Fretting fatigue under variable loading below fretting fatigue limit

The fatigue limit diagram provides the critical condition of non‐failure against fatigue under constant amplitude loading. The fatigue limit diagram is usually considered to give the allowable stress if every stress component is kept within the fatigue limit diagram. In the case of variable amplitude fretting fatigue, however, this study showed that fatigue failure could occur even when all stresses were within the fatigue limit diagram. An example of such a condition is a repeated two‐step loading such as when the first step stress is R=?1 and the second step stress has a high mean value. The reason why such a phenomenon occurs was investigated. A non‐propagating crack was formed by the first step stress even when well below the fatigue limit. The resultant non‐propagating crack functioned as a pre‐crack for the second step stress with a high mean value. Consequently, fatigue failure occurred even when every stress was within the fatigue limit diagram of constant amplitude loading. The fatigue limit diagram obtained in constant amplitude fatigue test does not necessarily guarantee safety in the case of variable amplitude loading in fretting fatigue.     

Fatigue damage of medium carbon steel under sequential application of axial and torsional loading

Fatigue tests were conducted on S45C steel under fully reversed strain control conditions with axial/torsional ( at ) and torsional/axial ( ta ) loading sequences. The linear damage value (n₁/N₁+n₂/N₂) was found to depend on the sequence of loading mode ( at or ta ), sequence of strain amplitude (low/high or high/low) and life fraction spent in the first loading. In general, at loading yields larger damage values than ta loading and the low–high sequence of equivalent strain leads to larger damage values than the high–low sequence. The material exhibits cyclic softening under axial cyclic strain. Cyclic hardening occurs in the torsion part of ta loading, which elevates the axial stress in the subsequent loading, causing more damage than in pure axial fatigue at the same strain amplitude. Fatigue life is predicted based on the linear damage rule, the double linear damage rule, the damage curve approach and the plastic work model of Morrow. Results show that overly conservative lives are obtained by these models for at loading while overestimation of life is more likely for ta loading. A modified damage curve method is proposed to account for the load sequence effect, for which predicted lives are found to lie in the factor‐2 scatter band from experimental lives.     

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.     

Cumulative fatigue damage dynamic interference statistical model

After studying in depth the statistical characteristics of cumulative fatigue damage D(t) and its critical value D_c, a new dynamic interference statistical model for fatigue reliability analysis is presented in this paper. Because the non-linearity of fatigue damage accumulation has been taken into account, this model is able to predict the fatigue reliability for random spectrum loading. To verify the predicted results, two fatigue experiments were conducted in which the numbers of specimens were more than 100, using fighter spectrum loading (FALSTAFF spectrum) and constant-amplitude loading respectively. It is shown that the new model is reliable, practicable and better than existing models.     

Quadratic damage rule in random loading case

The simple mathematical structure of the quadratic damage rule (QDR) enables mathematical expression of the failure condition in the case of random loading. Random loading after modified rainflow analysis is considered as a random marked point process. Moments of the damage distribution can be expressed by use of ensemble averages. A condition for validity of the first damage moment solution is formulated. The QDR damage first moment solution involves failure predictions for both stationary and non‐stationary loadings. In these cases, final fracture conditions suitable for practical use are derived. QDR predicts fatigue lives that are always shorter than the linear damage rule (LDR) in the case of stationary loading with short interval of statistical dependence of random variables. QDR appears to be a suitable additional engineering tool for random loading fatigue life predictions considering loading sequence and loading level interactions.     

Stochastic modelling of low-cycle fatigue damage in 316L stainless steel under variable multiaxial loading

In the present study, a stochastic model is developed for the low-cycle fatigue life prediction and reliability assessment of 316L stainless steel under variable multiaxial loading. In the proposed model, fatigue phenomenon is considered as a Markov process, and damage vector and reliability are defined on every plane. Any low-cycle fatigue damage evaluating method can be included in the proposed model. The model enables calculation of statistical reliability and crack initiation direction under variable multiaxial loading, which are generally not available. In the present study, a critical plane method proposed by Kandil et al . ( Metals Soc., London 280, 203–210, 1982) maximum tensile strain range, and von Mises equivalent strain range are used to calculate fatigue damage. When the critical plane method is chosen, the effect of multiple critical planes is also included in the proposed model. Maximum tensile strain and von Mises strain methods are used for the demonstration of the generality of the proposed model. The material properties and the stochastic model parameters are obtained from uniaxial tests only. The stochastic model made of the parameters obtained from the uniaxial tests is applied to the life prediction and reliability assessment of 316L stainless steel under variable multiaxial loading. The predicted results show good aggreement with experimental results.     

