缺口应力集中系数对TC4 ELI合金低周疲劳性能的影响

钛合金具有比强度高、耐腐蚀和耐高温性能优异等特点 因此，在航空航天、生物医学、深海服役等领域得到了广泛的应用[1~5] Ti-6Al-4V(TC4)合金是一种应用最广的α+β型钛合金[6]，通过降低其中的C、N、O等元素含量便可制备出含超低间隙(Extra-low-interstitial, ELI)元素含量的TC4 ELI合金，其具有更高的可焊接性和冲压成型性[7~9] 深海潜水器是深海工程作业的重要装备，在潜水器下潜和上浮过程中其耐压壳承受极大的循环载荷[13,14] 随着深海潜水器下潜深度增加对其材料更高力学性能的需求，TC4 ELI合金在耐压壳上的应用备受关注[10~12]，而耐压壳用钛合金在循环大应变幅下的低周疲劳性能成为评价其服役性能的重要指标 同时，在较大循环载荷的作用下耐压壳材料将不可避免地产生局部应力集中[15]，其低周疲劳性能对缺口等缺陷引起的应力集中的敏感性直接关乎构件的服役可靠性

目前，对TC4 ELI合金疲劳性能的研究主要集中在显微组织对其疲劳性能的影响[16~21] 钛合金的低周疲劳性能强烈地依赖于其显微组织和疲劳加载应变幅[22]，而应变幅的增大将使合金疲劳寿命降低 在不同应变幅加载条件下，具有网篮组织的TC4 ELI合金往往呈现出循环软化特性，且随着应变幅的增大韧性断裂特征更显著[23] 在较低应变幅(0.6%)条件下，双态组织TC4合金中初生α相被拉长，表现为因α相参与疲劳变形而使材料寿命较长；而在较高应变幅(1.2%)条件下，疲劳裂纹穿过α相扩展，使材料的疲劳寿命变短[24] 同时，钛合金的疲劳性能对诸如缺口等缺陷极为敏感 随着缺口曲率半径的减小，缺口越尖锐，从而使得衡量零部件缺口处局部应力集中参数的疲劳缺口应力集中系数越大，材料疲劳失效的概率越高[25] 当具有网篮组织的TC17合金的缺口应力集中系数大于1.92时，缺口对疲劳寿命产生显著影响，使其疲劳寿命急剧降低[26] 为了更好地分析在循环载荷作用下钛合金的损伤情况，有研究者提出了多种预测钛合金疲劳寿命的模型[27]，包括基于应变能密度预测缺口构件疲劳寿命的模型[28]、基于临界应变法预测光滑和缺口试样的疲劳寿命模型[29]、基于剪应变的临界面法建立的预测TC4合金多轴疲劳寿命的模型[30]和基于表面缺口的总疲劳寿命的分离模型[31]

耐压壳结构因设计需求而不可避免地出现各种类型的缺口，在外载荷作用下这些缺口处必然会产生局部应力集中 由此产生的应力集中极易成为零部件最薄弱的环节而引发疲劳裂纹的萌生 缺口疲劳分析对结构完整性设计至关重要，缺口应力集中系数能衡量零部件局部应力集中的大小 因此，通过建立缺口应力集中系数与低周疲劳相对裂纹萌生寿命间的预测模型可为设计和研发深潜器提供理论参考 鉴于此，本文研究具有不同缺口应力集中系数的TC4 ELI合金的低周疲劳性能，通过对不同循环应变幅条件下合金的循环应力-应变响应及循环变形行为的研究，获得了不同缺口应力集中系数试样的低周疲劳寿命，探讨了缺口对合金低周疲劳性能的影响及其疲劳损伤机理，获得了合金低周疲劳性能参数与缺口应力集中系数之间的关系，建立了这种合金相对裂纹萌生寿命的预测模型

1 实验方法

实验用轧制态TC4 ELI合金板材的名义化学成分列于表1 按照GB/T15248-2008标准加工疲劳试样，图1给出了光滑试样和含缺口试样的尺寸及其加工精度 试样轴向加载方向为板材的轧制方向 光滑试样和缺口试样的标距段直径均为6.5 mm，长度为13 mm；加工缺口试样时采用环切方式开缺口，缺口的应力集中系数(Kt)为

Table 1

表1

表1TC4 ELI合金的名义成分

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.

