疲勞統(tǒng)計(jì)基礎(chǔ)概念

1、The Two Basic Approaches疲勞是指在反復(fù)循環(huán)載荷作用下的材料退化。對(duì)于金屬主要指出現(xiàn)小裂紋。小裂紋的聯(lián)合形成大裂紋，最終導(dǎo)致零件的折斷或者性能嚴(yán)重衰退。估計(jì)裂紋出現(xiàn)壽命的兩種方法：應(yīng)力壽命方法和應(yīng)變壽命方法。根據(jù)失效模式選擇分析方法：靜態(tài)失效：結(jié)構(gòu)變形大低周疲勞：在應(yīng)力集中區(qū)域存在大的塑性變形高周疲勞：幾乎沒有塑性變形應(yīng)力壽命方法主要適用于應(yīng)力低于或者不很高出材料彈性極限的工況。應(yīng)變壽命方法主要用于出現(xiàn)材料屈服的工況，應(yīng)力水平高于材料屈服強(qiáng)度。Figure 1: Failure Modes are Different for Static Failure, Low Cyc

2、le Fatigue, and High Cycle Fatigue.Concepts in CommonFigure 2: Constant Amplitude Load History.Figure 3: Variable Amplitude Load History.Figure 4: Proportional Multiple Channel Load History.Figure 5: Non-Proportional Multiple Channel Load History.Fatigue Life and Fatigue Damage疲勞壽命：結(jié)構(gòu)承受載荷至失效所經(jīng)歷的載荷循環(huán)

3、數(shù)。疲勞損傷：失效的損傷值等于1（累積損傷限），即所有載荷循環(huán)造成的損傷是1，其中一個(gè)循環(huán)造成的損傷稱為部分損傷。Miner線性累積損傷準(zhǔn)則：總損傷是單個(gè)循環(huán)造成的部分損傷的線性累積。累積損傷限：通常設(shè)為1，可以調(diào)整為小于1（偏保守），或大于1。Loading and Local StressesFigure 7: Load Applied to a Component Induces a Nominal Stress and a Local Stress at the Notch.名義應(yīng)力：偽應(yīng)力（缺口應(yīng)力）： 應(yīng)力集中系數(shù). 影響系數(shù) Figure 8: Pseudo Stress for

4、 Non-Proportional Loading.設(shè)置影響系數(shù)：Geometric Work Sheet， Damage Based Data Reduction MethodsRate Independent Counting Methods基于疲勞的數(shù)據(jù)縮減方法之間的關(guān)系：Figure 10: Derivation of Counting Methods.Data PreprocessingPeak/Valley FilteringFigure 11: Stress-Time History.Figure 12: Peak-Picked Stress-Time History.Hyste

5、resis FilteringFigure 13: Hysteresis Filter.Discretization把載荷幅值范圍分成N個(gè)等間隔區(qū)間（bin），默認(rèn)值N100。 Rainflow Cycle CountingFigure 14: Illustration of a Hysteresis Loop.雨流計(jì)數(shù)最重要的優(yōu)勢(shì)是與疲勞損傷的一致性。 雨流計(jì)數(shù)始于1967年（Endo）。1969年出現(xiàn)程對(duì)計(jì)數(shù)法（De Jonge）。1986年Clormann/Seeger發(fā)表了一個(gè)變型。還有其它雨流計(jì)數(shù)的標(biāo)準(zhǔn)方法，如ASTMASTM E1049-85和SAESAE AE-10。 LMS D

6、urability Technologies GmbH開發(fā)了四點(diǎn)雨流計(jì)數(shù)法，與法國AFNOR標(biāo)準(zhǔn)相同。The 4-Point AlgorithmFigure 15: The 4-Point Algorithm.Figure 16: Schematic of From-to Matrix Construction.Load Histograms載荷直方圖顯示載荷循環(huán)的幅值和次數(shù)，可以顯示在SN圖上。Figure 17: Time History.Figure 18: Cumulative Cycle Count.Life Curves為了進(jìn)行whatif分析，LMS定義了壽命曲線和設(shè)計(jì)點(diǎn)概念。C

