Notch fatigue life prediction considering nonproportionality of local loading path under multiaxial cyclic loading

An innovative numerical methodology is presented for fatigue lifetime estimation of notched bodies experiencing multiaxial cyclic loadings. In the presented methodology, an evaluation approach of the local nonproportionality factor F for notched specimens, which defines F as the ratio of the pseudoshear strain range at 45° to the maximum shear plane and the maximum shear strain range, is proposed and discussed deeply. The proposed evaluation method is incorporated into the material cyclic stress‐strain equation for purpose of describing the nonproportional hardening behavior for some material. The comparison between multiaxial elastic‐plastic finite element analysis (FEA) and experimentally measured strains for S460N steel notched specimens shows that the proposed nonproportionality factor estimation method is effective. Subsequently, the notch stresses and strains calculated utilizing multiaxial elastic‐plastic FEA are used as input data to the critical plane‐based fatigue life prediction methodology. The prediction results are satisfactory for the 7050‐T7451 aluminum alloy and GH4169 superalloy notched specimens under multiaxial cyclic loading.     

Fatigue life assessment for metal alloys under nonproportional low-cycle loading

A procedure for nonproportional low-cycle fatigue life assessment is proposed for various metal alloys that differ in structure. It is based on the Pisarenko-Lebedev equivalent strain and a correcting function allowing for nonproportional loading effects such as additional hardening and life reduction in the case of nonproportional strain paths. The calculated results are compared to the experimental ones reported elsewhere for steels, titanium-, nickel-, and aluminum-based alloys. A good agreement between the results is observed for all the materials and strain paths studied. The accuracy of the calculations for nonproportional loading is found to be same as in the case of proportional loading. __________ Translated from Problemy Prochnosti, No. 4, pp. 31–39, July–August, 2007.     

A simple energy‐based model for nonproportional low‐cycle multiaxial fatigue life prediction under constant‐amplitude loading

From the literature concerning the traditional nonproportional (NP) multiaxial cyclic fatigue prediction, special attentions are usually paid to multiaxial constitutive relations to quantify fatigue damage accumulation. As a result, estimation of NP hardening effect decided by the entire history path is always proposed, which is a challenging and complex task. To simplify the procedure of multiaxial fatigue life prediction of engineering components, in this paper, a novel effective energy parameter based on simple material properties is proposed. The parameter combines uniaxial cyclic plastic work and NP hardening effects. The fatigue life has been assessed based on traditional multiaxial fatigue criterion and the proposed parameter, which has been validated by experimental results of 316 L stainless steel under different low‐cycle loading paths.     

Fatigue life prediction for metals using an improved strain energy density model

Abstract

An improved strain energy density model is proposed on the basis of critical plane concept to better predict the multiaxial fatigue life of metals, especially during nonproportional loadings. This approach is based on the normal and shear strain energy densities on maximum principal strain range plane. Procedures used to determine the normal and shear strain energy densities are also presented. Experimental data taken from the literature are used to validate the capabilities of the improved model, including 4 different metals and 24 different loading paths. The results show that the proposed model gives good predictions for most of these materials and loading paths.     

A plasticity model for calculating stress–strain sequences under multiaxial nonproportional cyclic loading

There is increasing demand for analytical methods that estimate the fatigue life of engineering components and structures with a high degree of accuracy. The fatigue life is determined by the stress–strain sequences at the critical locations. Therefore, these sequences have be calculated with sufficient accuracy for arbitrary nonproportional cyclic loading. Based on the experience with a variety of material models following macroscale continuum mechanics approaches, an improved set of constitutive equations is proposed. The stress–strain behaviour of a commercial structural steel has been investigated experimentally. Firstly, the results of this experimental study serve to identify the material parameters comprised in the model. Secondly, the predicted stress–strain paths are compared to their experimentally determined counterparts as well as to paths predicted by other models. The overall accuracy of the proposed model is quite satisfying, especially as far as calculated amplitudes are concerned.     

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.     

A critical plane-strain energy density criterion for multiaxial low-cycle fatigue life under non-proportional loading

A series of multiaxial low-cycle fatigue experiments was performed on 45 steel under non-proportional loading. The present evaluations of multiaxial low-cycle fatigue life were systematically analysed. A combined energy density and critical plane concept is proposed that considers different failure mechanisms for a shear-type failure and a tensile-type failure, and from which different damage parameters for the critical plane-strain energy density are proposed. For tensile-type failures in material 45 steel and shear-type failures in material 42CrMo steel, the new damage parameters permit a good prediction for multiaxial low-cycle fatigue failure under non-proportional loading. The currently used critical plane models are a special and simple form of the new model.     

Fatigue life prediction of a structural steel under service loading

Fatigue life prediction techniques for variable amplitude load histories are reviewed. The fatigue crack growth rate and crack closure responses of BS4360 50B steel are determined for a service load history experienced by a gas storage vessel. Crack propagation rates are found to be independent of specimen thickness. Crack growth is successfully predicted by linear summation using the Paris law; no significant improvement is achieved by incorporating crack closure into the analysis. The particular choice of cycle counting technique is also found to have an insignificant effect on the predicted fatigue life. The load-interaction model proposed by Willenborg et al correctly indicates the absence of retarded growth, whilst the Wheeler and Führing models erroneously predict retarded crack growth.     

