Rapid Determination of Fretting Fatigue Limit by Infrared Thermography

This paper demonstrates the feasibility of infrared thermography to determine the so-called fretting fatigue limit. Fretting fatigue tests are performed on aluminum and steel specimens. The coupled fatigue and tangential loads are sequentially increased (block loading) whilst the normal load is kept constant for all blocks. The temperature data is processed and analyzed using a Fast Fourier Transform (FFT) algorithm implemented in the commercial software Matlab. It is demonstrated that the second harmonic of the temperature signal can be linked to the specific loading block below which no or negligible damage is generated in the specimen. The stress amplitude of this block is considered to be a best estimate of the fretting fatigue limit. A constant amplitude fretting fatigue test with this stress amplitude confirmed that the specimen remains intact at 10⁷ cycles.     

一种基于耗散能计算的高周疲劳参数预测方法

在热力学框架下,基于薄板假设,建立金属材料薄板试样在高周疲劳载荷作用下的热传导方程,将试样温度场数据和实时载荷信号导入,准确计算与高周疲劳损伤相关的单个循环内耗散能. 基于该方法,以316L不锈钢材料为例,通过实时监测试样不同应力水平下高周疲劳破坏全过程中耗散能的变化,拟合出耗散能-疲劳寿命曲线,呈现与传统的应力-疲劳寿命曲线相同的规律;提出一种新的预测高周疲劳极限的能量法,确定的疲劳极限与实验值相近.     

基于非齐次复合Poisson过程的正交异性钢桥面板细节疲劳裂纹随机扩展研究

传统的正交异性钢桥面板疲劳损伤评估常采用确定性和可靠性分析方法,忽略了疲劳裂纹扩展的随机性影响,针对这一问题,提出钢桥面板细节疲劳随机扩展分析方法。本文以南溪长江大桥为工程背景,基于长期车辆荷载监测数据,建立了车辆荷载非齐次复合Poisson过程模型。建立钢桥面板有限元模型,采用瞬态分析方法将随机车辆荷载转化成细节疲劳应力,基于线弹性断裂力学理论推导U肋-顶板焊接细节疲劳裂纹扩展时变微分方程,实现宏观关系式疲劳应力幅次数-疲劳损伤至微观表达式应力时间序列-疲劳损伤转换,讨论了车载次序及超载对疲劳裂纹扩展的影响。研究结果表明,非齐次复合泊松过程模型能够较好描述随机车流运营状态,车辆荷载的次序对疲劳裂纹扩展速率的影响不可忽略,重车排序靠前时能够促使疲劳裂纹扩展增速,南溪长江大桥细节点的车辆超载迟滞效应修正系数取值0.804。     

A cohesive zone model for fatigue crack growth allowing for crack retardation

A damage-based cohesive model is developed for simulating crack growth due to fatigue loading. The cohesive model follows a linear damage-dependent traction–separation relation coupled with a damage evolution equation. The rate of damage evolution is characterized by three material parameters corresponding to common features of fatigue behavior captured by the model, namely, damage accumulation, crack retardation and stress threshold. Good agreement is obtained between finite element solutions using the model and fatigue test results for an aluminum alloy under different load ratios and for the overload effect on ductile 316 L steel.     

疲劳过程中生热机理的实验探讨

传统的疲劳试验方法确定材料的疲劳极限时试验周期长、需要试件多,故高试验成本成为疲劳试验中一个难以解决的问题.文中利用具有准确、快速、便捷、低成本等优点的热像法测定了多种载荷工况下Q235钢的疲劳极限,并对不同的黏或/和塑性效应主导的生热机制进行了探讨.材料疲劳过程中,疲劳极限之下的载荷引起的温度波动来源于热弹性效应,温升来源于材料的非弹、塑性效应(如黏性效应);而疲劳极限之上的载荷引起塑性功累计,导致疲劳损伤产生,使得温升机制出现转折.通过对试验数据的分析,求出了材料的黏性系数,给出了利用塑性能耗的起点确定材料疲劳极限的方法.     

