疲劳分析

Stress Life Analysis,Lec 16-1,Stress-Life (S-N) Theory,Stress Life Analysis,Lec 16-2,Stress-Life (S-N) Theory,S-N方法并不严格区分裂纹产生和裂纹扩展，而是给出结构发生突然失效前的全寿命估计 The S-N approach estimates total life without distinguishing crack initiation from crack propagation 通常需要材料S-N曲线It usually requires that the test data relate to the geometry of the structure under assessment (structure S-N curves)材料S-N曲线可由光滑试样测试得到，并可根据真实结构如凹槽、表面处理条件等因素的影响对之进行修正。Material S-N curves can also be generated from smooth specimen test data; they are subsequently modified to reflect the effects of notches, surface conditions, etc. of the real structure,Stress Life Analysis,Lec 16-3,Some Definitions,应力幅值,平均应力,应力比R=,Stress Life Analysis,Lec 16-4,输入应力循环Input is cycles of STRESS即高周疲劳或名义应力疲劳法Also known as “High Cycle Fatigue” or “Nominal Stress Approach”尽管在临界区域的局部应力会是塑性的但名义应力循环必须为弹性应力(因此为高周疲劳）Nominal stress cycles must be elastic (hence high cycle) though local stresses at the critical location will be plastic在MSC/FATIGUE SN分析中有限元弹性计算结果可直接利用（无塑性修正） In MSC/FATIGUE SN analysis, elastic FE results are used directly (no plasticity correction),测试的名义应力Measured nominal stresses,临界位置的真实应力Actual Stress at Critical location,SN Analysis,Stress Life Analysis,Lec 16-5,S-N Curve,Stress Life Analysis,Lec 16-6,沃勒疲劳实验机Wohlers Railway Component Test Rig (1852 to 1870),Stress Life Analysis,Lec 16-7,Some of Wohlers datafor rotating bending tests,应力幅值,光滑试样,缺口试样,Stress Life Analysis,Lec 16-8,S-N Approach,S-N方法用名义应力（弹性范围）作为疲劳载荷The S-N approach uses the (assumed elastic) nominal stress range (S) as a measure of the severity of fatigue loading疲劳寿命基于实验数据Life to failure (two pieces) is recorded in experiments通过测试不同应力水平描绘S-N曲线Tests at several levels of stress range characterise the S-N curve 该曲线可基于光滑试样、零部件或结构Such a curve can be derived for smooth specimens, for individual components, for sub-assemblies, or for complete structures,Stress Life Analysis,Lec 16-9,S-N Approach,S-N方法用途包括：The uses of the S-N approach include: 破坏概率（设计准则）establishing a well defined fatigue curve for the purposes of design 设计寿命下的疲劳强度determination of a fatigue strength at a specified life通过改变材料或表面处理提高抗疲劳能力demonstration of improved fatigue resistance from a material or surface treatment找出与加工相适应的材料acceptance of material for manufacturing purposes解决服役期失效问题answering questions posed by a service failure,Stress Life Analysis,Lec 16-10,S-N Curves,Stress Life Analysis,Lec 16-11,S-N Curves,结构钢和钛合金钢的S-N曲线水平区段的最大应力为疲劳极限应力低于该值不会发生应力破坏Steels tested with constant amplitude loading normally exhibit a fatigue limit - a stress below which no fatigue damage appears to occur.疲劳极限与裂纹萌生相关联。它在大负荷或腐蚀介质等情况下会降低。The fatigue limit is associated with the difficulty a crack has in getting past the first grain boundary, or dominant microstructural barrier. It can be reduced or eliminated after e.g. a few large loads, or in corrosive environment, etc.