图1



图1不同缺口应力集中系数的TC4 ELI低周疲劳试样的尺寸和加工精度

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为试样缺口处半径；r为缺口处曲率半径；v为泊松比；C为ar+1 分别设计了三种缺口试样，其Kt 值分别为1.97、2.64和3.62 为了对照，同时加工了Kt 值为1的光滑试样 进行疲劳实验前，对试样表面进行抛光处理

使用计算机控制的MTS-647液压伺服疲劳试验机进行低周疲劳性能测试实验，实验中采用恒总应变幅控制的轴向拉-压对称方式加载，加载频率为f =0.5 Hz，轴向应变速率为ε˙=3×10-3s-1 实验中选取的总应变幅(Δεt /2)为0.2%~0.9%，疲劳加载波形为三角波形

采用ZESIS Supra 35场发射扫描电子显微镜(SEM) 观察和分析疲劳断裂的断口 采用FEI Tecnai F20型透射电子显微镜(TEM) 观察和表征合金中的位错行为 制备TEM样品时，用体积分数为60%甲醇、35%正丁醇和5%高氯酸的混合溶液进行双喷减薄，操作电压为22 V，温度范围为从-28℃到-30℃

2 实验结果2.1 TC4 ELI合金的显微组织

图2给出了TC4 ELI合金轧制态的金相组织为典型的网篮组织，即在β转变基体上形成了α相的网篮编织结构，其中片状α相的长度为35±5 μm、宽度为4±1 μm

图2



图2轧制态TC4 ELI合金的光学显微组织

Fig.2Optical image of rolled TC4 ELI alloy

2.2 循环应力响应特性

图3a~d给出了Kt 值不同的TC4 ELI合金试样在不同Δεt /2条件下的循环应力幅随循环周次的变化 由图3a可见，当Δεt /2为0.9%和0.8%时，Kt =1的光滑试样表现出完全的循环软化行为，直至最终断裂失效；Δεt /2为0.7%和0.6%的试样呈现初始的循环硬化，随后逐渐循环软化而断裂失效 这一光滑试样在高应变幅加载条件下的循环软化现象，不仅在TC4 ELI合金中发生过[21,23]，在其它类型的钛合金中也发生过[4,24,32,33] 这种现象与高应变幅循环加载条件下材料内部高密度的位错重排和部分湮灭有关[34]；Δεt /2为0.4%和0.5%的光滑试样均表现出初始循环硬化和随后的循环饱和行为，但后者在循环末期还呈现出一定的循环二次硬化现象

图3



图3缺口应力集中系数不同的TC4 ELI合金的应力幅随循环周次的变化曲线

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

图3b~d给出了缺口试样的实验结果 可以看出，Δεt /2大于等于0.5%的试样均出现初始循环硬化及随后循环软化的现象 这是由于循环加载的初期，材料刚开始塑性变形时的位错增殖行为，且随着疲劳循环周次的增加位错密度随之提高[35] 当应变幅为0.3%和0.4%时，Kt =1.97的试样均呈现出初始循环硬化和随后的二次硬化现象；当应变幅为0.4%时，Kt =2.64试样也表现出上述现象 而Kt=3.62的试样在0.4%至0.2%的应变幅作用下则均呈现出初始循环硬化行为和随后循环饱和现象 缺口应力集中系数Kt 定义为缺口处的局部最大应力σmax与名义应力的比值 在循环变形过程中，缺口应力集中系数较大的试样在缺口处较高的局部最大应力使其变形程度更大，位错不断增殖使其密度提高，发生的位错缠结、塞积使材料发生循环硬化 同时，材料内部位错的湮灭使其发生软化，在此过程中位错的增殖、塞积比位错的湮灭表现得更加突出 因此，在循环变形初期发生循环硬化，而循环载荷作用一段时间后位错的增殖、塞积与湮灭达到动态平衡而出现循环饱和

2.3 循环应力-应变滞回线

图4给出了Kt 不同的试样在半寿命下的循环应力-应变滞回线 由图4a可见，当Δεt /2为0.4%和0.5%时，光滑试样的循环滞回线所围的面积趋于零，表明材料几乎未产生循环塑性变形；而当Δεt /2从0.5%增大到0.9%时，循环滞回线的面积随着循环周次增加逐渐增大，表明试样的累积循环塑性变形越来越明显 从图4a~d的对比可见，在相同的Δεt /2条件下，随着Kt 的增加滞回线所围面积不断减小，表明循环塑性变形减小

