verity焊接結(jié)構(gòu)疲勞評(píng)估教程(II)_王悅東101-200

1、The SS Method Must Accommodate the Following Practical Considerations結(jié)構(gòu)應(yīng)力法必須適應(yīng)下列實(shí)際因素Arbitrary mesh designs:任意網(wǎng)格設(shè)計(jì) Distorted mesh變形的網(wǎng)格 Mismatched element不匹配的網(wǎng)格 Triangle elements三角形網(wǎng)格 Continuously curved weld line in 3D space三維連續(xù)曲焊縫Line force/moment formulation strategy:線載荷/彎矩公式 “Work-equivalent” with

2、 respect to an entire weld line整條焊縫上“能量守恒” Traction continuity requirements at nodes along a weld line 在焊縫各節(jié)點(diǎn)處拉力連續(xù)Generalized Procedures for Shell/Plate Element Models Open Weld Ends殼/平面單元模型的通用求解過(guò)程-非閉合焊縫1. Collect force/moments wrt x-y-z在全局坐標(biāo)系下計(jì)算節(jié)點(diǎn)力及彎矩2. Definite local coordinate system along weld l

3、ine: x-y-z沿焊線定義局部坐標(biāo)系：-3. Rotate nodal forces/moments轉(zhuǎn)換節(jié)點(diǎn)力及彎矩4. Solving simultaneous equations求解方程Through-Thickness Traction Conditions Using Nodal Forces用節(jié)點(diǎn)力作為厚度方向上的拉伸條件對(duì)于閉合焊縫：Typical Weld Representation Schemes for Using Shell/Plate Element Models使用殼/平面單元模型的典型焊縫表達(dá)方式n Equivalent stiffness 等效剛度n Full

4、 penetration weld: two rows of plate elements with “triangle formation”全熔透：用兩排三角形平面單元n Partial penetration: one row of inclined elements部分熔透：用一排傾斜的單元A Lap Fillet Weld搭接焊A Padding Plate Fillet Joint墊板焊接接頭（？）“Continuous” Weld Line Definition for Curved Weld Lines曲焊縫的“連續(xù)”焊縫定義SS calculated long each wel

5、d line defined by average normal vectors at a node btw two adjacentelements在相鄰單元處，結(jié)構(gòu)應(yīng)力方向計(jì)算采用法線向量平均值A(chǔ) sharp angle of more than 45o may not produce a good mesh insensitivity in linear element models如果兩單元法線向量夾角大于45度，會(huì)導(dǎo)致線性單元網(wǎng)格不敏感的特性有所降低管接頭封閉焊縫A Wrap-Around Weld End “Continuous”環(huán)繞焊縫末端“連續(xù)”Weld Line Defini

6、tion Example焊縫定義示例Continuous weld linesalways preferred優(yōu)先選用連續(xù)的焊線定義Discontinuous weld linesmust be used in a model:非連續(xù)的焊線定義應(yīng)用在： Treated as separate weld line definitions按分開的焊縫來(lái)處理的情況 May show mesh-sensitivity in some cases, depending on load transfer在某些網(wǎng)格敏感度較高的情況，這與載荷傳遞模式有關(guān)Continuous Weld Line around

7、Corner Structural Stress Results (Linear Elements)拐角處連續(xù)焊線結(jié)構(gòu)應(yīng)力結(jié)果（線性單元）Continuous Weld Line Corner StructuralStress Results (Parabolic Elements)拐角處連續(xù)焊線結(jié)構(gòu)應(yīng)力結(jié)果（二階單元）Out-of-Plane versus In-Plane Notch Effects inStructural Stress Calculation結(jié)構(gòu)應(yīng)力計(jì)算中面內(nèi)及面外的缺口效應(yīng)對(duì)比Out-of-plane (through-thickness notch effects面