铝合金无明确的水平区段Aluminum alloys do not seem to exhibit no such limit,Stress Life Analysis,Material S-N Curves,Log(Stress),Log(Life),Steel or Ti,Al alloyor steel in seawater,铝合金或钢在海水中,Stress Life Analysis,Lec 16-13,S-N曲线的离散性Scatter in S-N curves,Stress Life Analysis,Lec 16-14,部件S-N曲线Component S-N curves,在某些情形如结构或特征存在点焊等需要修正材料S-N曲线（但通常是较困难的）For some components or features, especially structural joints such as welds, there are so many things modifying the behaviour of the base material that there is little point in applying corrections to a material S-N curve在此情形下最好采用适用于该部件或特征的名义应力-寿命曲线In cases like this it is best to use a nominal stress-life curve which applies particularly to that component or feature,Stress Life Analysis,部件S-N曲线可以使用远端的名义应力进行疲劳分析Component S-N Curves may use remote or nominal stress,P,P,Nominal Stress,P,_,A,A,CLASS F WELD DETAIL (BS7608),Stress Life Analysis,Lec 16-16,BS7608焊接件的S-N曲线BS7608 Weld S-N Curves,静应力强度,清洁空气下，常幅值载荷的情况,不同幅值载荷作用下的疲劳曲线,Stress Life Analysis,Lec 16-17,S-N Method - Similitude,The life of this . . . . . . . . . . . . . . . . is the same as the life of this . . . . .if both are subject to the same nominal stress,如果他们承受相同的名义应力，那么他们的疲劳寿命一致。,Stress Life Analysis,Lec 16-18,S-N方法假定零件或部件的寿命在同一名义应力下与测试试样一致The S-N method assumes that the life of a component or structure is the same as that of a laboratory test specimen if both are subject to the same nominal stresses.如果在结构中存在与实验条件不一致，需要进行修正（如平均应力、环境、表面处理等因素）If the conditions in the test are different to those in the structure, similitude breaks down, and we need to make corrections for factors such as mean stress, environment, surface finish, etc.,S-N Method - Similitude,Stress Life Analysis,Lec 16-19,对变幅载荷的处理-迈因纳线性累积损伤法则和雨流记数Handling Variable Amplitude Loads - Miners Rule and Rainflow Counting,Stress Life Analysis,Lec 16-20,名义应力有限寿命设计法是一种较早使用的有限寿命设计法，它是无限寿命设计法的直接发展，两者的基本设计参数都是名义应力。其设计思想也大体相似，都是从材料的S-N曲线出发，再考虑各种影响因素，得到零件的S-N曲线，并根据零件的S-N曲线进行疲劳设计。 所不同的是，无限寿命设计法使用的是S-N曲线的右段-水平部分，亦即疲劳极限；而有限寿命设计法使用的是S-N曲线的左段-斜线部分，亦即有限寿命部分。而有限寿命设计的设计应力一般都高于疲劳极限，这时就不能只考虑最高应力，而需要按照一定的累积损伤理论估算总的疲劳损伤。,名义应力有限寿命设计,Stress Life Analysis,Lec 16-21,累积损伤是有限寿命设计的核心问题。最早进行疲劳累积损伤研究的学者是Palmgren（帕尔姆格伦），他于1924年在估算滚动轴承寿命时，假设损伤累积与转动次数成线性关系，首先提出了疲劳损伤积累是线性的假设。其后，M.A. Miner（迈因纳）于1945年又将此理论公式化，形成了著名的Palmgren- Miner线性累积损伤法则。 但以后的研究发现，由于Miner法则没有考虑到加载顺序对疲劳寿命的影响，因此它估算出的疲劳寿命与实际寿命有较大的出入。于是许多学者又提出了一些新的累积损伤理论，其中比较著名的有Corten-Dolan理论与双线性理论。,疲劳累积损伤,Stress Life Analysis,Lec 16-22,Miners Rule - Block Loading,迈因纳法则假设：试样所能吸收能量的极限值的到达导致了疲劳破坏。吸收的能量与循环数间存在正比关系（某一循环数时吸收的能量与能量的极限值的比值等于该循环数与总循环数的比值）。各应力水平下的循环数与寿命的比值和为1吸收的能量达到极限。,Miners rule assigns a “damage” of 1/Nf to each cycle where Nf is the number of cycles to failure at that load level (determined from an S-N curve)Failure is predicted to occur when the total damage reaches a value of 1. If total damage D 1 life is predicted to be 1/D repeats,Nfi:不同应力水平下的寿命；Ni:不同应力下的循环次数。,Stress Life Analysis,Lec 16-23,Variable Amplitude Loads- Estimating Lifetime -,Stress Life Analysis,Lec 16-24,Stress or Strain Cycles:,Time History,Peak Valley Extraction,Rainflow Cycle Counting,Require Cycle Range & Mean,What Drives the Fatigue Crack?,Stress Life Analysis,Lec 16-25,计数法,Stress Life Analysis,Lec 16-26,Rainflow Cycle Counting,Stress Life Analysis,Lec 16-27,Rainflow Cycle Counting,样本记录犹如一系列屋面，雨水顺着屋面往下流，故称为雨流法。The story goes Matsuishi and Endo got the idea for the method while watching rain water cascading down a pagoda roof.雨流法有下列规则：（）雨流在试验记录的起点和依此在每一个峰值的内边开始，亦即从1，2，3等尖点开始。（）雨流在流到峰值处（即屋檐）竖直下滴，一直流到对面有一个比开始时最大值（或最小值）更正的最大值（或更负的最小值）为止。（）当雨流遇到来自上面屋顶流下的雨时，就停止流动。