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

High‐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.     

Low‐cycle fatigue life prediction of various metallic materials under multiaxial loading

This paper proposed a simple life prediction model for assessing fatigue lives of metallic materials subjected to multiaxial low‐cycle fatigue (LCF) loading. This proposed model consists of the maximum shear strain range, the normal strain range and the maximum normal stress on the maximum shear strain range plane. Additional cyclic hardening developed during non‐proportional loading is included in the normal stress and strain terms. A computer‐based procedure for multiaxial fatigue life prediction incorporating critical plane damage parameters is presented as well. The accuracy and reliability of the proposed model are systematically checked by using about 300 test data through testing nine kinds of material under both zero and non‐zero mean stress multiaxial loading paths.     

A non-local theory applied to high cycle multiaxial fatigue

ABSTRACT The stress gradient effect on the fatigue limit is an important factor which has to be taken into account for an efficient transfer of fatigue data from laboratory tests to design of industrial components. A short review of some multiaxial high cycle fatigue criteria considering this effect is presented. On the basis of the two local mesoscopic approaches of Papadopoulos, two new non‐local high cycle multiaxial fatigue criteria are developed. These proposals are based on the concept of volume influencing fatigue crack initiation. Their predictions are compared with experimental multiaxial fatigue data on four materials (a mild steel, two high strength steels and a spheroidal graphite cast iron). The accuracy of the two local Papadopoulos criteria and of the non‐local proposals are compared and discussed, together with the physical interpretation of the threshold defining the volume influencing fatigue crack initiation.     

A multiaxial fatigue criterion for random loading

ABSTRACT A multiaxial fatigue criterion for random loading is proposed. Firstly, the orientation of the critical plane, where fatigue life estimation is carried out, is determined from the weighted mean position of the principal stress directions. Then, the scalar value of the normal stress vector N (t) perpendicular to the critical plane is taken as the cycle counting variable since the direction of such a vector is fixed with respect to time (conversely to the time‐varying direction of the shear stress vector C (t)), and a nonlinear combination of normal and shear stress components acting on the critical plane is used to define an equivalent stress amplitude. Finally, a damage accumulation model is employed to process such an equivalent stress amplitude and to determine fatigue endurance. This criterion is herein applied to some relevant random fatigue tests (proportional bending and torsion).     

Multiaxial fatigue life prediction method based on path‐dependent cycle counting under tension/torsion random loading

A path‐dependent cycle counting method is proposed by applying the distance formula between two points on the tension‐shear equivalent strain plane for the identified half‐cycles first. The Shang–Wang multiaxial fatigue damage model for an identified half‐cycle and Miner's linear accumulation damage rule are used to calculate cumulative fatigue damage. Therefore, a multiaxial fatigue life prediction procedure is presented to predict conveniently fatigue life under a given tension and torsion random loading time history. The proposed method is evaluated by experimental data from tests on cylindrical thin‐walled tubes specimens of En15R steel subjected to combined tension/torsion random loading, and the prediction results of the proposed method are compared with those of the Wang–Brown method. The results showed that both methods provided satisfactory prediction.     

Three-dimensional calculations of high cycle fatigue life under out-of-phase multiaxial loading

In this study, we investigate the prediction of fatigue life at a high number of cycles (>5 × 10⁴ cycles) for three-dimensional structures. An approach has been developed that includes the results of fatigue tests in a program using the finite element method. Numerical fatigue life calculations using three fatigue criteria were conducted to predict S – N curves. To complete the study and validate this approach, tests were carried out on FGS 700/2 cast iron with different geometrical structures and different fatigue loadings.     

An improved multiaxial high‐cycle fatigue criterion based on critical plane approach

Several groups of fatigue damage parameters are discussed and then an improved multiaxial high‐cycle fatigue criterion based on critical plane defined by the plane of maximum shear stress range is presented in this paper. A compromising solution to consider the mean normal stress acting on the critical plane is also proposed. The new fatigue criterion extends the range of metallic materials which is valid for the ratio 1.25 < f_?1/t_?1 < 2. The predictions based on the presented model show a good agreement with test data.     

