Determination of constitutive relation and fracture criterion parameters for ZL114A aluminum alloy
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摘要: 针对航空发动机机匣材料ZL114A铝合金，构建描述该材料在较大温度范围下大变形及失效行为的材料模型。通过万能试验机及分离式霍普金森压杆试验装置测试ZL114A铝合金在常温准静态、高温和高应变率下的力学性能，分析温度和应变率对材料流动应力的影响。采用有限元程序和优化算法反求25~375 ℃内材料的硬化参数，结合高应变率(1310～5964 s−1)下材料的动态行为关系，构建包含塑性应变、温度及应变率的经验型本构模型。开展缺口拉伸、缺口压缩等试验并建立相对应的有限元模型，获取材料在不同应力三轴度下的失效应变，标定分段形式的Johnson-Cook (J-C)失效准则参数。通过不同温度下的平板侵彻试验和数值模拟验证失效准则及其参数的有效性。结果表明，ZL114A铝合金具有明显的应变硬化、温度软化及高应变率强化特性；具有应力饱和特征的Hockett-Sherby (H-S)硬化模型较为准确地描述材料大变形下的力学行为；构建的材料本构关系可以描述ZL114A铝合金在大应变、宽温度、高应变率下的力学行为；分段形式的失效准则具有预测不同温度下材料失效行为的能力。Abstract: In order to study the containment properties of aero-engine casing made of ZL114A (ZAlSi7Mg1A) aluminum alloy under the impact of blade fragments at different temperatures, the material models describing the large deformation and failure behavior of ZL114A aluminum alloy under a large range of temperatures were established. Firstly, quasi-static tensile tests at various temperatures and dynamic compression tests were conducted in the universal testing machine and the split Hopkinson pressure bar (SHPB), respectively. Based on the force-displacement data obtained in tensile tests, the finite element code and optimization algorithm were used to reversely identify the material hardening parameters at temperatures of 25–375°C. In this process, the accuracy of two hardening laws, Ludwik and Hockett/Sherby, describing the plastic flow behavior of ZL114A aluminum alloy under large deformation were compared. Subsequently, combined with the dynamic behavior relation of ZL114A aluminum alloy at strain rates of 1310–5964 s−1, a modified empirical constitutive model incorporating plastic strain, temperature, and strain rate was established, based on the Hockett/Sherby hardening law and Cowper-Symonds model. Further, the tests of notch tension, notch compression and shear were carried out, and the parallel finite element models were numerically calculated. The limitation of failure parameters related to failure criterion by the theoretical formula was analyzed, and the failure parameters are obtained by combining experiment and finite element method. Johnson-Cook failure criterion in branch form was used to describe the relationship between failure strain and stress triaxiality of ZL114A aluminum alloy. Considering the influence of temperature and strain rate, the failure criterion describing the failure behavior of ZL114A aluminum alloy was obtained. Finally, the validity of the fracture criterion and its parameters were verified by the ZL114A aluminum alloy flat plate penetration tests and the numerical simulations at various temperatures. The results show ZL114A aluminum alloy has obvious characteristics of strain hardening, temperature softening, and high strain rate strengthening. The Hockett/Sherby hardening law with stress saturation characteristics more accurately describes the stress flow behavior of ZL114A aluminum alloy than that of Ludwik under large deformation. The modified constitutive relation effectively describes the stress flow behavior of ZL114A aluminum alloy to a certain degree under large strain, wide temperature, and high strain rate. At the same time, the fracture criterion in branch form has good applicability to predict the impact failure behavior of flat plates at different temperatures.