8、外（沿厚度方向的缺口效應(yīng)） Equilibrium conditions enforced wrt to t平衡條件嚴(yán)格依賴于tIn-plane notch effects面內(nèi)缺口效應(yīng) Open-ended weld line with weld ends subjected to high stress concentration regime末端承受高應(yīng)力集中的非封閉焊縫 Using over-simplified weld representation 使用過(guò)簡(jiǎn)化的焊縫的表示 “Weld line definitions” for “Edge Detail” (in-plane crac

9、k) 為“邊緣細(xì)節(jié)”定義的焊縫（面內(nèi)裂紋） SS calculation using “virtual node method”“虛擬節(jié)點(diǎn)法”的結(jié)構(gòu)應(yīng)力計(jì)算Examples with Open-Ended Weld Line: Withand Without In-Plane Notch Effects非封閉焊縫示例：考慮及不考慮平面內(nèi)缺口效應(yīng)Small Edge Detail Test Specimens: In-PlaneNotch Effects in SS Calculation小邊緣細(xì)節(jié)試驗(yàn)試樣：結(jié)構(gòu)應(yīng)力計(jì)算中面內(nèi)缺口效應(yīng)n Small w 較小n Nominal stress w.

10、r.t. w is wellDefined依據(jù)的名義應(yīng)力容易確定n Failure criterion: full ligament(w) separation 破壞準(zhǔn)則：剩余寬度(w)全部斷開n In-plane notch effects are captured by 面內(nèi)缺口效應(yīng)的確定，通過(guò)： te=w in structural stress calculations結(jié)構(gòu)應(yīng)力計(jì)算中：te=w For symmetric edge detail te=w/2對(duì)于對(duì)稱結(jié)構(gòu)： te=w/2Virtual Node Method (VNM) for StructuralStress Calc

11、ulations in Structural Components結(jié)構(gòu)構(gòu)件中計(jì)算結(jié)構(gòu)應(yīng)力的虛擬節(jié)點(diǎn)法n Large w or not well-defined 較大或不容易確定n “Weld line” defined along w or an anticipated failure path 沿或預(yù)期的斷裂路徑定義“焊線”n Failure criterion: l1 w 失效準(zhǔn)則： l1 wn Stresses along “weld line” are not statically determined Load: Virtual Node Method 沿著“焊線”的應(yīng)力不由靜態(tài)的載

12、荷決定： 虛擬節(jié)點(diǎn)法Equilibrium conditions enforced within a reference distance l (Position 2) 平衡條件限定在參考距離l內(nèi)（號(hào)點(diǎn)位置）l1: final in-plane crack length at failure within l l1: 在l范圍內(nèi)面內(nèi)最終裂紋失效長(zhǎng)度Good mesh-insensitivity for l1 l/2如果l1 l/2會(huì)獲得較好的網(wǎng)格不敏感特性Single Element Based SS Calculation UsingVNM - An Over-Simplified Plat

13、e Element Model基于單個(gè)單元的使用虛擬節(jié)點(diǎn)法的結(jié)構(gòu)應(yīng)力計(jì)算過(guò)簡(jiǎn)化的平面單元模型Comparison of VNM and Results Using Refined Weld Representation Schemes虛擬節(jié)點(diǎn)法與細(xì)化網(wǎng)格方法對(duì)比A Box Fillet Weld Example Weld Toe on Attachment Plate方角焊縫例子附加板上的焊趾W/O Weld Representation沒(méi)有添加焊縫單元A Box Fillet Weld Example Weld Toe on Attachment Plate方角焊縫例子附加板上的焊趾n W/

14、 Weld Representation添加焊縫單元Intermittent Welds間斷焊縫Shell versus 3D Solid Models殼單元與3D單元模型對(duì)比SS Results versusSoftware Packages結(jié)構(gòu)應(yīng)力結(jié)果與商用軟件結(jié)果對(duì)比An Independent Evaluation of The SS and HSS Method at Rat Hole End (B. Healy, 04)結(jié)構(gòu)應(yīng)力法與熱點(diǎn)應(yīng)力法評(píng)估鼠洞結(jié)構(gòu)（B. Healy, 04 ）的結(jié)果ISSC Longitudinal Frame/Connection Tests Analyz

