鈦合金具有比強(qiáng)度高、耐腐蝕和耐高溫性能優(yōu)異等特點(diǎn) 因此，在航空航天、生物醫(yī)學(xué)、深海服役等領(lǐng)域得到了廣泛的應(yīng)用[1~5] Ti-6Al-4V(TC4)合金是一種應(yīng)用最廣的α+β型鈦合金[6]，通過(guò)降低其中的C、N、O等元素含量便可制備出含超低間隙(Extra-low-interstitial, ELI)元素含量的TC4 ELI合金，其具有更高的可焊接性和沖壓成型性[7~9] 深海潛水器是深海工程作業(yè)的重要裝備，在潛水器下潛和上浮過(guò)程中其耐壓殼承受極大的循環(huán)載荷[13,14] 隨著深海潛水器下潛深度增加對(duì)其材料更高力學(xué)性能的需求，TC4 ELI合金在耐壓殼上的應(yīng)用備受關(guān)注[10~12]，而耐壓殼用鈦合金在循環(huán)大應(yīng)變幅下的低周疲勞性能成為評(píng)價(jià)其服役性能的重要指標(biāo) 同時(shí)，在較大循環(huán)載荷的作用下耐壓殼材料將不可避免地產(chǎn)生局部應(yīng)力集中[15]，其低周疲勞性能對(duì)缺口等缺陷引起的應(yīng)力集中的敏感性直接關(guān)乎構(gòu)件的服役可靠性

目前，對(duì)TC4 ELI合金疲勞性能的研究主要集中在顯微組織對(duì)其疲勞性能的影響[16~21] 鈦合金的低周疲勞性能強(qiáng)烈地依賴(lài)于其顯微組織和疲勞加載應(yīng)變幅[22]，而應(yīng)變幅的增大將使合金疲勞壽命降低 在不同應(yīng)變幅加載條件下，具有網(wǎng)籃組織的TC4 ELI合金往往呈現(xiàn)出循環(huán)軟化特性，且隨著應(yīng)變幅的增大韌性斷裂特征更顯著[23] 在較低應(yīng)變幅(0.6%)條件下，雙態(tài)組織TC4合金中初生α相被拉長(zhǎng)，表現(xiàn)為因α相參與疲勞變形而使材料壽命較長(zhǎng)；而在較高應(yīng)變幅(1.2%)條件下，疲勞裂紋穿過(guò)α相擴(kuò)展，使材料的疲勞壽命變短[24] 同時(shí)，鈦合金的疲勞性能對(duì)諸如缺口等缺陷極為敏感 隨著缺口曲率半徑的減小，缺口越尖銳，從而使得衡量零部件缺口處局部應(yīng)力集中參數(shù)的疲勞缺口應(yīng)力集中系數(shù)越大，材料疲勞失效的概率越高[25] 當(dāng)具有網(wǎng)籃組織的TC17合金的缺口應(yīng)力集中系數(shù)大于1.92時(shí)，缺口對(duì)疲勞壽命產(chǎn)生顯著影響，使其疲勞壽命急劇降低[26] 為了更好地分析在循環(huán)載荷作用下鈦合金的損傷情況，有研究者提出了多種預(yù)測(cè)鈦合金疲勞壽命的模型[27]，包括基于應(yīng)變能密度預(yù)測(cè)缺口構(gòu)件疲勞壽命的模型[28]、基于臨界應(yīng)變法預(yù)測(cè)光滑和缺口試樣的疲勞壽命模型[29]、基于剪應(yīng)變的臨界面法建立的預(yù)測(cè)TC4合金多軸疲勞壽命的模型[30]和基于表面缺口的總疲勞壽命的分離模型[31]

