Variable Amplitude Multiaxial Loading Research Articles

A generalization ability-enhanced image recognition based multiaxial fatigue life prediction method for complex loading conditions

A generalization ability-enhanced image recognition based multiaxial low-cycle fatigue life prediction is proposed for complex conditions, including multiaxial variable amplitude fatigue, fatigue-creep interaction, and anisotropic materials. Notably, a novel modified dynamic hysteresis image plotting method is introduced for multiaxial variable amplitude loading. Building on a pre-trained convolution neural network (CNN) model, fine-tuning is used across three cases. It makes the error decrease to 25%. Besides, fine-tuning improves training efficiency and generalization. Based on fine-tuning results, each layer of the model is attributed with physics significance. Furthermore, regression activation map (RAM) is used for interpretation, illustrating that the model focuses on the inner and edges of hysteresis images.

Multiaxial cycle counting method based on path-dependent line integral

A multiaxial cycle counting method was proposed by path-dependent line integral (PDLI). In the proposed PDLI multiaxial cycle counting method, the length increment of loading path is assigned a positive or negative sign in the strain space, and the interval from zero to the maximum value of PDLI is defined as a half-cycle. A very concise recursive algorithm is provided to implement the proposed multiaxial cycle counting method. The experimental verification showed that the proposed multiaxal cycle counting method was used to count multiaxial cycle, which can obtain satisfactory life prediction results under multiaxial variable amplitude loading. In addition, the PDLI multiaxial cycle counting method can be reduced to a uniaxial rainflow counting form.

The Peak Stress Method for fatigue lifetime assessment of fillet-welded attachments in steel subjected to variable amplitude in-phase multiaxial local stresses

The Peak Stress Method (PSM) for the fatigue strength assessment of welded joints has been recently generalised to account also for variable amplitude (VA) multiaxial loading situations. In the present study, the previously published VA PSM has been verified against new experimental results generated by fatigue testing non-load-carrying (nlc) fillet-welded double transverse or inclined attachments made of S355 structural steel subjected to variable amplitude in-phase multiaxial local stresses. Combined with Miner’s Linear Damage Rule (LDR), the PSM proved effective in predicting the crack initiation location and accurate in estimating the experimental fatigue results.

Multiaxial fatigue life prediction by equivalent energy‐based critical plane damage parameter under variable amplitude loading

AbstractA new path‐independent multiaxial fatigue damage parameter , which is defined as the largest normal stress range between adjacent turning points of the maximum shear stress on the critical plane, is proposed to describe multiaxial fatigue damage. By combining the maximum normal stress or the largest normal stress range with the maximum shear stress range on the critical plane, two axial equivalent stress modification factors, and , are proposed, which can account for the influence of non‐proportional additional hardening. The sensitivity of the proposed axial equivalent stress modification factors to multiaxial variable amplitude loading sequences is analyzed. Furthermore, two new multiaxial fatigue damage models based on the axial equivalent stress modification factors are proposed to estimate fatigue life. The applicability of the presented methodology was verified by the experimental data of En15R steel and 7050‐T7451 aluminum alloy, and the results showed that the predicted fatigue lifetimes agree well with the experimental data under variable amplitude multiaxial loading.

Multiaxial thermo-mechanical fatigue life prediction based on notch local stress-strain estimation considering temperature change

The modified incremental multiaxial Neuber rule by considering the temperature change was firstly proposed, which combined with the Chaboche viscoplastic constitutive model to approximately compute the notch local stress and strain under multiaxial thermo-mechanical loading. Based on the proposed method, a life prediction method that can take into account fatigue, oxidation, and creep damage was developed, which can quickly predict notch fatigue failure lifetime under variable amplitude multiaxial thermo-mechanical loading. The proposed method was verified by the coupled thermal-structural nonlinear FEA and the experimental life results for the tenon joint structure specimens under eight thermo-mechanical loading paths. The comparison of computed and analyzed stress-strain history showed that a good agreement can be obtained. Comparing with experimental life data, all predicted lives fall in a 2-factor scatter band.

