為了低成本和長(zhǎng)壽命安全飛行，飛機(jī)設(shè)計(jì)必須遵守?fù)p傷容限準(zhǔn)則 這個(gè)準(zhǔn)則在航空航天領(lǐng)域的應(yīng)用，刺激了對(duì)高強(qiáng)度、斷裂韌性和低疲勞裂紋擴(kuò)展速率鈦合金的需求[1] Ti-6Al-4VELI和Ti-6-22-22S合金的應(yīng)用，提高了美國(guó)F-22、F-35和C-17等機(jī)型的使用壽命和戰(zhàn)斗力[2,3,4,5] 國(guó)內(nèi)通過優(yōu)化成分設(shè)計(jì)開發(fā)出一種新型高強(qiáng)高韌損傷容限型α+β雙相鈦合金，其成分體系為T-Al-Sn-Zr-Mo-Si-X(X表示一種或多種VB，VIB系列元素)[6,7] 這種合金可制成板材、棒材和各種模鍛件，有廣闊的應(yīng)用前景

Sellars and McTegart [8]提出，可用Arrhenius方程中的正弦-雙曲線定律表示材料的流變應(yīng)力 許多學(xué)者修改這個(gè)方程以擴(kuò)大其應(yīng)用范圍[9,10,11]，Mandal等[12]和Lin等[13]用應(yīng)變和應(yīng)變率補(bǔ)償?shù)恼译p曲本構(gòu)方程，分別預(yù)測(cè)了鈦改性?shī)W氏體不銹鋼和42CrMo鋼的流動(dòng)應(yīng)力 吳文祥等[14]為了預(yù)測(cè)NZ30K合金在熱變形過程中的流動(dòng)應(yīng)力，基于變形加熱的校正數(shù)據(jù)建立了基于應(yīng)變補(bǔ)償?shù)碾p曲-正弦本構(gòu)方程 本文進(jìn)行Ti-62A合金的熱壓縮試驗(yàn)研究其熱變形行為，對(duì)實(shí)驗(yàn)數(shù)據(jù)進(jìn)行多元線性回歸擬合研究材料參數(shù)與應(yīng)變量的多項(xiàng)式函數(shù)關(guān)系，根據(jù)應(yīng)變量對(duì)Ti-62A合金熱變形行為的影響建立基于應(yīng)變補(bǔ)償?shù)腡i-62A合金Arrhenius變形抗力模型

1 實(shí)驗(yàn)方法

實(shí)驗(yàn)用材料為100 mm厚的熱軋Ti-62A合金板材，其化學(xué)組成列于表1，其原始組織由網(wǎng)籃狀組織、魏氏組織以及晶間α相組成(圖1)，α→β相轉(zhuǎn)變溫度約為965℃ 壓縮實(shí)驗(yàn)用試樣，其直徑為8 mm長(zhǎng)度為12 mm 用Gleeble-3800熱模擬試驗(yàn)機(jī)對(duì)圓柱試樣進(jìn)行熱壓縮，應(yīng)變量為60%，變形溫度為800℃、850℃、900℃和950℃，應(yīng)變速率為0.001 s-1、0.01 s-1、0.1 s-1、1 s-1和10 s-1 變形前將試樣以10℃/s的速率加熱到變形溫度，保溫2 min以消除試樣內(nèi)溫度梯度，再以設(shè)定的應(yīng)變速率進(jìn)行壓縮實(shí)驗(yàn)，變形結(jié)束后將試樣水冷

Table 1

表1

表1Ti-62A鈦合金的化學(xué)成分

Table 1Chemical composition of Ti-62A titanium alloy (mass fraction， %)

Al	Cr	Mo	Zn	Zr	Si	Fe	C	N	H	O	Ti
5.25～6.25	1.75～2.25	1.75～2.25	1.75～2.25	1.75～2.25	0.20～0.27	≤0.15	≤0.04	≤0.03	≤0.0125	≤0.13	Bal.

