxial fatigue life prediction of steel bar specimens

The current paper presents a comprehensive analysis including experimental and numerical works that elucidate the effect of notch behavior on in-phase multiaxial fatigue life. Multiaxial fatigue experiments of 45 steel and 45QT steel considering the notch radius and opening angles were performed. An investigation including analytical and computational frameworks for multiaxial fatigue analysis on the basis of average strain energy density (SED) theory was conducted to deal with the energy gradient. A bulk of new fatigue data were summarized by normal and shear stress firstly and then reanalyzed by means of the local SED by control volumes surrounding the notch tip. The notch effect on the multiaxial fatigue life is further clarified by SED theory.

Multiaxial fatigue experiments and life prediction for silicone sealant bonding butt-joints

Uniaxial and multiaxial fatigue experiments were conducted on the adhesively bonded hollow cylindrical butt-joint specimen under load-controlled mode, and several prediction criteria were used for multiaxial fatigue life prediction. The experimental results showed that the fatigue life of uniaxial tensile cycle was shorter than that of uniaxial torsional cycle, and the fatigue life of the non-proportional circular loading path was shorter than that of the proportional loading path. In addition, the multiaxial fatigue life prediction results showed that Smith-Watson-Topper criterion based on the maximum principal strain as the critical plane had a conservative life prediction for the non-proportional circular loading path. Fatemi-Socie criterion mainly considered the influence of shear strain which yielded the non-conservative prediction for some data points of proportional loading path. Chen-Xu-Huang criterion combined energy density and critical plane achieved better fatigue life predictions than those from the previous two criteria. Furthermore, considering general failure modes of the adhesively bonded butt-joints, the modified Chen-Xu-Huang model was proposed, and the predicted results are good agreement with the experiments.

Crack initiation and propagation of 30CrMnSiA steel under uniaxial and multiaxial cyclic loading

Effects of stress amplitude ratio and phase angle on crack propagation and fatigue life of 30CrMnSiA steel were discussed by extensive uniaxial and multiaxial fatigue experiments. Crack morphologies were observed by a metallurgical microscope. The crack propagation behavior showed that few cracks of stage I are observed with very low stress amplitude ratios (λ = 0, 0.25). Under the loading conditions with higher stress amplitude ratios (λ ≥ 0.5), the crack length of the stage I increased from about 20 μm to about 50 μm with the increasing of stress amplitude ratio and phase angle. The stage II crack propagated along the maximum normal stress plane, and the propagation life of stage II accounted for more than 40% of the total fatigue life. In addition, through utilizing the replica technique, effects of shear stress level on surface crack morphologies were analyzed. It can be found that fatigue failures are mainly caused by crack propagation under low stress level, while also caused by coalescing of small cracks at the high stress level. Discussions of fatigue life indicated that the stress amplitude ratio affects the fatigue life of the material significantly, while the phase angle has less effect. The prediction results of fatigue life demonstrated that both the McDiarmid criterion and Findley criterion overestimate the multiaxial fatigue life of 30CrMnSiA steel, due to the fact that mechanisms of crack propagation are varied under different loading conditions.

Crack growth and microstructural changes in AISI 52100: white etching cracks (WEC) and fine granular area (FGA)

The service life of rolling element bearings can usually be predicted with good accuracy. However, the damage phenomenon „white etching cracks” (WEC) can lead to premature and unforeseeable failures. The formation of zones with strongly decreased grain sizes at the crack faces is a characteristic of this type of failure. An earlier study showed that it is possible to reproduce this type of failure by multiaxial fatigue experiments with superposed cyclic compression and torsion. The present study shows the analysis of the stress state of those multiaxial fatigue tests with stress-based critical plane criteria. Using the critical plane results as a basis for a fracture mechanical analysis, a correlation is found between the crack length, the associated plastic zone size, and the extent of the transformed microstructure. This correlation is very similar to our results of the study of fine granular areas (FGA), a very high cycle fatigue phenomenon in bearing steels. It is argued that a plasticity-driven mechanism similar to the one proposed for FGA formation is responsible for WEC formation, too. Additional factors that are often cited as promoting WEC formation could explain the shift from very high cycle fatigue in the case of FGA to the early failures due to WEC.

Critical plane analysis of multiaxial fatigue experiments leading to White Etching Crack formation

Various researchers have shown that rolling contact fatigue can be reproduced with cyclic compression-torsion experiments, with the load components either in-phase or out of phase. As reported previously, the authors used such experiments to reproduce the rolling contact fatigue phenomenon “White Etching Cracks” which can cause premature failures of rolling element bearings. It is characterized by subsurface crack initiation and propagation coupled with microstructural changes alongside the crack flanks. Surprisingly, only in-phase load superposition caused these microstructural changes to occur. This suggests that White Etching Crack formation is somehow linked to the multiaxial stress state in the specimens, as this was the only variable that changed between in-phase and out-of-phase testing. In this study, the multiaxial stress state in the two experiments is analysed and compared using different critical plane criteria. In contrast to common ways of characterizing the stress state, e.g. equivalent stress approaches, this class of criteria is explicitly designed for multiaxial stress states. Special attention is given to the Dang Van criterion, which has been used in a number of rolling contact fatigue studies.

