CN101763450B - Titanium alloy component quantifying design method - Google Patents

Titanium alloy component quantifying design method Download PDF

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CN101763450B
CN101763450B CN 200910248943 CN200910248943A CN101763450B CN 101763450 B CN101763450 B CN 101763450B CN 200910248943 CN200910248943 CN 200910248943 CN 200910248943 A CN200910248943 A CN 200910248943A CN 101763450 B CN101763450 B CN 101763450B
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CN101763450A (en
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林成
赵永庆
刘志林
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Liaoning University of Technology
Northwest Institute for Non Ferrous Metal Research
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Liaoning University of Technology
Northwest Institute for Non Ferrous Metal Research
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Abstract

The invention relates to a titanium alloy component quantifying design method, which comprises the following steps: proceeding from the practical phase change process of the titanium alloy and establishing a mathematical model of a strengthening weight and a strengthening factor of the titanium alloy under different heat treatment conditions on the electronic structure level, then taking a tensile strength and a tensile stretch value of alpha-Ti and beta-Ti as basic values, and utilizing the strengthening weight and the strengthening factor to calculate a strength increment and a reduction of the tensile stretch under different heat treatment conditions so as to calculate values of the tensile strength and the tensile stretch of the titanium alloy under different heat treatment conditions; and programming a calculation formula into a calculation software, observing the variation quantities of the tensile stretch and the tensile stretch of alloying elements under different heat treatment conditions on the computer, and repeatedly adjusting the chemical components of the alloy to make relative errors of theoretical calculated values and technical requirement values of the tensile strength and the tensile stretch of the designed alloy in the range of 10 percent so as to determine the components of the titanium alloy. The invention has rapid and economy design process and high accuracy of the design result, and provides the reference value for the component design of other alloy systems.

Description

Titanium alloy component quantifying design method
Technical field
The present invention relates to titanium alloy component quantifying design method, specifically, relate to from chemical constitution, utilize alloy the electronic structure parameter, combine the titanium alloy phase transformation that titanium alloy component is optimized method for designing.
Background technology
Titanium alloy is used widely in industries such as Aero-Space, chemical industry, naval vessels because of having excellent properties such as intensity height, corrosion-resistant, nonmagnetic, weldability.Nowadays, the trade mark of titanium alloy has surpassed kind more than 70 in the world, but these alloying components almost are experience or " cooking method " design entirely.At present, the alloy design method that is applied to the titanium alloy field mainly contains d-electron theory design method and based on alloy design method such as fuzzy logic, nerual network technique and expert databases.For polynary titanium alloy system, often relate to the interaction of complicated multiple alloying component and show complicated polyphase microstructure structure, make d-electron theory design method be difficult to quantitatively to confirm the relation between the performance-microstructure-composition of alloy.And fuzzy logic, nerual network technique and expert database simulation precision are high, but physical significance is indeterminate, is difficult to be deep into microscopic nature.The possessor once utilized the alloy valence electron structure to calculate the yield strength of TiAl-Nb alloy to the greatest extent; But because of not taking into full account the actual transformation process of titanium alloy; Theoretical Calculation and actual conditions deviation are bigger; Can't carry out the quantitative design that TiAl-Nb is an alloying component, let alone carry out the component quantifying design of polynary titanium alloy system.
Summary of the invention
The object of the present invention is to provide a kind of titanium alloy component quantifying design method, this method operates and calculates easy, and the design result accuracy is high.
Technical scheme provided by the invention is:
A kind of titanium alloy component quantifying design method, its special character is:
Calculate phase structure unit and phase interface electronic structure parameter n in the titanium alloy 1.1 utilize " solid and molecule experience electron theory " A', σ N, Δ ρ ', Δ ρ Max, σ, and set up database like table 1～table 8;
Table 1 β is the electronic structure parameter (900 ℃) of middle phase structure unit mutually
The phase structure unit n A′ The phase structure unit n A′
β-Ti 0.28626
β-Ti-Al 0.2640 β-Ti-Al* 0.25094
β-Ti-Zr 0.3098 β-Ti-Zr-Al 0.28808
β-Ti-Sn 0.31022 β-Ti-Sn-Al 0.28877
β-Ti-Mo 0.32364 β-Ti-Mo-Al 0.30370
β-Ti-V 0.30213 β-Ti-V-Al 0.30351
β-Ti-Nb 0.32011 β-Ti-Nb-Al 0.29655
β-Ti-Fe 0.29870 β-Ti-Fe-Al 0.26655
β-Ti-Cr 0.29088 β-Ti-Cr-Al 0.26905
β-Ti-Mn 0.32738 β-Ti-Mn-Al 0.28578
β-Ti-Hf 0.30708 β-Ti-Hf-Al 0.28437
β-Ti-Co 0.32458 β-Ti-Co-Al 0.29295
β-Ti-Si 0.29232 β-Ti-Si-Al 0.26637
β-Ti-Cu 0.31789 β-Ti-Cu-Al 0.29298
β-Ti-Ni 0.34389 β-Ti-Ni-Al 0.31127
β-Ti-W 0.29826 β-Ti-W-Al 0.27736
Annotate: " * " represents Al element wt percentage more than or equal to 6%; Down together.
Table 2 β is the electronic structure parameter (25 ℃) of middle structural unit mutually
The phase structure unit n A′ σ N The phase structure unit n A′ σ N
β-Ti 0.29889 2
β-Ti-Al 0.27321 13 β-Ti-Al* 0.24761 22
β-Ti-Zr 0.31605 44 β-Ti-Zr-Al 0.29209 361
β-Ti-Sn 0.32279 15 β-Ti-Sn-Al 0.29731 128
β-Ti-Mo 0.33544 41 β-Ti-Mo-Al 0.27904 309
β-Ti-V 0.30768 55 β-Ti-V-Al 0.31071 487
β-Ti-Nb 0.33326 44 β-Ti-Nb-Al 0.30050 587
β-Ti-Fe 0.3026 69 β-Ti-Fe-Al 0.27305 457
β-Ti-Cr 0.29556 50 β-Ti-Cr-Al 0.27236 551
β-Ti-Mn 0.33147 78 β-Ti-Mn-Al 0.29378 477
β-Ti-Hf 0.31238 41 β-Ti-Hf-Al 0.28914 380
β-Ti-Co 0.32893 71 β-Ti-Co-Al 0.30317 544
β-Ti-Si 0.28859 17 β-Ti-Si-Al 0.30084 690
β-Ti-Cu 0.32317 54 β-Ti-Cu-Al 0.27341 159
β-Ti-Ni 0.34503 56 β-Ti-Ni-Al 0.32378 698
β-Ti-W 0.30752 28 β-Ti-W-Al 0.28209 339
The electronic structure parameter (25 ℃) of table 3 β-Ti-M/ β-Ti phase interface
Phase interface Δρ′ σ Phase interface Δρ′ σ
β-Ti-Al/β-Ti 9.56 26 β-Ti-Al/β-Ti* 19.7 44
β-Ti-Zr/β-Ti 5.56 88 β-Ti-Zr-Al/β-Ti 6.08 722
β-Ti-Sn/β-Ti 7.79 30 β-Ti-Sn-Al/β-Ti 6.98 256
β-Ti-Mo/β-Ti 6.06 68 β-Ti-Mo-Al/β-Ti 9.57 618
β-Ti-V/β-Ti 3.49 110 β-Ti-V-Al/β-Ti 6.90 984
β-Ti-Nb/β-Ti 8.54 92 β-Ti-Nb-Al/β-Ti 6.45 1174
β-Ti-Fe/β-Ti 4.81 138 β-Ti-Fe-Al/β-Ti 9.74 914
β-Ti-Cr/β-Ti 2.61 100 β-Ti-Cr-Al/β-Ti 9.67 1102
β-Ti-Mn/β-Ti 10.2 156 β-Ti-Mn-Al/β-Ti 5.79 954
β-Ti-Hf/β-Ti 4.47 82 β-Ti-Hf-Al/β-Ti 6.39 760
β-Ti-Co/β-Ti 9.45 142 β-Ti-Co-Al/β-Ti 5.59 1088
β-Ti-Si/β-Ti 5.17 34 β-Ti-Si-Al/β-Ti 10.1 318
β-Ti-Cu/β-Ti 7.67 108 β-Ti-Cu-Al/β-Ti 6.11 1380
β-Ti-Ni/β-Ti 14.3 112 β-Ti-Ni-Al/β-Ti 8.70 1396
β-Ti-W/β-Ti 4.17 56 β-Ti-W-Al/β-Ti 8.41 678
The electronic structure parameter (25 ℃) of table 4 β-Ti-Al (Al-M)/β-Ti-Al (Al-M) phase interface
Phase interface Δρ′ σ Phase interface Δρ′ σ
β-Ti-Al/β-Ti-Al 7.56 91 β-Ti-Al/β-Ti-Al* 15.91 143
β-Ti-Zr/β-Ti-Zr 2.71 990 β-Ti-Zr-Al/β-Ti-Zr-Al 7.61 65341
β-Ti-Sn/β-Ti-Sn 5.34 120 β-Ti-Sn-Al/β-Ti-Sn-Al 9.68 8260
β-Ti-Mo/β-Ti-Mo 4.05 1021 β-Ti-Mo-Al/β-Ti-Mo-Al 10.8 48403
β-Ti-V/β-Ti-V 2.73 1275 β-Ti-V-Al/β-Ti-V-Al 8.25 121278
β-Ti-Nb/β-Ti-Nb 2.90 1081 β-Ti-Nb-Al/β-Ti-Nb-Al/ 8.08 172578
β-Ti-Fe/β-Ti-Fe 6.16 2415 β-Ti-Fe-Al/β-Ti-Fe-Al 8.08 104653
β-Ti-Cr/β-Ti-Cr 3.15 1275 β-Ti-Cr-Al/β-Ti-Cr-Al 8.34 152076
β-Ti-Mn/β-Ti-Mn 6.01 3081 β-Ti-Mn-Al/β-Ti-Mn-Al 7.70 114003
β-Ti-Hf/β-Ti-Hf 2.67 861 β-Ti-Hf-Al/β-Ti-Hf-Al 7.80 72390
β-Ti-Co/β-Ti-Co 5.72 2556 β-Ti-Co-Al/β-Ti-Co-Al 7.69 148240
β-Ti-Si/β-Ti-Si 5.86 153 β-Ti-Si-Al/β-Ti-Si-Al 10.4 12723
β-Ti-Cu/β-Ti-Cu 6.27 1485 β-Ti-Cu-Al/β-Ti-Cu-Al 8.87 238402
β-Ti-Ni/β-Ti-Ni 4.16 1596 β-Ti-Ni-Al/β-Ti-Ni-Al 8.18 243958
β-Ti-W/-Ti-W 4.69 464 β-Ti-W-Al/β-Ti-W-Al 10.1 58284
Table 5 α is the electronic structure parameter (25 ℃) of middle phase structure unit mutually
The phase structure unit n A′ σ N The phase structure unit n A′ σ N
α-Ti 0.24902 2
α-Ti-Al 0.23685 14 α-Ti-Zr-Al 0.25051 292
α-Ti-Zr 0.2631 39 α-Ti-Sn-Al 0.25318 88
α-Ti-Sn 0.26739 11 α-Ti-Mo-Al 0.261 275
α-Ti-Mo 0.27184 33 α-Ti-V-Al 0.26025 298
α-Ti-V 0.27330 43 α-Ti-Nb-Al 0.2601 282
α-Ti-Nb 0.27293 36 α-Ti-Fe-Al 0.24349 330
α-Ti-Fe 0.25488 40 α-Ti-Cr-Al 0.2408 288
α-Ti-Cr 0.25308 32 α-Ti-M?n-Al 0.25719 357
α-Ti-Mn 0.26948 41 α-Ti-Hf-Al 0.24976 276
α-Ti-Hf 0.26095 34 α-Ti-Co-Al 0.25789 321
α-Ti-Co 0.26939 48 α-Ti-Si-Al 0.23554 101
α-Ti-Si 0.25163 15 α-Ti-Cu-Al 0.25261 318
α-Ti-Cu 0.26576 35 α-Ti-Ni-Al 0.26616 322
α-Ti-Ni 0.27959 37 α-Ti-W-Al 0.24623 161
α-Ti-W 0.26019 20 α-Ti-O 0.62095 8
α-Ti-N 0.74635 8 α-Ti-C 0.70486 10
The electronic structure parameter of table 6 α-Ti-Al (Al-M)/α-Ti phase interface (25 ℃)
Phase interface Δρ′ σ Phase interface Δρ′ σ
α-Ti-Al/α-Ti 5.78 28 α-Ti-Zr-Al/α-Ti 3.97 584
α-Ti-Zr/α-Ti 5.46 78 α-Ti-Sn-Al/α-Ti 5.18 176
α-Ti-Sn/α-Ti 7.05 22 α-Ti-Mo-Al/α-Ti 5.59 332
α-Ti-Mo/α-Ti 4.68 46 α-Ti-V-Al/α-Ti 4.04 588
α-Ti-V/α-Ti 4.13 84 α-Ti-Nb-Al/α-Ti 5.34 564
α-Ti-Nb/α-Ti 9.13 72 α-Ti-Fe-Al/α-Ti 4.44 660
α-Ti-Fe/α-Ti 3.44 80 α-Ti-Cr-Al/α-Ti 13.0 576
α-Ti-Cr/α-Ti 5.46 64 α-Ti-Mn-Al/α-Ti 4.49 606
α-Ti-Mn/α-Ti 2.94 86 α-Ti-Hf-Al/α-Ti 3.94 552
α-Ti-Hf/α-Ti 4.65 68 α-Ti-Co-Al/α-Ti 5.16 642
α-Ti-Co/α-Ti 7.80 96 α-Ti-Si-Al/α-Ti 7.03 202
α-Ti-Si/α-Ti 4.25 30 α-Ti-Cu-Al/α-Ti 4.13 636
α-Ti-Cu/α-Ti 6.45 70 α-Ti-Ni-Al/α-Ti 6.84 644
α-Ti-Ni/α-Ti 11.5 74 α-Ti-W-Al/α-Ti 4.83 322
α-Ti-W/α-Ti 5.19 40 α-Ti-O/α-Ti 36.8 16
α-Ti-C/α-Ti 27.8 20 α-Ti-N/α-Ti 29.0 16
The electronic structure parameter (25 ℃) of table 7 α-Ti-Al (Al-M)/α-Ti-Al (Al-M) phase interface
Phase interface Δρ′ ?Δρ max σ Phase interface Δρ′ Δρ max σ
α-Ti-Al/α-Ti-Al 5.46 13.9 105 α-Ti-Zr-Al/α-Ti-Zr-Al 5.34 17.2 42778
α-Ti-Zr/α-Ti-Zr 2.99 7.80 780 α-Ti-Sn-Al/α-Ti-Sn-Al 6.74 23.6 3917
α-Ti-Sn/α-Ti-Sn 3.73 11.1 66 α-Ti-Mo-Al/α-Ti-Mo-Al 6.31 21.6 44850
α-Ti-Mo/α-Ti-Mo 4.23 13.1 703 α-Ti-V-Al/α-Ti-V-Al 5.51 20.9 43365
α-Ti-V/α-Ti-V 3.23 10.4 903 α-Ti-Nb-Al/α-Ti-Nb-Al 5.55 20.9 39903
α-Ti-Nb/α-Ti-Nb 2.81 9.98 666 α-Ti-Fe-Al/α-Ti-Fe-Al 5.70 23.3 54615
α-Ti-Fe/α-Ti-Fe 3.69 12.1 820 α-Ti-Cr-Al/α-Ti-Cr-Al 5.06 17.4 41616
α-Ti-Cr/α-Ti-Cr 2.03 7.69 528 α-Ti-Mn-Al/α-Ti-Mn-Al 5.57 17.4 46056
α-Ti-Mn/α-Ti-Mn 2.54 8.30 946 α-Ti-Hf-Al/α-Ti-Hf-Al 5.27 17.1 38226
α-Ti-Hf/α-Ti-Hf 2.63 8.20 595 α-Ti-Co-Al/α-Ti-Co-Al 6.19 24.4 51681
α-Ti-Co/α-Ti-Co 3.94 15.1 1176 α-Ti-Si-Al/α-Ti-Si-Al 7.03 24.5 5154
α-Ti-Si/α-Ti-Si 4.95 13.1 120 α-Ti-Cu-Al/α-Ti-Cu-Al 5.85 23.2 50724
α-Ti-Cu/α-Ti-Cu 3.83 11.3 630 α-Ti-Ni-Al/α-Ti-Ni-Al 5.40 19.6 52006
α-Ti-Ni/α-Ti-Ni 3.20 10.7 703 α-Ti-W-Al/α-Ti-W-Al 6.42 26.5 13403
α-Ti-W/α-Ti-W 3.76 17.4 250 α-Ti-O/α-Ti-O 4.21 — 36
α-Ti-N/α-Ti-N 2.83 — 36 α-Ti-C/α-Ti-C 2.05 — 55
The electronic structure parameter (25 ℃) of table 8 α-Ti-Al (Al-M)/β-Ti-Al (Al-M) phase interface
Phase interface Δρ′ Δρ max σ Phase interface Δρ′ Δρ max σ
α-Ti/β-Ti 9.21 10.7 4
α-Ti-Al/β-Ti-Al 8.59 22.6 182 α-Ti-Al/β-Ti-Al* 14.1 31.6 308
α-Ti-Zr/β-Ti-Zr 9.3 16.9 1716 α-Ti-Zr-Al/β-Ti-Zr-Al 7.46 23.3 124100
α-Ti-Sn/β-Ti-Sn 10.0 22.9 165 α-Ti-Sn-Al/β-Ti-Sn-Al 9.40 32.3 10472
α-Ti-Mo/β-Ti-Mo 8.58 29.1 782 α-Ti-Mo-Al/β-Ti-Mo-Al 9.67 35.1 44156
α-Ti-V/β-Ti-V 8.15 19.5 2310 α-Ti-V-Al/β-Ti-V-Al 7.58 26.9 139650
α-Ti-Nb/β-Ti-Nb 10.9 22.3 1584 α-Ti-Nb-Al/β-Ti-Nb-Al 8.10 30.0 137052
α-Ti-Fe/β-Ti-Fe 8.57 23.4 2760 α-Ti-Fe-Al/β-Ti-Fe-Al 7.52 27.7 148830
α-Ti-Cr/β-Ti-Cr 6.48 15.1 1600 α-Ti-Cr-Al/β-Ti-Cr-Al 7.53 21.2 179136
α-Ti-Mn/β-Ti-Mn 11.8 26.0 3198 α-Ti-Mn-Al/β-Ti-Mn-Al 8.14 26.1 153510
α-Ti-Hf/β-Ti-Hf 8.94 17.3 1394 α-Ti-Hf-Al/β-Ti-Hf-Al 7.21 23.4 109848
α-Ti-Co/β-Ti-Co 11.0 26.6 3408 α-Ti-Co-Al/β-Ti-Co-Al 7.33 28.0 164673
α-Ti-Si/β-Ti-Si 7.05 19.5 255 α-Ti-Si-Al/β-Ti-Si-Al 9.42 33.6 19998
α-Ti-Cu/β-Ti-Cu 10.5 25.6 1890 α-Ti-Cu-Al/β-Ti-Cu-Al 8.87 31.0 219102
α-Ti-Ni/β-Ti-Ni 11.9 25.7 2072 α-Ti-Ni-Al/β-Ti-Ni-Al 8.57 28.4 201894
α-Ti-W/β-Ti-W 8.31 29.1 560 α-Ti-W-Al/β-Ti-W-Al 9.28 35.1 51198
1.2 calculate the reinforcement weight of each phase structure unit under the titanium alloy Different Heat Treatment Conditions and the interface enhancing coefficient of solution strengthening coefficient and phase interface;
At first utilize the atomic percentage of alloying component when calculating the reinforcement weight of each phase structure unit under the titanium alloy Different Heat Treatment Conditions and characterize make a concerted effort in the phase structure unit of the size statistical value n of the shared electron logarithm on the strong covalent bond of atomic link A' calculating titanium alloy forms the reinforcement weight of each phase structure unit in the single β phase solid solution after the solution treatment+shrend of β phase region;
Utilize the β phase conditional stability COEFFICIENT K in the titanium alloy β,
Figure G2009102489435D00061
Figure G2009102489435D00062
Calculating from β separate out mutually primary mutually in the reinforcement weight of each phase structure unit;
Utilize the β phase conditional stability COEFFICIENT K in the titanium alloy β',
Figure G2009102489435D00063
And
Figure G2009102489435D00064
Calculating from β separate out mutually secondary α mutually in the reinforcement weight of each phase structure unit, the mathematical model of weight calculation is strengthened in each phase structure unit of titanium alloy:
