在多轴载荷下45钢的循环特性

通过多轴疲劳试验，研究了在多轴加载条件下45钢的循环特性变化规律，分析了非比例附加强化、多轴循环软化/硬化特性及疲劳寿命对加载路径参数的依赖性，结果表明，相位角主要影响非比例附加强化程度，幅值比主要影响多轴循环软化/硬化特性，二者都影响多轴疲劳寿命。     

Multiaxial notch fatigue life prediction based on the dominated loading control mode under variable amplitude loading

A new calculation approach is suggested to the fatigue life evaluation of notched specimens under multiaxial variable amplitude loading. Within this suggested approach, if the computed uniaxial fatigue damage by the pure torsional loading path is larger than that by the axial tension–compression loading path, a shear strain‐based multiaxial fatigue damage parameter is assigned to calculate multiaxial fatigue damage; otherwise, an axial strain‐based multiaxial fatigue damage parameter is assigned to calculate multiaxial fatigue damage. Furthermore, the presented method employs shear strain‐based and axial strain‐based multiaxial fatigue damage parameters in substitution of equivalent strain amplitude to consider the influence of nonproportional additional hardening. The experimental data of GH4169 superalloy and 7050‐T7451 aluminium alloy notched components are used to illustrate the presented multiaxial fatigue lifetime estimation approach for notched components, and the results reveal that estimations are accurate.     

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.     

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.     

Low cycle fatigue life of Ti–6Al–4V alloy under non-proportional loading

Multiaxial low cycle fatigue life of Ti–6Al–4V under non-proportional loading was studied. Strain-controlled multiaxial fatigue tests at room temperature were carried out using tubular specimens. The strain paths employed were push–pull loading, reversed torsion loading, and two kinds of 90° out-of-phase loadings. The former two loadings are proportional loading tests where the principal directions of stress and strain are fixed in the cycle. The latter two are non-proportional loading tests where there is a 90° phase difference between axial and shear loadings, and the principal directions are cyclically rotated continuously. Failure lives are reduced obviously by non-proportional loadings in comparison with those in proportional loading tests. This paper focuses on determining a suitable fatigue model for evaluating the failure lives of Ti–6Al–4V under multiaxial loading.     

Multiaxial fatigue of extruded ZK60 magnesium alloy

Multiaxial monotonic and cyclic behaviors of ZK60‐T5 magnesium extrusion are investigated. Strain‐controlled tests were performed at standard laboratory condition with fully reversed straining. Twinning‐detwinning deformation plays an important role in the cyclic axial behavior for tests that were performed under strain amplitudes higher than 0.4%. However, the hysteresis loop for the 0.4% was found symmetric and no sign of twinning‐detwinning deformation was observed. On the contrary, the cyclic shear behavior was found to be similar to conventional alloys and no significant asymmetric or twinning‐detwinning deformations were observed. The multiaxial fatigue tests suggest that multiaxiality and nonproportionality are not detrimental to fatigue life. Three multiaxial fatigue damage models were used: Smith‐Watson‐Topper, Fatemi‐Socie, and Jahed‐Varvani. While Fatemi‐Socie and Jahed‐Varvani models show comparable estimation, Smith‐Watson‐Topper overestimates shear and nonproportional lives.     

Fatigue life prediction method of face-centered cubic single-crystal metals under multiaxial nonproportional loading based on structural mechanical model

Based on the characteristics of the sliding surface, sliding direction, and fatigue damage mechanism of metal materials, the mechanical model of a body–bar–plate structure is proposed with consideration to the plastic damage mechanism. The elastoplastic constitutive equations and damage constitutive equations of the face-centered cubic (FCC) structure subjected to multiaxial cyclic loading were derived, and the damage evolution law of the body–bar–plate mechanical model was investigated. Then, the meso-damage evolution equation was established under multiaxial nonproportional loading. Subsequently, the relationship between the fatigue performance and microstructure under multiaxial nonproportional loading was investigated, and a damage mechanics–finite element method (FEM) with consideration to the damage evolution is proposed. The proposed model and method provide a new approach for predicting the fatigue life of metal materials.     

A survey on multiaxial fatigue damage parameters under non‐proportional loadings

In this paper, several multiaxial fatigue damage parameters taking into account nonproportional additional hardening are reviewed. According to the way nonproportional additional hardening is considered in the model, the damage parameters are classified into 2 categories: (1) equivalent damage parameters and (2) direct damage parameters. The equivalent damage parameters usually define a nonproportional coefficient to consider nonproportional additional cyclic hardening, and make a combination of this nonproportional coefficient with stress and/or strain quantities to calculate the equivalent damage parameters. In contrast, the direct damage parameters are directly estimated from the stress and strain quantities of interest. The accuracy of 4 multiaxial fatigue damage parameters in predicting fatigue lifetime is checked against about 150 groups of experimental data for 10 different metallic materials under multiaxial fatigue loading. The results revealed that both Itoh's model, one of equivalent damage parameters, and Susmel's model, which belong to direct damage parameters, could provide a better correlation with the experimental results than others assessed in this paper. So direct damage parameters are not better than the equivalent damage parameters in predicting fatigue lifetime.     

