Variable Amplitude Multiaxial Loading Research Articles

Performance of chosen multiaxial cycle counting method under non-proportional multiaxial variable loading.

One of the most crucial tasks in fatigue life-time estimation of components loaded with multiaxial variable amplitude loading is to correctly identify loading cycles that can be used with multiaxial damage criterions. During past years, several cycle counting methods have been proposed for multiaxial loading conditions. The aim of this text is the comparison of selected multiaxial cycle counting methods, namely Wang-Brown’s method, Modified Wang-Brown’s method, Bannantine-Socie’s method and then a critical analysis of the obtained results. For the comparison of chosen methods, a new data set, consisting of experimentally obtained results from multiaxial non-proportional variable amplitude loading tests carried on by authors, has been used. The tested specimens were made from S355J0 structural steel and the testing procedure has been carried out on the MTS Axial/Torsion servo hydraulic testing machine. Findley and McDiarmid multiaxial criterion with Palgren-Miner summation rule have been used for fatigue life-time estimation of the tested specimens.

A novel approach to simulate the stiffness behaviour of spot welded vehicle structures under multi axial variable amplitude loading

Under cyclic loading in combination with high local stress levels a change in stiffness of connection points, e.g. spot welds, self-piercing rivets or flow drill screws can be observed. This paper introduces a numerical approach for the simulation of stiffness changes in vehicle structures under multiaxial cyclic loading as a result of the stiffness degradation of individual spot welds. The basic approach is based on a conventional damage accumulation combined with a power law representing the change in the spot weld’s stiffness. Instead of an accumulated damage value D a residual stiffness is set as failure criterion. Extensions to the approach are presented for its application to multiaxial loading with variable amplitudes. A conventional multiaxial fatigue test of a complete vehicle, focusing on its rear end including global stiffness and local strain measurements at the beginning, median and at the end of the test are presented and compared to the simulated results. This computation approach allows a more reliable fatigue assessment in comparison to a fatigue analysis which does not consider stiffness changes. The damage propagation after the crack initiation at an individual spot weld is represented more accurately as subsequent changes in the load paths are considered.

Evaluation of Fatigue Life for TC4 Notched Components Under Variable Amplitude Multiaxial Loading

Fatigue tests under variable amplitude multiaxial loading were conducted on notched specimens of titanium alloy TC4. The key issues of fatigue life estimation under variable amplitude multiaxial loading for notched components have been researched. Multiaxial fatigue critical area of notched specimen was determined first. Then, fatigue damage control parameter based on Wu–Hu–Song model and rainflow cycle counting as well as Miner–Palmgren rule was applied in prediction approach. The proposed prediction procedures were checked against the test data of TC4 notched specimens under variable amplitude multiaxial loading. The prediction results are all within a factor of two scatter band of the test results.

Multiaxial variable amplitude fatigue life analysis using the critical plane approach, Part I: Un-notched specimen experiments and life estimations

Despite its importance in many engineering applications, fatigue life assessment is still not well understood under multiaxial variable amplitude loading conditions. Although critical plane-based analysis approaches have been shown to work well for constant amplitude multiaxial loading, results for variable amplitude life estimations have been mixed. This is likely due to the consideration of additional factors in a variable amplitude analysis, which can include load history effects, varying degrees of loading non-proportionality, changes in mean stress, cycle counting, and fatigue damage accumulation. In order to better understand the impact that each of these factors can have on life estimation accuracy, this study compares experimental results for both un-notched and notched specimens of 2024-T3 aluminum alloy to variable amplitude life estimations computed using a critical plane-based analysis approach. A modified version of the Fatemi-Socie parameter was used to calculate fatigue damage, while different analysis procedures were implemented to study the effect of transient material deformation behavior and crack initiation definition on life estimation accuracy. Part I of this two part paper presents the experimental results and analyses for un-notched specimen tests, while part II applies the same life assessment techniques to situations involving notched specimens. While the best analysis procedures investigated were able to estimate most un-notched specimen fatigue lives within a factor of 3 of experimental results, life estimations had a general tendency to be non-conservative and were not as accurate as those obtained under constant amplitude loading conditions.