β mutually in the reinforcement weight of each phase structure unit:
Figure G2009102489435D00071
In the following formula x Al = n A ′ β - Ti - AL n A ′ β - Ti - Al + Σ i = 1 z n A ′ β - Ti - Al - M i , y Al = C Al C Al + Σ i = 1 z C M i
x i = n A ′ β - Ti - Al - M i n A ′ β - Ti - Al + Σ i = 1 z n A ′ β - Ti - Al - M i , y i = C M i C Al + Σ i = 1 z C M i
W wherein β-Ti-Al, W β-Ti-Al-M, W β-Ti-MReinforcement weight for β-Ti-Al, β-Ti-Al-M, β-Ti-M phase structure unit; C AlAtomic percentage for Al; C MFor not comprising the alloy atom percentage of Al element; Z is the alloying element species number, and i representes the sequence number of alloying element M;
The reinforcement weight of the phase structure unit that impurity element forms:
Figure G2009102489435D00076
W wherein α-Ti-O, W α-Ti-N, W α-Ti-CThe solution strengthening weight of the α-Ti-O that forms for impurity element O, N, C, α-Ti-N, α-Ti-C phase structure unit; C ' O, C ' N, C ' CThe nominal atomic percentage of representing O, N, C has respectively promptly deducted the content of corresponding impurity in the iodide-process titanium, and corresponding impurity content is got middle limit in the iodide-process titanium;
Primary mutually in the reinforcement weight of each phase structure unit:
Figure G2009102489435D00081
W wherein p α-Ti-Al, W p α-Ti-Al-M, W p α-Ti-MReinforcement weight for α-Ti-Al, α-Ti-Al-M, α-Ti-M phase structure unit in the primary phase solid solution; K ββ phase conditional stability coefficient in the expression titanium alloy, promptly K β = C 1 C K 1 + C 2 C K 2 + C 3 C K 3 + · · · + C n C K n ;
Figure G2009102489435D00083
Be illustrated in β under a certain solid solubility temperature → α and change alloy when beginning
The corresponding K of β β MoValue, K β MoBe β phase conditional stability coefficient in the Ti-Mo bianry alloy, Rising with solid solubility temperature reduces gradually, and value is 0.3～2.3;
Figure G2009102489435D00085
Be illustrated in β under a certain solid solubility temperature → α and change the corresponding K of alloy β when stopping β MoValue, Less with the solid solubility temperature variation, value is 0.07;
Primary is separated out the reinforcement weights W of the middle mutually β-Ti-Al of back β, β-Ti-Al-M, β-Ti-M phase structure unit mutually p β-Ti-Al, W p β-Ti-Al-M, W p β-Ti-MFor
Figure G2009102489435D00087
The weights W of the middle mutually α of primary-Ti phase structure unit p α-TiFor
Figure G2009102489435D00088
Primary is the atomic fraction C of middle Ti mutually α p TiFor
Primary is separated out the back mutually and is not had secondary α when separating out, and β is the atomic fraction C of middle Ti mutually β TiFor
C β Ti = C Ti - C αp Ti . . . ( 7 )
Secondary α mutually in the reinforcement weight of each phase structure unit:
Figure G2009102489435D00093
W wherein s α-Ti-Al, W s α-Ti-Al-M, W s α-Ti-MReinforcement weight for secondary α-Ti-Al, α-Ti-Al-M, α-Ti-M phase structure unit; K β' separate out β phase conditional stability coefficient in the titanium alloy of back mutually for primary, with primary separate out back β mutually in the atomic percentage of alloying element be converted into percent by weight, press K then βComputing formula is calculated and is got final product; Be illustrated in β under a certain aging temp → α and change the corresponding K of alloy β when beginning β MoValue,
Figure G2009102489435D00095
Rising with the timeliness temperature reduces gradually, and value is 0.5～2.8;
Figure G2009102489435D00096
Be illustrated in β under a certain aging temp → α and change the corresponding K of alloy β when stopping β MoValue,
Figure G2009102489435D00097
Less with the timeliness temperature variation, value is 0.07;
Secondary α separates out the reinforcement weights W of the middle mutually β-Ti-Al of back β, β-Ti-Al-M, β-Ti-M phase structure unit mutually s β-Ti-Al, W s β-Ti-Al-M, W s β-Ti-MFor
Figure G2009102489435D00098
The weight of the middle mutually α of secondary α-Ti phase structure unit:
Figure G2009102489435D00101
The middle mutually Ti atomic percentage C of secondary α α s TiFor
Figure G2009102489435D00102
Secondary α separates out the middle mutually Ti atomic percentage of back β mutually:
C β Ti = C Ti - C αp Ti - C αs Ti . . . ( 12 )
When calculating the interface enhancing coefficient of solution strengthening coefficient and phase interface of phase structure unit in the titanium alloy, at first utilize to characterize make a concerted effort in the phase structure unit of the size statistical value n of the shared electron logarithm on the strong covalent bond of interatomic bond A' characterize β phase, primary phase, secondary α mutually in the solution strengthening coefficient of each phase structure unit; Use the interface electron density difference Δ ρ ', the Δ ρ that are complementary with interfacial stress MaxCharacterize β phase, primary phase, secondary α mutually in the interface enhancing coefficient of each phase interface;
The mathematical model of solution strengthening coefficient and interface enhancing coefficient calculations in the titanium alloy:
β mutually in the solution strengthening coefficient of each phase structure unit:
Figure G2009102489435D00104
S wherein β-Ti-Al, S β-Ti-Al-M, S β-Ti-MThe solution strengthening coefficient of representing β-Ti-Al, β-Ti-Al-M, β-Ti-M phase structure unit respectively; n A' β-Ti-Al, n A' β-Ti-Al-M, n A' β-Ti-M, n A' β-TiBe respectively the assembly average of the shared electron logarithm on β-Ti-Al, β-Ti-Al-M, β-Ti-M, the strong bond in β-Ti phase structure unit;
β is the interface enhancing coefficient at middle out-phase interface mutually:
Figure G2009102489435D00111
S wherein β-Ti-Al/ β-Ti, S β-Ti-Al-M/ β-Ti, S β-Ti-M/ β-TiThe interface enhancing coefficient of expression phase interface β-Ti-Al/ β-Ti, β-Ti-Al-M/ β-Ti, β-Ti-M/ β-Ti; Δ ρ ' β-Ti-Al/ β-Ti, Δ ρ ' β-Ti-Al-M/ β-Ti, Δ ρ ' β-Ti-M/ β-TiBe respectively the assembly average of the electron density difference of β-Ti-Al/ β-Ti, β-Ti-Al-M/ β-Ti, β-Ti-M/ β-Ti phase interface;
β mutually in the interface enhancing coefficient of phase interface:
Figure G2009102489435D00112
S wherein β-Ti-Al/ β-Ti-Al, S β-Ti-Al-M/ β-Ti-Al-M, S β-Ti-M/ β-Ti-MThe interface enhancing coefficient of expression phase interface β-Ti-Al/ β-Ti-Al, β-Ti-Al-M/ β-Ti-Al-M, β-Ti-M/ β-Ti-M; Δ ρ ' β-Ti-Al/ β-Ti-Al, Δ ρ ' β-Ti-Al-M/ β-Ti-Al-M, Δ ρ ' β-Ti-M/ β-Ti-MBe respectively the assembly average of β-Ti-Al/ β-Ti-Al, β-Ti-Al-M/ β-Ti-Al-M, β-Ti-M/ β-Ti-M phase interface electron density difference;
Primary phase, secondary α be the solution strengthening coefficient of middle phase structure unit mutually:
Figure G2009102489435D00113
S wherein α-Ti-Al, S α-Ti-Al-M, S α-Ti-MThe solution strengthening coefficient of representing α-Ti-Al during primary, secondary α are mutually, α-Ti-Al-M, α-Ti-M respectively; n A' α-Ti-Al, n A' α-Ti-Al-M, n A' α-Ti-M, n A' α-TiBe respectively the assembly average of the shared electron logarithm on α-Ti-Al, α-Ti-Al-M, α-Ti-M, the strong bond in α-Ti phase structure unit;
Primary is the interface enhancing coefficient at middle out-phase interface mutually:
Figure G2009102489435D00121
S wherein α-Ti-Al/ α-Ti, S α-Ti-Al-M/ α-Ti, S α-Ti-M/ α-TiThe interface enhancing coefficient of representing phase interface α-Ti-Al/ α-Ti during primary mutually, α-Ti-Al-M/ α-Ti, α-Ti-M/ α-Ti respectively; Δ ρ ' α-Ti-Al/ α-Ti, Δ ρ ' α-Ti-Al-M/ α-Ti, Δ ρ ' α-Ti-M/ α-TiThe assembly average of the interface electron density difference of expression α-Ti-Al/ α-Ti, α-Ti-Al-M/ α-Ti, α-Ti-M/ α-Ti phase interface;
Primary mutually in the interface enhancing coefficient of phase interface:
S wherein α-Ti-Al/ α-Ti-Al, S α-Ti-Al-M/ α-Ti-Al-M, S α-Ti-M/ α-Ti-MThe interface enhancing coefficient of representing α-Ti-Al/ α-Ti-Al during primary mutually, α-Ti-Al-M/ α-Ti-Al-M, α-Ti-M/ α-Ti-M phase interface respectively; Δ ρ ' α-Ti-Al/ α-Ti-Al, Δ ρ ' α-Ti-Al-M/ α-Ti-Al-M, Δ ρ ' α-Ti-M/ α-Ti-MThe assembly average of the interface electron density difference of expression α-Ti-Al/ α-Ti-Al, α-Ti-Al-M/ α-Ti-Al-M, α-Ti-M/ α-Ti-M phase interface;
Primary and β form the interface enhancing coefficient at out-phase interface mutually:
Figure G2009102489435D00123
S wherein α-Ti-Al/ β-Ti-Al, S α-Ti-Al-M/ β-Ti-Al-M, S α-Ti-M/ β-Ti-M, S α-Ti/ β-TiRepresent that respectively primary and β form the interface enhancing coefficient of out-phase interface α-Ti-Al/ β-Ti-Al, α-Ti-Al-M/ β-Ti-Al-M, α-Ti-M/ β-Ti-M, α-Ti/ β-Ti mutually; Δ ρ ' α-Ti-Al/ β-Ti-Al, Δ ρ ' α-Ti-Al-M/ β-Ti-Al-M, Δ ρ ' α-Ti-M/ β-Ti-M, Δ ρ ' α-Ti/ β-TiThe assembly average of the interface electron density difference of expression α-Ti-Al/ β-Ti-Al, α-Ti-Al-M/ β-Ti-Al-M, α-Ti-M/ β-Ti-M, α-Ti/ β-Ti phase interface;
Secondary α mutually in the interface enhancing coefficient of phase interface:
Figure G2009102489435D00131
S wherein s α-Ti-Al/ α-Ti-Al, S s α-Ti-Al-M/ α-Ti-Al-M, S s α-Ti-M/ α-Ti-M, S s α-Ti/ α-TiThe interface enhancing coefficient of representing α-Ti-Al/ α-Ti-Al in the secondary α phase solid solution, α-Ti-Al-M/ α-Ti-Al-M, α-Ti-M/ α-Ti-M phase interface respectively; Δ ρ Max α-Ti-Al/ α-Ti-Al, Δ ρ Max α-Ti-Al-M/ α-Ti-Al-M, Δ ρ Max α-Ti-M/ α-Ti-MBe respectively the maximal value of the interface electron density difference of α-Ti-Al/ α-Ti-Al, α-Ti-Al-M/ α-Ti-Al-M, α-Ti-M/ α-Ti-M phase interface;
Secondary α and parent phase β form the interface enhancing coefficient at out-phase interface:
Figure G2009102489435D00132
S wherein s α-Ti-Al/ β-Ti-Al, S s α-Ti-Al-M/ β-Ti-Al-M, S s α-Ti-M/ β-Ti-M, S s α-Ti/ β-TiRepresent that respectively secondary α and parent phase β form the interface enhancing coefficient at out-phase interface; Δ ρ Max α-Ti-Al/ β-Ti-Al, Δ ρ Max α-Ti-Al-M/ β-Ti-Al-M, Δ ρ Max α-Ti-M/ β-Ti-M, Δ ρ Max α-Ti/ β-TiThe maximal value of the interface electron density difference of expression α-Ti-Al/ β-Ti-Al, α-Ti-Al-M/ β-Ti-Al-M, α-Ti-M/ β-Ti-M, α-Ti/ β-Ti phase interface;
Impurity element forms the solution strengthening coefficient of phase structure unit:
Figure G2009102489435D00133
S wherein α-Ti-O, S α-Ti-N, S α-Ti-CRepresent impurity element O, N, C solution strengthening coefficient respectively in the α phase; n A' α-Ti-O, n A' α-Ti-N, n A' α-Ti-CAssembly average for shared electron logarithm on α-Ti-O, α-Ti-N, the strong covalent bond in α-Ti-C phase structure unit.
Impurity element forms the interface enhancing coefficient at out-phase interface:
Figure G2009102489435D00141
S wherein α-Ti-O/ α-Ti, S α-Ti-N/ α-Ti, S α-Ti-C/ α-TiThe interface enhancing coefficient of representing α-Ti-O/ α-Ti, α-Ti-N/ α-Ti, α-Ti-C/ α-Ti phase interface respectively; Δ ρ ' α-Ti-O/ α-Ti, Δ ρ ' α-Ti-N/ α-Ti, Δ ρ ' α-Ti-C/ α-TiAssembly average for α-Ti-O/ α-Ti, α-Ti-N/ α-Ti, α-Ti-C/ α-Ti phase interface electron density difference;
Impurity element forms the interface enhancing coefficient with phase interface:
Figure G2009102489435D00142
S wherein α-Ti-O/ α-Ti-O, S α-Ti-N/ α-Ti-N, S α-Ti-C/ α-Ti-CThe interface enhancing coefficient of representing α-Ti-O/ α-Ti-O, α-Ti-N/ α-Ti-N, α-Ti-C/ α-Ti-C phase interface respectively; Δ ρ ' α-Ti-Al/ α-Ti-O, Δ ρ ' α-Ti-N/ α-Ti-N, Δ ρ ' α-Ti-C/ α-Ti-CAssembly average for α-Ti-O/ α-Ti-O, α-Ti-N/ α-Ti-N, α-Ti-C/ α-Ti-C phase interface electron density difference.
1.3 calculate titanium alloy tensile strength; Intensity with matrix α-Ti, β-Ti is base value, utilizes coefficient of intensification, strengthens the titanium alloy tensile strength increment under the weight calculation Different Heat Treatment Conditions, with the titanium alloy tensile strength increment summation that calculates; Draw the titanium alloy tensile strength values
The mathematical model of titanium alloy calculation of Tensile Strength:
β mutually in the solution strengthening intensity increment of each phase structure unit:
Figure G2009102489435D00143
Δ σ wherein b β-Ti-Al, Δ σ b β-Ti-Al-M, Δ σ b β-Ti-MThe solution strengthening intensity increment of β-Ti-Al, β-Ti-Al-M, β-Ti-M phase structure unit in the expression β phase solid solution; σ b β-TiBe the tensile strength values of matrix β-Ti, σ b β - Ti = 200 MPa .
β is the interface enhancing intensity increment at middle out-phase interface mutually:
Figure G2009102489435D00153
Δ σ wherein b β-Ti-Al/-Ti, Δ σ b β-Ti-Al-M/ β-Ti, Δ σ b β-Ti-M/ β-TiThe reinforcement intensity increment of β-Ti-Al/ β-Ti, β-Ti-Al-M/ β-Ti, β-Ti-M/ β-Ti phase interface in the expression β phase solid solution;
β mutually in the interface enhancing intensity increment of phase interface:
Figure G2009102489435D00154
Δ σ wherein b β-Ti-Al/ β-Ti-Al, Δ σ b β-Ti-Al-M/ β-Ti-Al-M, Δ σ b β-Ti-M/ β-Ti-Mβ-Ti-Al/ β-Ti-Al in the expression β phase solid solution, β-Ti-Al-M/ β-Ti-Al-M, β-Ti-M/ β-Ti-M are with the reinforcement intensity increment of phase interface.
Primary mutually in the solution strengthening intensity increment of each phase structure unit:
Figure G2009102489435D00155
Δ σ wherein Bp α-Ti-Al, Δ σ Bp α-Ti-Al-M, Δ σ Bp α-Ti-MThe solution strengthening intensity increment of α-Ti-Al, α-Ti-Al-M, α-Ti-M phase structure unit in the expression primary phase solid solution; σ b α-TiBe the tensile strength values of matrix α-Ti, σ b α - Ti = 275 MPa ;
Primary is the interface enhancing intensity increment at middle out-phase interface mutually:
Figure G2009102489435D00161
Δ σ wherein Bp α-Ti-Al/ α-Ti, Δ σ Bp α-Ti-Al-M/ α-Ti, Δ σ Bp α-Ti-M/ α-Tiα-Ti-Al/ α-Ti, α-Ti-Al-M/ α-Ti, α-Ti-M/ α-Ti phase interface are strengthened intensity increment in the expression primary phase solid solution;
In the primary with the interface enhancing intensity increment of phase interface:
Figure G2009102489435D00162
Δ σ wherein Bp α-Ti-Al/ α Ti-Al, Δ σ Bp α-Ti-Al-M/ α-Ti-Al-M, Δ σ Bp α-Ti-M/ α-Ti-MThe interface enhancing intensity increment of α-Ti-Al/ α-Ti-Al, α-Ti-Al-M/ α-Ti-Al-M, α-Ti-M/ α-Ti-M phase interface in the expression primary phase solid solution.