耐壓殼結(jié)構(gòu)因設(shè)計(jì)需求而不可避免地出現(xiàn)各種類(lèi)型的缺口，在外載荷作用下這些缺口處必然會(huì)產(chǎn)生局部應(yīng)力集中 由此產(chǎn)生的應(yīng)力集中極易成為零部件最薄弱的環(huán)節(jié)而引發(fā)疲勞裂紋的萌生 缺口疲勞分析對(duì)結(jié)構(gòu)完整性設(shè)計(jì)至關(guān)重要，缺口應(yīng)力集中系數(shù)能衡量零部件局部應(yīng)力集中的大小 因此，通過(guò)建立缺口應(yīng)力集中系數(shù)與低周疲勞相對(duì)裂紋萌生壽命間的預(yù)測(cè)模型可為設(shè)計(jì)和研發(fā)深潛器提供理論參考 鑒于此，本文研究具有不同缺口應(yīng)力集中系數(shù)的TC4 ELI合金的低周疲勞性能，通過(guò)對(duì)不同循環(huán)應(yīng)變幅條件下合金的循環(huán)應(yīng)力-應(yīng)變響應(yīng)及循環(huán)變形行為的研究，獲得了不同缺口應(yīng)力集中系數(shù)試樣的低周疲勞壽命，探討了缺口對(duì)合金低周疲勞性能的影響及其疲勞損傷機(jī)理，獲得了合金低周疲勞性能參數(shù)與缺口應(yīng)力集中系數(shù)之間的關(guān)系，建立了這種合金相對(duì)裂紋萌生壽命的預(yù)測(cè)模型

1 實(shí)驗(yàn)方法

實(shí)驗(yàn)用軋制態(tài)TC4 ELI合金板材的名義化學(xué)成分列于表1 按照GB/T15248-2008標(biāo)準(zhǔn)加工疲勞試樣，圖1給出了光滑試樣和含缺口試樣的尺寸及其加工精度 試樣軸向加載方向?yàn)榘宀牡能堉品较?光滑試樣和缺口試樣的標(biāo)距段直徑均為6.5 mm，長(zhǎng)度為13 mm；加工缺口試樣時(shí)采用環(huán)切方式開(kāi)缺口，缺口的應(yīng)力集中系數(shù)(Kt)為

Table 1

表1

表1TC4 ELI合金的名義成分

Table 1Nominal composition of TC4 ELI alloy (%, mass fraction)

Al	V	Fe	C	O	N	H	Ti
5.50~6.50	3.60~4.40	≤0.25	≤0.08	≤0.13	≤0.03	≤0.0125	Bal.

圖1



圖1不同缺口應(yīng)力集中系數(shù)的TC4 ELI低周疲勞試樣的尺寸和加工精度

Fig. 1Dimensions and surface finish of TC4 ELI specimens with different notch stress concentration factors for low-cycle fatigue tests (a) Kt =1, (b) Kt =1.97, (c) Kt =2.64, (d) Kt =3.62

Kt=1ar+2vC+2

arC+v+0.5+(1+v)(C+1)

(1)

式中a為試樣缺口處半徑；r為缺口處曲率半徑；v為泊松比；C為ar+1 分別設(shè)計(jì)了三種缺口試樣，其Kt 值分別為1.97、2.64和3.62 為了對(duì)照，同時(shí)加工了Kt 值為1的光滑試樣 進(jìn)行疲勞實(shí)驗(yàn)前，對(duì)試樣表面進(jìn)行拋光處理

使用計(jì)算機(jī)控制的MTS-647液壓伺服疲勞試驗(yàn)機(jī)進(jìn)行低周疲勞性能測(cè)試實(shí)驗(yàn)，實(shí)驗(yàn)中采用恒總應(yīng)變幅控制的軸向拉-壓對(duì)稱(chēng)方式加載，加載頻率為f =0.5 Hz，軸向應(yīng)變速率為ε˙=3×10-3s-1 實(shí)驗(yàn)中選取的總應(yīng)變幅(Δεt /2)為0.2%~0.9%，疲勞加載波形為三角波形

采用ZESIS Supra 35場(chǎng)發(fā)射掃描電子顯微鏡(SEM) 觀(guān)察和分析疲勞斷裂的斷口 采用FEI Tecnai F20型透射電子顯微鏡(TEM) 觀(guān)察和表征合金中的位錯(cuò)行為 制備TEM樣品時(shí)，用體積分?jǐn)?shù)為60%甲醇、35%正丁醇和5%高氯酸的混合溶液進(jìn)行雙噴減薄，操作電壓為22 V，溫度范圍為從-28℃到-30℃

2 實(shí)驗(yàn)結(jié)果2.1 TC4 ELI合金的顯微組織

圖2給出了TC4 ELI合金軋制態(tài)的金相組織為典型的網(wǎng)籃組織，即在β轉(zhuǎn)變基體上形成了α相的網(wǎng)籃編織結(jié)構(gòu)，其中片狀α相的長(zhǎng)度為35±5 μm、寬度為4±1 μm