图4



图4缺口应力集中系数不同的TC4 ELI试样的循环应力-应变滞回线

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 疲劳损伤行为

图5给出了TC4 ELI合金光滑试样分别在0.4%低应变幅和0.9%高应变幅下的低周疲劳断口的SEM对比观察 由图5a和b的低倍对比观察可以发现，TC4 ELI合金无缺口的光滑试样的低周疲劳裂纹均从试样表面萌生，断裂面均由疲劳裂纹萌生区、疲劳裂纹扩展区和瞬断区组成，较高应变幅下试样的疲劳断口(图5b)更为粗糙；图5c和d表明，在两个应变幅条件下的疲劳裂纹萌生区都呈现出解理小台阶的断裂特征，其疲劳裂纹扩展区都有明显的疲劳条纹(图5e和f)，且Δεt /2=0.9%试样的疲劳条纹间距为7.7 μm，明显大于Δεt /2=0.4%试样的疲劳条纹间距(2.5 μm) 这表明，随着应变幅的增加，每个循环周次下疲劳条纹扩展的距离增大 对比图5g和h的最终瞬断区可见，Δεt /2=0.9%试样的韧窝深度大于Δεt /2=0.4%试样的韧窝深度

图5



图5不同应变幅控制下TC4 ELI合金光滑试样疲劳断口的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%

图6给出了三种缺口应力集中系数的缺口试样在应变幅为0.3%控制下的疲劳断口的SEM照片 图6a~c给出了Kt 分别为1.97、2.64和3.62的低倍疲劳断口形貌，可见高Kt 试样的疲劳断口形貌较低Kt 试样的疲劳断口形貌更光滑；图6d~f给出了缺口试样的疲劳裂纹扩展区 可以看出，疲劳裂纹扩展区均有明显的疲劳条纹，Kt 为1.97、2.64和3.62三种试样的疲劳条纹间距分别为4.6 μm、1.3 μm和0.9 μm，表明试样的Kt 越高其疲劳条纹间距越小；图6g~i给出了三种Kt 缺口试样的最终断裂区 可以看出，最终断裂区均由大小不同的韧窝组成，Kt 为1.97、2.64和3.62试样的疲劳断口韧窝的尺寸分别为5.8±0.5 μm、9.4±1.2 μm和8.8±2.1 μm 这表明，Kt 越小疲劳断口的韧窝尺寸越小且尺寸越均匀

图6



图6三种缺口应力集中系数的TC4 ELI合金缺口试样在应变幅为0.3%控制下疲劳断口的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

结合图3b~d可见，缺口试样在不同应变幅控制下的循环初期均发生循环硬化，而光滑试样仅在低应变幅下发生循环硬化，而在高应变幅下发生循环软化 为了进一步分析在材料循环硬化和循环软化过程中内部位错结构可能发生的变化，图7给出了应变幅为0.4%和0.9%两个典型加载条件下合金出现循环硬化和软化的疲劳断口的TEM照片 对比低应变幅条件下的疲劳断裂(图7a~c)和高应变幅条件下疲劳断裂(图7d~f)可以发现，在两种循环载荷作用下位错源都开动而产生了大量位错 对比图7a与图7d可见，位错在沿滑移面运动的过程中遇到晶界而形成位错塞积，在低应变幅(0.4%)下(图7a)晶界处塞积的位错数目比高应变幅(0.9%)下(图7d)晶界处塞积的位错数目多；对比图7b、c和e、f可见，在晶粒内大量位错交互作用形成位错缠结，在低应变幅(0.4%)下的位错缠结比高应变幅(0.9%)下的位错缠结严重 同时，许多有序排列的短位错线形成了带状的密集位错束，且在0.4%应变幅下试样中位错束的密集程度(69条短位错线/μm)明显高于0.9%应变幅下试样中的位错束的密集程度(50条短位错线/μm) 缺口试样的Kt 越大则在循环变形过程中缺口处的局部最大应力越高，在晶界处塞积的位错数目越多，大量位错的交互作用越容易发生位错缠结，进而使试样在循环载荷作用下发生循环硬化

图7



图7TC4 ELI合金光滑试样在不同应变幅控制下疲劳断口处的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 讨论3.1 缺口应力集中程度对合金低周疲劳性能的影响

采用Ramberg-Osgood模型[36]来描述TC4 ELI合金材料的循环应力-应变特征

Δεt2=Δσ2E+?σ2K'n'