The interface enhancing intensity increment at the out-phase interface that primary and β form mutually:
Figure G2009102489435D00163
Δ σ wherein Bp Alpha-beta-Ti-Al, Δ σ Bp α-Ti-Al-M/ β-Ti-Al-M, Δ σ Bp α-Ti-M/ β-Ti-M, Δ σ Bp α-Ti/ β-TiThe interface enhancing intensity increment of α-Ti-Al/ β-Ti-Al that expression primary and β form mutually, α-Ti-Al-M/ β-Ti-Al-M, α-Ti-M/ β-Ti-M, α-Ti/ β-Ti phase interface;
Secondary α mutually in the solution strengthening intensity increment of each phase structure unit:
Figure G2009102489435D00164
Δ σ wherein Bs α-Ti-Al, Δ σ Bs α-Ti-Al-M, Δ σ Bs α-Ti-MThe solution strengthening intensity increment of representing α-Ti-Al in the secondary α phase solid solution, α-Ti-Al-M, α-Ti-M phase structure unit;
Secondary α mutually in the interface enhancing intensity increment of phase interface:
Figure G2009102489435D00171
Δ σ wherein Bs α-Ti-Al/ α-Ti-Al, Δ σ Bs α-Ti-Al-M/ α-Ti-Al-M, Δ σ Bs α-Ti-M/ α-Ti-MThe interface enhancing intensity increment of representing α-Ti-Al/ α-Ti-Al in the secondary α phase solid solution, α-Ti-Al-M/ α-Ti-Al-M, α-Ti-M/ α-Ti-M phase interface;
Secondary α and parent phase β form the interface enhancing intensity increment at out-phase interface:
Figure G2009102489435D00172
Δ σ wherein Bs α-Ti-Al/ β-Ti-Al, Δ σ Bs α-Ti-Al-M/ β-Ti-Al-M, Δ σ Bs α-Ti-M/ β-Ti-M, Δ σ Bs α-Ti/ β-TiThe interface enhancing intensity increment of representing α-Ti-Al/ β-Ti-Al that secondary α phase solid solution and parent phase β solid solution forms, α-Ti-Al-M/ β-Ti-Al-M, α-Ti-M/ β-Ti-M phase interface;
The solution strengthening intensity increment of each phase structure unit that impurity element forms:
Figure G2009102489435D00173
Δ σ wherein b α-Ti-O, Δ σ b α-Ti-N, Δ σ b α-Ti-CExpression impurity element O, N, C form the solution strengthening intensity increment of α-Ti-O, α-Ti-N, α-Ti-C phase structure unit in α phase solid solution;
The interface enhancing intensity increment at the out-phase interface that impurity element forms:
Figure G2009102489435D00174
Δ σ wherein b α-Ti-O/ α-Ti, Δ σ b α-Ti-N/ α-Ti, Δ σ b α-Ti-C/ α-TiExpression impurity element O, N, C form the solution strengthening intensity increment of α-Ti-O/ α-Ti, α-Ti-N/ α-Ti, α-Ti-C/ α-Ti phase structure unit in α phase solid solution; The interface enhancing intensity increment of the same phase interface that impurity element forms:
Figure G2009102489435D00181
Δ σ wherein b α-Ti-O/ α-Ti-O, △ σ b α-Ti-N/ α-Ti-N, Δ σ b α-Ti-C/ α-Ti-CExpression impurity element O, N, C form the reinforcement intensity increment of α-Ti-O/ α-Ti-O, α-Ti-N/ α-Ti-N, α-Ti-C/ α-Ti-C phase interface in α phase solid solution;
The computing formula of titanium alloy tensile strength:
Figure G2009102489435D00182
1.4. calculate the titanium alloy length growth rate; Length growth rate with α-Ti, β-Ti is a base value, utilizes coefficient of intensification, strengthens the titanium alloy length growth rate reduction amount under the weight calculation Different Heat Treatment Conditions, with the titanium alloy length growth rate reduction amount summation that calculates; Draw the titanium alloy length growth rate
Titanium alloy length growth rate calculation mathematic model:
β mutually in the solution strengthening length growth rate reduction amount of each phase structure unit:
Figure G2009102489435D00183
Δ δ wherein β-Ti-Al, Δ δ β-Ti-Al-M, Δ δ β-Ti-MThe solution strengthening length growth rate reduction amount of β-Ti-Al, β-Ti-Al-M, β-Ti-M phase structure unit in the expression β phase solid solution; σ N β-Ti-Al, σ N β-Ti-Al-M, σ N β-Ti-MBe the state of atom group number that possibly exist in β-Ti-Al, β-Ti-Al-M, the β-Ti-M phase structure unit; δ β-TiBe the elongation values of matrix β-Ti, δ β-Ti=75%;
β is the interface enhancing length growth rate reduction amount at middle out-phase interface mutually:
Figure G2009102489435D00191
Δ δ wherein β-Ti-Al/ β-Ti, Δ δ β-Ti-Al-M/ β-Ti, Δ δ β-Ti-M/ β-TiThe interface enhancing length growth rate reduction amount of β-Ti-Al/ β-Ti, β-Ti-Al-M/ β-Ti, β-Ti-M/ β-Ti phase interface in the expression β phase solid solution; σ β-Ti-Al/ β-Ti, σ β-Ti-Al-M/ β-Ti, σ β-Ti-M/ β-TiBe the state of atom group number that possibly exist in β-Ti-Al/ β-Ti, β-Ti-Al-M/ β-Ti, the β-Ti-M/ β-Ti phase interface;
β mutually in the interface enhancing length growth rate reduction amount of phase interface:
Figure G2009102489435D00192
Δ δ wherein β-Ti-Al/ β-Ti-Al, Δ δ β-Ti-Al-M/ β-Ti-Al-M, Δ δ β-Ti-M/ β-Ti-MThe interface enhancing length growth rate reduction amount of β-Ti-Al/ β-Ti-Al, β-Ti-Al-M/ β-Ti-Al-M, β-Ti-M/ β-Ti-M phase interface in the expression β phase solid solution; σ β-Ti-Al/ β-Ti-Al, σ β-Ti-Al-M/ β-Ti-Al-M, σ β-Ti-M/ β-Ti-MBe the state of atom group number that possibly exist in β-Ti-Al/ β-Ti-Al, β-Ti-Al-M/ β-Ti-Al-M, the β-Ti-M/ β-Ti-M phase interface;
Primary mutually in the solution strengthening length growth rate reduction amount of each phase structure unit:
Figure G2009102489435D00201
Δ δ wherein p α-Ti-Al, Δ δ p α-Ti-Al-M, Δ δ p α-Ti-MThe solution strengthening length growth rate reduction amount of α-Ti-Al, α-Ti-Al-M, α-Ti-M phase structure unit in the expression primary phase solid solution; σ N α-Ti-Al, σ N α-Ti-Al-M, σ N α-Ti-MBe the state of atom group number that possibly exist in α-Ti-Al, α-Ti-Al-M, the α-Ti-M phase structure unit; δ α-TiBe the elongation values of matrix α-Ti, δ α-Ti=49%;
Primary is the interface enhancing length growth rate reduction amount at middle out-phase interface mutually:
Figure G2009102489435D00202
Δ δ wherein p α-Ti-Al/ α-Ti, Δ δ p α-Ti-Al-M/ α-Ti, Δ δ p α-Ti-M/ α-TiThe interface enhancing length growth rate reduction amount of α-Ti-Al/ α-Ti, α-Ti-Al-M/ α-Ti, α-Ti-M/ α-Ti phase interface in the expression primary phase solid solution; σ α-Ti-Al/ α-Ti, σ α-Ti-Al-M/ α-Ti, σ α-Ti-M/ α-TiBe the state of atom group number that possibly exist in α-Ti-Al/ α-Ti, α-Ti-Al-M/ α-Ti, the α-Ti-M/ α-Ti phase interface;
Primary mutually in the interface enhancing length growth rate reduction amount of phase interface:
Figure G2009102489435D00203
Δ δ wherein p α-Ti-Al/ α-Ti-Al, Δ δ p α-Ti-Al-M/ α-Ti-Al-M, Δ δ p α-Ti-M/ α-Ti-MThe interface enhancing length growth rate reduction amount of α-Ti-Al/ α-Ti-Al, α-Ti-Al-M/ α-Ti-Al-M, α-Ti-M/ α-Ti-M phase interface in the expression primary phase solid solution; σ α-Ti-Al/ α-Ti-Al, σ α-Ti-Al-M/ α-Ti-Al-M, σ α-Ti-M/ α-Ti-MBe the state of atom group number that possibly exist in α-Ti-Al/ α-Ti-Al, α-Ti-Al-M/ α-Ti-Al-M, the α-Ti-M/ α-Ti-M phase interface;
Primary and β form the interface enhancing length growth rate reduction amount at out-phase interface mutually:
Figure G2009102489435D00211
Δ δ wherein p α-Ti-Al/ β-Ti-Al, Δ δ p α-Ti-Al-M/ β-Ti-Al-M, Δ δ p α-Ti-M/ β-Ti-M, Δ δ p α-Ti/ β-TiRepresent that primary and β form the interface enhancing length growth rate reduction amount of α-Ti-Al/ β-Ti-Al, α-Ti-Al-M/ β-Ti-Al-M, α-Ti-M/ β-Ti-M phase interface mutually; σ α-Ti-Al/ β-Ti-Al, σ α-Ti-Al-M/ β-Ti-Al-M, σ α-Ti-M/ β-Ti-M, σ α-Ti/ β-TiBe the state of atom group number that possibly exist in α-Ti-Al/ β-Ti-Al, α-Ti-Al-M/ β-Ti-Al-M, α-Ti-M/ β-Ti-M, the α-Ti/ β-Ti phase interface;
Secondary α mutually in the solution strengthening length growth rate reduction amount of each phase structure unit:
Figure G2009102489435D00212
Δ δ wherein s α-Ti-Al, Δ δ s α-Ti-Al-M, Δ δ s α-Ti-MThe solution strengthening length growth rate reduction amount of representing α-Ti-Al in the secondary α phase solid solution, α-Ti-Al-M, α-Ti-M phase structure unit; δ when primary is separated out Matrix=δ α-Ti, otherwise δ Matrix=δ β-Ti
Secondary α mutually in the interface enhancing length growth rate reduction amount of phase interface:
Δ δ wherein s α-Ti-Al/ α-Ti-Al, Δ δ s α-Ti-Al-M/ α-Ti-Al-M, Δ δ s α-Ti-M/ α-Ti-MThe interface enhancing length growth rate reduction amount of representing α-Ti-Al/ α-Ti-Al in the secondary α phase solid solution, α-Ti-Al-M/ α-Ti-Al-M, α-Ti-M/ α-Ti-M phase interface;
Secondary α and β form the interface enhancing length growth rate reduction amount at out-phase interface mutually:
Figure G2009102489435D00221
Δ δ wherein s α-Ti-Al/ β-Ti-Al, Δ δ s α-Ti-Al-M/ β-Ti-Al-M, Δ δ s α-Ti-M/ β-Ti-M, Δ δ s α-Ti/ β-TiRepresent that secondary α and β form the interface enhancing length growth rate reduction amount of α-Ti-Al/ β-Ti-Al, α-Ti-Al-M/ β-Ti-Al-M, α-Ti-M/ β-Ti-M, α-Ti/ β-Ti phase interface mutually; σ α-Ti/ β-TiThe state of atom group number that possibly exist for α-Ti/ β-Ti phase interface;
Impurity element forms the solution strengthening length growth rate reduction amount of phase structure unit:
Figure G2009102489435D00222
Δ δ wherein α-Ti-O, Δ δ α-Ti-N, Δ δ α-Ti-CSolution strengthening length growth rate reduction amount for α-Ti-O, α-Ti-N, α-Ti-C structural unit;
Impurity element forms the interface enhancing length growth rate reduction amount at out-phase interface:
Δ δ wherein α-Ti-O/ α-Ti, Δ δ α-Ti-N/ α-Ti, Δ δ α-Ti-C/ α-TiInterface enhancing length growth rate reduction amount for α-Ti-O/ α-Ti, α-Ti-N/ α-Ti, α-Ti-C/ α-Ti phase interface;
Impurity element forms the interface enhancing length growth rate reduction amount with phase interface:
Δ δ wherein α-Ti-O/ α-Ti, Δ δ α-Ti-N/ α-Ti, Δ δ α-Ti-C/ α-TiInterface enhancing length growth rate reduction amount for α-Ti-O/ α-Ti-O, α-Ti-N/ α-Ti-N, α-Ti-C/ α-Ti-C phase interface;
Titanium alloy length growth rate computing formula:
Figure G2009102489435D00232
Figure G2009102489435D00233
Figure G2009102489435D00234
Figure G2009102489435D00235
Figure G2009102489435D00238
Figure G2009102489435D00239
Figure G2009102489435D002310
Figure G2009102489435D002311
Figure G2009102489435D002312
Figure G2009102489435D002313
Figure G2009102489435D002314
Figure G2009102489435D002315
Aforementioned calculation formula (1)～formula (52) is compiled into software for calculation; Carry out after the alloying component of the choosing of input examination on computers and the corresponding Technology for Heating Processing and calculate; Through observing the change amount of alloying element tensile strength, length growth rate under Different Heat Treatment Conditions; Adjust the relative error of calculated value and technical requirement value that alloy composition makes design tensile strength of alloys, length growth rate repeatedly in 10%, so just can confirm the chemical constitution of titanium alloy under the solution treatment+shrend of β phase region, the solution treatment+shrend of alpha+beta phase region and solution treatment+aging condition.
Above-mentioned titanium alloy component quantifying design method; Can carry out the adjustment alloy composition on computers 5～10 times, and the pairing alloying component of minimum value of the calculated value of getting design tensile strength of alloys, length growth rate and the relative error of technical requirement value is as designing the optimized chemical constitution of alloy.
From the chemical constitution of alloy, combine preparation technology, the performance that calculates alloy theoretically is to calculate the important content of materialogy, also is alloy designs truly.For this reason, the lot of domestic and foreign scholar is just from different levels, approach to accurate quantitative Analysis from approximate with different modes.The present invention is based on " solid and molecule experience electron theory ", utilize the phase transformation of alloy electronic structure parameter, combination titanium alloy, propose quantitative Analysis titanium alloy tensile strength sigma b, length growth rate δ mathematical model, with tensile strength sigma b, length growth rate δ calculated value be the quantitative design that condition is carried out titanium alloy component.Although; The same electronic structure parameter that is adopted separately with d-electron theory design method of the present invention all can reflect the characteristic of alloy atom outer-shell electron, but the present invention but can solve the problem that d-electron theory design method is difficult to quantitative Analysis strength of alloy, length growth rate at an easy rate.Compare with fuzzy logic, nerual network technique, expert database, input was not the sample data of gathering and simulating in producing when the present invention calculated, but had the electronic structure characteristic parameter of the alloy system self of clear and definite physical significance.
The present invention is from the actual transformation process of titanium alloy; On the electronic structure level, set up the reinforcement weight of titanium alloy, the mathematical model of coefficient of intensification under the Different Heat Treatment Conditions; Tensile strength, elongation values with α-Ti, β-Ti is base value then; The intensity increment under utilization reinforcement weight, the coefficient of intensification calculating Different Heat Treatment Conditions and the reduction amount of length growth rate, thus the tensile strength of titanium alloy under Different Heat Treatment Conditions, the calculated value of length growth rate provided.Computing formula is compiled into software for calculation; Observe the change amount of alloying element tensile strength, length growth rate under Different Heat Treatment Conditions on computers; Adjust the relative error of calculated value and technical requirement value that alloy composition makes design tensile strength of alloys, length growth rate repeatedly in 10%, so just can confirm titanium alloy component.Its principal feature is, design based on the electronic structure parameter derive from the atom outer-shell electron number that can characterize the alloy atom characteristic, have clear physical meaning; The mathematical model that β phase solid solution, primary reach the reinforcement weight of secondary α phase solid solution has mutually embodied the phase transition process under the titanium alloy Different Heat Treatment Conditions; The mathematical model of solution strengthening coefficient has embodied under the Different Heat Treatment Conditions size of alloy atom adhesion in the titanium alloy, so can use solution strengthening coefficient sign with the atomic link relevant titanium alloy solution strengthening mechanism of making a concerted effort; The mathematical model of interface enhancing coefficient has embodied under the Different Heat Treatment Conditions in the titanium alloy interface stress level between phase interface, so ageing strengthening mechanism, the machine-processed interface enhancing coefficient of can using of dislocation strengthening characterize in the titanium alloy relevant with interfacial stress.Design based on mathematical model advanced, simple; Design process is quick and economical; The design result accuracy is high, and application prospect is very wide, has not only reduced the alloy designs cost; Also enrich titanium alloy component design theory system, also be simultaneously the composition design of other alloy system value of offering reference.
Embodiment
Instance 1
The quantitative design of metastable beta-titanium alloy composition during β phase region solution treatment+shrend.Metastable beta-titanium alloy is organized as single β phase after the solution treatment+shrend of β phase region, promptly the reinforcement weight of primary, secondary α phase is zero, and correspondingly the intensity increment of phase structure unit and phase interface and length growth rate reduction amount also are zero among primary, the secondary α.Software for calculation is when executing the task in this example, although need to carry out all calculation procedures of formula (1)～formula (52), the result of calculation of the intensity increment of phase structure unit and phase interface and length growth rate reduction amount is zero among primary, the secondary α.So only handed in the argumentation of practical implementation process below and the reinforcement non-vanishing relevant phase structure unit of weight and the calculation procedure of phase interface, concrete steps are following:
1. utilize " solid and molecule experience electron theory " to calculate middle mutually phase structure unit of β and phase interface electronic structure parameter n A', σ N, Δ ρ ', Δ ρ Max, σ, and set up database like table 1～table 4.
2. utilize the statistical value n of the shared electron logarithm on the strong covalent bond in the atomic percentage of alloy composition, the phase structure unit in the table 1 A' and formula (1) calculate β mutually in the reinforcement weight of each phase structure unit; Utilize atomic percentage and the formula (2) of impurity element to calculate the reinforcement weight of the phase structure unit that impurity element forms, utilize formula (6) to calculate impurity element and be solid-solubilized in the atomic percentage C that occupy Ti of α in mutually α p TiAnd utilize formula (7) to calculate the β atomic percentage C of middle Ti mutually β Ti
Utilize table 2 and formula (13) calculate β mutually in the solution strengthening coefficient of each phase structure unit; Utilize table 3 and formula (14) to calculate the β interface enhancing coefficient at middle out-phase interface mutually; Utilize table 4 and formula (15) calculate β mutually in the interface enhancing coefficient of phase interface, utilize in α-Ti-O in the table 5, α-Ti-N, the α-Ti-C phase structure unit statistical value n of shared electron logarithm on the strong covalent bond A' reach formula (22) to calculate the solution strengthening coefficient that impurity element forms the phase structure unit; Utilize the statistical value Δ ρ ' and the formula (23) of α in the table 6-Ti-O/ α-Ti, α-Ti-N/ α-Ti, α-Ti-C/ α-Ti phase interface electron density difference to calculate the interface enhancing coefficient that impurity element forms the out-phase interface, utilize the statistical value Δ ρ ' of α in the table 7-Ti-O/ α-Ti-O, α-Ti-N/ α-Ti-N, α-Ti-C/ α-Ti-C phase interface electron density difference and formula (24) calculating impurity element to form interface enhancing coefficient with phase interface.
