The Mesh-Insensitive Structural Stress Methodfor Fatigue Evaluation of Welded Structures焊接结构疲劳评估的网格不敏感结构应力方法Dr. Pingsha Dong 董平沙董平沙 博士博士Professor and Northrop Grumman Endowed Chair教授 诺斯普 格鲁门荣誉主席Director, Center for Advanced Marine Structures and Fabrication (CAM-SF)先进船舶结构与工艺中心主任School of Naval Architecture and Marine Engineering海洋结构与船舶工程学院The University of New Orleans新奥尔良大学Training Course 培训教程pdonguno.edu2006-2009 Pingsha DongAll Rights Reserved目录目录焊接疲劳基本l相关术语和定义l材料性能的影响l残余应力的影响l几何不连续性的影响l传统方法描述结构应力方法（I）l结构应力定义与数值实现l焊缝的表示方法l与其它方法（如ASME，IIW等）的比较和示例l结构应力的度量方法与确认结构应力方法（II）l一般的结构应力计算过程l边界细节的处理l计算实例l多轴结构应力状态的特征l点焊l激光焊l演示/工作流程结构应力后处理器试用版主S-N曲线方法l基于K的结构应力求解技巧与验证l双态裂纹生长模型与验证l等效结构应力幅参数与验证基于结构应力的寿命预测过程l失效、焊线定义、焊缝表示方法等l疲劳测试的含义l寿命预测实例其它应用l焊喉开裂l多轴疲劳l低周疲劳与l热疲劳l电子封装中的焊料疲劳8121631475763717587103115118130135140144158165174185216226234249254268282289Major Awards and Recognitions RecentlyReceived 最近获得的主要奖励与荣誉最近获得的主要奖励与荣誉IIW 2008 Paton PrizeSNAME 2007 Elmer L Hann AwardR&D Magazines R&D 100 Award (2006)TIME Magazine 2005 Math InnovatorsAviation Week & Space Technology: Aerospace 2004 Laurels AwardSAE 2004 Weld Challenge: Best Life Prediction WinnerAWS 2004 R.D. Thomas AwardSAE 2003 Henry Ford II Distinguished Award for Excellence in Automotive EngineeringASME 2002 G.E.O. Widera Literature Award, An Overview of Advanced Weld ModelingCapabilities: Fusion Welding先进焊接建模能力概览：熔化焊An Overview of Advanced Weld ModelingCapabilities: Solid Joining先进焊接建模能力概览：固态连接Fatigue of Weldments: Some Fundamentals焊件疲劳：基本知识Some relevant terminologies and definitions 一些相关术语和定义Whats special about weldments?焊件有哪些特性、 Stress concentration 应力集中 Material properties 材料属性 Residual stresses 残余应力 What decades of research say? 近几十年的研究对此的描述 Limitations of conventional fatigue design methods传统疲劳设计方法的局限 What constitutes a good fatigue parameter?哪些物理量构成好的疲劳参数Terminologies Describing A Typical Welded Joint描述一个典型焊接接头的术语描述一个典型焊接接头的术语Material zones in a joint接头材料区域lBase metal母材（BM）lHeat-affected zonel热影响区（HAZ）lWeld metall焊材（WM）Geometric locations几何位置lWeld toel焊趾lWeld throat/depthl焊喉/焊深lWeld rootl焊根Relevant Fatigue Terminologies andRelevant Fatigue Terminologies andDefinitions Definitions I I 相关疲劳术语和定义相关疲劳术语和定义-I-ICyclic loading循环载荷Nominal stress at a failurelocation, e.g., weld crackinto base plate失效位置的名义应力，例如，侵入母材的焊接裂纹处lF/（Wt）lMc/lNominal stress range名义应力变化范围lF /（Wt）lMc/lRelevant Fatigue Terminologies andRelevant Fatigue Terminologies andDefinitions Definitions I II I相关疲劳术语和定义相关疲劳术语和定义-II-IIMaximum stress最大应力Minimum stress最小应力Stress range应力变化范围（ ）Mean stress平均应力What s Special about Welded Joints?焊接焊接接头的特殊之处接头的特殊之处Property Heterogeneity材料性质的多样性(母材BM,焊材 WM, 热影响区HAZ)Residual Stresses残余应力Geometric Discontinuities几何不连续性Property Variation in Welded Joints焊接接焊接接头材料性质的变化头材料性质的变化Process-induced induced property heterogeneity焊接过程导致的材料性质的多样性焊接过程导致的材料性质的多样性WM strength mismatch by design焊材强度设计的不匹配焊材强度设计的不匹配Hardenable Steel可硬化的钢材可硬化的钢材BM/WM/HAZ Property Has Little Effect onBM/WM/HAZ Property Has Little Effect on Fatigue of Welded JointsFatigue of Welded Joints BM/WM/HAZBM/WM/HAZ的的性质对焊接接头疲劳影响很小对焊接接头疲劳影响很小Comparison of Fatigue Strength between Plain Metal, Notch Bar, and Welded Specimens普通金属普通金属、带缺口金属条与焊接试件之间疲劳、带缺口金属条与焊接试件之间疲劳强度的比较强度的比较Figure 2: Influence of tensile strength on the fatigue strength图图2： 抗拉强度对疲劳强度的影响抗拉强度对疲劳强度的影响BM Strengths vs. Fatigue Life (Lewis, BM Strengths vs. Fatigue Life (Lewis, 2001)2001)母材强度与疲劳寿命母材强度与疲劳寿命 (Lewis, 2001)(Lewis, 2001)TRIP v CMn350 Unwelded Steel TRIP vs CMn350 and Mild Steel Welded Steel 未焊接钢材未焊接钢材 焊接钢材焊接钢材Weld Residual Stress Effects on FatiguePerformance: Weld Sequencing焊接残余应力对疲劳性能的影响焊接顺序Pass Sequence Effects on TransverseResidual Stresses焊道顺序对横向残余应力的影响Travel Speed (Linear Heat Input) Effects Transverse Residual Stresses焊接速度(线性热输入)对横向残余应力的影响Restraint Effects on Transverse ResidaulStresses约束对横向残余应力的影响High Restraint Low Restraint强约束 弱约束Residual Stress Distributions in Some TypicalJoint Types一些典型焊接接头的残余应力分布一些典型焊接接头的残余应力分布Then, How to Treat Residual Stress Effects inFatigue Design in Practice?