Uniaxial ratcheting and fatigue failure of tempered 42CrMo steel: Damage evolution and damage-coupled visco-plastic constitutive model

Uniaxial ratcheting and fatigue failure of tempered 42CrMo steel were observed by the tests under the uniaxial stress-controlled cyclic loading with non-zero mean stress [G.Z. Kang, Y.J. Liu, Mater. Sci. Eng. A 472 (2008) 258–268]. Based on the obtained experimental results, the evolution features of whole-life ratcheting behavior and low-cycle fatigue (LCF) damage of the material were discussed first. Then, in the framework of unified visco-plasticity and continuum damage mechanics, a damage-coupled visco-plastic cyclic constitutive model was proposed to simulate the whole-life ratcheting and predict the fatigue failure life of the material presented in the uniaxial stress cycling with non-zero mean stress. In the proposed model, the damage was divided into two parts, i.e., elastic damage and plastic damage, which were described by the evolution equations with the same form but different constants, since the maximum applied stresses in most of loading cases were lower than the nominal yielding strength of the material. The ratcheting of the material was still described by employing a nonlinear kinematic hardening rule based on the Abdel-Karim–Ohno combined kinematic hardening model [M. Abdel Karim, N. Ohno, Int. J. Plast. 16 (2000) 225–240] but extended by considering the effect of damage. The maximum strain criterion combined with an elastic damage threshold was employed to determine the failure life of the material caused by two different failure modes, i.e., fatigue failure (caused by low-cycle fatigue due to plastic shakedown) and ductile failure (caused by large ratcheting strain). The simulated whole-life ratcheting behavior and predicted failure life of tempered 42CrMo steel are in a fairly good agreement with the experimental ones.     

The evolution of crystalline stresses of a polycrystalline metal during cyclic loading

The presence of a positive average applied stress during cyclic uniaxial loading leads to a reduction in fatigue life of metallic parts. The metals are typically polycrystalline, with stresses varying from crystal to crystal due to differences in lattice orientation and slip system strength. Simulations enable us to better understand how polycrystals behave under cyclic loading and how the changing stress over many cycles influences fatigue life. Specifically, uniaxial cyclic simulations of pre-strained HY100 steel were conducted using an elastic viscoplastic continuum slip model employing a Taylor hypothesis. Stress-controlled loading conditions were employed to mimic fatigue tests on cold-bent bar specimens for three different load levels. The macroscopic axial strains and the crystal axial stresses were monitored during the cycles. The stress–strain response for the first cycle was used to determine the load input for the material point simulations. The peak values of crystal axial stress were found to evolve continuously with the number of loading cycles. It was found that the stress change in a crystal is influenced not only by its own orientation but also by the orientations of the other crystals in the aggregate. Furthermore, the distribution of crystal stresses after thousands of cycles at a lower stress amplitude closely resembled the distribution after tens of cycles at a larger stress amplitude.     

Modeling the low-cycle fatigue behavior of visco-hyperelastic elastomeric materials using a new network alteration theory: Application to styrene-butadiene rubber

Although several theories were more or less recently proposed to describe the Mullins effect, i.e. the stress-softening after the first load, the nonlinear equilibrium and non-equilibrium material response as well as the continuous stress-softening during fatigue loading need to be included in the analysis to propose a reliable design of rubber structures. This contribution presents for the first time a network alteration theory, based on physical interpretations of the stress-softening phenomenon, to capture the time-dependent mechanical response of elastomeric materials under fatigue loading, and this until failure. A successful physically based visco-hyperelastic model is revisited by introducing an evolution law for the physical material parameters affected by the network alteration. The general form of the model can be basically represented by two parallel networks: a nonlinear equilibrium response and a time-dependent deviation from equilibrium, in which the network parameters become functions of the damage rate (defined as the ratio of the applied cycle over the applied cycle to failure). The mechanical behavior of styrene-butadiene rubber was experimentally investigated, and the main features of the constitutive response under fatigue loading are highlighted. The experimental results demonstrate that the evolution of the normalized maximum stress only depends on the damage rate endured by the material during the fatigue loading history. The average chain length and the average chain density are then taken as functions of the damage rate in the proposed network alteration theory. The new model is found to adequately capture the important features of the observed stress-strain curves under loading-unloading for a large spectrum of strain and damage levels. The model capabilities to predict variable amplitude tests are critically discussed by comparisons with experiments.     