3. with the β that calculates mutually in solution strengthening weight, the solution strengthening coefficient substitution formula (25) of each phase structure unit calculate β mutually in the solution strengthening intensity increment of each phase structure unit; With the β that calculates mutually in each phase structure unit solution strengthening weight, β mutually in the interface enhancing coefficient substitution formula (26) at out-phase interface calculate β mutually in the interface enhancing intensity increment at out-phase interface; With the β that calculates mutually in each phase structure unit solution strengthening weight and β mutually in the interface enhancing coefficient substitution formula (27) of phase interface calculate β mutually in the interface enhancing intensity increment of phase interface; The reinforcement weight and the solution strengthening coefficient substitution formula (35) of the phase structure unit that the impurity element that calculates is formed calculate the solution strengthening intensity increment that impurity element forms the phase structure unit; The reinforcement weight of the phase structure unit that the impurity element that calculates is formed and the interface enhancing coefficient substitution formula (36) that impurity element forms the out-phase interface calculate the interface enhancing intensity increment that impurity element forms the out-phase interface; The reinforcement weight of the phase structure unit that the impurity element that calculates is formed and impurity element form interface enhancing coefficient substitution formula (37) with phase interface and calculate impurity element and form the interface enhancing intensity increment with phase interface.C with aforementioned calculation α p Ti, C β Ti, C α s Ti = 0 And the tensile strength of metastable beta-titanium alloy when respectively strengthening intensity increment substitution formula (38) and calculating β phase region solution treatment+shrend.
The state of atom group that 4. β that calculates possibly existed in the phase structure unit in the solution strengthening weight, solution strengthening coefficient, interface enhancing coefficient, table 2 of each phase structure unit in is mutually counted σ N, the state of atom group that possibly exist on the phase interface in table 3～table 4 count σ respectively substitution formula (39-41) calculate each phase structure unit and phase interface length growth rate reduction amount in the β phase solid solution; The state of atom group that possibly exist in the phase structure unit of impurity element in the reinforcement weight of the phase structure unit that the impurity element that calculates is formed, solution strengthening coefficient, interface enhancing coefficient, the table 5 is counted σ N, the state of atom group that possibly exist on the phase interface of impurity element in the table 6-table 7 count σ respectively substitution formula (49-51) calculate the length growth rate reduction amount that impurity element forms phase structure unit and phase interface; The length growth rate of metastable beta-titanium alloy when utilizing formula (52) to calculate β phase region solution treatment+shrend at last.
Computing formula (1)～formula (52) is compiled into software for calculation; Carry out after the heat-treat condition of the alloying component of the choosing of input examination on computers and the solution treatment+shrend of selection β phase region and calculate; Through observing the change amount of alloying element tensile strength, length growth rate under Different Heat Treatment Conditions; Adjust relative error that alloy composition makes design tensile strength of alloys, elongation values and technical requirement value repeatedly within 10%, the chemical constitution of metastable beta-titanium alloy in the time of so just can having confirmed β phase region solution treatment+shrend.Be not more than under 10% the precondition satisfying relative error; Can carry out 5-10 time adjustment alloy composition on computers, and the optimized design mix of metastable beta-titanium alloy when getting the relative error of calculated value and technical requirement value of tensile strength, length growth rate hour pairing alloying component is as β phase region solution treatment+shrend.
In order to verify the reliability of formula, table 9 has provided β-21, BT-22, Ti-B20 titanium alloy tensile strength ρ when β phase region solution treatment+shrend b, the measured value of length growth rate δ and the contrast of calculated value, the relative error of the two is all within 10%.See that from result of calculation the theoretical model of quantitative design has higher reliability.
The contrast of calculated value and experiment value during the solution treatment of table 9 β phase region
Figure G2009102489435D00281
Annotate: 1) β-21 alloy: chemical constitution (wt%) is Al=3.0, Mo=15.0, Nb=2.7, Si=0.20, Fe=0.08, N=0.011, O=0.08, C=0.04, H=0.001; Transformation temperature is about 815 ℃.2) BT-22 alloy: chemical constitution (wt%) is Al=5.0, Mo=5.0, V=5.0, Cr=1.0, Fe=1.0, N=0.011, O=0.085, C=0.04, H=0.001; Transformation temperature is about 830 ℃.3) Ti-B20 alloy: chemical constitution (wt%) is Al=3.7, Mo=4.7, V=4.0, Cr=1.9, Fe=1.0, Zr=2.1, Sn=1.9, N=0.027, O=0.08, C=0.03, H=0.001; Transformation temperature is about 810 ℃.
Instance 2
The quantitative design of titanium alloy component during alpha+beta phase region solution treatment+shrend.Titanium alloy is organized as nascent alpha+beta phase after the solution treatment+shrend of alpha+beta phase region, the reinforcement weight of promptly secondary α phase is zero, and the intensity increment of phase structure unit and phase interface and length growth rate reduction amount also are zero among the correspondingly secondary α.Software for calculation is when executing the task in this example, although need to carry out all calculation procedures of formula (1)～formula (52), the result of calculation of the intensity increment of phase structure unit and phase interface and length growth rate reduction amount is zero among the secondary α.So only handed in the argumentation of practical implementation process below and the reinforcement non-vanishing relevant phase structure unit of weight and the calculation procedure of phase interface, concrete steps are following:
1. utilize " solid and molecule experience electron theory " calculate β mutually, the middle mutually phase structure unit of primary and phase interface electronic structure parameter n A', σ N, Δ ρ ', Δ ρ Max, σ, and set up database like table 1～table 8.
2. utilize the statistical value n of the shared electron logarithm on the strong covalent bond in the atomic percentage of alloy composition, the phase structure unit in the table 1 A' and formula (1) calculate β mutually in the reinforcement weight of each phase structure unit; Utilize the atomic percentage of impurity element and the reinforcement weight that formula (2) calculates impurity element phase structure unit; Utilize formula (3) calculate primary mutually in the reinforcement weight of each phase structure unit, utilize formula (4) calculate primary separate out mutually back β mutually in the reinforcement weight of each phase structure unit; Utilize formula (5) to calculate the weight of the middle mutually α of primary-Ti structural unit, utilize formula (6) to calculate the primary atomic percentage C of middle Ti mutually α p TiAnd utilize formula (7) to calculate the β atomic percentage C of middle Ti mutually β Ti
Utilize table 2 and formula (13) calculate β mutually in the solution strengthening coefficient of each phase structure unit; Utilize table 3 and formula (14) to calculate the β interface enhancing coefficient at middle out-phase interface mutually; Utilize table 4 and formula (15) calculate β mutually in the interface enhancing coefficient of phase interface; Utilize table 5 and formula (16) to calculate the solution strengthening coefficient of phase structure unit in the primary; Utilize table 6 and formula (17) to calculate the interface enhancing coefficient at out-phase interface in the primary; Utilize in table 7 and formula (18) primary with the interface enhancing coefficient of phase interface, utilize table 8 and formula (19) to calculate the interface enhancing coefficient that primary and β form the out-phase interface mutually, utilize in α-Ti-O in the table 5, α-Ti-N, the α-Ti-C phase structure unit statistical value n of the shared electron logarithm on the strong covalent bond A' reach formula (22) to calculate the solution strengthening coefficient that impurity element forms the phase structure unit; Utilize the statistical value Δ ρ ' and the formula (23) of α in the table 6-Ti-O/ α-Ti, α-Ti-N/ α-Ti, α-Ti-C/ α-Ti phase interface electron density difference to calculate the interface enhancing coefficient that impurity element forms the out-phase interface, utilize the statistical value Δ ρ ' of α in the table 7-Ti-O/ α-Ti-O, α-Ti-N/ α-Ti-N, α-Ti-C/ α-Ti-C phase interface electron density difference and formula (24) calculating impurity element to form interface enhancing coefficient with phase interface.
3. with the primary that calculates separate out mutually back β mutually in reinforcement weight, the solution strengthening coefficient substitution formula (25) of each phase structure unit calculate β mutually in the solution strengthening intensity increment of each phase structure unit; With the primary that calculates separate out mutually back β mutually in each phase structure unit reinforcement weight, β mutually in the interface enhancing coefficient substitution formula (26) at out-phase interface calculate β mutually in the interface enhancing intensity increment at out-phase interface; With the primary that calculates separate out mutually back β mutually in each phase structure unit reinforcement weight, β mutually in the interface enhancing coefficient substitution formula (27) of phase interface calculate β mutually in the interface enhancing intensity increment of phase interface; With the primary that calculates mutually in solution strengthening weight, the solution strengthening coefficient substitution formula (28) of phase structure unit calculate primary mutually in the solution strengthening intensity increment of each phase structure unit; With the primary that calculates mutually in the phase structure unit solution strengthening weight, primary mutually in the interface enhancing coefficient substitution formula (29) at out-phase interface calculate primary mutually in the interface enhancing intensity increment at out-phase interface; With the primary that calculates mutually in the phase structure unit solution strengthening weight, primary mutually in the interface enhancing coefficient substitution formula (30) of phase interface calculate primary mutually in the interface enhancing intensity increment of phase interface; With the primary that calculates mutually in the interface enhancing coefficient substitution formula (31) at the out-phase interface that forms mutually of solution strengthening weight, primary and the β of phase structure unit calculate the interface enhancing intensity increment at the out-phase interface that primary and β form mutually, the reinforcement weight of the phase structure unit that the impurity element that calculates is formed and the solution strengthening intensity increment of solution strengthening coefficient substitution formula (35) calculating impurity element formation phase structure unit; The reinforcement weight of the phase structure unit that the impurity element that calculates is formed and the interface enhancing coefficient substitution formula (36) that impurity element forms the out-phase interface calculate the interface enhancing intensity increment that impurity element forms the out-phase interface; The reinforcement weight of the phase structure unit that the impurity element that calculates is formed and impurity element form interface enhancing coefficient substitution formula (37) with phase interface and calculate impurity element and form the interface enhancing intensity increment with phase interface.C with aforementioned calculation α p Ti, C β Ti, C α s Ti = 0 And the tensile strength of titanium alloy when respectively strengthening intensity increment substitution formula (38) and calculating alpha+beta phase region solution treatment+shrend.
4. the primary that calculates is separated out the state of atom group that back β possibly exist in the interface enhancing coefficient, phase structure unit in the table 2 of reinforcement weight, solution strengthening coefficient and phase interface of each phase structure unit in mutually mutually and count σ N, the state of atom group that possibly exist on the phase interface in the table 3-table 4 count σ respectively substitution formula (39-41) calculate each phase structure unit and phase interface length growth rate reduction amount in the β phase solid solution; The state of atom group that the primary that calculates possibly exist in the interface enhancing coefficient, phase structure unit in the table 5 of reinforcement weight, solution strengthening coefficient and phase interface of each phase structure unit in is mutually counted σ N, the state of atom group that possibly exist on the phase interface in the table 6-table 7 count σ respectively substitution formula (42-45) calculate the length growth rate reduction amount of primary phase structure unit and phase interface; The state of atom group that possibly exist in the phase structure unit of impurity element in the reinforcement weight of the phase structure unit that the impurity element that calculates is formed, solution strengthening coefficient, interface enhancing coefficient, the table 5 is counted σ N, the state of atom group that possibly exist on the phase interface of impurity element in the table 6-table 7 count σ respectively substitution formula (49-51) calculate the length growth rate reduction amount that impurity element forms phase structure unit and phase interface; The length growth rate of titanium alloy when utilizing formula (52) to calculate alpha+beta phase region solution treatment+shrend at last.
Computing formula (1)～formula (52) is compiled into software for calculation; Carry out after the heat-treat condition of the alloying component of the choosing of input examination on computers and the solution treatment+shrend of selection alpha+beta phase region and calculate; Through observing the change amount of alloying element tensile strength, length growth rate under Different Heat Treatment Conditions; Adjust relative error that alloy composition makes design tensile strength of alloys, elongation values and technical requirement value repeatedly within 10%, the chemical constitution of titanium alloy in the time of so just can having confirmed alpha+beta phase region solution treatment+shrend.Be not more than under 10% the precondition satisfying relative error; Can carry out 5-10 time adjustment alloy composition on computers, and the optimal design composition of titanium alloy when getting the relative error of calculated value and technical requirement value of tensile strength, length growth rate hour pairing alloying component is as alpha+beta phase region solution treatment+shrend.
In order to verify the reliability of formula, table 10 has provided the contrast of existing β-21, Ti-B20, TC21 titanium alloy calculated value and experiment value when alpha+beta phase region solution treatment+shrend, and the relative error of the two is all within 10%.See that from result of calculation the theoretical model of quantitative design has higher reliability.
The contrast of calculated value and experiment value during table 10 alpha+beta phase region solution treatment+shrend
Figure G2009102489435D00321
Annotate: the composition of alloy is identical with table 9; Ti-B20 alloy error is by mean value calculation
Instance 3
The quantitative design of titanium alloy component during solution treatment+timeliness.Titanium alloy is organized as matrix β phase+primary phase+secondary α phase after solution treatment+timeliness.The practical implementation process is following:
1. utilize " solid and molecule experience electron theory " calculate β mutually, primary phase, the middle mutually phase structure unit of secondary α and phase interface electronic structure parameter n A', σ N, Δ ρ ', Δ ρ Max, σ, and set up database like table 1～table 8.
2. utilize in the atomic percentage, table 1 of alloy composition the phase structure unit in the statistical value n of shared electron logarithm on the strong covalent bond A' and formula (1) calculate β mutually in the reinforcement weight of each phase structure unit; Utilize the atomic percentage of impurity element and the reinforcement weight that formula (2) calculates impurity element phase structure unit; Utilize formula (3) calculate primary mutually in the reinforcement weight of each phase structure unit, utilize formula (4) calculate primary separate out mutually back β mutually in the reinforcement weight of each phase structure unit; Utilize formula (5) to calculate the weight of the middle mutually α of primary-Ti structural unit, utilize formula (6) to calculate the primary atomic percentage C of middle Ti mutually α p TiUtilize formula (8) calculate secondary α mutually in the reinforcement weight of each phase structure unit; Utilize formula (9) to calculate secondary α and separate out the back β reinforcement weight of middle phase structure unit mutually mutually; Utilize formula (10) to calculate the weight of the middle mutually α of secondary α-Ti phase structure unit, utilize formula (11) to calculate the middle mutually Ti atomic percentage C of secondary α α s Ti, utilize formula (12) to calculate secondary α and separate out the middle mutually Ti atomic percentage C of back β mutually β Ti
Utilize table 2 and formula (13) calculate β mutually in the solution strengthening coefficient of each phase structure unit; Utilize table 3 and formula (14) to calculate the β interface enhancing coefficient at middle out-phase interface mutually; Utilize table 4 and formula (15) calculate β mutually in the interface enhancing coefficient of phase interface; Utilize table 5 and formula (16) to calculate primary, the secondary α solution strengthening coefficient of middle phase structure unit mutually; Utilize table 6 and formula (17) to calculate the interface enhancing coefficient at out-phase interface in the primary; Utilize in table 7 and formula (18) primary with the interface enhancing coefficient of phase interface, utilize table 8 and formula (19) primary and β to form the interface enhancing coefficient of phase interface mutually, utilize table 7 and formula (20) calculate secondary α mutually in the interface enhancing coefficient of phase interface; Utilize table 8 and formula (21) to calculate the interface enhancing coefficient that secondary α and parent phase β form the out-phase interface, calculating utilizes in α-Ti-O in the table 5, α-Ti-N, the α-Ti-C phase structure unit statistical value n of the shared electron logarithm on the strong covalent bond A' reach formula (22) to calculate the solution strengthening coefficient that impurity element forms the phase structure unit; Utilize the statistical value Δ ρ ' and the formula (23) of the interface electron density difference of α in the table 6-Ti-O/ α-Ti, α-Ti-N/ α-Ti, α-Ti-C/ α-Ti phase interface to calculate the interface enhancing coefficient that impurity element forms the out-phase interface, utilize the statistical value Δ ρ ' and formula (24) the calculating impurity element of the interface electron density difference of α in the table 7-Ti-O/ α-Ti-O, α-Ti-N/ α-Ti-N, α-Ti-C/ α-Ti-C phase interface to form interface enhancing coefficient with phase interface.
The secondary α that 3. will calculate separate out mutually back β mutually in the reinforcement weight, solution strengthening coefficient substitution formula (25) of phase structure unit calculate β mutually in the solution strengthening intensity increment of each phase structure unit; With the secondary α that calculates separate out mutually back β mutually in the phase structure unit reinforcement weight, β mutually in the interface enhancing coefficient substitution formula (26) at out-phase interface calculate β mutually in the interface enhancing intensity increment at out-phase interface; With the secondary α that calculates separate out mutually back β mutually in the phase structure unit reinforcement weight, β mutually in the interface enhancing coefficient substitution formula (27) of phase interface calculate β mutually in the interface enhancing intensity increment of phase interface; With the primary that calculates mutually in solution strengthening weight, the solution strengthening coefficient substitution formula (28) of phase structure unit calculate primary mutually in the solution strengthening intensity increment of each phase structure unit; With the primary that calculates mutually in the phase structure unit solution strengthening weight, primary mutually in the interface enhancing coefficient substitution formula (29) at out-phase interface calculate primary mutually in the interface enhancing intensity increment at out-phase interface; With the primary that calculates mutually in the phase structure unit solution strengthening weight, primary mutually in the interface enhancing coefficient substitution formula (30) of phase interface calculate primary mutually in the interface enhancing intensity increment of phase interface; With the primary that calculates mutually in the interface enhancing intensity increment at the out-phase interface that forms mutually of interface enhancing coefficient substitution formula (31) calculating primary and the β at the out-phase interface that forms mutually of solution strengthening weight, primary and the β of phase structure unit; With the secondary α that calculates mutually in reinforcement weight, the solution strengthening coefficient substitution formula (32) of each phase structure unit calculate secondary α mutually in the solution strengthening intensity increment of each phase structure unit; With the secondary α that calculates mutually in each phase structure unit reinforcement weight, secondary α mutually in the interface enhancing coefficient substitution formula (33) of phase interface calculate secondary α mutually in the interface enhancing intensity increment of phase interface; With the secondary α that calculates mutually in reinforcement weight, secondary α and the parent phase β of each the phase structure unit interface enhancing coefficient substitution formula (34) that forms the out-phase interface calculate the interface enhancing intensity increment that secondary α and parent phase β form the out-phase interface, the reinforcement weight of the phase structure unit that the impurity element that calculates is formed and the solution strengthening intensity increment of solution strengthening coefficient substitution formula (35) calculating impurity element formation phase structure unit; The reinforcement weight of the phase structure unit that the impurity element that calculates is formed and the interface enhancing coefficient substitution formula (36) that impurity element forms the out-phase interface calculate the interface enhancing intensity increment that impurity element forms the out-phase interface; The reinforcement weight of the phase structure unit that the impurity element that calculates is formed and impurity element form interface enhancing coefficient substitution formula (37) with phase interface and calculate impurity element and form the interface enhancing intensity increment with phase interface.C with aforementioned calculation α p Ti, C β Ti, C α s TiAnd the tensile strength of titanium alloy when respectively strengthening intensity increment substitution formula (38) and calculating solution treatment+timeliness.