在实际疲劳设计中应如何处理在实际疲劳设计中应如何处理残余应力的影响？残余应力的影响？Conduct controlled fatigue testing采用控制疲劳测试lEffects on applied mean stressesl对施加的平均应力的影响lAs-welded versus stress-relievedl焊态与应力释放Test specimens must contain representative residualstress state in structures试件必须包含结构中主要的残余应力状态lSpecimen sizing试件尺寸lResidual stress induced tri-axiality versus “shake-down”Effects残余应力引起的三轴与失稳（？）的影响Model or Specimen Size Must Be SufficientlyLarge to Quantify Residual Stress Effects模型或者试件模型或者试件的尺寸应该足够大以量化残余应力的影响的尺寸应该足够大以量化残余应力的影响A Butt Joint对接接头Plate joints: w/t=6平板接头平板接头 w/t=6Residual Stress and Joint Constraint Effectson Local Stress/Strain Behavior残余应力和接头约束对局部应力/应变行为的影响Test Specimen Size Requirements forContaining Weld Residual Stress Effects试件尺寸要求包含焊接残余应力效应Axial Residual Stress轴向残余应力轴向残余应力Tube girth weld length: 2.5 sqrt(rt)圆管环焊缝长度: 2.5 sqrt(rt)Tubular Girth Weld管状环焊缝Residual Stress Effects on Fatigue Behavior ofWelded Joints - Experimental Evidence残余应力对焊接残余应力对焊接接头疲劳行为的影响接头疲劳行为的影响试验验证试验验证Stress ratio is NOT important应力比并不重要应力比并不重要Stress range is important应力幅是关键因素应力幅是关键因素Compressive cyclic loading can be equally damaging压缩循环载荷同样可以引起材料破坏压缩循环载荷同样可以引起材料破坏Recent S-N Data from HHI Mean StressEffects on S-N Behavior HHI的最新S-N数据平均应力对S-N行为的影响Comparison of Fatigue Test Data with DifferentStress Ratio or Mean Stress Effects: As-Welded在不同应力比或平均应力效应下疲劳测试数据的比较焊态Comparison of Fatigue Test Data with Different Stress Ratio or Mean Stress Effects: As As-Welded vs Stress-Relieved在不同应力比或平均应力效应下疲劳测试数据的比较焊态与应力释放Stress Relief Post-Weld Heat Treatment(PWHT)焊后热处理(PWHT)的应力释放Uniform PWHT: Certain magnitude of residual stresses still retained in ideal PWHT整体热处理：理想的热处理下仍然存整体热处理：理想的热处理下仍然存在一定的残余应力在一定的残余应力Other treatments such as local PWHT其它处理方式比如局部热处理其它处理方式比如局部热处理lhigher residual stresses retained than uniform PWHT比比整体热处理方式存在更多的残余整体热处理方式存在更多的残余应力应力lhigher residual stresses than as-welded conditions maylresult可能比焊态条件下的残余应可能比焊态条件下的残余应力水平更高力水平更高Observations Residual Stress Effects onFatigue小结：残余应力对疲劳的影响Adequate specimen size is important in fatigue testing to retain representative residual stress states in actual structures为包含实际结构中主要的的残余应力状态，要求进行疲劳测试时要保证足够的试件尺寸Perhaps, the most significant effects of residual stresses in welded joints:焊接接头中残余应力最重要的影响：（？）lS-N data not sensitive to applied mean load or mean stress S-N数据对施加的平均载荷或平均应力不敏感lStress range serves as a good parameter for implicitly incorporating residual stress effects 应力变化范围是一个包含残余应力效应的很好的参数Without adequate control of welding/assembly procedures, any attempts to incorporate residual stresses in fatigue assessment are futile对焊接/组装过程没有足够的控制，任何在疲劳评估中考虑残余应力都没有效果Stress relieved conditions: the improvement in fatigue is not Significant 应力松弛条件：对疲劳性能的改善不明显Global Geometric Discontinuities整体几何不连续性GMA weldsGMA焊缝焊缝RSW or plug weldRSW或塞焊或塞焊Laser welds激光焊激光焊Global versus Local Discontinuities in Welded Joints焊接接头中的整体和局部不连续性Effects of Geometric Discontinuities on FatigueBehavior in Welded Joints: Unique S-N Curve Slope几何不连续性对焊接接头疲劳行为的影响唯一的S-N曲线斜率Unique features for weldments: 焊接件的特性焊接件的特性Different slope from smooth barspecimens光滑试件具有不同的斜率光滑试件具有不同的斜率Unique slope of about 3唯一的大约为唯一的大约为3斜率斜率Different JointGeometries不同的接头几何不同的接头几何Effects of Global Geometric Discontinuities:Well-Defined Failure Modes in Welded Joints整体几何不连续性的影响焊接接头合适的失效模式Dominant Modes:主要模式主要模式lMode (A)l模式（模式（A）lMode (B )l模式（模式（B）Mode (A)模式（模式（A）lDesirablel需要的需要的lEasier to analyzel更易于分析更易于分析Mode (B)模式（模式（B）lLeast desirablel很少需要很少需要lLarge data scatterl大量数据呈离散性大量数据呈离散性Joint geometr and loading modedetermines which mode dominates接头几何和载荷模式决定哪种失效模式接头几何和载荷模式决定哪种失效模式为主为主Joint Geometry Effects on Nominal Stress Rangeversus Cycle to Failure (Weld Toe Failure)接头几何对名义应力变化范围与失效(焊趾失效)循环次数的影响Stress definition: Nominal stress range (F/A)应力定义：名义应力副应力定义：名义应力副(F/A)Thickness Effects厚度的影响Loading Mode Effects Tension versusBending载荷模式的影响拉伸与弯曲Implication: Stress Concentration is the Most ImportantParameter Governing Fatigue Life in Welded Joints推论：应力集中是决定焊接接头疲劳寿命的最重要的参数Dominated by geometric and loading conditions取决于几何和载荷取决于几何和载荷条件条件lJoint type/geometry接头类型接头类型/几何几何lLoading mode载荷模式载荷模式lThicknessl厚度厚度l(Weld size, etc)l(焊缝尺寸等焊缝尺寸等)Stress concentration determination: deceptively simple应力集中的确定：看起来简单应力集中的确定：看起来简单Notch Stress Determination缺口应力的确定“Kt” only well-defined for a given notch radius“Kf”只在给只在给定缺口半径时才有很好的定义定缺口半径时才有很好的定义lToo arbitrary to work in practice太随意以至于无法应太随意以至于无法应用用lToo small an element size to be practical太小的单元尺寸不太小的单元尺寸不切实际切实际Local notch geometry in welded joints: random in nature焊接接焊接接头中的局部缺口几何：本质上是随头中的局部缺口几何：本质上是随机的机的Notch Radius=?缺口半径缺口半径=?Stress Concentration Behavior at WeldedJoints焊接接头处的应力集中行为Difficulties:一些困难一些困难lSingularity at sharp notchl在尖锐缺口处奇异在尖锐缺口处奇异lArtificial radius: well, too artificiall人为定义的半径：太随意人为定义的半径：太随意Typical SCF determination methods典型的确定应力集中因子的方法典型的确定应力集中因子的方法lStrain gauge based measurementsl基于应变片的测量基于应变片的测量Gauge location/size?应变片位置应变片位置/尺寸尺寸Reference position?参考位置参考位置Finite element analysis有限元分析有限元分析lMesh-size sensitivel对单元尺寸敏感对单元尺寸敏感lElement type sensitivel对单元类型敏感对单元类型敏感How About Extrapolation to the Weld Toe Using Surface Stresses Hot Spot Stress (HSS) Methods?将表面应力外推到焊趾位置热点应力(HSS)方法e.g., an IIW recommended procedure例如，一种例如，一种IIW 推荐的方法推荐的方法(a concept used for offshore tubular Structures)一种用于船体管状结构的概念Severe element size/type sensitivity!严重的单元尺寸严重的单元尺寸/类型敏感性类型敏感性Surface Extrapolation Based HSS Method When Using Converged Mesh Plate Joints当使用收敛网格时基于HSS方法的表面应力外推板接头 S-N data from the six joint types can be grouped into at least four distinct S-N curves从六种接头类型得到的从六种接头类型得到的S-N数据至少可以归纳为四条不同的数据至少可以归纳为四条不同的S-N曲线曲线Detailed stress calculations:详细的应力计算：详细的应力计算：two distinct types of distributions两种不同的分布类型两种不同的分布类型SCF=?Linear Solid Element Models with Mesh Size 0.1t尺寸约为尺寸约为0.1t的线性实体单元模型的线性实体单元模型Difference in Surface Stress Gradientsbetween Tubular versus Plate Joints管接头和板接头之间表面应力梯度的区别Stress gradients:应力梯度：应力梯度：Tubular joints: more globall管接头：更具整体性管接头：更具整体性Plate joints: more localizedl板接头：更具局部性板接头：更具局部性Distance from Weld ToeSummary: Important Observations on FatigueBehavior in Welded Joints小结：焊接接头疲劳行为的重要结论Fatigue failures follow a few distinct failure modes, e.g., toe crack, throat crack, etc.疲劳失效遵从几种截然不同的模式，例如，焊趾裂纹，焊喉裂纹等疲劳失效遵从几种截然不同的模式，例如，焊趾裂纹，焊喉裂纹等BM/WM/HAZ properties are not important within a broad class of materials对这一类材料来说？，对这一类材料来说？，BM/WM/HAZ 材料属性是不重要的材料属性是不重要的Mean stress effects are not significant平均应力的影响不显著平均应力的影响不显著Presence of high residual stresses高残余应力的存在高残余应力的存在Stress range should be used应当使用应力变化范围应当使用应力变化范围S-N curves exhibit a distinct slope ( 1/3)S-N 曲线表现为一个唯一的斜率曲线表现为一个唯一的斜率( 1/3)lDominated by crack propagation决定于裂纹扩展决定于裂纹扩展Inherent crack-like discontinuities activated by global stress concentration characteristics at weldsl由整体应力集中导致的内在的类裂纹不连续性焊缝处的特性？由整体应力集中导致的内在的类裂纹不连续性焊缝处的特性？