Multiaxial Variable Amplitude Loading for Automotive Parts Fatigue Life Assessment: A Loading Classification-based Approach Proposal

This work reports the different steps of a frequency decomposition method applied for fatigue lifetime assessment. The studied loadings are multiaxial time series measured at the vehicle wheel. The proposed decomposition presupposes that the loading results from both dynamic vehicle effects at low frequencies (Driven Road loadings) and random loads at high frequencies (Random Road loadings). This signal partition has two assets for fatigue purposes. First, the spectral methods can be applied to the Random effects. Two spectral damage formulations are tested in this paper. Then, the Driven Road loadings, related to the vehicle manoeuvre, enables to implement the Rainflow counting method on only one time series instead of the initial set of six per wheel, or twelve per axle. The implemented approach illustrated on a braking manoeuvre is validated, comparing the damage summation of the Random and Driven Road loadings with the one based on the usual Rainflow counting method applied to the overall time series.

Various parameters of the multiaxial variable amplitude loading and their effect on fatigue life and fatigue life computation

AbstractThe paper discusses various partial solutions used for estimating fatigue life under variable amplitude multiaxial loading in the high‐cycle fatigue domain. The concurring effects are treated, and their proposed solutions are commented upon. The major focus is on the categories of the phase shift effect and of cycle counting and on the scope and quality of data, which support discussed theories. Results of own new experimental data set on specimens from S355 steel are provided. Fatigue life estimates for McDiarmid and Findley multiaxial methods and for two different methods of load path decomposition to cycles are shown to highlight some of the points open for discussion. It is concluded that the available experimental data are not sufficient to substantiate a clear decision to follow a definite algorithm.

Multiaxial fatigue assessment for outer cylinder of landing gear by critical plane method

The in-service loadings on the landing gear are usually complex and from different directions, which lead to the fatigue critical locations in the landing gear structure mostly in multiaxial stress state. A methodology based on the critical plane method was proposed for estimating the fatigue lifetime of outer cylinder of the main landing gear undergoing variable amplitude (VA) multiaxial proportional loading. The orientation of the critical plane was determined by the so-called maximum variance method. The Bannantine–Socie’s cycle counting method and Miner’s linear rule were applied with Zhang–Yao’s criterion in this research. The calculated results on the fatigue lifetime of the outer cylinder were compared with the experimental data. The results indicate that the methodology proposed in this article is a sound method for fatigue life prediction of engineering components bearing complex VA multiaxial fatigue loading.

Fatigue life prediction for the AISI 4340 steel under multiaxial variable-amplitude loading with respect to the calculated rainflow damage based on the path length

The high-cycle fatigue life with respect to the multiaxial variable-stress amplitude was evaluated by applying the newly proposed total path length method for calculating the stress amplitude. Variable-stress-amplitude fatigue tests were conducted for verification based on the combined axial and torsional loads on AISI 4340 steel. The fatigue test load waveform denoted that the stress amplitude, mean stress, and load direction varied within one loop. The obtained lives were shorter than those predicted using the Wang–Brown method, longer than those predicted using the PDMR method, and comparable to those predicted using the total path length method.

Nominal stresses to assess damage in notched additively manufactured steel subjected to constant and variable amplitude multiaxial fatigue loading

The present paper reports on the use of the Modified Wöhler Curve Method (MWCM) applied along with nominal stresses to estimate lifetime of notched additively manufactured metallic materials subjected to constant and variable amplitude multiaxial fatigue loading. The MWCM is applied by defining the critical plane via the direction that experiences the maximum variance of the resolved shear stress. In this setting, owing to the fact that the shear stress resolved along this direction is a monodimensional stress quantity, fatigue cycles are counted directly by using the standard Rain-Flow method. Based on a large data set taken from the literature, the validation exercise being performed strongly supports the idea that the MWCM used in conjunction with nominal stresses is successful in estimating fatigue damage also in notched 3D-printed metallic materials subjected to constant/variable amplitude multiaxial load histories.