A Novel Methodology to Estimate Life of Gas Turbine Components Under Multiaxial Variable Amplitude Loading

A novel and highly effective methodology is presented in this study to estimate the stresses and strains and also the life of gas turbine components operating in multiaxial variable amplitude loading conditions. The methodology uses a cyclic plasticity model based on multilinear kinematic hardening (MLKH) for estimation of stress-strain response and Wang and Brown algorithm for counting the reversals in the loading cycle. The stress and strain response extracted for each reversal using the MLKH model where then integrated with multiaxial fatigue damage model based on critical planes (Wang and Brown model) suitable for LCF applications, to predict the fatigue life. The proposed methodology was initially compared with experimental test results of 42CrMo4 low alloy steel specimen, under different loading conditions like proportional, non-proportional and sequential loadings available in the literature. To reinforce the life prediction capability of the methodology, an application level study was undertaken. An air-cooled high-pressure turbine disk of an aero gas turbine engine was used as the model for this study. The fatigue life obtained from the multiaxial fatigue damage model was then compared with the experimental LCF life of the disk obtained from the field data. In order to be conservative in approach, lower bound of the 95% confidence limit of the fatigue data fitted using Weibull probability distribution function was used to compare the numerical life. The study shows a good correlation between the fatigue life arrived experimentally and the predicted life using the proposed methodology.

Evaluation of different techniques in estimating orientation of crack initiation planes and fatigue lifetime under complex multiaxial loading paths

In the present investigation, the accuracy of two methods, i.e., the Shear Strain-Maximum Variance Method (γ-MVM) and the Maximum Damage Method (MDM), in predicting the orientation of the crack initiation planes was checked by considering several results taken from the literature and generated by testing five different metallic materials under complex multiaxial loading. The γ-MVM postulates that the critical plane is that material plane containing the direction experiencing the maximum variance of the resolved shear strain. In contrast, the MDM defines the critical plane as that material plane on which the accumulated damage reaches its maximum value. In the present investigation, the MDM was applied in conjunction with Fatemi-Socie’s (FS) multiaxial fatigue criterion, Bannantine-Socie’s (BS) cycle counting method, and Miner’s linear rule. The validation exercise being performed demonstrated that both the γ-MVM and the MDM were capable of accurately predicting the orientation of the crack initiation planes in the selected metals. Subsequently, the reliability of three different design methodologies suitable for estimating fatigue lifetime of metals subjected to variable amplitude multiaxial loading was assessed quantitatively by using a number of experimental results taken from the literature. In more detail, Methodology A was based on the MDM applied along with the FS criterion, the BS cycle counting method, and Miner’s rule. Methodology B made use of the γ-MVM, the FS criterion, the BS cycle counting method, and Miner’s linear rule. Finally, Methodology C involved the γ-MVM, the Modified Manson Coffin Curve Method (MMCCM), the classical Rain-Flow cycle counting method, and Miner’s linear rule. According to this systematic validation exercise, the usage of these three design procedures was seen to result in satisfactory predictions, with the estimates falling within an error band of three.

Fatigue damage assessment under random and variable amplitude multiaxial loading conditions in structural steels

Fatigue damage assessment of multiaxial random loadings is a complex issue and a subject of actual interest in mechanical design. In this work, the performance of the stress scale factor (SSF) criterion is evaluated under variable amplitude loading conditions, and damage accumulation approaches. This evaluation is performed by taking into account two types of loading spectra, namely the loading block spectra (where the loading pattern is well identified and repeated until rupture), and the random loading spectra (where the stochastic behaviour of the axial and shear loading components do not allow a direct identification of the loading pattern). Moreover, the validity of the hypothesis in which the SSF damage map remains valid for any high strength steel under variable amplitude loading conditions is also inspected by analysing fatigue life correlation of the 1050 QT steel and the 304L stainless steel under a multiaxial loading block.

