Multiaxial creep–fatigue life prediction for cruciform specimen

This paper describes the high temperature multiaxial creep–fatigue life prediction for type 304 stainless steel. Finite element analyses were performed for determining the stress–strain state in the gage part of a cruciform specimen subjected to creep–fatigue loading under four strain waves at three principal strain ratios. Creep–fatigue lives of cruciform specimens were discussed in relation to the principal stress amplitude calculated by finite element analysis. Creep–fatigue damage was evaluated by linear damage rule and the suitability of three low cycle fatigue and three creep damage parameters was discussed.     

基于应力概率密度和功率谱密度法的随机声疲劳寿命预估方法研究

针对航空发动机燃烧室火焰筒结构的声疲劳问题,研究了一种用于随机载荷下结构疲劳寿命预估的有效方法。首先,对薄壁结构在随机载荷作用下的Von Mises应力过程的概率分布作了研究,给出了应力峰值概率密度函数的表达式。基于Miner线性理论,提出了基于应力概率密度和功率谱密度法的随机声疲劳寿命预估方法,并建立了疲劳寿命预估模型。以某型航空发动机燃烧室火焰筒结构为例,在采用耦合的有限元和边界元方法计算出随机声疲劳应力基础上,应用所建立的模型进行了疲劳寿命估算,并对计算结果进行了宽带修正。结果表明,该方法对航空薄壁结构随机疲劳寿命分析具有实用性。     

An energy‐based critical fatigue life prediction method for AL6061‐T6

An energy‐based critical fatigue life prediction method is developed and analysed. The original energy‐based fatigue life prediction theory states that the number of cycles to failure is estimated by dividing the total energy accumulated during a monotonic fracture by the strain energy per cycle. Because the accuracy of this concept is heavily dependent on the cyclic behaviour of the material, a precise understanding of the strain energy behaviour throughout each failure process is necessary. Examination of the stress and strain during fatigue tests shows that the cyclic strain energy behaviour is not perfectly stable as initially presumed. It was discovered that fatigue hysteresis energy always accumulates to the same amount of energy by the end of the stable energy region, which has led to a new ‘critical energy’ material property. Characterization of strain energy throughout the fatigue process has thus improved the understanding of an energy‐based fatigue life prediction method.     

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.     

State‐of‐the‐art review on the local strain energy density concept and its relation to the J‐integral and peak stress method

The local average strain energy density (SED) approach has been proposed and elaborated by Lazzarin for strength assessments in respect of brittle fracture and high‐cycle fatigue. Pointed and rounded (blunt) V‐notches subjected to tensile loading (mode 1) are primarily considered. The method is systematically extended to multiaxial conditions (mode 3, mixed modes 1 and 2). The application to brittle fracture is documented for PMMA flat bar specimens with pointed or rounded V‐notches inclusive of U‐notches. Results for other brittle materials (ceramics, PVC, duraluminum and graphite) are also recorded. The application to high‐cycle fatigue comprises fillet‐welded joints, weld‐like shaped and V‐notched base material specimens as well as round bar specimens with a V‐notch. The relation of the local SED concept to comparable other concepts is investigated, among them the Kitagawa, Taylor and Atzori–Lazzarin diagrams, the Neuber concept of fictitious notch rounding applied to welded joints and also the J‐integral approach. Alternative details of the local SED concept such as a semicircular control volume, microrounded notches and slit‐parallel loading are also mentioned. Coarse FE meshes at pointed or rounded notch tips are proven to be acceptable for accurate local SED evaluations. The peak stress method proposed by Meneghetti, which is based on a notch stress intensity factor consideration combined with a globally even coarse FE mesh and is used for the assessment of the fatigue strength of welded joints, is also presented.     