Stress concentration is most important 应力集中是最重要的应力集中是最重要的Local notch stress effects (e.g., weld bead, toe profile, under cuts, etc): random in nature and captured in S-N data 局部缺口应力效应局部缺口应力效应 (例如，焊道例如，焊道, 焊趾轮廓焊趾轮廓, 切割痕等切割痕等): 本质上是随本质上是随机的并且可以反映在机的并且可以反映在S-N数据中数据中A reliable method is needed for characterizing global stress concentration (overalljoint geometry effect)为反映整体应力集中的特性，需要一种值得信赖的方法为反映整体应力集中的特性，需要一种值得信赖的方法 (整体的接头几何效应整体的接头几何效应)Considerations for SCF Characterization对SCF特性的一些考虑Local stresses cannot be readily determined for most practicalapplications对于大多数的实际应用，局部应力并不容易得到 Singular behavior at a sharp notch尖锐缺口处的奇异性Random nature of weld toe/root local details for assuming a definite radius对于假定的一个半径值来说，焊趾/焊根处的局部细节本质上是随机的 Conceptually, there should exist a global stress parameter：理论上来说，应当存在一个整体应力参数： Dominated by overall joint geometry excluding the local effects排除局部效应，而决定于整体接头几何形状 Load mode, etc.载荷模式等The simplest global stress parameter: nominal stress definition perstrength of material, if applicable最简单的整体应力参数：如果适合的话，名义应力以材料强度来定义A Brief Overview of Conventional Stress Concentration Determination Methods传统的应力集中计算方法简介Global stress parameter based:整体应力参数基于Nominal stress名义应力Extrapolation based spot stress基于热点应力的外推Local notch stress parameter based基于局部缺口应力参数Classical Weld Classification Approach Basedon Joint Geometry 基于接头几何的传统焊缝分类方法 Also referred to as “weld category approach”, “cartoonapproach”, “fatigue design rules”(Gurney, 1967)也称为“焊缝分类方法”，“图表方法”，“疲劳设计准则”(Gurney, 1967) Nominal stress S-N curves (mean and -2 ) in log-logscale from fatigue tests:由疲劳测试得到的对数坐标中的名义应力S-N曲线(平均和-2) Different joint geometries不同的接头几何 Mostly applicable for weld toe failure mode大部分适用于焊趾失效模式 Limited considerations for weld throat failure modes很少考虑焊喉失效模式Weld Classification Approach: Mean S-N CurveBS 7608 of (Ref. Plate Thickness: 16mm)焊缝分类方法：BS 7608的平均S-N曲线（参考板厚：16mm）A total of 8 S-N curves provided based lab specimen tests实验室试件测试一共提供了8条S-N曲线 Fatigue evaluation procedure:疲劳计算过程 Determine which curve (“B”-“W”) is applicable to a joint of concern确定哪条曲线适合于这种接头 Calculate nominal stress (range)per strength of material由材料力学计算名义应力（变化范围） Calculate mean life directly fromthe S-N chart, if constant amplitude loading如果是等幅载荷，直接由S-N图计算平均寿命 Miners rule summation if variable amplitude loading如果是变幅载荷，根据Miner准则进行累积In Practice, A Family of Infinite S-N Curves is Needed,e.g., IIW s Fatigue Design Recommendations (2004)实际应用中，需要一族无限条实际应用中，需要一族无限条S-N曲线，例如，曲线，例如，IIW的疲劳设计建议（的疲劳设计建议（2004）FEA-Based Fatigue Design and Life Prediction基于有限元的疲劳设计与寿命预测基于有限元的疲劳设计与寿命预测Nominal stresses: difficult to extract in most cases名义应力：在大多数情况下难以提取 Cartoon-based S-N curve definitions: difficult to apply基于图表的S-N曲线的定义：难以应用 Solution?求解？ Almost all research has been focused on how to refinesurface extrapolation procedures几乎所有的研究都集中在如何完善表面外推过程上 The objectives:目标 Reduced the number of S-N curves needed for fatigue design for engineering structures减少对工程结构进行疲劳设计所需的S-N曲线的数量 Improve the mesh-sensitivity in HSS calculations在热点应力计算时改善网格敏感性Extrapolation-Based Hot Spot StressApproach Basic Definition and Assumptions基于外推法的热点应力方法基本定义与假定Developed in 70s for offshoretubular joints发展于70s船体结构的管接头 Used membrane + bendingdecomposition as an argument forexistence of such a stress definition使用膜力+弯曲分解作为这种应力定义存在的证明？ Recommends extrapolations using surface stress extrapolationwithout justifying the linkage建议使用without justifying the linkage表面应力外推方法进行外推？ Extrapolation positions should be outside of the region dominated by local notch stress外推位置应当在局部缺口应力控制区域之外Surface Extrapolation Based Hot Spot Stress Methods基于表面外推的热点应力方法 Also referred to as:也被称为 Hot spot structural stress热点结构应力 Structural stress结构应力 Geometric stress几何应力 More attractive in principle than nominal stress:从原理上比名义应力更吸引人 Applications where nominal stress cannot be defined应用于名义应力无法定义的地方 Potentially reduced the number of S-N curves needed潜在地减少了所需S-N曲线的数目 Adopted by various fatigue design codes: IIW Recommendations, AWSD1.1, API RP2A, BS 7608, Class Societies Fatigue Guidance,Eurocode, etc.