Reliability Study and Life Estimation of a Centrifugal Impeller, Under Multiaxial Variable Amplitude Loading

An application level study of multiaxial variable amplitude loading condition is presented here, by taking centrifugal impeller used in a gas turbine engine as the model for the study. Algorithms proposed by Bannantine and Socie (BS) and Wang and Brown (WB) were used for counting the damage cycles resulting from the service loading conditions. To estimate the damage parameter and fatigue damage, multiaxial fatigue damage models proposed by Fatemi and Socie (FS) and Smith–Watson–Topper (SWT) were used. The theoretical results were validated through a reliability study using Weibull models. Field data for this study were collected from 18 centrifugal impeller sets removed from different gas turbine engines that were brought to the shop for inspection. The reliabilities of life estimated by the FS model using algorithms proposed by BS and WB were found to fall within 80 and 82%, respectively. The SWT model estimated the life of the centrifugal impeller with reliabilities of 98 and 98.5% using the same algorithms. Appreciable differences in fatigue life were not observed for this application when algorithms proposed by BS or WB were used to count the damage cycles.

Estimation of fatigue lifetime for selected metallic materials under multiaxial variable amplitude loading

This paper initially investigates the accuracy of two methods, i.e., the Maximum Variance Method (MVM) and the Maximum Damage Method (MDM), in predicting the orientation of the crack initiation plane in three different metallic materials subjected to multiaxial variable amplitude loading. According to the validation exercise being performed, the use of both the MVM and the MDM resulted in a satisfactory level of accuracy for selected three metals. Subsequently, three procedures to estimate the fatigue lifetime of metals undergoing multiaxial variable amplitude loading were assessed quantitatively. Procedure A was based on the MDM applied along with Fatemi-Socie’s (FS) criterion, Bannantine-Socie’s (BS) cycle counting method and Miner’s linear rule. Procedure B was based on the MVM, FS criterion, BS cycle counting method and Miner’s linear rule. Procedure C involved the MVM, the Modified Manson Coffin Curve Method (MMCCM), the classical rainflow cycle counting method and Miner’s linear rule. The results show that the usage of these three design procedures resulted in satisfactory predictions for the materials being considered, with estimates falling within an error band of three.

An elasto-plastic approach to estimate lifetime of notched components under variable amplitude fatigue loading: a preliminary investigation

The present paper is concerned with the formulation of an elasto-plastic strain based approach suitable for assessing fatigue strength of notched components subjected to in-service variable amplitude cyclic loading. The hypothesis is formed that the crack initiation plane is closely aligned with the plane of maximum shear strain amplitude, its orientation and the associated stress/strain quantities being determined using the Maximum Variance Method. Fatigue damage is estimated by applying the Modified Manson-Coffin Curve Method (MMCCM) along with the Point Method (PM). In the proposed approach, the required critical distance is treated as a material property whose value is not affected either by the sharpness of the notch being assessed or by the profile of the load spectrum being applied. The detrimental effect of non-zero mean stresses and degree of multiaxiality of the local stress/strain histories is also considered. The accuracy and reliability of the proposed design methodology was checked against several experimental data taken from the literature and generated under different uniaxial variable amplitude load histories. In order to determine the required local stress/strain states, refined elasto-plastic finite element models were solved using commercial software ANSYS®. This preliminary validation exercise allowed us to prove that the proposed approach is capable of estimates laying within an error factor of about 2. These preliminary results are certainly promising, strongly supporting the idea that the proposed design strategy can successfully be used to assess the fatigue lifetime of notched metallic components subjected to in-service multiaxial variable amplitude loading sequences.

