确定性疲劳累积损伤理论进展

著名的Miner-Palmgren线性累积损伤理论的提出已有70余年，但由于疲劳问题的复杂性，迄今为止还没有一个模型的工程应用价值能与该理论媲美。疲劳累积损伤理论仍在发展与完善中。文章根据疲劳损伤与疲劳累积损伤理论的特点，将确定性疲劳累积损伤理论分成两大类，即线性累积损伤理论和非线性累积损伤理论，并将主要的非线性累积损伤理论分成五类：a. 基于损伤曲线法的非线性累积损伤理论；b. 基于材料物理性能退化概念的非线性累积损伤理论；c. 基于连续损伤力学概念的非线性累积损伤理论；d. 考虑载荷间相互作用效应的非线性累积损伤理论；e. 基于能量法的非线性累积损伤理论。文章分析了每一类模型中有代表性模型的物理背景，回答了模型在疲劳累积损伤理论中存在的主要问题，简要评述了模型的优缺点，讨论了确定性疲劳累积损伤理论的几个关键问题。     

Application of a material fatigue damage model in 4PB tests

The fatigue property of an asphalt mix is an important issue in pavement design. This property is often determined with the aid of a four-point bending (4PB) test in controlled deflection mode. The fatigue property is related to the decrease in the calculated complex stiffness modulus, however, due to the non- homogenous stress and strain field in the beam, the measured response does not represent the stiffness modulus of the material but a weighted stiffness value. For a correct interpretation, a fatigue damage material model like the Asphalt Concrete Pavement-Fatigue model is needed. After integration, the calculated and measured responses are compared. By varying the model parameters, an excellent comparison between the two responses is obtained up to a certain number of cycles. This number of cycles is denoted as the fatigue life N _PH . The accumulated dissipated energy at the surface of the beam in the midsection can be expressed as a constant times the fatigue life N _PH to the power z and also as a constant times the product of the fatigue life N _PH and the initial dissipated energy in the first cycle. Using these two findings, a Wöhler curve was established similar to the one directly based on the strain amplitudes and fatigue life data.     

An efficient fatigue and creep‐fatigue life prediction method by using the hysteresis energy density rate concept

Fatigue damage, time‐dependent creep damage and their interaction are considered as the main failure mechanisms for many high temperature structural components. A generalized methodology for predicting both the high temperature low cycle fatigue (HTLCF) and creep‐fatigue lives by using the hysteresis energy density rate (HEDR) and fatigue damage stress concepts was proposed. Experimental data for HTLCF and creep‐fatigue in Alloy 617, Haynes 230 and P92 steel were respectively collected to validate the method. A better prediction capacity and most of the data points that fall within a 1.5 scatter band were obtained compared with the traditional energy‐based method, time fraction rule and ductility exhaustion model. Moreover, a creep‐fatigue damage diagram was also constructed by using the proposed approach.     

基于劲度模量分析的橡胶沥青混合料疲劳寿命研究

变幅加载下沥青的疲劳损伤累积具有明显的非线性特征,传统的Miner’s线性疲劳损伤累积准则无法表征不同变幅加载次序下沥青的非线性疲劳损伤累积(NLFDA)。该研究旨在建立考虑加载次序影响的NLFDA模型,准确表征加载次序对沥青疲劳损伤累积的影响。通过开展应力控制的沥青恒幅加载疲劳试验,采用耗散伪应变能(DPSE)表征沥青疲劳损伤,分析恒幅加载下沥青的疲劳损伤累积规律;采用低-高和高-低两种加载次序,开展应力控制的沥青变幅加载疲劳试验,分析变幅加载下沥青的疲劳损伤累积规律;基于损伤等效准则,建立考虑加载次序影响的NLFDA模型,分析加载次序对疲劳损伤累积的影响。结果表明：应力控制模式下的沥青疲劳损伤,呈先缓慢后急剧的非线性增加演化趋势;恒幅加载下沥青疲劳损伤服从Miner’s准则发生线性累积,且累积寿命分数等于1;变幅加载下沥青疲劳损伤不服从Miner’s准则而发生非线性累积。低-高和高-低变幅加载次序下,沥青累积疲劳寿命随一级寿命分数的增大而分别增加和减小,累积寿命分数分别大于1和小于1;建立的NLFDA模型可克服Miner’s准则缺陷,并较为准确地表征加载次序对沥青疲劳损伤累积的影响。

