Stress intensity factors with the surface cracked plate of commercial pure titanium TA2 under compression
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摘要: 以压载荷下工业纯钛TA2含表面裂纹板为研究对象。采用有限元方法，建立了压载荷下含复合型半椭圆表面裂纹板模型，计算了裂纹体应力强度因子，研究了裂纹倾角β、裂纹相对深度a/t、裂纹相对形状a/c、裂纹面摩擦系数μ和侧压系数λ对应力强度因子的影响。结果表明：裂纹倾角，裂纹相对形状对应力强度因子影响显著，裂纹相对深度对应力强度因子影响不明显。摩擦系数和测压系数的增大可明显减小应力强度因子，抑制剪切破坏。最后基于应力强度因子有限元解，回归得到了适用于受单轴压载下含半椭圆表面裂纹板的应力强度因子KⅡ和KⅢ解。研究结果对工业纯钛TA2压载荷下含半椭圆表面裂纹结构安全性评价具有参考价值。Abstract: The surface cracked plate of commercial pure titanium TA2 under compressive load was studied. The plate model with mixed mode semi-elliptical surface crack was established by finite element method, and the stress intensity factor was calculated. At the same time, the effects of stress intensity factor were investigated with different inclined angles (β), relative crack depths (a/t), aspect ratios (a/c), friction coefficients of crack surface (μ), lateral pressure coefficients (λ). The results show that the inclined angles and aspect ratios have significant effects on the stress intensity factor, while the crack relative depth has insignificant effects on the stress intensity factor. With the increase of friction coefficients and lateral pressure coefficients can significantly reduce the stress intensity factor and inhibit shear damage. Based on the finite element solutions of stress intensity factor, the equations of stress intensity factors KⅡ and KⅢ fit for plates with semi-elliptical surface crack under uniaxial compression were obtained by nonlinear regression. The results are of important reference for the safety assessment of structure with semi-elliptical surface crack of commercial pure titanium TA2 under compressive load.
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图 3 含半椭圆表面裂纹板有限元模型
Figure 3. Finite element model of semi-elliptical surface crack in plate
图 4 有限元结果与Newman-Raju和GB/T 19624应力强度因子解对比
Figure 4. Comparison of stress intensity factor by finite element results, Newman-Raju and GB/T 19624 solutions
图 7 应力强度因子KⅡ，KⅢ随β变化曲线
Figure 7. Variation of stress intensity factors KⅡ, KⅢ along crack front with β
图 8 应力强度因子KⅡ，KⅢ随a/t变化曲线(β=45°)
Figure 8. Variation of stress intensity factors KⅡ, KⅢ along crack front with a/t (β=45°)
图 9 应力强度因子KⅡ，KⅢ随a/c变化曲线(β=45°)
Figure 9. Variation of stress intensity factors KⅡ, KⅢ along crack front with a/c (β=45°)
图 10 应力强度因子KⅡ，KⅢ随μ变化曲线(β=45°)
Figure 10. Variation of stress intensity factors KⅡ, KⅢ along crack front with μ (β=45°)
图 11 应力强度因子KⅡ，KⅢ随β变化曲线(μ=0，0.3)
Figure 11. Variation of stress intensity factors KⅡ, KⅢ along crack front with β (μ=0，0.3)
图 12 拉伸/压缩载荷下，应力强度因子KⅠ，KⅡ，KⅢ随β变化曲线
Figure 12. Variation of stress intensity factors KⅠ, KⅡ, KⅢ along crack front with β under the tensile/compressive loads
图 13 应力强度因子KⅡ，KⅢ随λ变化曲线
Figure 13. Variation of stress intensity factors KⅡ, KⅢ along crack front with λ
表 1 最小网格尺寸网格敏感性分析（a/c=0.2，a/t=0.4，β=45°，θ=30°）
Table 1. Verification of meshing on minimum sizes of element（a/c=0.2，a/t=0.4，β=45°，θ=30°）
最小网格尺寸/mm KⅡ/(MPa·mm1/2) KⅢ/(MPa·mm1/2) 0.025 −29.25 −120.20 0.05 −29.30 −120.26 0.1 −29.43 −121.16 0.15 −29.44 −121.44 0.2 −29.43 −121.13 注：KⅡ最大相对误差0.06%，KⅢ最大相对误差1.03%. 
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表 2 裂纹前缘裂尖周向网格敏感性分析（a/c=0.2，a/t=0.4，β=45°，θ=30°）
Table 2. Verification of meshing on numbers of element along crack front（a/c=0.2，a/t=0.4，β=45°，θ=30°）
裂尖周向网格数 KⅡ/(MPa·mm1/2) KⅢ/(MPa·mm1/2) 90 −30.15 −124.46 120 −29.43 −121.16 150 −29.14 −119.88 180 −29.65 −120.74 注：KⅡ最大相对误差3.47%，KⅢ最大相对误差3.82%.
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表 3 裂纹表面点处KⅡ对比
Table 3. Comparison of KⅡ at surface point of crack
a/t KⅡ（a/c=0.2） KⅡ（a/c=0.4） KⅡ（a/c=0.6） KⅡ（a/c=0.8） 近似解 FEM解 近似解 FEM解 近似解 FEM解 近似解 FEM解 0.2 94.79 93.68 169.32 182.92 224.08 240.01 263.51 279.78 0.4 101.02 94.99 178.12 185.36 233.66 242.21 272.87 281.74 0.6 107.92 97.10 187.99 189.72 245.24 246.69 285.00 286.38 0.8 109.27 101.76 190.24 196.01 250.82 253.86 293.55 292.59 注：a/c为0.2、0.4、0.6、0.8时，KⅡ平均相对误差依次为6.01%、4.01%、3.14%、2.56%。
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表 4 裂纹最深处点KⅢ对比
Table 4. Comparison of KⅢ at deepest point of crack
a/t KⅢ（a/c=0.2） KⅢ（a/c=0.4） KⅢ（a/c=0.6） KⅢ（a/c=0.8） 近似解 FEM解 近似解 FEM解 近似解 FEM解 近似解 FEM解 0.2 −161.54 −167.24 −203.96 −206.79 −220.27 −218.38 −224.1 −218.28 0.4 −169.45 −173.9 −209.62 −210.68 −223.97 −220.99 −226.30 −219.86 0.6 −187.01 −184 −221.20 −218.56 −231.25 −226.75 −230.46 −224.22 0.8 −213.32 −211.61 −236.21 −239.74 −239.91 −242.18 −234.98 −236.22 注：a/c为0.2、0.4、0.6、0.8时，KⅢ平均相对误差依次为2.14%、1.15%、1.27%、2.18%。
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