圖2



圖2軋制態(tài)TC4 ELI合金的光學(xué)顯微組織

Fig.2Optical image of rolled TC4 ELI alloy

2.2 循環(huán)應(yīng)力響應(yīng)特性

圖3a~d給出了Kt 值不同的TC4 ELI合金試樣在不同Δεt /2條件下的循環(huán)應(yīng)力幅隨循環(huán)周次的變化 由圖3a可見(jiàn)，當(dāng)Δεt /2為0.9%和0.8%時(shí)，Kt =1的光滑試樣表現(xiàn)出完全的循環(huán)軟化行為，直至最終斷裂失效；Δεt /2為0.7%和0.6%的試樣呈現(xiàn)初始的循環(huán)硬化，隨后逐漸循環(huán)軟化而斷裂失效 這一光滑試樣在高應(yīng)變幅加載條件下的循環(huán)軟化現(xiàn)象，不僅在TC4 ELI合金中發(fā)生過(guò)[21,23]，在其它類(lèi)型的鈦合金中也發(fā)生過(guò)[4,24,32,33] 這種現(xiàn)象與高應(yīng)變幅循環(huán)加載條件下材料內(nèi)部高密度的位錯(cuò)重排和部分湮滅有關(guān)[34]；Δεt /2為0.4%和0.5%的光滑試樣均表現(xiàn)出初始循環(huán)硬化和隨后的循環(huán)飽和行為，但后者在循環(huán)末期還呈現(xiàn)出一定的循環(huán)二次硬化現(xiàn)象

圖3



圖3缺口應(yīng)力集中系數(shù)不同的TC4 ELI合金的應(yīng)力幅隨循環(huán)周次的變化曲線(xiàn)

Fig.3Stress amplitude of TC4 ELI alloy with different notched stress concentration coefficient varies with cycle number (a) Kt =1, (b) Kt =1.97, (c) Kt =2.64, (d) Kt =3.62

圖3b~d給出了缺口試樣的實(shí)驗(yàn)結(jié)果 可以看出，Δεt /2大于等于0.5%的試樣均出現(xiàn)初始循環(huán)硬化及隨后循環(huán)軟化的現(xiàn)象 這是由于循環(huán)加載的初期，材料剛開(kāi)始塑性變形時(shí)的位錯(cuò)增殖行為，且隨著疲勞循環(huán)周次的增加位錯(cuò)密度隨之提高[35] 當(dāng)應(yīng)變幅為0.3%和0.4%時(shí)，Kt =1.97的試樣均呈現(xiàn)出初始循環(huán)硬化和隨后的二次硬化現(xiàn)象；當(dāng)應(yīng)變幅為0.4%時(shí)，Kt =2.64試樣也表現(xiàn)出上述現(xiàn)象 而Kt=3.62的試樣在0.4%至0.2%的應(yīng)變幅作用下則均呈現(xiàn)出初始循環(huán)硬化行為和隨后循環(huán)飽和現(xiàn)象 缺口應(yīng)力集中系數(shù)Kt 定義為缺口處的局部最大應(yīng)力σmax與名義應(yīng)力的比值 在循環(huán)變形過(guò)程中，缺口應(yīng)力集中系數(shù)較大的試樣在缺口處較高的局部最大應(yīng)力使其變形程度更大，位錯(cuò)不斷增殖使其密度提高，發(fā)生的位錯(cuò)纏結(jié)、塞積使材料發(fā)生循環(huán)硬化 同時(shí)，材料內(nèi)部位錯(cuò)的湮滅使其發(fā)生軟化，在此過(guò)程中位錯(cuò)的增殖、塞積比位錯(cuò)的湮滅表現(xiàn)得更加突出 因此，在循環(huán)變形初期發(fā)生循環(huán)硬化，而循環(huán)載荷作用一段時(shí)間后位錯(cuò)的增殖、塞積與湮滅達(dá)到動(dòng)態(tài)平衡而出現(xiàn)循環(huán)飽和

2.3 循環(huán)應(yīng)力-應(yīng)變滯回線(xiàn)

圖4給出了Kt 不同的試樣在半壽命下的循環(huán)應(yīng)力-應(yīng)變滯回線(xiàn) 由圖4a可見(jiàn)，當(dāng)Δεt /2為0.4%和0.5%時(shí)，光滑試樣的循環(huán)滯回線(xiàn)所圍的面積趨于零，表明材料幾乎未產(chǎn)生循環(huán)塑性變形；而當(dāng)Δεt /2從0.5%增大到0.9%時(shí)，循環(huán)滯回線(xiàn)的面積隨著循環(huán)周次增加逐漸增大，表明試樣的累積循環(huán)塑性變形越來(lái)越明顯 從圖4a~d的對(duì)比可見(jiàn)，在相同的Δεt /2條件下，隨著Kt 的增加滯回線(xiàn)所圍面積不斷減小，表明循環(huán)塑性變形減小

