CN100334240C - 镍基高温合金成分的优化设计方法 - Google Patents

镍基高温合金成分的优化设计方法 Download PDF

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CN100334240C
CN100334240C CNB2005100192394A CN200510019239A CN100334240C CN 100334240 C CN100334240 C CN 100334240C CN B2005100192394 A CNB2005100192394 A CN B2005100192394A CN 200510019239 A CN200510019239 A CN 200510019239A CN 100334240 C CN100334240 C CN 100334240C
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彭志方
李军伟
王春水
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Wuhan University WHU
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Abstract

镍基高温合金成分的优化设计方法,将收集的镍基变形高温合金或镍基单晶高温合金的数据作为人工神经网络初始训练数据进行网络训练,并通过常规优化隐含层神经单元数、归一化条件及动量因子等神经网络参量,获得镍基变形高温合金的持久强度或镍基单晶高温合金的持久寿命预测值与实测值误差最小的网络训练最佳权值矩阵;将所获得的最佳权值矩阵与成本的比值作为镍基变形高温合金或镍基单晶高温合金成分优化设计的目标函数,建立高温合金成分优化设计的约束条件,以抑制有害相σ和μ相的形成和控制合金的密度;设置所要设计的镍基变形或镍基单晶高温合金中各元素含量Ci的范围,通过优化计算,搜索出能使目标函数值达到最大值的合金的成分配方。

Description

镍基高温合金成分的优化设计方法
技术领域
本发明涉及高温合金的成分设计方法,具体地说,涉及通过人工神经网络与优化计算相结合对镍基高温合金成分进行优化设计。
背景技术
高温合金是制造航空发动机部件和热力设备部件及核动力设备部件最为广泛的金属材料。合金的显微组织即各组成相特别是析出相的性质、形态、大小、含量及分布决定了其高温力学性能及运行寿命。然而,合金的组织状态是由其成分所决定的。因此,决定合金性能的源头在于合金成分本身,即构成合金成分的各元素的种类及其含量。长期以来,高温合金设计主要有以下几种方法:1)基于控制有害相的电子空位数法(源于60年代);2)基于γ′(有序结构析出相)与γ相(基体相)成分、相含量及两相共格错配度与持久寿命关系的多元回归法(源于80年代);3)基于合金稳定性的d电子能量法(源于90年代);4)基于‘烹调式’操作的‘试错’法(源于50年代)等。上述方法中有的基于半经验、半理论(如1)和3));有的出自对试验结果的回归处理(如2)),而有的则完全通过改变成分的逐一试验来获得所需性能指标的成分设计结果(如4))。上述设计方法在不同年代的高温合金设计过程中起到了应有的积极作用。然而,随着航空发动机及燃气动力设备事业的发展,对高承温能力高温合金的需求愈来愈迫切,对这类材料的设计既需要先进的理论指导,又需要大量合金配方的实验;此外,对广普型高性能低成本的军用及民用高温合金材料的开发是国防及国民经济建设必不可少的,如何使现有高温合金材料的成分配方更为合理以提高其性能指标并降低原材料成本是高温合金设计必须考虑的重要因素。
本发明就是针对上述现状和围绕发展需求提出的。其核心在于利用发达国家高温合金设计所用各种不同元素及其含量的配方与高温持久试验的数据作为人工神经网络的训练数据库,通过网络训练获得最佳权值矩阵(数学模型),并用以作为满足设计条件的合金成分优化的目标函数,在给定合金成分及试验条件范围内找到最佳持久性能的合金成分配方。该设计方法克服了现有其它方法的诸多不足,它基于任何一个独立的试验部门都不可能获取的大量实验数据(合金成分与持久试验条件),利用先进的数学物理方法获得用常规数理统计方法所无法获得的数据之间复杂的复杂非线性定量关系,并用之进行合金设计。其主要特点是,设计所基于的试验数据涉及广泛的合金化学成分及高温持久试验条件,设计所用目标函数的获取方法先进,设计是通过最优化法寻找指定成分范围内获最佳性能的配方,设计结果准确性高,设计过程快速而经济。
发明内容
本发明的目的在于提供一种镍基高温合金成分的优化设计方法,该方法操作及计算简便,设计结果准确度高。
本发明提供的技术方案是:镍基高温合金成分的优化设计方法,①收集镍基变形高温合金的成分、持久试验温度、持久断裂时间及其对应的持久强度数据或镍基单晶高温合金的成分、持久试验温度、持久应力及其对应的持久寿命数据,然后将上述数据作为人工神经网络初始训练数据进行网络训练,并通过常规优化隐含层神经单元数、归一化条件及动量因子等神经网络参量,获得镍基变形高温合金的持久强度或镍基单晶高温合金的持久寿命预测值与实测值误差最小的网络训练最佳权值矩阵;②将所获得的最佳权值矩阵与成本的比值作为镍基变形高温合金或镍基单晶高温合金成分优化设计所使用的目标函数,在此基础上建立镍基变形高温合金或镍基单晶高温合金成分优化设计的约束条件,以抑制有害相σ和μ相的形成和控制合金的密度;
镍基变形高温合金成分优化设计的数学模型为:
Figure C20051001923900061
式(1)、式(2)为镍基变形高温合金成分优化设计所使用的目标函数;式(3)至式(6)为镍基变形高温合金成分优化设计的约束条件;
式中,σc(MPa)为合金持久强度的目标函数,w1、w2、b1、b2为通过神经网络训练得到的最佳权值矩阵,purelin为线性激活函数,tansig为带有偏差的双曲正切S型激活函数,其输入变量的转置矩阵s=[X1,X2,…,Xn,t,T]′,X1,X2,…,Xn依次为合金元素C、Cr、Co、Mo、Ti、Al、Fe、B、Zr、Ni、Nb、W、Ta、Mn、Si、V、Cb、Y的原子百分数(at.%),t为持久断裂时间(h),T为持久试验温度(℃);p为合金成本(元/公斤);pi为合金元素的单价(元/公斤);ci为元素i的重量百分数(wt%),i=1,2,……n,n=18,依次对应C、Cr、Co、Mo、Ti、Al、Fe、B、Zr、Ni、Nb、W、Ta、Mn、Si、V、Cb、Y共18种合金元素;(σc/p) max为性能与价格比的目标函数;
Figure C20051001923900071
为控制有害6相的合金平均电子能级, 为基体γ相的平均电子能级,Xi和Xir分别表示合金和γ相中元素i的原子百分数,i=1,2,……n,n=18;(Md)iz为元素i的d电子能级,可通过查表获得;XMo和XW分别为合金中Mo和W的原子百分数;合金密度 ρ = W alloy - cell V alloy - cell = N alloy - cell at · Σ i = 1 n ( X it · M i ) / N A a 3 ( g / c m 3 ) , Walloy,Valloy分别为合金中一个晶胞内所含各元素的原子总质量和一个晶胞的体积;Xit、a分别为合金中元素i的原子百分数和合金的点阵常数;Nalloy-cell at表示一个晶胞的原子数;Mi为元素i的摩尔质量;NA为Avogadro常数;
对镍基单晶高温合金成分优化设计的数学模型:
Figure C20051001923900074
式(7)、式(8)为镍基单晶高温合金成分优化设计所使用的目标函数;式(9)至式(14)为镍基单晶高温合金成分优化设计的约束条件;式中,f为合金的持久寿命,W1、W2、B1、B2为通过神经网络训练得到的最佳权值矩阵,S是一个输入变量转置矩阵S=[C1 C2 C3 C4C5 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种元素的重量百分数,Cil和Cik分别表示在设计合金时所给成分范围内元素i的下限和上限值,T为持久试验温度,σ为持久应力;P为合金成本;Pi为合金元素的单价;Ci为元素i的重量百分数;i=1,2,……n,n=11,依次对应Co、Cr、W、Mo、Al、Ti、Nb、Ta、Re、Hf、V共11种合金元素;(f/P) max为性能与价格比的目标函数;Mdi为i元素的控制有害σ相的合金电子能级Md值,Mdt为整个合金的Md值,Zi为价电子数,M为合金元素的摩尔质量,Ai为合金元素的原子百分数;A2、A3和A4分别表示合金中Cr、W和Mo的原子百分数,控制密度的约束条件为:ρ<9.0(g/cm3);
按上述优化步骤和约束条件,在本训练数据库中各元素含量范围内(分别见表1和表2),根据需要任意设置所要设计的镍基变形高温合金中各元素含量的范围(Cil<C<Cik),通过优化计算,即可在给定成分范围和上述约束条件下搜索出能使目标函数值达到最大值的合金的成分配方、在给定成分范围内搜索出高性能与价格比的合金成分配方。
上述镍基变形高温合金的成分、持久试验温度、持久断裂时间及其对应的持久强度数据选自下述数据库A(镍基变形高温合金神经网络训练数据库A)中的国外牌号合金409组数据;镍基单晶高温合金的成分、持久试验温度、持久应力及其对应的持久寿命数据选自下述数据库B(镍基单晶高温合金神经网络训练数据库B)中的所示的国外牌号合金700组数据。
本发明采用现有设计方法所不能反映的多组元合金成分(对于镍基变形合金可达18种元素;对于镍基单晶合金可达11种元素)与复杂试验条件(对于镍基变形合金,持久试验温度范围:404~1149℃,持久断裂时间:14.7~1860h,持久强度:3~823.2MPa;对于镍基单晶合金,持久试验温度:700-1200℃,持久试验应力:50-1000MPa,持久断裂寿命:30-15000h)及试验结果(对于镍基变形高温合金为持久强度;对于镍基单晶高温合金为持久断裂寿命)之间错综复杂的非线性关系的数学模型。这个数学模型的获得既不来源于纯理论推导,也不来自常用的数理统计方法(数理统计回归法在表达上述参量之间复杂非线性关系方面的误差很大),它来自用先进人工神经网络训练现有的对镍基高温合金的试验数据所得。
本发明基于广泛使用的人工神经网络反向传播法(BP法)建立网络模型,引用近20多年来国外专利及相关试验研究者报告的关于镍基变形高温合金和镍基单晶高温合金的试验数据进行网络训练,将所获得的最佳权值矩阵作为高温合金最优化设计所用的目标函数;网络训练数据库中包含409组镍基变形高温合金的成分、持久试验温度、持久断裂时间(输入变量)及其对应的持久强度(输出变量)数据和700组镍基单晶高温合金的成分、持久试验温度、持久应力(输入变量)及其对应的持久寿命(输出变量)数据,因此本高温合金设计方法所建立的数学模型以及所使用的试验数据量(输入变量与输出变量)之庞大是空前未有的;在建立目标函数方面,首次将人工神经网络与最优化计算相接合进行合金设计,即将人工神经网络训练所获得的最佳权值矩阵作为合金最优化设计的目标函数(在除高温合金以外的其它类型合金设计方面也未见雷同报道);与现有统计回归法相比,采用人工神经网络法能反映众多变量和数据(见表1和表2)之间复杂的非线性关系,并使输出变量预测的准确性大大提高;表3列出了7种未参与训练的镍基变形高温合金的成分、试验温度、试验时间以及实测持久强度值与本网络训练所得最佳权值矩阵算得的持久强度预测值;表4列出了16种未参与训练的镍基单晶高温合金的成分、试验温度、试验应力,表5列出了对应合金的实测持久寿命值与本网络训练所得最佳权值矩阵算得的持久寿命预测值,结果表明了本设计方法所得神经网络最佳权值矩阵的准确性;以镍基单晶合金为例,表5列出了线性误差error(1)的数据表明,除16号合金的预测误差较大以外,其余15种合金的预测误差均较小,表5所用error(2)为对数误差,其平均误差率为0.93%。本发明预测对数误差率最小;此外,本发明方法用于网络训练的合金成分及试验条件(温度及应力)范围更宽,数据来源错综复杂,但其预测的准确性却明显提高;本发明方法集合了用人工神经网络法获取准确预测输出变量的数学模型,用优化法在给定合金成分范围内寻找满足各项约束条件(控制有害相形成、控制合金密度及控制合金成本的各项指标条件)而获得目标函数输出变量所表征的最佳高温持久性能的合金成分配方。以上两步过程实现的人工神经网络运算程序以及优化设计运算程序是利用通用软件Matlab中的神经网络工具箱和优化工具箱编制而成,过程简单,计算速度快,结果准确性高,可直接应用于现代镍基高温合金的设计,是目前运用实验数据量最大,目标函数获取的科学性高,综合考虑对有害相、合金密度及合金成本进行有效控制的新设计方法,该方法不仅可运用于镍基高温合金设计,并可推广到其它所有民用工业及军用工业合金的设计领域,其应用前景十分宽广,不仅可为合金设计的科学与技术进步作出重要贡献,而且为工业应用提供了更为科学合理的设计工具。
具体实施方式
本发明镍基高温合金成分的优化设计方法,包括以下步骤:①数据及优化设计目标函数的来源,分别收集国外牌号的409组镍基变形高温合金的成分、持久试验温度、持久断裂时间及其对应的持久强度数据和700组镍基单晶高温合金的成分、持久试验温度、持久应力及其对应的持久寿命数据,然后将上述两类数据分别作为所对应两类合金的人工神经网络初始训练数据进行网络训练(利用通用软件Matlab 6.0的神经网络工具箱编制程序,建立网络模型,进行网络训练),并通过常规优化隐含层神经单元数、归一化条件及动量因子等神经网络参量,分别获得对应上述两类合金的持久强度(变形合金)和持久寿命(单晶合金)预测值与实测值误差最小的网络训练权值矩阵,即最佳权值矩阵,将该权值矩阵保存下来并作为成分优化设计的目标函数;②优化过程的实现:利用通用软件Matlab 6.0的优化工具箱编制程序,将所获得的两种最佳权值矩阵分别作为镍基变形高温合金和镍基单晶高温合金成分优化设计所计算用的目标函数,并建立约束条件,以抑制有害相σ和μ相的形成以及控制合金的密度;由于在优化计算前,已将价格昂贵的合金元素以及会促进有害相形成的合金元素的含量范围作了设定,因此优化计算过程中只会在各参量设定的范围内进行优化搜索,以找到低成本、高性能的最佳结果;③优化计算结果包含,在指定试验条件下的最佳性能及其对应的合金成分配方,对于镍基变形高温合金,试验条件为持久温度和持久断裂时间,所得最佳性能指标是持久断裂强度值,对于镍基单晶高温合金,试验条件为持久温度和持久应力,所得最佳性能指标是持久寿命。
对镍基变形高温合金:
持久强度的目标函数:σc=purelin(w2*tansig(s*w1+b1)+b2)
其输入变量的转置矩阵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种合金元素的原子百分数(即按上述合金元素的顺序分别以1、2、3…n作为下标编号,其中n=18)和持久断裂时间t及持久试验温度T(℃),其输出变量为持久断裂强度σ(MPa);合金成本计算是根据合金元素的单价(Pi,元/公斤)乘以每种元素的重量百分数(Ci)确定的,即:
P = Σ i = 1 n p i * C i
Σ i = 1 n C i = 1 i=1,2,……n(合金中有n种元素)
则性能与价格比的目标函数是:
(σ/P)max
