Plastic flow properties and constitutive model of metallic materials under complex stress states
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摘要: 工程应用中，金属材料和结构往往处于复杂应力状态。材料的塑性行为会受到应力状态的影响，要精确描述材料在复杂应力状态下的塑性流动行为，必须在本构模型中考虑应力状态效应的影响。然而，由于在动态加载下材料的应变率效应和应力状态效应相互耦合、难以分离，给应力状态效应的研究和模型的建立造成很大困难。通过对Ti-6Al-4V钛合金材料开展不同加载条件下的力学性能测试，提出了一个包含应力三轴度和罗德角参数影响的新型本构模型，并通过VUMAT用户子程序嵌入ABAQUS/Explicit软件。分别采用新提出的塑性模型和Johnson-Cook模型对压剪复合试样的动态实验进行了数值模拟。结果表明，新模型不仅在对材料本构曲线的拟合方面具有较强的优势，而且由该模型所得到的透射脉冲和载荷-位移曲线均更加准确。因此，该模型能够更精确地描述和预测金属材料在复杂应力状态下的塑性流变行为。Abstract: Metallic materials are widely used in automotive, aerospace, energy, national defense, and other important fields due to their excellent mechanical properties. During service periods, metallic materials are generally subjected to complex stress states. Recent researches reveal that the plastic behavior of materials is affected by the stress state. Therefore, to accurately describe the plastic flow behavior of materials under complex stress states, the influence of the stress state must be considered in the constitutive model. Under dynamic loading, however, the effects of strain rate and stress state are coupled, which makes it difficult to study the effect of stress state and to establish a stress-state-dependent constitutive model. In this work, mechanical tests were performed under various loading conditions including uniaxial compression, uniaxial tension, and simple shear using the MTS universal testing machine and the split Hopkinson bars technique. The stress-strain curves of Ti-6Al-4V were obtained over a wide range of strain rates and temperatures. It is observed that stress states have an obvious effect on the plastic flow properties and work-hardening characteristics of the material. Based on the experimental results, a new constitutive model that incorporates the influence of the stress triaxiality and the Lode angle parameter was proposed. Under tensile or compressive loading conditions, the flow stress determined by the J-C model is significantly lower than the test results, while the present model can predict the flow stress accurately. To check the applicability of the proposed model, the dynamic experiment of a specimen under the compression-shear combined load was simulated by both the J-C model and the proposed model implemented in the ABAQUS/Explicit software via the VUMAT user subroutine. The results show that the present model exhibits a higher accuracy in the prediction of the flow stress curves. Moreover, this model can predict both the transmitted pulse and the force-displacement curves more accurately. Therefore, the new model can describe the stress state effect successfully and predict the plastic behavior of the material under complex stress states more precisely.
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Key words:
- stress state effect /
- stress triaxiality /
- Lode angle parameter /
- constitutive model
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图 4 不同应力状态下的等效应力-等效应变曲线
Figure 4. The equivalent stress-equivalent strain curves under different stress states
图 8 压缩试验结果与两种模型（J-C模型和新模型）结果比较
Figure 8. Comparison of the compression test results with the J-C model and the new model
图 9 拉伸试验结果与两种模型（J-C模型和新模型）结果比较
Figure 9. Comparison of the tension test results with the J-C model and new model
图 10 15°压剪试样和有限元模型示意图
Figure 10. Schematic diagrams of a 15° compression-shear specimen and the finite element model
图 11 模拟结果（J-C模型和新模型）与实验曲线对比
Figure 11. Comparison of the experimental and simulation results (J-C model and new model)
图 13 压剪试样在不同加载时刻的等效应力分布
Figure 13. Equivalent stress evolutions of the compression-shear specimen in the simulation
表 1 新模型材料常数
Table 1. Material constants of the new model
A/MPa B/MPa n C m $ {c_\eta } $ $ {\eta _0} $ $ {c_1} $ $ {c_2} $ 971.59 362.39 0.1298 0.0160 0.5839 0.0501 0 0.1692 0.4264 
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表 2 不同应力状态下新模型和J-C模型（根据剪切试验结果建立）与拉压试验结果的平均误差
Table 2. Average error of the new and J-C models under different stress states compared with the experimental results
应力状态 准静态加载误差/% 动态加载误差/% J-C model New model J-C model New model 单轴压缩 25.2 3.7 21.1 3.9 单轴拉伸 10.5 1.5 9.7 4.8
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表 3 有限元分析中各部件的物理参数
Table 3. Physical parameters of each component in the finite element analysis
部位 材料 ρ/
(g·mm−3)E/
GPa$ \mu$ λ/
(W·m−1·°C)c/
(J·kg−1·°C)入射杆/透射杆 18Ni钢 8.0 190 0.3 − − 试样 Ti-6Al-4V 4.43 114 0.33 6.7 586
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