The secondary α that 4. will calculate separates out the state of atom group that back β possibly exist in the interface enhancing coefficient, the phase structure unit in the table 2 of reinforcement weight, solution strengthening coefficient and phase interface of phase structure unit in mutually mutually and counts σ N, the state of atom group that possibly exist on the phase interface in the table 3-table 4 count σ respectively substitution formula (39-41) calculate each phase structure unit and phase interface length growth rate reduction amount in the β phase solid solution; The state of atom group that the primary that calculates possibly exist in the interface enhancing coefficient, phase structure unit in the table 5 of reinforcement weight, solution strengthening coefficient and phase interface of each phase structure unit in is mutually counted σ N, the state of atom group that possibly exist on the phase interface in the table 6-table 7 count σ respectively substitution formula (42-45) calculate the length growth rate reduction amount of primary phase structure unit and phase interface; The state of atom group that the secondary α that calculates possibly exist in the interface enhancing coefficient, phase structure unit in the table 5 of reinforcement weight, solution strengthening coefficient and phase interface of each phase structure unit in is mutually counted σ N, the state of atom group that possibly exist on the phase interface in the table 6-table 7 count σ respectively substitution formula (46-48) calculate secondary α mutually in the length growth rate reduction amount of phase structure unit and phase interface, the state of atom group that possibly exist in the phase structure unit of impurity element in the reinforcement weight of the phase structure unit that the impurity element that calculates is formed, solution strengthening coefficient, interface enhancing coefficient, the table 5 is counted σ N, the state of atom group that possibly exist on the phase interface of impurity element in the table 6-table 7 count σ respectively substitution formula (49-51) calculate the length growth rate reduction amount that impurity element forms phase structure unit and phase interface; The length growth rate of titanium alloy when utilizing formula (52) to calculate solution treatment+timeliness at last.
Computing formula (1)～formula (52) is compiled into software for calculation; Carry out after the alloying component of the choosing of input examination on computers and the heat-treat condition of selection solution treatment+timeliness and calculate; Through observing the change amount of alloying element tensile strength, length growth rate under Different Heat Treatment Conditions; Adjust relative error that alloy composition makes design tensile strength of alloys, elongation values and technical requirement value repeatedly within 10%, the chemical constitution of titanium alloy in the time of so just can having confirmed solution treatment+timeliness.Be not more than under 10% the precondition satisfying relative error; Can carry out 5-10 time adjustment alloy composition on computers, and the optimal design composition of titanium alloy when getting the relative error of calculated value and technical requirement value of tensile strength, length growth rate hour pairing alloying component being done solution treatment+timeliness.
In order to verify the reliability of formula, table 11～table 13 has provided the contrast of existing β-21, Ti-B20, TC21 titanium alloy calculated value and experiment value when solution treatment+timeliness.See that from result of calculation except that the relative error of indivedual length growth rates exceeds 10%, calculated value and experiment test value meet also fine.Show that through existing alloy checking theoretical calculation model of the present invention has higher reliability, can carry out the quantitative design of titanium alloy component.
The contrast of calculated value and experiment value during table 11 β-21 bar solid solution aging
Figure G2009102489435D00361
Annotate: the composition of alloy is identical with table 9
The contrast of table 12 Ti-B20 calculated value and experiment value when solid solution aging
Annotate: the composition of alloy is identical with table 9
The contrast of table 13 TC21 alloy theory calculated value and experiment value
Figure G2009102489435D00363
Figure G2009102489435D00371
Annotate: alloy composition (wt%): 1# is Al=6.1, Sn=2.05, Zr=1.60, Mo=2.65, Cr=1.50, Nb=1.85, Si=0.07, Fe=0.07, C=0.01, N=0.02, H=0.001, O=0.10; 2# is Al=5.5, Sn=2.0, Zr=1.65, Mo=3.1, Cr=1.60, Nb=1.95, Si=0.03, Fe=0.09, C=0.02, N=0.017, H=0.001, O=0.10; 3# is Al=6.25, Sn=2.05, Zr=1.70, Mo=2.59, Cr=1.60, Nb=1.98, Si=0.13, Fe=0.03, C=0.03, N=0.014, H=0.001, O=0.090.

Claims (2)

1. titanium alloy component quantifying design method is characterized in that:
Calculate phase structure unit and phase interface electronic structure parameter n ' in the titanium alloy 1.1 utilize " solid and molecule experience electron theory " A, σ N, Δ ρ ', Δ ρ Max, σ, wherein n ' ABe to characterize interatomic bond make a concerted effort in the phase structure unit of size statistical value, the σ of the shared electron logarithm on the strong covalent bond NBe the state of atom group number that possibly exist in the phase structure unit, assembly average, the Δ ρ of electron density difference that Δ ρ ' is phase interface MaxMaximal value, the σ that is the electron density difference of phase interface is the state of atom group number that possibly exist in the phase interface, and sets up the database like table 1～table 8;
During 900 ℃ in table 1 β mutually in the electronic structure parameter of phase structure unit
The phase structure unit n′ A The phase structure unit n′ A β-Ti 0.28626 β-Ti-Al 0.2640 β-Ti-Al* 0.25094 β-Ti-Zr 0.3098 β-Ti-Zr-Al 0.28808 β-Ti-Sn 0.31022 β-Ti-Sn-Al 0.28877 β-Ti-Mo 0.32364 β-Ti-Mo-Al 0.30370 β-Ti-V 0.30213 β-Ti-V-Al 0.30351 β-Ti-Nb 0.32011 β-Ti-Nb-Al 0.29655 β-Ti-Fe 0.29870 β-Ti-Fe-Al 0.26655 β-Ti-Cr 0.29088 β-Ti-Cr-Al 0.26905 β-Ti-Mn 0.32738 β-Ti-Mn-Al 0.28578 β-Ti-Hf 0.30708 β-Ti-Hf-Al 0.28437 β-Ti-Co 0.32458 β-Ti-Co-Al 0.29295 β-Ti-Si 0.29232 β-Ti-Si-Al 0.26637 β-Ti-Cu 0.31789 β-Ti-Cu-Al 0.29298 β-Ti-Ni 0.34389 β-Ti-Ni-Al 0.31127 β-Ti-W 0.29826 β-Ti-W-Al 0.27736
Annotate: " * " represents Al element wt percentage more than or equal to 6%; Down together;
During 25 ℃ in table 2 β mutually in the electronic structure parameter of structural unit
The phase structure unit n′ A σ N The phase structure unit n′ A σ N β-Ti 0.29889 2 β-Ti-Al 0.27321 13 β-Ti-Al* 0.24761 22 β-Ti-Zr 0.31605 44 β-Ti-Zr-Al 0.29209 361 β-Ti-Sn 0.32279 15 β-Ti-Sn-Al 0.29731 128 β-Ti-Mo 0.33544 41 β-Ti-Mo-Al 0.27904 309 β-Ti-V 0.30768 55 β-Ti-V-Al 0.31071 487 β-Ti-Nb 0.33326 44 β-Ti-Nb-Al 0.30050 587 β-Ti-Fe 0.3026 69 β-Ti-Fe-Al 0.27305 457 β-Ti-Cr 0.29556 50 β-Ti-Cr-Al 0.27236 551 β-Ti-Mn 0.33147 78 β-Ti-Mn-Al 0.29378 477 β-Ti-Hf 0.31238 41 β-Ti-Hf-Al 0.28914 380 β-Ti-Co 0.32893 71 β-Ti-Co-Al 0.30317 544 β-Ti-Si 0.28859 17 β-Ti-Si-Al 0.30084 690 β-Ti-Cu 0.32317 54 β-Ti-Cu-Al 0.27341 159 β-Ti-Ni 0.34503 56 β-Ti-Ni-Al 0.32378 698 β-Ti-W 0.30752 28 β-Ti-W-Al 0.28209 339
The electronic structure parameter of β-Ti-M/ β-Ti phase interface during 25 ℃ in table 3
Phase interface Δρ′ σ Phase interface Δρ′ σ β-Ti-Al/β-Ti 9.56 26 β-Ti-Al/β-Ti* 19.7 44 β-Ti-Zr/β-Ti 5.56 88 β-Ti-Zr-Al/β-Ti 6.08 722 β-Ti-Sn/β-Ti 7.79 30 β-Ti-Sn-Al/β-Ti 6.98 256 β-Ti-Mo/β-Ti 6.06 68 β-Ti-Mo-Al/β-Ti 9.57 618 β-Ti-V/β-Ti 3.49 110 β-Ti-V-Al/β-Ti 6.90 984 β-Ti-Nb/β-Ti 8.54 92 β-Ti-Nb-Al/β-Ti 6.45 1174 β-Ti-Fe/β-Ti 4.81 138 β-Ti-Fe-Al/β-Ti 9.74 914 β-Ti-Cr/β-Ti 2.61 100 β-Ti-Cr-Al/β-Ti 9.67 1102 β-Ti-Mn/β-Ti 10.2 156 β-Ti-Mn-Al/β-Ti 5.79 954 β-Ti-Hf/β-Ti 4.47 82 β-Ti-Hf-Al/β-Ti 6.39 760 β-Ti-Co/β-Ti 9.45 142 β-Ti-Co-Al/β-Ti 5.59 1088 β-Ti-Si/β-Ti 5.17 34 β-Ti-Si-Al/β-Ti 10.1 318 β-Ti-Cu/β-Ti 7.67 108 β-Ti-Cu-Al/β-Ti 6.11 1380 β-Ti-Ni/β-Ti 14.3 112 β-Ti-Ni-Al/β-Ti 8.70 1396 β-Ti-W/β-Ti 4.17 56 β-Ti-W-Al/β-Ti 8.41 678
The electronic structure parameter of β-Ti-Al (Al-M)/β-Ti-Al (Al-M) phase interface during 25 ℃ in table 4
Phase interface Δρ′ σ Phase interface Δρ′ σ β-Ti-Al/β-Ti-Al 7.56 91 β-Ti-Al/β-Ti-Al* 15.91 143 β-Ti-Zr/β-Ti-Zr 2.71 990 β-Ti-Zr-Al/β-Ti-Zr-Al 7.61 65341 β-Ti-Sn/β-Ti-Sn 5.34 120 β-Ti-Sn-Al/β-Ti-Sn-Al 9.68 8260 β-Ti-Mo/β-Ti-Mo 4.05 1021 β-Ti-Mo-Al/β-Ti-Mo-Al 10.8 48403 β-Ti-V/β-Ti-V 2.73 1275 β-Ti-V-Al/β-Ti-V-Al 8.25 121278 β-Ti-Nb/β-Ti-Nb 2.90 1081 β-Ti-Nb-Al/β-Ti-Nb-Al/ 8.08 172578 β-Ti-Fe/β-Ti-Fe 6.16 2415 β-Ti-Fe-Al/β-Ti-Fe-Al 8.08 104653 β-Ti-Cr/β-Ti-Cr 3.15 1275 β-Ti-Cr-Al/β-Ti-Cr-Al 8.34 152076 β-Ti-Mn/β-Ti-Mn 6.01 3081 β-Ti-Mn-Al/β-Ti-Mn-Al 7.70 114003 β-Ti-Hf/β-Ti-Hf 2.67 861 β-Ti-Hf-Al/β-Ti-Hf-Al 7.80 72390 β-Ti-Co/β-Ti-Co 5.72 2556 β-Ti-Co-Al/β-Ti-Co-Al 7.69 148240 β-Ti-Si/β-Ti-Si 5.86 153 β-Ti-Si-Al/β-Ti-Si-Al 10.4 12723 β-Ti-Cu/β-Ti-Cu 6.27 1485 β-Ti-Cu-Al/β-Ti-Cu-Al 8.87 238402 β-Ti-Ni/β-Ti-Ni 4.16 1596 β-Ti-Ni-Al/β-Ti-Ni-Al 8.18 243958 β-Ti-W/β-Ti-W 4.69 464 β-Ti-W-Al/β-Ti-W-Al 10.1 58284
During 25 ℃ in table 5 α mutually in the electronic structure parameter of phase structure unit
The phase structure unit n′ A σ N The phase structure unit n′ A σ N α-Ti 0.24902 2 α-Ti-Al 0.23685 14 α-Ti-Zr-Al 0.25051 292 α-Ti-Zr 0.2631 39 α-Ti-Sn-Al 0.25318 88 α-Ti-Sn 0.26739 11 α-Ti-Mo-Al 0.261 275 α-Ti-Mo 0.27184 33 α-Ti-V-Al 0.26025 298 α-Ti-V 0.27330 43 α-Ti-Nb-Al 0.2601 282 α-Ti-Nb 0.27293 36 α-Ti-Fe-Al 0.24349 330 α-Ti-Fe 0.25488 40 α-Ti-Cr-Al 0.2408 288 α-Ti-Cr 0.25308 32 α-Ti-Mn-Al 0.25719 357 α-Ti-Mn 0.26948 41 α-Ti-Hf-Al 0.24976 276 α-Ti-Hf 0.26095 34 α-Ti-Co-Al 0.25789 321 α-Ti-Co 0.26939 48 α-Ti-Si-Al 0.23554 101 α-Ti-Si 0.25163 15 α-Ti-Cu-Al 0.25261 318 α-Ti-Cu 0.26576 35 α-Ti-Ni-Al 0.26616 322 α-Ti-Ni 0.27959 37 α-Ti-W-Al 0.24623 161 α-Ti-W 0.26019 20 α-Ti-O 0.62095 8 α-Ti-N 0.74635 8 α-Ti-C 0.70486 10
The electronic structure parameter of α-Ti-Al (Al-M)/α-Ti phase interface during 25 ℃ in table 6
Phase interface Δρ′ σ Phase interface Δρ′ σ α-Ti-Al/α-Ti 5.78 28 α-Ti-Zr-Al/α-Ti 3.97 584 α-Ti-Zr/α-Ti 5.46 78 α-Ti-Sn-Al/α-Ti 5.18 176 α-Ti-Sn/α-Ti 7.05 22 α-Ti-Mo-Al/α-Ti 5.59 332 α-Ti-Mo/α-Ti 4.68 46 α-Ti-V-Al/α-Ti 4.04 588 α-Ti-V/α-Ti 4.13 84 α-Ti-Nb-Al/α-Ti 5.34 564 α-Ti-Nb/α-Ti 9.13 72 α-Ti-Fe-Al/α-Ti 4.44 660 α-Ti-Fe/α-Ti 3.44 80 α-Ti-Cr-Al/α-Ti 13.0 576 α-Ti-Cr/α-Ti 5.46 64 α-Ti-Mn-Al/α-Ti 4.49 606 α-Ti-Mn/α-Ti 2.94 86 α-Ti-Hf-Al/α-Ti 3.94 552 α-Ti-Hf/α-Ti 4.65 68 α-Ti-Co-Al/α-Ti 5.16 642 α-Ti-Co/α-Ti 7.80 96 α-Ti-Si-Al/α-Ti 7.03 202 α-Ti-Si/α-Ti 4.25 30 α-Ti-Cu-Al/α-Ti 4.13 636 α-Ti-Cu/α-Ti 6.45 70 α-Ti-Ni-Al/α-Ti 6.84 644 α-Ti-Ni/α-Ti 11.5 74 α-Ti-W-Al/α-Ti 4.83 322 α-Ti-W/α-Ti 5.19 40 α-Ti-O/α-Ti 36.8 16 α-Ti-C/α-Ti 27.8 20 α-Ti-N/α-Ti 29.0 16
The electronic structure parameter of α-Ti-Al (Al-M)/α-Ti-Al (Al-M) phase interface during 25 ℃ in table 7
Phase interface Δρ′ Δρ max σ Phase interface Δρ′ Δρ max σ α-Ti-Al/α-Ti-Al 5.46 13.9 105 α-Ti-Zr-Al/α-Ti-Zr-Al 5.34 17.2 42778 α-Ti-Zr/α-Ti-Zr 2.99 7.80 780 α-Ti-Sn-Al/α-Ti-Sn-Al 6.74 23.6 3917 α-Ti-Sn/α-Ti-Sn 3.73 11.1 66 α-Ti-Mo-Al/α-Ti-Mo-Al 6.31 21.6 44850 α-Ti-Mo/α-Ti-Mo 4.23 13.1 703 α-Ti-V-Al/α-Ti-V-Al 5.51 20.9 43365 α-Ti-V/α-Ti-V 3.23 10.4 903 α-Ti-Nb-Al/α-Ti-Nb-Al 5.55 20.9 39903 α-Ti-Nb/α-Ti-Nb 2.81 9.98 666 α-Ti-Fe-Al/α-Ti-Fe-Al 5.70 23.3 54615 α-Ti-Fe/α-Ti-Fe 3.69 12.1 820 α-Ti-Cr-Al/α-Ti-Cr-Al 5.06 17.4 41616 α-Ti-Cr/α-Ti-Cr 2.03 7.69 528 α-Ti-Mn-Al/α-Ti-Mn-Al 5.57 17.4 46056 α-Ti-Mn/α-Ti-Mn 2.54 8.30 946 α-Ti-Hf-Al/α-Ti-Hf-Al 5.27 17.1 38226 α-Ti-Hf/α-Ti-Hf 2.63 8.20 595 α-Ti-Co-Al/α-Ti-Co-Al 6.19 24.4 51681 α-Ti-Co/α-Ti-Co 3.94 15.1 1176 α-Ti-Si-Al/α-Ti-Si-Al 7.03 24.5 5154 α-Ti-Si/α-Ti-Si 4.95 13.1 120 α-Ti-Cu-Al/α-Ti-Cu-Al 5.85 23.2 50724 α-Ti-Cu/α-Ti-Cu 3.83 11.3 630 α-Ti-Ni-Al/α-Ti-Ni-Al 5.40 19.6 52006 α-Ti-Ni/α-Ti-Ni 3.20 10.7 703 α-Ti-W-Al/α-Ti-W-Al 6.42 26.5 13403 α-Ti-W/α-Ti-W 3.76 17.4 250 α-Ti-O/α-Ti-O 4.21 - 36 α-Ti-N/α-Ti-N 2.83 - 36 α-Ti-C/α-Ti-C 2.05 - 55
The electronic structure parameter of α-Ti-Al (Al-M)/β-Ti-Al (Al-M) phase interface during 25 ℃ in table 8
Phase interface Δρ′ Δρ max σ Phase interface Δρ′ Δρ max σ α-Ti/β-Ti 9.21 10.7 4 α-Ti-Al/β-Ti-Al 8.59 22.6 182 α-Ti-Al/β-Ti-Al* 14.1 31.6 308 α-Ti-Zr/β-Ti-Zr 9.3 16.9 1716 α-Ti-Zr-Al/β-Ti-Zr-Al 7.46 23.3 124100 α-Ti-Sn/β-Ti-Sn 10.0 22.9 165 α-Ti-Sn-Al/β-Ti-Sn-Al 9.40 32.3 10472 α-Ti-Mo/β-Ti-Mo 8.58 29.1 782 α-Ti-Mo-Al/β-Ti-Mo-Al 9.67 35.1 44156 α-Ti-V/β-Ti-V 8.15 19.5 2310 α-Ti-V-Al/β-Ti-V-Al 7.58 26.9 139650 α-Ti-Nb/β-Ti-Nb 10.9 22.3 1584 α-Ti-Nb-Al/β-Ti-Nb-Al 8.10 30.0 137052 α-Ti-Fe/β-Ti-Fe 8.57 23.4 2760 α-Ti-Fe-Al/β-Ti-Fe-Al 7.52 27.7 148830 α-Ti-Cr/β-Ti-Cr 6.48 15.1 1600 α-Ti-Cr-Al/β-Ti-Cr-Al 7.53 21.2 179136 α-Ti-Mn/β-Ti-Mn 11.8 26.0 3198 α-Ti-Mn-Al/β-Ti-Mn-Al 8.14 26.1 153510 α-Ti-Hf/β-Ti-Hf 8.94 17.3 1394 α-Ti-Hf-Al/β-Ti-Hf-Al 7.21 23.4 109848 α-Ti-Co/β-Ti-Co 11.0 26.6 3408 α-Ti-Co-Al/β-Ti-Co-Al 7.33 28.0 164673 α-Ti-Si/β-Ti-Si 7.05 19.5 255 α-Ti-Si-Al/β-Ti-Si-Al 9.42 33.6 19998 α-Ti-Cu/β-Ti-Cu 10.5 25.6 1890 α-Ti-Cu-Al/β-Ti-Cu-Al 8.87 31.0 219102 α-Ti-Ni/β-Ti-Ni 11.9 25.7 2072 α-Ti-Ni-Al/β-Ti-Ni-Al 8.57 28.4 201894 α-Ti-W/β-Ti-W 8.31 29.1 560 α-Ti-W-Al/β-Ti-W-Al 9.28 35.1 51198
1.2 calculate the reinforcement weight of each phase structure unit under the titanium alloy Different Heat Treatment Conditions and the interface enhancing coefficient of solution strengthening coefficient and phase interface;