被多种疲劳设计标准采用：IIW Recommendations, AWSD1.1, API RP2A, BS 7608, Class Societies Fatigue Guidance,Eurocode,等 Recent EN 13445, PD5500 etc for pressure vessel and pipingapplications最近在 EN 13445, PD5500 等压力容器与管道标准中得到应用Extrapolation Based HSS Approach (IIW,04)基于外推的热点应力方法(IIW,04)Notch Stress Methods缺口应力方法 Notch stress is ill-defined if assuming sharp notches如果是尖锐的缺口，缺口应力很难定义 Some researchers are investigating the use of notch stress with a fictitious notch radius in FE model一些研究人员正在研究有限元模型中假定缺口半径下的缺口应力的使用 Classical ASME fatigue procedure is by definition is a notch stress approach经典的ASME疲劳设计方法从定义来看是一种缺口应力方法 relying empirical methods to determine FSRF (Kf)确定FSRF(Kf)时依赖于经验方法 cant be directly and consistently used for FEA based fatigue design in general不能直接和一致地应用于一般的基于有限元方法的疲劳设计 Kt is not equal to KfKt不等于Kf Kf: joint type dependent and normalized w.r.t nominal stressesKf：依赖于接头类型和名义应力的正则化 Linearized “stress intensity” definitions in ASME are not the nominal stressesASME中线性化的“应力强度”的定义不是名义应力Kf is also Dependent Upon Cycles to Failure When Scaling from Smooth Bar Data 从光滑试样数据进行缩放时，Kf还要依赖于失效循环数ASME Fatigue Design Curve DefinitionASME疲劳设计曲线定义Used smooth bar mean S-N data使用光滑试样的平均S-N数据Displacement controlledtests位移控制测试 Expressed using either nominal strain orpseudo-elastic nominalstress amplitude使用名义应变或者伪弹性名义应力幅来表达Apply 2/20 rule应用2/20规则Nominal Stress Range Versus N Pressure Vesseland Pipe Weld Data versus ASME Fatigue Curves名义应力变化范围与N压力容器和管道焊接结构与ASME疲劳曲线In Summary: The Two Major Issues Must beResolved for Reliable FE-Based Fatigue Evaluation总之，为得到可信的基于有限元的疲劳评估结果，两个问题必须解决 What stress to use? Which S-N curve to use? 使用什么应力？使用什么应力？ 使用哪条使用哪条S-N曲线？曲线？What Constitutes a Good Stress-Based Fatigue Parameter?哪些物理量构成好的基于应力的疲劳参数 Necessary conditions必要条件 Consistency in calculation:计算一致性 Good mesh-insensitivity好的网格不敏感性 Ability to measure global stress concentration effects seen inTests 能够度量试验中捕捉到的整体应力集中效应 Sufficient conditions:充分条件 Effectiveness in S-N data correlation:S-N数据相关的有效性 Different joint geometries不同的接头几何 Different loading modes不同的载荷模式 Different plate thicknesses, etc不同的板厚，等 Robustness for practical applications实际应用的稳健性The Structural Stress Method Part I结构应力方法第一部分 Requirements for an effective fatigue parameter对有效的疲劳参数的要求 The new structural stress definition新的结构应力的定义 Mechanics basis力学基础 Equilibrium arguments平衡条件 SS determination procedures结构应力计算过程 Simple FEA-based procedures简单的基于有限元方法的过程 Measurement procedures测量过程 Validation by correlating S-N data 与S-N数据相关的证明 Similarities and differences between the SS and other global stress parameters结构应力与其它整体应力方法的异同Symmetry and anti-symmetry对称与反对称 Demo of manual SS calculation procedures using FE model使用有限元模型，手动计算结构应力的过程示例 Straight and curved lap fillet welds直线和曲线搭接焊缝 In-plane gusset attachments面内搭接附件 SS measurements and calculations from FE model基于有限元模型的结构应力度量与计算 Shear locking effects剪切锁死的影响Requirements for a FE Based Stress Parameter Definition for Fatigue Evaluation疲劳评估对基于有限元应力参数定义的要求 Consistency in stress determination:计算应力时的一致性 e.g., good mesh-insensitivity例如，良好的网格不敏感性 Effectiveness in S-N data correlation:与S-N数据相关的有效性 Robustness for practical applications实际应用的稳健性The Structural Stress Definition for a 2D Problem Traction Based2D问题的结构应力定义基于拉伸情况Structural Stress: Equilibrium Equivalent结构应力：平衡等效Notch Stress: Self-Equilibrating缺口应力：自平衡Traction-Based Structural Stress Definition in 3D3D问题基于拉伸的结构应力定义In general, three structural stress components exist corresponding to the linear representations of three traction components一般情况下，相应于三个拉伸分量的线性表示，存在三个结构应力分量 Normal法向 In-plane shear面内剪切 Transverse shear横向剪切Section A-A in a 2D Cross-Section Section A-A-C-C in a 3D Cross-Section2D横截面中的截面横截面中的截面A-A 3D横截面中的截面横截面中的截面A-A-C-C Equilibrium Considerations in Numerical