     

机械滚压对A473M钢疲劳性能的影响

采用机械滚压对A473M马氏体不锈钢轴套材料进行表面处理,研究滚压工艺对其力学性能的影响。采用SEM、白光干涉仪、X射线衍射仪、显微硬度计、EBSD、拉伸试验机和疲劳试验机分别对试样表面形貌、表面粗糙度、残余应力、显微硬度、拉伸性能和疲劳性能进行系统表征。结果表明:滚压加工试样表面的粗糙度明显降低,仅为车削加工的1/5;滚压加工在材料近表面引入残余压应力,其值最高可达946 MPa,沿深度方向逐渐减小,残余压应力层深度约为200μm,表面硬度提高30%左右,硬度影响层深度可达200μm;抗拉强度、屈服强度和伸长率分别提升了40%,22%和8%,疲劳寿命由基体材料的5.4×10^4周次提高到1×10^7周次。采用滚压加工后材料的力学性能明显提升,疲劳寿命显著增加。     

Experimental and theoretical studies on thermo‐mechanical fatigue test for aluminium cast alloy

Evaluation of the thermo‐mechanical behaviour and prediction of the service life of cast aluminium alloys are important for the design of automobile engine cylinder heads. In this study, cast Al alloy specimens are extracted from cylinder heads and subjected to in‐phase thermo‐mechanical cyclic loading. The hysteresis curves related to stress and strain were recorded under the individual thermo‐mechanical loading conditions. The number cycles to failure corresponding to multiple mechanical strain and temperature ranges were obtained. It is found that the cyclic stress amplitude decreases and the cyclic softening rate increases with increasing maximum temperature rise. A modified fatigue‐creep model based on energy conservation has been developed for prediction of the fatigue life of cylinder heads. The proposed method shows good agreement with the well‐established Ostergren model and low standard deviations. In summary, the proposed method described in this study provides an option for prediction of the thermo‐mechanical behaviour of metals.     

Prediction of fatigue crack growth path in mechanical joints using a weight function approach

Cracks often initiate from the mechanical joints which are widely used in structural components. It has been reported that cracks in mechanical joints are under mixed‐mode condition and there is a critical angle at which mode I stress intensity factor becomes maximum. The crack propagates in an arbitrary direction and the prediction of fatigue crack growth path is needed to provide against crack propagation and examine safety. In this study, mixed‐mode fatigue crack growth tests are performed for horizontal and critical inclined cracks in mechanical joints. Fatigue crack growth paths are predicted using a weight function approach and maximum tangential stress criterion.     

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.     

Low cycle fatigue of a titanium 829 alloy

The fatigue behaviour of titanium 829 in its oil quenched (‘basketweave’) and air cooled (‘aligned’) microstructural forms has been examined at 600°C and room temperature under fully reversed, total strain controlled conditions. Identical endurances are observed for each microstructure together with a low transition life. Similarly, almost perfect cyclic stability is exhibited irrespective of microstructure, temperature, strain range and rate. This is tentatively attributed to the ability of the aligned colonies present in both microstructures to accomodate plasticity. It is argued that a reduction in strain rate shortens life due to environmental effects. Multiple crack initiation is generally associated with facet-like features, with later growth surfaces bearing striations only after fatigue at 600°C.     

An analysis of thermal gradient impact in thermal–mechanical fatigue testing

Thermal–mechanical fatigue (TMF) testing is a good method to decrease the number of isothermal tests for non‐isothermal behaviour laws identification. Based on experimental results of the TMF Standard European Working Group, this study aims to investigate the impact of thermal gradients on mechanical heterogeneity within the gage length specimen. The quality of the TMF test is examined by an energy criterion related to error bounds for nonlinear behaviour. A sensitivity analysis is then made for a given behaviour law identified on a TMF test to answer to the above question. Moreover the geometric instability phenomenon, already noticed by Sheffler and Coffin, is modelled herein.     

