SECONDARY ORIENTATION EFFECTS OF NI-BASED ALLOYS WITH COOLING HOLES: A STRAIN GRADIENT CRYSTAL PLASTICITY FEM STUDY
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摘要: 单晶镍基合金具有优异的耐高温、高强、高韧等性能, 这些力学性能受制造过程引入的次级取向和冷却孔的影响. 已有研究大多关注单孔薄板的变形机理和力学性能, 而工程中应用的往往是多孔薄板, 当前亟需阐明多孔的塑性滑移带变形机理、次级取向效应以及冷却孔引起的应变梯度效应. 文章采用基于位错机制的非局部晶体塑性本构模型对含冷却孔镍基单晶薄板的单拉变形进行了数值模拟. 此模型基于塑性滑移梯度与几何必需位错的关系引入了位错流动项, 因此可有效刻画非均匀变形过程中的应变梯度效应. 为了全面揭示含孔镍基薄板的次级取向效应, 系统研究了[100]和[110]取向(两种次级取向)下镍基薄板的单拉变形行为, 并重点探究了在两种次级取向下冷却孔数量对薄板塑性行为的影响. 此外, 还分析了镍基合金板变形过程中各个滑移系上分切应力变化、主导滑移系开动以及几何必需位错密度的演化过程, 并讨论了塑性滑移量及其分布特征对不同次级取向镍基合金板强度的影响. 研究表明, 单孔和多孔的[110]薄板抗拉强度均低于[100]薄板, 多孔薄板的塑性变形过程比单孔薄板更为复杂且受次级取向影响更大, 并且发生滑移梯度位置主要位于冷却孔附近以及塑性滑移带区域. 研究结果可为工程中镍基合金的设计和服役提供理论指导.Abstract: Single crystal Ni-based alloys possess excellent properties such as high temperature resistance, high strength and high toughness. Thses mechanical properties are affected by secondary orientation and cooling holes induced during complex manufacturing processes. The current research mainly focuses on the deformation mechanism and mechanical response of plates with one hole. While, the plate with multiple holes is often used in engineering. At present, it is urgent to clarify the deformation mechanism of the plate with multiple holes, the secondary orientation effect, and the strain gradient effect caused by cooling holes. In this paper, a nonlocal crystal plasticity constitutive model based on the dislocation mechanism is used to numerically simulate the uniaxial tensile deformation behavior of the Ni-based single crystal plate with cooling holes. A dislocation flux term is derived based on the relationship between the plastic slip gradient and geometrically necessary dislocations, enabling this crystal plasticity model to effectively describe the strain gradient effect. In order to comprehensively reveal the secondary orientation effect of Ni-based alloys with cooling holes, this paper systematically studies the uniaxial tensile deformation behavior of sheets with [100] and [110] orientations (two secondary orientations). The influence of the number of holes on the plastic behavior of the plate with two secondary orientations is investigated. By analyzing the variation of the resolved stress on slip systems, activation of the dominant slip systems and the evolution of geometrically necessary dislocation density during the deformation of Ni-based alloy plates, the effects of plastic slip and its distribution on the strength of Ni-based alloy plates with different secondary orientations are discussed. The results show that the tensile strength of [110] plate is lower than that of [100] plate. Furthermore, the plastic deformation process of the five-hole plate is more complicated than that of the one-hole plate and is easier to be affected by secondary orientation. Finally, the location of the slip gradient is mainly located near the cooling hole and the plastic slip zone. The research results can provide theory basis for the design and service of Ni-based alloys in engineering.
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Key words:
- crystal plasticity /
- Ni-based alloy /
- cooling holes /
- secondary orientation /
- plastic slip /
- strain gradient
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图 1 镍基合金薄板有限元模型示意图: (a), (b)单孔薄板; (c), (d)多孔薄板 (单位: mm)
Figure 1. Finite element model of Ni-based alloy plate: (a), (b) plate with a hole; (c), (d) plate with five holes
图 4 不同单元数目单孔和多孔薄板单轴拉伸模拟结果
Figure 4. Uniaxial tensile simulation results of one-hole plates and five-hole plates with different element numbers
图 5 两种次级取向的单孔和多孔薄板单轴拉伸模拟结果
Figure 5. Uniaxial tensile simulation results of one-hole plates and five-hole plates in two secondary orientations
图 6 应变为2%时总塑性滑移分布: (a), (c) [100]; (b), (d) [110]
Figure 6. Total plastic slip at 2% strain: (a), (c) [100]; (b), (d) [110]
图 8 应变为2%时滑移系开动数量: (a), (c) [100]; (b), (d) [110]
Figure 8. The number of activated slip system at 2% strain: (a), (c) [100]; (b), (d) [110]
图 9 应变为2%时不同冷却孔分布的总塑性滑移: (a) 45°分布含4孔, (b)30°分布含5孔, (c) 45°分布含5孔, (d) 60°分布含5孔
Figure 9. Total plastic slip at 2% strain with different cooling hole distribution: plate with (a) four-hole of 45° distribution, (b) five-hole of 30° distribution, (c) five-hole of 45° distribution, (d) five-hole of 60° distribution
