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      鎳基高溫合金成分的優(yōu)化設(shè)計(jì)方法

      文檔序號(hào):5096291閱讀:1455來源:國知局
      專利名稱:鎳基高溫合金成分的優(yōu)化設(shè)計(jì)方法
      技術(shù)領(lǐng)域
      本發(fā)明涉及高溫合金的成分設(shè)計(jì)方法,具體地說,涉及通過人工神經(jīng)網(wǎng)絡(luò)與優(yōu)化計(jì)算相結(jié)合對(duì)鎳基高溫合金成分進(jìn)行優(yōu)化設(shè)計(jì)。
      背景技術(shù)
      高溫合金是制造航空發(fā)動(dòng)機(jī)部件和熱力設(shè)備部件及核動(dòng)力設(shè)備部件最為廣泛的金屬材料。合金的顯微組織即各組成相特別是析出相的性質(zhì)、形態(tài)、大小、含量及分布決定了其高溫力學(xué)性能及運(yùn)行壽命。然而,合金的組織狀態(tài)是由其成分所決定的。因此,決定合金性能的源頭在于合金成分本身,即構(gòu)成合金成分的各元素的種類及其含量。長期以來,高溫合金設(shè)計(jì)主要有以下幾種方法1)基于控制有害相的電子空位數(shù)法(源于60年代);2)基于γ′(有序結(jié)構(gòu)析出相)與γ相(基體相)成分、相含量及兩相共格錯(cuò)配度與持久壽命關(guān)系的多元回歸法(源于80年代);3)基于合金穩(wěn)定性的d電子能量法(源于90年代);4)基于‘烹調(diào)式’操作的‘試錯(cuò)’法(源于50年代)等。上述方法中有的基于半經(jīng)驗(yàn)、半理論(如1)和3));有的出自對(duì)試驗(yàn)結(jié)果的回歸處理(如2)),而有的則完全通過改變成分的逐一試驗(yàn)來獲得所需性能指標(biāo)的成分設(shè)計(jì)結(jié)果(如4))。上述設(shè)計(jì)方法在不同年代的高溫合金設(shè)計(jì)過程中起到了應(yīng)有的積極作用。然而,隨著航空發(fā)動(dòng)機(jī)及燃?xì)鈩?dòng)力設(shè)備事業(yè)的發(fā)展,對(duì)高承溫能力高溫合金的需求愈來愈迫切,對(duì)這類材料的設(shè)計(jì)既需要先進(jìn)的理論指導(dǎo),又需要大量合金配方的實(shí)驗(yàn);此外,對(duì)廣普型高性能低成本的軍用及民用高溫合金材料的開發(fā)是國防及國民經(jīng)濟(jì)建設(shè)必不可少的,如何使現(xiàn)有高溫合金材料的成分配方更為合理以提高其性能指標(biāo)并降低原材料成本是高溫合金設(shè)計(jì)必須考慮的重要因素。
      本發(fā)明就是針對(duì)上述現(xiàn)狀和圍繞發(fā)展需求提出的。其核心在于利用發(fā)達(dá)國家高溫合金設(shè)計(jì)所用各種不同元素及其含量的配方與高溫持久試驗(yàn)的數(shù)據(jù)作為人工神經(jīng)網(wǎng)絡(luò)的訓(xùn)練數(shù)據(jù)庫,通過網(wǎng)絡(luò)訓(xùn)練獲得最佳權(quán)值矩陣(數(shù)學(xué)模型),并用以作為滿足設(shè)計(jì)條件的合金成分優(yōu)化的目標(biāo)函數(shù),在給定合金成分及試驗(yàn)條件范圍內(nèi)找到最佳持久性能的合金成分配方。該設(shè)計(jì)方法克服了現(xiàn)有其它方法的諸多不足,它基于任何一個(gè)獨(dú)立的試驗(yàn)部門都不可能獲取的大量實(shí)驗(yàn)數(shù)據(jù)(合金成分與持久試驗(yàn)條件),利用先進(jìn)的數(shù)學(xué)物理方法獲得用常規(guī)數(shù)理統(tǒng)計(jì)方法所無法獲得的數(shù)據(jù)之間復(fù)雜的復(fù)雜非線性定量關(guān)系,并用之進(jìn)行合金設(shè)計(jì)。其主要特點(diǎn)是,設(shè)計(jì)所基于的試驗(yàn)數(shù)據(jù)涉及廣泛的合金化學(xué)成分及高溫持久試驗(yàn)條件,設(shè)計(jì)所用目標(biāo)函數(shù)的獲取方法先進(jìn),設(shè)計(jì)是通過最優(yōu)化法尋找指定成分范圍內(nèi)獲最佳性能的配方,設(shè)計(jì)結(jié)果準(zhǔn)確性高,設(shè)計(jì)過程快速而經(jīng)濟(jì)。

      發(fā)明內(nèi)容
      本發(fā)明的目的在于提供一種鎳基高溫合金成分的優(yōu)化設(shè)計(jì)方法,該方法操作及計(jì)算簡便,設(shè)計(jì)結(jié)果準(zhǔn)確度高。
      本發(fā)明提供的技術(shù)方案是鎳基高溫合金成分的優(yōu)化設(shè)計(jì)方法,①收集鎳基變形高溫合金的成分、持久試驗(yàn)溫度、持久斷裂時(shí)間及其對(duì)應(yīng)的持久強(qiáng)度數(shù)據(jù)或鎳基單晶高溫合金的成分、持久試驗(yàn)溫度、持久應(yīng)力及其對(duì)應(yīng)的持久壽命數(shù)據(jù),然后將上述數(shù)據(jù)作為人工神經(jīng)網(wǎng)絡(luò)初始訓(xùn)練數(shù)據(jù)進(jìn)行網(wǎng)絡(luò)訓(xùn)練,并通過常規(guī)優(yōu)化隱含層神經(jīng)單元數(shù)、歸一化條件及動(dòng)量因子等神經(jīng)網(wǎng)絡(luò)參量,獲得鎳基變形高溫合金的持久強(qiáng)度或鎳基單晶高溫合金的持久壽命預(yù)測值與實(shí)測值誤差最小的網(wǎng)絡(luò)訓(xùn)練最佳權(quán)值矩陣;②將所獲得的最佳權(quán)值矩陣與成本的比值作為鎳基變形高溫合金或鎳基單晶高溫合金成分優(yōu)化設(shè)計(jì)所使用的目標(biāo)函數(shù),在此基礎(chǔ)上建立鎳基變形高溫合金或鎳基單晶高溫合金成分優(yōu)化設(shè)計(jì)的約束條件,以抑制有害相σ和μ相的形成和控制合金的密度;鎳基變形高溫合金成分優(yōu)化設(shè)計(jì)的數(shù)學(xué)模型為 式(1)、式(2)為鎳基變形高溫合金成分優(yōu)化設(shè)計(jì)所使用的目標(biāo)函數(shù);式(3)至式(6)為鎳基變形高溫合金成分優(yōu)化設(shè)計(jì)的約束條件;式中,σc(MPa)為合金持久強(qiáng)度的目標(biāo)函數(shù),w1、w2、b1、b2為通過神經(jīng)網(wǎng)絡(luò)訓(xùn)練得到的最佳權(quán)值矩陣,purelin為線性激活函數(shù),tansig為帶有偏差的雙曲正切S型激活函數(shù),其輸入變量的轉(zhuǎn)置矩陣s=[X1,X2,...,Xn,t,T]′,X1,X2,…,Xn依次為合金元素C、Cr、Co、Mo、Ti、Al、Fe、B、Zr、Ni、Nb、W、Ta、Mn、Si、V、Cb、Y的原子百分?jǐn)?shù)(at%),t為持久斷裂時(shí)間(h),T為持久試驗(yàn)溫度(℃);p為合金成本(元/公斤);pi為合金元素的單價(jià)(元/公斤);ci為元素i的重量百分?jǐn)?shù)(wt%),i=1,2,……n,依次對(duì)應(yīng)C、Cr、Co、Mo、Ti、Al、Fe、B、Zr、Ni、Nb、W、Ta、Mn、Si、V、Cb、Y共18種合金元素;(σc/p)max為性能與價(jià)格比的目標(biāo)函數(shù);Md為控制有害σ相的合金平均電子能級(jí),Mdγ為基體γ相的平均電子能級(jí),Xi和Xiγ分別表示合金和γ相中元素i的原子百分?jǐn)?shù),i=1,2,……n,n=18;(Md)i為元素i的d電子能級(jí),可通過查表獲得;XMo和XW分別為合金中Mo和W的原子百分?jǐn)?shù);合金密度&rho;=Walloy-cellValloy-cell=Nalloy-cellat&CenterDot;&Sigma;i=1n(Xit&CenterDot;Mt)/NAa3(g/(cm3)),]]>Walloy,Valloy分別為合金中一個(gè)晶胞內(nèi)所含各元素的原子總質(zhì)量和一個(gè)晶胞的體積;Xit、a分別為合金中元素i的原子百分?jǐn)?shù)和合金的點(diǎn)陣常數(shù);Nalloy-cellat表示一個(gè)晶胞的原子數(shù);Mi為元素i的摩爾質(zhì)量;NA為Avogadro常數(shù);對(duì)鎳基單晶高溫合金成分優(yōu)化設(shè)計(jì)的數(shù)學(xué)模型 式(7)、式(8)為鎳基單晶高溫合金成分優(yōu)化設(shè)計(jì)所使用的目標(biāo)函數(shù);式(9)至式(14)為鎳基單晶高溫合金成分優(yōu)化設(shè)計(jì)的約束條件;式中,f為合金的持久壽命,W1、W2、B1、B2為通過神經(jīng)網(wǎng)絡(luò)訓(xùn)練得到的最佳權(quán)值矩陣,S是一個(gè)輸入變量轉(zhuǎn)置矩陣S=[C1C2C3C4C5C6C7C8C9C10C11Tσ]‘,C1C2C3C4C5C6C7C8C9C10C11依次代表合金元素Co、Cr、W、Mo、Al、Ti、Nb、Ta、Re、Hf、V共11種元素的重量百分?jǐn)?shù),Cil和Cik分別表示在設(shè)計(jì)合金時(shí)所給成分范圍內(nèi)元素i的下限和上限值,T為持久試驗(yàn)溫度,σ為持久應(yīng)力;P為合金成本;Pj為合金元素的單價(jià);Ci為元素i的重量百分?jǐn)?shù);i=1,2……n,依次對(duì)應(yīng)Co、Cr、W、Mo、Al、Ti、Nb、Ta、Re、Hf、V共11種合金元素;(f/P)max為性能與價(jià)格比的目標(biāo)函數(shù);Mdi為i元素的控制有害σ相的合金電子能級(jí)Md值,Mdt為整個(gè)合金的Md值,Zi為價(jià)電子數(shù),M為合金元素的摩爾質(zhì)量,Ai為合金元素的原子百分?jǐn)?shù);A2、A3和A4分別表示合金中Cr、W和Mo的原子百分?jǐn)?shù),控制密度的約束條件為ρ<9.0(g/cm3);按上述優(yōu)化步驟和約束條件,在本訓(xùn)練數(shù)據(jù)庫中各元素含量范圍內(nèi)(分別見表1和表2),根據(jù)需要任意設(shè)置所要設(shè)計(jì)的鎳基變形高溫合金中各元素含量的范圍(Cil<C<Cik),通過優(yōu)化計(jì)算,即可在給定成分范圍和上述約束條件下搜索出能使目標(biāo)函數(shù)值達(dá)到最大值的合金的成分配方、在給定成分范圍內(nèi)搜索出高性能與價(jià)格比的合金成分配方。
      上述鎳基變形高溫合金的成分、持久試驗(yàn)溫度、持久斷裂時(shí)間及其對(duì)應(yīng)的持久強(qiáng)度數(shù)據(jù)選自下述數(shù)據(jù)庫A(鎳基變形高溫合金神經(jīng)網(wǎng)絡(luò)訓(xùn)練數(shù)據(jù)庫A)中的國外牌號(hào)合金409組數(shù)據(jù);鎳基單晶高溫合金的成分、持久試驗(yàn)溫度、持久應(yīng)力及其對(duì)應(yīng)的持久壽命數(shù)據(jù)選自下述數(shù)據(jù)庫B(鎳基單晶高溫合金神經(jīng)網(wǎng)絡(luò)訓(xùn)練數(shù)據(jù)庫B)中的所示的國外牌號(hào)合金700組數(shù)據(jù)。
      本發(fā)明采用現(xiàn)有設(shè)計(jì)方法所不能反映的多組元合金成分(對(duì)于鎳基變形合金可達(dá)18種元素;對(duì)于鎳基單晶合金可達(dá)11種元素)與復(fù)雜試驗(yàn)條件(對(duì)于鎳基變形合金,持久試驗(yàn)溫度范圍404~1149℃,持久斷裂時(shí)間14.7~1860h,持久強(qiáng)度3~823.2MPa;對(duì)于鎳基單晶合金,持久試驗(yàn)溫度700-1200℃,持久試驗(yàn)應(yīng)力50-1000MPa,持久斷裂壽命30-15000h)及試驗(yàn)結(jié)果(對(duì)于鎳基變形高溫合金為持久強(qiáng)度;對(duì)于鎳基單晶高溫合金為持久斷裂壽命)之間錯(cuò)綜復(fù)雜的非線性關(guān)系的數(shù)學(xué)模型。這個(gè)數(shù)學(xué)模型的獲得既不來源于純理論推導(dǎo),也不來自常用的數(shù)理統(tǒng)計(jì)方法(數(shù)理統(tǒng)計(jì)回歸法在表達(dá)上述參量之間復(fù)雜非線性關(guān)系方面的誤差很大),它來自用先進(jìn)人工神經(jīng)網(wǎng)絡(luò)訓(xùn)練現(xiàn)有的對(duì)鎳基高溫合金的試驗(yàn)數(shù)據(jù)所得。
      本發(fā)明基于廣泛使用的人工神經(jīng)網(wǎng)絡(luò)反向傳播法(BP法)建立網(wǎng)絡(luò)模型,引用近20多年來國外專利及相關(guān)試驗(yàn)研究者報(bào)告的關(guān)于鎳基變形高溫合金和鎳基單晶高溫合金的試驗(yàn)數(shù)據(jù)進(jìn)行網(wǎng)絡(luò)訓(xùn)練,將所獲得的最佳權(quán)值矩陣作為高溫合金最優(yōu)化設(shè)計(jì)所用的目標(biāo)函數(shù);網(wǎng)絡(luò)訓(xùn)練數(shù)據(jù)庫中包含409組鎳基變形高溫合金的成分、持久試驗(yàn)溫度、持久斷裂時(shí)間(輸入變量)及其對(duì)應(yīng)的持久強(qiáng)度(輸出變量)數(shù)據(jù)和700組鎳基單晶高溫合金的成分、持久試驗(yàn)溫度、持久應(yīng)力(輸入變量)及其對(duì)應(yīng)的持久壽命(輸出變量)數(shù)據(jù),因此本高溫合金設(shè)計(jì)方法所建立的數(shù)學(xué)模型以及所使用的試驗(yàn)數(shù)據(jù)量(輸入變量與輸出變量)之龐大是空前未有的;在建立目標(biāo)函數(shù)方面,首次將人工神經(jīng)網(wǎng)絡(luò)與最優(yōu)化計(jì)算相接合進(jìn)行合金設(shè)計(jì),即將人工神經(jīng)網(wǎng)絡(luò)訓(xùn)練所獲得的最佳權(quán)值矩陣作為合金最優(yōu)化設(shè)計(jì)的目標(biāo)函數(shù)(在除高溫合金以外的其它類型合金設(shè)計(jì)方面也未見雷同報(bào)道);與現(xiàn)有統(tǒng)計(jì)回歸法相比,采用人工神經(jīng)網(wǎng)絡(luò)法能反映眾多變量和數(shù)據(jù)(見表1和表2)之間復(fù)雜的非線性關(guān)系,并使輸出變量預(yù)測的準(zhǔn)確性大大提高;表3列出了7種未參與訓(xùn)練的鎳基變形高溫合金的成分、試驗(yàn)溫度、試驗(yàn)時(shí)間以及實(shí)測持久強(qiáng)度值與本網(wǎng)絡(luò)訓(xùn)練所得最佳權(quán)值矩陣算得的持久強(qiáng)度預(yù)測值;表4列出了16種未參與訓(xùn)練的鎳基單晶高溫合金的成分、試驗(yàn)溫度、試驗(yàn)應(yīng)力,表5列出了對(duì)應(yīng)合金的實(shí)測持久壽命值與本網(wǎng)絡(luò)訓(xùn)練所得最佳權(quán)值矩陣算得的持久壽命預(yù)測值,結(jié)果表明了本設(shè)計(jì)方法所得神經(jīng)網(wǎng)絡(luò)最佳權(quán)值矩陣的準(zhǔn)確性;以鎳基單晶合金為例,表5列出了線性誤差error(1)的數(shù)據(jù)表明,除16號(hào)合金的預(yù)測誤差較大以外,其余15種合金的預(yù)測誤差均較小,表5所用error(2)為對(duì)數(shù)誤差,其平均誤差率為0.93%。本發(fā)明預(yù)測對(duì)數(shù)誤差率最??;此外,本發(fā)明方法用于網(wǎng)絡(luò)訓(xùn)練的合金成分及試驗(yàn)條件(溫度及應(yīng)力)范圍更寬,數(shù)據(jù)來源錯(cuò)綜復(fù)雜,但其預(yù)測的準(zhǔn)確性卻明顯提高;本發(fā)明方法集合了用人工神經(jīng)網(wǎng)絡(luò)法獲取準(zhǔn)確預(yù)測輸出變量的數(shù)學(xué)模型,用優(yōu)化法在給定合金成分范圍內(nèi)尋找滿足各項(xiàng)約束條件(控制有害相形成、控制合金密度及控制合金成本的各項(xiàng)指標(biāo)條件)而獲得目標(biāo)函數(shù)輸出變量所表征的最佳高溫持久性能的合金成分配方。以上兩步過程實(shí)現(xiàn)的人工神經(jīng)網(wǎng)絡(luò)運(yùn)算程序以及優(yōu)化設(shè)計(jì)運(yùn)算程序是利用通用軟件Matlab中的神經(jīng)網(wǎng)絡(luò)工具箱和優(yōu)化工具箱編制而成,過程簡單,計(jì)算速度快,結(jié)果準(zhǔn)確性高,可直接應(yīng)用于現(xiàn)代鎳基高溫合金的設(shè)計(jì),是目前運(yùn)用實(shí)驗(yàn)數(shù)據(jù)量最大,目標(biāo)函數(shù)獲取的科學(xué)性高,綜合考慮對(duì)有害相、合金密度及合金成本進(jìn)行有效控制的新設(shè)計(jì)方法,該方法不僅可運(yùn)用于鎳基高溫合金設(shè)計(jì),并可推廣到其它所有民用工業(yè)及軍用工業(yè)合金的設(shè)計(jì)領(lǐng)域,其應(yīng)用前景十分寬廣,不僅可為合金設(shè)計(jì)的科學(xué)與技術(shù)進(jìn)步作出重要貢獻(xiàn),而且為工業(yè)應(yīng)用提供了更為科學(xué)合理的設(shè)計(jì)工具。
      具體實(shí)施例方式
      本發(fā)明鎳基高溫合金成分的優(yōu)化設(shè)計(jì)方法,包括以下步驟①數(shù)據(jù)及優(yōu)化設(shè)計(jì)目標(biāo)函數(shù)的來源,分別收集國外牌號(hào)的409組鎳基變形高溫合金的成分、持久試驗(yàn)溫度、持久斷裂時(shí)間及其對(duì)應(yīng)的持久強(qiáng)度數(shù)據(jù)和700組鎳基單晶高溫合金的成分、持久試驗(yàn)溫度、持久應(yīng)力及其對(duì)應(yīng)的持久壽命數(shù)據(jù),然后將上述兩類數(shù)據(jù)分別作為所對(duì)應(yīng)兩類合金的人工神經(jīng)網(wǎng)絡(luò)初始訓(xùn)練數(shù)據(jù)進(jìn)行網(wǎng)絡(luò)訓(xùn)練(利用通用軟件Matlab 6.0的神經(jīng)網(wǎng)絡(luò)工具箱編制程序,建立網(wǎng)絡(luò)模型,進(jìn)行網(wǎng)絡(luò)訓(xùn)練),并通過常規(guī)優(yōu)化隱含層神經(jīng)單元數(shù)、歸一化條件及動(dòng)量因子等神經(jīng)網(wǎng)絡(luò)參量,分別獲得對(duì)應(yīng)上述兩類合金的持久強(qiáng)度(變形合金)和持久壽命(單晶合金)預(yù)測值與實(shí)測值誤差最小的網(wǎng)絡(luò)訓(xùn)練權(quán)值矩陣,即最佳權(quán)值矩陣,將該權(quán)值矩陣保存下來并作為成分優(yōu)化設(shè)計(jì)的目標(biāo)函數(shù);②優(yōu)化過程的實(shí)現(xiàn)利用通用軟件Matlab 6.0的優(yōu)化工具箱編制程序,將所獲得的兩種最佳權(quán)值矩陣分別作為鎳基變形高溫合金和鎳基單晶高溫合金成分優(yōu)化設(shè)計(jì)所計(jì)算用的目標(biāo)函數(shù),并建立約束條件,以抑制有害相σ和μ相的形成以及控制合金的密度;由于在優(yōu)化計(jì)算前,已將價(jià)格昂貴的合金元素以及會(huì)促進(jìn)有害相形成的合金元素的含量范圍作了設(shè)定,因此優(yōu)化計(jì)算過程中只會(huì)在各參量設(shè)定的范圍內(nèi)進(jìn)行優(yōu)化搜索,以找到低成本、高性能的最佳結(jié)果;③優(yōu)化計(jì)算結(jié)果包含,在指定試驗(yàn)條件下的最佳性能及其對(duì)應(yīng)的合金成分配方,對(duì)于鎳基變形高溫合金,試驗(yàn)條件為持久溫度和持久斷裂時(shí)間,所得最佳性能指標(biāo)是持久斷裂強(qiáng)度值,對(duì)于鎳基單晶高溫合金,試驗(yàn)條件為持久溫度和持久應(yīng)力,所得最佳性能指標(biāo)是持久壽命。