Implementation在数值实现中考虑的平衡条件 Displacement based FE procedures:基于位移的有限元方法 Nodal forces and displacements are the most fundamental quantities节点力和位移是最基本的物理量 Equilibrium conditions are always guaranteed in terms of nodal forces at nodes, but not in terms of stresses以节点上的节点力表示的平衡条件总能得到保证，然而应力却不能保证 The equilibrium-equivalent structural stresses can be extracted using:平衡等效结构应力可以提取出来，通过使用： Balanced nodal forces from finite element output有限元输出的平衡节点力 The key step: “work equivalent” based transformation fromnodal force/moments to line force/moments关键步骤：基于“功等效”将节点力/弯矩转换为线力/弯矩Balanced Nodal Forces from Finite Element Solutions从有限元解获得的平衡的节点力 “GPFORCE” in NASTRANNASTRAN中的“GPFORCE” “NFORC” in ABAQUSABAQUS中的“NFORC” “NLOAD” in ANSYSANSYS中的“NLOAD” Property of these forces: equilibrium conditions with respect to each element and all elements together are exactly satisfied这些力的性质: 无论是对于每一个单元还是所有单元，平衡条件总能精确满足From Nodal Forces/Moments to SS Simple Calculation Method for Shell/Plate Models从节点力/弯矩到结构应力板壳模型的简单计算方法Extract nodal force/moment (M/F) w.r.t each element along a weld line沿着焊线对每一个单元提取节点力/弯矩（M/F）Obtain line force/moment (m/f) distribution and maintain equilibrium Structural stress can thenbe calculated在保证平衡条件的情况下，获得线力/弯矩（m/f）分布然后可以计算结构应力Equilibrium conditions between nodal forces and line forces节点力与线力之间的平衡关系Equilibrium conditions betweennodal moments and line moments节点弯矩与线弯矩的平衡关系Equilibrium-Based Transformation from Nodal Forces to Line Forces基于平衡的从节点力到线力的转换Structural Stress at Node i:节点 i 的结构应力A Simple Beam Bending Example: CalculateStructural Stresses at Section A-A一个简单的梁弯曲的例子：计算截面A-A的结构应力A simple beam bending example cited in many FE text book no weld!很多有限元教科书中引用的一个简单的梁弯曲的例子-无焊缝 Due to bending effects, element A-A sizes must be small, as required for conventional stress calculations由于弯曲效应，应该像传统应力计算的要求那样，单元尺寸一定要小SS=Nominal Stress结构应力=名义应力t=1mm, L=10mm, h=2mmNominal Stress (Beam Theory): 750MPa at node 2, -750MPa at node 5名义应力名义应力(梁理论梁理论): 节点节点2为为750MPa, 节点节点5为为-750MPaComparison of the Nodal Force Based StressCalculation versus FE Stress Output基于节点力的应力计算与有限元的应力输出之间的比较FE Stresses:有限元应力 118 MPa w.r.t element (2)相对于单元(2)的应力为118 MPa 235MPa averaged between (1) and (2)单元(1)与(2)的应力平均值为235 MPa Structural stress calculation:结构应力计算FE stress results will improve as mesh is being refined当网格细化后，有限元应力结果会有所改善Weld Representation Using Shell/Plate Element Model使用板壳单元模型时焊缝的表示方法Full penetration weld: two rows of plate elements with “triangle formation”全熔透焊缝：两排成 “三角形形态” 的板单元Partial penetration: one row of inclined elements部分熔透焊缝：一排倾斜单元An Example:一个例子:Partial Penetration Weld:部分熔透焊缝:SS Insensitivity to Both Element Size and Element Types Used结构应力对于所使用的单元尺寸和单元类型的不敏感性Steps for Manual Calculations of Equilibrium- Equivalent Structural Stresses手工计算平衡等效结构应力的步骤Identify a location of interest along a weld line确定沿着焊线的感兴趣的位置 Output all 6 DOF nodal forces/moments (in global x-y-z system) at nodes for theweld element containing the position在这个位置的焊缝单元的节点，输出包含所有6个自由度的节点力/弯矩(整体坐标系下) Rotate the 6 DOF nodal forces/moments to obtain Fy and Mx旋转6个自由度节点力/弯矩以获得Fy和Mx Calculate line forces/moments at each node, i.e., for a linear element,计算每一个节点的线力/弯矩，对于线性单元Calculate the structural stress as计算结构应力Transformation From Nodal Forces to LineForce/Moments 2D and Axisymmetric Solid Models从节点力到线力/弯矩的转换2D轴对称实体模型Transformation from nodal force to line force/moment is straight forward直接将节点力转换为线力/弯矩Stress output may be used to approximate line forces/moments应力输出可以用来近似线力/弯矩 Axisymmetric solid models轴对称实体模型 Nodal forces may be defined differently节点力定义方法可能不同 Typically，Fi=FFEA /(2ri)典型地，Fi=FFEA /(2ri)Similarities and Differences between the SS and ASME Definitions结构应力与ASME定义之间的异同 ASME linearization-based stress intensity