圖4



圖4缺口應(yīng)力集中系數(shù)不同的TC4 ELI試樣的循環(huán)應(yīng)力-應(yīng)變滯回線(xiàn)

Fig.4Fatigue hysteresis loops of TC4 ELI specimens with different notch stress concentration factors (a) Kt =1, (b) Kt =1.97, (c) Kt =2.64, (d) Kt =3.62

2.4 疲勞損傷行為

圖5給出了TC4 ELI合金光滑試樣分別在0.4%低應(yīng)變幅和0.9%高應(yīng)變幅下的低周疲勞斷口的SEM對(duì)比觀(guān)察 由圖5a和b的低倍對(duì)比觀(guān)察可以發(fā)現(xiàn)，TC4 ELI合金無(wú)缺口的光滑試樣的低周疲勞裂紋均從試樣表面萌生，斷裂面均由疲勞裂紋萌生區(qū)、疲勞裂紋擴(kuò)展區(qū)和瞬斷區(qū)組成，較高應(yīng)變幅下試樣的疲勞斷口(圖5b)更為粗糙；圖5c和d表明，在兩個(gè)應(yīng)變幅條件下的疲勞裂紋萌生區(qū)都呈現(xiàn)出解理小臺(tái)階的斷裂特征，其疲勞裂紋擴(kuò)展區(qū)都有明顯的疲勞條紋(圖5e和f)，且Δεt /2=0.9%試樣的疲勞條紋間距為7.7 μm，明顯大于Δεt /2=0.4%試樣的疲勞條紋間距(2.5 μm) 這表明，隨著應(yīng)變幅的增加，每個(gè)循環(huán)周次下疲勞條紋擴(kuò)展的距離增大 對(duì)比圖5g和h的最終瞬斷區(qū)可見(jiàn)，Δεt /2=0.9%試樣的韌窩深度大于Δεt /2=0.4%試樣的韌窩深度

圖5



圖5不同應(yīng)變幅控制下TC4 ELI合金光滑試樣疲勞斷口的SEM照片

Fig.5SEM images of fatigue fracture surfaces of TC4 ELI alloy smooth specimens under the control of different strain amplitudes (a, c, e, g) 0.4%, (b, d, f, h) 0.9%

圖6給出了三種缺口應(yīng)力集中系數(shù)的缺口試樣在應(yīng)變幅為0.3%控制下的疲勞斷口的SEM照片 圖6a~c給出了Kt 分別為1.97、2.64和3.62的低倍疲勞斷口形貌，可見(jiàn)高Kt 試樣的疲勞斷口形貌較低Kt 試樣的疲勞斷口形貌更光滑；圖6d~f給出了缺口試樣的疲勞裂紋擴(kuò)展區(qū) 可以看出，疲勞裂紋擴(kuò)展區(qū)均有明顯的疲勞條紋，Kt 為1.97、2.64和3.62三種試樣的疲勞條紋間距分別為4.6 μm、1.3 μm和0.9 μm，表明試樣的Kt 越高其疲勞條紋間距越小；圖6g~i給出了三種Kt 缺口試樣的最終斷裂區(qū) 可以看出，最終斷裂區(qū)均由大小不同的韌窩組成，Kt 為1.97、2.64和3.62試樣的疲勞斷口韌窩的尺寸分別為5.8±0.5 μm、9.4±1.2 μm和8.8±2.1 μm 這表明，Kt 越小疲勞斷口的韌窩尺寸越小且尺寸越均勻

圖6



圖6三種缺口應(yīng)力集中系數(shù)的TC4 ELI合金缺口試樣在應(yīng)變幅為0.3%控制下疲勞斷口的SEM照片

Fig.6SEM images of fatigue fracture surfaces of TC4 ELI alloy notched specimens with three different notch stress concentration factors under the control of strain amplitude of 0.3% (a, d, g) Kt =1.97, (b, e, h) Kt =2.64, (c, f, i) Kt =3.62