A simplified cyclic plasticity model for calculating stress-strain response under multiaxial non-proportional loadings

Abstract Given the dependence of many fatigue damage parameters on both stress and strain values, being able to produce accurate stress-strain estimations is an essential first step when performing a fatigue life analysis. However, more advanced cyclic plasticity models, capable of capturing complex material behavior under multiaxial non-proportional loadings, often require the determination of a large number of material constants from experimental data that are not always available to the analyst. Therefore, in this study, a simplified Armstrong-Frederick-Chaboche style plasticity model, based on the assumption of Masing material behavior and a newly proposed transient hardening formulation, was evaluated in terms of its ability to predict stress-strain response under complex multiaxial loading conditions. To do this, experimental stress-strain data were generated for 2024-T3 aluminum alloy using both constant and variable amplitude multiaxial block loading histories designed to reflect a wide variety of stress states that might be encountered in any given service loading history. Stress-strain predictions were performed both with and without the consideration of non-proportional hardening effects in order to provide a baseline for evaluating the results. Although all stress-strain predictions were found to agree well with the experimental data, both quantitatively and qualitatively, it was shown that, in general, predictions for axial stress amplitudes and mean axial stresses were consistently better than those for shear stress.

Life prediction based on weight‐averaged maximum shear strain range plane under multiaxial variable amplitude loading

AbstractBased on Wang and Brown's reversal counting method, a new approach to the determination of the critical plane is proposed by the defined plane with a weight‐averaged maximum shear strain range under multiaxial variable amplitude loading. According to the determined critical plane, a detailed procedure of multiaxial fatigue life prediction is introduced to predict lives in the low‐cycle multiaxial fatigue regime. The proposed approach is verified by two multiaxial fatigue damage models and Miner's linear cumulative damage law. The results showed that the proposed approach can effectively predict the orientation of the failure plane under multiaxial variable amplitude loading and give a satisfactory life prediction.

Estimating the orientation of crack initiation planes under constant and variable amplitude multiaxial fatigue loading

This paper investigates the accuracy of the shear strain Maximum Variance Method (γ–MVM) and Maximum Damage Method (MDM) in predicting the orientation of crack initiation planes under both constant and variable amplitude multiaxial fatigue loading. The γ–MVM defines the critical plane as the plane on which the variance of the resolved shear strain reaches its maximum value. In contrast, a specific multiaxial fatigue criterion is needed to be used along with the MDM to predict the orientation of the critical plane under multiaxial fatigue loading. As far as variable amplitude multiaxial loading is concerned, the MDM have to be used by applying with a certain fatigue criterion, a cycle counting method and a cumulative damage rule. In this paper, the MDM is applied with Fatemi & Socie’s criterion, Bannantine & Socie’s cycle counting method and Palmgren-Miner’s linear rule. The MDM assumes that the critical plane is the plane experiencing the maximum accumulated damage. Experimental data for several metals tested under constant and variable amplitude multiaxial fatigue loading taken from literature are used to assess the accuracy of these two methodologies. The results show that the predictions made by both the γ–MVM and MDM have good accuracy for the investigated materials and investigated load histories: 90% of the predictions made by the γ–MVM and 80% of the predictions made by the MDM fall within a scatter band of 20%.

Multiaxial variable amplitude fatigue life analysis including notch effects

This paper evaluates the methodology for, and effectiveness of, common equivalent stress- and strain-based fatigue life analysis approaches when applied to variable amplitude multiaxial service loading conditions. Experimental results for both un-notched and notched specimens of 2024-T3 aluminum alloy, tested under axial, torsion, and combined axial–torsion loadings, are compared to predictions based on von Mises equivalent stress and strain. Mean stresses were considered using Smith–Watson–Topper, modified Goodman, and modified Morrow models. Variable amplitude life predictions are compared to constant amplitude predictions to highlight similarities and differences in life prediction trends. Overall, mixed results were obtained. Both constant and variable amplitude fatigue lives are predicted well for notched specimens, where a local uniaxial stress state always exists for the geometry considered. However, for un-notched specimens, where multiaxial loading effects come into play, no approach considered is able to predict more than 60% of fatigue data within a factor of ±3 of experimental life. A consistent trend of non-conservative life predictions for variable amplitude loading conditions is observed. The importance of considering stress gradient effects in notched specimen life prediction is also demonstrated. An extensive discussion on areas where improvements can be made with respect to fatigue damage quantification completes the paper.