15、ed by ABS (Wang et al, 2004)ISSC縱向架構(gòu)連接試驗(yàn)（ Wang et al, 2004）ISSC Bilge Knuckle Test Analyzed by ABS (Wanget al, 2004) ISSC艙底關(guān)節(jié)連接試驗(yàn)（ Wang et al, 2004）Structural Stress Calculation Results結(jié)構(gòu)應(yīng)力法計(jì)算結(jié)果Applications of the Structural Stress Method in Multi-Axial Fatigue結(jié)構(gòu)應(yīng)力法在多軸疲勞中的應(yīng)用Quality data are scarce缺乏

16、良好的數(shù)據(jù)Some well-known multi-axial fatigue data: EPRI, LBF,TWI, UIUC一些著名的多軸疲勞數(shù)據(jù)： EPRI, LBF,TWI, UIUC Observations: 總結(jié)： Crack tends to propagates along weld toe into plate at least for the most part of life time至少在大部分使用期限內(nèi)，裂紋傾向沿焊趾向板內(nèi)擴(kuò)展 Based “nominal stress range”:基于名義應(yīng)力幅值 Torsion is more damaging than

17、 bending扭轉(zhuǎn)的破壞強(qiáng)于彎曲的破壞 Out-of-phase is more damagingthan in-phase loading異步載荷破壞強(qiáng)于同步載荷 Transverse shear often negligiblefrom these tests測(cè)試中橫向剪切常常忽略Through-Thickness Normal Structural Stress厚度截面法線方向的結(jié)構(gòu)應(yīng)力Through-Thickness In-Plane Shear Structural Stress厚度截面的面內(nèi)剪切結(jié)構(gòu)應(yīng)力Transverse shear (Fz) is negligible in

18、 shell/plate structures殼/板結(jié)構(gòu)中橫向剪切力(Fz)忽略Multi-Axial Fatigue Specimens Used by Sonsino & Kuepper (2001)多軸疲勞試樣（Sonsino & Kuepper 2001）Specimen Geometry Stress calculations Using very fine mesh通過(guò)精細(xì)的網(wǎng)格來(lái)計(jì)算試樣幾何應(yīng)力Structural Stress Calculations for A Plate toTube Fillet (Sonsino and Kuepper, 01)板管接頭

19、的結(jié)構(gòu)應(yīng)力計(jì)算(Sonsino and Kuepper, 01)SAE FD&E “Weld Challenge” Tests A RHS Joint Loading in Bending and Torsion SAE FD&E 焊接挑戰(zhàn)實(shí)驗(yàn)-承受彎扭的接頭Fatigue Behavior of Resistance Spot Welds電阻點(diǎn)焊的疲勞行為The same structural stress procedure applies結(jié)構(gòu)應(yīng)力法同樣適用 Specifically: 特殊之處： Two dominant failure modes: 兩種失效模式： Sh

20、eet failure at nugget edge controlled bystress in sheet由板內(nèi)應(yīng)力引起的焊核邊緣處板的失效 Nugget interfacial failure controlled bystresses across nugget由焊核內(nèi)力引起的焊核破壞 Sheet failure mode is most important焊核邊緣處板的失效更為突出 Nugget failure should be prevented byspecifying dmin焊核的失效可通過(guò)指定最小焊核直徑解決Resistance Spot Welds Sheet Fail

21、ure (Mode A)電阻點(diǎn)焊-板材失效（模式）n Closed weld line around nugget periphery 封閉的焊線圍繞焊核外圍n Inside nugget periphery: 焊核內(nèi)部區(qū)域 Either shell elements with MPC (plane remains plane)殼單元與MPC相連（平面仍保持平面） Or right beams (plane remains plane)或者合適的梁?jiǎn)卧ㄆ矫嫒员３制矫妫﹏ SS calculation procedure is identical to fusion welds結(jié)構(gòu)應(yīng)力法計(jì)算過(guò)