At first utilize the atomic percentage of alloying component when calculating the reinforcement weight of each phase structure unit under the titanium alloy Different Heat Treatment Conditions and characterize make a concerted effort in the phase structure unit of the size statistical value n ' of the shared electron logarithm on the strong covalent bond of atomic link ACalculate titanium alloy forms each phase structure unit in the single β phase solid solution after the solution treatment+shrend of β phase region reinforcement weight;
Utilize the β phase conditional stability COEFFICIENT K in the titanium alloy β,
Figure FSB00000689113100051
Calculating from β separate out mutually primary mutually in the reinforcement weight of each phase structure unit;
Utilize β phase conditional stability COEFFICIENT K in the titanium alloy ' β,
Figure FSB00000689113100052
And
Figure FSB00000689113100053
Calculating from β separate out mutually secondary α mutually in the reinforcement weight of each phase structure unit,
The mathematical model of weight calculation is strengthened in each phase structure unit of titanium alloy:
β mutually in the reinforcement weight of each phase structure unit:
Figure FSB00000689113100061
In the following formula x Al = n A ′ β - Ti - Al n A ′ β - Ti - Al + Σ i = 1 z n A ′ β - Ti - Al - M i , y Al = C Al C Al + Σ i = 1 z C M i
x i = n A ′ β - Ti - Al - M i n A ′ β - Ti - Al + Σ i = 1 z n A ′ β - Ti - Al - M i , y i = C M i C Al + Σ i = 1 z C M i
W wherein β-Ti-Al, W β-Ti-Al-M, W β-Ti-MReinforcement weight for β-Ti-Al, β-Ti-Al-M, β-Ti-M phase structure unit; C AlAtomic percentage for Al; C MFor not comprising the alloy atom percentage of Al element; Z is the alloying element species number, and i representes the sequence number of alloying element M;
The reinforcement weight of the phase structure unit that impurity element forms:
W α - Ti - O = C ′ O × 100 % W α - Ti - N = C ′ N × 100 % W α - Ti - C = C ′ C × 100 % . . . ( 2 )
W wherein α-Ti-O, W α-Ti-N, W α-Ti-CThe solution strengthening weight of the α-Ti-O that forms for impurity element O, N, C, α-Ti-N, α-Ti-C phase structure unit; C ' O, C ' N, C ' CThe nominal atomic percentage of representing O, N, C has respectively promptly deducted the content of corresponding impurity in the iodide-process titanium, and corresponding impurity content is got middle limit in the iodide-process titanium;
Primary mutually in the reinforcement weight of each phase structure unit:
W p α - Ti - Al = K C β - K β K C β - K C α W β - Ti - Al W p α - Ti - Al - M = K C β - K β K C β - K C α W β - Ti - Al - M W p α - Ti - M = K C β - K β K C β - K C α W β - Ti - M K C β > K β . . . ( 3 )
Wherein
Figure FSB00000689113100072
Reinforcement weight for α-Ti-Al, α-Ti-Al-M, α-Ti-M phase structure unit in the primary phase solid solution; K ββ phase conditional stability coefficient in the expression titanium alloy, promptly
Figure FSB00000689113100073
Figure FSB00000689113100074
Be illustrated in β under a certain solid solubility temperature → α and change the corresponding K of alloy β when beginning β MoValue, K β MoBe β phase conditional stability coefficient in the Ti-Mo bianry alloy,
Figure FSB00000689113100075
Rising with solid solubility temperature reduces gradually, and value is 0.3～2.3;
Figure FSB00000689113100076
Be illustrated in β under a certain solid solubility temperature → α and change the corresponding K of alloy β when stopping β MoValue,
Figure FSB00000689113100077
Less with the solid solubility temperature variation, value is 0.07;
Primary is separated out the reinforcement weight of the middle mutually β-Ti-Al of back β, β-Ti-Al-M, β-Ti-M phase structure unit mutually W p β - Ti - Al , W p β - Ti - Al - M , W p β - Ti - M For
W p β - Ti - Al = W β - Ti - Al - W p α - Ti - Al W p β - Ti - Al - M = W β - Ti - Al - M - W p α - Ti - Al - M W p β - Ti - M = W β - Ti - M - W p α - Ti - M . . . ( 4 )
The weight
Figure FSB000006891131000710
of the middle mutually α of primary-Ti phase structure unit does
The primary atomic fraction
Figure FSB00000689113100081
of middle Ti mutually does
C αp Ti = ( 4 Σ W p α - Ti - Al - M + 5 W p α - Ti - Al + 5 Σ W p α - Ti - M + 6 ( W α - Ti - O + W α - Ti - N + W α - Ti - C ) ) / 100 + 6 W p α - Ti . . . ( 6 )
Primary is separated out the back mutually and is not had secondary α when separating out, and the β atomic fraction
Figure FSB00000689113100083
of middle Ti mutually does
C β Ti = C Ti - C αp Ti . . . ( 7 )
Secondary α mutually in the reinforcement weight of each phase structure unit:
W s α - Ti - Al = K C β ′ - K β ′ K C β ′ - K C α ′ W p β - Ti - Al W s α - Ti - Al - M = K C β ′ - K β ′ K C β ′ - K C α ′ W p β - Ti - Al - M W s α - Ti - M = K C β ′ - K β ′ K C β ′ - K C α ′ W p β - Ti - M K C β ′ > K β ′ . . . ( 8 )
Wherein
Figure FSB00000689113100086
Reinforcement weight for secondary α-Ti-Al, α-Ti-Al-M, α-Ti-M phase structure unit; K ' βFor primary is separated out β phase conditional stability coefficient in the titanium alloy of back mutually, with primary separate out back β mutually in the atomic percentage of alloying element be converted into percent by weight, press K then βComputing formula is calculated and is got final product;
Figure FSB00000689113100087
Be illustrated in β under a certain aging temp → α and change the corresponding K of alloy β when beginning β MoValue,
Figure FSB00000689113100088
Rising with the timeliness temperature reduces gradually, and value is 0.5～2.8;
Figure FSB00000689113100089
Be illustrated in β under a certain aging temp → α and change the corresponding K of alloy β when stopping β MoValue,
Figure FSB000006891131000810
Less with the timeliness temperature variation, value is 0.07;
Secondary α separates out the reinforcement weight of the middle mutually β-Ti-Al of back β, β-Ti-Al-M, β-Ti-M phase structure unit mutually W s β - Ti - Al , W s β - Ti - Al - M , W s β - Ti - M For
W s β - Ti - Al = W p β - Ti - Al - W s α - Ti - Al W s β - Ti - Al - M = W p β - Ti - Al - M - W s α - Ti - Al - M W s β - Ti - M = W p β - Ti - M - W s α - Ti - M . . . ( 9 )
The weight of the middle mutually α of secondary α-Ti phase structure unit:
Figure FSB00000689113100091
The middle mutually Ti atomic percentage
Figure FSB00000689113100092
of secondary α does
C αs Ti = ( 4 Σ W s α - Ti - Al - M + 5 W s α - Ti - Al + 5 Σ W s α - Ti - M ) / 100 + 6 W s α - Ti . . . ( 11 )
Secondary α separates out the middle mutually Ti atomic percentage of back β mutually:
C β Ti = C Ti - C αp Ti - C αs Ti . . . ( 12 )
When calculating the interface enhancing coefficient of solution strengthening coefficient and phase interface of phase structure unit in the titanium alloy, at first utilize to characterize make a concerted effort in the phase structure unit of the size statistical value n ' of the shared electron logarithm on the strong covalent bond of interatomic bond ACharacterize β phase, primary phase, secondary α mutually in the solution strengthening coefficient of each phase structure unit; Use the interface electron density difference Δ ρ ', the Δ ρ that are complementary with interfacial stress MaxCharacterize β phase, primary phase, secondary α mutually in the interface enhancing coefficient of each phase interface;
The mathematical model of solution strengthening coefficient and interface enhancing coefficient calculations in the titanium alloy:
β mutually in the solution strengthening coefficient of each phase structure unit:
S β - Ti - Al = n A ′ β - Ti - Al / n A ′ β - Ti S β - Ti - Al - M = n A ′ β - Ti - Al - M / n A ′ β - Ti S β - Ti - M = n A ′ β - Ti - M / n A ′ β - Ti . . . ( 13 )
S wherein β-Ti-Al, S β-Ti-Al-M, S β-Ti-MThe solution strengthening coefficient of representing β-Ti-Al, β-Ti-Al-M, β-Ti-M phase structure unit respectively;
Figure FSB00000689113100096
Be respectively the assembly average of the shared electron logarithm on β-Ti-Al, β-Ti-Al-M, β-Ti-M, the strong bond in β-Ti phase structure unit;
β is the interface enhancing coefficient at middle out-phase interface mutually:
S β - Ti - Al / β - Ti = Δρ ′ β - Ti - Al / β - Ti S β - Ti - Al - M / β - Ti = Δρ ′ β - Ti - Al - M / β - Ti S β - Ti - M / β - Ti = Δρ ′ β - Ti - M / β - Ti . . ( 14 )
S wherein β-Ti-Al/ β-Ti, S β-Ti-Al-M/ β-Ti, S β-Ti-M/ β-TiThe interface enhancing coefficient of expression phase interface β-Ti-Al/ β-Ti, β-Ti-Al-M/ β-Ti, β-Ti-M/ β-Ti; Δ ρ ' β-Ti-Al/ β-Ti, Δ ρ ' β-Ti-Al-M/ β-Ti, Δ ρ ' β-Ti-M/ β-TiBe respectively the assembly average of the electron density difference of β-Ti-Al/ β-Ti, β-Ti-Al-M/ β-Ti, β-Ti-M/ β-Ti phase interface;
β mutually in the interface enhancing coefficient of phase interface:
S β - Ti - Al / β - Ti - Al = Δρ ′ β - Ti - Al / β - Ti - Al S β - Ti - Al - M / β - Ti - Al - M = Δρ ′ β - Ti - Al - M / β - Ti - Al - M S β - Ti - M / β - Ti - M = Δρ ′ β - Ti - M / β - Ti - M . . ( 15 )
S wherein β-Ti-Al/ β-Ti-Al, S β-Ti-Al-M/ β-Ti-Al-M, S β-Ti-M/ β-Ti-MThe interface enhancing coefficient of expression phase interface β-Ti-Al/ β-Ti-Al, β-Ti-Al-M/ β-Ti-Al-M, β-Ti-M/ β-Ti-M; Δ ρ ' β-Ti-Al/ β-Ti-Al, Δ ρ ' β-Ti-Al-M/ β-Ti-Al-M, Δ ρ ' β-Ti-M/ β-Ti-MBe respectively the assembly average of β-Ti-Al/ β-Ti-Al, β-Ti-Al-M/ β-Ti-Al-M, β-Ti-M/ β-Ti-M phase interface electron density difference;
Primary phase, secondary α be the solution strengthening coefficient of middle phase structure unit mutually:
S α - Ti - Al = n A ′ α - Ti - Al / n A ′ α - Ti S α - Ti - Al - M = n A ′ α - Ti - Al - M / n A ′ α - Ti S α - Ti - M = n A ′ α - Ti - M / n A ′ α - Ti . . . ( 16 )
S wherein α-Ti-Al, S α-Ti-Al-M, S α-Ti-MThe solution strengthening coefficient of representing α-Ti-Al during primary, secondary α are mutually, α-Ti-Al-M, α-Ti-M respectively;
Figure FSB00000689113100104
Be respectively the assembly average of the shared electron logarithm on α-Ti-Al, α-Ti-Al-M, α-Ti-M, the strong bond in α-Ti phase structure unit;
Primary is the interface enhancing coefficient at middle out-phase interface mutually:
S α - Ti - Al / α - Ti = Δρ ′ α - Ti - Al / α - Ti S α - Ti - Al - M / α - Ti = Δρ ′ α - Ti - Al - M / α - Ti S α - Ti - M / α - Ti = Δρ ′ α - Ti - M / α - Ti . . ( 17 )
S wherein α-Ti-Al/ α-Ti, S α-Ti-Al-M/ α-Ti, S α-Ti-M/ α-TiThe interface enhancing coefficient of representing phase interface α-Ti-Al/ α-Ti during primary mutually, α-Ti-Al-M/ α-Ti, α-Ti-M/ α-Ti respectively; Δ ρ ' α-Ti-Al/ α-Ti, Δ ρ ' α-Ti-Al-M/ α-Ti, Δ ρ ' α-Ti-M/ α-TiThe assembly average of the interface electron density difference of expression α-Ti-Al/ α-Ti, α-Ti-Al-M/ α-Ti, α-Ti-M/ α-Ti phase interface;
Primary mutually in the interface enhancing coefficient of phase interface:
S α - Ti - Al / α - Ti - Al = Δρ ′ α - Ti - Al / α - Ti - Al S α - Ti - Al - M / α - Ti - Al - M = Δρ ′ α - Ti - Al - M / α - Ti - Al - M S α - Ti - M / α - Ti - M = Δρ ′ α - Ti - M / α - Ti - M . . ( 18 )
S wherein α-Ti-Al/ α-Ti-Al, S α-Ti-Al-M/ α-Ti-Al-M, S α-Ti-M/ α-Ti-MThe interface enhancing coefficient of representing α-Ti-Al/ α-Ti-Al during primary mutually, α-Ti-Al-M/ α-Ti-Al-M, α-Ti-M/ α-Ti-M phase interface respectively; Δ ρ ' α-Ti-Al/ α-Ti-Al, Δ ρ ' α-Ti-Al-M/ α-Ti-Al-M, Δ ρ ' α-Ti-M/ α-Ti-MThe assembly average of the interface electron density difference of expression α-Ti-Al/ α-Ti-Al, α-Ti-Al-M/ α-Ti-Al-M, α-Ti-M/ α-Ti-M phase interface;
Primary and β form the interface enhancing coefficient at out-phase interface mutually:
S α - Ti - Al / β - Ti - Al = Δρ ′ α - Ti - Al / β - Ti - Al S α - Ti - Al - M / β - Ti - Al - M = Δρ ′ α - Ti - Al - M / β - Ti - Al - M S α - Ti - M / β - Ti - M = Δρ ′ α - Ti - M / β - Ti - M S α - Ti / β - Ti = Δρ ′ - α - Ti / β - Ti . . . ( 19 )
S wherein α-Ti-Al/ β-Ti-Al, S α-Ti-Al-M/ β-Ti-Al-M, S α-Ti-M/ β-Ti-M, S α-Ti/ β-TiRepresent that respectively primary and β form the interface enhancing coefficient of out-phase interface α-Ti-Al/ β-Ti-Al, α-Ti-Al-M/ β-Ti-Al-M, α-Ti-M/ β-Ti-M, α-Ti/ β-Ti mutually; Δ ρ ' α-Ti-Al/ β-Ti-Al, Δ ρ ' α-Ti-Al-M/ β-Ti-Al-M, Δ ρ ' α-Ti-M/ β-Ti-M, Δ ρ ' α-Ti/ β-TiThe assembly average of the interface electron density difference of expression α-Ti-Al/ β-Ti-Al, α-Ti-Al-M/ β-Ti-Al-M, α-Ti-M/ β-Ti-M, α-Ti/ β-Ti phase interface;
Secondary α mutually in the interface enhancing coefficient of phase interface:
S s α - Ti - Al / α - Ti - Al = Δρ max α - Ti - Al / α - Ti - Al S s α - Ti - Al - M / α - Ti - Al - M = Δρ max α - Ti - Al - M / α - Ti - Al - M S s α - Ti - M / α - Ti - M = Δρ max α - Ti - M / α - Ti - M S s α - Ti / α - Ti = Δρ max α - Ti / α - Ti . . . ( 20 )
Wherein S s α - Ti - Al / α - Ti - Al , S s α - Ti - Al - M / α - Ti - Al - M , S s α - Ti - M / α - Ti - M , S s α - Ti / α - Ti The interface enhancing coefficient of representing α-Ti-Al/ α-Ti-Al in the secondary α phase solid solution, α-Ti-Al-M/ α-Ti-Al-M, α-Ti-M/ α-Ti-M phase interface respectively; Δ ρ Max α - Ti - Al / α - Ti - Al , Δ ρ Max α - Ti - Al - M / α - Ti - Al - M , Δ ρ Max α - Ti - M / α - Ti - M Be respectively the maximal value of the interface electron density difference of α-Ti-Al/ α-Ti-Al, α-Ti-Al-M/ α-Ti-Al-M, α-Ti-M/ α-Ti-M phase interface;
Secondary α and parent phase β form the interface enhancing coefficient at out-phase interface:
S s α - Ti - Al / β - Ti - Al = Δρ max α - Ti - Al / β - Ti - Al S s α - Ti - Al - M / β - Ti - Al - M = Δρ max α - Ti - Al - M / β - Ti - Al - M S s α - Ti - M / β - Ti - M = Δρ max α - Ti - M / β - Ti - M S s α - Ti / β - Ti = Δρ max α - Ti / β - Ti . . . ( 21 )
