Prediction of strength and fatigue life for 2D plain-woven high-alumina fiber reinforced alumina matrix composites under a complex in-plane stress state
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摘要: 针对平面编织氧化铝基复合材料提出了一种复杂面内应力状态下的强度准则和疲劳寿命预测方法。通过拉伸、压缩及纯剪切试验,分别获得了材料的静强度指标。考虑材料拉、压性能的差异和面内拉-剪联合作用对材料强度的影响机制,提出了修正的Hoffman强度理论。采用该强度理论预测得到的偏轴拉伸强度与试验结果基本一致,偏差不超过10%。开展了偏轴角θ=0°、15°、30°、45°,应力比R=0.1,频率f=10 Hz的拉伸疲劳试验,试验结果表明随着偏轴角的增加,相同轴向拉伸载荷下的疲劳寿命逐渐降低。由于面内剪切应力分量的作用,疲劳失效由纤维主导逐渐过渡到纤维和基体共同主导的模式。基于单轴疲劳寿命曲线,采用Broutman-Sahu剩余强度模型表征剩余强度随疲劳循环次数的变化规律,结合剩余强度演化模型和修正的Hoffman强度理论,提出了一种面内复杂载荷条件下的疲劳寿命预测模型,并引入疲劳剪切损伤影响因子表征拉-剪应力联合作用对材料疲劳行为的影响。采用本文提出的疲劳寿命预测模型,预测不同偏轴角拉伸疲劳寿命,预测结果与试验结果基本一致,偏差在1倍寿命范围内。比较结果表明在给定应力比、温度和疲劳载荷频率条件下,该疲劳寿命预测模型可以用来预测平面编织氧化铝基复合材料拉-剪复杂面内载荷条件下疲劳寿命。
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关键词:
- 编织复合材料 /
- Hoffman失效准则 /
- 剪切损伤影响因子 /
- 疲劳寿命;预测模型
Abstract: This paper presents a strength criterion and fatigue life prediction method for 2D braided alumina matrix composites under a complex in-plane stress state. The static strength of the material was obtained by in-plane tensile, compression, and pure shear tests. Considering the difference between tensile and compressive properties of materials and the influence mechanism of in-plane tensile and shear coupling on material strength, a revised Hoffman strength theory was proposed. The predicted off-axis tensile strength is consistent with the test results, and the deviation is not more than 10%. Tensile fatigue tests were carried out with the off-axis angle θ=0°, 15°, 30°, 45°, the stress ratio R=0.1, and frequency f=10 Hz. The test results show that the fatigue life decreases with the increase of off-axis angle. Due to the in-plane shear stress component, the fatigue failure is gradually changed from fiber-dominated to fiber-matrix dominated mode. Based on a combination of the uniaxial tensile fatigue life curve, the Broutman-Sahu residual strength model, which is used to characterize the variation of the residual strength with the fatigue cycles, and the modified Hoffman strength theory, the paper proposes a fatigue life prediction model under complex in-plane loading conditions. The fatigue shear damage factor is defined to characterize the effect of the normal and shear stress interaction on fatigue life. The fatigue life prediction model is used to predict the fatigue life of specimens in the off-axis tensile fatigue tests. The predicted result agrees with the test result, and the deviation is within the 1-time life span. The results indicate that the proposed fatigue life prediction model can be used to predict the fatigue life of 2D braided alumina matrix composites under the complex in-plane stress condition with the given stress ratio, temperature, and fatigue load frequency. -
图 1 拉伸试样尺寸(a)、拉伸试样照片(b)、压缩试样尺寸(c)、压缩试样照片(d)、面内纯剪试样尺寸(e)和贴有加强片的剪切试样照片(f)
Figure 1. Dimension of tensile specimen (a), picture of tensile specimen (b), dimension of compression specimen (c), picture of compression specimen (d), dimension of in-plane pure shear specimen (e) and picture of in-plane pure shear specimen with strengthening film (f)
图 3 高铝纤维增强氧化铝基复合材料15°偏轴拉伸DIC实测位移场和应变场分布(F=893.8 N)((a) x方向位移u;(b) y方向的位移v;(c)
${\varepsilon _{xx}}$ ;(d)${\varepsilon _{yy}}$ ;(e)${\tau _{xy}}$ )Figure 3. Distribution of displacement and strain measured by DIC under 15° off-axial tension test of high-alumina fiber reinforced alumina matrix composites (F=893.8 N)((a) Displacement u along x-direction; (b) Displacement v along y-direction; (c)