Fatigue life prediction under conditions where cyclic creep–fatigue interaction occurs

A stress-based model is proposed for correlating data and predicting fatigue life under conditions where cyclic creep–fatigue interaction occurs. This model is an extension of the Basquin’s stress–life relation and considers that both the fatigue strength coefficient and fatigue strength exponent b are sensitive to mean stress, both decreasing as an exponential function of the ratio of mean stress-to-stress amplitude. By combining the respective mean-stress functions with the Basquin relation, an equivalent stress–equivalent life relation is derived which is very similar to the original Basquin equation. Thus, the Basquin equation is a particular case of the present model for the case where mean stress is zero. The model depends on a single parameter λ, known as the mean stress sensitivity factor to cyclic loading, and depends on material and probably on test conditions as well. The mean stress sensitivity factor may be determined from experimental data at fixed ratio of mean stress-to-stress amplitude, other than zero, or by trial-and-error method to fit experimental mean-stress data onto the S–N curve due to zero mean stress. The model is tested on published creep–fatigue data of copper, steels and β-Ti-alloy and agreement is found to be very good.     

An assessment of three creep–fatigue life prediction methods for nickel‐based superalloy GH4049

High‐temperature low‐cycle fatigue tests with and without a 10‐s strain hold period in a cycle were performed on a nickel base superalloy GH4049 under a fully reversed axial total strain control mode. Three creep–fatigue life prediction methods are chosen to analyse the experimental data. These methods are the linear damage summation method (LDS), the strain range partitioning method (SRP) and the strain energy partitioning method (SEP). Their ability to predict creep‐fatigue lives of GH4049 at 700, 800 and 850 °C has been evaluated. It is found that the SEP method shows an advantage over the SRP method for all the tests under consideration. At 850 °C, the LDS and SEP methods give a more satisfactory prediction for creep–fatigue lives. At the temperatures of 700 and 800 °C, the SRP and SEP methods can correlate the life data better than the LDS method. In addition, the differences in predictive ability of these methods have also been analysed. The scanning electron microscopy (SEM) examination of fracture surfaces reveals that under creep–fatigue test conditions crack initiation mode is transgranular, while crack propagation mode is either intergranular plus transgranular or entirely intergranular, dependent on test temperature.     

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.     

用应变能密度法分析纤维金属层板的微动疲劳特性

为研究纤维金属层板的微动疲劳特性,首先,基于三维坐标系下的临界平面法求解了纤维金属层板铝层临界平面上的应力和应变分量,并进一步求解了Smith-Watson-Topper （SWT）和I型Nita-Ogatta-Kuwabara （NOK）应变能密度参数;然后,建立了应变能密度参数-微动疲劳寿命关系式,并通过实验数据得到了寿命预测公式中的待定参数;最后,采用I型NOK应变能密度准则分析了铝层厚度、纤维层厚度、各层相对厚度和桥足圆角半径等对微动疲劳损伤位置和寿命的影响,并为纤维金属层板抗微动疲劳设计提出了一些合理化建议。结果表明:增加铝层厚度可以延长微动疲劳寿命,但增加纤维层厚度和桥足圆角半径不会改善微动疲劳特性。提出的方法可为分析纤维金属层板铆接和螺栓连接中的微动疲劳问题提供理论依据。      

A critical plane‐energy model for multiaxial fatigue life prediction

A new critical plane‐energy model is proposed in this paper for multiaxial fatigue life prediction of metals. A brief review of existing methods, especially on the critical plane‐based and energy‐based methods, is given first. Special focus is on the Liu–Mahadevan critical plane approach, which has been shown to work for both brittle and ductile metals. One potential drawback of the Liu–Mahadevan model is that it needs an empirical calibration parameter for non‐proportional multiaxial loadings because only the strain terms are used and the out‐of‐phase hardening cannot be explicitly considered. An energy‐based model using the Liu–Mahadevan concept is proposed with the help of the Mróz–Garud plasticity model. Thus, the empirical calibration for non‐proportional loading is not needed because the out‐of‐phase hardening is naturally included in the stress calculation. The model predictions are compared with experimental data from open literature, and the proposed model is shown to work for both proportional and non‐proportional multiaxial loadings without the empirical calibration.     