Multiaxial fatigue of extruded AZ61A magnesium alloy

Strain-controlled multiaxial fatigue experiments were conducted on extruded AZ61A magnesium alloy using thin-walled tubular specimens in ambient air. The experiments included fully reversed tension–compression, cyclic torsion, proportional axial-torsion, and 90° out-of-phase axial-torsion. For the same equivalent strain amplitude, fatigue life under proportional loading was the highest and the nonproportional loading resulted in the shortest fatigue life. Detectable kinks were identified in the strain–life curves for all the loading paths. Fatigue experiments subjected to fully reversed strain-controlled torsion with a static axial load were also conducted. A positive static axial stress reduced the fatigue life and a compressive static axial stress was found to significantly enhance the fatigue life. Two critical plane multiaxial fatigue criteria were evaluated in terms of fatigue life predictions based on the experimental results. The Fatemi–Socie criterion correlated well with the fatigue life in the low-cycle fatigue regime which was characterized by shear cracking. The fatigue life predictions made by the Fatemi–Socie criterion did not agree well with the experimental results in the high-cycle fatigue regime. A modified Smith–Watson–Topper (SWT) criterion was found to be able to predict fatigue lives well for all the loading paths conducted in the current investigation.

Assessment of multiaxial fatigue life prediction methodologies for Inconel 718

Fatigue life prediction methodologies for the assessment of the structural integrity of safety critical components in modern turbine engines require a close integration of advanced multiaxial fatigue life prediction procedures and of specific multiaxial tests, representative of the service conditions of turbine engine components and materials. The objective of the research work presented in this paper is to extend currently employed methodologies for the assessment of fatigue strength of turbine engines disks by integrating suitable multiaxial fatigue criteria and test results of multiaxial fatigue experiments conducted on Inconel 718 material at temperatures similar to those experienced by the disc materials during service. Smooth tubular specimens of Inconel 718 have been employed for conducting tension/torsion strain controlled high temperature fatigue tests. Specimens have been cut out from forged parts utilised for the production of engine discs, thus preserving the typical properties of disc materials (microstructure, basic mechanical properties, etc.). Different models/criteria have been evaluated by comparing fatigue life predictions and multiaxial fatigue experiments. It’s well known that agreement of life predictions with experimental life is strongly affected not only by the choice of the multiaxial fatigue criteria but also by the way the reference fatigue data are integrated in the criteria. Therefore, specific multiaxial fatigue tests have been carried out, in order to validate and to improve the assessment capabilities of the lifing procedures. Moreover, multiaxial fatigue tests permit advances in the basic understanding of materials behaviour that might be utilised in the processes of declaring component service lives.

On the heuristic extension of Haigh’s diagram for the fatigue of elastomers to arbitrary loadings

A new approach is proposed for the prediction of multiaxial fatigue of elastomers. This approach is inspired in principle, if not in details, from Dang Van’s work on a criterion for non-initiation of fatigue cracks in metals subjected to arbitrary periodic loadings. It consists of heuristically extending Haigh’s diagram, which provides the experimental fatigue lifetime for 1D cyclic loadings as a function of the mean stress and the stress amplitude, to completely arbitrary 3D loadings. This is achieved by defining, for every arbitrary periodic loading, some “equivalent” 1D loading. To do so, one considers the smallest sphere containing the closed path of some suitably chosen stress variable in the 6D stress space, and approximately characterizes this path through the norm of the center and the radius of this so-called Dang Van sphere. These parameters, which are equivalent in the 1D case to the mean stress and the stress amplitude, are then heuristically used as entries of Haigh’s diagram to predict the fatigue lifetime. Multiaxial fatigue experiments performed by Mars and Saintier are used to critically assess this proposal, and it is found to improve upon previous ones.

Multiaxial fatigue of rubber: Part II: experimental observations and life predictions

ABSTRACTFatigue experiments were conducted with an axial‐torsion specimen covering a wide range of stretch biaxiality and a range of fatigue lives between 103 and 2 × 106 cycles. These experiments include combined torsion–compression, pure torsion, combined torsion–tension and pure axial tension. Both in‐phase and out‐of‐phase combinations of axial and torsion loading were considered. The multiaxial fatigue experiments described provide empirical evidence from which an understanding of the mechanics of the fatigue process in rubber can be developed. Each of the four equivalence parameters described in Part I has been applied to the axial‐torsion fatigue experiments described in this paper (Part II). These results provide the basis for an analysis of the effects of multiaxial loading on fatigue life, and an assessment of the degree to which the various equivalence parameters are able to rationalize the results in a unified way. For the combined axial and shear strain histories in this study, the maximum principal strain criterion gave the best correlation to fatigue life. Strain energy density gave the worst correlation. The cracking energy density criterion was generally found to give good correlation of fatigue crack nucleation lives from combined axial‐torsion tests. Because it provides a plane‐specific analysis, this criterion appears to be particularly well suited for use in crack nucleation analyses of multiaxial strain histories.