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考虑长径比与应变率耦合效应的砂质泥岩动态损伤本构模型

Dynamic damage constitutive model of sandy mudstone considering the coupling effect of length-to-diameter ratio and strain rate

  • 摘要: 长径比对岩石试样在冲击载荷下的力学特性和能量演化规律具有重要影响,目前针对同时考虑长径比和应变率因素耦合的岩石损伤本构模型尚需完善。采用分离式霍普金森压杆(SHPB)系统,开展了4组长径比(0.4、0.6、0.8、1.0)和5级冲击气压水平(0.2~0.6 MPa)的动态压缩试验。分析了强度、变形、能量等参数与长径比的关系,推导了反射能、透射能、破碎耗能与入射能理论斜率,并基于韦伯分布和D-P准则建立了考虑长径比和应变率因素耦合的损伤本构模型。结果表明:① 冲击载荷下砂质泥岩试样动态应力–应变曲线可分为压密阶段、类弹性阶段、塑性阶段和破坏阶段;在试验涉及的冲击气压范围内,动态增强因子与长径比呈正相关,软化系数与长径比呈负相关。② 随长径比增加,试样破碎耗能密度呈降低趋势;随试样长径比由0.4增至1.0,反射能占比由19%增至31%,透射能占比由37%减至21%,破碎耗能占比在43%~48%;对试验数据进行拟合,发现反射能、透射能、破碎耗能与入射能均呈一次正相关关系;基于应力波从入射杆传至试样的界面反射系数\lambda ,理论推导得到反射能、透射能、破碎耗能与入射能理论斜率分别为\lambda^10 、\left(1-\lambda^6\right)^2 、1-\lambda^10-\left(1-\lambda^6\right)^2。③ 基于试验获取的动态强度与应变率和长径比的函数关系,对采用韦伯分布和D-P准则推导的初始本构模型进行修正,得到的损伤本构模型与试验曲线一致性良好,可用于表征砂质泥岩动态力学特性。

     

    Abstract: The length-to-diameter ratio has a significant impact on the mechanical properties and energy evolution of rock samples under impact loads, and the current constitutive model for rock damage that considers the coupling of length-to-diameter ratio and strain rate still needs to be improved. The split Hopkinson pressure bar (SHPB) system was used to conduct dynamic compression tests with four length-to-diameter ratios (0.4, 0.6, 0.8, 1.0) and five levels of impact air pressure (0.2–0.6 MPa). The relationships between parameters such as strength, deformation, and energy with length-to-diameter ratio were analyzed. The theoretical slopes of reflection energy, transmission energy, fragmentation energy, and incident energy have been derived. Based on the Weber distribution and D-P criterion, a damage constitutive model considering the coupling of length-to-diameter ratio and strain rate was established. The research results show that: ① The dynamic stress-strain curve of sandy mudstone specimens under impact loads can be divided into the compaction stage, quasi-elastic stage, plastic stage, and failure stage. Within the range of impact air pressure involved in the experiment, the dynamic strength growth factor is positively correlated with the aspect ratio, while the softening coefficient is negatively correlated with the aspect ratio. ② With the increase in length-to-diameter ratio, the energy density of specimen fragmentation decreases. As the length-to-diameter ratio of the sample increases from 0.4 to 1.0, the proportion of reflected energy increases from 19% to 31%, the proportion of transmitted energy decreases from 37% to 21%, and the proportion of dissipated energy ranges from 43% to 48%. By fitting the experimental data, it was found that there is a positive correlation between reflected energy, transmitted energy, dissipated energy, and incident energy. Based on the interface reflection coefficient \lambda of stress waves transmitted from the incident bar to the specimen, the theoretical slopes of reflected energy, transmitted energy, dissipated energy, and incident energy are are derived as \lambda^10 , \left(1-\lambda^6\right)^2 and 1-\lambda^10-\left(1-\lambda^6\right)^2, respectively. ③ Based on the dynamic strength obtained from experiments and its function with strain rate and length-to-diameter ratio, the initial constitutive model derived from the Weber distribution and D-P criterion was modified. The resulting damage constitutive model shows good consistency with the experimental curves and can be used to characterize the dynamic mechanical properties of sandy mudstone.

     

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