圖1



圖1實(shí)驗(yàn)用Ti-62A合金的原始組織

Fig.1Micrograph of the as received Ti-62A alloy

2 結(jié)果和討論2.1 Ti-62A 合金的流變行為

圖2表明，在Ti-62A合金試樣受壓變形的初始階段加工硬化占主導(dǎo)，隨著應(yīng)變量的增加流變應(yīng)力急劇增大，經(jīng)歷很小的應(yīng)變即達(dá)到峰值應(yīng)力，隨后動(dòng)態(tài)回復(fù)和動(dòng)態(tài)再結(jié)晶引起的軟化大于加工硬化，使流變應(yīng)力迅速減小 當(dāng)變形量達(dá)到某一值時(shí)加工硬化與動(dòng)態(tài)軟化達(dá)到動(dòng)態(tài)平衡，在真應(yīng)力-應(yīng)變曲線上流變應(yīng)力基本上保持不變 圖2還表明，在一定的應(yīng)變速率下流變應(yīng)力隨著變形溫度的提高而降低

圖2



圖2在不同變形條件下Ti-62A合金的流變應(yīng)力曲線

Fig.2Flow stress curves of Ti-62A alloy under different deformation conditions (a) 0.001 s-1; (b) 0.01 s-1; (c) 0.1 s-1; (d) 1 s-1; (e) 10 s-1

2.2 鈦合金在熱壓縮過程中的動(dòng)態(tài)軟化率

無論應(yīng)變速率多大，Ti-62A合金的動(dòng)態(tài)軟化速率都隨著變形溫度的提高而降低 變形溫度較低(800℃)時(shí)流變應(yīng)力曲線大多為動(dòng)態(tài)軟化型，而變形溫度較高(950℃)時(shí)流變應(yīng)力曲線大多屬于動(dòng)態(tài)回復(fù)型，中間變形溫度(850℃)的流變應(yīng)力曲線大多屬于動(dòng)態(tài)再結(jié)晶型，如圖2所示 結(jié)果表明[15,16,17,18]，隨著變形溫度的提高流變應(yīng)力曲線表現(xiàn)出的動(dòng)態(tài)軟化速率都是降低的 本文根據(jù)熱力學(xué)理論解釋這種反?，F(xiàn)象 使用JmatPro材料模擬軟件分別計(jì)算了Ti-62A合金、TC11合金[15]、工業(yè)純鈦[19]和TB17合金[23]中關(guān)鍵元素的原子相對(duì)活性，結(jié)果如圖3所示 從圖3a可見，溫度對(duì)Ti-62A合金中Cr和Mo兩種元素的原子活性有顯著的影響 從800℃升高到950℃，Cr和Mo的原子活性都顯著降低 Cr原子的活性從0.206降低到0.074(降幅達(dá)到64.1%)，Mo的降幅也達(dá)到64.3% 溫度對(duì)TC11合金中Mo元素的原子活性也有顯著的影響，從300℃升高到950℃元素Mo的原子活性顯著降低(圖3b)，從0.613降低到0.034(降幅達(dá)94.5%) 但是，溫度對(duì)工業(yè)純鈦和TB17合金中各元素的原子活性并沒有顯著的影響(圖3c和3d) α型鈦合金[19,20,21,22]和β型鈦合金[23,24]的熱加工流變應(yīng)力曲線都表明，隨著加工溫度的升高動(dòng)態(tài)軟化速率降低 為此，本文使用JmatPro材料模擬軟件分別計(jì)算了Ti-62A合金、工業(yè)純鈦和TB17合金中α和β相的比例(圖4) 可以看出，三種合金中β相的含量均隨著變形溫度的升高而提高 溫度由800℃升高到950℃，Ti-62A合金中的β相含量由32.1%提高到84.3%，工業(yè)純鈦和β鈦合金中β相的比例均已提高到100% 在三種鈦合金的高溫變形過程中都可能存在形變誘導(dǎo)α相向β相的轉(zhuǎn)變(存在晶體結(jié)構(gòu)有hcp結(jié)構(gòu)向bcc結(jié)構(gòu)的轉(zhuǎn)變)，消耗部分變形能使其在較高溫度下變形的動(dòng)態(tài)軟化率較低

圖3



圖3鈦合金中合金元素的活性隨溫度的變化

Fig.3Change of alloy element activity with temperature in titanium alloy (a) Ti-62A alloy; (b) TC11 alloy; (c) Commercially pure titanium; (d) TB17 alloy

圖4



圖4鈦合金中α相和β相的比例隨溫度的變化

Fig.4Change of the ratio of α phase and β phase with temperature in titanium alloy (a) Ti-62A alloy; (b) Commercially pure titanium; (c) TB17 alloy

