Maximum Shear Stress Amplitude Research Articles

Hybrid finite element modeling of subsurface-originated spalling in flexible bearings with hoop stresses

The flexible bearing in a harmonic reducer undergoes structural deformation after being mounted on the cam, causing the bearing to operate under a complex stress state. A hybrid finite element model is developed to investigate crack initiation and propagation in flexible bearings with hoop stress under rolling contact fatigue loading. The model is coupled with continuum damage mechanics, and the damage evolution equation takes the maximum shear stress amplitude as the damage-causing stress since the hoop stress inevitably affects the fatigue life. The model is verified by comparison with the fatigue life of the inner ring without hoop stress. The crack initiation and spalling formation mechanisms in the inner ring assembled with the cam are analyzed in detail. Moreover, the effects of contact load and equivalent interference on the inner ring’s spalling morphology and fatigue life are studied.

Evaluation of the accuracy and efficiency of the modified maximum variance method for multiaxial fatigue analysis under constant amplitude loading

An optimized version of the Maximum Variance Method (MVM) is employed to determine maximum shear stress amplitudes in high-cycle multiaxial fatigue analysis using the critical plane approach, increasing accuracy and reducing computational burden. This refined approach posits that the MVM assumes that the critical plane is the one subjected to the maximum variance of the shear stress history. Comprehensive statistical analyses, including Analysis of Variance (ANOVA) and multiple comparison techniques such as Tukey’s HSD and Bonferroni correction, were conducted to systematically investigate the impact of critical factors on fatigue resistance, such as mean stress, phase, synchrony, failure criteria, and the strategy for calculating maximum shear stress amplitude. These analyses highlighted significant effects of mean stress and phase on the accuracy of fatigue strength predictions, underscoring the effectiveness of the enhanced MVM in managing complex loading scenarios. The results demonstrate that the proposed methodology performs equal to or better than conventional methods, with significantly lower computational costs.

Dynamic Characteristics of Post-Cyclic Saturated Loess

Damage to soil structure caused by strong earthquakes is one of the main reasons for post-earthquake geohazard development. To investigate the nonlinear dynamic behaviors of the post-earthquake loess, a pre-shock reconsolidation test was designed to simulate the process of the loess undergoing earthquake and post-earthquake reconsolidation in a natural state. Furthermore, dynamic triaxial tests of the specimens before and after pre-shock action and consolidation stabilization with different over-consolidation ratios (OCR) were conducted to investigate the variety of the dynamic modulus and damping ratio of the saturated loess. The influence of pre-shock and reconsolidation on the dynamic behaviors was determined. Moreover, the mechanism of the changes after pre-shock and consolidation was discussed by combining the microstructure test results of soil samples before and after pre-shock and reconsolidation. The results suggest that the kinetic stiffness of the pre-shock saturated loess decreases significantly under the same consolidation conditions. The growth of the damping ratio-dynamic strain curve increases, and the deformation potential of the loess has a remarkable growth. With an increase in OCR, the dynamic elastic modulus after pre-shock increases continuously; however, the damping ratio decreases significantly. The dynamic stiffness increases and the deformation potential weakens significantly. The strong earthquake leads to the weakening of interparticle cementation, pore penetration, and structural reorganization in the local area, causes connecting of the macropores, and produces microfractures in the soil, which makes a significant decrease in the dynamic shear modulus ratio and an increase in the damping ratio of the loess, leading to the enhancement of soil dynamic nonlinearity and the attenuation of the dynamic strength. Moreover, the compaction effect of reconsolidation on the soil increases the interparticle friction and heals some microfractures, which leads to an increase in soil stiffness. This makes the maximum dynamic shear modulus and the maximum dynamic shear stress amplitude of the post-cyclic saturated loess perform at the same level compared with the natural loess without shock when the OCR equals three. However, the dynamic shear modulus and the damping ratio of the post-cyclic saturated loess are close to the natural loess when the OCR equals two.