22、程與熔焊相同Mesh-Insensitivity Demonstration FE Models and Mesh Sizes Used網(wǎng)格不敏感的示例-有限元模型及所用的網(wǎng)格尺寸Comparison of Structural Stress Results with Three Models三種模式的結(jié)構(gòu)應(yīng)力計(jì)算結(jié)果對(duì)比Validation by Correlating S-N Data from Lap Corus Shear and Coach Peel Tests (Corus, 2001)使用相關(guān)的-曲線證明Weld Representations for Structural St

23、ress Calculations Shell/Plate Models結(jié)構(gòu)應(yīng)力計(jì)算的焊縫模型-殼/板模型Laser Welded Couch-Peel Specimens激光焊模型Nominal Stress Range versus Cycles at Failure: L1 L4 specimens名義應(yīng)力范圍及失效循環(huán)次數(shù)：L1L4試樣nFailure Mode: Sheet Failures, Aluminum Alloy Laser Welds失效模式：板材破壞，鋁合金激光焊nL1-Lap Shear; L3: Coach Peel) Nominal Stress Range St

24、ructural Stress Range名義應(yīng)力變動(dòng)范圍 結(jié)構(gòu)應(yīng)力變動(dòng)范圍Courtesy Ford Motor CompanySummary Part II: Generalized Structural Stress Method總結(jié)-第二部分：通用結(jié)構(gòu)應(yīng)力法nConsistency and robustness 一致性和穩(wěn)定性 Good mesh-insensitivity: 良好的網(wǎng)格不敏感 Mesh-sizes網(wǎng)格尺寸 Distorted elements扭曲單元 Element types/integration orders單元類型/積分階數(shù) Capable of handli

25、ng both through thickness and in-plane fatigue Failures能夠處理厚度方向和面內(nèi)的疲勞失效 Identical calculation procedure for:用相同的計(jì)算過(guò)程可計(jì)算 Resistance spot welds, plug welds,etc 電阻點(diǎn)焊，塞焊等 Laser welds, etc激光焊等 Directly applicable for characterization of multi-axial stress state可直接應(yīng)用于多軸應(yīng)力狀態(tài)nEffectiveness in test data corr

26、elation與試驗(yàn)數(shù)據(jù)相關(guān)的有效性 Effective over different joint types可用于不同接頭類型 Effective in correlating S-N data for:用于如下S-N數(shù)據(jù) Resistance spot welds電阻點(diǎn)焊 Laser welds, etc激光焊等Demo Version of SS Post-Processor and Working Session結(jié)構(gòu)應(yīng)力法的后處理及運(yùn)行部分的演示版n Input requirements 輸入要求n Demonstration on how to use the post-proces

27、sor with selected examples示范如何通過(guò)例子使用后處理n Working session: 運(yùn)行部分 Lap fillet welds 搭接焊 Edge detail 邊界細(xì)節(jié) Spot and laser welds 點(diǎn)焊及激光焊 RHS joint SAE “WELD CHALLENGE” problem RHS接頭-SAE“焊接挑戰(zhàn)”Demo Version of Battelles Structural Stress Post-Processor Battelle結(jié)構(gòu)應(yīng)力法后處理的演示版nNumber of nodes describing a weld lin

28、e is limited to18 nodes焊縫的節(jié)點(diǎn)數(shù)目不能多于18個(gè)nElement type: linear shell/plate elements單元類型：線性的殼/板單元nCommercial FE package: NASTRAN有限元軟件包： NASTRANnRequires:要求 An input file describes weld line nodes and elements一個(gè)描述焊線節(jié)點(diǎn)及單元的輸入文件 NASTRAN input file NASTRAN的輸入文件 NASTRAN punch file containing GPFORCE output 包含G