可以推測(cè)，α型鈦合金和β型鈦合金出現(xiàn)動(dòng)態(tài)軟化率隨變形溫度升高而降低的現(xiàn)象和相比例的變化，與β相比例的增大密切相關(guān)；但是，α+β雙相鈦合金的這一現(xiàn)象則可能是主要合金元素Mo、Cr等β穩(wěn)定元素的原子活性隨溫度升高逐漸降低與β相比例增大共同作用的結(jié)果 這表明，合金元素、相比例和變形溫度對(duì)Ti-62A合金的熱變形行為都有顯著的影響 這種合金的α→β相的轉(zhuǎn)變溫度約為965℃，即隨著變形溫度(800~950℃)的提高變形試樣中β相的比例增大 上述兩種元素在β相(bcc結(jié)構(gòu))中的活性較低，導(dǎo)致上述反?，F(xiàn)象

2.3 變形溫度對(duì)Ti-62A 合金顯微組織的影響

圖5給出了Ti-62A合金在應(yīng)變速率為0.001 s-1、不同溫度下熱壓縮變形后的金相照片 變形溫度為800℃時(shí)，合金的顯微組織由片狀的初生α相和β轉(zhuǎn)變組織組成(圖5a)；變形溫度為850℃時(shí)片狀α相的數(shù)量減少，β轉(zhuǎn)變組織的尺寸增大(圖5b)；變形溫度為900℃時(shí)α相發(fā)生了動(dòng)態(tài)再結(jié)晶或球化，β相發(fā)生再結(jié)晶，產(chǎn)生新的等軸β晶粒(圖5c)；變形溫度為950℃時(shí)β晶粒完全回復(fù)與再結(jié)晶，出現(xiàn)粗大的等軸 β晶粒，α相幾乎消失(圖5d) 可以看出，隨著變形溫度的升高β晶粒通過晶界遷移粗化，使變形合金中β相的比例增高 這表明，隨著變形溫度的升高更多的α相向β相轉(zhuǎn)變 這個(gè)轉(zhuǎn)變需要能量且隨著變形溫度的升高Ti-62A中主要合金元素Cr、Mo的活性降低，使流變應(yīng)力曲線表現(xiàn)出的應(yīng)變軟化速率隨著變形溫度的升高反而降低

圖5



圖5在應(yīng)變速率為 0. 001 s-1、不同溫度條件下熱壓縮變形后Ti-62A 合金的顯微組織

Fig.5Microstructure of Ti-62A alloy deformed by hot compression at different temperatures with strain rate of 0.001 s-1 (a) 800℃, (b) 850℃, (c) 900℃, (d) 950℃

圖6給出了Ti-62A合金經(jīng)應(yīng)變速率為1 s-1、在不同溫度熱壓縮變形后的顯微組織照片 與圖5中金相相比，盡管應(yīng)變速率高了3個(gè)數(shù)量，Ti-62A合金的微觀組織仍表現(xiàn)出相同的變化規(guī)律 變形溫度為800℃時(shí)α相與β轉(zhuǎn)變組織都發(fā)生了彎曲(圖6a)；圖 6b、6c和6d中的變形分別為經(jīng)1 s-1和850℃、900℃和950℃熱壓縮變形，Ti-62A合金的顯微組織由片層狀的初生α相與β轉(zhuǎn)變組織組成 隨著變形溫度的升高α相含量降低，β轉(zhuǎn)變組織逐漸增多，且β晶粒尺寸增大(圖6b~d) 但是圖5d和圖6d表明，變形溫度同為950℃，應(yīng)變速率對(duì)等軸β相的晶粒尺寸影響顯著，前者的晶粒尺寸明顯大于后者 從圖6d還可以看出，在1 s-1和950℃變形條件下仍有少量的片狀α相沒有向β相轉(zhuǎn)變

圖6



圖6在應(yīng)變速率為1 s-1、不同溫度條件下變形的Ti-62A合金的顯微組織

Fig.6Microstructure of Ti-62A alloy deformed by hot compression at different temperatures with strain rate of 1 s-1 (a) 800℃, (b) 850℃, (c) 900℃, (d) 950℃