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.     

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.     

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.     

Cumulative damage model based on equivalent fatigue under multiaxial thermomechanical random loading

A new creep–fatigue damage cumulative model is proposed under multiaxial thermomechanical random loading, in which the damage at high temperature can be divided into the pure fatigue damage and the equivalent fatigue damage from creep. During the damage accumulation process, the elementary percentage of the equivalent fatigue damage increment is proportional to that of the creep damage increment, and the creep damage is converted to the equivalent fatigue damage. Moreover, combined with a multiaxial cyclic counting method, a life prediction method is developed based on the proposed creep–fatigue damage cumulative model. In the developed life prediction method, the effects of nonproportional hardening on the fatigue and creep damages are considered, and the influence of mean stress on damage is also taken into account. The thermomechanical fatigue experimental data for thin‐walled tubular specimen of superalloy GH4169 under multiaxial constant amplitude and variable amplitude loadings were used to verify the proposed model. The results showed that the proposed method can obtain satisfactory life prediction results.     

Fatigue life assessment under a complex multiaxial load history: an approach based on damage mechanics

In order to assess the fatigue behaviour of structural components under a complex (cyclic or random) multiaxial stress history, methods based on damage mechanics concepts can be employed. In this paper, a model for fatigue damage evaluation in the case of an arbitrary multiaxial loading history is proposed by using an endurance function which allows us to determine the damage accumulation up to the final failure of the material. By introducing an evolution equation for the endurance function, the final collapse can be assumed to occur when the damage D is complete, that is when D reaches the unity. The parameters of this model, which adopts the stress invariants and the deviatoric stress invariants to quantify the damage phenomenon, are determined through a Genetic Algorithm once experimental data on the fatigue behaviour of the material being examined are known for some complex stress histories. With respect to traditional approaches to multiaxial fatigue assessment, the proposed model presents the following advantages: (1) the evaluation of a critical plane is not necessary; (2) no cycle counting algorithm to determine the fatigue life is required, because it considers the progressive damage process during the fatigue load history; (3) the model can be applied to any kind of stress history (uniaxial cyclic loading, multiaxial in‐phase or out‐of‐phase cyclic loading, uniaxial or multiaxial random loading).     

超声载荷下TC4钛合金的疲劳寿命分析

通过计算裂纹尖端应力强度因子及疲劳裂纹扩展速率da/d N,由C.Paris模型推导出安全寿命Nf,由Bathias公式计算"哑铃"状钛合金试样的裂纹扩展寿命。通过理论计算和有限元分析超声疲劳"哑铃"状试样,得出应力最大位置。利用有限元仿真和实验数据分析TC4钛合金疲劳寿命。在20 k Hz的超声疲劳试验中,试样的断口位置表明:TC4钛合金材料内部缺陷是试样萌生裂纹使断裂位置偏离最大应力处的主要原因。并得出疲劳裂纹萌生阶段寿命决定"哑铃"状试样的疲劳寿命。     

Validating generality of recently developed critical plane model for fatigue life assessments using multiaxial test database on seventeen different materials

The present studies are aimed at validation of a newly developed critical plane model with respect to large variety of engineering materials used for different applications. This newly developed model has been recently reported by present authors. To strengthen general applicability of this model, multiaxial test database consisting of a wide variety of multiaxial loading paths have been considered. The strain paths include pure axial, pure torsion, in‐phase axial‐torsion, out‐of‐phase axial‐torsion with phase shift angles varying from 30° to 180° having sine/trapezoidal/triangular strain waveforms, with/without mean axial/shear strains and asynchronous axial‐torsion strain paths of different frequency ratios etc. The materials covered in present study are mainly categorized as ferrous and nonferrous alloys. In ferrous alloy category, material grades from plain carbon steel (mild steel, 16MnR, SA333 Gr. 6, E235 and E355), low‐alloy steel (1Cr‐Mo‐V and S460 N) and austenitic stainless steel (SS304, SS316L and SS347) have been considered. In nonferrous alloy category, aluminium alloys (2024T3‐Al, 7075T651‐Al, and PA38‐T6‐Al), titanium (pure titanium and TC4 alloy), cobalt base super‐alloy (Haynes 188), and nickel alloy (Inconel‐718) have been considered. The predicted and test fatigue lives are found in good agreement for all these materials and complex multiaxial loading paths.     

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.     

Fatigue life analysis and predictions for NR and SBR under variable amplitude and multiaxial loading conditions

This paper investigates the effects of variable amplitude loading conditions on the fatigue lives of multiaxial rubber specimens. Two filled rubber materials were used and compared to investigate the effects of strain-crystallization on crack development NR, which strain crystallizes, and SBR, which does not. The applicability of Miner’s linear damage rule for predicting fatigue lives of variable amplitude tests in rubber and the use of both scalar and plane-specific equivalence parameters to characterize fatigue life results were also investigated. A fatigue life prediction approach that utilizes normal strain to find the critical plane and the cracking energy density on that plane to determine fatigue life is introduced and compared to other approaches. The effects of load sequence and temperature on fatigue life, as well as differences in fatigue lives using both stiffness and critical crack length failure criteria are discussed.     

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.     

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.