      對(duì)鎳基變形高溫合金持久強(qiáng)度的目標(biāo)函數(shù)σc=purelin(w2*tan sig(s*w1+b1)+b2)其輸入變量的轉(zhuǎn)置矩陣s=[X1,X2,...,Xn,t,T]′,包括C、Cr、Co、Mo、Ti、Al、Fe、B、Zr、Ni、Nb、W、Ta、Mn、Si、V、Cb、Y等18種合金元素的原子百分?jǐn)?shù)(即按上述合金元素的順序分別以1、2、3…n作為下標(biāo)編號(hào),其中n=18)和持久斷裂時(shí)間t及持久試驗(yàn)溫度T(℃),其輸出變量為持久斷裂強(qiáng)度σ(MPa);合金成本計(jì)算是根據(jù)合金元素的單價(jià)(pt,元/公斤)乘以每種元素的重量百分?jǐn)?shù)(Ci)確定的,即P=&Sigma;i=1npi*Ci&Sigma;i=1nCi=1i=1,2,&CenterDot;&CenterDot;&CenterDot;&CenterDot;&CenterDot;&CenterDot;n]]>(合金中有n種元素)則性能與價(jià)格比的目標(biāo)函數(shù)是(σ/P)max優(yōu)化約束條件為,(1)引用限制元素Mo、W和Cr的含量以控制有害相產(chǎn)生的算式,控制有害σ相的Md電子能級(jí)相計(jì)算法,即Md=∑Xi(Md)i<0.99,Mdγ=∑Xiγ(Md)i<0.94,Xi和Xiγ分別表示合金和γ相中組元i的原子百分含量,(Md)i為組元i的d電子能級(jí);(2)引用控制有害μ相的Mo、W含量限制法,即R&OverBar;MoW=XMoXMo+XW&lt;0.27,]]>XMo和XW分別為合金中Mo和W的原子百分?jǐn)?shù);(3)控制密度,使合金密度ρ低于8.9g/cm3,&rho;=Walloy-cellValloy-cell=Nalloy-cellat&CenterDot;&Sigma;i=1n(Xit&CenterDot;Mi)/NAaalloy3,]]>Walloy,Valloy分別為合金中一個(gè)晶胞內(nèi)所含各元素的原子質(zhì)量(g)和一個(gè)晶胞的體積(nm3);Xit、a分別為合金中組元i的原子百分含量(at.%)和合金的點(diǎn)陣常數(shù)(nm);Nalloy-cellat表示一個(gè)晶胞的原子數(shù);Mi為組元i的摩爾質(zhì)量;NA為Avogadro常數(shù),此外,合金中各元素的原子百分?jǐn)?shù)應(yīng)為1,即&Sigma;i=1nXi=1,]]>i=1,2,……n,合金中有n種元素)。
      對(duì)鎳基單晶高溫合金合金的持久壽命目標(biāo)函數(shù)為f=purelin(W2*tan sig((W1*S),B1),B2)max其中,輸入變量的轉(zhuǎn)置矩陣S=[C1C2C3C4C5C6C7C8C9C10C11Tσ]‘合金成本計(jì)算是根據(jù)合金元素的單價(jià)(pi,元/公斤)乘以每種元素的重量百分?jǐn)?shù)(Ci)確定的(i=1,2,…,n),即P=&Sigma;i=1npi*Ci&Sigma;i=1nCi=1i=1,2,&CenterDot;&CenterDot;&CenterDot;&CenterDot;&CenterDot;&CenterDot;n]]>(合金中有n種元素)設(shè)計(jì)時(shí)人為設(shè)置CtCil<Ct<Cik,Cil和Cik分別表示在設(shè)計(jì)合金時(shí)所給成分范圍內(nèi)元素i的下限和上限值,則性能與價(jià)格比的目標(biāo)函數(shù)是(σ/P)max優(yōu)化約束條件為Mdt=∑Ai*Mdi<0.99ΔE=∑Ai*Zi-(6.28+0.036*∑Ai*M)<0.03Mdi為i元素的Md值,Mdt為整個(gè)合金的Md值,Zi為價(jià)電子數(shù),M為合金元素的摩爾質(zhì)量,Ai為合金元素的原子百分?jǐn)?shù),控制有害μ相的約束條件為A2+A3+A4<11A3+A4<4.3A4/(A3+A4)<0.3&Sigma;i=1nAi=1]]>i=1,2,……n(合金中有n種元素)式中,A2、A3和A4分別表示合金中Cr、W和Mo的原子百分?jǐn)?shù)含量,控制密度的約束條件為ρ<9.0(g/cm3),其算法同于鎳基變形合金;優(yōu)化過程的實(shí)現(xiàn),對(duì)現(xiàn)有合金進(jìn)行成分優(yōu)化設(shè)計(jì)時(shí),設(shè)置所設(shè)計(jì)的合金中各元素含量的范圍及試驗(yàn)條件(在網(wǎng)絡(luò)初始訓(xùn)練數(shù)據(jù)庫輸入變量成分范圍及試驗(yàn)條件范圍內(nèi)),通過優(yōu)化計(jì)算在給定成分范圍和上述約束條件下,搜索出能使目標(biāo)函數(shù)值(鎳基變形合金的持久強(qiáng)度和鎳基單晶合金的持久壽命)達(dá)到最大值的合金的成分配方,然后對(duì)合金配方的經(jīng)濟(jì)成本進(jìn)行測算,即將優(yōu)化出的合金的各元素的重量百分?jǐn)?shù)與對(duì)應(yīng)元素的單價(jià)相乘并求和即得,于是在給定成分和試驗(yàn)條件范圍內(nèi),即可搜索出滿足目標(biāo)函數(shù)和約束條件的高性能與價(jià)格比的合金成分配方。
      實(shí)例實(shí)例1優(yōu)化鎳基變形高溫合金的成分。以GH150合金為例,對(duì)該合金進(jìn)行成分優(yōu)化,并預(yù)測其在816℃、1000h下的持久斷裂強(qiáng)度。按‘具體實(shí)施方式
      ’中的①~③步驟,先后將反映持久斷裂強(qiáng)度與合金成分及試驗(yàn)條件(持久試驗(yàn)溫度及斷裂時(shí)間)之間復(fù)雜非線性關(guān)系的人工神經(jīng)網(wǎng)絡(luò)最佳權(quán)值矩陣作為最優(yōu)化設(shè)計(jì)的目標(biāo)函數(shù),將控制有害相(Md相計(jì)算)及合金密度的因素作為約束條件,進(jìn)行合金優(yōu)化設(shè)計(jì)計(jì)算,結(jié)果得到改良合金的成分配方和持久斷裂強(qiáng)度的預(yù)測值,如表6所示。即在原GH150合金成分基礎(chǔ)上,設(shè)計(jì)出的合金在816℃、1000h時(shí)的持久斷裂強(qiáng)度(130MPa)比原合金在同等試驗(yàn)條件下的持久斷裂強(qiáng)度(112.45MPa)能提高近16%,性/價(jià)比提升了17%,為該合金的改良提供了重要參考意義。
      實(shí)例2優(yōu)化鎳基單晶高溫合金的成分。以無錸第二代鎳基單晶高溫合金DD98(我國近期研制的合金牌號(hào))和MC2(法國牌號(hào))以及含錸第二代鎳基單晶高溫合金CMSX-4(美國牌號(hào))合金為例進(jìn)行比較,在設(shè)定成分范圍內(nèi)進(jìn)行成分優(yōu)化設(shè)計(jì),分別獲得表7所示的各合金的成分配方,即獲得無錸Alloy1和含錸Alloy2兩種合金,各給定牌號(hào)合金的實(shí)測持久壽命及用本發(fā)明方法預(yù)測的持久斷裂壽命值也一并列于表7中,需要說明錸的價(jià)格為黃金價(jià)格的三分之一;其結(jié)果的獲得是按‘具體實(shí)施方式
      ’中的①~③步驟,先后將反映持久壽命與合金成分及試驗(yàn)條件(持久試驗(yàn)溫度及應(yīng)力)之間復(fù)雜非線性關(guān)系的人工神經(jīng)網(wǎng)絡(luò)最佳權(quán)值矩陣作為最優(yōu)化設(shè)計(jì)的目標(biāo)函數(shù),將對(duì)有害相(σ、μ相)及合金密度(ρ)的控制因素作為約束條件,進(jìn)行合金優(yōu)化設(shè)計(jì)計(jì)算,結(jié)果得到改良合金(無錸第二代單晶合金Alloy1和含錸第二代單晶合金Alloy2)的成分配方和持久斷裂壽命值的預(yù)測值,見表7;可見,用本發(fā)明方法采用的人工神經(jīng)網(wǎng)絡(luò)預(yù)測,所得壽命預(yù)測值與實(shí)測值很接近;所設(shè)計(jì)改良合金的持久壽命預(yù)測值及性/價(jià)比明顯提高將本發(fā)明設(shè)計(jì)的不含錸的Alloy1合金與國內(nèi)同類的DD98合金相比其性/價(jià)比提高了50%,與法國同類的MC2合金相比提高了20%;而本發(fā)明設(shè)計(jì)的含錸的Alloy2合金的性/價(jià)比為美國同類合金CMSX-4的一倍。
      表1用于鎳基變形高溫合金網(wǎng)絡(luò)訓(xùn)練數(shù)據(jù)的各變量范圍

      表2用于鎳基單晶高溫合金網(wǎng)絡(luò)訓(xùn)練數(shù)據(jù)的各變量范圍

      表3對(duì)鎳基變形高溫合金建立的網(wǎng)絡(luò)進(jìn)行可靠性檢驗(yàn)

      表4對(duì)鎳基單晶高溫合金建立的網(wǎng)絡(luò)進(jìn)行可靠性檢驗(yàn)所用參量

      表5對(duì)鎳基單晶高溫合金建立的網(wǎng)絡(luò)進(jìn)行可靠性檢驗(yàn)

      *誤差(1)=|tf′-tf|/tf×100%誤差(2)=|lgtf′-lgtf|/lgtf×100%
      表6在給定成分范圍內(nèi)對(duì)鎳基變形高溫合金GH150進(jìn)行成分優(yōu)化并預(yù)測其在816℃/1000h下的持久斷裂強(qiáng)度

      注σ為持久強(qiáng)度設(shè)計(jì)值表7第二代鎳基單晶高溫合金在980℃/250MPa下的持久壽命

      注范圍1為無錸鎳基單晶合金成分優(yōu)化設(shè)計(jì)的元素含量范圍;范圍2為含錸鎳基單晶合金成分優(yōu)化設(shè)計(jì)的元素含量范圍;Alloy1用本發(fā)明法設(shè)計(jì)的無錸(Re)鎳基單晶高溫合金,Alloy2用本發(fā)明法設(shè)計(jì)的含錸(Re)第二代鎳基單晶高溫合金;CMSX-4合金還含元素0.1%Hf
      數(shù)據(jù)庫A(鎳基變形高溫合金神經(jīng)網(wǎng)絡(luò)訓(xùn)練數(shù)據(jù)庫)合金牌號(hào)CCr Co Mo Ti Al Fe BZr NiNb WTa Mn Si VCb Y測試溫度(C) 壽命(h) 測試應(yīng)力(Mpa)A 0.1 8 10 6 1 60 0.06 0.1 64.49 004.250000 0760 31 648A-1 0.12 7.8710.156.061.085.95 0 0.1 0.05 64.22 004.4 0000 0760 229.6 648B 0.1 10 10 3 1 60 0.0150.1 62.785007 0000 0760 102.1 648B-1 0.11 10.210 3.051.126.3 0 0.1 0.14 62.23 006.750000 0760 297.2 648C 0.15 9 10 0 2 50 0.0150.05 60.285012.5 0 0001 0760 46.7648C-1 0.15 8.7510.1 0 1.984.99 0 0.1 0.06 60.64 012 0 0001.230760 400.6 648C-2 0.09 9.3 10.3 0 2.084.8 0 0.13 0.03 59.26 012.810 0001.2 0760 442.6 648C-3 0.15 8.7510.1 0 1.984.99 0 0.2 0.06 60.54 012 0 0001.230760 245.5 648E-1 0.18 10.115.1 3.014.8 5.33 0 0.1 0.06 60.46 000 000.86 0 0760 345 648A 0.1 8 10 6 1 60 0.0160.1 64.534004.250000 0982 53.2200A-2 0.0149.7512.155.890.965.95 0 0.0810.07361.422003.710000 0760 146.5 648A-2 0.0149.7512.155.890.965.95 0 0.0810.07361.422003.710000 0982 44.8200B 0.1 10 10 3 1 60 0.0150.1 62.785007 0000 0982 50.3200B-2 0.04 10.56 11.763.1 0.996.03 0 0.1090.08461.627005.7 0000 0760 206 648B-2 0.04 10.56 11.763.1 0.996.03 0 0.1090.08461.627005.7 0000 0982 52.4200D 0.15 9 10 2.5 1.5 5.5 0 0.0150.05 59.785010 1.5 0000 0760 120 648D 0.15 9 10 2.5 1.5 5.5 0 0.0150.05 59.785010 1.5 0000 0982 50 200D-1 0.0099.6610.912.431.385.19 0 0.0840.06259.11509.66 1.5 0000 0760 432.8 648F 0.21 12.592 4.2 3.2 0 0.02 0.1 60.97 03.9 3.9 0000 0760 62 648F 0.21 12.592 4.2 3.2 0 0.02 0.1 60.97 03.9 3.9 0000 0982 30 200F-1 0.00911.35 9.43 2.043.693.92 0 0.0960.08360.97204.18 4.230000 0982 79.2200C-4 0.0119.3310.660 1.765.65 0 0.02 0.07759.132012.410 0000.950760 314.8 648C-4 0.0119.3310.660 1.765.65 0 0.02 0.07759.132012.410 0000.950982 73.6200C-5 0.01 8.3310.7 0 1.785.53 0 0.03 0.07560.195012.4 0 0000.950760 392.2 648C-5 0.01 8.3310.7 0 1.785.53 0 0.03 0.07560.195012.4 0 0000.950982 85.2200C-6 0.0148.8910.640 1.775.63 0 0.08 0.07959.237012.740 0000.920760 448 648C-6 0.0148.8910.640 1.775.63 0 0.08 0.07959.237012.740 0000.920982 113.9 200
      C-70.0128.61 10.660 1.785.8 00.14 0.06859.17 012.8400000.920760452.9648C-70.0128.61 10.660 1.785.8 00.14 0.06859.17 012.8400000.920982122.4200C-80.0118.64 10.710 1.755.4100.15 0.07459.495012.8400000.920760468.6648C-90.0188.97 10.780 1.775.1300.2 0.06559.607012.5500000.910760459.8648C-90.0188.97 10.780 1.775.1300.2 0.06559.607012.5500000.910982117.1200C-10 0.0188.96 10.6 0 1.765.1500.2350.15459.863012.4100000.850760458.6648C-10 0.0188.96 10.6 0 1.765.1500.2350.15459.863012.4100000.85098264.8 200C-11 0.0459.5 10.5 0 2 4.9800.1 0.06 49.415012.5 000010.90760397.2648C-11 0.0459.5 10.5 0 2 4.9800.1 0.06 49.415012.5 000010.9098292.3 200C-12 0.0239.54 10.690 1.754.7600.28 0.05360.184011.8400000.880760347.4648C-12 0.0239.54 10.690 1.754.7600.28 0.05360.184011.8400000.88098243 200C-13 0.03310 10.540 1.754.7600.39 0.03858.189013.5100000.79076080.7 648C-13 0.03310 10.540 1.754.7600.39 0.03858.189013.5100000.79098214.7 200E-20.01 8.56 16.6 3.014.895.5800.0180.07960.193000001.06 0 076038.6 648E-20.01 8.56 16.6 3.014.895.5800.0180.07960.193000001.06 0 098227 200E-30.0089.1 16.672.944.9 5.7100.0440.06759.491000001.07 0 076068.1 648E-30.0089.1 16.672.944.9 5.7100.0440.06759.491000001.07 0 098248.6 200E-40.0088.95 16.623.174.885.6 00.0880.07459.54 000001.07 0 0760104.2648E-40.0088.95 16.623.174.885.6 00.0880.07459.54 000001.07 0 098241.3 200E-50.0089.67 16.423.064.745.6100.09 0.07159.251000001.08 0 0760117.2648E-50.0089.67 16.423.064.745.6100.09 0.07159.251000001.08 0 098238.1 200E-60.01 9.87 16.623.034.915.6300.1250.06 58.685000001.06 0 0760174.1648E-60.01 9.87 16.623.034.915.6300.1250.06 58.685000001.06 0 098241.2 200E-70.0119.87 16.863.254.645.2200.17 0.06758.916000000.9960 0760266.3648E-70.0119.87 16.863.254.645.2200.17 0.06758.916000000.9960 098236.5 200E-80.01210.2216.8 3.334.645.2300.18 0.06958.509000001.01 0 0760302.2648E-80.01210.2216.8 3.334.645.2300.18 0.06958.509000001.01 0 098231.9 200E-90.01210.0516.693.324.565.2300.22 0.06458.844000001.01 0 0760357.6648E-90.01210.0516.693.324.565.2300.22 0.06458.844000001.01 0 098227.6 200