一种考虑非比例附加损伤的多轴低周疲劳模型

在实际工作环境中,机械结构往往承受着多轴非比例循环载荷.相比多轴比例循环加载,多轴非比例循环加载由于产生了附加强化现象,造成机械结构疲劳寿命下降.通过分析薄壁圆筒管件在非比例加载工况下应力应变变化规律和发生破坏位置,本文基于临界面法提出一种考虑多轴非比例附加损伤的疲劳模型.该模型将最大剪切应变幅平面作为临界面,提出一个新的附加强化因子,结合临界面上切应变幅和正应变幅组成新的多轴疲劳损伤参量.此参量不仅考虑了非比例加载下临界面上正应变幅和切应变幅对材料造成的疲劳损伤,还考虑到应变路径的变化和材料非比例加载敏感特性对材料疲劳寿命的影响.考虑到实际情况下模型所需材料附加强化系数有时难以获得的情况,给出了材料附加强化系数的有关近似计算公式.只需要材料基本力学参数便可得到材料附加强化系数,方便工程实际应用.采用8种材料的多轴疲劳寿命数据对提出的新模型进行检验,结果表明所提出的新模型与传统多轴疲劳模型相比预测寿命精度更高.      

疲劳过程中的能量耗散和疲劳寿命的预测

试验测量了A3钢和铝合金LY12CZ在疲劳过程中的耗散能密度与应力幅的关系和破坏时的临界累积耗散能密度。通过一系列不同加载频率和应力比的比较试验,结果表明耗散能密度与应力幅的关系和临界累积耗散能密度在不同加载频率下变化不大,但是受应力比的影响较大。本文还建立了临界累积耗散能密度疲劳寿命预测判据,并用此判据进行了带中心孔板条构件的疲劳寿命预测,取得了较好的结果（误差在25％以内）。这种方法对于构件局部的疲劳主要由一个方向应力控制的工程问题,使用简便有效。     

Modeling of fatigue crack growth from a notch

When a fatigue crack is nucleated and propagates into the vicinity of the notch, the crack growth rate is generally higher than that can be expected by using the stress intensity factor concept. The current study attempted to describe the crack growth at notches quantitatively with a detailed consideration of the cyclic plasticity of the material. An elastic–plastic finite element analysis was conducted to obtain the stress and strain histories of the notched component. A single multiaxial fatigue criterion was used to determine the crack initiation from the notch and the subsequent crack growth. Round compact specimens made of 1070 steel were subjected to Mode I cyclic loading with different R-ratios at room temperature. The approach developed was able to quantitatively capture the crack growth behavior near the notch. When the R-ratio was positive, the crack growth near a notch was mainly influenced by the plasticity created by the notch and the resulted fatigue damage during crack initiation. When the R-ratio was negative, the contact of the cracked surfaces during a part of a loading cycle reduced the cyclic plasticity of the material near the crack tip. The combined effect of notch plasticity and possible contact of cracked surface were responsible for the observed crack growth phenomenon near a notch.     

Determination of effective stress range and its application on fatigue stress assessment of existing bridges

This paper presents a unified approach on determination of the effective stress range based on equivalent law of strain energy and fatigue damage model, so as to provide an efficient approach for accurately assessing effective fatigue stress of existing bridge under traffic loading. A new theoretical framework to relate variable- and constant-amplitude fatigue is proposed in this paper. Different formulation for calculating effective stress range can be derived by the proposed theory, which include the effective stress range by the root mean square, by Miner's law and a new effective stress range based on the nonlinear fatigue damage model. Comparison of the theoretical results of fatigue damage under the effective stress range of the variable-amplitude stress spectrum and experimental data of fatigue damage under realistic traffic loading has confirmed the validity of the proposed theory. As a way to relate variable-amplitude fatigue data with constant-amplitude data, the effective stress range provides the most convenient way for evaluating fatigue damage under variable-amplitude loading. The proposed theory is then applied to provide an efficient approach for accurately assessing fatigue damage of existing bridges under traffic loading, in which online strain history data measured from bridge structural health monitoring system is available. The proposed approach is applied to evaluate the effective stress range for the purpose of the fatigue analysis of a deck section of a long-span steel bridge––the Tsing Ma Bridge in Hong Kong.     