Wherein S s α - Ti - Al / β - Ti - Al , S s α - Ti - Al - M / β - Ti - Al - M , S s α - Ti - M / β - Ti - M , S s α - Ti / β - Ti Represent that respectively secondary α and parent phase β form the interface enhancing coefficient at out-phase interface; Δ ρ Max α - Ti - Al / β - Ti - Al , Δ ρ Max α - Ti - Al - M / β - Ti - Al - M , Δ ρ Max α - Ti - M / β - Ti - M , Δ ρ Max α - Ti / β - Ti The maximal value of the interface electron density difference of expression α-Ti-Al/ β-Ti-Al, α-Ti-Al-M/ β-Ti-Al-M, α-Ti-M/ β-Ti-M, α-Ti/ β-Ti phase interface;
Impurity element forms the solution strengthening coefficient of phase structure unit:
S α - Ti - O = n A ′ α - Ti - O / n A ′ α - Ti S α - Ti - N = n A ′ α - Ti - N / n A ′ α - Ti S α - Ti - C = n A ′ α - Ti - C / n A ′ α - Ti . . . ( 22 )
S wherein α-Ti-O, S α-Ti-N, S α-Ti-CRepresent impurity element O, N, C solution strengthening coefficient respectively in the α phase;
Figure FSB00000689113100131
Assembly average for shared electron logarithm on α-Ti-O, α-Ti-N, the strong covalent bond in α-Ti-C phase structure unit;
Impurity element forms the interface enhancing coefficient at out-phase interface:
S α - Ti - O / α - Ti = Δρ ′ α - Ti - O / α - Ti S α - Ti - N / α - Ti = Δρ ′ α - Ti - N / α - Ti S α - Ti - C / α - Ti = Δρ ′ α - Ti - C / α - Ti . . ( 23 )
S wherein α-Ti-O/ α-Ti, S α-Ti-N/ α-Ti, S α-Ti-C/ α-TiThe interface enhancing coefficient of representing α-Ti-O/ α-Ti, α-Ti-N/ α-Ti, α-Ti-C/ α-Ti phase interface respectively; Δ ρ ' α-Ti-O/ α-Ti, Δ ρ ' α-Ti-N/ α-Ti, Δ ρ ' α-Ti-C/ α-TiAssembly average for α-Ti-O/ α-Ti, α-Ti-N/ α-Ti, α-Ti-C/ α-Ti phase interface electron density difference;
Impurity element forms the interface enhancing coefficient with phase interface:
S α - Ti - O / α - Ti - O = Δρ ′ α - Ti - O / α - Ti - O S α - Ti - N / α - Ti - N = Δρ ′ α - Ti - N / α - Ti - N S α - Ti - C / α - Ti - C = Δρ ′ α - Ti - C / α - Ti - C . . ( 24 )
S wherein α-Ti-O/ α-Ti-O, S α-Ti-N/ α-Ti-N, S α-Ti-C/ α-Ti-CThe interface enhancing coefficient of representing α-Ti-O/ α-Ti-O, α-Ti-N/ α-Ti-N, α-Ti-C/ α-Ti-C phase interface respectively; Δ ρ ' α-Ti-Al/ α-Ti-O, Δ ρ ' α-Ti-N/ α-Ti-N, Δ ρ ' α-Ti-C/ α-Ti-CAssembly average for α-Ti-O/ α-Ti-O, α-Ti-N/ α-Ti-N, α-Ti-C/ α-Ti-C phase interface electron density difference;
1.3 calculate titanium alloy tensile strength; Intensity with matrix α-Ti, β-Ti is base value, utilizes coefficient of intensification, strengthens the titanium alloy tensile strength increment under the weight calculation Different Heat Treatment Conditions, with the titanium alloy tensile strength increment summation that calculates; Draw the titanium alloy tensile strength values
The mathematical model of titanium alloy calculation of Tensile Strength:
β mutually in the solution strengthening intensity increment of each phase structure unit:
Δσ b β - Ti - Al = σ b β - Ti · | S β - Ti - Al - 1 | · W β - Ti - Al Δσ b β - Ti - Al - M = σ b β - Ti · | S β - Ti - Al - M - 1 | · W β - Ti - Al - M Δσ b β - Ti - M = σ b β - Ti · | S β - Ti - M - 1 | · W β - Ti - M . . . ( 25 )
Wherein
Figure FSB00000689113100141
The solution strengthening intensity increment of β-Ti-Al, β-Ti-Al-M, β-Ti-M phase structure unit in the expression β phase solid solution; Be the tensile strength values of matrix β-Ti, σ b β - Ti = 200 Mpa ;
β is the interface enhancing intensity increment at middle out-phase interface mutually:
Δσ b β - Ti - Al / β - Ti = ( σ b β - Ti + Δσ b β - Ti - Al ) · S β - Ti - Al / β - Ti · W β - Ti - Al Δσ b β - Ti - Al - M / β - Ti = ( σ b β - Ti + Δσ b β - Ti - Al - M ) · S β - Ti - Al - M / β - Ti · W β - Ti - Al - M Δσ b β - Ti - M / β - Ti = σ b β - Ti · S β - Ti - M / β - Ti · W β - Ti - M . . . ( 26 )
Wherein Δ σ b β - Ti - Al / β - Ti , Δ σ b β - Ti - Al - M / β - Ti , Δ σ b β - Ti - M / β - Ti The reinforcement intensity increment of β-Ti-Al/ β-Ti, β-Ti-Al-M/ β-Ti, β-Ti-M/ β-Ti phase interface in the expression β phase solid solution;
β mutually in the interface enhancing intensity increment of phase interface:
Δσ b β - Ti - Al / β - Ti - Al = ( σ b β - Ti + Δσ b β - Ti - Al ) · S β - Ti - Al / β - Ti - Al · W β - Ti - Al Δσ b β - Ti - Al - M / β - Ti - Al - M = ( σ b β - Ti + Δσ b β - Ti - Al - M ) · S β - Ti - Al - M / β - Ti - Al - M · W β - Ti - Al - M Δσ b β - Ti - M / β - Ti - M = σ b β - Ti · S β - Ti - M / β - Ti - M · W β - Ti - M . . . ( 27 )
Wherein Δ σ b β - Ti - Al / β - Ti - Al , Δ σ b β - Ti - Al - M / β - Ti - Al - M , Δ σ b β - Ti - M / β - Ti - M β-Ti-Al/ β-Ti-Al in the expression β phase solid solution, β-Ti-Al-M/ β-Ti-Al-M, β-Ti-M/ β-Ti-M are with the reinforcement intensity increment of phase interface;
Primary mutually in the solution strengthening intensity increment of each phase structure unit:
Δσ bp α - Ti - Al = σ b α - Ti · | S α - Ti - Al - 1 | · W p α - Ti - Al Δσ bp α - Ti - Al - M = σ b α - Ti · | S α - Ti - Al - M - 1 | · W p α - Ti - Al - M Δσ bp α - Ti - M = σ b α - Ti · | S α - Ti - M - 1 | · W p α - Ti - M . . . ( 28 )
Wherein Δ σ Bp α - Ti - Al , Δ σ Bp α - Ti - Al - M , Δ σ Bp α - Ti - M The solution strengthening intensity increment of α-Ti-Al, α-Ti-Al-M, α-Ti-M phase structure unit in the expression primary phase solid solution;
Figure FSB000006891131001411
Be the tensile strength values of matrix α-Ti, σ b α - Ti = 275 Mpa ;
Primary is the interface enhancing intensity increment at middle out-phase interface mutually:
Δσ bp α - Ti - Al / α - Ti = ( σ b α - Ti + Δσ bp α - Ti - Al ) · S α - Ti - Al / α - Ti · W p α - Ti - Al Δσ bp α - Ti - Al - M / α - Ti = ( σ b α - Ti + Δσ bp α - Ti - Al - M ) · S α - Ti - Al - M / α - Ti · W p α - Ti - Al - M Δσ bp α - Ti - M / α - Ti = ( σ b α - Ti + Δσ bp α - Ti - M ) · S α - Ti - M / α - Ti · W p α - Ti - M . . . ( 29 )
Wherein Δ σ Bp α - Ti - Al / α - Ti , Δ σ Bp α - Ti - Al - M / α - Ti , Δ σ Bp α - Ti - M / α-Ti α-Ti-Al/ α-Ti, α-Ti-Al-M/ α-Ti, α-Ti-M/ α-Ti phase interface are strengthened intensity increment in the expression primary phase solid solution;
In the primary with the interface enhancing intensity increment of phase interface:
Δσ bp α - Ti - Al / α - Ti - Al = ( σ b α - Ti + Δσ bp α - Ti - Al ) · S α - Ti - Al / α - Ti - Al · W p α - Ti - Al Δσ bp α - Ti - Al - M / α - Ti - Al - M = ( σ b α - Ti + Δσ bp α - Ti - Al - M ) · S α - Ti - Al - M / α - Ti - Al - M · W p α - Ti - Al - M Δσ bp α - Ti - M / α - Ti - M = ( σ b α - Ti + Δσ bp α - Ti - M ) · S α - Ti - M / α - Ti - M · W p α - Ti - M . . . ( 30 )
Wherein Δ σ Bp α - Ti - Al / α - Ti - Al , Δ σ Bp α - Ti - Al - M / α - Ti - Al - M , Δ σ Bp α - Ti - M / α - Ti - M The interface enhancing intensity increment of α-Ti-Al/ α-Ti-Al, α-Ti-Al-M/ α-Ti-Al-M, α-Ti-M/ α-Ti-M phase interface in the expression primary phase solid solution;
The interface enhancing intensity increment at the out-phase interface that primary and β form mutually:
Δσ bp α - Ti - Al / β - Ti - Al = ( σ b β - Ti + Δσ bp α - Ti - Al ) · S α - Ti - Al / β - Ti - Al · W p α - Ti - Al Δ σ bp α - Ti - Al - M / β - Ti - Al - M = ( σ b β - Ti + Δσ bp α - Ti - Al - M ) · S α - Ti - Al - M / β - Ti - Al - M · W p α - Ti - Al - M Δσ bp α - Ti - M / β - Ti - M = ( σ b β - Ti + Δσ bp α - Ti - M ) · S α - Ti - M / β - Ti - M · W p α - Ti - M Δσ bp α - Ti / β - Ti = σ b β - Ti · S α - Ti / β - Ti · W p α - Ti . . . ( 31 )
Wherein Δ σ Bp α - Ti - Al / β - Ti - Al , Δ σ Bp α - Ti - Al - M / β - Ti - Al - M , Δ σ Bp α - Ti - M / β - Ti - M , Δ σ Bp α - Ti / β - Ti The interface enhancing intensity increment of α-Ti-Al/ β-Ti-Al that expression primary and β form mutually, α-Ti-Al-M/ β-Ti-Al-M, α-Ti-M/ β-Ti-M, α-Ti/ β-Ti phase interface;
Secondary α mutually in the solution strengthening intensity increment of each phase structure unit:
Δσ bs α - Ti - Al = σ b α - Ti · | S α - Ti - Al - 1 | · W s α - Ti - Al Δσ bs α - Ti - Al - M = σ b α - Ti · | S α - Ti - Al - M - 1 | · W s α - Ti - Al - M Δσ bs α - Ti - M = σ b α - Ti · | S α - Ti - M - 1 | · W s α - Ti - M . . . ( 32 )
Wherein representes the solution strengthening intensity increment of α-Ti-Al, α-Ti-Al-M, α-Ti-M phase structure unit in the secondary α phase solid solution;
Secondary α mutually in the interface enhancing intensity increment of phase interface:
Δσ bs α - Ti - Al / α - Ti - Al = ( σ b α - Ti + Δσ bs α - Ti - Al ) · S s α - Ti - Al / α - Ti - Al · W s α - Ti - Al Δσ bs α - Ti - Al - M / α - Ti - Al - M = ( σ b α - Ti + Δσ bs α - Ti - Al - M ) · S s α - Ti - Al - M / α - Ti - Al - M · W s α - Ti - Al - M Δσ bs α - Ti - M / α - Ti - M = ( σ b α - Ti + Δσ bs α - Ti - M ) · S s α - Ti - M / α - Ti - M · W s α - Ti - M . . . ( 33 )
Wherein Δ σ Bs α - Ti - Al / α - Ti - Al , Δ σ Bs α - Ti - Al - M / α - Ti - Al - M , Δ σ Bs α - Ti - M / α - Ti - M The interface enhancing intensity increment of representing α-Ti-Al/ α-Ti-Al in the secondary α phase solid solution, α-Ti-Al-M/ α-Ti-Al-M, α-Ti-M/ α-Ti-M phase interface;
Secondary α and parent phase β form the interface enhancing intensity increment at out-phase interface:
Δσ bs α - Ti - Al / β - Ti - Al = ( σ b α - Ti + Δσ bs α - Ti - Al ) · S s α - Ti - Al / β - Ti - Al · W s α - Ti - Al Δ σ bs α - Ti - Al - M / β - Ti - Al - M = ( σ b α - Ti + Δσ bs α - Ti - Al - M ) · S s α - Ti - Al - M / β - Ti - Al - M · W s α - Ti - Al - M Δσ bs α - Ti - M / β - Ti - M = ( σ b α - Ti + Δσ bs α - Ti - M ) · S s α - Ti - M / β - Ti - M · W s α - Ti - M Δσ bs α - Ti / β - Ti = σ b α - Ti · S s α - Ti / β - Ti · W s α - Ti . . . ( 34 )
Wherein Δ σ Bs α - Ti - Al / β - Ti - Al , Δ σ Bs α - Ti - Al - M / β - Ti - Al - M , Δ σ Bs α - Ti - M / β - Ti - M , Δ σ Bs α - Ti / β - Ti The interface enhancing intensity increment of representing α-Ti-Al/ β-Ti-Al that secondary α phase solid solution and parent phase β solid solution forms, α-Ti-Al-M/ β-Ti-Al-M, α-Ti-M/ β-Ti-M phase interface;
The solution strengthening intensity increment of each phase structure unit that impurity element forms:
Δσ b α - Ti - O = σ b α - Ti · | S α - Ti - O - 1 | · W α - Ti - O Δσ b α - Ti - N = σ b α - Ti · | S α - Ti - N - 1 | · W α - Ti - N Δσ b α - Ti - C = σ b α - Ti · | S α - Ti - C - 1 | · W α - Ti - C . . . ( 35 )
Wherein
Figure FSB00000689113100166
expression impurity element O, N, C form the solution strengthening intensity increment of α-Ti-O, α-Ti-N, α-Ti-C phase structure unit in α phase solid solution;
The interface enhancing intensity increment at the out-phase interface that impurity element forms:
Δσ b α - Ti - O / α - Ti = ( σ b α - Ti + Δσ b α - Ti - O ) · S α - Ti - O / α - Ti · W α - Ti - O Δσ b α - Ti - N / α - Ti = ( σ b α - Ti + Δσ b α - Ti - N ) · S α - Ti - N / α - Ti · W α - Ti - N Δσ b α - Ti - C / α - Ti = ( σ b α - Ti + Δσ b α - Ti - C ) · S α - Ti - C / α - Ti · W α - Ti - C . . . ( 36 )
Wherein expression impurity element O, N, C form the solution strengthening intensity increment of α-Ti-O/ α-Ti, α-Ti-N/ α-Ti, α-Ti-C/ α-Ti phase structure unit in α phase solid solution;
The interface enhancing intensity increment of the same phase interface that impurity element forms:
Δσ b α - Ti - O / α - Ti - O = ( σ b α - Ti + Δσ b α - Ti - O ) · S α - Ti - O / α - Ti - O · W α - Ti - O Δσ b α - Ti - N / α - Ti - N = ( σ b α - Ti + Δσ b α - Ti - N ) · S α - Ti - N / α - Ti - N · W α - Ti - N Δσ b α - Ti - C / α - Ti - C = ( σ b α - Ti + Δσ b α - Ti - C ) · S α - Ti - C / α - Ti - C · W α - Ti - C . . . ( 37 )
Wherein
Figure FSB00000689113100172
expression impurity element O, N, C form the reinforcement intensity increment of α-Ti-O/ α-Ti-O, α-Ti-N/ α-Ti-N, α-Ti-C/ α-Ti-C phase interface in α phase solid solution;
The computing formula of titanium alloy tensile strength:
σ b = σ b α - Ti · C αp Ti + ( σ b α - Ti + σ b β - Ti ) · C αs Ti + σ b β - Ti · C β Ti
+ Δσ b β - Ti - Al + ΣΔ σ b β - Ti - Al - M + ΣΔ σ b β - Ti - M
+ Δσ b β - Ti - Al / β - Ti + ΣΔ σ b β - Ti - Al - M / β - Ti + ΣΔ σ b β - Ti - M / β - Ti
+ Δσ b β - Ti - Al / β - Ti - Al + Σ Δσ b β - Ti - Al - M / β - Ti - Al - M + ΣΔ σ b β - Ti - M / β - Ti - M
+ Δσ bp α - Ti - Al + Σ Δσ bp α - Ti - Al - M + ΣΔ σ bp α - Ti - M
+ Δσ bp α - Ti - Al / α - Ti + Σ Δσ bp α - Ti - Al - M / α - Ti + ΣΔ σ bp α - Ti - M / α - Ti
+ Δσ bp α - Ti - Al / α - Ti - Al + Σ Δσ bp α - Ti - Al - M / α - Ti - Al - M + ΣΔ σ bp α - Ti - M / α - Ti - M
+ Δσ bp α - Ti - Al / β - Ti - Al + Σ Δσ bp α - Ti - Al - M / β - Ti - Al - M + ΣΔ σ bp α - Ti - M / β - Ti - M + Δσ bp α - Ti / β - Ti
+ Δσ bs α - Ti - Al + Σ Δσ bs α - Ti - Al - M + ΣΔ σ bs α - Ti - M
+ Δσ bs α - Ti - Al / α - Ti - Al + Σ Δσ bs α - Ti - Al - M / α - Ti - Al - M + ΣΔ σ bs α - Ti - M / α - Ti - M
+ Δσ bs α - Ti - Al / β - Ti - Al + Σ Δσ bs α - Ti - Al - M / β - Ti - Al - M + ΣΔ σ bs α - Ti - M / β - Ti - M + Δσ bs α - Ti / β - Ti
+ Δσ b α - Ti - O + Δσ b α - Ti - N + Δ σ b α - Ti - C . . . ( 38 )
+ Δσ b α - Ti - O / α - Ti + Δσ b α - Ti - N / α - Ti + Δ σ b α - Ti - C / α - Ti
+ Δσ b α - Ti - O / α - Ti - O + Δσ b α - Ti - N / α - Ti - N + Δ σ b α - Ti - C / α - Ti - C
1.4. calculate the titanium alloy length growth rate; Length growth rate with α-Ti, β-Ti is a base value, utilizes coefficient of intensification, strengthens the titanium alloy length growth rate reduction amount under the weight calculation Different Heat Treatment Conditions, with the titanium alloy length growth rate reduction amount summation that calculates; Draw the titanium alloy length growth rate
