Constitutive modelling for additive manufacturing superalloys considering the porosity and anisotropy
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摘要:
针对金属增材制造构件中各向异性与孔隙损伤协同演化的力学响应行为，建立了一种耦合各向异性与孔隙演化机制的宏观本构模型。模型融合各向异性屈服准则、非线性混合硬化机制与多孔介质损伤演化理论，系统描述了复杂加载路径下的增材制造高温合金的屈服行为、应变硬化与孔隙演化过程。通过数值模拟与试验数据对比，验证所提模型在单调拉伸、循环加载及各构建方向下均具有良好的预测精度，能够准确反映包辛格效应主导的非对称循环响应特征及孔隙缺陷演化的控制作用。研究结果表明：模型对增材制造高温合金V向与H向试样的单调拉伸响应预测误差与循环载荷下的应力幅值预测偏差均小于5%，同时有效量化了孔隙演化对力学性能的影响，预测得出当孔隙率从0.004%增至0.010%时，材料延性下降约15%。具有良好的工程实用性与推广潜力。
Abstract:A macroscopic constitutive model was developed to characterize the coupled evolution of anisotropy and porosity-induced damage in the mechanical response of metal additive manufacturing (AM) components. The model integrated an anisotropic yield criterion, a nonlinear mixed hardening mechanism, and a porous media damage theory to systematically describe the yield behavior, strain hardening, and damage evolution under complex loading paths. Numerical simulations were performed and compared with experimental data under monotonic tension, cyclic loading, and various build orientations. The results demonstrated that the model exhibited prediction errors of less than 5% for monotonic tensile responses of both H and V-oriented specimens made of additively manufactured high-temperature alloy, with stress amplitude deviations under cyclic loading not exceeding 4%. Furthermore, it effectively quantified the influence of pore evolution on the mechanical properties, predicting approximately 15% reduction in material ductility when porosity increased from 0.004% to 0.010%. The proposed model demonstrated strong potential for engineering application and broader implementation.
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图 8 H向增材IN718合金的单调不同阶段拉伸Mises应力云图
Figure 8. Monotonic tensile Mises stress contour map of H-oriented additive IN718 alloy at different stages
图 9 H向增材IN718合金的单调不同阶段拉伸孔隙率云图
Figure 9. Monotonic tensile porosity cloud map of H-oriented additive IN718 alloy at different stages
图 10 H向增材IN718合金的单调不同阶段拉伸等效塑性应变云图
Figure 10. Monotonic tensile equivalent plastic strain contour map of H-oriented additive IN718 alloy at different stages
图 11 V向增材IN718合金的单调不同阶段拉伸Mises应力云图
Figure 11. Monotonic tensile mises stress contour map of V-oriented additive IN718 alloy at different stages
图 12 V向增材IN718合金的单调不同阶段拉伸孔隙率云图
Figure 12. Monotonic tensile porosity cloud map of V-oriented additive IN718 alloy at different stages
图 13 V向增材IN718合金的单调不同阶段拉伸等效塑性应变云图
Figure 13. Monotonic tensile equivalent plastic strain contour map of V-oriented additive IN718 alloy at different stages
图 14 拉伸试样标距段平均应力、孔隙率、等效塑性应变响应
Figure 14. Average stress, porosity, and equivalent plastic strain responses in the gauge section of the tensile specimen
材料参数 数值 材料参数 数值 材料参数 数值 材料参数 数值 E/MPa 205000 $ \gamma $ 40 $ {\varphi }_{\mathrm{f}} $ 0.0005 $ H $ 0.375 $ v $ 0.321 $ {q}_{1} $ 0 $ {\varphi }_{\mathrm{n}} $ 0.04 $ L $ 1.5 Q0/MPa 1290 $ {q}_{2} $ 0 $ {\varepsilon }_{\mathrm{n}} $ 0.3 $ M $ 1.5 Q/MPa 500 $ {q}_{3} $ 0 $ {s}_{\mathrm{n}} $ 0.1 $ N $ 1.5 $ b $ 13.5 $ {\varphi }_{0} $/10−5 1 $ F $ 0.625 $ n $ 3 C/MPa 800 $ {\varphi }_{\mathrm{c}} $/10−4 1 $ G $ 0.575 
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材料参数 数值 材料参数 数值 材料参数 数值 材料参数 数值 E/MPa 180000 $ \gamma $ 100 $ {\varphi }_{\mathrm{f}} $ 0.0005 $ H $ 0.85 $ v $ 0.321 $ {q}_{1} $ 0 $ {\varphi }_{\mathrm{n}} $ 0.04 $ L $ 1.5 Q0/MPa 1030 $ {q}_{2} $ 0 $ {\varepsilon }_{\mathrm{n}} $ 0.3 $ M $ 1.5 Q/MPa 250 $ {q}_{3} $ 0 $ {s}_{\mathrm{n}} $ 0.1 $ N $ 1.5 $ b $ 40 $ {\varphi }_{0} $/10−5 1 $ F $ 0.4 $ n $ 3 C/MPa 500 $ {\varphi }_{\mathrm{c}} $/10−4 1 $ G $ 0.5
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表 4 SLM IN718材料参数（课题组）
Table 4. Material Parameters for the SLM IN718 （research group）
材料参数 数值 材料参数 数值 材料参数 数值 材料参数 数值 E/MPa 205000 $ \gamma $ 100 $ {\varphi }_{\mathrm{f}} $ 0.000101 $ H $ 0.6 $ v $ 0.321 $ {q}_{1} $ 1.5 $ {\varphi }_{\mathrm{n}} $ 0.04 $ L $ 1.5 Q0/MPa 710 $ {q}_{2} $ 1 $ {\varepsilon }_{\mathrm{n}} $ 0.3 $ M $ 1.5 Q/MPa 400 $ {q}_{3} $ 2.25 $ {s}_{\mathrm{n}} $ 0.1 $ N $ 1.5 $ b $ 5.5 $ {\varphi }_{0} $/10−5 3.79 $ F $ 0.341 $ n $ 3 C/MPa 400 $ {\varphi }_{\mathrm{c}} $/10−5 9.30 $ G $ 0.5
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