      ASTROLOY 0.0615175.3 3.54 0 0.030 55.110 000 0 000 6491000770ASTROLOY 0.0615175.3 3.54 0 0.030 55.110 000 0 000 7041000580ASTROLOY 0.0615175.3 3.54 0 0.030 55.110 000 0 000 7601000430ASTROLOY 0.0615175.3 3.54 0 0.030 55.110 000 0 000 8161000290ASTROLOY 0.0615175.3 3.54 0 0.030 55.110 000 0 000 8711000175ASTROLOY 0.0615175.3 3.54 0 0.030 55.110 000 0 000 9271000110ASTROLOY 0.0615175.3 3.54 0 0.030 55.110 000 0 000 982100055D-979 0.05150 4 3 1 27 0.010 49.490 000.25 0.2000 6491000515D-979 0.05150 4 3 1 27 0.010 49.490 000.25 0.2000 7041000380D-979 0.05150 4 3 1 27 0.010 49.490 000.25 0.2000 7601000250D-979 0.05150 4 3 1 27 0.010 49.490 000.25 0.2000 8161000145D-979 0.05150 4 3 1 27 0.010 49.490 000.25 0.2000 871100069HASTELLOYS0.0215.5 0 14.50 0.21 0.009 0 67.871 0 000.50.4000 6491000270HASTELLOYS0.0215.5 0 14.50 0.21 0.009 0 67.871 0 000.50.4000 7041000170HASTELLOYS0.0215.5 0 14.50 0.21 0.009 0 67.871 0 000.50.4000 7601000105HASTELLOYS0.0215.5 0 14.50 0.21 0.009 0 67.871 0 000.50.4000 816100068HASTELLOYS0.0215.5 0 14.50 0.21 0.009 0 67.871 0 000.50.4000 871100038INCONEL6000.0815.5 0 0 0 1.48 0 0 74.320 000.50.2000 816100039INCONEL6000.0815.5 0 0 0 1.48 0 0 74.320 000.50.2000 982100012INCONEL6000.0815.5 0 0 0 1.48 0 0 74.320 000.50.2000 1093 10006INCONEL6010.05230 0 0 1.414.1 0 0 60.750 000.50.2000 6491000195INCONEL6010.05230 0 0 1.414.1 0 0 60.750 000.50.2000 704100090INCONEL6010.05230 0 0 1.414.1 0 0 60.750 000.50.2000 760100063INCONEL6010.05230 0 0 1.414.1 0 0 60.750 000.50.2000 816100043INCONEL6010.05230 0 0 1.414.1 0 0 60.750 000.50.2000 871100030INCONEL6010.05230 0 0 1.414.1 0 0 60.750 000.50.2000 982100014INCONEL6010.05230 0 0 1.414.1 0 0 60.750 000.50.2000 1093 10007INCONEL6010.05230 0 0 1.414.1 0 0 60.750 000.50.2000 1149 10006A 0.018 280 0 0.02 0.02 0 0.005 0.0456.739 0.0215.1 00.01 0.02 000.008 900100553.9
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      0.15 15 18.5 5.23.54.25 10.050 52.35000000006491000702.660.15 15 18.5 5.23.54.25 10.050 52.35000000008161000295.960.15 15 18.5 5.23.54.25 10.050 52.35000000008711000186.20.07 18 153 5 2.50.5 0.020 55.91000000008161000320.460.15 19 1010 2.61 00.005 0 57.245 000000006491000550.760.15 19 1010 2.61 00.005 0 57.245 000000008161000151.90.24 16.25 7.2 16 3.21.99.5 0.008 0.06 45.642 000000006491000675.220.24 16.25 7.2 16 3.21.99.5 0.008 0.06 45.642 000000008161000234.220.24 16.25 7.2 16 3.21.99.5 0.008 0.06 45.642 000000008711000151.90.24 16.25 7.2 16 3.21.99.5 0.008 0.06 45.642 00000000982100045.080.09 19 1110 3.11.500.010 55.3 000000006491000702.660.09 19 1110 3.11.500.010 55.3 000000007321000445.90.09 19 1110 3.11.500.010 55.3 000000008161000199.920.09 19 1110 3.11.500.010 55.3 000000008711000117.60.05 15 0 9 2.51.25 22 0 0 50.2 000000006491000537.040.05 15 0 9 2.51.25 22 0 0 50.2 000000007321000254.80.27 9.3 153.25 3.25 5.25 00.015 0 58.315 05.35 0000008161000392.980.27 9.3 153.25 3.25 5.25 00.015 0 58.315 05.35 000000982100068.60.116 1.5 5.53 15 80 0 50.9 00000000649100 5880.116 1.5 5.53 15 80 0 50.9 00000000816100 274.40.116 1.5 5.53 15 80 0 50.9 00000000982100 54.880.05 15 0 0 2.50.75 70 0 74.7 00000000816100 131.320.05 15 0 0 2.50.75 70 0 74.7 00000000982100 22.050.08 15 0 0 2.50.770 0 73.820.9 0000000649100 551.740.08 15 0 0 2.50.770 0 73.820.9 0000000732100 344.960.08 15 0 0 2.50.770 0 73.820.9 0000000816100 193.060.08 15 0 0 2.50.770 0 73.820.9 0000000871100 124.460.08 15 0 0 2.50.770 0 73.820.9 0000000982100 22.540.115 293 2.25 2.85 10.005 0.05 46.745 00000000649100 686
      0.1 15293 2.252.8510.0050.05 46.74500000000732100519.40.1 15293 2.252.8510.0050.05 46.74500000000816100295.960.1 15293 2.252.8510.0050.05 46.745000000008711001960.1 15293 2.252.8510.0050.05 46.7450000000098210041.160.0819184 2.9 2.9 40.0050 49.11500000000816100302.820.0819184 2.9 2.9 40.0050 49.115000000008711001960.0819184 2.9 2.9 40.0050 49.11500000000982100823.20.0519126 3 2 00.0050 57.94500000000816100302.820.1518174 3 4 00.04 0 53.81 0000000098210089.180.151518.5 5.2 3.5 4.2510.05 0 52.35 00000000871100282.240.151518.5 5.2 3.5 4.2510.05 0 52.35 00000000982100110.740.0718153 5 2.5 0.5 0.02 0 55.91 00000000816100468.440.151910102.6 1 00.0050 57.24500000000649100661.50.151910102.6 1 00.0050 57.24500000000816100241.080.2416.25 7.2 163.2 1.9 9.5 0.0080.06 45.64200000000816100323.40.2416.25 7.2 163.2 1.9 9.5 0.0080.06 45.64200000000871100220.5Unitemp1753 0.2416.25 7.2 163.2 1.9 9.5 0.0080.06 45.6420000000098210068.60.091911103.1 1.5 00.01 0 55.3 00000000649100757.540.091911103.1 1.5 00.01 0 55.3 00000000732100555.660.091911103.1 1.5 00.01 0 55.3 00000000816100309.680.091911103.1 1.5 00.01 0 55.3 00000000871100192.080.091911103.1 1.5 00.01 0 55.3 0000000098210068.60.05150 9 2.5 1.2522 00 50.2 00000000649100688.940.05150 9 2.5 1.2522 00 50.2 00000000732100382.20.05150 9 2.5 1.2522 00 50.2 00000000816100172.480.279.3 153.25 3.255.2500.0150 58.31505.35 000000816100495.880.279.3 153.25 3.255.2500.0150 58.31505.35 000000982100138.18E 0.1810153 4.7 5.5 00.0150.06 60.54500000100760266648INCONEL6000.0815.5 0 0 0 1.4 800 74.32 0000.5 0.2 0008711000 24
      INCONEL617 0.0722 12.5 9 0 1 0 00 55.430 0 000000760100016512 0.0222.8 00 0.30 0 00 58.720 18.1 000000.06 1000 723 29.42pene95 0.1514 83.5 2.53.50 0.01 0.0561.293.53.5 0000007041000525AF2-10A 0.3512 10 3 3 4.60.526 0.0140.0159 0 6 1.5 000007601000525AF2-10A 0.3512 10 3 3 4.60.526 0.0140.0159 0 6 1.5 000008161000380GH1500.0515 04.5 2.11.128.1220.0080.0245 1.13 000000600100 7850.0515 04.5 2.11.128.1220.0080.0245 1.13 000000600500 7000.0515 04.5 2.11.128.1220.0080.0245 1.13 00000060010006700.0515 04.5 2.11.128.1220.0080.0245 1.13 000000700100 5000.0515 04.5 2.11.128.1220.0080.0245 1.13 000000700500 4000.0515 04.5 2.11.128.1220.0080.0245 1.13 00000070010003600.0515 04.5 2.11.128.1220.0080.0245 1.13 000000800100 2550.0515 04.5 2.11.128.1220.0080.0245 1.13 000000800500 1750.0515 04.5 2.11.128.1220.0080.0245 1.13 00000080010001400.0515 04.5 2.11.128.1220.0080.0245 1.13 000000900100 900.0515 04.5 2.11.128.1220.0080.0245 1.13 000000900500 550.0515 04.5 2.11.128.1220.0080.0245 1.13 000000900100040
      數(shù)據(jù)庫B(鎳基單晶高溫合金神經(jīng)網(wǎng)絡(luò)訓(xùn)練數(shù)據(jù)庫)美國專利號(hào) 合金編號(hào)元素試驗(yàn)條件 試驗(yàn)結(jié)果4707129 Co Cr W Mo Al Ti Nb Ta Re Hf V Ni 溫度(℃) 應(yīng)力(MPa) 持久壽命(h)TMS-17.50 5.5016.60 0.005.200.00 0.005.100.000.000.0060.101040 137 1751TMS-27.30 5.5018.60 0.005.300.00 0.003.400.000.000.0059.901040 137 1707A14545.00 10.00 4.000.005.001.50 0.0012.00 0.000.000.0062.501040 137 440A203E0.00 5.005.002.005.501.10 0.006.503.000.000.0071.901040 137 400NA1000.00 9.0010.50 1.005.751.20 0.003.300.000.000.0069.251040 137 5104629521 A. 5.00 16.00 7.002.003.503.50 0.000.000.000.000.0063.00982152 93.6B. 5.00 16.20 7.002.003.503.50 0.000.000.000.000.5062.30982152 119.7C. 0.01 16.30 4.102.993.503.60 0.000.000.000.000.0069.51982152 50.8H. 5.00 15.70 5.911.553.483.60 0.000.000.000.000.0064.76982152 82.1I. 5.00 15.60 5.901.543.563.70 0.000.000.000.000.0064.70982152 74.5J. 5.00 16.00 5.901.504.502.00 0.000.000.000.000.5064.60982152 113.4A. 5.00 16.00 7.002.003.503.50 0.000.000.000.000.0063.00760621 203.1B. 5.00 16.20 7.002.003.503.50 0.000.000.000.000.5062.30760621 242.7C. 0.01 16.30 4.102.993.503.60 0.000.000.000.000.0069.51760621 53.9D. 5.00 16.20 4.103.033.503.60 0.000.000.000.000.0064.57760621 128.6E. 5.00 15.70 5.871.533.563.60 0.000.000.000.000.0064.74760621 97.9H. 5.00 15.70 5.911.553.483.60 0.000.000.000.000.0064.76760621 89.9I. 5.00 15.60 5.901.543.563.70 0.000.000.000.000.0064.70760621 114.9J. 5.00 16.00 5.901.504.502.00 0.000.000.000.000.5064.60760621 132.44791080 B1*5.00 7.906.902.005.401.00 0.005.900.000.100.0065.80982248.2 107.5B10*10.007.504.902.005.501.00 0.003.902.900.100.0062.20982248.2 164.7B22 10.007.008.101.005.500.00 0.006.103.100.100.0059.10982248.2 273.8B35*10.007.003.500.005.500.00 0.0010.90 4.000.100.0059.00982248.2 272.9B46 10.006.803.801.005.500.00 0.007.405.100.100.0060.30982248.2 276.7B48 10.005.004.002.005.600.00 0.0010.90 3.100.100.0059.30982248.2 319.6B49 10.005.006.002.005.600.00 0.009.003.100.100.0059.20982248.2 406.8
      4209348Al444(a)0.009.00 12.000.005.002.000.000.00 0.000.000.0072.0092734582.6Al454(a)5.0010.004.00 0.005.001.500.0012.000.000.000.0062.50980248.2 100PWA1422(b) 10.00 9.00 12.000.005.002.001.000.00 0.002.000.0059.0092734576SM200(b,c,d) 10.00 9.00 12.500.005.002.001.000.00 0.000.000.0060.50760655728.4Al444(a)0.009.00 12.000.005.002.000.000.00 0.000.000.0072.00982200310Al454(a)5.0010.004.00 0.005.001.500.0012.000.000.000.0062.50871483161PWA1422(b) 10.00 9.00 12.000.005.002.001.000.00 0.002.000.0059.00982200160SM200(b,c,d) 10.00 9.00 12.500.005.002.001.000.00 0.000.000.0060.50982207124.5Al454(a)5.0010.004.00 0.005.001.500.0012.000.000.000.0062.507606551200Al454(a)5.0010.004.00 0.005.001.500.0012.000.000.000.0062.50760758475Al454(a)5.0010.004.00 0.005.001.500.0012.000.000.000.0062.50927345165.6Al454(a)5.0010.004.00 0.005.001.500.0012.000.000.000.0062.50982200350Al454(a)5.0010.004.00 0.005.001.500.0012.000.000.000.0062.509822072404222794203E0.005.00 5.00 2.005.501.100.006.50 3.000.000.4071.50982248.2 264201E0.005.00 5.00 2.004.752.250.006.50 3.000.000.0071.50982248.2 182202E0.005.00 5.00 2.005.501.500.006.50 3.000.000.0071.50982248.2 180204E0.005.00 5.00 2.005.500.700.006.50 3.000.000.8071.50982248.2 172203E0.005.00 5.00 2.005.501.100.006.50 3.000.000.4071.508714833894371404225 9.8010.004.00 0.005.001.400.0011.600.000.000.0058.20982221134.3228 4.8010.304.00 0.005.100.900.0011.600.000.000.7062.60982221143.6230 4.9010.403.90 0.005.400.900.009.80 0.000.000.8063.90982221123.4231 5.007.50 3.90 2.005.001.000.0012.100.000.000.0063.50982221271.5231 5.007.50 3.90 2.005.001.000.0012.100.000.000.0063.50980248.2 150231 5.007.50 3.90 2.005.001.000.0012.100.000.000.0063.50871483234AlloyR 5.0010.1010.000.005.400.900.004.00 0.000.100.0064.50871483147Alloy4545.0010.004.00 0.005.001.500.0012.000.000.000.0062.50871483165PWA1422 10.00 9.00 12.000.005.002.000.000.00 0.002.000.0060.0087148370Alloy7055.108.00 6.80 1.055.600.920.006.00 0.000.100.0066.439821721040Alloy4545.0010.004.00 0.005.001.500.0012.000.000.000.0062.50982172608