結(jié)合圖3b~d可見(jiàn)，缺口試樣在不同應(yīng)變幅控制下的循環(huán)初期均發(fā)生循環(huán)硬化，而光滑試樣僅在低應(yīng)變幅下發(fā)生循環(huán)硬化，而在高應(yīng)變幅下發(fā)生循環(huán)軟化 為了進(jìn)一步分析在材料循環(huán)硬化和循環(huán)軟化過(guò)程中內(nèi)部位錯(cuò)結(jié)構(gòu)可能發(fā)生的變化，圖7給出了應(yīng)變幅為0.4%和0.9%兩個(gè)典型加載條件下合金出現(xiàn)循環(huán)硬化和軟化的疲勞斷口的TEM照片 對(duì)比低應(yīng)變幅條件下的疲勞斷裂(圖7a~c)和高應(yīng)變幅條件下疲勞斷裂(圖7d~f)可以發(fā)現(xiàn)，在兩種循環(huán)載荷作用下位錯(cuò)源都開(kāi)動(dòng)而產(chǎn)生了大量位錯(cuò) 對(duì)比圖7a與圖7d可見(jiàn)，位錯(cuò)在沿滑移面運(yùn)動(dòng)的過(guò)程中遇到晶界而形成位錯(cuò)塞積，在低應(yīng)變幅(0.4%)下(圖7a)晶界處塞積的位錯(cuò)數(shù)目比高應(yīng)變幅(0.9%)下(圖7d)晶界處塞積的位錯(cuò)數(shù)目多；對(duì)比圖7b、c和e、f可見(jiàn)，在晶粒內(nèi)大量位錯(cuò)交互作用形成位錯(cuò)纏結(jié)，在低應(yīng)變幅(0.4%)下的位錯(cuò)纏結(jié)比高應(yīng)變幅(0.9%)下的位錯(cuò)纏結(jié)嚴(yán)重 同時(shí)，許多有序排列的短位錯(cuò)線(xiàn)形成了帶狀的密集位錯(cuò)束，且在0.4%應(yīng)變幅下試樣中位錯(cuò)束的密集程度(69條短位錯(cuò)線(xiàn)/μm)明顯高于0.9%應(yīng)變幅下試樣中的位錯(cuò)束的密集程度(50條短位錯(cuò)線(xiàn)/μm) 缺口試樣的Kt 越大則在循環(huán)變形過(guò)程中缺口處的局部最大應(yīng)力越高，在晶界處塞積的位錯(cuò)數(shù)目越多，大量位錯(cuò)的交互作用越容易發(fā)生位錯(cuò)纏結(jié)，進(jìn)而使試樣在循環(huán)載荷作用下發(fā)生循環(huán)硬化

圖7



圖7TC4 ELI合金光滑試樣在不同應(yīng)變幅控制下疲勞斷口處的TEM照片

Fig.7TEM images of fatigue fracture surfaces of TC4 ELI alloy smooth specimens under control of different strain amplitudes (a~c) 0.4%, (d~f) 0.9%

3 討論3.1 缺口應(yīng)力集中程度對(duì)合金低周疲勞性能的影響

采用Ramberg-Osgood模型[36]來(lái)描述TC4 ELI合金材料的循環(huán)應(yīng)力-應(yīng)變特征

Δεt2=Δσ2E+?σ2K'n'

(2)

式中Δεt /2為總應(yīng)變幅；Δσ/2為應(yīng)力幅；E為彈性模量；K'為循環(huán)強(qiáng)度系數(shù)；n'為循環(huán)應(yīng)變硬化指數(shù)

采用塑性分量計(jì)算的結(jié)果表明，在雙對(duì)數(shù)坐標(biāo)系中應(yīng)力幅與塑性應(yīng)變幅呈線(xiàn)性關(guān)系

Δσ2=K'?εp2n'

(3)

式中Δεp /2為塑性應(yīng)變幅

圖8a給出了不同Kt 試樣應(yīng)力幅與塑性應(yīng)變幅的擬合曲線(xiàn) 進(jìn)行雙對(duì)數(shù)線(xiàn)性擬合計(jì)算出的不同Kt 試樣的n'和K'值，列于表2 建立的不同Kt 試樣的n'和K'值與Kt 的關(guān)系如圖8b所示 將光滑試樣數(shù)據(jù)擬合得到的n'和K'代入到 式(2)，得到光滑試樣循環(huán)總應(yīng)變幅和應(yīng)力幅之間的關(guān)系

Δεt2=Δσ2E+Δσ2×11116.410.059

(4)

