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.     

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 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.     

Multiaxial low‐cycle fatigue life evaluation under different non‐proportional loading paths

This paper presents analytical and experimental investigations for fatigue lives of structures under uniaxial, torsional, multiaxial proportional, and non‐proportional loading conditions. It is known that the rotation of principal stress/strain axes and material additional hardening due to non‐proportionality of cycle loading are the 2 main causes resulting in shorter fatigue lives compared with those under proportional loading. This paper treats these 2 causes as independent factors influencing multiaxial fatigue damage and proposes a new non‐proportional influencing parameter to consider their combined effects on the fatigue lives of structures. A critical plane model for multiaxial fatigue lives prediction is also proposed by using the proposed non‐proportional influencing factor to modify the Fatemi‐Socie model. The comparison between experiment results and theoretical evaluation shows that the proposed model can effectively predict the fatigue life due to multiaxial non‐proportional loading.     

A modification of Morrow and Smith–Watson–Topper mean stress correction models

A modification of the Morrow and the Smith, Watson and Topper (SWT) mean stress correction models is proposed to account for the mean stress effect on fatigue life. The capability and accuracy of the proposed model are compared to those of the original Morrow and the SWT model using published mean stress fatigue test data. The proposed mean stress correction model was found to be superior to both the SWT and the Morrow model in the case of the Incoloy 901 superalloy and the ASTM A723 steel. On the other hand both the proposed and the original SWT model provided equally good correlation with experimental data in the case of 7075‐T561 aluminium alloy and 1045 HRC 55 steel. The Morrow model was found to give the least accurate predictions for all four materials analysed.     

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).     

Use of an energy‐based/critical plane model to assess fatigue life under low‐cycle multiaxial cycles

For engineering components subjected to multiaxial loading, fatigue life prediction is crucial for guaranteeing their structural security and economic feasibility. In this respect, energy‐based models, integrating the stress and strain components, are widely used because of their availability in fatigue prediction. Through employing the plastic strain energy concept and critical plane approach, a new energy‐based model is proposed in this paper to evaluate the low‐cycle fatigue life, in which the critical plane is defined as the maximum damage plane. In the proposed model, a newly defined NP factor κ^*  is used to quantify the nonproportional (NP) effect so that the damage parameter can be conveniently calculated. Moreover, a simple estimation method of weight coefficient is developed, which can reflect different contributions of shear and normal plastic strain energy on total fatigue damage. Experimental data of 10 kinds of materials are employed to assess the effectiveness of this model as well as three other energy‐based models.     

Online multiaxial fatigue damage evaluation method by real‐time cycle counting and energy‐based critical plane criterion

To realize online multiaxial fatigue damage assessment for the mechanical components in service, an online multiaxial cycle counting method is proposed coupled with the segment processing technique and Wang‐Brow's relative equivalent strain concept. Meanwhile, considering all the stress and strain components, which contribute to the fatigue damage on the critical plane, a multiaxial fatigue damage model without any weight coefficients is also proposed in an equivalent form of shear strain energy. Then, an online fatigue damage evaluation method for multiaxial random loading is developed by combining with the proposed damage model and online cycle counting method. The experimental results showed that the proposed online cycle counting method can be successfully applied to the calculation of multiaxial fatigue damage under random loading. Moreover, the proposed online multiaxial fatigue damage evaluation method can provide satisfactory predictions.     