Improvement of life prediction in AISI H11 tool steel by integration of thermo-mechanical fatigue and creep damage models

In hot forging operations, the die surfaces and the nearest surface layers of the die undergo mechanical and thermal cycles which significantly influence their service life. The real thermal and mechanical cycles have been previously investigated in forging plants by measurements and numerical simulation, and a reasonable variation window of process parameters has been determined. A new simulative test applied to AISI H11 hot working die steel has been used to generate failure data in conditions similar to those of the forging dies, but under a more controlled and economical method. Fracture surfaces of specimens for different tests observed by scanning electron microscopy (SEM) indicate that both thermo-mechanical fatigue (TMF) and creep phenomena can be considered to be main damage mechanisms and their contribution to the failure differs as testing conditions vary. As a result of the experiments, the failure is affected by both thermo-mechanical cycle and resting time at high temperature. Therefore, the authors developed a new lifetime prediction model obtained by combining the damage evolution laws, at each cycle, for pure creep and pure TMF. This combination was based on the linear accumulation rule. The damage evolution law for pure creep is obtained by modifying Rabotnov's law in order to suit the case of actual hot forging cycles, where temperature and stress vary widely. The damage evolution law for pure TMF is based on a generalization of the Wöhler–Miner law. This law is modified in order to take into account the presence of thermal cycle and thermal gradient. Comparison between the experimental cycles to failure and the predicted ones was performed using tests excluded in the determination of the coefficients. The conclusion was that the accuracy of prediction appears to be quite good and that the linear accumulation and interaction of TMF and creep is confirmed.     

A fatigue driving energy approach to high‐cycle fatigue life estimation under variable amplitude loading

In this paper, a concept of fatigue driving energy is formulated to describe the process of fatigue failure. The parameter is taken as a combination of the fatigue driving stress and strain energy density. By assessing the change of this parameter, a new non‐linear damage model is proposed for residual life estimation within high‐cycle fatigue regime under variable amplitude loading. In order to consider the effects of loading histories on damage accumulation under such condition, the load interaction effects are incorporated into the new model, and a modified version is thus developed. Life predictions by these two models and Miner rule are compared using experimental data from literature. The results show that the proposed model gives lower deviations than the Miner rule, while the modified model shows better prediction performances than the others. Moreover, the proposed model and its modifications are ease of implementation with the use of S–N curve.     

Damage evolution with growing cyclic creep and life prediction of MDYB‐3 PMMA

The influence of cyclic creep accumulation rate on the damage evolution of MDYB‐3 polymethyl methacrylate (PMMA) was experimentally investigated. Fatigue tests were carried out at four stress levels by stress control mode. The steady cyclic creep accumulation stage was observed occupying a substantial proportion of all specimens fatigue processes. Cyclic creep strain growth speed and relaxed modulus degradation rate were deduced as two important indicators for describing the damage evolution characteristics. Linear evolution relations of cyclic creep strain and modulus degradation with cycle times were retrieved from different terms of hysteresis loops. A preliminary model was proposed to be able to estimate the damage extent at different cyclic stress levels. The life predictions by the proposed model were compared with the experiment results and the classical power S–N model, which were demonstrated as a good estimation for the fatigue life. It is feasible to make durability evaluations by the characteristics of steady cyclic creep for multiaxis directed PMMA material.     

Evaluating a strain energy fatigue method using cyclic plasticity models

For the development of constitutive equations that describe the behaviour of materials under cyclic plastic strains, different kinds of formulations can be adopted. Recently, an energy‐based fatigue damage parameter has been developed to present energy‐fatigue life curves using a calculation of the total strain energy. In this study, the damage criterion is examined by calculation of the plastic strain energy from stress–strain hysteresis loops in the cyclic plasticity models under condition of multi‐axial fatigue. These cyclic plasticity models are the Garud multi‐surface model and the Chaboche nonlinear kinematic hardening model. The models are briefly explained and the general features of their computational procedure are presented. Then, the hysteresis loops of these models will be obtained and the fatigue lives are predicted and compared to experimental data by the ratio of predicted life to experimental life. Consequently, a weighting factor on shear plastic work is presented to decrease the life factors.     