29、PFORCE 的NASTRAN punch 文件Hands-On Session: Structural Stress Analysisof Welded Joints Using a SS Post-processorJK HongWeld definition file format demo version焊縫定義文件格式演示版本nWeld information input file: 焊縫信息輸入文件： Nodal numbers describing a “weldline” from start to end (N1-Nn)描述焊線的節(jié)點(diǎn)號(hào)碼從N1到Nn Node Sequenc

30、e is required.要求節(jié)點(diǎn)順序 Element numbers along the weldline from start to end (E1-En-1)沿焊線的單元號(hào)碼從E1到En-1 Element sequence does not matter. 單元順序無(wú)所謂nElement normal directions must be consistent, pointing to local zdirection 單元法線方向必須一致，指向局部坐標(biāo)ZnStructural stress calculated: with respect to y direction結(jié)構(gòu)應(yīng)力計(jì)算：

31、 指向y 方向nIf N =N1 a closed weldline is considered (e.g. pipe girth weld, spot weld) 如果Nn=N1 則為封閉焊縫（如：環(huán)焊、點(diǎn)焊）Post processor Demo Version演示版后處理Cover plate joint- straight fillet weld蓋板接頭-直線角焊縫Post processor output后處理輸出Cover plate Straight weld (a refined mesh)蓋板直線焊縫（精細(xì)網(wǎng)格）Curved weld-One side doubling pl

32、ate曲線焊縫-單邊雙面n Calculate SS along the weld toe.Detail - Weld End Effect細(xì)節(jié)-焊縫末端影響Crack propagation directionSAE FD&E Weld Challenge Problem SAE FD&E 的焊接挑戰(zhàn)SAE FD&E Weld Challenge Problem SAE FD&E 的焊接挑戰(zhàn)Calculate SS along the top weld toe on the 2”x6” tube.沿2”x6” 管的焊趾上面計(jì)算結(jié)構(gòu)應(yīng)力Current Forma

33、t for Weld Definition File (for bothJIP and VerityTM in fe-safeTM) Verity safe目前的焊接定義文件格式（ fe-safeTM）Hand Calculation Using Single-Element BasedVNM A Simplified Plate Element Model基于單個(gè)單元的虛擬節(jié)點(diǎn)法的手算簡(jiǎn)化的板單元模型Master S-N Curve Approach主SN曲線方法nHow to introduce thickness and loading mode effects? 如何引入厚度與載荷模式

34、的影響?n Needs and challenges in introducing fracture mechanicsn引入斷裂力學(xué)的必要性及問(wèn)題n Generalized fracture mechanics K solutions using SS parameter通用的以結(jié)構(gòu)應(yīng)力為參數(shù)的斷裂力學(xué)K值表達(dá)式 Elements of linear fracture mechanics 線性斷裂力學(xué)單元 K solutions K值表達(dá)式 Crack growth rate and Paris law裂紋擴(kuò)展速率及Paris 公式 Notch stress estimation schem

35、e缺口應(yīng)力評(píng)估方法 Generalized self-equilibrating notch stress estimation Mkn通用的自平衡缺口應(yīng)力估值 MknnA two-stage crack growth law and its integration兩階段裂紋擴(kuò)展規(guī)律及其合并nFormulation of an equivalent structural stress parameter等效結(jié)構(gòu)應(yīng)力參數(shù)公式n Validation tests: correlation of a massive amount S-N data驗(yàn)證試驗(yàn)：與大量S-N數(shù)據(jù)關(guān)聯(lián)n Master S-N

36、 curve representation主S-N曲線的表示Is Structural Stress Parameter Effective in Consolidating Existing S-N Data?結(jié)構(gòu)應(yīng)力參數(shù)是否對(duì)加強(qiáng)已有的S-N數(shù)據(jù)有效果?S-N Data: Similar thickness Remote tensionHow about Considering a Wide Range of Thickness (2-100mm) and Loading Modes (Remote Tension to Bending)考慮較大變化范圍的厚度 (2-100mm)及載荷模式