Analytical and experimental studies on fatigue crack path under complex multi-axial loading

In real engineering components and structures, many accidental failures are due to unexpected or additional loadings, such as additional bending or torsion, etc. Fractographical analyses of the failure surface and the crack orientation are helpful for identifying the effects of the non‐proportional multi‐axial loading. There are many factors that influence fatigue crack paths. This paper studies the effects of multi‐axial loading path on the crack path. Two kinds of materials were studied and compared in this paper: AISI 303 stainless steel and 42CrMo4 steel. Experiments were conducted in a biaxial testing machine INSTRON 8800. Six different biaxial loading paths were selected and applied in the tests to observe the effects of multi‐axial loading paths on the additional hardening, fatigue life and the crack propagation orientation. Fractographic analyses of the plane orientations of crack initiation and propagation were carried out by optical microscope and SEM approaches. It was shown that the two materials studied had different crack orientations under the same loading path, due to their different cyclic plasticity behaviour and different sensitivity to non‐proportional loading. Theoretical predictions of the damage plane were made using the critical plane approaches such as the Brown–Miller, the Findley, the Wang–Brown, the Fatemi–Socie, the Smith–Watson–Topper and the Liu's criteria. Comparisons of the predicted orientation of the damage plane with the experimental observations show that the critical plane models give satisfactory predictions for the orientations of early crack growth of the 42CrMo4 steel, but less accurate predictions were obtained for the AISI 303 stainless steel. This observation appears to show that the applicability of the fatigue models is dependent on the material type and multi‐axial microstructure characteristics.     

Multiaxial fatigue damage parameter and life prediction for medium-carbon steel based on the critical plane approach

The tension–torsion fatigue characteristics were investigated under proportional and non-proportional loading in this paper. The fatigue cracks on the surface of multiaxial fatigue specimens were observed and analyzed by a scan electron microscope. On the basis of the investigation on the Kindil–Brown–Miller and Fatemi–Socie’s critical plane approaches, a shear strain based multiaxial fatigue damage parameter was proposed by von Mises criterion based on combining the maximum shear strain and the normal strain excursion between adjacent turning points of the maximum shear strain on the critical plane. The proposed multiaxial fatigue damage parameter does not include the weight constants. According to the proposed multiaxial fatigue damage parameter, the multiaxial fatigue life prediction model was established with the Coffin–Manson equation, which is used to predict the multiaxial fatigue life of medium-carbon steel. The results showed that the proposed multiaxial fatigue damage parameter could be used under either multiaxial proportional or non-proportional loading.     

Biaxial fatigue for proportional and non‐proportional loading paths

In order to study the use of a local approach to predict crack‐initiation life on notches in mechanical components under multiaxial fatigue conditions, the study of the local cyclic elasto‐plastic behaviour and the selection of an appropriate multiaxial fatigue model are essential steps in fatigue‐life prediction. The evolution of stress–strain fields from the initial state to the stabilized state depends on the material type, loading amplitude and loading paths. A series of biaxial tension–compression tests with static or cyclic torsion were carried out on a biaxial servo‐hydraulic testing machine. Specimens were made of an alloy steel 42CrMo4 quenched and tempered. The shear stress relaxations of the cyclic tension–compression with a steady torsion angle were observed for various loading levels. Finite element analyses were used to simulate the cyclic behaviour and good agreement was found. Based on the local stabilized cyclic elastic–plastic stress–strain responses, the strain‐based multiaxial fatigue damage parameters were applied and correlated with the experimentally obtained lives. As a comparison, a stress‐invariant‐based approach with the minimum circumscribed ellipse (MCE) approach for evaluating the effective shear stress amplitude was also applied for fatigue life prediction. The comparison showed that both the equivalent strain range and the stress‐invariant parameter with non‐proportional factors correlated well with the experimental results obtained in this study.     

Multiaxial notch fatigue life prediction based on pseudo stress correction and finite element analysis under variable amplitude loading

A new computational methodology is proposed for fatigue life prediction of notched components subjected to variable amplitude multiaxial loading. In the proposed methodology, an estimation method of non‐proportionality factor (F) proposed by authors in the case of constant amplitude multiaxial loading is extended and applied to variable amplitude multiaxial loading by using Wang‐Brown's reversal counting approach. The pseudo stress correction method integrated with linear elastic finite element analysis is utilized to calculate the local elastic‐plastic stress and strain responses at the notch root. For whole local strain history, the plane with weight‐averaged maximum shear strain range is defined as the critical plane in this study. Based on the defined critical plane, a multiaxial fatigue damage model combined with Miner's linear cumulative damage law is used to predict fatigue life. The experimentally obtained fatigue data for 7050‐T7451 aluminium alloy notched shaft specimens under constant and variable amplitude multiaxial loadings are used to verify the proposed methodology and equivalent strain‐based methodology. The results show that the proposed methodology is superior to equivalent strain‐based methodology.     