Fatigue performance of additive manufactured metals under variable amplitude service loading conditions including multiaxial stresses and notch effects: Experiments and modelling

Additive manufacturing technology has gained significant attention in recent years. However, due to lack of sufficient understanding of their fatigue behavior under service loading conditions, design of critical load carrying parts using this technique is still at early stages. These conditions include multiaxial stress states, notches and stress concentrations, and variable amplitude load cycles. Some of the distinguishing features of AM metals as compared to the conventionally fabricated metals include defects, surface roughness, anisotropy and build orientation effects, and residual stresses due to the fast solidification during the fabrication process. These factors resulting from AM processes may significantly affect the fatigue performance of AM parts under multiaxial variable amplitude loading. In this work, unnotched and notched fatigue behavior of two commonly used AM metals with different surface roughness conditions were studied under variable amplitude multiaxial loads. Both crack initiation approach using critical plane-based model and fracture mechanics approach using crack growth from the rough surface or surface defects at the notch were used to estimate the fatigue lives. Fatigue estimations are then compared to the experimental results.

An improved critical plane and cycle counting method to assess damage under variable amplitude multiaxial fatigue loading

AbstractThe plane with the maximum variance of the resolved shear stress is taken as the critical plane. Two algorithms are used along with the maximum variance method (MVM) to determine the orientation of the critical plane. The maximum variance of the normal stress on the potential critical planes is calculated to determine the one experiencing the maximum extent of fatigue damage. A new multiaxial cycle counting method is proposed to count cycles on the critical plane. The modified Wöhler curve method is used to assess fatigue damage. About 200 experimental results were collected from the technical literature to validate the approaches being proposed. The results show that the improved design technique being proposed is successful in assessing fatigue damage under variable amplitude multiaxial cyclic loading.

Application of life-dependent material parameters to lifetime calculation under multiaxial constant- and variable-amplitude loading

This study investigated the application of the life-dependent material parameter concept to stress-based fatigue criteria for fatigue life prediction under multiaxial variable-amplitude loading. Different multiaxial fatigue criteria were applied to the fatigue life calculation with fixed and life-dependent material parameters under constant- and variable amplitude loading. Uniaxial variable-amplitude loading was applied to select the appropriate damage accumulation rule. The verification was based on experimental tests with 133 specimens made of S355 steel. Significant improvements in the fatigue life prediction under both constant- and variable-amplitude loading were observed with the applied concept.

Online fatigue damage evaluation method based on real-time cycle counting under multiaxial variable amplitude loading

To realize on-line multiaxial fatigue damage evaluation for the servicing mechanical components, a real-time multiaxial cycle counting method is proposed, meanwhile, an online multiaxial fatigue damage evaluation method based strain-critical plane model is given and validated by the fatigue experimental data of En15r steel. Investigation showed that the proposed on-line multiaxial fatigue damage evaluation method could provide satisfactory evaluation results, and the real-time performance of the proposed cycle counting method is path-dependent.

Effects of Axial and Multiaxial Variable Amplitude Loading Conditions on the Fatigue Life Assessment of Automotive Steering Knuckle

In this paper, the author has attempted to investigate the effects of different loading conditions including axial and multiaxial variable amplitude loading (VAL) on the fatigue life assessment of automotive components under various maneuvers. To this end, a case study was conducted on the cast iron steering knuckle of a passenger car. In fact, the various VAL histories are entered on the three joints of knuckle, namely steering linkage, lower control arm, and MacPherson strut. However, previous studies have shown that this high super-critical component fails through the steering linkage. Moreover, the rotation of the steering linkage is the most destructive load. Hence, in this research, different loading cases such as axial (destructive load as means 1 channel), multiaxial (only relates to loading on the joint of knuckle and steering linkage means 3 channels), and full multiaxial (including all loading time histories means 9 channels) were considered. Afterward, finite element analysis was performed for each case, and fatigue life of the component was predicted under different conditions. Next, fatigue life of the component was evaluated using the time histories of stress tensor in the root of steering linkage which is extracted by transient dynamic analysis and applying probabilistic approach based on the Liu–Zenner equivalent stress criterion. Eventually, the responses from both techniques were compared in different cases. The results reveal that life predicted using two methods are slightly different. But, the results of probabilistic approach are more accurate than the results of FEM in comparison with experimental data for the axial state. Also, one of the major achievements of this study is that for the components with complex geometry and under multi-input loading like the steering knuckle, it is essential to perform fatigue analysis by considering all real conditions and cannot be only focused to the destructive loading.