图 10 冷却孔单侧节点不同变形阶段分切应力的演化
Figure 10. Evolution of resolved stress at one side nodes of cooling hole
图 11 应变为2%时最大分切应力云图: (a), (c) [100]; (b), (d) [110]
Figure 11. Maximum resolved stress at 2% strain: (a), (c) [100]; (b), (d) [110]
图 12 冷却孔单侧节点不同变形阶段塑性滑移的演化
Figure 12. Evolution of plastic slip at one side nodes of cooling hole
12 冷却孔单侧节点不同变形阶段塑性滑移的演化(续)
12. Evolution of plastic slip at one side nodes of cooling hole (continued)
图 13 应变为2%时主导滑移系: (a), (c) [100]; (b), (d) [110]
Figure 13. Dominant slip system at 2% strain: (a), (c) [100]; (b), (d) [110]
图 15 不同变形阶段塑性滑移特征
Figure 15. Plastic slip characteristics in different deformation stages
图 17 应变为2%时几何必需位错密度分布: (a), (c) [100]; (b), (d) [110]
Figure 17. Geometrically necessary dislocation density distribution at 2% strain: (a), (c) [100]; (b), (d) [110]
图 18 应变为2%时Mises应力分布: (a), (c) [100]; (b), (d) [110]
Figure 18. Mises stress distribution at 2% strain: (a), (c) [100]; (b), (d) [110]
图 19 几何必需位错密度随应变的演化
Figure 19. Evolution of geometrically necessary dislocation density with increasing strain
表 1 镍基合金的非局部晶体塑性模型参数
Table 1. Model parameters for nonlocal crystal plasticity used for Ni-based alloys
Property Symbol Value Reference elastic moduli/GPa $ {{C}}_{\text{11}} $ 252 [32] $ {{C}}_{\text{12}} $ 161 [32] $ {{C}}_{\text{44}} $ 131 [32] initial overall dislocation density/m−2 ${\rho }_{\text{0} }$ $ \text{2.4 × }{\text{10}}^{\text{12}} $ edge contribution to multiplication ${{k} }_{\text{1} }$ 0.1 [43] dislocation multiplication constant ${k} _{\text{2} }$ 45 [43] length of Burgers vector/m b $ \text{2.4 × }{\text{10}}^{-\text{10}} $ [2] minimum edge dipole separation/m ${\stackrel{\mathrm{˘} }{{d} } }_{\text{e} }^{\text{α} }$ $ \text{2.6 × }{\text{10}}^{-\text{9}} $ [43] minimum screw dipole separation/m ${\stackrel{\mathrm{˘} }{{d} } }_{\text{s} }^{\text{α} }$ $\text{1.2 × }{\text{10} }^{-\text{8} }$ [43] self-diffusivity activation entropy/J ${\Delta {H} }_{\text{SD} }$ $ \text{3.2 × }{\text{10}}^{-\text{1}\text{9}} $ [43] self-diffusivity coefficent/($ {\text{m}}^{\text{2}}\cdot{\text{s}}^{-\text{1}} $) ${{D} }_{\text{SD} }^{\text{0} }$ $ \text{4.4 × }{\text{10}}^{-\text{6}} $ [43] atomic volume/m3 Ω $ \text{1.29 × }{\text{10}}^{-\text{29}} $ [43] edge jog formation factor ${{k} }_{\text{3} }$ 0.01 [43] solid-solution concentration ${{c} }_{\text{at} }$ $ \text{1.6 × }{\text{10}}^{-\text{3}} $ attack frequency/Hz ${f}$ $ \text{5 × }{\text{10}}^{\text{10}} $ [43] strength of barrier/MPa $\tau$ 5 solid-solution size b ${{d} }_{\text{obst} }$ 1 [43] double kink width b ${{w} }_{\text{k} }$ 10 [43] dislocation viscosity/(Pa·s) η 0.1 [43] energy barrier profile constants p 1 [43] q 1 [43] 
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表 2 镍基合金沿[001]加载时各滑移系Schmid因子
Table 2. Schmid factor of the Ni-based alloys loaded along [001] direction
Slip
systemSlip plane Slip
directionSchmidt factor $ \xi_{\text{1}} $ $ \left(1\mathrm{ }1\mathrm{ }1\right) $ $\left[0\mathrm{ }\;1\stackrel{-}{1}\right]$ 0.408 $ \xi_{\text{2}} $ $ \left(1\mathrm{ }11\right) $ $\left[\stackrel{-}{1}0\;\mathrm{ }1\right]$ 0.408 $ \xi_{\text{3}} $ $ \left(1\mathrm{ }11\right) $ $ \left[1\stackrel{-}{1}0\right] $ 0 $ \xi_{\text{4}} $ $ \left(1\mathrm{ }1\stackrel{-}{1}\right) $ $\left[0\stackrel{-}{1}\;\stackrel{-}{1}\right]$ 0.408 $ \xi_{\text{5}} $ $ \left(1\mathrm{ }1\stackrel{-}{1}\right) $ $\left[1\;0\mathrm{ }\;1\right]$ 0.408 $ \xi_{\text{6}} $ $ \left(1\mathrm{ }1\stackrel{-}{1}\right) $ $\left[\stackrel{-}{1}1\;\mathrm{ }0\right]$ 0 $ \xi_{\text{7}} $ $ \left(\stackrel{-}{1}1\mathrm{ }1\right) $ $ \left[0\stackrel{-}{1}1\right] $ 0.408 $ \xi_{\text{8}} $ $ \left(\stackrel{-}{1}1\mathrm{ }1\right) $ $ \left[\stackrel{-}{1}0\stackrel{-}{1}\right] $ 0.408 $ \xi_{\text{9}} $ $ \left(\stackrel{-}{1}1\mathrm{ }1\right) $ $\left[1\;\mathrm{ }1\;\mathrm{ }0\right]$ 0 $ \xi_{\text{10}} $ $ \left(1\stackrel{-}{1}1\right) $ $\left[0\;\mathrm{ }1\;\mathrm{ }1\right]$ 0.408 $ \xi_{\text{11}} $ $ \left(1\stackrel{-}{1}1\right) $ $\left[1\;0\stackrel{-}{1}\right]$ 0.408 $ \xi_{\text{12}} $ $ \left(1\stackrel{-}{1}1\right) $ $\left[\stackrel{-}{1}\;\stackrel{-}{1}0\right]$ 0
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