37、（遠(yuǎn)端的拉力及彎矩）的情況The Results are not bad, but still not good enough結(jié)果不差但也不夠好Further Consolidation Must Consider a Parameter Measuring the Following:進(jìn)一步要考慮的參數(shù)：Remote Loading遠(yuǎn)端載荷模式影響？Mode effects? Thickness Effects?厚度影響Fracture Mechanics Based Considerations基于斷裂力學(xué)的考慮n If crack propagation dominates fatigu

38、e life:是否裂紋的擴(kuò)展決定疲勞壽命n Stress intensity factor (K) provides a unique one-parametercharacterization of the stress state at a crack tip應(yīng)力強(qiáng)度因子(K) 提供單參數(shù)來(lái)描述裂紋尖端的應(yīng)力狀態(tài)n K is a function of crack size, stress state, and geometryK是裂紋尺寸、應(yīng)力狀態(tài)和幾何形狀的函數(shù)n Closed-form K solutions not available for most joint types 封閉

39、形式的K值表達(dá)式不適合多數(shù)接頭類型n Most of applications in welded joints:焊接接頭多應(yīng)用于： Case-specific life predictions特殊工況壽命預(yù)測(cè) Finite initial crack size有限的初始裂紋尺寸Needs for Developing a Single Fatigue Parameter for all Joint Types需要開發(fā)一種適合所有接頭的疲勞參數(shù)n Generalized K solutions通用的K值求解算式n Generalized S-N expression of Paris-type

40、 crack growth law通用的符合Paris的裂紋擴(kuò)展公式的S-N表達(dá)式 “short” crack anomalous behavior?“短”裂紋不規(guī)則行為？ Long crack growth behavior長(zhǎng)裂紋擴(kuò)展行為 Is there a unified crack growth exponent m?有一致的裂紋擴(kuò)展的指數(shù)m嗎？n Validations of above 證實(shí)上述內(nèi)容n The ultimate tests: the collapse of massive amount S-N data 最終試驗(yàn)：大量S-N數(shù)據(jù)的縮減Mechanics-Based

41、Interpretation of the Structural Stress Parameter基于力學(xué)的結(jié)構(gòu)應(yīng)力參數(shù)解釋n Through-thickness Based Weld separation in terms of membrane and bending that satisfy equilibrium conditions沿厚度方向?qū)⒘Ψ譃槟ち皬澗厍覞M足平衡條件n Statically-equivalent to the far-field stress in fracture mechanics:與斷裂力學(xué)中遠(yuǎn)場(chǎng)應(yīng)力靜力等效：Structural Stress Base

42、d Single Edge Notch (SEN) K Solution基于結(jié)構(gòu)應(yīng)力的單邊缺口K值遠(yuǎn)端承受拉伸與彎曲載荷的單邊缺口試樣K值的表達(dá)式，這里拉伸與彎曲應(yīng)力均為結(jié)構(gòu)應(yīng)力。Structural Stress Calculations can be Viewed as a Stress Transformation Process結(jié)構(gòu)應(yīng)力計(jì)算可認(rèn)為是應(yīng)力轉(zhuǎn)換過(guò)程How About Contributions from the Self-Equilibrating Stress State or Notch Stress自平衡應(yīng)力或缺口應(yīng)力的作用Notch Stress Estimatio

43、n缺口應(yīng)力的估算Analytically Expressed K Solution with Notch Stress Effects考慮缺口應(yīng)力影響的K值解析表達(dá)式Validations of The Structural Stress Based K Solutions基于結(jié)構(gòu)應(yīng)力的K值的確定Comparison of The Current and Handbook K Solutions CT Specimen with a Key Hole同手冊(cè)K值對(duì)比帶有中心孔的CT試樣n CT Specimen with Key Hole (Ramulus, 1987)Center-Notche