Low‐cycle fatigue of 316L stainless steel under proportional and nonproportional loadings

This paper discusses low‐cycle fatigue characteristics of 316L stainless steel under proportional and nonproportional loadings. Tension–torsion multiaxial low‐cycle fatigue tests were performed using five strain paths. Additional hardening was observed under nonproportional loadings and was more significant in tests with larger nonproportionality. Mises equivalent strain, Smith–Watson–Topper, Fatemi–Socie, Kandil–Brown–Miller and nonproportional strain parameters were applied to the experimental data to evaluate the multiaxial low‐cycle fatigue damage. The applicability of the damage laws to practical design was discussed.     

Changes in mechanical properties of vehicle components after strengthening under low-amplitude loads below the fatigue limit

Changes in the mechanical properties of vehicle components were investigated after strengthening under low-amplitude loads below the fatigue limit (SLAL). The strengths of vehicle components including fatigue strength, static strength and yield strength were significantly increased by SLAL. The surface hardness of the front axle, composed of a kind of low strength steel without heat treatment, was enhanced with increased strengthening and damaging. The change of surface hardness was reversed completely for the transmission gear, composed of a kind of high strength steel with surface heat treatment. The natural frequency of the transmission gear was appreciably increased by SLAL.     

Long life fatigue under multiaxial loading

A life prediction model in the field of high-cycle (i.e. long-life) fatigue is presented in this paper. The proposed model applies in the case of constant amplitude multiaxial proportional and non-proportional loading. The problems of the fatigue limit criterion and of the fatigue life prediction are both addressed and comparisons with experimental data are shown. Some limited discussion of the stress gradient effect is also offered. Although the particular model developed here is better suited for ferritic steels, it is explained in the paper that the methodology used to obtain this model can be adequately adapted to derive mathematically consistent models for other classes of metallic materials.     

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.     

Cumulative fatigue damage and life prediction of elastomeric components

Elastomeric components are widely used in many applications due to their good damping and energy absorption characteristics. The type of loading normally encountered by these components in service is variable amplitude cyclic loading. Therefore, fatigue failure is a major consideration in their design. In this work capabilities of Rainflow cycle counting procedure, maximum principal strain as a damage criterion, and Miner's linear cumulative damage rule are evaluated with both specimen and component tests. An automotive cradle mount is used as an illustrative component. Comparison of predicted and experimental fatigue lives in both specimen and cradle mount variable amplitude load tests indicate satisfactory predictions in both cases.     

循环荷载作用下钢桥面铺装疲劳损伤失效行为研究

针对钢桥面铺装工程中普遍采用的改性沥青(Stone Matrix Asphalt,SMA)、浇筑式沥青(Guss asphalt,GA)、环氧沥青(Epoxy asphalt,EP)混合料双层铺装结构,进行了循环车载作用下钢桥面与沥青混凝土铺装疲劳损伤特性理论分析与试验研究。基于疲劳损伤度,研究了钢桥面铺装疲劳损伤失效行为和疲劳开裂过程中损伤场、应力和应变场动态演变机制,推导出疲劳失效时的损伤场、应力和应变场计算表达式,并给出钢桥面铺装疲劳寿命理论公式。以三座钢箱梁桥桥面铺装(润扬长江大桥2005,南京长江三桥2005,苏通大桥2008)为例,对不同铺装结构组合方案下的复合梁进行疲劳试验分析和使用寿命理论预测。实例研究结果表明,钢桥面铺装疲劳损伤失效行为预估模型合理可行;相较于改性沥青、浇筑式沥青,环氧沥青混合料具有较强高的强度低变形能力,更适合于大跨径钢桥面铺装抗疲劳的设计要求;由环氧沥青混合料组合而成的“双层环氧沥青混凝土”和“浇注式沥青混凝土(下层)+环氧沥青混凝土(上层)”的抗疲劳性能优于其它沥青混合料铺装结构组合方案,同等厚度组合情况下疲劳使用寿命可延长1倍~2倍以上;“双层环氧沥青混凝土”已应用于润扬长江大桥、南京长江三桥和苏通长江大桥钢桥面工程,并已成功运行10年以上,其跟踪观测结果良好。     

An experimental approach to estimate damage and remaining life of metals under uniaxial fatigue loading

An experimental procedure to estimate damage evolution and remaining fatigue life of metals associated with fatigue loading is presented. Experimental phase involves uniaxial tension–compression fatigue tests performed with solid API 5L X52 and tubular carbon steel 1018 specimens subjected to both constant and variable amplitude loading. A correlation between the so-called damage parameter and the thermal response of a material at different damage levels is proposed. Results demonstrate that the correlation can estimate damage evolution with reasonable accuracy in both constant and variable amplitude fatigue processes. It is shown that under the conditions tested the evolution of damage parameter with respect to the normalized fatigue life is independent of the load amplitude, load ratio, loading sequence, material properties, and specimen geometry. The proposed correlation and the relationship between the damage parameter and the normalized fatigue life are employed to develop a non-destructive method to predict the remaining fatigue life of metallic specimens with prior fatigue damage. The method is applied to both constant and variable amplitude loading and the predicted results are found to be in good agreement with those obtained from the experiments.     