（i）取出所有的全循环，并记录下各自的变程和均值.Basic rules: rain flows down from each turning point and continues until either:it is interrupted by flow from above, or it reaches a turning point which is larger that the one it started from and in the same senseGood way of representing cycles is Rainflow Cycle Count Matrix,Stress Life Analysis,Lec 16-28,Stress Life Analysis,Lec 16-29,Stress Life Analysis,Lec 16-30,Cycle Count Matrix,Stress Life Analysis,Lec 16-31,Rainflow Counting and Stress/Strain Space,用雨流法判别滞回环,Stress Life Analysis,Lec 16-32,材料在循环载荷下受“材料记忆特性”影响（它们有保持记忆先前达到的最大应力应变率的能力）Materials under cyclic loading exhibit “material memory” effect (they “remember” the largest previously reached stress-strain state)单向载荷下的应力应变曲线在交变循环载荷下会存在滞回环What is stress-strain curve in monotonic loading is hysteresis loop in cyclic loading雨流循环计数法可鉴别出滞回环Rainflow counting identifies closed hysteresis loops as cyclesSome cycles stand within the largest hysteresis loop and some hang; this depends on cycle sequence,Rainflow Counting and Stress/Strain Space,Stress Life Analysis,Lec 16-33,Range,Mean,Material Life Curve,Life,damage,d,Accumulate,%,5,.,0,60000,300,=,=,300 Cycles,100 MPa,=,i,f,i,N,N,Damage,Damage Counting with Miner,Stress Life Analysis,Lec 16-34,Time History,Peak Valley Extraction,Rainflow Cycle Counting,Damage Counting,Damage Histogram,LIFE,Analysis Route - An Overview,Loose FrequencyInformation,Loose SequenceInformation,Life,Stress Life Analysis,Lec 16-35,Influences on Fatigue Life,Stress Life Analysis,Lec 16-36,Factors Influencing Fatigue Life,平均应力Mean stress,Stress Life Analysis,Lec 16-37,Mean Stresses,Stress Life Analysis,Lec 16-38,应力比R = smin/smax Stress ratio: R = smin/smax大部分疲劳测试是在R = -1（全 对称循环载荷）下 Most fatigue tests are conducted at R = -1 (fully reversed loading). 如果在其他R值下须对S-N曲线修正If we have cycles with other R values we should make corrections to the stress range in order to be able to compare the cycles to the S-N curve determined at R=-1.Note: compressive mean stresses do not influence fatigue life.,Mean Stresses,Stress Life Analysis,Lec 16-39,常用的平均应力修正有古德曼与戈贝尔法Most popular mean stress corrections are Goodman and Gerber methods. 真实测试值位于两者之间，古德曼法偏于保守Real test data tend to lie between the two, with the Goodman method being more conservative (i.e. safer).,Mean Stress Corrections,Stress Life Analysis,Correcting for the Effect of Mean Stress,Goodman methodGerber method,2,疲劳极限振幅：sa=(s max- s min)/2,平均应力：sm=(s max+ s min)/2,强度极限：sb,s-1：对称循环下的材料疲劳极限；即对称弯曲疲劳极限应力幅。,Stress Life Analysis,Lec 16-41,平均应力修正Mean Stress Corrections,（海夫图）Haigh Diagram,sa,sm,产生疲劳破坏的应力水平,不产生疲劳破坏的应力水平,Stress Life Analysis,Lec 16-42,平均应力修正Mean Stress Corrections,1935年的Soderberg（索特倍尔格）直线：sa= s-1 （ 1 - sm/ ss ） ss：屈服极限,Stress Life Analysis,Lec 16-43,Factors Influencing Fatigue Life,平均应力Mean stress,尺寸效应Component size,Stress Life Analysis,Lec 16-44,Component Size,试样和零件的尺寸对其疲劳强度影响很大。一般说来，零件与试件的尺寸增大时疲劳强度降低。Small laboratory specimens and large engineering structures,Stress Life Analysis,Lec 16-45,Factors Influencing Fatigue Life,平均应力Mean stress 尺寸效应Component size,载荷类型Type of loading,Stress Life Analysis,Lec 16-46,Type of Loading,Problem: 数据来自扭转弯曲测试Data from rotating bend tests 结构表现为弯曲或扭转Structure sees tension or torsion,Stress Life Analysis,Lec 16-47,Factors Influencing Fatigue Life,缺口与不连续形状Notches and discontinuities,载荷类型Type of loading,平均应力Mean stress 尺寸效应Component size,Stress Life Analysis,Lec 16-48,Notches,Kt:理论应力集中系数，它表示在缺口或其它应力集中处的局部应力与名义应力的比值。