圖8



圖8缺口應(yīng)力集中系數(shù)不同的TC4 ELI合金的應(yīng)力幅與塑性應(yīng)變幅擬合曲線(xiàn)圖及循環(huán)強(qiáng)度系數(shù)和循環(huán)應(yīng)變硬化指數(shù)隨缺口應(yīng)力集中系數(shù)的變化

Fig.8Fitting curves of stress amplitude and plastic strain amplitude of TC4 ELI alloy with different notch stress concentration factors (a), Variations of cyclic strength coefficient and cyclic strain hardening exponent (b) of TC4 ELI alloy with notch stress concentration factor

Table 2

表2

表2缺口應(yīng)力集中系數(shù)不同的TC4 ELI合金的疲勞性能參數(shù)

Table 2Fatigue performance parameter of TC4 ELI alloy with different notch stress concentration factors

Kt	n'	K'
1	0.059	1116.4
1.97	0.127	2217.4
2.64	0.148	2388.9
3.62	0.216	5755.6

圖8b給出了循環(huán)強(qiáng)度系數(shù)和循環(huán)應(yīng)變硬化指數(shù)隨缺口應(yīng)力集中系數(shù)的變化 線(xiàn)性擬合結(jié)果表明，循環(huán)應(yīng)變硬化指數(shù)n'和循環(huán)強(qiáng)度系數(shù)K'都隨著缺口應(yīng)力集中系數(shù)的增大而增大，試樣的循環(huán)強(qiáng)度系數(shù)和循環(huán)應(yīng)變硬化指數(shù)基本上都與缺口應(yīng)力集中系數(shù)呈線(xiàn)性增大關(guān)系 金屬材料的循環(huán)應(yīng)變硬化指數(shù)反映金屬材料抵抗均勻塑性變形的能力，是表征其應(yīng)變硬化行為的指標(biāo)，而循環(huán)強(qiáng)度系數(shù)體現(xiàn)材料開(kāi)始發(fā)生集中塑性變形時(shí)的最大應(yīng)力 當(dāng)缺口應(yīng)力集中系數(shù)增大時(shí)，試樣在同樣疲勞加載條件下的局部應(yīng)力增大，試樣發(fā)生集中塑性變形時(shí)的最大應(yīng)力也相應(yīng)地增大

3.2 TC4ELI合金的低周疲勞損傷機(jī)制

為了揭示TC4 ELI合金在整個(gè)循環(huán)變形過(guò)程中損傷的演變規(guī)律，根據(jù)材料的循環(huán)應(yīng)力-應(yīng)變滯回線(xiàn)計(jì)算了試樣在循環(huán)變形過(guò)程中滯回能的變化 滯回能定義為應(yīng)力-應(yīng)變滯回線(xiàn)圍成的面積，指材料在循環(huán)過(guò)程中消耗的不可逆循環(huán)塑性功[37]，反映試樣在循環(huán)加載過(guò)程中的變形特征以及材料吸收循環(huán)塑性應(yīng)變能的能力[38] 滯回環(huán)越飽滿(mǎn)，表明試樣的塑性變形能力越強(qiáng)，材料吸收循環(huán)塑性應(yīng)變能的能力越好

圖9給出了TC4 ELI合金光滑試樣在Δεt /2=0.9%控制下的滯回能與相對(duì)循環(huán)周次的關(guān)系以及部分周次的滯回線(xiàn) 這里定義相對(duì)循環(huán)周次(N/Nf )為任意循環(huán)周次N與試樣循環(huán)至斷裂的疲勞周次Nf 的比值 由圖9a可以看出，光滑試樣在Δεt /2=0.9%控制下的滯回能曲線(xiàn)在循環(huán)后期出現(xiàn)了極值點(diǎn)，即在循環(huán)后期出現(xiàn)了滯回能下降 因此，選取圖9a中的滯回能曲線(xiàn)上的A(循環(huán)初始階段)、B(滯回能上升階段)、C(極值點(diǎn))、D(滯回能下降階段)和E(循環(huán)終了階段)五個(gè)參考點(diǎn)的滯回線(xiàn)進(jìn)一步探討循環(huán)變形過(guò)程中試樣的應(yīng)力-應(yīng)變變化 由圖9b可以看出，C點(diǎn)處的最大應(yīng)力高于D、E兩點(diǎn)處的最大應(yīng)力 在循環(huán)載荷作用過(guò)程中，到達(dá)C點(diǎn)對(duì)應(yīng)的循環(huán)周次時(shí)應(yīng)力達(dá)到最高值，隨后逐漸下降 這表明，此時(shí)材料內(nèi)部出現(xiàn)明顯的裂紋，在這種情況下(相同的應(yīng)變幅) 合金的承載能力降低

