Dynamic compressive mechanical properties and constitutive models of flexible polyurethane foam
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摘要: 采用Instron 9350落锤试验机研究了中低应变率下软质聚氨酯泡沫的动态压缩力学性能，分析了其应力-应变响应特征和应变率敏感性，讨论了应变率对材料应变率敏感性指数和能量吸收特性的影响，并基于实验结果建立了可准确描述其压缩力学响应的率相关本构模型。结果表明，软质聚氨酯泡沫的静动态压缩应力-应变响应具有典型的三阶段特征，且呈现出明显的应变率强化效应。准静态加载下，材料具有较高的吸能效率但能量吸收值较小，应变率对最大吸能效率和比吸能的影响较小；动态加载下，随着应变率的增加，最大吸能效率显著减小而比吸能明显增大。考虑应变率影响的修正Sherwood-Frost模型和修正Avalle模型都能够很好地表征软质聚氨酯泡沫的静动态压缩应力-应变响应，但修正Avalle模型的参数较少，更便于工程应用。研究结果可为软质聚氨酯泡沫抗冲击结构的设计和优化提供指导。Abstract: The quasi-static and dynamic compressive mechanical properties of flexible polyurethane foam were studied by using a DDL-200 electronic universal testing machine and an Instron 9350 drop-weight testing machine in a range of strain rates from 0.001 to 100 s−1. The stress-strain characteristics and strain rate sensitivity were analyzed, and the effect of strain rate on strain rate sensitivity index and energy absorption performance was discussed. Based on the experimental results, the strain rate-independent constitutive model was established to accurately describe the dynamic compressive mechanical behavior of the flexible polyurethane foam. The results show that the compressive stress-strain responses of flexible polyurethane foam exhibit typical three-stage deformation characteristics including initial elastic region, extended plateau region and final densification region, and the characteristics of material mesostructure at different deformation regions were analyzed. In addition, the material display an obvious strain rate-strengthening effect, both the yield stress and platform stress increase with the increase of strain rate, and the strain rate sensitivity index is affected by the coupling of strain rate and compressive strain. The energy absorption, energy absorption efficiency and specific energy absorption of flexible polyurethane foam at different strain rates were compared and the material shows higher energy absorption efficiency but less energy absorption, and strain rate has little effect on maximum energy absorption efficiency and specific energy absorption under quasi-static loading. With the increase of strain rate, the maximum energy absorption efficiency significantly reduces and the specific energy absorption significantly increases under dynamic loading. Both the modified Sherwood-Frost model and the modified Avalle model considering the effect of strain rate can well characterize the static and dynamic compressive stress-strain responses of the flexible polyurethane foam, but the modified Avalle model is easier to apply in engineering due to its fewer parameters. The research results can provide a guide for the design and optimization of flexible polyurethane foam on impact-resistant structures.
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图 2 准静态和动态压缩实验装置
Figure 2. Equipment for quasi-static and dynamic compression experiments
图 3 在不同应变率下FPUF的压缩应力-应变关系
Figure 3. Compressive stress-strain curves of FPUF at different strain rates
图 4 0.001 s−1应变率下FPUF的压缩应力和吸能效率随应变的变化
Figure 4. Variation of compressive stress and energy absorption efficiency of FPUF with strain at the strain rate of 0.001 s−1
图 6 不同应变率下FPUF的平台应力和屈服应力
Figure 6. Plateau stress and yield stress of FPUF at different strain rates
图 7 不同泡沫材料的平台应力与应变率之间的关系
Figure 7. Relationships between plateau stress and strain rate for different foams
图 8 动态压缩下FPUF的应变率敏感性指数与应变之间的关系
Figure 8. Relationship between strain rate sensitivity index of FPUF and strain under dynamic compression
图 9 不同应变率下单位体积FPUF吸收的能量随应变的变化
Figure 9. Variation of energy absorbed per unit volume of FPUF with strain at different strain rates
图 10 单位体积FPUF在密实化应变时吸收的能量随压缩应变率的变化
Figure 10. Variation of energy absorbed per unit volume of FPUF at densification strain with compressive strain rates
图 11 不同应变率下FPUF的最大吸能效率和最大理想吸能效率
Figure 11. The maximum energy absorption efficiencies and the maximum ideal energy absorption efficiencies of FPUF at different strain rates
图 12 不同泡沫材料的比吸能与应变率的关系
Figure 12. Relationship between specific energy absorption of different foams and strain rate
图 13 S-F模型的预测结果和实验结果的对比
Figure 13. Comparison of the prediction by the S-F model with the experimental result
图 14 修正后的S-F模型的预测结果和实验结果的对比
Figure 14. Comparison of the predictions by the modified S-F models with the experimental results
图 15 Avalle模型的预测结果与实验结果的对比
Figure 15. Comparison of the prediction by the Avalle model with the experimental result
图 16 修正后的Avalle模型的预测结果与实验结果的对比
Figure 16. Comparison of the predictions by the modified Avalle model with the experimental results
表 1 形状函数
$f(\varepsilon) $ 的参数Table 1. Fitting parameters of the shape function
$f(\varepsilon) $ A1 A2 A3 A4 A5 A6 A7 A8 −0.014 4.75 −59.04 332.27 −997.66 1653.19 −1426.30 501.74 
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