优化约束条件为,(1)引用限制元素Mo、W和Cr的含量以控制有害相产生的算式,控制有害σ相的
Figure C20051001923900103
电子能级相计算法,即 M &OverBar; d = &Sigma; X i ( M d ) i < 0.99 , M &OverBar; d&gamma; = &Sigma; X i&gamma; ( M d ) i < 0.94 , Xi和X分别表示合金和γ相中组元i的原子百分含量,(Md)i为组元i的d电子能级;(2)引用控制有害μ相的Mo、W含量限制法,即 R &OverBar; MoW = X Mo X Mo + X W < 0.27 , XMo和XW分别为合金中Mo和W的原子百分数;(3)控制密度,使合金密度ρ低于8.9g/cm3 &rho; = W alloy - cell V alloy - cell = N alloy - cell ay &CenterDot; &Sigma; i = 1 n ( X it &CenterDot; M t ) / N A a alloy 3 , Walloy,Valloy分别为合金中一个晶胞内所含各元素的原子质量(g)和一个晶胞的体积(nm3);Xit、a分别为合金中组元i的原子百分含量(at.%)和合金的点阵常数(nm);Nalloy-cell at表示一个晶胞的原子数;Mi为组元i的摩尔质量;NA为Avogadro常数,此外,合金中各元素的原子百分数应为1,即 &Sigma; i = 1 n X i = 1 , i=1,2,……n,合金中有n种元素)。
对镍基单晶高温合金:
合金的持久寿命目标函数为:f=purelin(W2*tansig((W1*S),B1),B2)max其中,输入变量的转置矩阵S=[C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 Tσ]′合金成本计算是根据合金元素的单价(pi,元/公斤)乘以每种元素的重量百分数(Ci)确定的(i=1,2,…,n),即
P = &Sigma; i = 1 n p i * C i
&Sigma; i = 1 n C i = 1 i=1,2,……n(合金中有n种元素)
设计时人为设置Ci:Cil<Ci<Cik
Cil和Cik分别表示在设计合金时所给成分范围内元素i的下限和上限值,则性能与价格比的目标函数是:
(σ/P)max
优化约束条件为:
Ndt=∑Ai*Mdi<0.99
ΔE=∑Ai*Zi-(6.28+0.036*∑Ai*M)<0.03
Mdi为i元素的Md值,Mdt为整个合金的Md值,Zi为价电子数,M为合金元素的摩尔质量,Ai为合金元素的原子百分数,控制有害μ相的约束条件为:
A2+A3+A4<11
A3+A4<4.3
A4/(A3+A4)<0.3
&Sigma; i = 1 n A i = 1 i=1,2,……n(合金中有n种元素)
式中,A2、A3和A4分别表示合金中Cr、W和Mo的原子百分数含量,控制密度的约束条件为:ρ<9.0(g/cm3),其算法同于镍基变形合金;优化过程的实现,对现有合金进行成分优化设计时,设置所设计的合金中各元素含量的范围及试验条件(在网络初始训练数据库输入变量成分范围及试验条件范围内),通过优化计算在给定成分范围和上述约束条件下,搜索出能使目标函数值(镍基变形合金的持久强度和镍基单晶合金的持久寿命)达到最大值的合金的成分配方,然后对合金配方的经济成本进行测算,即将优化出的合金的各元素的重量百分数与对应元素的单价相乘并求和即得,于是在给定成分和试验条件范围内,即可搜索出满足目标函数和约束条件的高性能与价格比的合金成分配方。
实例
实例1:优化镍基变形高温合金的成分。以GH150合金为例,对该合金进行成分优化,并预测其在816℃、1000h下的持久断裂强度。按‘具体实施方式’中的①~③步骤,先后将反映持久断裂强度与合金成分及试验条件(持久试验温度及断裂时间)之间复杂非线性关系的人工神经网络最佳权值矩阵作为最优化设计的目标函数,将控制有害相(
Figure C20051001923900114
相计算)及合金密度的因素作为约束条件,进行合金优化设计计算,结果得到改良合金的成分配方和持久断裂强度的预测值,如表6所示。即在原GH150合金成分基础上,设计出的合金在816℃、1000h时的持久断裂强度(130MPa)比原合金在同等试验条件下的持久断裂强度(112.45MPa)能提高近16%,性/价比提升了17%,为该合金的改良提供了重要参考意义。
实例2:优化镍基单晶高温合金的成分。以无铼第二代镍基单晶高温合金DD98(我国近期研制的合金牌号)和MC2(法国牌号)以及含铼第二代镍基单晶高温合金CMSX-4(美国牌号)合金为例进行比较,在设定成分范围内进行成分优化设计,分别获得表7所示的各合金的成分配方,即获得无铼Alloy1和含铼Alloy2两种合金,各给定牌号合金的实测持久寿命及用本发明方法预测的持久断裂寿命值也一并列于表7中,需要说明铼的价格为黄金价格的三分之一;其结果的获得是按‘具体实施方式’中的①~③步骤,先后将反映持久寿命与合金成分及试验条件(持久试验温度及应力)之间复杂非线性关系的人工神经网络最佳权值矩阵作为最优化设计的目标函数,将对有害相(σ、μ相)及合金密度(ρ)的控制因素作为约束条件,进行合金优化设计计算,结果得到改良合金(无铼第二代单晶合金Alloy1和含铼第二代单晶合金Alloy2)的成分配方和持久断裂寿命值的预测值,见表7;可见,用本发明方法采用的人工神经网络预测,所得寿命预测值与实测值很接近;所设计改良合金的持久寿命预测值及性/价比明显提高:将本发明设计的不含铼的Alloy1合金与国内同类的DD98合金相比其性/价比提高了50%,与法国同类的MC2合金相比提高了20%;而本发明设计的含铼的Alloy2合金的性/价比为美国同类合金CMSX-4的一倍。
表1用于镍基变形高温合金网络训练数据的各变量范围
                               合金成分,wt.%
    C     Cr     Co     Mo   Ti   Al   Fe   B   Zr      Ni    Nb   W
  0~1.1   4~30.4   0~29   0~16  0~5  0~15  0~40 0~0.4   0~0.2  37.92~80.5   0~5.1  0~36
    Ta     Mn     Si     V    Cb    Y    时间(h)     温度(℃) 持久强度(MPa)
  0~23.3   0~0.9   0~0.7   0~1.1  0~10.9  0~0.6  14.7~1860   404~1149   3~823.2
表2用于镍基单晶高温合金网络训练数据的各变量范围
合金成分,wt.%       Co       Cr       W       Mo       Al       Ti
    0.0-16.9     0.0-20.5     0.0-18.6     0.0-10.5     1.05-7.5     0.0-9.0
      Nb       Ta       Re       Hf       V
    0.0-5.6     0.0-14     0.0-7.6     0.0-2.0     0.0-5.4
       温度(℃) 700-1200
       应力(MPa) 50-1000
    持久寿命(h)                                          30-15000
表3对镍基变形高温合金建立的网络进行可靠性检验
合金序号 合金成分,wt.% 温度(℃) 时间(h) 持久强度(MPa) 相对误差(%)
C Cr Co Mo Ti Al Fe B Zr Ni Nb W Ta 实验值 预测值
 1234567  0.030.050.150.150.0090.0090.011  1615141511.359.668.64   00818.59.4310.910.7   003.55.22.042.430   1.82.52.53.53.691.381.75   0.20.753.54.253.925.195.41  40701000  000.010.050.0960.0840.15  000.0500.0830.0620.074  38.6774.761.2952.3560.97259.11559.495   2.903.50000  003.504.189.6612.84   00004.231.50   649649649816760982982   10001001000100254.458.1128.3   580509.6865399.84648200200  614466832387673191216  5.968.653.853.243.834.648.22
表4对镍基单晶高温合金建立的网络进行可靠性检验所用参量
合金序号     合金成分,wt.%   温度,(℃)   应力,(MPa)
  Co   Cr   W   Mo  Al  Ti  Nb  Ta  Re  Hf   V
  12345678910111213141516   15.010.012.010.07.59.59.59.59.55.09.910.010.08.66.46.5   20.50.00.00.07.06.56.56.56.515.77.17.07.112.01.82.5   2.35.05.05.08.06.56.56.56.56.06.96.07.08.65.25.5   0.51.01.01.02.00.60.60.60.61.62.02.02.10.00.00.5  2.65.55.55.85.35.65.75.65.73.55.85.55.42.85.55.6  3.72.10.00.01.50.60.60.60.63.60.00.00.05.50.00.7  1.00.00.00.00.00.00.00.00.00.00.00.00.00.00.30.2  1.66.06.06.06.08.26.78.26.70.03.96.96.22.79.58.2  0.03.03.03.00.03.03.03.03.00.02.93.03.00.07.24.6  0.01.51.51.50.00.20.20.20.20.00.10.10.10.00.20.1   0.00.02.21.60.00.00.00.00.00.00.00.00.00.00.00.0   816899899899950950950950950982982982982100010501100   300414414414240200200165165152248.2248.2248.282.7140100
表5对镍基单晶高温合金建立的网络进行可靠性检验
合金序号 持久寿命实测值tf,h lgtf   持久寿命平均预测值tf′,h lgtf 误差(1),%* 误差(2),%* 平均误差(2),%
    12345678910111213141516     2785208200182603228022035040518074.4219.6271.5299.2199.11648908   3.442.322.302.262.783.363.343.703.711.872.342.432.482.303.222.96   2663.73226.62209.23197.61591.442423.762126.485509.515057.1572.52228.76258.36293.66217.891594.40762.25   3.432.362.322.302.773.383.333.743.701.862.362.412.472.343.202.88     4.358.954.618.581.926.313.479.322.372.534.174.841.859.443.2516.05     0.291.720.871.770.360.600.301.080.270.530.850.820.401.740.622.70 0.93
*:误差(1)=|tf′-tf|/tf×100%
误差(2)=|lgtf′-lgtf|/lgtf×100%
表6在给定成分范围内对镍基变形高温合金GH150进行成分优化并
预测其在816℃/1000h下的持久断裂强度
                                    合金成分,at% 6(MPa) 性/价比
  元素   C  Cr     Co   Mo   Ti   Al    Fe  B  Zr   Ni   Nb     W
  原合金  0.24  16.74     0   2.72   2.54   2.36    29.22  0.04  0.01   44.49   0.69     0.95   112.45    1.35
优化范围  0.2~0.5  8~17     0~0   0.8~3   1~3   1.5~3    23~35  0.01~0.03  0.01~0.03   40~48   0.3~1.2     0.4~1.5 -
  改良合金  0.41  16.9     0   0.7   2.71   2.53    29.38  0.13  0.13   44.65   0.85     1.6   130     1.59
注:σ为持久强度设计值
表7第二代镍基单晶高温合金在980℃/250MPa下的持久寿命
合金                                             合金成分,wt.% 密度(g.cm-3) 持久寿命预测值(h) 持久寿命实测值(h) 性/价比
  Co  Cr   W   Mo   Al   Ti   Ta   Re  Ni
  DD98   4.96  5.39   6.55   2.05   5.22   0.96   5.32   0  69.55  8.55     147     150     0.8
  MC2   5.00  8.00   8.00   2.00   5.00   1.50   6.0   0  64.5  8.63     181     200     1.0
  CMSX-4   9.00  6.50   6.00   0.60   5.60   1.00   6.50   3.00  61.7  8.68     209     178     0.2
  范围1   0.3~0.5  0.1~0.3   0.05~0.3   0.7~0.8   0.6~0.8   0.7-0.9   0.1~0.3   0~0.8  余量
  Alloy1   5.90  7.17   8.84   1.58   5.16   1.35   6.27   0  63.73  8.70     228     1.2
  范围2   0.4~0.6  0.2~0.4   0.05~0.3   0.8~0.9   0.5~0.7   0.5~0.7   0~0.2   0.4~0.6  余量
  Alloy2   5.05  6.15   8.84   0.53   4.84   2.03   6.62   1.52  64.42  8.82     250     0.4