Influence of effective stress intensity factor range on mixed mode fatigue crack propagation

ABSTRACT The behaviour of fatigue crack propagation of rectangular spheroidal graphite cast iron plates, each consisting of an inclined semi‐elliptical crack, subjected to axial loading was investigated both experimentally and theoretically. The inclined angle of the crack with respect to the axis of loading varied between 0° and 90°. In the present investigation, the growth of the fatigue crack was monitored using the AC potential drop technique, and a series of modification factors, which allow accurate sizing of such defects, is recommended. The rate of fatigue crack propagation db/dN is postulated to be a function of the effective strain energy density factor range, ΔS_eff. Subsequently, this concept is applied to predict crack growth due to fatigue loads. The mixed mode crack growth criterion is discussed by comparing the experimental results with those obtained using the maximum stress and minimum strain energy density criteria. The threshold condition for nongrowth of the initial crack is established based on the experimental data.     

A two scale damage concept applied to fatigue

The ductile type of damage is a phenomenon now well understood. Once the fully coupled set of constitutive equations is identified, Damage Mechanics is a powerful tool to predict failure. Brittle materials do not exhibit such a damageable macroscopic behavior. Nevertheless, they still fail. On the idea that damage is localized at the microscopic scale, a scale smaller than the mesoscopic one of the Representative Volume Element (RVE), we propose a three-dimensional failure modeling for monotonic as well as for fatigue loading. We develop a two scale model of what we shall call brittle damage: at the microscopic scale, micro-cracks or micro-voids exhibit a damageable plastic-like behavior with no effect on the global (mesoscopic) elastic behavior. Microscopic failure is assumed to coincide with the RVE failure. This model turns out to represent quite well physical phenomena related to high cycle fatigue such as the mean stress effect, the nonlinear accumulation of damage, initial strain hardening or damage effect and the nonproportional loading effect for bi-axial fatigue. The model has been implemented as a post-processor computer code. A simplified identification procedure for the determination of the material properties is given. This revised version was published online in July 2006 with corrections to the Cover Date.     

A notch stress intensity approach to assess the multiaxial fatigue strength of welded tube-to-flange joints subjected to combined loadings

Full penetration T butt weld joints between a tube and its flange are considered, subjected to pure bending, pure torsion and a combination of these loading modes. The model treats the weld toe like a sharp V‐notch, in which mode I and mode III stress distributions are combined to give an equivalent notch stress intensity factor (N‐SIF) and assess the high cycle fatigue strength of the welded joints. The N‐SIF‐based approach is then extended to low/medium cycle fatigue, considering fatigue curves for pure bending and pure torsion having the same slope or, alternatively, different slopes. The expression for the equivalent N‐SIF is justified on the basis of the variation of the deviatoric strain energy in a small volume of material surrounding the weld toe. The energy is averaged in a critical volume of radius R_C and given in closed form as a function of the mode I and mode III N‐SIFs. The value of R_C is explicitly referred to high cycle fatigue conditions, the material being modelled as isotropic and linear elastic. R_C is thought of as a material property, independent in principle of the nominal load ratio. To validate the proposal, several experimental data taken from the literature are re‐analysed. Such data were obtained by testing under pure bending, pure torsion and combined bending and torsion, welded joints made of fine‐grained Fe E 460 steel and of age‐hardened AlSi1MgMn aluminium alloy. Under high cycle fatigue conditions the critical radius R_C was found to be close to 0.40 mm for welded joints made of Fe E 460 steel and close to 0.10 mm for those made of AlSi1MgMn alloy. Under low/medium cycle fatigue, the expression for energy has been modified by using directly the experimental slopes of the pure bending and pure torsion fatigue curves.     