      PWA1422 10.00 9.0012.00 0.005.002.000.000.000.002.000.0060.00982172 220AlloyH 5.0010.00 7.001.505.001.400.006.000.000.100.0064.00982248.2100Alloy7055.108.006.801.055.600.920.006.000.000.100.0066.43982248.2101AlloyQ 5.0010.30 10.00 0.005.000.900.004.000.000.100.0064.70982248.275AlloyR 5.0010.10 10.00 0.005.400.900.004.000.000.100.0064.50982248.2107Alloy4545.0010.00 4.000.005.001.500.0012.00 0.000.000.0062.50982248.290PWA1422 10.00 9.0012.00 0.005.002.000.000.000.002.000.0060.00982248.232AlloyH 5.0010.00 7.001.505.001.400.006.000.000.100.0064.001093 103 495AlloyR 5.0010.10 10.00 0.005.400.900.004.000.000.100.0064.501093 103 690Alloy4545.0010.00 4.000.005.001.500.0012.00 0.000.000.0062.501093 103 272PWA1422 10.00 9.0012.00 0.005.002.000.000.000.002.000.0060.001093 103 30Alloy7055.108.006.801.055.600.920.006.000.000.100.0066.431093 82.7 909Alloy4545.0010.00 4.000.005.001.500.0012.00 0.000.000.0062.501093 82.7 765PWA1422 10.00 9.0012.00 0.005.002.000.000.000.002.000.0060.001093 82.7 704639280 A 8.007.005.002.005.001.801.008.000.000.000.0062.20760750 857B 7.507.008.002.005.301.500.006.000.000.000.0062.70760840 410C 6.507.507.001.505.301.800.006.500.000.000.0063.90760750 1000D 5.0010.00 6.000.505.251.250.009.000.000.000.0063.00760750 732A 8.007.005.002.005.001.801.008.000.000.000.0062.20950240 545C 6.507.507.001.505.301.800.006.500.000.000.0063.90950240 480D 5.0010.00 6.000.505.251.250.009.000.000.000.0063.00950240 528A 8.007.005.002.005.001.801.008.000.000.000.0062.201050 120 1073B 7.507.008.002.005.301.500.006.000.000.000.0062.701050 140 496C 6.507.507.001.505.301.800.006.500.000.000.0063.901050 140 435A 8.007.005.002.005.001.801.008.000.000.000.0062.201050 140 3384765850 MAR-M247*0.0010.00 3.3010.00 1.058.400.650.005.500.000.0061.10982248.270NAS-AIR100 0.000.003.3010.50 1.209.001.000.005.750.000.0069.25982248.239120 10.00 5.005.002.005.501.500.006.302.000.000.0062.70982248.2160.9125 5.005.005.002.005.501.500.006.302.500.000.0067.20982248.2135.1
      130 10.50 5.005.002.005.501.500.006.303.000.000.0061.20982248.2205.3406Re 10.00 5.007.001.004.501.902.004.302.500.000.0061.80982248.2164.8NAS-AIR1000.000.003.3010.50 1.209.001.000.005.750.000.0069.251093 124 120120 10.00 5.005.002.005.501.500.006.302.000.000.0062.701093 124 200130 10.50 5.005.002.005.501.500.006.303.000.000.0061.201093 124 346406Re 10.00 5.007.001.004.501.902.004.302.500.000.0061.801093 124 181.9NAS-AIR1000.000.003.3010.50 1.209.001.000.005.750.000.0069.25871124 70TMS-268.205.6010.90 1.905.100.000.007.700.000.000.0060.601040 137 1775TMS-257.905.5012.90 0.005.200.000.007.600.000.000.0060.901040 137 599TMS-278.105.9012.90 0.004.900.900.006.000.000.000.0061.301040 137 741TMS-288.405.8011.00 1.904.900.900.006.000.000.000.0061.101040 137 13394885216 A 2.5210.10 6.500.924.403.180.004.420.000.000.0067.96982221 244.9F 5.0010.60 6.500.924.153.680.004.420.000.000.0064.73982221 304.6G 5.0010.60 6.500.924.153.680.004.420.000.200.0064.53982221 276.7F 5.0010.60 6.500.924.153.680.004.420.000.000.0064.73871448 277.1A 2.5210.10 6.500.924.403.180.004.420.000.000.0067.96760758 606.6F 5.0010.60 6.500.924.153.680.004.420.000.000.0064.73760758 697.6G 5.0010.60 6.500.924.153.680.004.420.000.200.0064.53760758 528.54908183 Alloy307 9.804.602.001.804.901.000.0011.90 3.000.000.0061.00871517 259Alloy311 10.20 5.105.002.005.100.920.009.103.000.100.5058.98871517 440PWA1422 10.00 9.0012.00 0.005.002.001.000.000.002.000.0059.00871517 105Alloy307 9.804.602.001.804.901.000.0011.90 3.000.000.0061.00982248.2242Alloy311 10.20 5.105.002.005.100.920.009.103.000.100.5058.98982248.2283PWA1422 10.00 9.0012.00 0.005.002.001.000.000.002.000.0059.00982248.291Alloy311 10.20 5.105.002.005.100.920.009.103.000.100.5058.981093 138 112Alloy307 9.804.602.001.804.901.000.0011.90 3.000.000.0061.001093 124 120PWA1422 10.00 9.0012.00 0.005.002.001.000.000.002.000.0059.001093 124 524935072 A 9.905.615.051.535.341.030.008.102.900.100.0060.44982248.2188B 9.905.655.102.085.450.520.008.702.940.000.0059.66982248.2181.5
      C 10.00 5.565.091.505.290.520.009.002.900.100.0060.04982248.2 180.4D 9.805.515.081.585.461.060.007.801.950.000.0061.76982248.2 141.5E 9.905.625.072.025.470.520.008.401.940.180.0060.88982248.2 152.5F 0.105.605.131.625.560.510.008.501.860.130.0060.99982248.2 138.4G 9.905.595.081.695.400.750.008.402.520.070.0060.60982248.2 162.3H 10.60 5.765.482.005.811.020.009.602.590.110.0057.03982248.2 136.4I 10.50 5.914.511.495.811.010.009.803.420.100.0057.45982248.2 233.7J 10.10 5.324.731.795.510.750.009.303.050.100.0059.35982248.2 199.4K 9.904.714.851.935.391.000.008.302.920.090.0060.91982248.2 148.6L 10.10 5.214.952.005.570.790.007.702.890.080.0060.71982248.2 131.4M 10.60 5.845.001.755.811.020.009.703.010.100.0057.17982248.2 200.4A 9.905.615.051.535.341.030.008.102.900.100.0060.441093 124290.3B 9.905.655.102.085.450.520.008.702.940.000.0059.661093 124328.7C 10.00 5.565.091.505.290.520.009.002.900.100.0060.041093 124229.1D 9.805.515.081.585.461.060.007.801.950.000.0061.761093 124130.1E 9.905.625.072.025.470.520.008.401.940.180.0060.881093 124230.7F 10.10 5.605.131.625.560.510.008.501.860.130.0060.991093 124110.2G 9.905.595.081.695.400.750.008.402.520.070.0060.601093 124211.7I 10.50 5.914.511.495.811.010.009.803.420.100.0057.451093 124189.1J 10.10 5.324.731.795.510.750.009.303.050.100.0059.351093 124364.6K 9.904.714.851.935.391.000.008.302.920.090.0060.911093 124138.4L 10.10 5.214.952.005.570.790.007.702.890.080.0060.711093 124146.5M 10.60 5.845.001.755.811.020.009.703.010.100.0057.171093 124136.55007004 V1040.0010.30 7.500.005.600.000.006.200.000.000.0070.4087141490.8V1040.0010.30 7.500.005.600.000.006.200.000.000.0070.401037 124344.6V1040.0010.30 7.500.005.600.000.006.200.000.000.0070.401037 103816.5#9387.505.006.000.005.501.000.008.006.000.000.0061.001093 138167.9#B1112.50 4.803.001.506.600.000.007.005.500.000.0059.101093 138132.8#94712.50 4.004.502.005.500.000.508.406.000.000.0056.601093 138476.4
      #9484.00 4.004.501.305.500.000.508.406.000.000.0065.801093 138248.3#9507.50 4.004.501.005.500.000.508.407.000.000.0061.601093 138267.9#9514.00 4.004.501.005.500.000.508.406.000.000.0066.101093 138667.2C7 12.504.505.000.006.600.000.007.005.500.000.0058.901093 138258.1C9 12.504.006.000.005.501.000.008.005.500.000.0057.501093 138305.1G 13.004.004.700.705.800.700.008.106.500.000.0056.501093 1384331A 12.004.506.000.006.200.000.007.006.500.000.0057.801093 124566.21B 12.004.506.000.506.200.000.007.006.500.000.0057.301093 124408#2A 12.504.004.502.005.600.000.008.006.000.000.0057.401093 124922.5#2B 12.504.004.502.005.600.000.508.006.000.000.0056.901093 1249893A 12.404.405.200.006.600.000.007.105.500.000.0058.801093 124474.5#4 4.00 4.004.501.005.700.000.508.006.000.000.0066.301093 1249205A 12.504.505.800.006.100.000.007.006.200.000.0057.901093 124444.45B 12.504.506.000.006.200.000.007.006.500.000.0057.301093 1242996A 12.504.505.500.006.100.000.007.506.000.000.0057.901093 1244206B 12.505.005.500.006.000.000.008.006.000.000.0057.001093 1244205151249#20 7.50 4.505.001.005.500.000.008.007.500.000.0061.00983310142.9#9387.50 5.006.000.005.501.000.008.006.000.000.0061.00983310175.5#B1 6.00 5.006.701.005.300.000.0010.40 4.000.000.0061.60983310110#B2 0.00 5.006.001.005.700.000.009.005.000.000.0068.30983310102.4#B6 7.50 5.006.701.005.500.500.009.004.000.000.0060.80983310143.8#B7 7.50 5.006.001.005.500.500.009.004.700.000.0060.80983310103.7#B1112.504.803.001.506.600.000.007.005.500.000.0059.10983310106.3#94712.504.004.502.005.500.000.508.406.000.000.0056.60983310147#9484.00 4.004.501.305.500.000.508.406.000.000.0065.80983310120.9#9507.50 4.004.501.005.500.000.508.407.000.000.0061.60983310175.6#9514.00 4.004.501.005.500.000.508.406.000.000.0066.10983310193.7C9 12.504.006.000.005.501.000.008.005.500.000.0057.50983310181.51A 12.004.506.000.006.200.000.007.006.500.000.0057.80871276282.6
      1B 12.004.506.000.506.200.000.007.006.500.000.0057.30871276277#2A 12.504.004.502.005.600.000.008.006.000.000.0057.408712763003A 12.404.405.200.006.600.000.007.105.500.000.0058.80871276326.33B 12.505.005.500.005.700.500.008.006.000.000.0056.80871276484.25A 12.504.505.800.006.100.000.007.006.200.000.0057.908712763355B 12.504.506.000.006.200.000.007.006.500.000.0057.308712762216A 12.504.505.500.006.100.000.007.506.000.000.0057.908712762936B 12.505.005.500.006.000.000.008.006.000.000.0057.008712763475154884 17.50 7.507.601.443.354.300.523.720.000.000.0064.07899414210.327.40 7.505.201.433.304.300.503.522.980.000.0063.87899414289.737.40 8.157.501.483.504.400.493.750.000.000.0063.3389941413647.60 8.956.001.463.504.450.513.720.000.000.0063.81899414102.657.30 8.956.401.463.404.500.513.810.000.000.0063.6789941456.367.40 10.10 7.701.463.403.950.533.400.000.000.0062.0689941412997.30 10.90 7.601.453.403.350.513.380.000.000.0062.11899414108.813 7.10 13.50 5.851.472.703.950.522.970.000.000.0061.9489941435.415 7.00 14.00 7.701.463.952.000.513.090.000.000.0060.2989941447.6Rene′15012.005.005.001.005.500.000.006.003.001.502.2058.8089941418017.50 7.507.601.443.354.300.523.720.000.000.0064.0798224114927.40 7.505.201.433.304.300.503.522.980.000.0063.87982241210.737.40 8.157.501.483.504.400.493.750.000.000.0063.33982241113.447.60 8.956.001.463.504.450.513.720.000.000.0063.81982241107.257.30 8.956.401.463.404.500.513.810.000.000.0063.6798224155.667.40 10.10 7.701.463.403.950.533.400.000.000.0062.06982241157.897.30 10.90 7.601.453.403.350.513.380.000.000.0062.11982241110.113 7.10 13.50 5.851.472.703.950.522.970.000.000.0061.9498224135.115 7.00 14.00 7.701.463.952.000.513.090.000.000.0060.2998224138.3Rene′12510.008.907.002.504.802.500.003.500.001.500.0059.3098224180Rene′15012.005.005.001.005.500.000.006.003.001.502.2058.80982241100
