娄菊红
, 杨延清
LOU Juhong, YANG Yanqing
文献标识码: 分类号 TB331 文章编号 1005-3093(2016)07-0503-06
通讯作者:
收稿日期: 2015-06-5
网络出版日期: 2016-07-25
版权声明: 2016 《材料研究学报》编辑部 《材料研究学报》编辑部
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作者简介:
本文联系人: 娄菊红
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摘要
采用ANSYS有限元法建立三维模型, 研究了基体热膨胀系数和弹性模量对复合材料界面径向、轴向和周向残余应力大小和分布的影响。结果表明, 界面残余应力的改变量均与基体热膨胀系数的改变量成正比, 且随着基体热膨胀系数的减小界面周向残余应力沿着纤维周向分布的不均匀性减弱; 界面残余应力变化的总趋势是随着基体弹性模量的增大而增大, 但是增加的幅度不断减小。
关键词：
Abstract
The magnitude and distribution of the interfacial stresses along the radial-, axial- and circumferential directions at fiber side of fiber reinforced composites SiCf / Ti-6Al-4V with the change of thermal expansion coefficient and elasticity modulus of the matrix are analysed by three-dimensional model established by using finite element method. The results show that the change of interfacial residual stress is proportional to that of thermal expansion coefficient of matrix, and the no-uniformity of distribution of the residual stress along the circumferential direction of fiber decreases with the decrease of thermal expansion coefficient. In addition, interfacial residual stress usually increases with the increase of elasticity modulus of matrix, but the increase of which reduces gradually.
Keywords：
金属基复合材料(MMCs)具有较高的比强度、比刚度、比模量、极佳的蠕变和疲劳性能以及良好的高温性能, 在航空、航天、电子及运输等高技术领域有广阔的应用前景[1-4]。但是, 由于SiC纤维和Ti合金基体热膨胀系数有较大差异, 当SiCf/Ti复合材料从制备态、热处理或二次加工温度冷却到室温时在材料中产生热残余应力[5, 6], 影响其力学性能。例如, 纤维/基体界面的径向残余压应力使其在横向载荷作用下界面的脱粘延迟[7]; 纤维中, 沿轴向方向的残余压应力使其在纵向载荷作用下的承载能力增强[8, 9]; 环向的残余拉应力使得复合材料基体中产生一些垂直于界面的径向裂纹, 特别是当纤维间距较小时 [10, 11]。因此, 全面了解复合材料热残余应力的各种影响因素、热残余应力的状态及分布规律, 对复合材料强度估算和寿命预测等有重要意义。
本文以Ti-6Al-4V合金为基础, 以最常见的纤维四方和六方排布的代表性体元为模型(纤维体积分数35%), 研究SiCf/Ti基复合材料从高温制备态冷却至室温时, 基体热膨胀系数和弹性模量的变化对SiCf/Ti复合材料界面径向、轴向和周向热残余应力大小和分布的影响, 并分析这些热残余应力与复合材料宏观响应之间的关系。
所用的材料为SiCf/Ti-6Al-4V复合材料, 设基体为理想弹—塑性应变硬化材料, 服从Von Mises屈服准则, 在不同温度下热膨胀系数和弹性模量的原始值与变化值分别列于表1和表2[12, 13]; 设纤维为线弹性材料, 直径为100 μm, 其性能列于表3[14]。
表1 Ti-6Al-4V基体热膨胀系数的原始值及变化值(10-6/℃)
Table 1 Original data and change value of thermal expansion coefficient for Ti-6Al-4V matrix (10-6/℃)
| T(℃) | α1 | α2 | α3 | α4 |
|---|---|---|---|---|
| 20 | 8.8 | 7.04 | 5.28 | 3.52 |
| 200 | 9.4 | 7.52 | 5.64 | 3.76 |
| 400 | 10.3 | 8.24 | 6.18 | 4.12 |
| 600 | 10.8 | 8.64 | 6.48 | 4.32 |
| 800 | 11.5 | 9.2 | 6.9 | 4.6 |
表2 Ti-6Al-4V基体弹性模量的原始值及变化值(GPa)
Table 2 Original data and change value of elastic modulus for Ti-6Al-4V matrix(GPa)
| T(℃) | E1 | E2 | E3 | E4 |
|---|---|---|---|---|
| 20 | 114.0 | 228.0 | 342 | 456 |
| 200 | 103.8 | 207.6 | 311.4 | 415.2 |
| 400 | 92.6 | 185.3 | 277.8 | 370.4 |
| 600 | 76.4 | 152.8 | 229.2 | 305.6 |
| 800 | 62.8 | 125.6 | 188.4 | 251.2 |
表3 国产SiC纤维的性能
Table 3 Main properties of domestic SiC fiber