Titanium alloy length growth rate calculation mathematic model:
β mutually in the solution strengthening length growth rate reduction amount of each phase structure unit:
Δδ β - Ti - Al = δ β - Ti · | 1 / S β - Ti - Al - 1 | · W β - Ti - Al / σ N β - Ti - Al Δδ β - Ti - Al - M = δ β - Ti · | 1 / S β - Ti - Al - M - 1 | · W β - Ti - Al - M / σ N β - Ti - Al - M Δδ β - Ti - M = δ β - Ti · | 1 / S β - Ti - M - 1 | · W β - Ti - M / σ N β - Ti - M . . . ( 39 )
Δ δ wherein β-Ti-Al, Δ δ β-Ti-Al-M, Δ δ β-Ti-MThe solution strengthening length growth rate reduction amount of β-Ti-Al, β-Ti-Al-M, β-Ti-M phase structure unit in the expression β phase solid solution;
Figure FSB00000689113100181
Be the state of atom group number that possibly exist in β-Ti-Al, β-Ti-Al-M, the β-Ti-M phase structure unit; δ β-TiBe the elongation values of matrix β-Ti, δ β-Ti=75%;
β is the interface enhancing length growth rate reduction amount at middle out-phase interface mutually:
Δδ β - Ti - Al / β - Ti = δ β - Ti · S β - Ti - Al / β - Ti · W β - Ti - Al / σ β - Ti - Al / β - Ti Δδ β - Ti - Al - M / β - Ti = δ β - Ti · S β - Ti - Al - M / β - Ti · W β - Ti - Al / ( σ β - Ti - Al - M / β - Ti / σ N β - Ti - Al - M ) Δδ β - Ti - M / β - Ti = δ β - Ti · S β - Ti - M / β - Ti · W β - Ti - M / σ β - Ti - M / β - Ti . . . ( 40 )
Δ δ wherein β-Ti-Al/ β-Ti, Δ δ β-Ti-Al-M/ β-Ti, Δ δ β-Ti-M/ β-TiThe interface enhancing length growth rate reduction amount of β-Ti-Al/ β-Ti, β-Ti-Al-M/ β-Ti, β-Ti-M/ β-Ti phase interface in the expression β phase solid solution; σ β-Ti-Al/ β-Ti, σ β-Ti-Al-M/ β-Ti, σ β-Ti-M/ β-TiBe the state of atom group number that possibly exist in β-Ti-Al/ β-Ti, β-Ti-Al-M/ β-Ti, the β-Ti-M/ β-Ti phase interface;
β mutually in the interface enhancing length growth rate reduction amount of phase interface:
Δδ β - Ti - Al / β - Ti - Al = δ β - Ti · S β - Ti - Al / β - Ti - Al · W β - Ti - Al / σ β - Ti - Al / β - Ti - Al Δδ β - Ti - Al - M / β - Ti - Al - M = δ β - Ti · S β - Ti - Al - M / β - Ti - Al - M · W β - Ti - Al - M / ( σ β - Ti - Al - M / β - Ti - Al - M / σ N β - Ti - Al - M ) Δδ β - Ti - M / β - Ti - M = δ β - Ti · S β - Ti - M / β - Ti - M · W β - Ti - M / σ β - Ti - M / β - Ti - M . . . ( 41 )
Δ δ wherein β-Ti-Al/ β-Ti-Al, Δ δ β-Ti-Al-M/ β-Ti-Al-M, Δ δ β-Ti-M/ β-Ti-MThe interface enhancing length growth rate reduction amount of β-Ti-Al/ β-Ti-Al, β-Ti-Al-M/ β-Ti-Al-M, β-Ti-M/ β-Ti-M phase interface in the expression β phase solid solution; σ β-Ti-Al/ β-Ti-Al, σ β-Ti-Al-M/ β-Ti-Al-M, σ β-Ti-M/ β-Ti-MBe the state of atom group number that possibly exist in β-Ti-Al/ β-Ti-Al, β-Ti-Al-M/ β-Ti-Al-M, the β-Ti-M/ β-Ti-M phase interface;
Primary mutually in the solution strengthening length growth rate reduction amount of each phase structure unit:
Δδ p α - Ti - Al = δ α - Ti · | 1 / S α - Ti - Al - 1 | · W p α - Ti - Al / σ N α - Ti - Al Δδ p α - Ti - Al - M = δ α - Ti · | 1 / S α - Ti - Al - M - 1 | · W p α - Ti - Al - M / σ N α - Ti - Al - M Δδ p α - Ti - M = δ α - Ti · | 1 / S α - Ti - M - 1 | · W p α - Ti - M / σ N α - Ti - M . . . ( 42 )
Wherein
Figure FSB00000689113100192
The solution strengthening length growth rate reduction amount of α-Ti-Al, α-Ti-Al-M, α-Ti-M phase structure unit in the expression primary phase solid solution;
Figure FSB00000689113100193
Be the state of atom group number that possibly exist in α-Ti-Al, α-Ti-Al-M, the α-Ti-M phase structure unit; δ α-TiBe the elongation values of matrix α-Ti, δ α-Ti=49%;
Primary is the interface enhancing length growth rate reduction amount at middle out-phase interface mutually:
Δδ p α - Ti - Al / α - Ti = δ α - Ti · S α - Ti - Al / α - Ti · W p α - Ti - Al / σ α - Ti - Al / α - Ti Δδ p α - Ti - Al - M / α - Ti = δ α - Ti · S α - Ti - Al - M / α - Ti · W p α - Ti - Al - M / σ α - Ti - Al - M / α - Ti Δδ p α - Ti - M / α - Ti = δ α - Ti · S α - Ti - M / α - Ti · W p α - Ti - M / σ α - Ti - M / α - Ti . . . ( 43 )
Wherein
Figure FSB00000689113100195
The interface enhancing length growth rate reduction amount of α-Ti-Al/ α-Ti, α-Ti-Al-M/ α-Ti, α-Ti-M/ α-Ti phase interface in the expression primary phase solid solution; σ α-Ti-Al/ α-Ti, σ α-Ti-Al-M/ α-Ti, σ α-Ti-M/ α-TiBe the state of atom group number that possibly exist in α-Ti-Al/ α-Ti, α-Ti-Al-M/ α-Ti, the α-Ti-M/ α-Ti phase interface;
Primary mutually in the interface enhancing length growth rate reduction amount of phase interface:
Δδ p α - Ti - Al / α - Ti - Al = δ α - Ti · S α - Ti - Al / α - Ti - Al · W p α - Ti - Al / σ α - Ti - Al / α - Ti - Al Δδ p α - Ti - Al - M / α - Ti - Al - M = δ α - Ti · S α - Ti - Al - M / α - Ti - Al - M · W p α - Ti - Al - M / σ α - Ti - Al - M / α - Ti - Al - M Δδ p α - Ti - M / α - Ti - M = δ α - Ti · S α - Ti - M / α - Ti - M · W p α - Ti - M / σ α - Ti - M / α - Ti - M . . . ( 44 )
Wherein Δ δ p α - Ti - Al / α - Ti - Al , Δ δ p α - Ti - Al - M / α - Ti - Al - M , Δ δ p α - Ti - M / α - Ti - M The interface enhancing length growth rate reduction amount of α-Ti-Al/ α-Ti-Al, α-Ti-Al-M/ α-Ti-Al-M, α-Ti-M/ α-Ti-M phase interface in the expression primary phase solid solution; σ α-Ti-Al/ α-Ti-Al, σ α-Ti-Al-M/ α-Ti-Al-M, σ α-Ti-M/ α-Ti-MBe the state of atom group number that possibly exist in α-Ti-Al/ α-Ti-Al, α-Ti-Al-M/ α-Ti-Al-M, the α-Ti-M/ α-Ti-M phase interface;
Primary and β form the interface enhancing length growth rate reduction amount at out-phase interface mutually:
Δδ p α - Ti - Al / β - Ti - Al = δ α - Ti · S α - Ti - Al / β - Ti - Al · W p α - Ti - Al / σ α - Ti - Al / β - Ti - Al Δδ p α - Ti - Al - M / β - Ti - Al - M = δ α - Ti · S α - Ti - Al - M / β - Ti - Al - M · W p α - Ti - Al - M / σ α - Ti - Al - M / β - Ti - Al - M Δδ p α - Ti - M / β - Ti - M = δ α - Ti · S α - Ti - M / β - Ti - M · W p α - Ti - M / σ α - Ti - M / β - Ti - M Δδ p α - Ti / β - Ti = δ β - Ti · S α - Ti / β - Ti · W p α - Ti / σ α - Ti / β - Ti . . . ( 45 )
Wherein Δ δ p α - Ti - Al / β - Ti - Al , Δ δ p α - Ti - Al - M / β - Ti - Al - M , Δ δ p α - Ti - M / β - Ti - M , Δ δ p α - Ti / β - Ti Represent that primary and β form the interface enhancing length growth rate reduction amount of α-Ti-Al/ β-Ti-Al, α-Ti-Al-M/ β-Ti-Al-M, α-Ti-M/ β-Ti-M phase interface mutually; σ α-Ti-Al/ β-Ti-Al, σ α-Ti-Al-M/ β-Ti-Al-M, σ α-Ti-M/ β-Ti-M, σ α-Ti/ β-TiBe the state of atom group number that possibly exist in α-Ti-Al/ β-Ti-Al, α-Ti-Al-M/ β-Ti-Al-M, α-Ti-M/ β-Ti-M, the α-Ti/ β-Ti phase interface;
Secondary α mutually in the solution strengthening length growth rate reduction amount of each phase structure unit:
Δδ s α - Ti - Al = δ matrix · | 1 / S α - Ti - Al - 1 | · W s α - Ti - Al / σ N α - Ti - Al Δδ s α - Ti - Al - M = δ matrix · | 1 / S α - Ti - Al - M - 1 | · W s α - Ti - Al - M / σ N α - Ti - Al - M Δδ s α - Ti - M = δ matrix · | 1 / S α - Ti - M - 1 | · W s α - Ti - M / σ N α - Ti - M . . . ( 46 )
Wherein
Figure FSB00000689113100204
The solution strengthening length growth rate reduction amount of representing α-Ti-Al in the secondary α phase solid solution, α-Ti-Al-M, α-Ti-M phase structure unit; δ when primary is separated out Matrix=δ α-Ti, otherwise δ Matrix=δ β-Ti
Secondary α mutually in the interface enhancing length growth rate reduction amount of phase interface:
Δδ s α - Ti - Al / α - Ti - Al = δ matrix · S s α - Ti - Al / α - Ti - Al · W s α - Ti - Al / ( σ α - Ti - Al / α - Ti - Al / σ N α - Ti - Al ) Δδ s α - Ti - Al - M / α - Ti - Al - M = δ matrix · S s α - Ti - Al - M / α - Ti - Al - M · W s α - Ti - Al - M / ( σ α - Ti - Al - M / α - Ti - Al - M / σ N α - Ti - Al - M ) Δδ s α - Ti - M / α - Ti - M = δ matrix · S s α - Ti - M / α - Ti - M · W s α - Ti - M / ( σ α - Ti - M / α - Ti - M / σ N α - Ti - M ) . . . ( 47 )
Wherein Δ δ s α - Ti - Al / α - Ti - Al , Δ δ s α - Ti - Al - M / α - Ti - Al - M , Δ δ s α - Ti - M / α - Ti - M The interface enhancing length growth rate reduction amount of representing α-Ti-Al/ α-Ti-Al in the secondary α phase solid solution, α-Ti-Al-M/ α-Ti-Al-M, α-Ti-M/ α-Ti-M phase interface;
Secondary α and β form the interface enhancing length growth rate reduction amount at out-phase interface mutually:
Δδ s α - Ti - Al / β - Ti - Al = δ matrix · S s α - Ti - Al / β - Ti - Al · W s α - Ti - Al / ( σ α - Ti - Al / β - Ti - Al / σ N α - Ti - Al ) Δδ s α - Ti - Al - M / β - Ti - Al - M = δ matrix · S s α - Ti - Al - M / β - Ti - Al - M · W s α - Ti - Al - M / ( σ α - Ti - Al - M / β - Ti - Al - M / σ N α - Ti - Al - M ) Δδ s α - Ti - M / β - Ti - M = δ matrix · S s α - Ti - M / β - Ti - M · W s α - Ti - M / ( σ α - Ti - M / β - Ti - M / σ N α - Ti - M ) Δδ s α - Ti / β - Ti = δ matrix · S s α - Ti / β - Ti · W s α - Ti / ( σ α - Ti / β - Ti / σ N α - Ti ) . . . ( 48 )
Wherein Δ δ s α - Ti - Al / β - Ti - Al , Δ δ s α - Ti - Al - M / β - Ti - Al - M , Δ δ s α - Ti - M / β - Ti - M , Δ δ s α - Ti / β - Ti Represent that secondary α and β form the interface enhancing length growth rate reduction amount of α-Ti-Al/ β-Ti-Al, α-Ti-Al-M/ β-Ti-Al-M, α-Ti-M/ β-Ti-M, α-Ti/ β-Ti phase interface mutually; σ α-Ti/ β-TiThe state of atom group number that possibly exist for α-Ti/ β-Ti phase interface;
Impurity element forms the solution strengthening length growth rate reduction amount of phase structure unit:
Δδ α - Ti - O = δ α - Ti · | 1 / S α - Ti - O - 1 | · W α - Ti - O Δδ α - Ti - N = δ α - Ti · | 1 / S α - Ti - N - 1 | · W α - Ti - N Δδ α - Ti - C = δ α - Ti · | 1 / S α - Ti - C - 1 | · W α - Ti - C . . . ( 49 )
Δ δ wherein α-Ti-O, Δ δ α-Ti-N, Δ δ α-Ti-CSolution strengthening length growth rate reduction amount for α-Ti-O, α-Ti-N, α-Ti-C structural unit;
Impurity element forms the interface enhancing length growth rate reduction amount at out-phase interface:
Δδ α - Ti - O / α - Ti = δ α - Ti · S α - Ti - O / α - Ti ( W α - Ti - O + W α - Ti - C + W α - Ti - N ) · W α - Ti - O Δδ α - Ti - N / α - Ti = δ α - Ti · S α - Ti - N / α - Ti ( W α - Ti - O + W α - Ti - C + W α - Ti - N ) · W α - Ti - N Δδ α - Ti - C / α - Ti = δ α - Ti · S α - Ti - C / α - Ti ( W α - Ti - O + W α - Ti - C + W α - Ti - N ) · W α - Ti - C . . . ( 50 )
Δ δ wherein α-Ti-O/ α-Ti, Δ δ α-Ti-N/ α-Ti, Δ δ α-Ti-C/ α-TiInterface enhancing length growth rate reduction amount for α-Ti-O/ α-Ti, α-Ti-N/ α-Ti, α-Ti-C/ α-Ti phase interface;
Impurity element forms the interface enhancing length growth rate reduction amount with phase interface:
Δδ α - Ti - O / α - Ti - O = δ α - Ti · S α - Ti - O / α - Ti - O ( W α - Ti - O + W α - Ti - C + W α - Ti - N ) · W α - Ti - O Δδ α - Ti - N / α - Ti - N = δ α - Ti · S α - Ti - N / α - Ti - N ( W α - Ti - O + W α - Ti - C + W α - Ti - N ) · W α - Ti - N Δδ α - Ti - C / α - Ti - C = δ α - Ti · S α - Ti - C / α - Ti - C ( W α - Ti - O + W α - Ti - C + W α - Ti - N ) · W α - Ti - C . . . ( 51 )
Δ δ wherein α-Ti-O/ α-Ti, Δ δ α-Ti-N/ α-Ti, Δ δ α-Ti-C/ α-TiInterface enhancing length growth rate reduction amount for α-Ti-O/ α-Ti-O, α-Ti-N/ α-Ti-N, α-Ti-C/ α-Ti-C phase interface;
Titanium alloy length growth rate computing formula:
δ = δ α - Ti · C αp Ti + δ α - Ti · C αs Ti + δ β - Ti · C β Ti
+ Δδ β - Ti - Al + ΣΔδ β - Ti - Al - M + ΣΔδ β - Ti - M
+ Δδ β - Ti - Al / β - Ti + ΣΔδ β - Ti - Al - M / β - Ti + ΣΔδ β - Ti - M / β - Ti
+ Δδ β - Ti - Al / β - Ti - Al + ΣΔδ β - Ti - Al - M / β - Ti - Al - M + ΣΔδ β - Ti - M / β - Ti - M
+ Δδ p α - Ti - Al + ΣΔδ p α - Ti - Al - M + ΣΔδ p α - Ti - M
+ Δδ p α - Ti - Al / α - Ti + ΣΔδ p α - Ti - Al - M / α - Ti + ΣΔδ p α - Ti - M / α - Ti
+ Δδ p α - Ti - Al / α - Ti - Al + ΣΔδ p α - Ti - Al - M / α - Ti - Al - M + ΣΔδ p α - Ti - M / α - Ti - M
+ Δδ p α - Ti - Al / β - Ti - Al + ΣΔδ p α - Ti - Al - M / β - Ti - Al - M + ΣΔδ p α - Ti - M / β - Ti - M + Δδ p α - Ti / β - Ti
+ Δδ s α - Ti - Al + ΣΔδ s α - Ti - Al - M + ΣΔδ s α - Ti - M
+ Δδ s α - Ti - Al / α - Ti - Al + ΣΔδ s α - Ti - Al - M / α - Ti - Al - M + ΣΔδ s α - Ti - M / α - Ti - M
+ Δδ s α - Ti - Al / β - Ti - Al + ΣΔδ s α - Ti - Al - M / β - Ti - Al - M + ΣΔδ s α - Ti - M / β - Ti - M + Δδ s α - Ti / β - Ti
+ Δδ α - Ti - O + Δδ α - Ti - N + Δδ α - Ti - C
+ Δδ α - Ti - O / α - Ti + Δδ α - Ti - N / α - Ti + Δδ α - Ti - C / α - Ti
+ Δδ α - Ti - O / α - Ti - O + Δδ α - Ti - N / α - Ti - N + Δδ α - Ti - C / α - Ti - C . . . ( 52 )
Aforementioned calculation formula (1)～formula (52) is compiled into software for calculation; Carry out after the alloying component of the choosing of input examination on computers and the corresponding Technology for Heating Processing and calculate; Through observing the change amount of alloying element tensile strength, length growth rate under Different Heat Treatment Conditions; Adjust the relative error of calculated value and technical requirement value that alloy composition makes design tensile strength of alloys, length growth rate repeatedly in 10%, so just can confirm the chemical constitution of titanium alloy under the solution treatment+shrend of β phase region, the solution treatment+shrend of alpha+beta phase region and solution treatment+aging condition.
2. method according to claim 1; It is characterized in that: can carry out the adjustment alloy composition on computers five～ten times, and the pairing alloying component of minimum value of the calculated value of getting design tensile strength of alloys, length growth rate and the relative error of technical requirement value is as designing the optimized chemical constitution of alloy.
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