(2)

式中Δεt /2为总应变幅；Δσ/2为应力幅；E为弹性模量；K'为循环强度系数；n'为循环应变硬化指数

采用塑性分量计算的结果表明，在双对数坐标系中应力幅与塑性应变幅呈线性关系

Δσ2=K'?εp2n'

(3)

式中Δεp /2为塑性应变幅

图8a给出了不同Kt 试样应力幅与塑性应变幅的拟合曲线 进行双对数线性拟合计算出的不同Kt 试样的n'和K'值，列于表2 建立的不同Kt 试样的n'和K'值与Kt 的关系如图8b所示 将光滑试样数据拟合得到的n'和K'代入到 式(2)，得到光滑试样循环总应变幅和应力幅之间的关系

Δεt2=Δσ2E+Δσ2×11116.410.059

(4)

图8



图8缺口应力集中系数不同的TC4 ELI合金的应力幅与塑性应变幅拟合曲线图及循环强度系数和循环应变硬化指数随缺口应力集中系数的变化

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缺口应力集中系数不同的TC4 ELI合金的疲劳性能参数

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

图8b给出了循环强度系数和循环应变硬化指数随缺口应力集中系数的变化 线性拟合结果表明，循环应变硬化指数n'和循环强度系数K'都随着缺口应力集中系数的增大而增大，试样的循环强度系数和循环应变硬化指数基本上都与缺口应力集中系数呈线性增大关系 金属材料的循环应变硬化指数反映金属材料抵抗均匀塑性变形的能力，是表征其应变硬化行为的指标，而循环强度系数体现材料开始发生集中塑性变形时的最大应力 当缺口应力集中系数增大时，试样在同样疲劳加载条件下的局部应力增大，试样发生集中塑性变形时的最大应力也相应地增大

3.2 TC4ELI合金的低周疲劳损伤机制

为了揭示TC4 ELI合金在整个循环变形过程中损伤的演变规律，根据材料的循环应力-应变滞回线计算了试样在循环变形过程中滞回能的变化 滞回能定义为应力-应变滞回线围成的面积，指材料在循环过程中消耗的不可逆循环塑性功[37]，反映试样在循环加载过程中的变形特征以及材料吸收循环塑性应变能的能力[38] 滞回环越饱满，表明试样的塑性变形能力越强，材料吸收循环塑性应变能的能力越好

图9给出了TC4 ELI合金光滑试样在Δεt /2=0.9%控制下的滞回能与相对循环周次的关系以及部分周次的滞回线 这里定义相对循环周次(N/Nf )为任意循环周次N与试样循环至断裂的疲劳周次Nf 的比值 由图9a可以看出，光滑试样在Δεt /2=0.9%控制下的滞回能曲线在循环后期出现了极值点，即在循环后期出现了滞回能下降 因此，选取图9a中的滞回能曲线上的A(循环初始阶段)、B(滞回能上升阶段)、C(极值点)、D(滞回能下降阶段)和E(循环终了阶段)五个参考点的滞回线进一步探讨循环变形过程中试样的应力-应变变化 由图9b可以看出，C点处的最大应力高于D、E两点处的最大应力 在循环载荷作用过程中，到达C点对应的循环周次时应力达到最高值，随后逐渐下降 这表明，此时材料内部出现明显的裂纹，在这种情况下(相同的应变幅) 合金的承载能力降低

图9



图9光滑试样在总应变幅为0.9%控制下TC4 ELI合金的滞回能与相对循环周次(N/Nf )的关系以及滞回能曲线中五个参考点对应的滞回线

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)

图10a~d给出了Kt 不同的合金的滞回能与试样相对循环周次的关系 可以看出：所有试样的滞回能曲线分为先升后降两个连续的阶段，且滞回能随着应变幅的增加而增加 这表明，随着应变幅的增加，试样在循环过程中消耗的不可逆循环塑性功增加，进而加速了损伤；而光滑试样的滞回能变化呈现先增高后平稳的规律，如图10a所示；所有缺口试样的滞回能曲线在循环后期均出现极值点，如图10b~d所示 随着应变幅的增加，试样的滞回能曲线极值点向低周次方向移动 为此，用疲劳断裂周次(Nf )对极值点处对应的疲劳裂纹萌生寿命(Ni )做归一化处理，定义为用Ni/Nf 表示的相对疲劳裂纹萌生寿命 图10e和f分别给出了相对疲劳裂纹萌生寿命与Δεt /2、Kt 的关系 从图10f可见，随着Kt 的增大，极值点向低周次方向移动，表现为提前出现极值点，即相对裂纹萌生寿命缩短 这是由于缺口的存在以及Kt 的增大使试样过早萌生裂纹，试样对循环塑性应变能的吸收有较大的削弱，因而在图中Kt 较高的试样其滞回能小，且相对疲劳裂纹萌生寿命较短