The Modified Manson–Coffin Curve Method to estimate fatigue lifetime under complex constant and variable amplitude multiaxial fatigue loading

This paper investigates the accuracy of the so-called Modified Manson–Coffin Curve Method (MMCCM) in estimating fatigue lifetime of metallic materials subjected to complex constant and variable amplitude multiaxial load histories. The MMCCM postulates that fatigue damage is maximised on that material plane experiencing the maximum shear strain amplitude. In the present investigation, the orientation of the critical plane was determined through that direction along which the variance of the resolved shear strain reaches it maximum value. Under variable amplitude complex load histories, this direction was also used to count the resolved shear strain cycles via the classic Rain-Flow method. Further, the degree of multiaxiality and non-proportionality of the time-variable stress states at the assumed critical locations was directly quantified through a suitable stress ratio which accounts for (i) the mean value and the variance of the stress perpendicular to the critical plane as well as for (ii) the variance of the shear stress resolved along the direction experiencing the maximum variance of the resolved shear strain. The accuracy and reliability of the proposed approach was checked against approximately 650 experimental data taken from the literature and generated by testing un-notched metallic materials under complex constant and variable amplitude multiaxial load histories. The sound agreement between estimates and experimental results which was obtained strongly supports the idea that the proposed design technique is a powerful engineering tool allowing metallic materials to be designed against constant and variable amplitude multiaxial fatigue by always reaching a remarkable level of accuracy. This approach offers a complete solution to the strain based multiaxial fatigue problem.

Critical plane approach to multiaxial variable amplitude fatigue loading

A new critical plane approach based on the modified Manson-Coffin curve method (MMCCM) is presented in this paper for predicting fatigue lifetime under variable amplitude (VA) multiaxial fatigue loading. The critical plane is assumed to coincide with that material plane experiencing the maximum variance of the resolved shear strain. Fatigue damage is hypothesized to be a function of both the amplitude of the resolved shear strain and the so-called critical plane stress ratio. The latter quantity depends on the mean value and the variance of the stress perpendicular to the critical plane as well as on the variance of the shear stress resolved along the direction experiencing the maximum variance of the resolved shear strain. Load cycles are counted from the resolved shear strain time history by using the classic rain flow counting method. Palmgren-Miner’s linear damage rule is applied to estimate cumulative fatigue damage. The accuracy and reliability of the proposed approach is checked by using several experimental data taken from the literature. The estimated fatigue lives based on the new approach are seen to be in sound agreement with the experimental results.

Evaluation of fatigue life for titanium alloy TC4 under variable amplitude multiaxial loading

AbstractFatigue tests under variable amplitude multiaxial loading were conducted on titanium alloy TC4 tubular specimens. A method to estimate the fatigue life under variable amplitude multiaxial loading has been proposed. Multiaxial fatigue parameter based on Wu–Hu–Song approach and rainflow cycle counting and Miner–Palmgren rule were applied in this method. The capability of fatigue life prediction for the proposed method was checked against the test data of TC4 alloy under variable amplitude multiaxial loading. The prediction results are all within a factor of two scatter band of the test results.

Comparison of HCF life prediction methods based on different critical planes under multiaxial variable amplitude loading

AbstractHigh‐cycle fatigue life prediction methods based on different critical planes, including the maximum shear stress (MSS) plane, the weighted average shear stress plane and the Maximum Variance shear stress plane, are compared by two multiaxial cycle counting methods, i.e. the main and auxiliary channels (MAC) counting and the relative equivalent stress counting. A modified damage model is used to calculate the multiaxial fatigue damage. Compared with the experimental lives for 7075‐T651 aluminium alloy, the predicted results show that the MSS method together with MAC counting is suitable for the multiaxial fatigue life prediction.

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.

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.