在熱變形過程中，溫度對(duì)Ti-62A合金的熱變形組織有顯著的影響 隨著加工溫度的升高，β相比例逐漸增大 由于β相的晶體結(jié)構(gòu)為體心立方結(jié)構(gòu)(bcc)，具有較高層錯(cuò)能，而且其中的滑移系比密排六方結(jié)構(gòu)的α相多，容易發(fā)生以位錯(cuò)攀移和滑移為機(jī)制的動(dòng)態(tài)回復(fù) 這使合金中難以儲(chǔ)存足夠能量使合金發(fā)生動(dòng)態(tài)再結(jié)晶，即抑制了Ti-62A合金熱變形過程中的動(dòng)態(tài)再結(jié)晶行為 因此，變形溫度較高(950℃)時(shí)，流變應(yīng)力曲線多屬于動(dòng)態(tài)回復(fù)型 同時(shí)，Ti-62A合金中Cr、Mo甚至Ti元素隨著變形溫度升高活性降低，也阻礙了合金在熱變形過程中的動(dòng)態(tài)再結(jié)晶

2.4 基于應(yīng)變補(bǔ)償?shù)?Arrhenius 本構(gòu)模型

圖2中的流變應(yīng)力曲線和文獻(xiàn)[14,25]的結(jié)果都表明，應(yīng)變量對(duì)流變應(yīng)力有顯著的影響 因此，建立材料本構(gòu)方程時(shí)考慮應(yīng)變，可能更準(zhǔn)確的預(yù)測(cè)流變應(yīng)力 假設(shè)材料常數(shù)(即α，n，Q和lnA)為應(yīng)變的多項(xiàng)式函數(shù)[12,13]，在材料的本構(gòu)方程中引入應(yīng)變這一影響因素 本文使用傳統(tǒng)的本構(gòu)模型計(jì)算出應(yīng)變?yōu)?.05~0.9(間隔為0.05)的Ti-62A合金的常數(shù)α，n，Q和lnA的值 對(duì)這些數(shù)據(jù)進(jìn)行2~8次多項(xiàng)式的擬合和比較，其中5次多項(xiàng)式適合表示應(yīng)變對(duì)Ti-62A合金常數(shù)的影響，即

α=C0+C1ε+C2ε2+C3ε3+C4ε4+C5ε5n=D0+D1ε+D2ε2+D3ε3+D4ε4+D5ε5Q=E0+E1ε+E2ε2+E3ε3+E4ε4+E5ε5lnA=F0+F1ε+F2ε2+F3ε3+F4ε4+F5ε5

(1)

式中C、D、E、F為擬合系數(shù) 表2給出了Ti-62A合金的常數(shù)α，n，Q和ln A的多項(xiàng)式擬合結(jié)果

Table 2

表2

表2Ti-62A合金常數(shù)擬合參數(shù)

Table 2Constant fitting parameters of Ti-62A alloy

α	n	Q	lnA
C0=0.00924	D0=1.91645	E0=398.95592	F0=36.20351
C1=0.01367	D1=3.79583	E1=-271.00142	F1=-21.10215
C2=-0.05939	D2=-13.6498	E2=137.81848	F2=-11.71244
C3=0.14321	D3=31.05524	E3=584.16655	F3=112.84221
C4=-0.1574	D4=-35.64127	E4=-1548.1067	F4=-209.55112
C5=0.06308	D5=15.75986	E5=960.56284	F5=116.99094

Ti-62A合金在試驗(yàn)條件范圍內(nèi)任意應(yīng)變下的流變應(yīng)力本構(gòu)方程可表示為

σ=1αln(ε˙exp(QRT)/A)1n+(ε˙exp(QRT)/A)2n+112

(2)

將使用公式(2)計(jì)算的流變應(yīng)力值與實(shí)測(cè)值的比較，驗(yàn)證了基于應(yīng)變補(bǔ)償所建立的本構(gòu)方程，圖7給出了在不同試驗(yàn)條件下Ti-62A合金流變應(yīng)力的計(jì)算值與實(shí)測(cè)值 從圖7可見，所建立本構(gòu)關(guān)系的計(jì)算值與實(shí)測(cè)值大部分曲線非常接近，較精確地反映了流變應(yīng)力與應(yīng)變速率、變形溫度和應(yīng)變量之間的關(guān)系

圖7



圖7應(yīng)變補(bǔ)償?shù)谋緲?gòu)方程模擬流變應(yīng)力曲線與實(shí)驗(yàn)流變應(yīng)力曲線

Fig.7Comparison of the flow stress curves simulated with strain-compensated constitutive equations and experimental flow stress curves (a) 0.001 s-1; (b) 1 s-1