History influence exponent in cumulative fatigue damage determined using two-step loading experiments

ABSTRACT The only material parameter, which appears in quadratic phenomenological hypothesis of cumulative fatigue damage, is the history influence exponent ϑ reflecting the material sensitivity to loading sequence and loading level interactions. Methods of its determination on the basis of two-step loading experiments are presented. One method is based on the least-squares method using linearizing transformation, other two ones are based on concept of individual fatigue life curves and statistical concept of inexact structural model. Parameter ϑ has been evaluated in 24 cases representing various materials and different test conditions. Possibility of existence of a common ϑ value holding for all materials is discussed. Such a value does not follow from analysed experimental data. However, ϑ = 0.5 is recommended for improving the reliability of engineering fatigue life estimates in case when required experimental material data are not available.     

Torsional fatigue with axial constant stress of oligo‐crystalline 316L stainless steel thin wire

A series of symmetric torsional fatigue with axial constant stress tests, a kind of multiaxial fatigue test, was conducted on oligo‐crystalline 316L stainless steel thin wire, which was less than 3.5 grains across diameter of 200 μm. The material presents significant cyclic hardening under symmetric torsion cycling, and hardening is more obvious with the increasing shear strain amplitude. However, symmetric torsional cycle with constant axial stresses tests characterize rapid initial hardening and then gradually softening until fatigue failure. The axial stress has a great effect on torsional fatigue life. Fractography observation shows a mixed failure mode combined torsional fatigue with tensile strain because of axial tensile stress. A newly proposed model with axial stress damage parameter is used to predict the torsional fatigue life with constant axial stress of small scale thin wire.     

A computerized procedure for long-life fatigue assessment under complex multiaxial loading

A computerized procedure is presented and evaluated for application examples of long-life fatigue analyses of metallic materials under complex multiaxial loading. The method is based on the stress invariants and uses the minimum circumscribed ellipse approach for evaluating the effective shear stress amplitude under complex multiaxial loading. The applicability of the procedure for handling non-proportional loading is examined through typical examples such as combined normal/shear stresses and combined bi-axial normal stresses with complex stress time histories. The effects of phase shift angles, frequency ratios and waveforms on fatigue endurance were re-analysed and compared with available experimental results from the literature. The comparison shows that the presented procedure based on stress invariants is a potential conservative engineering approach, very suitable for fast fatigue evaluation in the integrated computer aided fatigue design.     

Fatigue strength of small-notched specimens under variable amplitude loading within the fatigue limit diagram

Although the fatigue limit diagram is defined in principle for constant stress amplitude, it is often considered that fatigue failure would not occur, even in varying loading, if applied stresses were kept within the fatigue limit diagram. However, it was shown in the case of small‐notched specimens that fatigue failure occurred in some special cases of variable amplitude loading, even when all stress amplitudes were kept within the fatigue limit diagram. The cause of this phenomenon was examined using two‐step stress and repeated two‐step stress patterns in which the first step stress was chosen to be equal to the fatigue limit with zero mean stress and a mean stress was superposed on the second step stress. A non‐propagating crack was formed by the first step stress. This crack functioned as a pre‐crack for the second step stress with high mean stress. Consequently, fatigue failure occurred even when all stress amplitudes were kept within the fatigue limit diagram. It was an unexpected fracture caused by the interference effect of a non‐propagating crack and a mean stress change.     

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.     

High-cycle fatigue mechanisms in 1045 steel under non-proportional axial-torsional loading

Detailed microscopic analyses have been made on the high-cycle mechanisms in 1045 steel under various stress-controlled axial-torsional loadings. A special attention has been paid to a critical example of non-proportional loading, i.e., 90° out-of-phase loading with different stress ratios. The replica technique has been used to monitor crack initiation and propagation from the microstructure scale. The orientations of persistent slip bands and Stage I cracks are in good agreement with the critical plane concept. The evolutions of crack length with cycle life as well as the crack aspect ratios depend on the loading condition. However at a given life, the data are consolidated in terms of crack depth versus cycle life. The McDiarmid parameter correlates stress-life data under proportional loadings. However, it underestimates fatigue lives under out-of-phase loading at high stress ratio and it overestimates them in the case where all planes experience the same shear stress amplitude (stress ratio = 0.5). More damaging mechanisms are involved in crack initiation and crack propagation. It is recommended to test the fatigue performance of materials in this last condition that involves the worst damage mechanisms.