圖9



圖9光滑試樣在總應(yīng)變幅為0.9%控制下TC4 ELI合金的滯回能與相對(duì)循環(huán)周次(N/Nf )的關(guān)系以及滯回能曲線(xiàn)中五個(gè)參考點(diǎn)對(duì)應(yīng)的滯回線(xiàn)

Fig.9Relationships between hysteresis energy and relative cycles of TC4 ELI alloy smooth specimen under total strain amplitude of 0.9% (a), corresponding hysteretic loops of the five reference points in figure (a) (b)

圖10a~d給出了Kt 不同的合金的滯回能與試樣相對(duì)循環(huán)周次的關(guān)系 可以看出：所有試樣的滯回能曲線(xiàn)分為先升后降兩個(gè)連續(xù)的階段，且滯回能隨著應(yīng)變幅的增加而增加 這表明，隨著應(yīng)變幅的增加，試樣在循環(huán)過(guò)程中消耗的不可逆循環(huán)塑性功增加，進(jìn)而加速了損傷；而光滑試樣的滯回能變化呈現(xiàn)先增高后平穩(wěn)的規(guī)律，如圖10a所示；所有缺口試樣的滯回能曲線(xiàn)在循環(huán)后期均出現(xiàn)極值點(diǎn)，如圖10b~d所示 隨著應(yīng)變幅的增加，試樣的滯回能曲線(xiàn)極值點(diǎn)向低周次方向移動(dòng) 為此，用疲勞斷裂周次(Nf )對(duì)極值點(diǎn)處對(duì)應(yīng)的疲勞裂紋萌生壽命(Ni )做歸一化處理，定義為用Ni/Nf 表示的相對(duì)疲勞裂紋萌生壽命 圖10e和f分別給出了相對(duì)疲勞裂紋萌生壽命與Δεt /2、Kt 的關(guān)系 從圖10f可見(jiàn)，隨著Kt 的增大，極值點(diǎn)向低周次方向移動(dòng)，表現(xiàn)為提前出現(xiàn)極值點(diǎn)，即相對(duì)裂紋萌生壽命縮短 這是由于缺口的存在以及Kt 的增大使試樣過(guò)早萌生裂紋，試樣對(duì)循環(huán)塑性應(yīng)變能的吸收有較大的削弱，因而在圖中Kt 較高的試樣其滯回能小，且相對(duì)疲勞裂紋萌生壽命較短

圖10



圖10缺口應(yīng)力集中系數(shù)不同的合金的滯回能與相對(duì)循環(huán)周次關(guān)系以及相對(duì)疲勞裂紋萌生壽命與Δεt /2和Kt 的關(guān)系

Fig.10Relation diagram between hysteresis energy and relative cycle of alloy (a) Kt =1, (b) Kt =1.97, (c) Kt =2.64, (d) Kt =3.62, (e) the relationships between relative fatigue crack initiation life and Δεt /2, (f) the relationships between relative fatigue crack initiation life and Kt

同時(shí)，圖10e表明，在Kt 相同的條件下，相對(duì)疲勞裂紋萌生壽命Ni/Nf 與外加總應(yīng)變幅Δεt /2呈線(xiàn)性關(guān)系；從圖10f可見(jiàn)，在應(yīng)變幅相同的條件下，相對(duì)裂紋萌生壽命Ni /Nf 與缺口應(yīng)力集中系數(shù)Kt 呈線(xiàn)性關(guān)系 由于Kt =2.64試樣在Δεt /2=0.7%下的相對(duì)疲勞裂紋萌生壽命誤差較大，本文僅對(duì)Kt =1、1.97、3.62的試樣在不同Δεt /2的相對(duì)裂紋萌生壽命進(jìn)行擬合，得到三組相對(duì)疲勞裂紋萌生壽命與Δεt /2的表達(dá)式

NiNf=-0.472Δεt2+1.228

(5)

NiNf=-0.610Δεt2+1.168

(6)

NiNf=-0.721Δεt2+1.1665

(7)

根據(jù)式(5)~(7)建立了Kt 與式中的斜率和截距的關(guān)系，對(duì)不同Kt 試樣在不同Δεt /2下計(jì)算出的相對(duì)疲勞裂紋萌生壽命進(jìn)行擬合，并列用Ni /Nf 與Δεt /2、Kt 的關(guān)系預(yù)測(cè)含缺口TC4ELI合金試樣的相對(duì)裂紋萌生壽命