為了評(píng)價(jià)基于應(yīng)變補(bǔ)償?shù)谋緲?gòu)方程對(duì)流變應(yīng)力的預(yù)測(cè)能力，引入相關(guān)系數(shù)(R)和平均相對(duì)誤差(AARE)作為衡量應(yīng)變補(bǔ)償本構(gòu)方程準(zhǔn)確性的指標(biāo)，其表達(dá)式為

R=∑i=1N(Ei-Eˉ)(Pi-Pˉ)∑i=1N(Ei-Eˉ)2∑i=1N(Pi-Pˉ)2

(3)

AARE(%)=1N∑i=1NEi-PiEi×100%

(4)

式中Ei為實(shí)驗(yàn)所測(cè)的流變應(yīng)力值(MPa)；Pi為由應(yīng)變補(bǔ)償本構(gòu)方程計(jì)算的流變應(yīng)力值(MPa)；Eˉ，Pˉ分別為Ei，Pi的均值；N為熱模擬試驗(yàn)機(jī)采集數(shù)據(jù)點(diǎn)的數(shù)量

圖8給出了Ti-62A合金的應(yīng)變補(bǔ)償本構(gòu)方程的計(jì)算值與試驗(yàn)值的相關(guān)性對(duì)比 誤差分析結(jié)果表明，使用應(yīng)變補(bǔ)償本構(gòu)方程的計(jì)算值與試驗(yàn)值的相關(guān)性R為0.990；平均相對(duì)誤差(AARE)為8.983% 平均相對(duì)誤差小于10%，表明該模型與試驗(yàn)數(shù)據(jù)吻合良好 由此可見，本文建立的基于應(yīng)變補(bǔ)償?shù)腡i-62A合金流變應(yīng)力模型能較為準(zhǔn)確地描述Ti-62A鈦合金在熱變形過程中的應(yīng)力流動(dòng)變化行為

圖8



圖8Ti-62A合金的應(yīng)變補(bǔ)償方程計(jì)算值與實(shí)測(cè)流變應(yīng)力值的相關(guān)性

Fig.8Correlation between calculated value of strain compensation equation and measured value of flow stress in Ti-62A alloy

3 結(jié)論

(1) 在變形溫度800~950℃、應(yīng)變速率0.001~-10 s-1 條件下Ti-62A合金的流變應(yīng)力對(duì)變形溫度和應(yīng)變速率的影響較為敏感，流變應(yīng)力隨著變形溫度的降低和應(yīng)變速率的升高而升高 α鈦合金和β鈦合金出現(xiàn)動(dòng)態(tài)軟化率隨著變形溫度的升高而降低的現(xiàn)象，與β相比例的增大密切相關(guān)；而α+β雙相鈦合金的這一現(xiàn)象則與主要合金元素的Mo、Cr等β穩(wěn)定元素隨溫度升高而逐漸降低、β相比例增大有更大的相關(guān)性 從800℃升高到950℃變形試樣中β相的比例逐漸增大，Mo、Cr兩種元素在β相(bcc結(jié)構(gòu))中的活性降低 在變形溫度范圍內(nèi)Mo和Cr的活性降幅均達(dá)到64%，導(dǎo)致變形過程中Ti-62A合金的晶界遷移速度和動(dòng)態(tài)軟化速率均隨著變形溫度的升高而降低，其在較低變形溫度(800℃)下的流變應(yīng)力曲線呈現(xiàn)為動(dòng)態(tài)軟化型，在較高變形溫度(950℃)下的流變應(yīng)力曲線反而呈動(dòng)態(tài)回復(fù)型

(2) 變形溫度對(duì)Ti-62A合金熱變形組織的影響顯著，變形溫度在800~950℃升高合金的中α相由較粗大的片層狀發(fā)生球化，而且α相的數(shù)量逐漸減少；β相由α相片層間的微量比例隨著溫度的升高逐漸增大，在950℃變形條件下合金的組織完全轉(zhuǎn)變?yōu)榈容S狀的β相

(3) 考慮應(yīng)變對(duì)材料常數(shù)(即α，n，Q和ln A)的影響建立了Ti-62A合金的應(yīng)變補(bǔ)償?shù)谋緲?gòu)方程，預(yù)測(cè)應(yīng)力和實(shí)測(cè)值之間的相關(guān)系數(shù)(R)達(dá)到0.990，平均相對(duì)誤差(AARE)為8.983%，表明根據(jù)應(yīng)變補(bǔ)償本構(gòu)方程能較好地預(yù)測(cè)Ti-62A合金的流變應(yīng)力行為

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1

2002