Multiaxial high-cycle fatigue failure and life prediction based on critical plane method

Multiaxial high-cycle fatigue failure criterion and life prediction is important for structural components under complex low stress. A new multiaxial high-cycle fatigue damage parameter based on the plane of maximum shear stress is proposed, which includes the maximum shear stress amplitude, normal stress amplitude and maximum equivalent normal stress. The maximum equivalent normal stress is defined in the form of SWT stress function considering the influence of mean stress. The feasibility of the proposed failure criterion and life prediction model is verified by test data of different materials. The predicted results show that the life prediction error of the proposed fatigue model is basically within three times by comparing with McDiarmid, Matake, Crossland and Papadopoulos fatigue models.

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.

A multiaxial fatigue life prediction method for metallic material under combined random vibration loading and mean stress loading in the frequency domain

A spectral method for the determination of the critical plane is proposed for metallic material under random vibration loadings based on the criterion of maximum shear stress amplitude, where the direction of critical plane is obtained by solving the maximum value of a function using mathematical optimization method and the fatigue critical location of the structure can be determined. A multiaxial fatigue damage parameter is proposed for combined random vibration loading and mean stress loading cases based on Susmel’s criterion, which is a Power Spectral Density (PSD) of the equivalent shear stress and can be adopted for fatigue life evaluation. The fatigue life estimation of structures under multiaxial random vibration loadings with mean stresses in the frequency domain could be carried out based on this damage parameter constructed at the fatigue critical location with the spectral method for random vibration fatigue life. The multiaxial random vibration fatigue experiment with mean stress loadings is conducted on the notched plate specimens made of 2297-T87 aviation grade aluminum alloy, and the initiation sites of the fatigue cracks as well as the experimental fatigue lives are compared with those calculated by the proposed models, where satisfactory prediction capabilities on both the fatigue crack initiation locations and fatigue lives of the models are demonstrated.

A sectional critical plane model for multiaxial high‐cycle fatigue life prediction

AbstractA stress‐based sectional critical plane model is proposed to predict fatigue life under multiaxial constant amplitude loading. The proposed model considers the effects of material properties and loading paths including stress amplitude ratio, phase angle and mean stress. By introducing the ratio of maximum shear stress amplitude to maximum normal stress amplitude, the crack behaviour can be predicted and the critical planes can be divided into three sections: the maximum normal stress plane, maximum damage plane and maximum shear stress amplitude plane. To verify the accuracy and applicability of the proposed model, experimental data of 30CrMnSiA steel conducted by the authors and other test data of different materials from the existing literatures are utilized. The prediction results demonstrate that the proposed sectional critical plane model shows strong applicability for steel, aluminium and titanium alloy materials, especially under the multiaxial loadings with mean stresses. For steel materials, the prediction results of the proposed model are better than the commonly used criteria.

Prediction of fatigue damage region with the use of the notch critical plane approach for crack initiation and propagation

The advanced volumetric approaches are reviewed briefly to state the stress/strain-based or energy-based parameters of fatigue damage region are critical. A new approach is proposed to distinguish crack initiation and propagation stage. The angles of crack initiation are predicted by notch critical plane (NCP) approach (Luo et al. Fatigue Fract Eng Mater Struct, 2019, 42(4): 854–870). NCP is the plane which passes through the fatigue critical point (FCP) and undergoes the maximum shear stress amplitude. The experiment of thin-walled round tube components is conducted to check these approaches. The direction of crack initiation is basically the same as that of NCP. Most of the predicted lives fall within an error factor of 3.

Study on dynamic stress-strain response law of frozen saline soil

The subgrade saline soil in a certain area of western Qinghai province was studied, based on the British GDS dynamic triaxial test system, the dynamic triaxial test under laboratory test was carried out to study variation dynamic stress-strain and dynamic shear modulus under the different temperature, frequency and confining pressure. The test results show that the dynamic stress-strain relationship is significantly affected by temperature change under cyclic dynamic load, followed by frequency and confining pressure. Under the same strain amplitude, the lower the temperature, the larger the dynamic shear modulus. When frequency and confining pressure increase, dynamic shear modulus also increases. Whereas, the influence of confining pressure on the dynamic shear modulus is more obvious, and the backbone curve development trend is steeper. Both maximum dynamic shear modulus and final shear stress amplitude increase with the frequency increases when temperature and confining pressure remain unchanged. Meantime, the maximum dynamic shear modulus curve is a convex shape, and the final shear stress amplitude curve is a convex shape at positive temperature,while which a concave shape at negative temperature. At constant frequency and confining pressure, the maximum dynamic shear modulus and final shear stress amplitude increase with the decrease of temperature. Curves of change trend are slower above 0°C, and steeper below 0°C.