Kt=st /sn式中：,st 应力集中处的最大局部应力sn 有应力集中截面的名义应力,Stress Life Analysis,Lec 16-49,降低零件寿命另一因素是缺口或应力集中区域Another factor that will reduce the life of a component is a notch or stress concentration.通常，除非是高强度材料，零件的疲劳极限并非随Kt （理论应力集中系数）降低想象中那样大；即应力集中使零件疲劳强度降低的倍数和它使零件应力提高的倍数并不相同。Usually, unless the metal is of very high strength, the fatigue limit of the component is not reduced by as much as you might expect from the Kt factor. Kt and Kf （疲劳缺口系数）之不同在于材料对缺口的敏感度（一般： Kf Kt ）The difference between Kt and Kf is due to the notch sensitivity of the material, which is greatest for high strength metals.,Notches,Stress Life Analysis,Lec 16-50,Dealing with Stress Concentrations,Measured nominal stress = S,Actual Stress at Critical locations = S . Kt,不太可能在临界区域贴应变片It is seldom possible to stick the strain gauges at the critical location.实际操作中常将应变片放于靠近临界区域处，用应力修正因子 Kt得到临界值。 In practice put the strain gauges close to the critical location and use a stress correction factor Kt to scale them up to the critical value.,Stress Life Analysis,Lec 16-51,Two Ways of Using Kt (SN Analysis),乘上Kt. 得到新的时间历程Calculate new time history by multiplying the original by Kt.对大的时间历程需花很长时间This appears the easiest but could take a long time to compute with large time history files.,降低疲劳寿命曲线Reduce the fatigue life curve.利用疲劳缺口敏感系数Kf. This uses a value called the fatigue reduction factor Kf.Kf 表征Kt 的功能，是材料对缺口的敏感性。Kf is a function of Kt and a materials susceptibility to notches.保守地Kf = Kt Conservatively take Kf = Kt,修改时间历程Modify the time history,修改疲劳寿命曲线Modify the Fatigue Life Curve,Stress Life Analysis,Lec 16-52,Effect of Stress Concentration in Fatigue,应力集中降低疲劳强度，由疲劳强度缺口系数Kf表示。精确的 Kf 只能通过长寿命测试并由下式得到：In fatigue, the effect of a stress concentrating notch is to reduce the fatigue stress at a given life. This is defined as the “Fatigue Strength Reduction Factor” and is given the symbol Kf . Strictly, Kf can only be obtained from long life fatigue tests and is a ratio: Un-notched fatigue strengthKf = - Fatigue strength for the notchIt is dependant on material as well as local geometry and is generally less than Kt .,Stress Life Analysis,Lec 16-53,Relationship between Kf and Kt,Kt 只依赖几何相对较易获得而Kf 还依赖材料，里理论上是所有可能的综合。可否从Kt 中获得Kf ?(敏感系数法）。Kt depends on geometry only and is relatively easy to obtain but Kf depends on material as well, and in theory, should be measured for all possible combinations of both. Can we derive Kf from Kt ? 疲劳缺口敏感系数(q)是材料在交变载荷下对应力集中敏感性的一种度量。First, we define the parameter, q, the notch sensitivity factor as:q = Kf - 1-Kt - 1对疲劳缺口不敏感的材料：Kf =1 and q=0.对疲劳缺口极为敏感的材料： Kf = Kt and q=1.,Stress Life Analysis,Lec 16-54,疲劳缺口敏感系数首先取决于材料性质。一般来说：材料的强度极限sb提高时，q增大；而晶粒度和材料性质的不均匀性增大时q减小。不均匀性使q减小的原因，是因为材料性质的不均匀性相当于内在的应力集中，在没有外加的应力集中时它已经在起作用，因此减小了材料对外加应力集中的敏感性。疲劳缺口敏感系数除取决于材料的性质以外，还与缺口的曲率半径有关，因此q并不是材料常数。,Relationship between Kf and Kt,Stress Life Analysis,Lec 16-55,Kf = 1 + ( Kt - 1 ) / ( 1 + a / r ),Relationship between Kf and Kt,根据经验公式，有:（Peterson公式）q = 1 / ( 1 + a / r )r:缺口半径；a:材料常数，与材料的强度极限sb有关。a = 0.0254 ( 2079 / sb) 1.8 单位：a: mm sb :MpaCombining gives an EMPIRICAL rule for Kf from Kt:,Stress Life Analysis,Lec 16-56,1E3,1E4,1E5,1E6,1E7,1E8,200,400,600,800,1000,SMOOTH,Kt=3, Kf=2.67,Cross Plot of Data : KFEFFECT,NOTCHED,UNNOTCHED,Life(Cycles),Amplitude(MPa),The Effect of Kt and Kf on Fatigue Life,Stress Life Analysis,Lec 16-57,缺口主要对长寿命影响大The notch does not have such a large effect at short lives as it does at long. 