${\varepsilon _{xx}}$ ; (d)${\varepsilon _{yy}}$ ; (e)${\tau _{xy}}$ )图 4 高铝纤维增强氧化铝基复合材料纯剪切试验DIC实测位移场和应变场分布(F=125.5 N)((a) x方向位移u;(b) y方向的位移v;(c)
${\varepsilon _{xx}}$ ;(d)${\varepsilon _{yy}}$ ;(e)${\tau _{xy}}$ )Figure 4. Distribution of displacement and strain measured by DIC under pure shear test of high-alumina fiber reinforced alumina matrix composites (F=125.5 N)((a) Displacement u along x-direction; (b) Displacement v along y-direction; (c)
${\varepsilon _{xx}}$ ; (d)${\varepsilon _{yy}}$ ; (e)${\tau _{xy}}$ )图 5 高铝纤维增强氧化铝基复合材料偏轴拉伸试样在轴向拉伸条件下沿材料坐标系典型应力-应变曲线((a) 沿材料经向;(b) 沿材料纬向及面内剪切方向)
Figure 5. Typical stress-strain curves of off-axial tensile high-alumina fiber reinforced alumina matrix composites specimens in the material coordinate system((a) Along the material warp direction; (b) Along the in-plane shear direction and the material weft direction)
表 1 不同偏轴角下二维平面编织高铝纤维增强氧化铝基复合材料单轴拉伸试验结果
Table 1. Uniaxial tensile test results of 2D plain woven high-alumina fiber reinforced alumina-based composites for different off-axis angles
Off-axis
angle
$\theta $/(°)Elastic
modulus
$E_{22}^0{\rm{/GPa}}$Fracture
stress
$\sigma _{11}^{\rm{u}}/{\rm{MPa}}$Fracture
strain
$\varepsilon _{11}^{\rm{u}}/10^{-6}$Elastic
modulus
$E_{22}^0{\rm{/GPa}}$Fracture
stress
$\sigma _{22}^{\rm{u}}/{\rm{MPa}}$Fracture
strain
$\varepsilon _{22}^{\rm{u} }/10^{-6}$Shear
modulus
$G_{12}^0/{\rm{GPa}}$Fracture
stress
$\tau _{12}^{\rm{u}}/{\rm{MPa}}$Fracture
strain
$\gamma _{12}^{\rm{u}}/10^{-6}$0 $ {11.1\pm0.7} $ $ {43.69\pm6.4} $ $ {}{4\;991\pm810} $ 0 0 0 0 0 0 15 $ {7.98\pm}{1.}{5} $ $ {33\pm5.5} $ $ {6\;687\pm1\;031} $ $ {3.15\pm0.}{8} $ $ {2.35\pm}{0.4} $ $ {}{-1873\pm}{148} $ $ {2.27\pm}{0.4} $ $ {8.83\pm}{1.5} $ $ {-8\;093\pm4\;008} $ 30 $ {4.3\pm0.3} $ $ {19.4\pm1.}{6} $ $ {}{9\;916\pm2\;205} $ $ {3.7\pm0.6} $ $ {6.48\pm0.5} $ $ {-2\;983\pm914} $ $ {1.67\pm0.2} $ $ {11.2\pm0.9} $ $ {19\;025\pm7\;235} $ 45 $ {8.31\pm}{1.0} $ $ {9.88\pm0}{.7} $ $ {1\;509\pm696} $ $ {9.06\pm0.9} $ $ {9.79\pm0.9} $ $ {2\;027\pm653} $ $ {1.37\pm0.0}{9} $ $ {9.88\pm0.7} $ $ {20\;477\pm1\;784} $ 表 2 常温高铝纤维增强氧化铝基复合材料面内强度参数
Table 2. In-plane strength parameters of high-alumina fiber reinforced alumina matrix composites at room temperature
${X_{\rm{t}}}{\rm{/MPa}}$ ${Y_{\rm{t}}}{\rm{/MPa}}$ ${X_{\rm{c}}}{\rm{/MPa}}$ ${Y_{\rm{c}}}{\rm{/MPa}}$ ${S_{12}}{\rm{/MPa}}$ 43.7 43.7 −6.56 −6.56 10.8 Notes: ${X_{\rm{t}}}$—Tensile strength along off-axial angle $ \theta $=0°; ${Y_{\rm{t}}}$—Tensile strength along off-axial angle $ \theta $=90°; ${S_{12}}$—In-plane shear strength; ${X_{\rm{c}}}$—Compression strength along off-axial angle $ \theta $=0°; ${Y_{\rm{c}}}$—Compression strength along off-axial angle $ \theta $=90°. 表 3 常温应力比R=0.1高铝纤维增强氧化铝基复合材料偏轴拉-拉疲劳寿命试验结果
Table 3. Off-axis tension-tension fatigue life test results of high-alumina fiber reinforced alumina matrix composites at room temperature and stress ratio R=0.1
Off-axis
angle $\theta {{\rm{/}}(^ \circ) }$Fatigue life Nf /cycle ${\sigma _{\max }}$=0.85${\sigma _{\rm{u}}}$ ${\sigma _{\max }}$=0.8${\sigma _{\rm{u}}}$ ${\sigma _{\max }}$=0.75${\sigma _{\rm{u}}}$ ${\sigma _{\max }}$=0.7${\sigma _{\rm{u}}}$ ${\sigma _{\max }}$=0.65${\sigma _{\rm{u}}}$ ${\sigma _{\max }}$=0.6${\sigma _{\rm{u}}}$ ${\sigma _{\max }}$=0.55${\sigma _{\rm{u}}}$ ${\sigma _{\max }}$=0.5${\sigma _{\rm{u}}}$ 0 8763 91853 217568 243663 412487 — — — 15 — — — 9375 142410 175446 288482 321518 30 — — — 25350 133727 184454 287831 312318 45 — — — 9232 87726 191084 232976 305254 Note: ${\sigma _{\max }}$ (MPa)—Maximum cyclic stress. -
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