注:范围1为无铼镍基单晶合金成分优化设计的元素含量范围;范围2为含铼镍基单晶合金成分优化设计的元素含量范围;Alloy1:用本发明法设计的无铼(Re)镍基单晶高温合金,Alloy2:用本发明法设计的含铼(Re)第二代镍基单晶高温合金;CMSX-4合金还含元素0.1%Hf
数据库A(镍基变形高温合金神经网络训练数据库)
合金牌号     C     Cr   Co   Mo Ti  Al  Fe     B   Zr   Ni     Nb    W   Ta   Mn   Si   V     Cb     Y 测试温度(C)   寿命(h)    测试应力(Mpa)
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    UDIME400UDIME400UDIME400UDIME400UDIEE400UDIMET500UDIMET500UDIMET500UDIMET500UDIMET500UDIMET500520520520520520700700700700700700700710710710710710AF2-10A   0.060.060.060.060.060.080.080.080.080.080.080.050.050.050.050.050.080.080.080.080.080.080.080.070.070.070.070.070.35     17.517.517.517.517.5181818181818191919191915151515151515181818181812   141414141418.518.518.518.518.518.5121212121218.518.518.518.518.518.518.5151515151510   44444444444666665.25.25.25.25.25.25.2333333   2.52.52.52.52.52.92.92.92.92.92.9333333.53.53.53.53.53.53.5555553   1.51.51.51.51.52.92.92.92.92.92.9222224.34.3434.34.34.34.32.52.52.52.52.54.6   00000000000000000000000000000.526   0.0080.0080.0080.0080.0080.0060.0060.0060.0060.0060.0060.0050.0050.0050.0050.0050.030.030.030.030.030.030.030.020.020.020.020.020.014     0.060.060.060.060.060.050.050.050.050.050.05000000000000000000.01  59.87259.87259.87259.87259.87253.56453.56453.56453.56453.56453.56456.94556.94556.94556.94556.94553.3953.3953.3953.3953.3953.3953.3954.9154.9154.9154.9154.9159     0.50.50.50.50.5000000000000000000000000     000000000001111100000001.51.51.51.51.56     00000000000000000000000000001.5   00000000000000000000000000000     00000000000000000000000000000     00000000000000000000000000000   00000000000000000000000000000     00000000000000000000000000000     649704760816871649704760816871927649704760816871649704760816871927982760816871927982871     10001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000     600440305195110760510325205125835854753452301507055754302952001105246031020011569260
    AF2-10A     0.35     12     10   3   3   4.6    0.526     0.014     0.01     59   0   6     1.5  0  0     0     0     0     927   1000   150
    WASPALOY     0.08     19.5     13.5   4.3   3   1.3    0     0.006     0.06     58.254   0   0     0  0  0     0     0     0     649   1000   615
    WASPALOY     0.08     19.5     13.5   4.3   3   1.3    0     0.006     0.06     58.254   0   0     0  0  0     0     0     0     704   1000   450
    WASPAOY     0.08     19.5     13.5   4.3   3   1.3    0     0.006     0.06     58.254   0   0     0  0  0     0     0     0     760   1000   290
    WASPALOY     0.08     19.5     13.5   4.3   3   1.3    0     0.006     0.06     58.254   0   0     0  0  0     0     0     0     816   1000   180
    WASPALOY     0.08     19.5     13.5   4.3   3   1.3    0     0.006     0.06     58.254   0   0     0  0  0     0     0     0     871   1000   110
    I     1.1     7     8   0   0   6.5    0     0     0     54.1   0   0     23.3  0  0     0     0     0     927   57.8   275.8
    II     1.1     6.7     8.4   5   0.84   5    0     0     0     54.6   0   0     18.3  0  0     0     0     0     927   41.4   275.8
    III     1.10000000.140000     71620202424282323232323     800000000000   500000000000   00000000.350.400.20   6.500000000000    000000000000     000000000000     00000000.10000     54.168686060525258.4158.658.558.559   0000000000.50.30   01612201624201818181818     18.300000000000  000000000000  000000000000     000000000000     000000000000     000000000000     92710001000100010001000100010001000100010001000   62.713716349453475118620632480556281   275.829.4229.4229.4229.4229.42294229.4229.4229.4229.4229.42
    1     0.04     19.8     0   0   0.5   0    0     0     0.03     59.03   0   20.6     0  0  0     0     0     0     1000   494   29.42
    2     0.05     23.7     0   0   0.6   0    0     0     0.03     58.92   0   16.7     0  0  0     0     0     0     1000   534   29.42
    6     0.04     23.1     0   0   0.4   0    0     0     0     58.66   0   17.8     0  0  0     0     0     0     1000   632   29.42
    7     0.06     22.1     0   0   0   0    0     0     0     60.54   0.5   16.8     0  0  0     0     0     0     1000   480   29.42
    8     0.03     20.8     0   0   0.5   0    0     0     0     59.07   0   19.5     0  0  0     0     0     0     1000   762   29.42
    9     0.03     21.7     0   0   0   0    0     0     0.05     59.02   0.4   18.8     0  0  0     0     0     0     1000   653   29.42
    10     0.05     22.9     0   0   0.2   0    0     0     0     58.85   0.3   17.7     0  0  0     0     0     0     1000   556   29.42
    11     0.04     23.1     0   0   0.5   0    0     0.014     0     58.85   0   17.5     0  0  0     0     0     0     1000   957   29.42
    13     0.04     21.5     0   0   0.4   0.6    0     0     0     57.76   0   19.7     0  0  0     0     0     0     1000   641   29.42
    14     0.02     21.6     0   0   0.4  0     0     0   0.04     58.14     0     19.8   0   0   0   0   0     0     1000     660     29.42
    21     0.05     4     0   0   0  0     0     0   0     59.95     0     36   0   0   0   0   0     0     1000     80     29.42
    22     0.05     7.9     0   0   0.6  0     0     0   0.05     59.1     0     32.3   0   0   0   0   0     0     1000     136     29.42
    23     0.04     12     0   0   0.5  0     0     0   0.04     59.12     0     28.3   0   0   0   0   0     0     1000     176     29.42
    31     0.04     15.5     0   15.8   0  0     5.6     0   0     58.76     0     3.6   0   0.8   0.4   0.3   0     0     1000     133     29.42
    32     0.030.10.10.10.050.050.050.050.050.080.080.080.080.080.10.10.10.10.10.080.080.080.050.15     20.51616161515151515151515151515151515151919191918     121.51.51.5000000000029292929291818181217   8.55.55.55.500000000003333344464   0.43332.52.52.52.52.52.52.52.52.52.52.252.252.252.252.252.92.92.933  1.21515150.750.750.750.750.750.70.70.70.70.72.852.852.852.852.852.92.92.924     088877777777771111144400     0.00300000000000000.0050.0050.0050.0050.0050.0050.0050.0050.0050.04   000000000000000.050.050.050.050.0500000     56.9750.950.950.974.774.774.774.774.773.8273.8273.8273.8273.8246.74546.74546.74546.74546.74549.11549.11549.11557.94553.81     0000000000.90.90.90.90.90000000000     000000000000000000000000   000000000000000000000000   000000000000000000000000   0.400000000000000000000000   000000000000000000000000   000000000000000000000000     000000000000000000000000     1000649816982649732816871982649732816871982649732816871982649816871816982     15410001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000     29.42431.2205.834 3406.7233.2498.984918.62468.44275.38117.661.7415.68599.76372.4205.8107.823.52646.8220.5147220.558.8