Energy-based time derivative damage accumulation model under uniaxial and multiaxial random loadings

A new fatigue life prediction method using the energy-based approach under uniaxial and multiaxial random loadings is proposed. The uniqueness of the proposed model is based on a time-derivative damage accumulation unlike classical cycle-based damage accumulation models. Thus, damage under arbitrary random loading can be directly obtained using time-domain integration without cycle counting. First, a brief review of existing models is given focusing on their applicability to uniaxial/multiaxial, constant/random, and high cycle fatigue/low cycle fatigue loading regimes. Next, formulation of time-derivative damage model is discussed in detail under uniaxial random loadings. Then, an equivalent energy concept for general multiaxial loading conditions is used to convert the random multiaxial loading to an equivalent random uniaxial loading, where the time-derivative damage model can be used. Finally, the proposed model is validated with extensive experimental data from open literature and in-house testing under various constant and random spectrum loadings.     

Numerical analysis of low cycle fatigue for welded joints considering welding residual stress and plastic damage under combined bending and local compressive loads

The numerical analysis of low cycle fatigue of HTS‐A steel welded joints under combined bending and local compressive loads are implemented using the damage mechanics approach. First, a finite element numerical simulation of the welding process is employed to extract the welding residual stresses, which are then imported as initial stresses in the subsequent fatigue analysis. Second, a multiaxial fatigue damage model including damage coupled elasto‐plastic constitutive equations and plastic damage evolution formulation is applied to evaluate the mechanical degradation of the material under biaxial fatigue loads. Further, the fatigue lives of the HTS‐A steel welded joints are computed and compared with the experimental results from literature. A series of predicted load‐life curves clearly illustrates the variation of fatigue lives along with the combined loadings. Finally, the effects of local compression on accumulated plastic strain and fatigue damage are studied in detail. It is revealed that the local compression induces a damage competition between two critical zones.     

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.     

Proportional/nonproportional constant/variable amplitude multiaxial notch fatigue: cyclic plasticity,non‐zero mean stresses,and critical distance/plane

This paper deals with the formulation and experimental validation of a novel fatigue lifetime estimation technique suitable for assessing the extent of damage in notched metallic materials subjected to in‐service proportional/nonproportional constant/variable amplitude multiaxial load histories. The methodology being formulated makes use of the Modified Manson‐Coffin Curve Method, the Shear Strain–Maximum Variance Method, and the elasto‐plastic Theory of Critical Distances, with the latter theory being applied in the form of the Point Method. The accuracy and reliability of our novel fatigue lifetime estimation technique were checked against a large number of experimental results we generated by testing, under proportional/nonproportional constant/variable amplitude axial‐torsional loading, V‐notched cylindrical specimens made of unalloyed medium‐carbon steel En8 (080M40). Specific experimental trials were run to investigate also the effect of non‐zero mean stresses as well as of different frequencies between the axial and torsional stress/strain components. This systematic validation exercise allowed us to demonstrate that our novel multiaxial fatigue assessment methodology is remarkably accurate, with the estimates falling within an error factor of 2. By modelling the cyclic elasto‐plastic behaviour of metals explicitly, the design methodology being formulated and validated in the present paper offers a complete solution to the problem of estimating multiaxial fatigue lifetime of notched metallic materials, with this holding true independently of sharpness of the stress/strain raiser and complexity of the load history.     

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.     

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.     

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.     

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 novel accumulative fatigue damage model for multiaxial step spectrum considering the variations of loading amplitude and loading path

In this paper, based on the process of the fatigue crack initiation and the critical plane theory, a continuous stress parameter was proposed to quantify the driving force of the fatigue crack initiation for the fully reversed multiaxial fatigue loading. In this stress parameter, the shear stress amplitude and normal stress amplitude on the critical plane were combined with the variable coefficients which were affected by the normalized fatigue life and the loading non‐proportionality. Owing to these coefficients, for the multiaxial loadings with different non‐proportionalities, the driving force of the fatigue crack initiation during the whole life could be described. After that, a novel accumulative fatigue damage model was established for the multiaxial two‐stage step spectrum. In this model, the accumulative damage was calculated according to the variation of the proposed stress parameter on the critical plane. Considering the directionality of the multiaxial fatigue damage, for the spectrum in which the loading path was variable, the damage accumulation was carried out on the critical planes of the both loadings, and the larger one was chosen as the final accumulative fatigue damage. In order to verify the new model, up to 41 different multiaxial two‐stage step spectrum loading tests on 2024‐T4 aluminium alloy were collected. The new model, as well as other five commonly used models, was applied to calculate the accumulative fatigue damage. The final results showed that, compared with other commonly used models, the new model had the most accurate results with the smallest scatters.     

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.     

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

Based 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.     

Energy criteria of multiaxial fatigue failure

This paper contains a review of energy-based criteria of multiaxial fatigue. The criteria have been divided into three groups, depending on the kind of strain energy density per cycle which is assumed as a damage parameter. They are: (i) criteria based on elastic strain energy for high-cycle fatigue; (ii) criteria based on plastic strain energy for low-cycle fatigue; and (iii) criteria based on the sum of plastic and elastic strain energies for both low- and high-cycle fatigue. The criteria which take into account strain energy density in the critical plane seem to be the most promising. In the energy approach to multiaxial fatigue there is an important unsolved problem, i.e. the evaluation of energy, especially plastic strain energy density, from closed stress–strain hysteresis loops under random loadings.