      1 7.507.507.601.443.354.300.523.720.000.000.0064.071093103 200.92 7.407.505.201.433.304.300.503.522.980.000.0063.871093103 351.63 7.408.157.501.483.504.400.493.750.000.000.0063.331093103 163.34 7.608.956.001.463.504.450.513.720.000.000.0063.811093103 171.65 7.308.956.401.463.404.500.513.810.000.000.0063.671093103 78.46 7.4010.10 7.701.463.403.950.533.400.000.000.0062.061093103 2419 7.3010.90 7.601.453.403.350.513.380.000.000.0062.111093103 98.1Rene′150 12.00 5.005.001.005.500.000.006.003.001.502.2058.801093103 10010A8.502.907.400.686.000.690.297.505.100.070.0060.87871 517 534.410B8.102.706.950.696.000.690.297.804.800.060.0061.92982 248.2989.310C7.702.606.400.695.700.620.308.304.700.070.0062.92982 248.2635.710D5.004.006.000.625.440.590.318.104.700.040.0065.20982 248.242810E7.202.206.400.705.890.630.268.204.800.050.0063.67982 248.2664.510F7.702.406.400.655.960.630.287.905.000.040.0063.04982 248.2666.610G6.502.505.500.535.600.680.208.204.600.050.0065.64927 379 724.910Ga 4.002.406.200.415.790.550.148.306.000.030.0066.19982 248.2730.910H5.602.306.200.515.580.760.177.805.400.050.0065.63982 248.2594.510I4.802.606.600.525.650.670.147.405.400.040.0066.18982 248.2581.910Ia 3.502.705.200.475.800.600.108.005.800.040.0067.79982 248.253212A4.603.005.300.395.610.960.019.405.000.050.0065.68982 248.2491.912B3.003.505.100.385.520.840.018.806.100.050.0066.701080194 108.212C3.502.705.400.455.620.750.018.806.000.040.0066.73982 248.2713.310Ri 7.002.656.400.605.670.800.407.605.500.070.0063.32913 517 231.612Ri 8.003.406.100.485.540.990.017.605.300.070.0062.51913 517 209.810B8.102.706.950.696.000.690.297.804.800.060.0061.92982 276 436.710C7.702.606.400.695.700.620.308.304.700.070.0062.921010248.2298.110D5.004.006.000.625.440.590.318.104.700.040.0065.201010248.216610E7.202.206.400.705.890.630.268.204.800.050.0063.671010248.2260.510F7.702.406.400.655.960.630.287.905.000.040.0063.041010248.2285.9
      10G6.502.505.500.535.600.680.208.204.600.050.0065.64982248.2 799.110Ga 4.002.406.200.415.790.550.148.306.000.030.0066.191010 248.2 300.110H5.602.306.200.515.580.760.177.805.400.050.0065.631010 248.2 242.910I4.802.606.600.525.650.670.147.405.400.040.0066.181010 248.2 260.510Ia 3.502.705.200.475.800.600.108.005.800.040.0067.791010 248.2 25612A4.603.005.300.395.610.960.019.405.000.050.0065.681010 248.2 208.512B3.003.505.100.385.520.840.018.806.100.050.0066.70982248.2 536.412C3.502.705.400.455.620.750.018.806.000.040.0066.731010 248.2 338.910Ri 7.002.656.400.605.670.800.407.605.500.070.0063.32954345 460.812Ri 8.003.406.100.485.540.990.017.605.300.070.0062.51954345 448.110A8.502.907.400.686.000.690.297.505.100.070.0060.87982207 1016.210B8.102.706.950.696.000.690.297.804.800.060.0061.921037 172 295.710C7.702.606.400.695.700.620.308.304.700.070.0062.921050 140 637.510D5.004.006.000.625.440.590.318.104.700.040.0065.201050 140 680.310E7.202.206.400.705.890.630.268.204.800.050.0063.671050 140 859.910F7.702.406.400.655.960.630.287.905.000.040.0063.041050 140 649.210G6.502.505.500.535.600.680.208.204.600.050.0065.641010 248.2 354.410Ga 4.002.406.200.415.790.550.148.306.000.030.0066.191080 194 122.310H5.602.306.200.515.580.760.177.805.400.050.0065.631050 140 574.710I4.802.606.600.525.650.670.147.405.400.040.0066.181050 140 934.810Ia 3.502.705.200.475.800.600.108.005.800.040.0067.791080 194 85.712A4.603.005.300.395.610.960.019.405.000.050.0065.681050 140 829.612B3.003.505.100.385.520.840.018.806.100.050.0066.701010 248.2 262.612C3.502.705.400.455.620.750.018.806.000.040.0066.731080 194 118.110Ri 7.002.656.400.605.670.800.407.605.500.070.0063.32982248.2 698.512Ri 8.003.406.100.485.540.990.017.605.300.070.0062.51982248.2 62710A8.502.907.400.686.000.690.297.505.100.070.0060.87982248.2 586.510B8.102.706.950.696.000.690.297.804.800.060.0061.921093 124 192.710C7.702.606.400.695.700.620.308.304.700.070.0062.921093 124 293.1
      10D5.004.006.000.625.440.590.318.104.700.040.0065.201093124401.510E7.202.206.400.705.890.630.268.204.800.050.0063.671093124379.710F7.702.406.400.655.960.630.287.905.000.040.0063.04109312429010G6.502.505.500.535.600.680.208.204.600.050.0065.641050140753.410Ga 4.002.406.200.415.790.550.148.306.000.030.0066.191080130592.110H5.602.306.200.515.580.760.177.805.400.050.0065.631093124437.310Ia 3.502.705.200.475.800.600.108.005.800.040.0067.791121103528.612A4.603.005.300.395.610.960.019.405.000.050.0065.681121103424.812B3.003.505.100.385.520.840.018.806.100.050.0066.701121103507.510I4.802.606.600.525.650.670.147.405.400.040.0066.181080194116.110Ia 6.502.705.200.475.800.600.208.004.600.040.0065.891100100930.212B6.502.505.100.385.520.840.208.104.600.050.0066.211100100107812C6.502.706.400.455.620.750.018.204.600.040.0064.7311001001001.810Ga 6.502.406.200.415.790.550.148.304.600.030.0065.091100100875.212Ri 6.502.406.100.485.540.990.018.204.600.070.0065.111100100105010Ri 6.502.656.400.605.670.800.408.204.600.070.0064.121100100962.512A4.603.005.300.395.610.960.019.405.000.050.0065.681093124500.310Ri 7.002.656.400.605.670.800.407.605.500.070.0063.321010248.2 272.312Ri 8.003.406.100.485.540.990.017.605.300.070.0062.511010248.2 314.410A8.502.907.400.686.000.690.297.505.100.070.0060.871037172423.410B8.102.706.950.696.000.690.297.804.800.060.0061.921121103219.610C7.702.606.400.695.700.620.308.304.700.070.0062.921121103196.610D5.004.006.000.625.440.590.318.104.700.040.0065.201121103465.310E7.202.206.400.705.890.630.268.204.800.050.0063.671121103476.910F7.702.406.400.655.960.630.287.905.000.040.0063.041121103255.410G6.502.505.500.535.600.680.208.204.600.050.0065.641080194108.210Ga 4.002.406.200.415.790.550.148.306.000.030.0066.191121103560.110H5.602.306.200.515.580.760.177.805.400.050.0065.631121103420.210I4.802.606.600.525.650.670.147.405.400.040.0066.181093124483.8
      L3 10.00 6.806.600.705.800.900.007.803.200.250.0057.95950 250 895L4 8.006.106.200.505.500.500.007.202.700.150.0063.15950 250 847VL109.506.506.500.605.600.600.008.203.000.200.0059.30950 250 94710Ri7.002.656.400.605.670.800.407.605.500.070.0063.321010190 61412Ri8.003.406.100.485.540.990.017.605.300.070.0062.511080194 91.510A 8.502.907.400.686.000.690.297.505.100.070.0060.871093124 245.210G 6.502.505.500.535.600.680.208.204.600.050.0065.641093124 464.410I 4.802.606.600.525.650.670.147.405.400.040.0066.181121103 487.710Ia3.502.705.200.475.800.600.108.005.800.040.0067.79114982.7616.412A 4.603.005.300.395.610.960.019.405.000.050.0065.68114982.748312B 3.003.505.100.385.520.840.018.806.100.050.0066.70114982.7444.912C 3.502.705.400.455.620.750.018.806.000.040.0066.731121103 546.410Ri7.002.656.400.605.670.800.407.605.500.070.0063.321080194 99.710Ga4.002.406.200.415.790.550.148.306.000.030.0066.19114982.749110I 4.802.606.600.525.650.670.147.405.400.040.0066.18114982.7501.312C 3.502.705.400.455.620.750.018.806.000.040.0066.73114982.7545.110Ri7.002.656.400.605.670.800.407.605.500.070.0063.321080130 278.812Ri8.003.406.100.485.540.990.017.605.300.070.0062.511121103 243.410Ga4.002.406.200.415.790.550.148.306.000.030.0066.19114982.749110I 4.802.606.600.525.650.670.147.405.400.040.0066.18114982.7501.312C 3.502.705.400.455.620.750.018.806.000.040.0066.73114982.7545.110Ri7.002.656.400.605.670.800.407.605.500.070.0063.321080130 278.812Ri8.003.406.100.485.540.990.017.605.300.070.0062.511121103 243.410G 6.502.505.500.535.600.680.208.204.600.050.0065.641121103 410.812Ri8.003.406.100.485.540.990.017.605.300.070.0062.51114982.748810G 6.502.505.500.535.600.680.208.204.600.050.0065.64114982.7419.810G 6.502.505.500.535.600.680.208.204.600.050.0065.64114986 387.310Ri7.002.656.400.605.670.800.407.605.500.070.0063.321121103 31810Ri7.002.656.400.605.670.800.407.605.500.070.0063.32114982.7400.3