NiNf=1.394-0.074Kt-0.585Δεt2-0.046KtΔεt2

(8)

式中Ni /Nf 為相對(duì)裂紋萌生壽命；Δεt /2為外加總應(yīng)變幅；Kt 為缺口應(yīng)力集中系數(shù)

將Kt 和Δεt /2代入 式(8)，可計(jì)算出Ni /Nf 的預(yù)測(cè)值 圖11給出了外加總應(yīng)變幅Δεt /2與相對(duì)疲勞裂紋萌生壽命Ni /Nf 的關(guān)系 圖11同時(shí)給出了實(shí)驗(yàn)值與用 式(8)計(jì)算出的預(yù)測(cè)值，可見(jiàn)理論預(yù)測(cè)值與實(shí)驗(yàn)值的相對(duì)誤差小于10%，表明預(yù)測(cè)結(jié)果較好 同時(shí)，從圖11可見(jiàn)，模型預(yù)測(cè)Kt 較小的鈦合金試樣在較高應(yīng)變幅下(圖11中紅色和藍(lán)色數(shù)據(jù)點(diǎn)與預(yù)測(cè)值對(duì)比)的疲勞裂紋萌生壽命其相對(duì)誤差更小，而對(duì)較低應(yīng)變幅下Kt 較高的(見(jiàn)圖11中黑色虛線(xiàn)上方數(shù)據(jù)點(diǎn))試樣的相對(duì)疲勞裂紋萌生壽命預(yù)測(cè)值大于1，表明在這種情況下用此模型預(yù)測(cè)較為危險(xiǎn) 其次，Kt =1.00和1.97的鈦合金試樣的實(shí)驗(yàn)值與預(yù)測(cè)值數(shù)據(jù)吻合較好 綜上，分析和對(duì)比實(shí)驗(yàn)值與預(yù)測(cè)值可說(shuō)明該模型能較好地預(yù)測(cè)Kt 較低的鈦合金試樣在高應(yīng)變幅下的相對(duì)疲勞裂紋萌生壽命 缺口應(yīng)力集中系數(shù)和應(yīng)變幅值共同影響TC4 ELI合金的相對(duì)疲勞裂紋萌生壽命； 式(8)還表明，缺口應(yīng)力集中系數(shù)對(duì)相對(duì)裂紋萌生壽命的影響比應(yīng)變幅對(duì)相對(duì)裂紋萌生壽命的影響小 綜上，本文提出的模型可用于預(yù)測(cè)給定的較高實(shí)驗(yàn)應(yīng)變幅和較低缺口應(yīng)力集中系數(shù)材料的相對(duì)疲勞裂紋萌生壽命

圖11



圖11TC4 ELI合金的相對(duì)疲勞裂紋萌生壽命與總應(yīng)變幅的關(guān)系

Fig.11Relationships between relative fatigue crack initiation life and total strain amplitude of TC4 ELI alloy

4 結(jié)論

(1) 在外加總應(yīng)變幅為0.9%和0.8%條件下TC4 ELI合金光滑試樣僅出現(xiàn)循環(huán)軟化特性，在外加總應(yīng)變幅為0.7%和0.6%條件下表現(xiàn)出先循環(huán)硬化后循環(huán)軟化特性，在外加總應(yīng)變幅為0.5%和0.4%下表現(xiàn)出先循環(huán)硬化再循環(huán)飽和的特性；

(2) TC4 ELI合金缺口試樣在循環(huán)變形初期均呈現(xiàn)出循環(huán)硬化特性；在0.6%和0.7%應(yīng)變幅條件下合金先呈現(xiàn)出循環(huán)硬化隨后出現(xiàn)循環(huán)軟化特性，而應(yīng)變幅低于0.4%時(shí)合金呈現(xiàn)出循環(huán)硬化和隨后二次硬化或循環(huán)飽和特性；

(3) 基于循環(huán)載荷作用過(guò)程中滯回能建立的含應(yīng)力集中系數(shù)的TC4 ELI鈦合金試樣的相對(duì)裂紋萌生壽命預(yù)測(cè)模型，能較好地預(yù)測(cè)具有較低缺口應(yīng)力集中系數(shù)的TC4 ELI合金在高應(yīng)變幅下的相對(duì)疲勞裂紋萌生壽命

參考文獻(xiàn)

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