Prediction of rubber fatigue life under multiaxial loading

The process of fatigue failure of materials is generally described by two phases: crack initiation and crack propagation. This study concerns the crack initiation in rubbers submitted to a cyclic loading. A parameter based on the strain energy density (SED) and predicting the onset of primary crack and its probable orientation has been identified for such materials according to the investigations of Mars and Fatemi. More precisely, this criterion has been analytically developed in the cases of simple tension, biaxial tension and simple shear loadings by assuming large strains. The results denote the possibility to predict the orientation plane in which the primary crack would be expected to occur in a material. Then, it was implemented in a finite‐elements (FE) program in order to be applied to structures under any kind of the strain states. A good agreement was obtained between FE and analytical results for the usual strain states. Finally, to evaluate lifetime up to crack nucleation, we have achieved a set of experimental fatigue tests using uniaxial tension (UT) and pure shear (PS) test specimens containing a hole in order to localize the crack initiation. The obtained results proved the efficiency of the criterion to describe the fatigue life of rubbers under multiaxial loading.     

Spectral methods to estimate local multiaxial fatigue failure for structures undergoing random vibrations

This paper proposes computationally efficient frequency domain formulations for two well-known multiaxial fatigue failure criteria, namely Matake's critical plane criterion and Crossland's criterion. For that purpose, it is shown how fatigue-related variables involved in both criteria can be estimated from the power spectral density matrix of the local stress vector. The finite element model of an example structure is then used to illustrate the application of the proposed frequency domain approaches. It is observed that both frequency domain formulations produce consistent results when compared with those obtained in the time domain from Monte-Carlo simulations of local stress vectors while offering tremendous computer savings. A frequency domain tool indicating whether the principal stress directions do rotate with time or not during the loading at a given location in the structure is also presented.     

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

Fatigue 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.     

The use of multiaxial fatigue models to predict fretting fatigue life of components subjected to different contact stress fields

This work describes the application of multiaxial fatigue criteria based on critical plane and mesoscopic (Dang Van, 1973, Sciences et Techniques de lÁrmement, 47 , 647—722) approaches to predict the fatigue initiation life of fretted components. To validate the analysis, several tests under closely controlled laboratory conditions are carried out in a Ti‐6Al‐4V alloy. These classical Hertzian tests reveal a size effect where fretting fatigue lives vary with contact size. Experimentally available data for fretting fatigue of an Al‐4Cu alloy are also used to assess the models. Neither the critical plane models nor the mesoscopic criterion considered can account for the effects of different contact stress fields on the initiation life, if the calculation is based only on highly stressed points on the surface. It is shown, however, that satisfactory results can be achieved if high values of the fatigue parameters are sustained over a critical volume.     

A weight function-critical plane approach for low-cycle fatigue under variable amplitude multiaxial loading

Low‐cycle fatigue data of type 304 stainless steel obtained under axial‐torsional loading of variable amplitudes are analyzed using four multiaxial fatigue parameters: SWT, KBM, FS and LKN. Rainflow cycle counting and Morrow's plastic work interaction rule are used to calculate fatigue damage. The performance of a fatigue model is dependent on the fatigue parameter, the critical plane and the damage accumulation rule employed in the model. The conservatism and non‐conservatism of predicted lives are examined for some combinations of these variables. A new critical plane called the weight function‐critical plane is introduced for variable amplitude loading. This approach is found to improve the KBM‐based life predictions.     