Fatigue Life Prediction Under Multiaxial Variable Amplitude Loading Using A Stress-Based Criterion

This article presents fatigue life calculations for metals under different multiaxial variable amplitude loading patterns. Developed from a stress-based multiaxial fatigue criterion, a damage parameter used in the fatigue life prediction method can capture correctly different damage mechanisms (proportional and non-proportional multiaxiality, mean stress, asynchronous and variable amplitude) of fatigue loading in the high cycle fatigue domain. The method is based on a reference S-N curve and a cumulative damage law. Assessment of the accuracy of the proposed method is carried out with three different materials from literature (EN-GS800-2 cast iron, 39NiCrMo3 steel and SAE 1045 steel) subjected to different patterns of variable amplitude loading (blocks, non-proportional asynchronous and proportional random loading). Results reveal that the prediction method is in good accordance with the experimental data.

Fatigue analysis of ductile and brittle behaving steels under variable amplitude multiaxial loading

AbstractThe analysis of fatigue behavior under multiaxial variable amplitude stress states, despite its wide applicability, has not been fully studied. Issues such as varying degrees of nonproportionality of the load history, cycle counting, damage accumulation, failure behavior of the material, and mean stress fluctuations which can significantly affect the results of these analyses have not been well understood. In this study, a methodology for the analysis of fatigue behavior under multiaxial variable amplitude loading conditions is employed which accounts for the aforementioned issues. At its core, the applied methodology uses critical plane analysis based on the failure behavior of each material to assess the fatigue damage. In order to evaluate the performance of the analysis method, axial, torsional, and combined axial‐torsional variable amplitude tests were performed on one ductile and one brittle behaving steel. The applied methodology resulted in close estimation of the experimental fatigue life for both ductile and brittle behaving steels.

Multiaxial creep–fatigue Life Prediction Under Variable Amplitude Loading at High Temperature

Based on the time–temperature parameter method, a modified von Mises stress is proposed to calculate the multiaxial creep damage at high temperature. By employing the strain-based multiaxial fatigue damage models, the modified von Mises stress is used to predict the creep–fatigue life under variable amplitude multiaxial loading at high temperature. The experimental data of GH4169 superalloy and 304 stainless steel conducted under both constant and variable amplitude loadings at high temperature are used to verify the proposed method, and a good agreement is obtained with the experimental data.

Influence of critical plane definition on fatigue lifetime estimation under variable amplitude nonproportional multiaxial loading.

In real operation, most of load bearing parts are commonly loaded with multiaxial variable amplitude loading. Fatigue lifetime estimation of such a component consists of multiple tasks. One of the most important problem to solve is how to handle multiaxiality of loading signal. Nowadays, the most commonly used way is use of multiaxial fatigue criterion based on critical plane theory. These criterions are based on assumption that fatigue lifetime of a component is determined by combination of shear and normal stresses (strains) in particular plane (critical plane). The definition of such a plane varies depending on different used criterions. While fatigue lifetime of component loaded with proportional loading signal can be estimated based on damage accumulated in critical plane, during the fatigue lifetime estimation under variable amplitude nonproportional loading the damage in noncritical plane has to be considered as well. This, however, leads to inaccuracy of the final results as multiaxial criterions often incorrectly calculate damage in noncritical plane. The aim of this paper is to discuss the influence of critical plane definition on fatigue lifetime estimation under variable amplitude nonproportional multiaxial loading. The results from fatigue lifetime estimations of component loaded by modeled signal using multiple different multiaxial criterions (with different critical plane definition) are presented and critically discussed.

Fatigue assessment of metallic components under uniaxial and multiaxial variable amplitude loading

AbstractIn the present paper, the fatigue lifetime of metallic structural components subjected to variable amplitude loading is evaluated by applying 2 different multiaxial high‐cycle fatigue criteria. Such criteria, proposed by some of the present authors, are based on the critical plane approach and aim at reducing a given multiaxial stress state to an equivalent uniaxial stress condition. In particular, the procedure employed by both criteria consists of the following 3 steps: (1) definition of the critical plane; (2) counting of loading cycles; and (3) estimation of fatigue damage. Finally, the previous criteria are validated by comparing the theoretical results with experimental data related to smooth metallic specimens subjected to uniaxial and multiaxial variable amplitude loading.