一个高周疲劳损伤演化修正模型

将连续损伤力学应用到疲劳问题中, 得到合理的疲劳损伤演化方程,被认为是预测疲劳寿命最有效的方法之一. 在研究Lemaitre最新疲劳损伤演化方程基础上, 根据试验数据提出了一个修正的高周疲劳损伤演化方程, 该方程可以考虑应力幅、平均应力等影响因素. 以2A12-T4铝合金为例, 得到了修正模型的材料常数. 将该修正模型以UMAT子程序形式嵌入ABAQUS主程序, 计算了两种构件14种不同受载情况下的疲劳寿命, 所得计算寿命与试验结果误差均值约15%, 说明修正的疲劳损伤演化方程可以很好地计算金属构件的高周疲劳寿命.      

Creep life predictions for structures subject to variable loading

Previous work which established upper and lower bounds on the creep life of steadily loaded structures is extended to cater for load and temperature variations in non-homogeneous structures. The investigation is limited to the range where short term plasticity and fatigue damage can be ignored. For proportional loading, the upper bound which is based on limit analysis, is similar in form to that for constant loading. In the more general case, the upper bound is less stringent and is based on the mean load and temperature distribution over the lifetime. A lower bound on life is taken as the time for the first part of the structure to fail.The bounds are applied to three simple structures. For proportional loading the upper bound predicts the lifetime with the same accuracy as for constant loading except for extreme load variations. The presence of a temperature distribution alters the accuracy of the upper bound prediction but in most cases the change is small. In contrast, the lower bound is very sensitive to the temperature gradient.The authors use these results to develop approximate techniques for estimating the creep life of components subjected to variable loads and temperature distributions. Simplified design procedures based on the upper bound are examined and suitable amendments are proposed.     

基于实测荷载的铁路钢桁梁桥疲劳可靠性评估

为了对钢桁梁桥疲劳进行评估,引入可靠性理论,提出了基于实测荷载的桥梁疲劳可靠性评估方法。根据某铁路钢桁梁桥实测车辆荷载数据,建立了随机车辆荷载模型。并在考虑车辆荷载随机性的基础上,结合Monte-Carlo法与有限元,分析了钢桁梁桥构件疲劳应力谱,计算了构件疲劳可靠性随时间的变化,并探讨了车辆荷载及荷载效应变异性对构件疲劳可靠性的影响,最后采用β约界法与静力分析法对钢桁梁桥系统疲劳可靠性进行了研究。结果表明,基于随机车辆荷载的构件疲劳应力谱呈现单峰分布;构件疲劳可靠性随运营时间的增加而减小;车辆荷载的增长及荷载效应变异性的增加对构件疲劳可靠性影响较大,当车辆荷载增长率和等效应力变异系数分别增加到5%时,构件疲劳寿命大幅减小;β约界法结合静力分析法可快速确定钢桁梁桥失效模式,桥梁系统疲劳寿命小于构件疲劳寿命。总的来看,基于实测荷载的钢桁梁桥疲劳可靠性评估方法能有效地利用监测数据,对桥梁疲劳评估具有良好的适用性。     

基于SWT方法的钢绞线索微动疲劳特性分析

为得到钢绞线索丝间接触区的应力场分布并预测微动疲劳裂纹萌生位置和微动疲劳寿命，本文利用参数化方法建立了精细化的钢绞线拉索有限元模型，包括整索模型和不同层丝间接触区域的局部精细化子模型．分析了钢绞线索在两种交变荷载工况下的应力场变化情况，并基于多轴疲劳SWT(Smith-Watson-Topper)临界平面法进行了疲劳特性分析和疲劳寿命预测．主要结论如下：钢绞线索内接触区边缘处的微动幅值较大，中心处几乎没有相对滑动，微动疲劳的初始裂纹萌生点位于接触区域边缘；经不同区域子模型分析比较，在轴向循环荷载作用下，外层钢丝的接触区域比内层钢丝更易发生微动疲劳损伤；在横向位移循环荷载作用下，同层钢丝因位置角度不同而产生了较大的疲劳特性差异，且相比轴向循环拉伸，该工况下最不利单丝的微动疲劳寿命更低；与非接触区域相比，接触区的疲劳寿命大幅降低，微动现象对钢绞线索的抗疲劳性能有明显降低作用．     