The Modified Wöhler Curve Method applied along with the Theory of Critical Distances to estimate finite life of notched components subjected to complex multiaxial loading paths

This paper is concerned with the use of the Modified Wöhler Curve Method (MWCM) applied in conjunction with the Theory of Critical Distances (TCD) to estimate fatigue lifetime of mechanical components subjected to multiaxial cyclic loading and experiencing stress concentration phenomena. In more detail, our engineering approach takes as its starting point the idea that accurate estimates can be obtained by simply assuming that the value of the critical length, L_M, to be used to evaluate fatigue damage in the medium–cycle multiaxial fatigue regime is a function of the number of cycles to failure, N_f. In other words, the MWCM, which is a bi‐parametrical critical plane approach, is suggested here to be applied by directly post‐processing the linear‐elastic stress state damaging a material point whose distance from the notch tip increases as N_f decreases. According to the main feature of the TCD, the above L_M versus N_f relationship is assumed to be a material property to be determined experimentally: such an hypothesis results in a great simplification of the fatigue assessment problem because, for a given material, the same critical length can be used to estimate fatigue damage independent of the considered geometrical feature. The accuracy of the devised approach was checked by analysing about 150 experimental results we generated by testing V‐notched cylindrical samples made of a commercial cold‐rolled low‐carbon steel. The above specimens were tested under in‐phase and out‐of‐phase combined tension and torsion, considering the damaging effect of superimposed static stresses as well. Moreover, in order to better check its accuracy in assessing notched components subjected to complex loading paths, our method was also applied to several data sets taken from the literature. This extensive validation exercise allowed us to prove that the MWCM applied along with the TCD is successful in estimating medium‐cycle multiaxial fatigue damage (N_f values in the range 10⁴–10⁶), resulting in predictions falling within the widest scatter band between the two used to calibrate the method itself. Such a high accuracy level is very promising, especially in light of the fact that the proposed approach predicts multiaxial fatigue lifetime by post‐processing the linear elastic stress fields in the fatigue process zone: this makes our method suitable for being used to assess real components by performing the stress analysis through simple linear‐elastic FE models.     

Fatigue life prediction of vulcanized natural rubber under proportional and non-proportional loading

To investigate the multiaxial fatigue properties of vulcanized natural rubber (NR), a series of tests including both proportional and non-proportional loading paths on small specimens were performed. The existing fatigue life prediction approaches are evaluated with life data obtained in the tests. It is shown that the equivalent strain approach presents a good prediction of the fatigue life although it has a certain shortcoming. Compared with the strain energy density (SED) model, the cracking energy density (CED) model represents the portion of SED that is available to be released by virtue of crack growth on a given material plane, so it gives better results in the life prediction. Some of the approaches based on critical plane which are widely used for metal fatigue are also tested in this paper, and the results show that the Chen-Xu-Huang (CXH) model gives a better prediction, compared with the Smith-Watson-Topper (SWT) and Wang–Brown (WB) model. A modified Fatemi–Socie's model has also been introduced, and the results show that the modified model can be used to predict the fatigue life of rubber material well.     

Critical plane approach for the assessment of the fatigue behaviour of welded aluminium under multiaxial loading

ABSTRACT Multiaxial stress states occur in many welded constructions like chemical plants, railway carriages and frames of trucks. Those stresses can have constant and changing principal stress directions, depending on the loading mode. Latest research results on welded steel joints show a loss of fatigue life for changing principal stress directions simulated by out‐of‐phase bending and torsion compared to constant directions given by in‐phase loading. However, aluminium welds reveal no influence of changing principal directions on fatigue life compared to multiaxial loading with constant principal stress directions. This behaviour is not predictable by any conventional hypothesis. A hypothesis on the basis of local normal and shear stresses in the critical plane has been developed and applied to aluminium weldings.     

Fatigue life estimation under random loading using the energy criterion

A procedure for estimating the useful life of a component for a given (admissable) probability of fatigue fracture origination under random loading is presented. The method uses material constants obtained from the S/N and cyclic stress/strain curves, standard deviation and probability density distribution of the loading process and a macroblock of harmonic cycles obtained by applying the rainflow cycle counting method to the random loading process. Theoretical and experimental lives are found to exhibit good agreement.     