definition:ASME基于线性化的应力强度的定义 Linearize all six stress components线性化所有6个应力分量 Note: only three of out of the six need tosatisfy equilibrium conditions 注意：只有6个之中的3个需要满足平衡条件p is only well determined with a notch radius只有缺口半径给定时，才能得到较准确的p Not applicable to shell/plate models对板壳单元模型不适用 Battelle structural stress method maybe interpreted as:Battelle结构应力方法可以解释为： “Linearization” applied to hypotheticalcrack face stresses (3 traction components)线性化应用于假想的裂纹面应力(三个拉伸分量) Equilibrium-equivalent to “cut” face traction conditions represented by FE-based stresses用基于有限元的应力表示的“切” 面拉伸力平衡与等效Comparison of SS HSS and ASME Methods结构应力、热点应力和ASME方法的比较Surface point value: HSS method表面点的取值：HSS方法Sampling stresses away from weldToe 取样应力点远离焊趾Assuming either linear or quadraticDistributions假定线性或二次分布Through-thickness stress measure厚度方向应力度量SS method: SS方法Nodal force based (equilibrium based)基于节点力（基于平衡条件）Stress integration based if fine elements are used (solid model only)如果使用精细单元(仅对实体模型)，则基于应力积分ASME Sec III method:ASME第III节方法Membrane and bending components can be the same as those from the SS procedure if linearizing only the traction components如果仅对拉伸分量线性化，膜分量和弯曲分量与SS方法得到的值相同Difficult to apply for 3D geometries难于应用在3D模型ASME Stress Intensity Results for the Weld Toe Notch Modeled as a Singularity (Osage, et al, 06)焊趾缺口作为一个奇点建模时ASME应力强度结果(Osage, et al, 06)ASME Stress Intensity Results for the Weld Toe Notch Modeled as a Singularity (Osage, et al, 06)焊趾缺口作为一个奇点建模时ASME应力强度结果(Osage, et al, 06)Calculation Procedures for 2D Solid Models2D实体模型计算过程FEA Post-Processing有限元后处理 Conduct FE analysis as usual进行正常的有限元分析 Select one row of elements (in plate at weld toe) as a group, as shown选择一排单元（焊趾位置）作为一组，如图所示 Extract nodal forces (Fx) or nodal stresses (sx) for those nodes along A-A提取沿着A-A截面节点的节点力(Fx)或节点应力(sx) Extract nodal positions (y) along A-A提取沿着A-A截面节点的节点位置(y) Parabolic elements with reduced integration减缩积分二次单元减缩积分二次单元Structural Stress Calculation Example: a LapFillet Joint 2D结构应力计算实例：搭接接头2DNote:注意： Effects of Boundary Conditions边界条件的影响 Implications: Lower life W/Grip than W/o Grip结果表明：带夹具的比不带夹具的寿命较低 Parabolic elements with reduced integration减缩积分二次单元减缩积分二次单元Structural Calculation and Results: SS versusASME Linearization Procedures结构计算与结果：SS与ASME线性化方法比较One Element Through-Thickness厚度方向只有一个单元2D- 4 node full integration2D- 4 节点全积分节点全积分Comparison of SS Results Using Stress Integrationand Nodal Force Method: Shear Locking Effects分别用应力积分和节点力方法得到的SS结果比较：剪切锁死效应Comparison of SS Calculations Using Nodal Forces and Stresses用节点力和应力方法得到的SS结果比较Transformation From Nodal Forces to LineForce/Moments 3D Solid Models节点力到线力/弯矩的转换：3D实体模型Rotate nodal forces on weld toe face w.r.t. weld toe elements onto the mid surface (nodalforces and moments) 旋转相对于焊趾单元焊趾面的节点力到中面(节点力和弯矩) Transform nodal force/momentto line force/moment in the sameway as that for shell/plate models象板壳单元一样将节点力转换为线力/弯矩Or use stress integration methodat a particular location along Weld Line 或在沿着焊线的一个特殊位置使用应力积分方法HHI Detail 3HHI细节3Structural Stress Measurement Technique结构应力测量技巧Note:注意 A series of strain gages are recommended建议使用一系列应变片 Measurements at gage pairs should be located inapprox. linear regime测量的应变片对位置应当位于近似线性区域If = const at A A to C C SS=HSS如果从A-A到C-C截面m=常数，则SS=HSSSS Calculation Procedure for SimpleSpecimens of “ 2D Edge Details”2D”边界细节“简单试件结构应力计算方法Membrane/bending calculated with respect to w along the crack path沿着裂纹路径相应于w计算膜力与弯曲2D calculation proceduresare directly applicable with t=w当t=w时，2D计算方法可以直接应用Strain Gauge Data fromHHI Edge Detail #2-1HHI-边界细节#2-1的应变片数据Surface stresses: strain gauges and FEA表面应力：应变片数据与有限元结果Measured andCalculated SSSS的测量与计算Specimen after fatigue testing疲劳测试后的试件Specimen after fatigue testingMeasured and