A notch critical plane approach of multiaxial fatigue life prediction for metallic notched specimens

AbstractAn approach based on the local stress response is proposed to locate the fatigue critical point for metallic blunt notched specimens under multiaxial fatigue loading. According to the stress analysis, both stress gradient and gradient of loading nonproportionality exist at notch root. The plane in the vicinity of the notch that passes through the fatigue critical point and experiences the maximum shear stress amplitude is defined as the critical plane for notch specimens (CPN). Furthermore, the Susmel's fatigue damage parameter is modified to assess fatigue life of notched components by combining CPN and the theory of critical distance (TCD). The multiaxial fatigue test of the thin‐walled round tube specimens made of Ni‐base alloy GH4169 is carried out to verify the above approaches. In addition, test data of two kinds of materials are collected. The results show that the maximum absolute error of the fatigue critical point is 9.6° and the majority of the predicted life falls within the three‐time scatter band.

On the estimation of finite lifetime under fretting fatigue loading

The aim of this paper is to formulate and validate an alternative design approach suitable for predicting finite lifetime of mechanical assemblies subjected to constant amplitude (CA) fretting fatigue loading. The design methodology being proposed is based on the use of the Modified Wӧhler Curve Method (MWCM) applied in conjunction with both the Theory of Critical Distance (TCD) and the Shear Stress-Maximum Variance Method (τ-MVM). In more detail, the TCD, applied in the form of the Point Method (PM), is used to take into account the damaging effect of the multiaxial stress gradients acting on the material in the vicinity of the contact region. The time-variable linear-elastic stress state at the critical locations is then post-processed according to the MWCM which is a bi-parametrical criterion that estimates fatigue lifetime via the stress components relative to those planes experiencing the maximum shear stress amplitude. Thanks to its specific features, the MWCM is capable of modelling not only the presence of non-zero mean stresses, but also the degree of multiaxiality and non-proportionality of the local load history being investigated. In this setting, the τ-MVM is used to calculate the stress quantities relative to the critical plane whose orientation is determined numerically by locating that plane containing the direction experiencing the maximum variance of the resolved shear stress. The accuracy and reliability of the proposed design methodology was checked against a number of experimental data taken from the literature and generated by testing four different metallic materials. The agreement between experiments and estimates being obtained strongly supports the idea that the proposed approach can be used to perform a rapid assessment of mechanical assemblies damaged by in-service fretting fatigue loading.

Fatigue life assessment of steel samples under various multiaxial loading spectra by means of Smith‐Watson‐Topper type damage descriptions

AbstractFatigue damage and life of SS304, S45C, and SNCM630 steel samples tested at various irregular axial‐torsional loading spectra were evaluated by means of 7 Smith‐Watson‐Topper (SWT) type damage descriptions. The overall damage was calculated over peak‐valley events of counted cycles by means of the product of stress and strain corresponding to the areas within stress‐strain hysteresis loops. Fatigue lives of 304 steel samples predicted by the SWT, Lorenzo‐Laird, Szolwinski‐Farris, and Chen‐Xu‐Huang models were found noticeably larger than those of experimentally obtained at various loading spectra. Predicted lives by these descriptions were found moderately in agreement with experimental data of S45C and SNCM630 steel samples. The predicted lives of steel samples by Socie, Lv et al, and the one presented in this study were closely agreed with experimental data due to their different descriptions. The modified SWT model further included the product of maximum shear stress and shear strain amplitude and related the overall damage to fatigue life through Coffin‐Manson equation. The choice of model descriptions for damage assessment was discussed based on their terms, areas underneath of hysteresis loops, and material damage mechanism.