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 prediction for butt‐welded joints considering weld‐induced residual stresses and initial damage,relaxation of residual stress,and elasto‐plastic fatigue damage

Fatigue damage of butt‐welded joints is investigated by a damage mechanics method. First, the weld‐induced residual stresses are determined by using a sequentially coupled thermo‐mechanical finite element analysis. The plastic damage of material is then calculated with the use of Lemaitre's plastic damage model. Second, during the subsequent fatigue damage analysis, the residual stresses are superimposed on the fatigue loading, and the weld‐induced plastic damage is considered as the initial damage via an elasto‐plastic fatigue damage model. Finally, the fatigue damage evolution, the relaxation of residual stress, and the fatigue lives of the joints are evaluated using a numerical implementation. The predicted results agree well with the experimental data.     

A modification of Smith–Watson–Topper damage parameter for fatigue life prediction under non‐proportional loading

In this paper, the shortcomings of the Smith–Watson–Topper (SWT) damage parameter are analysed on the basis of the critical plane concept. It is found that the SWT model usually overestimates the fatigue lives of materials since it only takes into account the fatigue damage caused by the tensile components. To solve this problem, Chen et al. (CXH) modified the SWT model through considering the shear components. However, there are at least two problems present in CXH model: (1) the mean stress is not considered and (2) the different influence of the normal and shear components on fatigue life is not included. Besides, experimental validations show that the modification by Chen et al. usually leads to conservative fatigue life predictions during non‐proportional loading. In order to overcome the shortcomings of SWT and CXH models, a damage parameter as the effective strain energy density (ESED) is proposed. Experimental validations by using eight kinds of materials show that the ESED model can give satisfactory fatigue life predictions under the non‐proportional loading.     

Multiaxial fatigue of V‐notched steel specimens: a non‐conventional application of the local energy method

The paper deals with the multi‐axial fatigue strength of notched specimens made of 39NiCrMo3 hardened and tempered steel. Circumferentially V‐notched specimens were subjected to combined tension and torsion loading, both in‐phase and out‐of‐phase, under two nominal load ratios, R=?1 and R= 0, also taking into account the influence of the biaxiality ratio, λ=τ_a/σ_a. The notch geometry of all axi‐symmetric specimens was a notch tip radius of 0.1 mm, a notch depth of 4 mm, an included V‐notch angle of 90° and a net section diameter of 12 mm. The results from multi‐axial tests are discussed together with those obtained under pure tension and pure torsion loading on plain and notched specimens. Furthermore the fracture surfaces are examined and the size of non‐propagating cracks measured from some run‐out specimens at 5 million cycles. Finally, all results are presented in terms of the local strain energy density averaged in a given control volume close to the V‐notch tip. The control volume is found to be dependent on the loading mode.     

Time‐dependent multiaxial fatigue and life prediction for nickel‐based GH4169 alloy

The fatigue behaviour of nickel‐based GH4169 alloy was studied under multiaxial loading at 650 °C. During the middle and late stages of the fatigue life at 650 °C, the axial and shear maximum stresses continue to decrease and plastic strains continue to increase, while at 360 °C different phenomena are observed. The intergranular cracks and certain quantities oxygen were observed in the fracture surfaces. The damage of creep and oxidation are related to temperature and strain range. The life prediction results with a time‐dependent fatigue damage model show the time‐related factors have a certain influence on the fatigue damage.     

Sharp V‐notches in viscoplastic solids: Strain energy rate density rule and fracture toughness

Different from Neuber's rule or Glinka's energy method which are always adopted to characterize the notch tip field under elastoplastic condition, in this paper, the strain energy rate density (SERD) rule is used for viscoplastic materials. In particular, based on the definition of generalized notch stress intensity factor (G‐NSIF) for sharp V‐notch in viscoplastic solids, the concept of SERD for sharp V‐notch in viscoplastic solids is presented. Subsequently, by taking as a starting point the SERD, the averaged strain energy density (SED) for sharp V‐notch in viscoplastic solids is derived with integration of time. The fracture toughness relation between sharp V‐notch specimens and crack specimen in viscoplastic materials is given based on the transformation of SERD. A numerical approach is presented to compute the SERD and SED based on finite element method. Some crucial comments on the G‐NSIF have been discussed. Some typical solutions for SERD and SED for sharp V‐notched specimens are investigated.