      48 7.609.806.001.504.203.500.504.700.000.150.0062.0587140014649 7.509.706.001.504.203.500.504.700.000.150.0062.2587140030450 7.509.706.101.504.203.500.504.800.000.200.0062.0098219323490 7.509.706.001.504.203.500.504.800.000.150.0062.15982207118.849 7.509.706.001.504.203.500.504.700.000.150.0062.2592731092.249 7.509.706.001.504.203.500.504.700.000.150.0062.25982207108.790 7.509.706.001.504.203.500.504.800.000.150.0062.15982165.4 296.15888451L1 9.506.506.000.605.600.600.008.203.000.200.1059.70950250880423 10.00 0.008.001.005.500.000.006.000.001.502.2065.80899414112424 10.00 0.005.001.005.501.100.006.003.001.501.1065.80899414242433 12.00 0.005.001.005.800.000.006.003.001.501.6064.10899414177VL119.506.506.500.605.700.600.006.703.000.200.0060.70950250918VL17(CMSX-4)9.706.406.400.605.651.000.006.502.900.100.0060.759502501018L1 9.506.506.000.605.600.600.008.203.000.200.1059.709502001850L3 10.00 6.806.600.705.800.900.007.803.200.250.0057.959502002035L4 8.006.106.200.505.500.500.007.202.700.150.0063.159502002138VL1510.00 7.006.600.706.001.000.007.803.200.250.0057.459502002150VL167.805.806.000.505.300.400.007.002.500.150.0064.559502001990VL17(CMSX-4)9.706.406.400.605.651.000.006.502.900.100.0060.759502002438L1 9.506.506.000.605.600.600.008.203.000.200.1059.709501655050L3 10.00 6.806.600.705.800.900.007.803.200.250.0057.959501655280L4 8.006.106.200.505.500.500.007.202.700.150.0063.159501654830VL1510.00 7.006.600.706.001.000.007.803.200.250.0057.459501654430VL167.805.806.000.505.300.400.007.002.500.150.0064.559501653690VL17(CMSX-4)9.706.406.400.605.651.000.006.502.900.100.0060.759501654760L1 9.506.506.000.605.600.600.007.503.000.200.0060.5095014015000VL109.506.506.500.605.600.600.008.203.000.200.0059.3095014011700VL119.506.506.500.605.700.600.006.703.000.200.0060.70950140126144169742341 3.500.003.000.005.800.000.008.003.001.102.5073.10899414170
      3853.500.004.001.005.500.000.006.003.001.502.2073.30899414923863.500.005.001.005.500.000.006.003.001.502.2072.308994141783917.000.005.001.005.500.000.006.003.001.502.2068.8089941436839210.00 0.005.001.005.500.000.006.003.001.502.2065.8089941423439410.00 0.003.000.005.800.000.008.003.001.202.5066.508994141343978.500.005.001.005.500.000.006.003.001.502.2067.308994141623988.500.004.501.005.500.000.006.003.001.502.2067.8089941420147 9.4712.75 8.710.003.703.890.002.450.000.000.0059.051000 82.7 398.748 12.19 12.54 6.600.003.285.000.002.480.000.000.0057.921000 82.7 244.165 9.9513.87 8.690.003.463.640.002.440.000.000.0057.951000 82.7 283.343414.00 0.005.001.005.800.000.006.003.001.501.6062.1089941419439210.00 0.005.001.005.500.000.006.003.001.502.2065.8098224113042410.00 0.005.001.005.501.100.006.003.001.501.1065.8098224112442510.00 0.005.001.005.502.100.006.003.001.500.0065.90982241874209438Alloy454(a)5.0010.00 4.000.005.001.500.0012.00 0.000.000.0062.507606551200SM200(b,c,d) 10.00 9.0012.50 0.005.002.001.000.000.000.000.0060.50760655728.4Alloy454(a)5.0010.00 4.000.005.001.500.0012.00 0.000.000.0062.507657584754207098A 8.5015.80 2.551.743.363.570.851.750.000.000.0061.887605502501 8.4016.00 2.591.733.343.560.851.750.000.000.0061.787605502672 8.4016.30 2.731.733.453.530.861.730.000.000.0061.277605503213 8.6016.50 2.631.763.433.630.841.770.000.000.0060.847605503634 8.5016.50 2.721.763.433.630.851.730.000.000.0060.887605504546 15.00 20.00 2.200.502.503.601.001.500.000.000.0053.707605506587 15.00 20.50 2.310.532.643.700.981.630.000.000.0052.71760620498A 8.5015.80 2.551.743.363.570.851.750.000.000.0061.8881633010011 8.4016.00 2.591.733.343.560.851.750.000.000.0061.7881633010072 8.4016.30 2.731.733.453.530.861.730.000.000.0061.2781633010674 8.5016.50 2.721.763.433.630.851.730.000.000.0060.8881633011736 15.00 20.00 2.200.502.503.601.001.500.000.000.0053.70816330910
      C 9.0012.603.911.983.624.300.003.950.000.000.0060.64760620 499A 8.5015.802.551.743.363.570.851.750.000.000.0061.88927228 621 8.4016.002.591.733.343.560.851.750.000.000.0061.78927228 712 8.4016.302.731.733.453.530.861.730.000.000.0061.27927228 623 8.6016.502.631.763.433.630.841.770.000.000.0060.84927228 584 8.5016.502.721.763.433.630.851.730.000.000.0060.88927228 80C 9.0012.603.911.983.624.300.003.950.000.000.0060.64760500 16687 15.00 20.502.310.532.643.700.981.630.000.000.0052.71816545 1337 15.00 20.502.310.532.643.700.981.630.000.000.0052.71816414 6817 15.00 20.502.310.532.643.700.981.630.000.000.0052.71816400 8737 15.00 20.502.310.532.643.700.981.630.000.000.0052.71927269 977 15.00 20.502.310.532.643.700.981.630.000.000.0052.71927228 1997 15.00 20.502.310.532.643.700.981.630.000.000.0052.71927200 5167 15.00 20.502.310.532.643.700.981.630.000.000.0052.71927154 13367 15.00 20.502.310.532.643.700.981.630.000.000.0052.71980152 185C 9.0012.603.911.983.624.300.003.950.000.000.0060.64816414 543C 9.0012.603.911.983.624.300.003.950.000.000.0060.64816400 917C 9.0012.603.911.983.624.300.003.950.000.000.0060.64816345 2085C 9.0012.603.911.983.624.300.003.950.000.000.0060.64816300 1439C 9.0012.603.911.983.624.300.003.950.000.000.0060.64927269 133C 9.0012.603.911.983.624.300.003.950.000.000.0060.64927200 692C 9.0012.603.911.983.624.300.003.950.000.000.0060.64927154 9854205985 384.0913.826.710.004.922.830.002.510.000.000.0065.131000 82.7241.4466.4612.986.510.003.603.800.004.880.000.000.0061.771000 82.7344.1662.4111.698.770.003.126.120.000.920.000.000.0066.971000 82.7208.83911.50 13.716.790.004.414.040.000.000.000.000.0059.541000 82.7202.54911.81 12.028.820.003.195.660.000.000.000.000.0058.501000 82.7207.4Mar-M200 9.908.91 12.36 0.004.992.011.090.000.000.000.0060.741000 82.7206.1IN-7928.9512.333.771.963.084.490.004.010.000.000.0061.391000 82.7180
      Rikiloy481 9.955.9914.03 2.022.985.980.000.000.000.000.0059.051000 82.7 250Rikiloy37579.9413.95 9.930.973.003.960.000.000.000.000.0058.241000 82.7 1704781722 A 5.008.006.001.506.500.000.003.003.000.000.0067.008503 79 508.7B 5.008.006.001.506.501.000.003.003.000.000.0066.008503791202.4C 0.009.006.002.007.000.000.001.003.000.000.0072.00850379771.8C 0.009.006.002.007.000.000.001.003.000.000.0072.00760655403B 5.008.006.001.506.501.000.003.003.000.000.0066.00850500124.4C 0.009.006.002.007.000.000.001.003.000.000.0072.00850500109.45100484 SeriesI800 7.508.004.001.505.801.500.005.003.000.150.0063.5587155294.58017.508.005.900.505.751.500.005.003.000.150.0062.70871552878027.508.005.900.005.751.500.005.003.000.150.0063.2087155286.88037.508.004.000.005.751.500.005.004.500.150.0063.6087155266.78047.508.002.000.005.751.500.005.006.000.150.0064.1087155254.28057.508.000.003.655.901.500.005.003.100.150.0065.2087155256.38067.508.000.003.005.801.500.005.004.500.150.0064.5587155285.68077.508.003.001.506.001.000.006.003.000.150.0063.8587155275.78087.508.003.001.506.500.000.006.003.000.150.0064.3587155255.68107.508.002.000.006.400.000.006.006.000.150.0063.9587155262.28117.508.000.003.006.400.000.006.004.500.150.0064.45871552101.9SeriesII8125.007.003.001.506.001.000.006.000.000.150.0070.3587155235.18137.507.003.001.506.001.000.006.003.000.150.0064.8587155253.881410.00 7.003.001.506.001.000.006.003.000.150.0062.3587155257.98157.505.003.001.506.500.500.007.503.000.150.0065.3587155276.58167.505.003.001.506.500.500.008.003.000.150.0064.85871552103.98187.505.003.001.506.500.500.007.003.500.150.0065.3587155284.38197.505.003.001.506.500.500.007.004.500.150.0064.35871552147.48207.505.003.001.506.500.000.007.005.500.150.0063.85871552257.28217.507.005.001.506.200.000.006.503.000.150.0063.15871552114.38227.506.005.001.506.200.000.006.503.000.150.0064.1587155264.2
      SeriesIII824 10.00 5.006.501.506.500.000.007.002.000.150.0061.3587155297.182510.00 5.005.501.506.500.000.007.003.000.150.0061.358715527482610.00 5.004.001.506.500.000.007.004.000.150.0061.85871552113.182810.00 7.006.001.506.200.000.006.502.500.150.0060.15871552119.182910.00 7.007.001.506.200.000.006.502.000.150.0059.6587155211083010.00 7.005.001.505.801.500.005.003.000.150.0061.0587155259.883110.00 7.006.001.505.801.500.005.002.000.150.0061.0587155292.783210.00 7.007.001.505.801.500.005.001.000.150.0061.0587155290.183310.00 7.004.002.505.801.500.005.002.000.150.0062.0587155296.583410.00 6.005.501.507.000.000.004.003.000.150.0062.85871552119.283510.00 7.004.001.507.500.000.002.003.000.150.0064.8587155243.5SeriesI800 7.508.004.001.505.801.500.005.003.000.150.0063.5598227668.58017.508.005.900.505.751.500.005.003.000.150.0062.7098227644.58027.508.005.900.005.751.500.005.003.000.150.0063.2098227663.18037.508.004.000.005.751.500.005.004.500.150.0063.6098227667.18047.508.002.000.005.751.500.005.006.000.150.0064.109822761038057.508.000.003.655.901.500.005.003.100.150.0065.2098227656.38067.508.000.003.005.801.500.005.004.500.150.0064.5598227643.88077.508.003.001.506.001.000.006.003.000.150.0063.8598227660.18087.508.003.001.506.500.000.006.003.000.150.0064.3598227653.58097.508.004.000.006.400.000.006.004.500.150.0063.4598227669.68107.508.002.000.006.400.000.006.006.000.150.0063.9598227664.7SeriesII8125.007.003.001.506.001.000.006.000.000.150.0070.3598227649.18137.507.003.001.506.001.000.006.003.000.150.0064.8598227651.481410.00 7.003.001.506.001.000.006.003.000.150.0062.3598227663.78157.505.003.001.506.500.500.007.503.000.150.0065.3598227665.48167.505.003.001.506.500.500.008.003.000.150.0064.8598227683.68177.505.003.000.506.501.000.008.003.000.150.0065.3598227655.58187.505.003.001.506.500.500.007.003.500.150.0065.3598227685.6