Cyclic strength of saturated sand under bi-directional cyclic loading

Subject to cyclic loading due to ocean waves and earthquakes, both the shear stress and axial cyclic stress need to be accounted for in the analyses of stress state and cyclic strength. For laboratory soil test, the loading condition can be simulated by performing hollow cylindrical apparatus test, and also the effects of ratios and phase angles between dynamic axial and horizontal shear stress can be considered. In the present study, the maximum shear stress amplitude of soil element is defined as a measure of cyclic strength. Based on the theoretical analysis and experimental tests, this study investigates the influence from the ratios and phase angles on the number of load cycles leading to liquefaction failures. In addition, the characteristics of pore water pressure development are also studied. The theoretical and experimental results indicate that the ratios and phases between the axial dynamic load and torsional dynamic load significantly affect the dynamic strength of sands. Moreover, ratios and phases between the axial dynamic load and torsional dynamic load influence the accumulation speed of pore water pressure significantly. Nevertheless, when the pore water pressure is normalized, the sensitivity of their influences on the pore water pressure development cannot be identified.

Comparison of multiaxial fatigue parameters using biaxial tests of Waspaloy

In laboratories most fatigue testing is uniaxial as many aeronautical components such as wing spars are uniaxially loaded. However important components, such as aero engine disks, operate under multiaxial loading conditions. Hence multiaxial data is desirable to safely design them. This paper describes biaxial fatigue tests carried out under a range of loading conditions with cruciform specimens made of Waspaloy, a nickel based superalloy widely used in the fabrication of aero engine disks. Finite Element modeling of the specimen was performed to set the test conditions and to predict stress-strain fields and failure location. In order to investigate the effect of strain biaxiality, different biaxiality ratios with the same maximum principal stress were considered. Results demonstrate a variation in total life to failure and failure location, confirming the FE predictions. Then the experimental results obtained were used with three groups of multiaxial criteria. Initially, von Mises and elastic strain energy density yield theories were extended to the multiaxial fatigue context. Secondly, the stress invariant based criterion proposed by Crossland was considered, where the maximum shear stress amplitude was calculated through the Minimum Circumscribed Circle and the Maximum Prismatic Hull methods. Lastly, the critical plane approach was investigated by considering the propositions made by Findley and Matake. In general all the criteria probed here gave good predictions. As for the first group, better correlation was obtained with the energy parameter. For the last two groups, Crosslands formulation performed the best, with close agreement with experimental observations. The critical plane criteria gave conservative predictions for uniaxial stress cases and non-conservative for the other assessed conditions. In addition, both criteria misbehaved outside their calibration region, i.e. outside the tension-torsion region, and were unable to properly describe equi-biaxial conditions.

Effect of Mean Stress on 2A12-T4 Aluminum Alloy under Tension-Torsion Constant Amplitude Loading

Fatigue tests have been carried out to investigate the effects of mean-stress and phase-difference on the tension-torsion fatigue failure of 2A12-T4 aluminum alloy. The results show that for fully reversed tension-torsion loading, the fatigue life increases with the increase of phase angle, but the fatigue life decreases with the increase of phase angle, when mean-stress exists, both for shear mean-stress and normal mean-stress. Fracture appearance shows that the crack initiation is on the direction of maximum shear stress amplitude plane. Critical plane criteria based on the linear combination of the maximum shear stress amplitude and maximum normal stress are studied and further discussion on the drawbacks of this kind of criteria are performed.