    0.150.150.150.070.150.150.240.240.240.240.090.090.090.090.050.050.270.270.10.10.10.050.050.080.080.080.080.080.1     15151518191916.2516.2516.2516.251919191915159.39.31616161515151515151515     18.518.518.51510107.27.27.27.2111111110015151.51.51.5000000029     5.25.25.2310101616161610101010993.253.255.55.55.500000003   3.53.53.552.62.63.23.23.23.23.13.13.13.12.52.53.253.253332.52.52.52.52.52.52.52.25   4.254.254.252.5111.91.91.91.91.51.51.51.51.251.255.255.251515150.750.750.70.70.70.70.72.85     1110.5009.59.59.59.5000022220088877777771     0.050.050.050.020.0050.0050.0080.0080.0080.0080.010010.010.01000.0150.01500000000000.005     0000000.060.060.060.060000000000000000000.05   52.3552.3552.3555.9157.24557.24545.64245.64245.64245.64255.355.355.355 350.250.258.31558.31550.950.950.974.774.773.8273.8273.8273.8273.8246.745    000000000000000000000000.90.90.90.90.90     00000000000000005.355.3500000000000     00000000000000000000000000000   00000000000000000000000000000   00000000000000000000000000000   00000000000000000000000000000   00000000000000000000000000000     00000000000000000000000000000     649816871816649816649816871982649732816871649732816982649816982816982649732816871982649     100010001000100010001000100010001000100010001000100010001000100010001000100100100100100100100100100100100     702.66295.96186.2320.46550.76151.9675.22234.22151.945.08702.66445.9199.92117.6537.04254.8392.9868.6588274.454.88131.3222.05551.74344.96193.06124.4622.54686
        0.10.10.10.10.080.080.080.050.150.150.150.070.150.150.240.24   151515151919191918151518191916.2516.25   29292929181818121718.518.51510107.27.2     3333444645.25.2310101616   2.252.252.252.252.92.92.9333.53.552.62.63 23.2   2.852.852.852.852.92.92.9244.254.252.5111.91.9   111144400110.5009.59.5   0.0050.0050.0050.0050.0050.0050.0050.0050.040.050.050.020.0050.0050.0080.008     0.050.050.050.0500000000000.060.06     46.74546.74546.74546.74549.11549.11549.11557.94553.8152.3552.3555.9157.24557.24545.64245.642  0000000000000000     0000000000000000     0000000000000000     0000000000000000   0000000000000000  0000000000000000  0000000000000000  0000000000000000     732816871982816871982816982871982816649816816871     100100100100100100100100100100100100100100100100     519.4295.9619641.16302.82196823.2302.8289.18282.24110.74468.44661.5241.08323.4220.5
 Unitemp1753   0.240.090.090.090.090.090.050.050.050.270.27   16.2519191919191515159.39.3   7.211111111110001515     1610101010109993.253.25   3.23.13.13.13.13.12.52.52.53.253.25   1.91.51.51.51.51.51.251.251.255.255.25   9.50000022222200   0.0080.010.010.010.010.010000.0150.015     0.060000000000     45.64255.355.355.355.355.350.250.250.258.31558.315  00000000000     0000000005.355.35     00000000000     00000000000   00000000000   00000000000   00000000000   00000000000     982649732816871982649732816816982     100100100100100100100100100100100     68.6757.54555.66309.68192.0868.6688.94382.2172.48495.88138.18
E   0.18   10   15     3   4.7   5.5   0   0.015     0.06     60.545  0     0     0     0   0   1   0   0     760     26.6     648
INCONEL600   0.08   15.5   0     0   0   1.4   8   0     0     74.32  0     0     0     0.5   0.2   0   0   0     871     1000     24
    INCONEL61712pene95AF2-10AAF2-10A   0.070.020.150.350.35     2222.8141212     12.5081010  903.533  00.32.533 103.54.64.6   0000.5260.526   000.010.0140.014   000.050.010.01   55.4358.7261.295959   003.500   018.13.566   0001.51.5   00000   00000   00000   00000   00.06000   7601000704760816     1000723100010001000    16529.42525525380
    GH150   0.050.050.050.050.050.050.050.050.050.050.050.05     151515151515151515151515     000000000000  4.54.54.54.54.54.54.54.54.54.54.54.5  2.12.12.12.12.12.12.12.12.12.12.12.1 1.11.11.11.11.11.11.11.11.11.11.11.1   28.12228.12228.12228.12228.12228.12228.12228.12228.12228.12228.12228.122   0.0080.0080.0080.0080.0080.0080.0080.0080.0080.0080.0080.008   0.020.020.020.020.020.020.020.020.020.020.020.02   454545454545454545454545   1.11.11.11.11.11.11.11.11.11.11.11.1   333333333333   000000000000   000000000000   000000000000   000000000000   000000000000   000000000000   600600600700700700800800800900900900     1005001000100500100010050010001005001000    785700670500400360255175140905540
数据库B(镍基单晶高温合金神经网络训练数据库)
    美国专利号     合金编号     元素           试验条件   试验结果
    4707129     Co   Cr  W  Mo  Al Ti  Nb  Ta  Re   Hf  V  Ni   温度(℃)   应力(MPa)  持久寿命(h)
    TMS-1TMS-2A1454A203ENA100     7.507.305.000.000.00   5.505.5010.005.009.00  16.6018.604.005.0010.50  0.000.000.002.001.00  5.205.305.005.505.75 0.000.001.501.101.20  0.000.000.000.000.00  5.103.4012.006.503.30  0.000.000.003.000.00  0.000.000.000.000.00  0.000.000.000.000.00  60.1059.9062.5071.9069.25     10401040104010401040     137137137137137     17511707440400510
    4629521     A.B.C.H.I.J.A.B.C.D.E.H.I.J.     5.005.000.015.005.005.005.005.000.015.005.005.005.005.00  16.0016.2016.3015.7015.6016.0016.0016.2016.3016.2015.7015.7015.6016.00  7.007.004.105.915.905.907.007.004.104.105.875.915.905.90  2.002.002.991.551.541.502.002.002.993.031.531.551.541.50  3.503.503.503.483.564.503.503.503.503.503.563.483.564.50 3.503.503.603.603.702.003.503.503.603.603.603.603.702.00  0.000.000.000.000.000.000.000.000.000.000.000.000.000.00  0.000.000.000.000.000.000.000.000.000.000.000.000.000.00  0.000.000.000.000.000.000.000.000.000.000.000.000.000.00  0.000.000.000.000.000.000.000.000.000.000.000.000.000.00  0.000.500.000.000.000.500.000.500.000.000.000.000.000.50  63.0062.3069.5164.7664.7064.6063.0062.3069.5164.5764.7464.7664.7064.60     982982982982982982760760760760760760760760     152152152152152152621621621621621621621621     93.6119.750.882.174.5113.4203.1242.753.9128.697.989.9114.9132.4