图10



图10缺口应力集中系数不同的合金的滞回能与相对循环周次关系以及相对疲劳裂纹萌生寿命与Δεt /2和Kt 的关系

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

同时，图10e表明，在Kt 相同的条件下，相对疲劳裂纹萌生寿命Ni/Nf 与外加总应变幅Δεt /2呈线性关系；从图10f可见，在应变幅相同的条件下，相对裂纹萌生寿命Ni /Nf 与缺口应力集中系数Kt 呈线性关系 由于Kt =2.64试样在Δεt /2=0.7%下的相对疲劳裂纹萌生寿命误差较大，本文仅对Kt =1、1.97、3.62的试样在不同Δεt /2的相对裂纹萌生寿命进行拟合，得到三组相对疲劳裂纹萌生寿命与Δεt /2的表达式

NiNf=-0.472Δεt2+1.228

(5)

NiNf=-0.610Δεt2+1.168

(6)

NiNf=-0.721Δεt2+1.1665

(7)

根据式(5)~(7)建立了Kt 与式中的斜率和截距的关系，对不同Kt 试样在不同Δεt /2下计算出的相对疲劳裂纹萌生寿命进行拟合，并列用Ni /Nf 与Δεt /2、Kt 的关系预测含缺口TC4ELI合金试样的相对裂纹萌生寿命

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

(8)

式中Ni /Nf 为相对裂纹萌生寿命；Δεt /2为外加总应变幅；Kt 为缺口应力集中系数

将Kt 和Δεt /2代入 式(8)，可计算出Ni /Nf 的预测值 图11给出了外加总应变幅Δεt /2与相对疲劳裂纹萌生寿命Ni /Nf 的关系 图11同时给出了实验值与用 式(8)计算出的预测值，可见理论预测值与实验值的相对误差小于10%，表明预测结果较好 同时，从图11可见，模型预测Kt 较小的钛合金试样在较高应变幅下(图11中红色和蓝色数据点与预测值对比)的疲劳裂纹萌生寿命其相对误差更小，而对较低应变幅下Kt 较高的(见图11中黑色虚线上方数据点)试样的相对疲劳裂纹萌生寿命预测值大于1，表明在这种情况下用此模型预测较为危险 其次，Kt =1.00和1.97的钛合金试样的实验值与预测值数据吻合较好 综上，分析和对比实验值与预测值可说明该模型能较好地预测Kt 较低的钛合金试样在高应变幅下的相对疲劳裂纹萌生寿命 缺口应力集中系数和应变幅值共同影响TC4 ELI合金的相对疲劳裂纹萌生寿命； 式(8)还表明，缺口应力集中系数对相对裂纹萌生寿命的影响比应变幅对相对裂纹萌生寿命的影响小 综上，本文提出的模型可用于预测给定的较高实验应变幅和较低缺口应力集中系数材料的相对疲劳裂纹萌生寿命

图11



图11TC4 ELI合金的相对疲劳裂纹萌生寿命与总应变幅的关系

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

4 结论

(1) 在外加总应变幅为0.9%和0.8%条件下TC4 ELI合金光滑试样仅出现循环软化特性，在外加总应变幅为0.7%和0.6%条件下表现出先循环硬化后循环软化特性，在外加总应变幅为0.5%和0.4%下表现出先循环硬化再循环饱和的特性；

(2) TC4 ELI合金缺口试样在循环变形初期均呈现出循环硬化特性；在0.6%和0.7%应变幅条件下合金先呈现出循环硬化随后出现循环软化特性，而应变幅低于0.4%时合金呈现出循环硬化和随后二次硬化或循环饱和特性；

(3) 基于循环载荷作用过程中滞回能建立的含应力集中系数的TC4 ELI钛合金试样的相对裂纹萌生寿命预测模型，能较好地预测具有较低缺口应力集中系数的TC4 ELI合金在高应变幅下的相对疲劳裂纹萌生寿命

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