A reexamination of plasticity-induced crack closure in fatigue crack propagation

The crack closure concept is often used to consider the R-ratio and overload effects on fatigue crack growth. The presumption is that when the crack is closed, the external load produces negligible fatigue damage in the cracked component. The current investigation provides a reassessment of the frequently used concept with an emphasis on the plasticity-induced crack closure. A center cracked specimen made of 1070 steel was investigated. The specimen was subjected to plane-stress mode I loading. An elastic–plastic stress analysis was conducted for the cracked specimens using the finite element method. By applying the commonly used one-node-per-cycle debonding scheme for the crack closure simulations, it was shown that the predicted crack opening load did not stabilize when the extended crack was less than four times of the plastic zone size. The predicted opening load was strongly influenced by the plasticity model used. When the elastic–perfectly plastic (EPP) stress–strain relationship was used together with the kinematic hardening plasticity theory, the predicted crack opening load was found to be critically dependent on the element size of the finite element mesh model. For R = 0, the predicted crack opening load was greatly reduced when the finite element size became very fine. The kinematic hardening rule with the bilinear (BL) stress–strain relationship predicted crack closure with less dependence on the element size. When a recently developed cyclic plasticity model was used, the element size effect on the predicted crack opening level was insignificant. While crack closure may occur, it was demonstrated that cyclic plasticity persisted in the material near the crack tip. The cyclic plasticity was reduced but not negligible when the crack was closed. The traditional approaches may have overestimated the effect of crack closure in fatigue crack growth predictions.     

薄壁圆管空间结构的热疲劳可靠性分析

针对薄壁圆管的空间结构,分析其在交变热载荷下的疲劳可靠性问题。为同时考虑由截面平均温度和截面温差造成的疲劳损伤,提出了综合利用剩余强度和疲劳累积损伤模型的分析方法。首先根据疲劳累积损伤相等原理,将截面温差造成的多级扰动应力载荷作用频次等效为平均温度下的常幅应力载荷作用次数,从而将两者产生的热应力载荷统一为一常幅载荷,再利用剩余强度模型基于动态应力-强度干涉理论对疲劳可靠度进行分析,得到了结构在综合考虑两种热疲劳状态下的动态可靠度。本方法可避免直接利用疲劳累积损伤理论临界损伤值难以确定的问题,且能体现金属疲劳损伤的真实情况。最后以哈勃望远镜为例,分析了其主梁随疲劳热载荷循环作用下的动态可靠度,得出了一些有意义的结论。     

Estimation of Fatigue Limits from Temperature Data Measured by IR Thermography

To determine the fatigue limits of materials, fatigue testing, which is time-consuming and very expensive, is required. In order to overcome these shortcomings, estimating methods for fatigue limits based on temperature changes measured by IR camera have been proposed, and research and development of such methods have been widely conducted. In the current paper, a non-lock-in type, inexpensive IR camera was used for rotational bending fatigue testing to estimate the fatigue limit from temperature changes independent from loading signals. The results indicated that it is possible to estimate the fatigue limit from the time-temperature change curves measured under various stress conditions and converted stress amplitude-temperature change curves. The estimated results were sufficiently accurate and thus we confirmed that it is promising to estimate the fatigue limit by a non-lock-in type, inexpensive IR camera. The inflection point of a stress amplitude-temperature change curve can be determined by approximating a curve by two straight lines and finding the combination of the lines for which the sum of the residuals between the curve and the lines is the smallest. Although the temperature changes depended on the loading history (the number of loading cycles), the results of fatigue limit estimation changed little. Therefore, the proposed method is practically accurate as a simple estimation method. We also measured the behavior of stress-stroke for each loading history (the number of loading cycles) in tension-compression fatigue testing and confirmed that temperature changes during fatigue testing are associated with plastic strain energy.