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       1234569Rene′15010A10B10C10D10E10F10G10Ga10H10I10Ia12A12B12C10Ri12Ri10B10C10D10E10F   7.507.407.407.607.307.407.3012.008.508.107.705.007.207.706.504.005.604.803.504.603.003.507.008.008.107.705.007.207.70   7.507.508.158.958.9510.1010.905.002.902.702.604.002.202.402.502.402.302.602.703.003.502.702.653.402.702.604.002.202.40   7.605.207.506.006.407.707.605.007.406.956.406.006.406.405.506.206.206.605.205.305.105.406.406.106.956.406.006.406.40   1.441.431.481.461.461.461.451.000.680.690.690.620.700.650.530.410.510.520.470.390.380.450.600.480.690.690.620.700.65   3.353.303.503.503.403.403.405.506.006.005.705.445.895.965.605.795.585.655.805.615.525.625.675.546.005.705.445.895.96   4.304.304.404.454.503.953.350.000.690.690.620.590.630.630.680.550.760.670.600.960.840.750.800.990.690.620.590.630.63   0.520.500.490.510.510.530.510.000.290.290.300.310.260.280.200.140.170.140.100.010.010.010.400.010.290.300.310.260.28   3.723.523.753.723.813.403.386.007.507.808.308.108.207.908.208.307.807.408.009.408.808.807.607.607.808.308.108.207.90   0.002.980.000.000.000.000.003.005.104.804.704.704.805.004.606.005.405.405.805.006.106.005.505.304.804.704.704.805.00   0.000.000.000.000.000.000.001.500.070.060.070.040.050.040.050.030.050.040.040.050.050.040.070.070.060.070.040.050.04   0.000.000.000.000.000.000.002.200.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00   64.0763.8763.3363.8163.6762.0662.1158.8060.8761.9262.9265.2063.6763.0465.6466.1965.6366.1867.7965.6866.7066.7363.3262.5161.9262.9265.2063.6763.04   1093109310931093109310931093109387198298298298298292798298298298298210809829139139821010101010101010     103103103103103103103103517248.2248.2248.2248.2248.2379248.2248.2248.2248.2248.2194248.2517517276248.2248.2248.2248.2     200.9351.6163.3171.678.424198.1100534.4989.3635.7428664.5666.6724.9730.9594.5581.9532491.9108.2713.3231.6209.8436.7298.1166260.5285.9
       10G10Ga10H10I10Ia12A12B12C10Ri12Ri10A10B10C10D10E10F10G10Ga10H10110Ia12A12B12C10Ri12Ri10A10B10C     6.504.005.604.803.504.603.003.507.008.008.508.107.705.007.207.706.504.005.604.803.504.603.003.507.008.008.508.107.70   2.502.402.302.602.703.003.502.702.653.402.902.702.604.002.202.402.502.402.302.602.703.003.502.702.653.402.902.702.60   5.506.206.206.605.205.305.105.406.406.107.406.956.406.006.406.405.506.206.206.605.205.305.105.406.406.107.406.956.40   0.530.410.510.520.470.390.380.450.600.480.680.690.690.620.700.650.530.410.510.520.470.390.380.450.600.480.680.690.69   5.605.795.585.655.805.615.525.625.675.546.006.005.705.445.895.965.605.795.585.655.805.615.525.625.675.546.006.005.70   0.680.550.760.670.600.960.840.750.800.990.690.690.620.590.630.630.680.550.760.670.600.960.840.750.800.990.690.690.62   0.200.140.170.140.100.010.010.010.400.010.290.290.300.310.260.280.200.140.170.140.100.010.010.010.400.010.290.290.30   8.208.307.807.408.009.408.808.807.607.607.507.808.308.108.207.908.208.307.807.408.009.408.808.807.607.607.507.808.30   4.606.005.405.405.805.006.106.005.505.305.104.804.704.704.805.004.606.005.405.405.805.006.106.005.505.305.104.804.70   0.050.030.050.040.040.050.050.040.070.070.070.060.070.040.050.040.050.030.050.040.040.050.050.040.070.070.070.060.07   0.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00   65.6466.1965.6366.1867.7965.6866.7066.7363.3262.5160.8761.9262.9265.2063.6763.0465.6466.1965.6366.1867.7965.6866.7066.7363.3262.5160.8761.9262.92     982101010101010101010109821010954954982103710501050105010501010108010501050108010501010108098298298210931093     248.2248.2248.2248.2248.2248.2248.2248.2345345207172140140140140248.2194140140194140248.2194248.2248.2248.2124124     799.1300.1242.9260.5256208.5536.4338.9460.8448.11016.2295.7637.5680.3859.9649.2354.4122.3574.7934.885.7829.6262.6118.1698.5627586.5192.7293.1
      10D10E10F10G10Ga10H10Ia12A12B10I10Ia12B12C10Ga12Ri10Ri12A10Ri12Ri10A10B10C10D10E10F10G10Ga10H10I     5.007.207.706.504.005.603.504.603.004.806.506.506.506.506.506.504.607.008.008.508.107.705.007.207.706.504.005.604.80   4.002.202.402.502.402.302.703.003.502.602.702.502.702.402.402.653.002.653.402.902.702.604.002.202.402.502.402.302.60   6.006.406.405.506.206.205.205.305.106.605.205.106.406.206.106.405.306.406.107.406.956.406.006.406.405.506.206.206.60   0.620.700.650.530.410.510.470.390.380.520.470.380.450.410.480.600.390.600.480.680.690.690.620.700.650.530.410.510.52   5.445.895.965.605.795.585.805.615.525.655.805.525.625.795.545.675.615.675.546.006.005.705.445.895.965.605.795.585.65  0.590.630.630.680.550.760.600.960.840.670.600.840.750.550.990.800.960.800.990.690.690.620.590.630.630.680.550.760.67  0.310.260.280.200.140.170.100.010.010.140.200.200.010.140.010.400.010.400.010.290.290.300.310.260.280.200.140.170.14  8.108.207.908.208.307.808.009.408.807.408.008.108.208.308.208.209.407.607.607.507.808.308.108.207.908.208.307.807.40  4.704.805.004.606.005.405.805.006.105.404.604.604.604.604.604.605.005.505.305.104.804.704.704.805.004.606.005.405.40  0.040.050.040.050.030.050.040.050.050.040.040.050.040.030.070.070.050.070.070.070.060.070.040.050.040.050.030.050.04  0.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00  65.2063.6763.0465.6466.1965.6367.7965.6866.7066.1865.8966.2164.7365.0965.1164.1265.6863.3262.5160.8761.9262.9265.2063.6763.0465.6466.1965.6366.18     10931093109310501080109311211121112110801100110011001100110011001093101010101037112111211121112111211080112111211093     124124124140130124103103103194100100100100100100124248.2248.2172103103103103103194103103124     401.5379.7290753.4592.1437.3528.6424.8507.5116.1930.210781001.8875.21050962.5500.3272.3314.4423.4219.6196.6465.3476.9255.4108.2560.1420.2483.8
       L3L4VL1010Ri12Ri10A10G10I10Ia12A12B12C10Ri10Ga10I12C10Ri12Ri10Ga10I12C10Ri12Ri10G12Ri10G10G10Ri10Ri   10.008.009.507.008.008.506.504.803.504.603.003.507.004.004.803.507.008.004.004.803.507.008.006.508.006.506.507.007.00   6.806.106.502.653.402.902.502.602.703.003.502.702.652.402.602.702.653.402.402.602.702.653.402.503.402.502.502.652.65   6.606.206.506.406.107.405.506.605.205.305.105.406.406.206.605.406.406.106.206.605.406.406.105.506.105.505.506.406.40   0.700.500.600.600.480.680.530.520.470.390.380.450.600.410.520.450.600.480.410.520.450.600.480.530.480.530.530.600.60   5.805.505.605.675.546.005.605.655.805.615.525.625.675.795.655.625.675.545.795.655.625.675.545.605.545.605.605.675.67  0.900.500.600.800.990.690.680.670.600.960.840.750.800.550.670.750.800.990.550.670.750.800.990.680.990.680.680.800.80  0.000.000.000.400.010.290.200.140.100.010.010.010.400.140.140.010.400.010.140.140.010.400.010.200.010.200.200.400.40  7.807.208.207.607.607.508.207.408.009.408.808.807.608.307.408.807.607.608.307.408.807.607.608.207.608.208.207.607.60  3.202.703.005.505.305.104.605.405.805.006.106.005.506.005.406.005.505.306.005.406.005.505.304.605.304.604.605.505.50  0.250.150.200.070.070.070.050.040.040.050.050.040.070.030.040.040.070.070.030.040.040.070.070.050.070.050.050.070.07  0.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00  57.9563.1559.3063.3262.5160.8765.6466.1867.7965.6866.7066.7363.3266.1966.1866.7363.3262.5166.1966.1866.7363.3262.5165.6462.5165.6465.6463.3263.32  95095095010101080109310931121114911491149112110801149114911491080112111491149114910801121112111491149114911211149     25025025019019412412410382.782.782.710319482.782.782.713010382.782.782.713010310382.782.78610382.7     89584794761491.5245.2464.4487.7616.4483444.9546.499.7491501.3545.1278.8243.4491501.3545.1278.8243.4410.8488419.8387.3318400.3
