Dynamic damage constitutive model of sandstone based on component combination theory
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摘要: 采用分离式霍普金森压杆（SHPB）系统，对砂岩进行不同速度下的冲击试验，得到砂岩的应变率效应特征以及典型的动态本构曲线。该曲线分为近似线弹性阶段、塑性阶段、塑性增强阶段和正向卸载阶段。通过组合模型的方法，构建了砂岩含损伤的动态本构模型，借助LS-DYNA软件中的用户材料子程序UMAT接口实现对本构模型的二次开发，并对砂岩在冲击速度为7.5、9.5、11.5和13.5 m/s 4种情况下的SHPB动态冲击压缩试验进行模拟。结果表明：所构建的模型可以很好地描述砂岩的应变率效应和应力-应变曲线弹性段，并且动态峰值强度、最大应变均与试验结果一致，应变率、峰值强度、最大应变与试验结果的相对误差不超过10%。所构建的砂岩动态本构模型能够准确地描述砂岩在冲击作用下的动态力学特性。Abstract: In this study, using a split Hopkinson pressure bar (SHPB) system, we conducted the impact tests of sandstone at different impact velocities to collect the characteristics of the strain rate effect and obtained the typical dynamic constitutive curve of sandstone. The curve can be divided into an approximately linear elastic stage, a plastic stage, a plastic enhancement stage and a forward unloading stage. We constructed the dynamic damage constitutive model of sandstone adopting the combination model, and utilized the user subroutine UMAT interface of LS-DYNA to achieve the secondary development of the constitutive model, which was then used to simulate the SHPB dynamic impact compression tests of sandstone at four impact rates of 7.5, 9.5, 11.5 and 13.5 m/s. The calculation results showed that the as-constructed model gave a good description of the effect of the strain rate and the elastic stage of the stress-strain curve of sandstone. Moreover, the dynamic peak strength and maximum strain were in good agreement with the test results, and the relative errors of the strain rate, peak strength, maximum strain were less than 10%, thus indicating that the as-constructed dynamic constitutive model can accurately describe the dynamic mechanical properties of sandstone under impact.
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Key words:
- rock dynamic mechanics /
- split Hopkinson pressure bar /
- constitutive model /
- damage
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图 1 砂岩在不同冲击速度下的破坏形态
Figure 1. Failure patterns of sandstone at different impact velocities
图 2 不同应变率下砂岩的本构曲线
Figure 2. Stress-strain curves of sandstone at different strain rates
图 5 自定义本构模型在LS-DYNA中的计算流程
Figure 5. Calculation flow of user-defined constitutive model in LS-DYNA
图 6 不同冲击速度下试验与数值模拟结果对比
Figure 6. Comparison of tests and simulations at different impact velocities
表 1 砂岩动态力学特性的试验与模拟结果
Table 1. Tests and simulations of dynamic mechanical characteristics of sandstone
方法 v/(m·s-1) ${\dot{\varepsilon }}$/s-1 σd, max/MPa εmax/10-3 模拟 7.5 55.53 48.08 1.820 模拟 9.5 64.06 63.18 2.170 模拟 11.5 81.36 88.94 3.920 模拟 13.5 85.25 97.14 6.080 试验 7.5 52.39 50.93 2.000 试验 9.5 64.71 63.32 2.260 试验 11.5 78.23 95.87 3.900 试验 13.5 90.69 102.74 6.017 
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[1] 魏国齐, 张福东, 李君, 等.中国致密砂岩气成藏理论进展[J].天然气地球科学, 2016, 27(2):199-210. doi: 10.11764/j.issn.16721926.2016.02.0199WEI Guoqi, ZHANG Fudong, LI Jun, et al. New progress of tight sand gas accumulation theory and favorable exploration zones in China[J]. Natural Gas Geoscience, 2016, 27(2):199-210. doi: 10.11764/j.issn.16721926.2016.02.0199 [2] 郭迎春, 庞雄奇, 陈冬霞, 等.致密砂岩气成藏研究进展及值得关注的几个问题[J].石油与天然气地质, 2013, 34(6):717-724. doi: 10.11743/ogg20130601GUO Yingchun, PANG Xiongqi, CHEN Dongxia, et al. Progress of research on hydrocarbon accumulation of tight sand gas and several issues for concerns[J]. Oil & Gas Geology, 2013, 34(6):717-724. doi: 10.11743/ogg20130601 [3] 蔡灿, 伍开松, 袁晓红, 等.中低应变率下的岩石损伤本构模型研究[J].岩土力学, 2015, 36(3):795-803. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=ytlx201503025CAI Can, WU Kaisong, YUAN Xiaohong, et al. Damage constitutive model of rock under medium and low strain rates[J]. Rock and Soil Mechanics, 2015, 36(3):795-803. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=ytlx201503025 [4] 牛雷雷, 朱万成, 李少华, 等.摆锤冲击加载下砂岩中应变率动力特性的试验研究[J].岩石力学与工程学报, 2014, 33(12):2443-2450. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=yslxygcxb201412009NIU Leilei, ZHU Wancheng, LI Shaohua, et al. Experimental study of dynamic characteristics of sandstone under intermediate strain rate by using pendulum hammer driven "SHPB" apparatus[J]. Chinese Journal of Rock Mechanics and Engineering, 2014, 33(12):2443-2450. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=yslxygcxb201412009 [5] 朱晶晶. 循环冲击载荷下岩石力学特性与损伤模型的试验研究[D]. 长沙: 中南大学, 2012. http://www.wanfangdata.com.cn/details/detail.do?_type=degree&id=Y2199905 [6] 石祥超, 陶祖文, 孟英峰, 等.致密砂岩Johnson-Holmquist损伤本构模型参数求取及验证[J].岩石力学与工程学报, 2015, 34(增刊2):3750-3758. https://www.researchgate.net/profile/Xiangchao_Shi2/publication/284922523_Calculation_and_verification_for_Johnson-Holmquist_constitutive_model_parameters_of_tight_sandstone/links/56cc7b4f08ae96cdd071ba9d.pdf?origin=publication_listSHI Xiangchao, TAO Zuwen, MENG Yingfeng, et al. Calculation and verification for Johnson-Holmquist constitutive model parameters of tight sandstone[J]. Chinese Journal of Rock Mechanics and Engineering, 2015, 34(Suppl 2):3750-3758. https://www.researchgate.net/profile/Xiangchao_Shi2/publication/284922523_Calculation_and_verification_for_Johnson-Holmquist_constitutive_model_parameters_of_tight_sandstone/links/56cc7b4f08ae96cdd071ba9d.pdf?origin=publication_list [7] 赵光明, 谢理想, 孟祥瑞.软岩的动态力学本构模型[J].爆炸与冲击, 2013, 33(2):126-132. doi: 10.11883/1001-1455(2013)02-0126-07ZHAO Guangming, XIE Lixiang, MENG Xiangrui. A constitutive model for soft rock under impact load[J]. Explosion and Shock Waves, 2013, 33(2):126-132. doi: 10.11883/1001-1455(2013)02-0126-07 [8] 李夕兵, 左宇军, 马春德.中应变率下动静组合加载岩石的本构模型[J].岩石力学与工程学报, 2006, 25(5):865-874. http://www.cnki.com.cn/Article/CJFDTOTAL-YSLX200605000.htmLI Xibing, ZUO Yujun, MA Chunde. Constitutive model of rock under coupled static-dynamic loading with intermediate strain rate[J]. Chinese Journal of Rock Mechanics and Engineering, 2006, 25(5):865-874. http://www.cnki.com.cn/Article/CJFDTOTAL-YSLX200605000.htm [9] 梁书锋, 吴帅峰, 李胜林, 等.岩石材料SHPB实验试件尺寸确定的研究[J].工程爆破, 2015, 21(5):1-5. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=gcbp201505001LIANG Shufeng, WU Shuaifeng, LI Shenglin, et al. Study on the determination of specimen size in SHPB experiments of rock materials[J]. Engineering Blasting, 2015, 21(5):1-5. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=gcbp201505001 [10] 吴帅峰. 冲击荷载下砂岩损伤演化模型研究[D]. 北京: 中国矿业大学(北京), 2017. [11] 魏明彬.拉普拉斯变换的作用及意义[J].成都师范学院学报, 2013, 29(1):101-105. http://www.doc88.com/p-0093731742144.htmlWEI Mingbin. Function and meaning of Laplace transform[J]. Journal of Chengdu Normal University, 2013, 29(1):101-105. http://www.doc88.com/p-0093731742144.html [12] HALLQUIST J O. LS-DYNA key-word user's manual[M]. California: Livermore Software Technology Corporation, 2003. [13] 张安康, 陈士海.LS-DYNA用户自定义材料模型开发与验证[J].计算机应用与软件, 2011, 28(4):71-73. http://mall.cnki.net/magazine/Article/JYRJ201104020.htmZHANG Ankang, CHEN Shihai. Exploiting and verifying user-defined material model in LS-DYNA[J]. Computer Applications and Software, 2011, 28(4):71-73. http://mall.cnki.net/magazine/Article/JYRJ201104020.htm -
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