      8197.505.003.001.506.500.500.007.004.500.150.0064.35982276 115.58207.505.003.001.506.500.000.007.005.500.150.0063.85982276 158.78217.507.005.001.506.200.000.006.503.000.150.0063.15982276 80.48227.506.005.001.506.200.000.006.503.000.150.0064.15982276 70.38237.505.005.001.506.200.000.006.503.000.150.0065.15982276 48.7SeriesIII824 10.00 5.006.501.506.500.000.007.002.000.150.0061.35982276 91.982510.00 5.005.501.506.500.000.007.003.000.150.0061.35982276 94.782610.00 5.004.001.506.500.000.007.004.000.150.0061.85982276 119.882710.00 7.005.001.506.200.000.006.503.000.150.0060.65982276 76.282810.00 7.006.001.506.200.000.006.502.500.150.0060.15982276 72.782910.00 7.007.001.506.200.000.006.502.000.150.0059.65982276 72.783010.00 7.005.001.505.801.500.005.003.000.150.0061.05982276 126.583110.00 7.006.001.505.801.500.005.002.000.150.0061.05982276 68.983210.00 7.007.001.505.801.500.005.001.000.150.0061.05982276 58.583310.00 7.004.002.505.801.500.005.002.000.150.0062.05982276 51.683410.00 6.005.501.507.000.000.004.003.000.150.0062.85982276 80.783510.00 7.004.001.507.500.000.002.003.000.150.0064.85982276 55.38027.508.005.900.005.751.500.005.003.000.150.0063.201093138908037.508.004.000.005.751.500.005.004.500.150.0063.60109313870.18047.508.002.000.005.751.500.005.006.000.150.0064.10109313852.48057.508.000.003.655.901.500.005.003.100.150.0065.20109313855.28067.508.000.003.005.801.500.005.004.500.150.0064.55109313857.48077.508.003.001.506.001.000.006.003.000.150.0063.851093138100.38087.508.003.001.506.500.000.006.003.000.150.0064.35109313831.68097.508.004.000.006.400.000.006.004.500.150.0063.451093138468117.508.000.003.006.400.000.006.004.500.150.0064.45109313844.181410.00 7.003.001.506.001.000.006.003.000.150.0062.35109313842.88157.505.003.001.506.500.500.007.503.000.150.0065.35109313864.88167.505.003.001.506.500.500.008.003.000.150.0064.85109313847.6
      817 7.505.003.000.506.501.000.008.003.000.150.0065.35109313842.3818 7.505.003.001.506.500.500.007.003.500.150.0065.35109313868819 7.505.003.001.506.500.500.007.004.500.150.0064.351093138100.6820 7.505.003.001.506.500.000.007.005.500.150.0063.851093138153.7821 7.507.005.001.506.200.000.006.503.000.150.0063.15109313898.4SeriesIII82410.00 5.006.501.506.500.000.007.002.000.150.0061.351093138118.8825 10.00 5.005.501.506.500.000.007.003.000.150.0061.351093138128.4826 10.00 5.004.001.506.500.000.007.004.000.150.0061.851093138135.6827 10.00 7.005.001.506.200.000.006.503.000.150.0060.651093138108.4828 10.00 7.006.001.506.200.000.006.502.500.150.0060.15109313895.7829 10.00 7.007.001.506.200.000.006.502.000.150.0059.65109313890.2830 10.00 7.005.001.505.801.500.005.003.000.150.0061.051093138162.2831 10.00 7.006.001.505.801.500.005.002.000.150.0061.05109313882.1832 10.00 7.007.001.505.801.500.005.001.000.150.0061.05109313885.4833 10.00 7.004.002.505.801.500.005.002.000.150.0062.05109313869.1834 10.00 6.005.501.507.000.000.004.003.000.150.0062.851093138105.7835 10.00 7.004.001.507.500.000.002.003.000.150.0064.85109313867.4SeriesI800 7.508.004.001.505.801.500.005.003.000.150.0063.55114990 90.4803 7.508.004.000.005.751.500.005.004.500.150.0063.60114990 82.9805 7.508.000.003.655.901.500.005.003.100.150.0065.20114990 30807 7.508.003.001.506.001.000.006.003.000.150.0063.85114990 66.4808 7.508.003.001.506.500.000.006.003.000.150.0064.35114990 39.2813 7.507.003.001.506.001.000.006.003.000.150.0064.85114990 52.2814 10.00 7.003.001.506.001.000.006.003.000.150.0062.35114990 47.1815 7.505.003.001.506.500.500.007.503.000.150.0065.35114990 143.2816 7.505.003.001.506.500.500.008.003.000.150.0064.85114990 121.4817 7.505.003.000.506.501.000.008.003.000.150.0065.35114990 55.5818 7.505.003.001.506.500.500.007.003.500.150.0065.35114990 113.3820 7.505.003.001.506.500.000.007.005.500.150.0063.85114990 220.1
      8217.507.005.001.506.200.000.006.503.000.150.0063.151149 9074.38227.506.005.001.506.200.000.006.503.000.150.0064.151149 9096.9SeriesIII824 10.00 5.006.501.506.500.000.007.002.000.150.0061.351149 9067.782510.00 5.005.501.506.500.000.007.003.000.150.0061.351149 9082.382610.00 5.004.001.506.500.000.007.004.000.150.0061.851149 90122.182710.00 7.005.001.506.200.000.006.503.000.150.0060.651149 907082810.00 7.006.001.506.200.000.006.502.500.150.0060.151149 9011982910.00 7.007.001.506.200.000.006.502.000.150.0059.651149 908883010.00 7.005.001.505.801.500.005.003.000.150.0061.051149 90147.883110.00 7.006.001.505.801.500.005.002.000.150.0061.051149 90137.683210.00 7.007.001.505.801.500.005.001.000.150.0061.051149 90107.383310.00 7.004.002.505.801.500.005.002.000.150.0062.051149 90132.783410.00 6.005.501.507.000.000.004.003.000.150.0062.851149 9069.15925189DMS-1 8.004.407.500.005.490.000.108.604.800.100.0061.01850500 2568DMS-2 4.803.806.800.005.780.000.507.505.800.100.0064.92850500 2696DMS-3 4.503.006.000.005.360.000.308.606.000.100.0066.14850500 3054DMS-4 4.002.405.500.005.180.000.309.006.500.100.0067.02850500 3243DMS-5 6.401.805.200.005.470.000.309.507.200.200.0063.93850500 2721DMS-6 3.101.405.000.004.750.000.2010.00 7.500.100.0067.95850500 2537CMSX-4 9.006.506.000.605.601.000.006.503.000.100.0061.70850500 917DMS-1 8.004.407.500.005.490.000.108.604.800.100.0061.01950240 3468DMS-4 4.002.405.500.005.180.000.309.006.500.100.0067.02950240 3917DMS-5 6.401.805.200.005.470.000.309.507.200.200.0063.93950240 3764DMS-6 3.101.405.000.004.750.000.2010.00 7.500.100.0067.95950240 3427CMSX-2 5.008.008.000.605.601.000.006.000.000.000.0065.80950240 380CMSX-4 9.006.506.000.605.601.000.006.503.000.100.0061.70950240 953ReneN5 8.007.005.002.006.200.000.007.003.000.200.0061.60950240 837DMS-1 8.004.407.500.005.490.000.108.604.800.100.0061.011050 140 1469DMS-2 4.803.806.800.005.780.000.507.505.800.100.0064.921050 140 1592
      DMS-34.503.006.000.005.360.000.308.606.000.100.0066.141050140 1752DMS-44.002.405.500.005.180.000.309.006.500.100.0067.021050140 1803DMS-63.101.405.000.004.750.000.2010.00 7.500.100.0067.951050140 1423CMSX-2 5.008.008.000.605.601.000.006.000.000.000.0065.801050140 270CMSX-4 9.006.506.000.605.601.000.006.503.000.100.0061.701050140 468ReneN5 8.007.005.002.006.200.000.007.003.000.200.0061.601050140 416DMS-18.004.407.500.005.490.000.108.604.800.100.0061.011100120 498DMS-24.803.806.800.005.780.000.507.505.800.100.0064.921100120 572DMS-34.503.006.000.005.360.000.308.606.000.100.0066.141100120 584DMS-44.002.405.500.005.180.000.309.006.500.100.0067.021100120 592DMS-56.401.805.200.005.470.000.309.507.200.200.0063.931100120 583DMS-63.101.405.000.004.750.000.2010.00 7.500.100.0067.951100120 487ReneN5 8.007.005.002.006.200.000.007.003.000.200.0061.601100120 319DMS-18.004.407.500.005.490.000.108.604.800.100.0061.01115090485DMS-24.803.806.800.005.780.000.507.505.800.100.0064.92115090593DMS-34.503.006.000.005.360.000.308.606.000.100.0066.14115090623DMS-44.002.405.500.005.180.000.309.006.500.100.0067.02115090650DMS-56.401.805.200.005.470.000.309.507.200.200.0063.93115090590DMS-63.101.405.000.004.750.000.2010.00 7.500.100.0067.95115090473DMS-18.004.407.500.005.490.000.108.604.800.100.0061.01120070182DMS-24.803.806.800.005.780.000.507.505.800.100.0064.92120070213DMS-34.503.006.000.005.360.000.308.606.000.100.0066.14120070261DMS-44.002.405.500.005.180.000.309.006.500.100.0067.02120070281DMS-56.401.805.200.005.470.000.309.507.200.200.0063.93120070232605108338 1.007.547.210.834.960.001.718.771.440.280.0066.261040137 333.549 1.017.277.000.835.180.000.0011.83 1.430.280.0065.171040137 328.350 1.017.407.110.835.070.000.8510.31 1.440.280.0065.701040137 388.951 0.997.158.990.835.070.000.858.701.430.280.0065.711040137 665.152 1.006.746.572.515.140.000.868.791.450.280.0066.661040137 507.3
      53 1.017.457.080.834.950.001.618.702.860.290.0065.221040137244.854 0.977.547.210.834.960.001.718.771.440.280.0066.291040137232.255 1.017.278.070.835.070.000.859.501.430.260.0065.711040137509.956 1.027.218.530.835.070.000.859.101.430.270.0065.691040137525.557 1.027.297.800.845.200.000.868.791.450.250.0066.50104013743058 1.017.366.560.845.280.000.868.782.890.260.0066.161040137436.559 1.017.356.790.835.150.000.859.502.870.250.0065.401040137433.460 1.017.505.610.845.270.000.869.592.890.260.0066.171040137415.461 1.007.108.800.835.080.000.808.901.420.250.0065.821040137555.562 1.007.188.760.835.070.000.858.901.430.250.0065.731040137611.11000.007.547.210.834.960.001.718.771.440.210.0067.331040137323.31012.317.367.050.824.850.001.688.571.410.260.0065.691040137298.71024.517.206.890.804.740.001.648.381.380.250.0064.211040137275.31038.636.896.590.764.530.001.578.021.320.240.0061.451040137240.410412.40 6.606.320.734.350.001.507.681.260.240.0058.921040137211.11050.895.758.890.825.100.000.848.612.830.220.0066.051040137508.91060.994.238.800.815.120.000.838.524.270.240.0066.191040137460.61070.994.277.560.815.200.000.838.525.610.220.0065.991040137454.31081.017.339.000.415.120.000.858.721.440.250.0065.871040137588.81091.057.677.320.844.850.002.597.221.450.280.0066.731040137220.31101.207.226.930.835.030.380.438.721.440.210.0067.611040137610.11140.987.799.350.884.750.000.818.181.570.210.0065.481040137580.91150.986.508.620.775.400.000.899.231.290.210.0066.111040137550.31161.019.796.630.845.170.000.878.881.460.290.0065.061040137220.31170.9911.73 5.590.005.200.001.777.421.490.250.0065.561040137205.51180.557.589.010.844.781.170.866.431.450.250.0067.081040137220.51191.017.198.410.845.340.000.877.251.460.260.0067.371040137351.21201.027.237.900.865.620.000.885.741.480.260.0069.011040137311.11211.006.156.094.215.210.000.877.251.460.210.0067.551040137477.5