Deterministic Processing of Complex Multiaxial Fatigue Load Data on a Tubular Specimen with Hole

A study of the use of deterministic fatigue life prediction methods for a set of multiaxial experimental data on broad‐band random loading applied to a tubular specimen with a hole is presented. There is a discussion of the applicability of stress‐based predictions and strain‐based predictions based on the linear cumulative rule under current conditions. The only feasible criteria finally chosen for the application are strain‐based methods for analysing the fatigue life until fatigue crack initiation. Several methods differing in the damage parameter and application of the mean stress effect (MSE) are evaluated. The MSE is optimised so that a comparison of the predicted and experimental data have the least scatter and similar mean values. The results are presented, and the most promising method (by Erdogan and Roberts) has been selected. The positive properties of Walker mean stress correction and the failure of SWT and Landgraf methods are commented on.     

Strain-based multiaxial fatigue damage modelling

A new multiaxial fatigue damage model named characteristic plane approach is proposed in this paper, in which the strain components are used to correlate with the fatigue damage. The characteristic plane is defined as a material plane on which the complex three‐dimensional (3D) fatigue problem can be approximated using the plane strain components. Compared with most available critical plane‐based models for multiaxial fatigue problem, the physical basis of the characteristic plane does not rely on the observations of the fatigue crack in the proposed model. The cracking information is not required for multiaxial fatigue analysis, and the proposed model can automatically adapt for different failure modes, such as shear or tensile‐dominated failure. Mean stress effect is also included in the proposed model by a correction factor. The life predictions of the proposed fatigue damage model under constant amplitude loading are compared with a wide range of metal fatigue results in the literature.     

Corrosion fatigue behaviour of 304 stainless steel under proportional and non‐proportional multiaxial loading condition

Corrosion fatigue and electrochemical tests under proportional loading and non‐proportional loading were conducted on 304 stainless steel in 0.63 mol L^?1 NaCl solution at room temperature. Two biaxial loading paths were applied to study the effect of proportional loading and non‐proportional loading on corrosion fatigue behaviour. Surface and fractographic observations of multiaxial corrosion fatigue specimens were carried out by scanning electron microscopy. It was shown that proportional loading had a more significant effect on the occurrence of local corrosion compared with non‐proportional loading because the continuous rotation of the principal stress plane under non‐proportional loading inhibits the pit formation.     

Comparative analysis of three thermal fatigue experiments

This paper presents an analysis of the ability of different criteria to predict fatigue crack initiation under thermal loading. More precisely the predictions of the number of cycles to crack initiation are compared with experimental results obtained using five different fatigue criteria in three types of thermal fatigue tests (namely the FAT3D, JRC and SPLASH test campaigns). This analysis has revealed that:

• ? The conventional criteria based on equivalent strain variation substantially overestimate the lifespan of a structure subjected to thermal loading.
• ? A criterion making account for loading multiaxiality is required to estimate thermal fatigue life.

Three of the criteria studied give satisfactory results: the Zamrik criterion, the Park and Nelson criterion and a criterion taking hydrostatic pressure into consideration proposed by Amiable et al. The latter should be preferred for the accuracy of its results and the Zamrik criterion for its simplicity.     