7、alculate Fatigue Life設(shè)計(jì)點(diǎn)（Design point）的默認(rèn)值是載荷水平（load level）1，載荷水平為k是把載荷放大k倍。Back Calculation of Load Levels給定數(shù)據(jù)塊的次數(shù)，求載荷幅值。把設(shè)計(jì)點(diǎn)的未知量設(shè)為Load Level即可。Consecutive Load Histories (Test Schedules)Introduction試驗(yàn)計(jì)劃由若干信號(hào)段編制而成，通常是5至50段信號(hào)，重復(fù)編排。Fatigue Background疲勞損傷依賴于載荷順序。處理順序效應(yīng)的方法有兩種：精確法，近似法。LMS Durability Imp

8、lementation在Method Parameters中，選項(xiàng)Calculate TSD Exact為TRUE（checked）是精確法，F(xiàn)ALSE（unchecked）是傳統(tǒng)法。只對(duì)時(shí)間歷程信號(hào)。Non-Local and Surface Effects基礎(chǔ)疲勞壽命數(shù)據(jù)是用拋光的試驗(yàn)樣件進(jìn)行旋轉(zhuǎn)彎曲試驗(yàn)得到的。實(shí)際零件的表面粗糙度，尺寸，載荷類型，以及平均應(yīng)力水平等因素，都會(huì)影響疲勞壽命。The Fatigue Notch Factor只用彈性應(yīng)力集中系數(shù)會(huì)導(dǎo)致過于保守的結(jié)果。隨著作用載荷的升高，有缺口和無缺口零件的疲勞壽命差別將減小。因?yàn)榫植克苄宰冃螘?huì)降低局部應(yīng)力。因此引入疲勞缺口系數(shù)

9、：Figure 19: Comparison Between the Fatigue Behavior of an Unnotched Component Compared to a Notched Component.What are Size Effects?Technological Size EffectsQuenched and Tempered Steel:硬度分布取決于直徑，而表面的耐久性極限取決于表面硬度。Figure 20: Hardness Profile in Tempered or Quenched Steel.High Strength Steel:非金屬雜質(zhì)顆粒的大

10、小，形狀和分布影響疲勞壽命。表面越大，出現(xiàn)雜質(zhì)顆粒的概率越大。Figure 21: Stress Distribution in High Strength Steel Due to Non-Metallic Inclusions.Size Effect of Surface Treatment表面強(qiáng)化的相對(duì)深度取決于零件尺寸，并且影響內(nèi)層的預(yù)應(yīng)力。Figure 23: Different Pre-Stresses at the Inner Layer After Surface Treatment.How to Account for Size Effects有很多方法，通常是用修正系數(shù)調(diào)整

11、耐久性極限。Stress GradientsStatistical Size EffectMacroscopic YieldingNeubers Approach to MicroyieldingSummaryConceptCorrection factor Stress gradientAdjustment for macro-yieldingWeakest-link conceptNeubers approach to micro-yieldingSurface Effects表面粗糙度越大，疲勞壽命越短。表面刮痕充當(dāng)應(yīng)力集中。Figure 30: Correction Factors D

12、ue to Surface Roughness.表面修正系數(shù)為.The Statistical Nature of Fatigue疲勞試驗(yàn)結(jié)果的分散性，源自材料屬性、零件尺寸、工作載荷和制造誤差的不同?？蛻羰褂们闆r的差異是最大的。在中、高周區(qū)域疲勞壽命差別系數(shù)為2并非異常。Figure 31: The Likelihood of Weak Components Subjected to High Loads is Minimized in a Probabilistic Design Approach.SN曲線的置信度通常取10%, 50%, 和90%的失效概率。分散度指標(biāo)是失效概率90%和10%對(duì)應(yīng)的載荷比：Property Influencing FatigueTypical Scatter Manufacturin