| T(℃) | E(GPa) | ν | α(10-6/℃) |
|---|---|---|---|
| All temperature | 402 | 0.25 | 4.0 |
复合材料中常见的纤维排布方式有四方排布和六方排布, 其二维截面示意图和对应的有限元模型如图1和图2所示。模型在Z方向的高度为1000 μm, “θ ”表示XOY坐标平面内从X方向到Y方向旋转的角度, 用于表示基体沿着界面的各个位置; “Z”表示沿纤维长度方向的尺寸。模拟过程中假定纤维和基体处于理想粘合状态, 其边界条件见文献[15]。
图1 三种纤维排布方式的二维截面示意图(单位: mm)
Fig.1 Two-dimensional cross-sections of different fiber arrays (unit: mm) (a) square array, (b) hexagonal array
图2 不同纤维排布方式的有限元模型
Fig.2 Finite element model for different fiber arrays (a) square array, (b) hexagonal array
图3给出了不同热膨胀系数下纤维一侧界面残余应力沿纤维周向(纤维四方排列θ=0°~45°位置和纤维六方排列的θ=0°~30°位置)在Z=500 μm平面上的分布。可以看出, 无论是四方还是六方排布, 界面径向、轴向和周向残余应力的改变量均与基体热膨胀系数的改变量成正比。在θ=0°处纤维四方和六方排布情况下基体热膨胀系数每减小0.2α1, 界面径向、残余压应力分别减小85 MPa和74 MPa, 且当室温下基体热膨胀系数小于纤维热膨胀系数时界面径向残余应力变为拉伸状态(图3a1和a2), 严重破坏纤维/基体界面结合, 甚至产生沿界面的环向裂纹; 界面轴向残余压应力分别减小201 MPa和200 MPa, 而且与径向残余应力的情况相同, 当基体热膨胀系数小于纤维热膨胀系数时界面轴向残余应力也变为拉伸状态(图3b1和b2), 使复合材料(纤维)承受纵向拉伸载荷的能力减弱; 界面周向残余压应力分别减小51 MPa和66 MPa, 甚至变为拉伸状态(图3c1和c2), 这有利于防止垂直于界面的径向裂纹。在θ=45°(四方排布)或θ=30°(六方排布)处纤维四方和六方排布情况下基体热膨胀系数每减小0.2α1, 界面径向残余压应力分别减小61 MPa和66 MPa, 减小的幅度比θ=0°位置的小, 这说明基体与纤维的热膨胀系数越接近径向残余应力沿纤维周向的不均匀程度越小(图3a1和a2); 界面轴向残余压应力分别减小204 MPa和199 MPa时, 变化幅度与θ=0°位置基本相等; 界面周向残余压应力分别减小90 MPa和71 MPa, 减小幅度比θ=0°位置的大, 即随着基体热膨胀系数的减小周向残余应力沿纤维周向的不均匀程度减小。
图3 不同基体热膨胀系数下纤维一侧界面残余应力的分布
Fig.3 Distributions of interfacial residual stresses in fiber with different coefficient of thermal expansion for matrix (a)radial residual stress (b) axial residual stress (c) hoop residual stress (“1”represents fiber square array and “2”represents fiber hexagonal array)
图4给出了不同弹性模量下纤维一侧界面残余应力沿纤维周向(纤维四方排列θ=0°~45°位置和纤维六方排列的θ=0°~30°位置)在Z=500 μm平面上的分布。可以看出, 随着基体弹性模量的增大(基体变形抗力随之增高)纤维一侧界面残余应力变化的总趋势是径向、轴向和周向残余压应力均增大, 而且基体弹性模量从E1开始增加第一个1倍的E1(即弹性模量从E1增为E2)时界面残余应力变化量最大, 增加第二个1倍的E1(即弹性模量从E2增为E3)时界面残余应力变化量次之, 增加第三个1倍的E1(即弹性模量从E3增为E4)时界面残余应力变化量最小。对于纤维四方排列, 在θ=0°和θ=45°位置随着基体弹性模量的不断增加, 界面径向残余压应力的增量依次为168 MPa、6 MPa、-27 MPa和149 MPa、141 MPa、85 MPa(图4a1), 即弹性模量从E1增为E2时径向残余压应力在θ=0°和45°位置都大大提高, 但是随着弹性模量的进一步增加径向残余压应力仅在θ=45°位置有所提高而在θ=0°位置变化不大, 使得界面结合的薄弱环节由θ=45°位置逐渐转向θ=0°位置; 界面轴向残余压应力的增量依次为282 MPa、110 MPa、67 MPa和307 MPa、203 MPa、88 MPa(图4b1), 即界面轴向残余压应力始终随着基体弹性模量的增加而增加, 但是当弹性模量增量恒定(1倍的E1)时界面轴向残余压应力的增幅逐渐减小, 且沿纤维周向的不均匀程度加大; 界面周向残余压应力的增量依次为92 MPa、-4 MPa、40 MPa和211 MPa、230 MPa、13 MPa(图4c1), 可见基体弹性模量的增加使界面周向残余压应力沿纤维周向的不均匀程度迅速提高(周向残余应力在θ=0°位置远远小于θ=45°位置), 即高的基体弹性模量很容易引起θ=45°位置的径向裂纹。对于纤维六方排列, 在θ=0°和θ=30°位置随着基体弹性模量的不断增加, 界面径向残余压应力的增量依次为173 MPa、72 MPa、6 MPa和164 MPa、113 MPa、49 MPa(图4a2), 与纤维四方排布情况下界面径向残余压应力的变化类似, 当基体弹性模量超过E2后界面结合的薄弱环节由θ=30°位置逐渐转向θ=0°位置, 但是径向残余压应力沿纤维周向的分布相对均匀; 界面轴向残余压应力的增量依次为300 MPa、144 MPa、77 MPa和301 MPa、165 MPa、73 MPa(图4b2), 即随着基体弹性模量的增加θ=0°和30°位置界面轴向热残余压应力的增幅基本一致, 说明轴向热残余压应力沿纤维周向的均匀分布不因基体弹性模量的变化而变化, 且弹性模量每次的增量恒定(1倍的E1)时界面轴向残余压应力增幅为上一次增幅的1/2左右; 界面周向残余压应力的增量依次为159 MPa、53 MPa、69 MPa和172 MPa、95 MPa、9 MPa(图4c2), 可见基体弹性模量的增加使界面周向热残余压应力沿纤维周向的不均匀程度先增加后减小, 这意味着弹性模量的进一步增加(高于E4)可能导致界面周向热残余压应力的最大值由θ=30°位置变为θ=0°位置。可见, 随着基体弹性模量的增加纤维六方排布时周向残余应力的变化比四方排布时平缓得多, 且六方排布时周向热残余压应力峰值越来越小于四方排布时的应力峰值。总之, 基体弹性模量的提高, 一方面使得径向与轴向热残余压应力增大有利于纤维/基体界面结合和纵向拉伸性能, 另一方面使得周向热残余压应力增大可能造成基体更大的塑性流变甚至径向裂纹[16]。