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图 4 各温度下ZL114A铝合金的工程应力-应变曲线
Figure 4. Engineering stress-strain curves at various temperatures of ZL114A Al alloy
图 5 屈服强度及抗拉强度随温度变化曲线
Figure 5. Curve of yield strength and tensile strength with temperature
图 9 基于LS-OPT的硬化模型参数反求流程
Figure 9. Reverse identification process of hardening model parameters based on LS-OPT
图 10 拉伸试样载荷-位移数值模拟与试验曲线对比
Figure 10. Comparison of force-displacement curves of tensile specimen between numerical simulation and test
图 11 加热条件下试样载荷-位移曲线数值模拟与试验对比
Figure 11. Comparison of force-displacement curves of tensile specimens between numerical simulation and experiment under heating conditions
图 12 应变项参数拟合曲线
Figure 12. Fitting curves of strain term parameters related to normalized temperature
图 13 模型计算值与试验值曲线对比
Figure 13. Comparison of curves between the MJC constitutive model and the test
图 16 缺口拉伸试样中心单元的应力三轴度与等效应变的关系
Figure 16. Relation between stress triaxiality and effective strain in central elements of notched tensile specimens
图 17 剪切试样数值模拟应变结果与试验损伤结果的对比
Figure 17. Comparison of shear specimen between strain result by the numerical simulation and the fracture by the test
图 18 剪切试样中心单元的应力三轴度与等效应变的关系
Figure 18. Relation between stress triaxiality and effective strain in central element of shear specimen
图 20 压缩试样中心单元的应力三轴度曲线
Figure 20. Curves of stress triaxiality of central element in compression specimens
图 22 失效准则温度项标定曲线
Figure 22. Calibration curves of temperature term in fracture criterion
图 24 侵彻试验子弹示意图（mm）
Figure 24. Schematic diagram of the projectile in the penetration test (mm)
图 26 平板损伤形貌数值模拟及试验对比
Figure 26. Comparison of damage morphology of flat plate between numerical simulation and test
图 27 常温下平板应变信号数值模拟与试验对比
Figure 27. Comparison of plate strain signals between numerical simulation and test at room temperature
表 1 ZL114A各成分的质量分数
Table 1. Mass fractions of the chemical compositions of ZL114A
% Si Mg Ti Be Fe Cu Zn Mn Al 6.5～7.5 0.45～0.60 0.10～0.20 0.05～0.07 0～0.20 0～0.10 0～0.10 0～0.10 其他 
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表 2 传统方法标定的常温硬化模型参数
Table 2. The parameters of the hardening model at room temperature with traditional forward calibration methods
A/MPa B/MPa nL Q/MPa b nH-S 249.4 394.5 0.435 297.0 2.205 0.526 注：nL和nH-S分别Ludwik模型和H-S模型中的硬化指数n.
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表 3 硬化模型参数设置及优化结果
Table 3. Parameters setting and optimization results of hardening models
参数 初始值 取值范围 反求结果 B/MPa 394.5 [100, 500] 273.0 nL 0.435 [0.1, 1] 0.297 Q/MPa 297.0 [100, 500] 221.2 b 2.205 [1, 10] 4.039 nH-S 0.526 [0.1, 1] 0.540
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表 4 加热条件下反求标定的H-S硬化模型参数
Table 4. H-S hardening model parameters with reverse identification method under heating condition
温度/℃ A/MPa Q/MPa b n 125 245.3 211.2 2.791 0.570 175 245.0 211.2 2.190 0.470 225 243.5 211.2 2.196 0.459 275 240.0 211.2 1.686 0.460 325 214.3 211.2 1.049 0.576 375 197.0 211.2 0.831 0.540
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表 5 ZL114A铝合金MJC本构模型参数
Table 5. Parameters of MJC constitutive model of ZL114A
σ0/MPa s1/MPa s2/MPa s3/MPa Q/MPa b0 b1 b2 b3 b4 b5 249.4 −59.9 342.0 −642.0 211.2 4.040 10.986 −247.838 1148.865 −2124.333 1369.762 n0 n1 m0 m1 m2 m3 m4 l0 l1 C/s−1 P 0.540 0.173 2.245 −20.828 91.583 −179.210 131.176 0.792 −0.414 45622 1.003
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表 6 不同温度下拉伸载荷数值模拟结果与试验结果的相对误差
Table 6. Relative errors of tensile force between numerical simulation and test at various temperatures
温度/℃ 平均误差/% 最大误差/% 温度/℃ 平均误差/% 最大误差/% 25 0.76 2.54 275 1.06 2.40 125 0.71 2.37 325 2.76 5.47 175 0.59 1.76 375 3.00 6.25 225 0.75 1.74
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表 7 不同应变率下应力计算值与试验值的相对误差
Table 7. Relative errors of stress between model and test at various strain rates
应变率/s−1 平均误差/% 最大误差/% 应变率/s−1 平均误差/% 最大误差/% 0.001 0.76 2.54 4084 4.92 13.92 1310 2.81 8.10 5122 2.52 17.86 2122 3.81 15.22 5964 2.61 17.41 3358 5.18 9.80 ― ― ―
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表 8 各类试样的应力三轴度和失效应变
Table 8. Stress triaxiality and fracture strain of specimens
试样 ηav εf 光滑圆棒 0.538 0.790 R20拉伸 0.665 0.381 R10拉伸 0.802 0.284 R5拉伸 1.003 0.216 剪切试样 0.237 0.956
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表 9 分段形式的J-C失效准则参数
Table 9. Paraments of J-C fracture criterion with segmented form
D1 D2 D3 D4 D5 D6 D7 D8 0.218 87.68 −9.37 1.09 −0.55 2.915 4.942 0.01
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