    48495090494990   7.607.507.507.507.507.507.50   9.809.709.709.709.709.709.70   6.006.006.106.006.006.006.00   1.501.501.501.501.501.501.50   4.204.204.204.204.204.204.20   3.503.503.503.503.503.503.50   0.500.500.500.500.500.500.50   4.704.704.804.804.704.704.80   0.000.000.000.000.000.000.00   0.150.150.200.150.150.150.15   0.000.000.000.000.000.000.00   62.0562.2562.0062.1562.2562.2562.15     871871982982927982982     400400193207310207165.4     146304234118.892.2108.7296.1
    5888451     L1423424433VL11VL17(CMSX-4)L1L3L4VL15VL16VL17(CMSX-4)L1L3L4VL15VL16VL17(CMSX-4)L1VL10VL11   9.5010.0010.0012.009.509.709.5010.008.0010.007.809.709.5010.008.0010.007.809.709.509.509.50   6.500.000.000.006.506.406.506.806.107.005.806.406.506.806.107.005.806.406.506.506.50   6.008.005.005.006.506.406.006.606.206.606.006.406.006.606.206.606.006.406.006.506.50   0.601.001.001.000.600.600.600.700.500.700.500.600.600.700.500.700.500.600.600.600.60   5.605.505.505.805.705.655.605.805.506.005.305.655.605.805.506.005.305.655.605.605.70   0.600.001.100.000.601.000.600.900.501.000.401.000.600.900.501.000.401.000.600.600.60   0.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00   8.206.006.006.006.706.508.207.807.207.807.006.508.207.807.207.807.006.507.508.206.70   3.000.003.003.003.002.903.003.202.703.202.502.903.003.202.703.202.502.903.003.003.00   0.201.501.501.500.200.100.200.250.150.250.150.100.200.250.150.250.150.100.200.200.20   0.102.201.101.600.000.000.100.000.000.000.000.000.100.000.000.000.000.000.000.000.00   59.7065.8065.8064.1060.7060.7559.7057.9563.1557.4564.5560.7559.7057.9563.1557.4564.5560.7560.5059.3060.70     950899899899950950950950950950950950950950950950950950950950950     250414414414250250200200200200200200165165165165165165140140140     8801122421779181018185020352138215019902438505052804830443036904760150001170012614
    4169742     341   3.50   0.00   3.00   0.00   5.80   0.00   0.00   8.00   3.00   1.10   2.50   73.10     899     414     170
         385386391392394397398474865434392424425     3.503.507.0010.0010.008.508.509.4712.199.9514.0010.0010.0010.00   0.000.000.000.000.000.000.0012.7512.5413.870.000.000.000.00   4.005.005.005.003.005.004.508.716.608.695.005.005.005.00   1.001.001.001.000.001.001.000.000.000.001.001.001.001.00   5.505.505.505.505.805.505.503.703.283.465.805.505.505.50   0.000.000.000.000.000.000.003.895.003.640.000.001.102.10   0.000.000.000.000.000.000.000.000.000.000.000.000.000.00   6.006.006.006.008.006.006.002.452.482.446.006.006.006.00   3.003.003.003.003.003.003.000.000.000.003.003.003.003.00   1.501.501.501.501.201.501.500.000.000.001.501.501.501.50   2.202.202.202.202.502.202.200.000.000.001.602.201.100.00   73.3072.3068.8065.8066.5067.3067.8059.0557.9257.9562.1065.8065.8065.90     899899899899899899899100010001000899982982982     41441441441441441441482.782.782.7414241241241     92178368234134162201398.7244.1283.319413012487
4209438     Alloy454(a)SM200(b,c,d)Alloy454(a)     5.0010.005.00   10.009.0010.00   4.0012.504.00   0.000.000.00   5.005.005.00   1.502.001.50   0.001.000.00   12.000.0012.00   0.000.000.00   0.000.000.00   0.000.000.00   62.5060.5062.50     760760765     655655758     1200728.4475
4207098     A123467A1246     8.508.408.408.608.5015.0015.008.508.408.408.5015.00   15.8016.0016.3016.5016.5020.0020.5015.8016.0016.3016.5020.00   2.552.592.732.632.722.202.312.552.592.732.722.20   1.741.731.731.761.760.500.531.741.731.731.760.50   3.363.343.453.433.432.502.643.363.343.453.432.50   3.573.563.533.633.633.603.703.573.563.533.633.60   0.850.850.860.840.851.000.980.850.850.860.851.00   1.751.751.731.771.731.501.631.751.751.731.731.50   0.000.000.000.000.000.000.000.000.000.000.000.00   0.000.000.000.000.000.000.000.000.000.000.000.00   0.000.000.000.000.000.000.000.000.000.000.000.00   61.8861.7861.2760.8460.8853.7052.7161.8861.7861.2760.8853.70     760760760760760760760816816816816816     550550550550550550620330330330330330     2502673213634546584981001100710671173910
       CA1234C77777777CCCCCCC  9.008.508.408.408.608.509.0015.0015.0015.0015.0015.0015.0015.0015.009.009.009.009.009.009.009.00  12.6015.8016.0016.3016.5016.5012.6020.5020.5020.5020.5020.5020.5020.5020.5012.6012.6012.6012.6012.6012.6012.60  3.912.552.592.732.632.723.912.312.312.312.312.312.312.312.313.913.913.913.913.913.913.91  1.981.741.731.731.761.761.980.530.530.530.530.530.530.530.531.981.981.981.981.981.981.98  3.623.363.343.453.433.433.622.642.642.642.642.642.642.642.643.623.623.623.623.623.623.62  4.303.573.563.533.633.634.303.703.703.703.703.703.703.703.704.304.304.304.304.304.304.30  0.000.850.850.860.840.850.000.980.980.980.980.980.980.980.980.000.000.000.000.000.000.00  3.951.751.751.731.771.733.951.631.631.631.631.631.631.631.633.953.953.953.953.953.953.95  0.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00  0.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00  0.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00  60.6461.8861.7861.2760.8460.8860.6452.7152.7152.7152.7152.7152.7152.7152.7160.6460.6460.6460.6460.6460.6460.64   760927927927927927760816816816927927927927980816816816816927927927     620228228228228228500545414400269228200154152414400345300269200154   4996271625880166813368187397199516133618554391720851439133692985
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    4781722     ABCCBC   5.005.000.000.005.000.00   8.008.009.009.008.009.00   6.006.006.006.006.006.00   1.501.502.002.001.502.00   6.506.507.007.006.507.00   0.001.000.000.001.000.00   0.000.000.000.000.000.00   3.003.001.001.003.001.00   3.003.003.003.003.003.00  0.000.000.000.000.000.00   0.000.000.000.000.000.00   67.0066.0072.0072.0066.0072.00     850850850760850850     379379379655500500     508.71202.4771.8403124.4109.4
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         821822SeriesIII824825826827828829830831832833834     7.507.5010.0010.0010.0010.0010.0010.0010.0010.0010.0010.0010.00   7.006.005.005.005.007.007.007.007.007.007.007.006.00   5.005.006.505.504.005.006.007.005.006.007.004.005.50   1.501.501.501.501.501.501.501.501.501.501.502.501.50   6.206.206.506.506.506.206.206.205.805.805.805.807.00  0.000.000.000.000.000.000.000.001.501.501.501.500.00   0.000.000.000.000.000.000.000.000.000.000.000.000.00   6.506.507.007.007.006.506.506.505.005.005.005.004.00   3.003.002.003.004.003.002.502.003.002.001.002.003.00   0.150.150.150.150.150.150.150.150.150.150.150.150.15   0.000.000.000.000.000.000.000.000.000.000.000.000.00   63.1564.1561.3561.3561.8560.6560.1559.6561.0561.0561.0562.0562.85     1149114911491149114911491149114911491149114911491149     90909090909090909090909090   74.396.967.782.3122.17011988147.8137.6107.3132.769.1