Comparison of crack paths in a forged and extruded aeronautical titanium alloy loaded in torsion in the gigacycle fatigue regime

This paper discusses features of fatigue crack initiation and growth in an extruded and forged VT3-1 titanium alloy loaded in pure torsion in the gigacycle regime. Torsion fatigue tests were performed at 20kHz up to a fatigue life of 109 cycles. It has been shown that regardless of the manufacturing process both surface and subsurface crack initiation may appear under ultrasonic torsion loads despite the fact that the maximum shear stress amplitude is located at the specimen surface. In the two cases cracks initiate on planes of maximum shear stress amplitude (mode II). After reaching a certain length the cracks turn and propagate in mode I. Surface crack initiation and growth mechanisms in VHCF regime are similar to HCF ones. Subsurface crack forms a typical “fish-eye” pattern on fracture surface with three different zones: (1) small crack growth in the plane of maximum shear stress, (2) crack growth on the plane of maximum normal stress with the formation of a quasi-flat failure surface covered by fretting debris, (3) crack branching under mixed mode loading conditions (I+II+III) with the formation of several secondary cracks. Subsurface crack initiation sites are located below the specimen surface (at a depth of approximately 200μm) for both the forged and the extruded materials. Subsurface crack growth is observed on the failure surface as being less rough. The mechanisms of subsurface crack initiation seems to be similar to these observed under fully reversed tensile loads.

Effect of Phase Angle on Fatigue Failure of 30CrMnSiA Steel under Tension-torsion Fatigue Loading

Tension-torsion high-cycle fatigue experiments with solid cylindrical bar specimens of 30CrMnSiA steel were carried out under different phase angles. And the experiment data, characteristics of stresses with plane orientation and fracture appearance under different loading conditions were analyzed and investigated. Experiment results show that fatigue life increases gradually with the increase of phase angle. The fatigue life is shortest for 0° phase angle, while the fatigue life is longest for 90° out-of-phase angle. It could be found from analysis of stress parameters that as the phase angle increases, the shear stress amplitude decreases and the maximum normal stress increases gradually, which are on the maximum shear stress amplitude plane close to the axial of specimen. Macro-analysis of the fracture appearances show that when the phase angle increases, the angel between crack initiation plane and specimen axial decreases, and cracks are inclined to initial and propagate on or near the maximum shear stress amplitude plane with larger maximum normal stress under proportional loading as well as non-proportional loading.

Crack initiation and early propagation plane orientation of 2A12-T4 aluminum alloy under tension-torsion fatigue loading including mean tensile stress

The specimen fractures appearances are analyzed to investigate the effects of mean tensile stress on the fatigue crack initiation and early propagation plane orientation under axial-torsion fatigue loading for 2A12T4 aluminum alloy. The fatigue crack initiation and early propagation plane orientations are measured by optical microscope, the results of macro-analysis show that both the maximum shear stress amplitude and normal mean stress have effects on the orientations of crack initiation and propagation plane orientation, which are close to the plane of the maximum shear stress amplitude plane. With increasing the mean tensile stress, more cracks are inclined to initial and propagate on or near the maximum shear stress amplitude plane with larger normal mean stress, and the angle of deviation from the plane of maximum shear stress amplitude increases. The predicted plane orientations based on critical plane methods are compared with experimental measured results.

Fretting fatigue tests on shrink-fit specimens and investigations into the strength enhancement induced by deep rolling

The shrink-fit connection undergoes fretting fatigue at the edge of the contact, where both stress concentration and micro-slip take place. A fretting test set-up with a round-shaped specimen is proposed that eliminates lateral edge contact and misalignment, and is also appropriate for deep rolling. Comparative experiments showed a notable strength improvement, induced by deep rolling, along with the beneficial effect of friction reduction due to lubrication. Multiple cracks with clear shallow paths were evident after SEM observation, thus the maximum shear stress amplitude was assumed as a correlating parameter, while the crack arrest was inappropriate especially for deep rolled specimens.

A multiaxial high-cycle fatigue life evaluation model for notched structural components

A model for multiaxial high-cycle fatigue life evaluation of notched structural components is proposed, which considers the impact of the stress field on fatigue life by utilizing the Theory of Critical Distances (TCD) and Finite Element Method (FEM). The maximum shear stress range plane is defined as the critical plane, and the damage parameters are the maximum effective shear stress amplitude and the maximum effective normal stress, which are obtained by averaging the stress in the hemisphere volume around the maximum stress point. To validate the accuracy of the model, multiaxial fatigue tests are carried out for both smooth and notched specimens of Aluminum–Silicon alloy. The results indicate that the evaluated life and experimental life have a good agreement.