FEA-Calculated SSSS的测量与有限元计算Specimen after fatigue testing疲劳测试后的试件疲劳测试后的试件Effects on Interpretation of S-N Test Data解释S-N测试数据的影响因素Comments Equilibrium-Equivalent StructuralStress Parameter注解：平衡等效结构应力参数 Equilibrium-based separation of membrane and bending components 基于平衡的膜力与弯曲分量的分解 Measurable可测量 Consistent with simple structural mechanics theory(shell/plate theory)与简单的结构力学理论(板壳理论)相协调 A global measure of stress concentration due to agiven joint geometry and loading mode (incl. BCs)是一个对给定接头几何与载荷模式(包括边界条件)的应力集中的整体性度量 Generalized nominal stress at a location of interestwhere nominal stress is not defined在感兴趣的但名义应力不能定义的位置可以作为名义应力使用What Happens If Structural Mechanics TheoryBecomes not Applicable?在结构力学理论不能应用的时候会发生什么情况？e.g., Symmetric joints undersymmetric or anti symmetric loading:例如，对称或反对称载荷下的对称接头Strictly speaking, 3D continuum models are needed严格来讲，应当使用3D实体模型Through-thickness bending is ignored when using shell/plate models当使用板壳模型时，厚度方向的弯曲会被忽略The SS method can be extended for such applications by introducingconsidering symmetry and anti-symmetry definitions通过引入考虑对称与反对称定义，结构应力方法可以拓展应用于这种情况Symmetry versus Anti-Symmetric StructuralStress States for Welded Joints焊接接头的对称与反对称结构应力状态(I) Symmetry:Symmetric JointAnd Symmetric Loading(I)对称：对称接头与反对称载荷Structural Stress Structural Stress Range 结构应力 结构应力变化范围(II) Anti-Symmetry:Symmetric JointAnd Anti-Symmetric Loading(II)反对称：对称接头与反对称载荷Case (I) Requires a solid element model情况(I)需要实体单元模型Calculation of Symmetric Structural Stress对称结构应力计算 Solid element model实体单元模型Separation of membraneand bending based oneffective thickness of t/2膜与弯曲的分解基于t/2有效厚度 Maximum element sizelimited within t/2最大单元尺寸限制在t/2以内Nodal force basedmethod: more robustthan stress-basedmethod基于节点力方法：比基于应力的方法更稳定Symmetric versus Non-Symmetric Joints:Single versus Double Cover Plate Joints对称与非对称接头：单盖板接头与双盖板接头Test Data(1996):测试数据(1996):Test Data(1970s):测试数据(1970s):Structural Stresss Ability to Correlate S-NData Same Plate Thickness结构应力与S-N数据相关的能力相同板厚Typical plate weld details with same base plate thicknessunder remote tension在远处拉伸时基板厚度相同的几种典型板焊缝细节Summary Structural Stress Part I小结：结构应力第I部分 A good fatigue parameter:一个好的疲劳参数 Consistent in calculation计算结果一致 Relevant to fatigue与疲劳相关 Robust in practice应用时的稳健性 The SS parameter meets the above criteria结构应力参数符合上述原则 Mesh-insensitive网格不敏感性 Equilibrium (traction)-based基于平衡条件（拉伸） Nodal force based implementation 基于节点力 Demonstrated ability to correlate fatigue data from different jointGeometries 证明与不同的接头几何疲劳数据相符 also measurable 也可以测量 Simple post-processing to commercial FEA codes对于商业有限元程序只需简单的后处理Structural Stress Method Part II结构应力方法第二部分 Limitations of the simple SS calculation procedures presented以上介绍的简单结构应力计算方法的局限性 Generalized structural stress method一般化的结构应力方法 Method of simultaneous equations for line force/moment transformation线力/弯矩转换的即时方程方法 Weld line with open ends 不闭合的焊线 Weld line with closed ends 闭合的焊线 Weld representation considerations 焊缝表示方法的注意事项 “Continuous” weld line definition and modeling considerations连续焊线定义与建模注意事项 “Continuous” and “discontinuous” examples 连续与不连续实例 Mesh-insensitivity validations using various joint configurations使用不同接头形式的网格不敏感性验证 Multi-axial stress state 多轴应力状态 Structural stress post-processor结构应力后处理 Input requirement 输入要求 Calculation examples 计算实例 Demo version of SS post-processor usage 结构应力后处理演示版使用方法 Model and input descriptions 模型与输入描述 Hands-on session 手算部分 Demo of advanced version of SS post-processor结构应力后处理高级版本示例Simple Structural Stress CalculationProcedures Discussed so far目前为止讨论的简单结构应力计算方法Shell/plate models: oneelement based formulation板壳模型：基于单个单元的方程Solid models calculationat a point a long a weld line:实体模型：在沿着一条焊线上的一点进行计算Nodal forces (2D)节点力（2D）Stress integration (2D or 3D)应力积分（2D或3D）