A novel engineering method based on the critical plane concept to estimate the lifetime of weldments subjected to variable amplitude multiaxial fatigue loading

This paper summarizes an attempt at proposing a new engineering method suitable for estimating the fatigue lifetime of steel‐ and aluminium‐welded connections subjected to variable amplitude multiaxial fatigue loading. In particular, the proposed approach is based on the use of the so‐called Modified Wöhler Curve Method (MWCM), i.e. a bi‐parametrical critical plane approach, whose accuracy has been checked so far solely in addressing the constant amplitude multiaxial fatigue problem. In order to extend the use of our criterion to variable amplitude situations, the critical plane is suggested here as being determined by taking full advantage of the maximum variance concept, that is, such a plane is assumed to be the one containing the direction along which the variance of the resolved shear stress reaches its maximum value. The main advantage of such a strategy is that the cycle counting can directly be performed by considering the shear stress resolved along the maximum variance direction: by so doing, the problem is greatly simplified, allowing those well‐established cycle counting methods specifically devised to address the uniaxial variable amplitude problem to be extended to those situations involving multiaxial fatigue loading. The validity of the proposed methodology was checked by using two different datasets taken from the literature and generated by testing both steel and aluminium tube‐to‐plate welded connections subjected to in‐phase and 90° out‐of‐phase variable amplitude bending and torsion. This new fatigue life assessment technique was seen to be highly accurate allowing the estimates to fall within the calibration scatter bands not only when the constants in the governing equations were calculated by using the experimental uniaxial and torsional fully reversed fatigue curves, but also when they were determined by using the reference curves supplied, for the investigated geometry, by the available standard codes. These results seem to strongly support the idea that, thanks to its peculiar features, our method can be considered as an effective engineering approach capable of performing multiaxial fatigue assessment under variable amplitude loading which fully complies with the recommendations of the available standard codes.     

Criteria of multiaxial random fatigue based on stress,strain and energy parameters of damage in the critical plane

In this paper generalized criteria of multiaxial random fatigue based on stress, strain and strain energy density parameters in the critical plane have been discussed. The proposed criteria reduce multiaxial state of stress to the equivalent uniaxial tension–compression or alternating bending. Relations between the coefficients occurring in the considered criteria have been derived. Thus, it is possible to take into account fatigue properties of materials under simple loading states during determination of the multiaxial fatigue life. Presented models have successfully correlated fatigue lives of cast iron GGG40 and steel 18G2A specimens under constant amplitude in‐phase and out‐of‐phase loadings including different frequencies.     

A method for low-cycle fatigue life assessment of metallic materials under multiaxial loading

A new method of fatigue life assessment under multiaxial low-cycle regular and irregular loading is proposed, which is based on the modified Pisarenko-Lebedev criterion, the linear damage accumulation hypothesis, and the nonlinear Manson approach. The results of low-cycle fatigue tests of titanium alloy VT9 under irregular proportional and non-proportional biaxial loading are given. The tests were carried out at three Mises strain levels (0.6, 0.8, and 1.0%) with various combinations of proportional and non-proportional strain paths. All the tests were carried out at room temperature. The proposed method turned out to be effective and to allow for such factors as strain state type, strain path type and loading irregularity. __________ Translated from Problemy Prochnosti, No. 1, pp. 56–59, January–February, 2008.     

A hybrid frequency–time domain method for predicting multiaxial fatigue life of 7075‐T6 aluminium alloy under random loading

A hybrid frequency–time domain method for predicting multiaxial fatigue life under random loading is developed on the basis of combination of the frequency domain and time domain analysis. The critical damage point of the structure is determined by the frequency domain equivalent stress method. Then, the fatigue life prediction is made in time domain by generating random load‐time histories from the power spectral density of the critical point. The method is validated with the random vibration fatigue test of 7075‐T6 aluminium alloy. It has been shown that the results of fatigue life calculated by hybrid method are well correlated with the experiment.