      381.007.547.210.834.960.001.718.771.440.280.0066.2692732485.1491.017.277.000.835.180.000.0011.83 1.430.280.0065.1792732460.1501.017.407.110.835.070.000.8510.31 1.440.280.0065.7092732478510.997.158.990.835.070.000.858.701.430.280.0065.7192732474.5521.006.746.572.515.140.000.868.791.450.280.0066.6692732457.3531.017.457.080.834.950.001.618.702.860.290.0065.2292732480.4540.977.547.210.834.960.001.718.771.440.280.0066.2992732446.1551.017.278.070.835.070.000.859.501.430.260.0065.7192732448.6561.027.218.530.835.070.000.859.101.430.270.0065.6992732450571.027.297.800.845.200.000.868.791.450.250.0066.5092732445.7581.017.366.560.845.280.000.868.782.890.260.0066.1692732473.2591.017.356.790.835.150.000.859.502.870.250.0065.4092732438.4601.017.505.610.845.270.000.869.592.890.260.0066.1792732448.6611.007.108.800.835.080.000.808.901.420.250.0065.8292732466.7621.007.188.760.835.070.000.858.901.430.250.0065.7392732470.7100 0.007.547.210.834.960.001.718.771.440.210.0067.3392732478.8101 2.317.367.050.824.850.001.688.571.410.260.0065.6992732479.7102 4.517.206.890.804.740.001.648.381.380.250.0064.2192732475.9103 8.636.896.590.764.530.001.578.021.320.240.0061.4592732477104 12.40 6.606.320.734.350.001.507.681.260.240.0058.9292732455.4105 0.895.758.890.825.100.000.848.612.830.220.0066.0592732460.5108 1.017.339.000.415.120.000.858.721.440.250.0065.8792732478109 1.057.677.320.844.850.002.597.221.450.280.0066.7392732435.5110 1.207.226.930.835.030.380.438.721.440.210.0067.6192732464.5114 0.987.799.350.884.750.000.818.181.570.210.0065.4892732464.4115 0.986.508.620.775.400.000.899.231.290.210.0066.1192732465.3116 1.019.796.630.845.170.000.878.881.460.290.0065.0692732438.3117 0.9911.73 5.590.005.200.001.777.421.490.250.0065.5692732435.5119 1.017.198.410.845.340.000.877.251.460.260.0067.3792732437.7
      1201.02 7.237.90 0.865.620.000.885.741.480.260.0069.0192732433.31211.00 6.156.09 4.215.210.000.877.251.460.210.0067.5592732473.3V2 4.10 4.303.20 2.205.700.000.006.807.100.001.7064.9090048385.98V3 4.10 4.402.50 1.806.000.000.005.607.200.002.6065.8090048382.47V4 4.20 4.501.80 1.205.900.000.004.407.300.003.5067.20900483112.77V6 4.40 4.700.20 0.206.100.000.001.907.600.005.4069.5090048332.864253 3.10 5.503.20 0.006.100.002.400.005.900.002.7071.10900483142V2 4.10 4.303.20 2.205.700.000.006.807.100.001.7064.901000 276189.31V3 4.10 4.402.50 1.806.000.000.005.607.200.002.6065.801000 276132.66V4 4.20 4.501.80 1.205.900.000.004.407.300.003.5067.201000 27699.8V5 4.30 4.601.00 0.706.000.000.003.207.500.004.4068.301000 276110.91V6 4.40 4.700.20 0.206.100.000.001.907.600.005.4069.501000 276110.954253 3.10 5.503.20 0.006.100.002.400.005.900.002.7071.101100 15546.8V2 4.10 4.303.20 2.205.700.000.006.807.100.001.7064.901100 162434.8V3 4.10 4.402.50 1.806.000.000.005.607.200.002.6065.801100 162311.67V4 4.20 4.501.80 1.205.900.000.004.407.300.003.5067.201100 138201.36RE29920A-110.157.870.00 6.065.951.080.004.400.000.000.0064.49760648229.6B-110.0010.20 0.00 3.056.301.120.006.750.000.000.0062.58760648297.2C-110.108.7512.000.004.991.981.230.000.000.000.0060.95760648400.6C-210.309.3012.810.004.802.081.200.000.000.000.0059.51760648442.6C-310.108.7512.000.004.991.981.230.000.000.000.0060.95760648245.5E-115.1010.10 0.00 3.015.334.800.000.000.000.000.8660.80760648345A-212.159.750.00 5.895.950.960.003.710.000.000.0061.59760648146.5B-211.7610.56 0.00 3.106.030.990.005.700.000.000.0061.86760648206D-110.919.669.66 2.435.191.380.001.500.000.000.0059.27760648432.8C-410.669.3312.410.005.651.760.950.000.000.000.0059.24760648314.8C-510.708.3312.400.005.531.780.950.000.000.000.0060.31760648392.2C-610.648.8912.740.005.631.770.920.000.000.000.0059.41760648448C-710.668.6112.840.005.801.780.920.000.000.000.0059.39760648452.9
      C-8 10.718.6412.48 0.005.411.750.920.000.000.000.0060.09760648468.6C-9 10.788.9712.55 0.005.131.770.910.000.000.000.0059.89760648459.8C-1010.608.9612.41 0.005.151.760.850.000.000.000.0060.27760648458.6C-1110.509.5012.50 0.004.982.001.090.000.000.000.0059.43760648397.2C-1210.699.5411.84 0.004.761.750.880.000.000.000.0060.54760648347.4E-5 16.629.670.003.065.614.740.000.000.000.001.0859.22760648117.2E-6 16.629.870.003.035.634.910.000.000.000.001.0658.88760648174.1E-7 16.869.870.003.255.224.640.000.000.000.001.0059.16760648266.3E-8 16.8010.22 0.003.335.234.640.000.000.000.001.0158.77760648302.2E-9 16.6910.05 0.003.325.234.560.000.000.000.001.0159.14760648357.6A-2 12.159.750.005.895.950.960.003.710.000.000.0061.5998220044.8B-2 11.7610.56 0.003.106.030.990.005.700.000.000.0061.8698220052.4F-1 9.43 11.35 4.182.043.923.690.004.230.000.000.0061.1698220079.2C-4 10.669.3312.41 0.005.651.760.950.000.000.000.0059.2498220073.6C-5 10.708.3312.40 0.005.531.780.950.000.000.000.0060.3198220085.2C-6 10.648.8912.74 0.005.631.770.920.000.000.000.0059.41982200113.9C-7 10.668.6112.84 0.005.801.780.920.000.000.000.0059.39982200122.4C-8 10.718.6412.48 0.005.411.750.920.000.000.000.0060.09982200128.3C-9 10.788.9712.55 0.005.131.770.910.000.000.000.0059.89982200117.1C-1010.608.9612.41 0.005.151.760.850.000.000.000.0060.2798220064.8C-1110.509.5012.50 0.004.982.001.090.000.000.000.0059.4398220092.3C-1210.699.5411.84 0.004.761.750.880.000.000.000.0060.5498220043E-3 16.679.100.002.945.714.900.000.000.000.001.0759.6198220048.6E-4 16.628.950.003.175.604.880.000.000.000.001.0759.7198220041.3E-5 16.629.670.003.065.614.740.000.000.000.001.0859.2298220038.1E-6 16.629.870.003.035.634.910.000.000.000.001.0658.8898220041.2E-7 16.869.870.003.255.224.640.000.000.000.001.0059.1698220036.5E-8 16.8010.22 0.003.335.234.640.000.000.000.001.0158.7798220031.94824637 NASAIR100 0.00 8.5710.62 1.015.511.130.003.350.000.000.0069.801040 137377.4
      TUT-230.008.3414.81 0.005.19 0.000.00 4.350.00 0.000.00 67.301040 1371681TUT-240.008.4413.64 0.005.25 0.000.00 4.050.00 0.000.00 68.621040 137917TUT-6 0.008.444.480.005.26 0.000.00 13.22 0.00 0.000.00 68.611040 137230TUT-7 0.008.384.710.005.22 0.000.00 13.94 0.00 0.000.00 67.751040 137178D.5.0 16.24.1 3.0 3.53.6 0.00.0 0.00.0 0.064.5798215277.3E.5.0 15.75.9 1.5 3.63.6 0.00.0 0.00.0 0.064.7498215276.5F.5.0 15.75.9 1.5 3.53.6 0.00.0 0.00.0 0.064.7898215262.8
      權(quán)利要求
      1.鎳基高溫合金成分的優(yōu)化設(shè)計(jì)方法,其特征在于①收集鎳基變形高溫合金的成分、持久試驗(yàn)溫度、持久斷裂時(shí)間及其對(duì)應(yīng)的持久強(qiáng)度數(shù)據(jù)或鎳基單晶高溫合金的成分、持久試驗(yàn)溫度、持久應(yīng)力及其對(duì)應(yīng)的持久壽命數(shù)據(jù),然后將上述數(shù)據(jù)作為人工神經(jīng)網(wǎng)絡(luò)初始訓(xùn)練數(shù)據(jù)進(jìn)行網(wǎng)絡(luò)訓(xùn)練,并通過常規(guī)優(yōu)化隱含層神經(jīng)單元數(shù)、歸一化條件及動(dòng)量因子等神經(jīng)網(wǎng)絡(luò)參量,獲得鎳基變形高溫合金的持久強(qiáng)度或鎳基單晶高溫合金的持久壽命預(yù)測值與實(shí)測值誤差最小的網(wǎng)絡(luò)訓(xùn)練最佳權(quán)值矩陣;②將所獲得的最佳權(quán)值矩陣與成本的比值作為鎳基變形高溫合金或鎳基單晶高溫合金成分優(yōu)化設(shè)計(jì)所使用的目標(biāo)函數(shù),在此基礎(chǔ)上建立鎳基變形高溫合金或鎳基單晶高溫合金成分優(yōu)化設(shè)計(jì)的約束條件,以抑制有害相σ和μ相的形成和控制合金的密度;鎳基變形高溫合金成分優(yōu)化設(shè)計(jì)的數(shù)學(xué)模型為 式(1)、式(2)為鎳基變形高溫合金成分優(yōu)化設(shè)計(jì)所使用的目標(biāo)函數(shù);式(3)至式(6)為鎳基變形高溫合金成分優(yōu)化設(shè)計(jì)的約束條件;式中,σc為合金持久強(qiáng)度的目標(biāo)函數(shù),w1、w2、b1、b2為通過神經(jīng)網(wǎng)絡(luò)訓(xùn)練得到的最佳權(quán)值矩陣,purelin為線性激活函數(shù),tansig為帶有偏差的雙曲正切S型激活函數(shù),其輸入變量的轉(zhuǎn)置矩陣s=[X1,X2,...,Xn,t,T]′,X1,X2,…,Xn依次為合金元素C、Cr、Co、Mo、Ti、Al、Fe、B、Zr、Ni、Nb、W、Ta、Mn、Si、V、Cb、Y的原子百分?jǐn)?shù),t為持久斷裂時(shí)間,T為持久試驗(yàn)溫度;p為合金成本;pi為合金元素的單價(jià);ci為元素i的重量百分?jǐn)?shù),i=1,2,……n,依次對(duì)應(yīng)C、Cr、Co、Mo、Ti、Al、Fe、B、Zr、Ni、Nb、W、Ta、Mn、Si、V、Cb、Y共18種合金元素;(σc/p)max為性能與價(jià)格比的目標(biāo)函數(shù);Md為控制有害σ相的合金平均電子能級(jí),Mdγ為基體γ相的平均電子能級(jí),Xi和Xiγ分別表示合金和γ相中元素i的原子百分?jǐn)?shù),i=1,2,……n,n=18;(Md)i為元素i的d電子能級(jí),可通過查表獲得;XMo和Xw分別為合金中Mo和W的原子百分?jǐn)?shù);合金密度&rho;=Walloy-cellValloy-cell=Nalloy-cellat&CenterDot;&Sigma;i=1n(Xit&CenterDot;Mi)/NAa3,]]>Walloy,Valloy分別為合金中一個(gè)晶胞內(nèi)所含各元素的原子總質(zhì)量和一個(gè)晶胞的體積;Xit、a分別為合金中元素i的原子百分?jǐn)?shù)和合金的點(diǎn)陣常數(shù);Nalloy-cellat表示一個(gè)晶胞的原子數(shù);Mi為元素i的摩爾質(zhì)量;NA為Avogadro常數(shù);鎳基單晶高溫合金成分優(yōu)化設(shè)計(jì)的數(shù)學(xué)模型為 式(7)、式(8)為鎳基單晶高溫合金成分優(yōu)化設(shè)計(jì)所使用的目標(biāo)函數(shù);式(9)至式(14)為鎳基單晶高溫合金成分優(yōu)化設(shè)計(jì)的約束條件;式中,f為合金的持久壽命,W1、W2、B1、B2為通過神經(jīng)網(wǎng)絡(luò)訓(xùn)練得到的最佳權(quán)值矩陣,S是一個(gè)輸入變量的轉(zhuǎn)置矩陣S=[C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 Tσ]′,C1、C2、C3、C4、C5、C6、C7、C8、C9、C10、C11依次代表合金元素Co、Cr、W、Mo、Al、Ti、Nb、Ta、Re、Hf、V共11種元素的重量百分?jǐn)?shù),Cil和Cik分別表示在設(shè)計(jì)合金時(shí)所給成分范圍內(nèi)元素i的下限和上限值,T為持久試驗(yàn)溫度,σ為持久應(yīng)力;P為合金成本;Pi為合金元素的單價(jià);Ci為元素i的重量百分?jǐn)?shù);i=1,2,……n,n=11,依次對(duì)應(yīng)Co、Cr、W、Mo、Al、Ti、Nb、Ta、Re、Hf、V共11種合金元素;(f/P)max為性能與價(jià)格比的目標(biāo)函數(shù);控制有害σ相的約束條件參量中Mdt為的合金平均電子能級(jí),Mdi為i元素的電子能級(jí),通過查表獲得;控制有害μ相的約束條件參量中,A2、A3和A4分別表示合金中Cr、W和Mo的原子百分?jǐn)?shù);ΔE為提高單晶合金穩(wěn)定性的參量,Zi為元素價(jià)電子數(shù),M為合金元素的摩爾質(zhì)量,Ai為合金元素的原子百分?jǐn)?shù);合金密度ρ的算法同于前述鎳基變形高溫合金;按上述優(yōu)化步驟和約束條件,設(shè)置所要設(shè)計(jì)的鎳基變形或鎳基單晶高溫合金中各元素含量Ci的范圍,通過優(yōu)化計(jì)算,即可在給定成分范圍和上述約束條件下搜索出能使目標(biāo)函數(shù)值達(dá)到最大值的合金的成分配方。
      2.根據(jù)權(quán)利要求1所述的方法,其特征在于上述鎳基變形高溫合金的成分、持久試驗(yàn)溫度、持久斷裂時(shí)間及其對(duì)應(yīng)的持久強(qiáng)度數(shù)據(jù)選自數(shù)據(jù)庫A中的數(shù)據(jù);鎳基單晶高溫合金的成分、持久試驗(yàn)溫度、持久應(yīng)力及其對(duì)應(yīng)的持久壽命數(shù)據(jù)選自數(shù)據(jù)庫B中的數(shù)據(jù)。
      全文摘要
      鎳基高溫合金成分的優(yōu)化設(shè)計(jì)方法,將收集的鎳基變形高溫合金或鎳基單晶高溫合金的數(shù)據(jù)作為人工神經(jīng)網(wǎng)絡(luò)初始訓(xùn)練數(shù)據(jù)進(jìn)行網(wǎng)絡(luò)訓(xùn)練,并通過常規(guī)優(yōu)化隱含層神經(jīng)單元數(shù)、歸一化條件及動(dòng)量因子等神經(jīng)網(wǎng)絡(luò)參量,獲得鎳基變形高溫合金的持久強(qiáng)度或鎳基單晶高溫合金的持久壽命預(yù)測值與實(shí)測值誤差最小的網(wǎng)絡(luò)訓(xùn)練最佳權(quán)值矩陣;將所獲得的最佳權(quán)值矩陣與成本的比值作為鎳基變形高溫合金或鎳基單晶高溫合金成分優(yōu)化設(shè)計(jì)的目標(biāo)函數(shù),建立高溫合金成分優(yōu)化設(shè)計(jì)的約束條件,以抑制有害相σ和μ相的形成和控制合金的密度;設(shè)置所要設(shè)計(jì)的鎳基變形或鎳基單晶高溫合金中各元素含量C
      文檔編號(hào)G06F19/00GK1718802SQ200510019239
      公開日2006年1月11日 申請(qǐng)日期2005年8月5日 優(yōu)先權(quán)日2005年8月5日
      發(fā)明者彭志方, 李軍偉, 王春水 申請(qǐng)人:武漢大學(xué)
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