44、d Specimen中心缺口試樣Issues in Integrating Classical Paris Law to Relate Stress State to Life將應(yīng)力狀態(tài)與壽命相關(guān)聯(lián)的經(jīng)典Paris公式n m is assumed 3 in most Codesand Standards for steel 在多數(shù)鋼結(jié)構(gòu)規(guī)范及標(biāo)準(zhǔn)中同M指定為3n Examination of some reported crack growth data showed a da wide scatter band 查看一些裂紋擴(kuò)展的報(bào)告顯示da形成寬分布帶n C varies more sig

45、nificantly thanm indicating specimen geometry dependenceC的變動(dòng)比m更為顯著說(shuō)明其依賴試樣的幾何形狀n “Short crack” phenomena maycontribute to some“短裂紋”現(xiàn)象可能貢獻(xiàn)一些n Crack growth data in un-weldedspecimens should be applicable裂紋擴(kuò)展數(shù)據(jù)在非焊接結(jié)構(gòu)上也是適用的Crack Growth Data from Tanaka and Nakai, Y(1983) Center Notched Specimens Tanaka 等

46、的裂紋擴(kuò)展數(shù)據(jù)中心缺口試樣 After Adding Additional Data: Specimen Geometry Effects附加數(shù)據(jù)中試樣幾何形狀的影響A Unified Approach for both Long and Short Crack Growth A Two Stage Growth Model長(zhǎng)、短裂紋擴(kuò)展的統(tǒng)一方法兩階段擴(kuò)展模型How to Reliably Determine n and m from Highly Controlled Crack Growth Rate Testing?如何從裂紋擴(kuò)展速率試驗(yàn)中可靠地確定n及mAluminum Alloys

47、 versus Steels and Short Cracks versus Long Cracks鋁合金同鋼的對(duì)比及長(zhǎng)、短裂紋的對(duì)比SS Based K Solutions and Crack Growth Rate Analysis基于結(jié)構(gòu)應(yīng)力的K值及裂紋擴(kuò)展速率分析n K solutions have been further validated K值求解已經(jīng)進(jìn)一步驗(yàn)證n Two-stage growth law unified short and long crack growth data 兩階段擴(kuò)展規(guī)律統(tǒng)一了長(zhǎng)、短裂紋數(shù)據(jù) Mkn dominated Mkn 控制 Kn domin

48、ated Kn控制n A unique slope exists (3.5 to 3.6) Similar between aluminum alloys and steels 一致的斜率(3.5 to 3.6) 鋁合金與鋼材相似n How to derive a simple SS based fatigue parameter? 如何得到簡(jiǎn)單的基于等效結(jié)構(gòu)應(yīng)力的疲勞參數(shù)？Two Classes of Mkn Curves兩種Mkn 曲線A Unified Mkn(a/t) by Superposition (approximation)疊加的統(tǒng)一Mkn(a/t)值（近似） Formulat

49、ion of Fracture Mechanics Based Equivalent Structural Stress Parameter Ss基于斷裂力學(xué)的等效結(jié)構(gòu)應(yīng)力參數(shù)Ss表達(dá)式Initial Crack Size (ai/t) and Mkn Effects on I(r) Integration初始裂紋尺寸(ai/t)及Mkn對(duì)I(r) 積分的影響Effectiveness of The Equivalent Structural Stress Parameter等效結(jié)構(gòu)應(yīng)力參數(shù)的有效性Some Comments on Edge Crack Based I (r)基于邊裂紋的I(r)相關(guān)問(wèn)題n Weak dependency on r 與r弱相關(guān)n K based on load controlled conditions K值基于載荷控制條件n Some S-N data showed stronger bending effects 一些S-N數(shù)據(jù)顯示較強(qiáng) 的彎曲效應(yīng)n