An energy‐based damage parameter for the life prediction of AISI 304 stainless steel subjected to mean strain

Abstract

This study extends the plastic strain energy approach to predict the fatigue life of AISI 304 stainless steel. A modified energy parameter based on the stable plastic strain energy density under tension conditions is proposed to account for the mean strain and stress effects in a low cycle fatigue regime. The fatigue life curve based on the proposed energy parameter can be obtained directly by modifying the parameters in the fatigue life curve based on the stable plastic strain energy pertaining to fully reversed cyclic loading. Hence, the proposed damage parameter provides a convenient means of evaluating fatigue life on the mean strain or stress effect. The modified energy parameter can also be used to explain the combined effect of alternating and mean strain/stress on the fatigue life. In this study, the mean strain effects on the fatigue life of AISI 304 stainless steel are examined by performing fatigue tests at different mean strain levels. The experimental results indicate that the combination of an alternating strain and a mean strain strongly influences the fatigue life. Meanwhile, it is found that the change in fatigue life is sensitive to changes in the proposed damage parameter under the condition of a constant strain amplitude at various mean strain levels. A good agreement is observed between the experimental fatigue life and the fatigue life predicted by the proposed damage parameter. The damage parameter proposed by Smith et al. (1970) is also employed to quantify the mean strain effect. The results indicate that this parameter also provides a reasonable estimate of the fatigue life of AISI 304 stainless steel. However, a simple statistical analysis confirms that the proposed damage parameter provides a better prediction of the fatigue life of AISI 304 stainless steel than the SWT parameter.     

On the estimation of the material fatigue properties required to perform the multiaxial fatigue assessment

To accurately perform the fatigue assessment of engineering components subjected to in‐service multiaxial fatigue loading, the adopted design criterion must properly be calibrated, the used information usually being the fatigue strength under both pure uniaxial and pure torsional fatigue loading. Because of the complex fatigue response of metallic materials to multiaxial loading paths, the only reliable way to generate the necessary pieces of calibration information is by running appropriate experiments. Unfortunately, because of a lack of both time and resources, very often, structural engineers are requested to perform the multiaxial fatigue assessment by guessing the necessary fatigue properties. In this complex scenario, initially, the available empirical rules suitable for estimating fatigue strength under both pure axial and pure torsional fatigue loading are reviewed in detail. Subsequently, several experimental results taken from the literature and generated by testing metallic materials under a variety of proportional and non‐proportional multiaxial loading paths are used to investigate the way such empirical rules affect the accuracy in estimating fatigue strength, the damage extent being evaluated according to the modified Wöhler curve method. Such a systematic validation exercise allowed us to prove that under proportional loading (with both zero and non‐zero mean stresses), an adequate margin of safety can be reached even when the necessary calibration information is directly estimated from the material ultimate tensile strength. On the contrary, in the presence of non‐proportional loading, the use of the empirical rules reviewed in the present paper can result, under particular circumstances, in a non‐conservative fatigue design.     

FATIGUE OF A PARTICULATE REINFORCED ALUMINIUM METAL MATRIX COMPOSITE SUBJECTED TO AXIAL, TORSIONAL AND COMBINED AXIAL/TORSIONAL LOADING CONDITIONS

Abstract— The goals in this research were to analytically and experimentally investigate the fatigue behavior of a particulate reinforced metal matrix composite subjected to axial, torsional and combined axial/torsional loadings. A series of fully-reversed uniaxial, torsional and combined axial/torsional fatigue tests were performed on a 6061/Al₂O₃/20p-T6 metal matrix composite material. This research investigated the ability of the Fatemi-Kurath and the Smith-Watson-Topper (SWT) damage parameters to correlate the experimentally obtained fatigue life data and also to represent the fatigue life using uniaxial strain-life constants. The Fatemi-Kurath damage parameter correlated the experimental fatigue data from all loading cases better than the SWT damage parameter. Using uniaxial strain-life constants, both damage parameters predicted fairly reasonable fatigue life calculations for the intermediate fatigue lives (10³ to 10⁴ cycles to failure), while producing non-conservative results for the shorter fatigue lives (< 10³ cycles to failure).