    5925189     DMS-1DMS-2DMS-3DMS-4DMS-5DMS-6CMSX-4DMS-1DMS-4DMS-5DMS-6CMSX-2CMSX-4ReneN5DMS-1DMS-2     8.004.804.504.006.403.109.008.004.006.403.105.009.008.008.004.80   4.403.803.002.401.801.406.504.402.401.801.408.006.507.004.403.80   7.506.806.005.505.205.006.007.505.505.205.008.006.005.007.506.80   0.000.000.000.000.000.000.600.000.000.000.000.600.602.000.000.00   5.495.785.365.185.474.755.605.495.185.474.755.605.606.205.495.78  0.000.000.000.000.000.001.000.000.000.000.001.001.000.000.000.00   0.100.500.300.300.300.200.000.100.300.300.200.000.000.000.100.50   8.607.508.609.009.5010.006.508.609.009.5010.006.006.507.008.607.50   4.805.806.006.507.207.503.004.806.507.207.500.003.003.004.805.80   0.100.100.100.100.200.100.100.100.100.200.100.000.100.200.100.10   0.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00   61.0164.9266.1467.0263.9367.9561.7061.0167.0263.9367.9565.8061.7061.6061.0164.92     85085085085085085085095095095095095095095010501050     500500500500500500500240240240240240240240140140   256826963054324327212537917346839173764342738095383714691592
       DMS-3DMS-4DMS-6CMSX-2CMSX-4ReneN5DMS-1DMS-2DMS-3DMS-4DMS-5DMS-6ReneN5DMS-1DMS-2DMS-3DMS-4DMS-5DMS-6DMS-1DMS-2DMS-3DMS-4DMS-5   4.504.003.105.009.008.008.004.804.504.006.403.108.008.004.804.504.006.403.108.004.804.504.006.40   3.002.401.408.006.507.004.403.803.002.401.801.407.004.403.803.002.401.801.404.403.803.002.401.80  6.005.505.008.006.005.007.506.806.005.505.205.005.007.506.806.005.505.205.007.506.806.005.505.20  0.000.000.000.600.602.000.000.000.000.000.000.002.000.000.000.000.000.000.000.000.000.000.000.00  5.365.184.755.605.606.205.495.785.365.185.474.756.205.495.785.365.185.474.755.495.785.365.185.47  0.000.000.001.001.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00  0.300.300.200.000.000.000.100.500.300.300.300.200.000.100.500.300.300.300.200.100.500.300.300.30  8.609.0010.006.006.507.008.607.508.609.009.5010.007.008.607.508.609.009.5010.008.607.508.609.009.50  6.006.507.500.003.003.004.805.806.006.507.207.503.004.805.806.006.507.207.504.805.806.006.507.20  0.100.100.100.000.100.200.100.100.100.100.200.100.200.100.100.100.100.200.100.100.100.100.100.20  0.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00  66.1467.0267.9565.8061.7061.6061.0164.9266.1467.0263.9367.9561.6061.0164.9266.1467.0263.9367.9561.0164.9266.1467.0263.93     105010501050105010501050110011001100110011001100110011501150115011501150115012001200120012001200     1401401401401401401201201201201201201209090909090907070707070     175218031423270468416498572584592583487319485593623650590473182213261281232
    6051083   3849505152   1.001.011.010.991.00   7.547.277.407.156.74  7.217.007.118.996.57  0.830.830.830.832.51  4.965.185.075.075.14  0.000.000.000.000.00  1.710.000.850.850.86  8.7711.8310.318.708.79  1.441.431.441.431.45  0.280.280.280.280.28  0.000.000.000.000.00  66.2665.1765.7065.7166.66     10401040104010401040     137137137137137     333.5328.3388.9665.1507.3
       53545556575859606162100101102103104105106107108109110114115116117118119120121   1.010.971.011.021.021.011.011.011.001.000.002.314.518.6312.400.890.990.991.011.051.200.980.981.010.990.551.011.021.00  7.457.547.277.217.297.367.357.507.107.187.547.367.206.896.605.754.234.277.337.677.227.796.509.7911.737.587.197.236.15  7.087.218.078.537.806.566.795.618.808.767.217.056.896.596.328.898.807.569.007.326.939.358.626.635.599.018.417.906.09  0.830.830.830.830.840.840.830.840.830.830.830.820.800.760.730.820.810.810.410.840.830.880.770.840.000.840.840.864.21  4.954.965.075.075.205.285.155.275.085.074.964.854.744.534.355.105.125.205.124.855.034.755.405.175.204.785.345.625.21  0.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.380.000.000.000.001.170.000.000.00  1.611.710.850.850.860.860.850.860.800.851.711.681.641.571.500.840.830.830.852.590.430.810.890.871.770.860.870.880.87  8.708.779.509.108.798.789.509.598.908.908.778.578.388.027.688.618.528.528.727.228.728.189.238.887.426.437.255.747.25  2.861.441.431.431.452.892.872.891.421.431.441.411.381.321.262.834.275.611.441.451.441.571.291.461.491.451.461.481.46  0.290.280.260.270.250.260.250.260.250.250.210.260.250.240.240.220.240.220.250.280.210.210.210.290.250.250.260.260.21  0.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00  65.2266.2965.7165.6966.5066.1665.4066.1765.8265.7367.3365.6964.2161.4558.9266.0566.1965.9965.8766.7367.6165.4866.1165.0665.5667.0867.3769.0167.55     10401040104010401040104010401040104010401040104010401040104010401040104010401040104010401040104010401040104010401040     137137137137137137137137137137137137137137137137137137137137137137137137137137137137137     244.8232.2509.9525.5430436.5433.4415.4555.5611.1323.3298.7275.3240.4211.1508.9460.6454.3588.8220.3610.1580.9550.3220.3205.5220.5351.2311.1477.5
       384950515253545556575859606162100101102103104105108109110114115116117119     1.001.011.010.991.001.010.971.011.021.021.011.011.011.001.000.002.314.518.6312.400.891.011.051.200.980.981.010.991.01   7.547.277.407.156.747.457.547.277.217.297.367.357.507.107.187.547.367.206.896.605.757.337.677.227.796.509.7911.737.19   7.217.007.118.996.577.087.218.078.537.806.566.795.618.808.767.217.056.896.596.328.899.007.326.939.358.626.635.598.41  0.830.830.830.832.510.830.830.830.830.840.840.830.840.830.830.830.820.800.760.730.820.410.840.830.880.770.840.000.84  4.965.185.075.075.144.954.965.075.075.205.285.155.275.085.074.964.854.744.534.355.105.124.855.034.755.405.175.205.34  0.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.380.000.000.000.000.00  1.710.000.850.850.861.611.710.850.850.860.860.850.860.800.851.711.681.641.571.500.840.852.590.430.810.890.871.770.87   8.7711.8310.318.708.798.708.779.509.108.798.789.509.598.908.908.778.578.388.027.688.618.727.228.728.189.238.887.427.25   1.441.431.441.431.452.861.441.431.431.452.892.872.891.421.431.441.411.381.321.262.831.441.451.441.571.291.461.491.46   0.280.280.280.280.280.290.280.260.270.250.260.250.260.250.250.210.260.250.240.240.220.250.280.210.210.210.290.250.26   0.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00   66.2665.1765.7065.7166.6665.2266.2965.7165.6966.5066.1665.4066.1765.8265.7367.3365.6964.2161.4558.9266.0565.8766.7367.6165.4866.1165.0665.5667.37     927927927927927927927927927927927927927927927927927927927927927927927927927927927927927     324324324324324324324324324324324324324324324324324324324324324324324324324324324324324     85.160.17874.557.380.446.148.65045.773.238.448.666.770.778.879.775.97755.460.57835.564.564.465.338.335.537.7