通常在循环1000次采用Kf This is often dealt with by having a separate Kf factor at 1000 cycles.,The Effect of Kt and Kf on Fatigue Life,Stress Life Analysis,Effect of Notch Factor,1000 cycles,Transition Life,unnotched,notched,Stress,Life,Kf,Kf,Stress Life Analysis,Curve for Estimation of Kf (From Juvinall),Stress Life Analysis,Lec 16-60,Factors Influencing Fatigue Life,表面处理及粗糙度Surface treatment & finish,平均应力Mean stress 尺寸效应Component size,载荷类型Type of loading,缺口与不连续形状Notches and discontinuities,Stress Life Analysis,Lec 16-61,Surface Treatment & Finish,疲劳裂纹通常起源于表面，因此表面条件对零件寿命有大的影响Fatigue cracks usually start at the surface, therefore the condition of the surface can have a large impact on the life of a component.表面越光滑，疲劳裂纹的萌生时间越长The smoother the surface, the longer it takes to initiate a fatigue crack.表面残余应力也会影响裂纹萌生率。残余压应力在高循环载荷情况下会延迟裂纹萌生。表面处理用来在表面产生残余应力Residual stresses in the surface can also affect the rate of initiation. Residual compression will delay the crack initiation in high cycle load cases. Surface treatments are used to induce residual surface stresses.,Stress Life Analysis,Lec 16-62,切削对疲劳强度有影响的因数,Stress Life Analysis,Lec 16-63,Dealing with Surface Effects,增加表面的残余压应力可以使疲劳曲线向上翘，它对提高高周、低应力的疲劳寿命特别有利；降低表面的压应力会相应地使疲劳曲线向下降。,Stress Life Analysis,Lec 16-64,Surface Finish,Note: the curves are for steels only.,Stress Life Analysis,Lec 16-65,上图所示为典型的不同表面光洁度下疲劳寿命曲线The effect of surface finish is typically obtained from curves such as on the previous slide. 疲劳强度换算系数与表面加工因数及钢强度有关The strength reduction factor is related to the surface finish factor and the strength of the steel. 某些曲线如“良好加工”只是定性的表面状态Sometimes the curves are for qualitative finishes such as “good machined”.表面粗糙度的影响计算是在应力抗力或疲劳极限上增加一个换算系数The effect of surface roughness is typically accounted for by applying a reduction factor to the stress at the endurance or fatigue limit. 在log-log 图表中，疲劳寿命曲线的斜度需要调整，在1000次循环处无影响。On a log-log plot, the slope of the stress life curve is adjusted, with the stress at 1000 cycles being unaffected.,Surface Finish,Stress Life Analysis,Correction for Surface Finish,1000 cycles,Transition Life,polished,rough,Stress,Life,Stress Life Analysis,Lec 16-67,The Effect of Residual Compression,Tension,Compression,Tension,Compression,Tension,Compression,表面压应力Surface CompressionStress,振荡弯曲应力Oscillating bendingStress,结果表面不存在拉应力，裂纹不萌生Resulting surface stress never goes into tension therefore surface crack doesnt initiate,+,=,该情况发生在高循环下表面应力不足以超过残余预压应力This effect only works for high cycle cases where the applied surface stress is insufficient to overcome the residual pre-compression.,Stress Life Analysis,Lec 16-68,How Can We Get Pre-Compression?,喷丸强化Shot PeeningFire ball bearings at the surface to induce pre-compression冷轧滚压Cold RollingRoll the component surface to induce pre-compression in the surface渗氮NitridingHeat up component in an ammonia environment. The component expands and Nitrates from the gas react with the metal. The component contracts on cooling and is compressed.,Stress Life Analysis,Lec 16-69,Stress-Life in MSC/FATIGUE,特点Features弹性应力Elastic Stresses雨流循环计数 Rainflow Cycle Counting平均应力修正Mean Stress Correction焊