Service loading test as a source for the fatigue curve parameters' estimation

Very important question of fatigue curve parameter estimation might be explored from the point of view of service loading. Comparative testing at varied stress levels with subsequent computation might reveal some peculiarities of fatigue curves and substantial changes of their parameters due to service loading factors. __________ Translated from Problemy Prochnosti, No. 1, pp. 76–82, January–February, 2009.     

A single parameter to evaluate stress state in rail head for rolling contact fatigue analysis

Based on the Smith‐Watson‐Topper (SWT) method, a phenomenological approach for multiaxial fatigue analysis, the maximum SWT parameter is proposed as a single parameter to evaluate the stress state in the rail head for assessing the fatigue integrity of the structure. A numerical procedure to calculate the maximum SWT parameter from a finite element analysis is presented and applied in a case study, where the stress and strain fields due to wheel/rail rolling contact are obtained from a three‐dimensional finite element simulation with the steady‐state transport analysis technique. The capability of the SWT method to predict fatigue crack initiation in the rail head is confirmed in the case study. Analogous to von Mises stress for strength analysis, the maximum SWT parameter can be applied to evaluate the fatigue loading state not only in rail head due to rolling contact fatigue but also in a generic structure subjected to a cyclic loading.     

Low cycle fatigue behaviour of dual-phase steel with different volume fractions of martensite

Completely reversed low cycle fatigue tests were carried out at a constant strain rate of 10^?2s^?1 on 3 mm thick sheet specimens of a dual-phase steel treated to give 1.5 to 28% martensite without changing the carbon content. Hysteresis loop shape, stress/strain response and plastic strain energy as a function of applied cycles are analysed for different microstructures. Strain/life and plastic strain energy per cycle ($\text{Δ}\text{W}\text{?}{}_{\mathrm{<mtext>p</mtext>}}$)/life (2N_f) plots are discussed in terms of microstructure. It is shown that during cycling the shape of the hysteresis loop continuously changes at lower volume fractions of martensite whereas it remains more or less constant for microstructures with a higher percentage of martensite. A Coffin-Manson type of plot between log ($\text{Δ}\text{W}\text{?}{}_{\mathrm{<mtext>p</mtext>}}$) and log (2N_f) is found to be applicable to test results of dual-phase steel with a wide range of martensite contents and is thus more versatile than the plot between log (Δ?_p/2) and log (2N_f) for predicting the fatigue life.     

基于开裂能密度及裂纹扩展特性的橡胶隔振器疲劳特性预测

基于开裂能密度的连续介质力学参数及橡胶材料裂纹扩展特性(裂纹扩展速率与撕裂能之关系),获得橡胶部件多轴疲劳特性计算公式,并计算某汽车动力总成橡胶隔振器的疲劳特性。计算与试验对比表明,橡胶隔振器疲劳特性预测(寿命、开裂位置及开裂方向)与实测较一致。预测疲劳寿命分布在实测疲劳寿命的1/2倍分散因子内,满足工程疲劳寿命预测要求。提出的橡胶隔振器多轴疲劳特性预测方法,可用试验效率较高、投入较少的材料裂纹扩展试验代替耗时较多的材料疲劳破坏试验,不仅能为橡胶部件前期疲劳设计提供参考,亦能大幅缩短产品疲劳设计周期。     

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.     

Analysis of nonlinear vibrations of a two-degree-of-freedom mechanical system with damping modelled by a fractional derivative

Free damped vibrations of a mechanical two-degree-of-freedom system are considered under the conditions of one-to-one or two-to-one internal resonance, i.e., when natural frequencies of two modes – a mode of vertical vibrations and a mode of pendulum vibrations – are approximately equal to each other or when one natural frequency is nearly twice as large as another natural frequency. Damping features of the system are defined by the fractional derivatives with fractional parameters (the orders of the fractional derivatives) changing from zero to one. It is assumed that the amplitudes of vibrations are small but finite values, and the method of multiple scales is used as a method of solution. The model put forward allows one to obtain the damping coefficient dependent on the natural frequency of vibrations, so it has been shown that the amplitudes of vertical and pendulum vibrations attenuate by an exponential law with damping ratios which are exponential functions of the natural frequencies. Damped soliton-like solutions have been found analytically.