         120121V2V3V4V64253V2V3V4V5V64253V2V3V4   1.021.004.104.104.204.403.104.104.104.204.304.403.104.104.104.20   7.236.154.304.404.504.705.504.304.404.504.604.705.504.304.404.50     7.906.093.202.501.800.203.203.202.501.801.000.203.203.202.501.80   0.864.212.201.801.200.200.002.201.801.200.700.200.002.201.801.20   5.625.215.706.005.906.106.105.706.005.906.006.106.105.706.005.90  0.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00  0.880.870.000.000.000.002.400.000.000.000.000.002.400.000.000.00  5.747.256.805.604.401.900.006.805.604.403.201.900.006.805.604.40   1.481.467.107.207.307.605.907.107.207.307.507.605.907.107.207.30   0.260.210.000.000.000.000.000.000.000.000.000.000.000.000.000.00   0.000.001.702.603.505.402.701.702.603.504.405.402.701.702.603.50   69.0167.5564.9065.8067.2069.5071.1064.9065.8067.2068.3069.5071.1064.9065.8067.20     927927900900900900900100010001000100010001100110011001100     324324483483483483483276276276276276155162162138     33.373.385.9882.47112.7732.86142189.31132.6699.8110.91110.9546.8434.8311.67201.36
  RE29920     A-1B-1C-1C-2C-3E-1A-2B-2D-1C-4C-5C-6C-7   10.1510.0010.1010.3010.1015.1012.1511.7610.9110.6610.7010.6410.66   7.8710.208.759.308.7510.109.7510.569.669.338.338.898.61     0.000.0012.0012.8112.000.000.000.009.6612.4112.4012.7412.84   6.063.050.000.000.003.015.893.102.430.000.000.000.00   5.956.304.994.804.995.335.956.035.195.655.535.635.80  1.081.121.982.081.984.800.960.991.381.761.781.771.78  0.000.001.231.201.230.000.000.000.000.950.950.920.92  4.406.750.000.000.000.003.715.701.500.000.000.000.00   0.000.000.000.000.000.000.000.000.000.000.000.000.00   0.000.000.000.000.000.000.000.000.000.000.000.000.00   0.000.000.000.000.000.860.000.000.000.000.000.000.00   64.4962.5860.9559.5160.9560.8061.5961.8659.2759.2460.3159.4159.39     760760760760760760760760760760760760760     648648648648648648648648648648648648648     229.6297.2400.6442.6245.5345146.5206432.8314.8392.2448452.9
        C-8C-9C-10C-11C-12E-5E-6E-7E-8E-9A-2B-2F-1C-4C-5C-6C-7C-8C-9C-10C-11C-12E-3E-4E-5E-6E-7E-8   10.7110.7810.6010.5010.6916.6216.6216.8616.8016.6912.1511.769.4310.6610.7010.6410.6610.7110.7810.6010.5010.6916.6716.6216.6216.6216.8616.80  8.648.978.969.509.549.679.879.8710.2210.059.7510.5611.359.338.338.898.618.648.978.969.509.549.108.959.679.879.8710.22  12.4812.5512.4112.5011.840.000.000.000.000.000.000.004.1812.4112.4012.7412.8412.4812.5512.4112.5011.840.000.000.000.000.000.00  0.000.000.000.000.003.063.033.253.333.325.893.102.040.000.000.000.000.000.000.000.000.002.943.173.063.033.253.33 5.415.135.154.984.765.615.635.225.235.235.956.033.925.655.535.635.805.415.135.154.984.765.715.605.615.635.225.23  1.751.771.762.001.754.744.914.644.644.560.960.993.691.761.781.771.781.751.771.762.001.754.904.884.744.914.644.64  0.920.910.851.090.880.000.000.000.000.000.000.000.000.950.950.920.920.920.910.851.090.880.000.000.000.000.000.00  0.000.000.000.000.000.000.000.000.000.003.715.704.230.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00 0.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00  0.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00  0.000.000.000.000.001.081.061.001.011.010.000.000.000.000.000.000.000.000.000.000.000.001.071.071.081.061.001.01  60.0959.8960.2759.4360.5459.2258.8859.1658.7759.1461.5961.8661.1659.2460.3159.4159.3960.0959.8960.2759.4360.5459.6159.7159.2258.8859.1658.77     760760760760760760760760760760982982982982982982982982982982982982982982982982982982     648648648648648648648648648648200200200200200200200200200200200200200200200200200200   468.6459.8458.6397.2347.4117.2174.1266.3302.2357.644.852.479.273.685.2113.9122.4128.3117.164.892.34348.641.338.141.236.531.9
 4824637    NASAIR100   0.00  8.57  10.62  1.01 5.51  1.13  0.00  3.35 0.00  0.00  0.00  69.80     1040     137   377.4
       TUT-23TUT-24TUT-6TUT-7D.E.F.     0.000.000.000.005.05.05.0  8.348.448.448.3816.215.715.7  14.8113.644.484.714.15.95.9   0.000.000.000.003.01.51.5  5.195.255.265.223.53.63.5  0.000.000.000.003.63.63.6  0.000.000.000.000.00.00.0  4.354.0513.2213.940.00.00.0  0.000.000.000.000.00.00.0  0.000.000.000.000.00.00.0  0.000.000.000.000.00.00.0  67.3068.6268.6167.7564.5764.7464.78     1040104010401040982982982   137137137137152152152     168191723017877.376.562.8

Claims (2)

1.镍基高温合金成分的优化设计方法,其特征在于:①收集镍基变形高温合金的成分、持久试验温度、持久断裂时间及其对应的持久强度数据或镍基单晶高温合金的成分、持久试验温度、持久应力及其对应的持久寿命数据,然后将上述数据作为人工神经网络初始训练数据进行网络训练,并通过常规优化隐含层神经单元数、归一化条件及动量因子等神经网络参量,获得镍基变形高温合金的持久强度或镍基单晶高温合金的持久寿命预测值与实测值误差最小的网络训练最佳权值矩阵;②将所获得的最佳权值矩阵与成本的比值作为镍基变形高温合金或镍基单晶高温合金成分优化设计所使用的目标函数,在此基础上建立镍基变形高温合金或镍基单晶高温合金成分优化设计的约束条件,以抑制有害相σ和μ相的形成和控制合金的密度;
镍基变形高温合金成分优化设计的数学模型为:
Figure C2005100192390002C1
式(1)、式(2)为镍基变形高温合金成分优化设计所使用的目标函数;式(3)至式(6)为镍基变形高温合金成分优化设计的约束条件;
式中,σc为合金持久强度的目标函数,w1、w2、b1、b2为通过神经网络训练得到的最佳权值矩阵,purelin为线性激活函数,tansig为带有偏差的双曲正切S型激活函数,其输入变量的转置矩阵s=[X1,X2,...,Xn,t,T]′,X1,X2,…,Xn依次为合金元素C、Cr、Co、Mo、Ti、Al、Fe、B、Zr、Ni、Nb、W、Ta、Mn、Si、V、Cb、Y的原子百分数,t为持久断裂时间,T为持久试验温度;p为合金成本;pi为合金元素的单价;ci为元素i的重量百分数,i=1,2,……n,n=18,  依次对应C、Cr、Co、Mo、Ti、Al、Fe、B、Zr、Ni、Nb、W、Ta、Mn、Si、V、Cb、Y共18种合金元素;(σc/p)max为性能与价格比的目标函数;
Figure C2005100192390003C1
为控制有害σ相的合金平均电子能级,
Figure C2005100192390003C2
为基体γ相的平均电子能级,Xi和X分别表示合金和γ相中元素i的原子百分数,i=1,2,……n,n=18;(Md)i为元素i的d电子能级,可通过查表获得;XMo和XW分别为合金中Mo和W的原子百分数;合金密度 &rho; = W alloy - cell V alloy - cell = N alloy - cell at &CenterDot; &Sigma; i = 1 n ( X it &CenterDot; M i ) / N A &alpha; 3 , Walloy,Valloy分别为合金中一个晶胞内所含各元素的原子总质量和一个晶胞的体积;Xit、a分别为合金中元素i的原子百分数和合金的点阵常数;Nalloy-cell at表示一个晶胞的原子数;Mi为元素i的摩尔质量;NA为Avogadro常数;镍基单晶高温合金成分优化设计的数学模型为:
Figure C2005100192390003C4
式(7)、式(8)为镍基单晶高温合金成分优化设计所使用的目标函数;式(9)至式(14)为镍基单晶高温合金成分优化设计的约束条件;式中,f为合金的持久寿命,W1、W2、B1、B2为通过神经网络训练得到的最佳权值矩阵,S是一个输入变量的转置矩阵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种元素的重量百分数,Cil和Cik分别表示在设计合金时所给成分范围内元素i的下限和上限值,T为持久试验温度,σ为持久应力;P为合金成本;Pi为合金元素的单价;Ci为元素i的重量百分数;i=1,2,……n,n=11,依次对应Co、Cr、W、Mo、Al、Ti、Nb、Ta、Re、Hf、V共11种合金元素;(f/P)max为性能与价格比的目标函数;控制有害σ相的约束条件参量中:Mdt为的合金平均电子能级,Mdi为i元素的电子能级,通过查表获得;控制有害μ相的约束条件参量中,A2、A3和A4分别表示合金中Cr、W和Mo的原子百分数;ΔE为提高单晶合金稳定性的参量,Zi为元素价电子数,M为合金元素的摩尔质量,Ai为合金元素的原子百分数;合金密度ρ的算法同于前述镍基变形高温合金;
按上述优化步骤和约束条件,设置所要设计的镍基变形或镍基单晶高温合金中各元素含量Ci的范围,通过优化计算,即可在给定成分范围和上述约束条件下搜索出能使目标函数值达到最大值的合金的成分配方。
2.根据权利要求1所述的方法,其特征在于:上述镍基变形高温合金的成分、持久试验温度、持久断裂时间及其对应的持久强度数据选自数据库A中的数据;镍基单晶高温合金的成分、持久试验温度、持久应力及其对应的持久寿命数据选自数据库B中的数据。
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