图4 不同基体弹性模量下纤维一侧界面残余应力的分布
Fig.4 Distributions of interfacial residual stresses in fiber with different elastic modulus for matrix (a) radial residual stress (b) axial residual stress (c) hoop residual stress (“1”represents fiber square array and “2”represents fiber hexagonal array)
1. SiCf/Ti复合材料纤维一侧的界面径向、轴向和周向残余压应力都随着基体热膨胀系数的减小而减小, 甚至变为拉伸状态, 且基体与纤维热膨胀系数越接近热残余应力沿纤维周向分布的均匀性越好。
2. SiCf/Ti复合材料纤维一侧界面径向、轴向和周向热残余压应力变化的总趋势是随着基体弹性模量的增大而增大, 但是随着基体弹性模量的增加热残余压应力增加的幅度在减小。
3. 随着SiCf/Ti复合材料基体弹性模量的增加纤维六方排布时热残余应力的变化比四方排布时更为平缓, 且六方排布时界面周向热残余压应力峰值越来越小于四方排布时的应力峰值。
The authors have declared that no competing interests exist.
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| [14] |
Preparation and tensile test of SiC fiber fabricated by three-stage chemical vapour deposition,
<p>Continuous silicon carbide (SiC) fiber with carbon coating was fabricated by three-stage chemical vapor deposition (CVD) on W filament heated by direct current (DC), using CH<sub>3</sub>SiCl<sub>3 </sub>as gaseous reactant for SiC as well as C<sub>2</sub>H<sub>2 </sub>for the outmost carbon coating. Young’s modulus and tensile strength of the fiber were tested at room temperature, while Weibull distribution was conducted for evaluation of the tensile properties of the fiber. Fracture morphology, phase structure and microstructure of the fiber were investigated by scanning electron microscope (SEM), X-ray diffraction (XRD) and transmission electron microscope (TEM). Results show that the SiC fiber, from W core to outside, exhibits a W/SiC interfacial reaction layer with a thickness of about 0.35μm, two layers of SiC and an even carbon coating. XRD pattern indicates that the SiC layers are all composed of β-SiC, which corresponds to diffraction angle of 35.6°, 60.1°, 72.1° and 75.7°. The mean tensile strength and Weibull modulus of the fiber reach 3266 MPa and 16.3, respectively. Furthermore, fracture mechanism of the fiber is discussed.</p>
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| [15] |
Finite element analysis for effects of fiber arrays on the residual stress of SiC fiber reinforced Ti-matrix composite,
纤维排布方式对SiC/Ti材料残余应力影响的有限元分析, URL 摘要
采用三维有限元法模拟SiC/Ti-6Al-4V复合材料界面的残余应力分布,分析纤维排列 方式对纤维一侧界面残余应力的影响。结果表明,纤维排列方式对纤维一侧界面径向、轴向和周向残余应力均有较大影响,其中纤维六方排列时纤维一侧界面残余应 力沿纤维周向分布均匀,且周向残余应力小,不易在界面形成径向裂纹,是较为理想的纤维排列方式。
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| [16] |
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