Study on Holmquist-Johnson-Cook Constitutive Model and Numerical Simulation of Red Sandstone Based on Static and Dynamic Mechanical Tests
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摘要: 岩石材料被广泛应用于防护工程和各种隧道等民用工程结构中，其动态力学性能研究具有重要意义。以山东济南某石矿的红砂岩为文章研究对象，利用三轴试验机和分离式霍普金森杆装置分别开展不同围压下和不同应变率下红砂岩的力学特性研究，并基于动静态力学试验对红砂岩的Holmquist-Johnson-Cook本构模型的参数进行确定。采用已经确定的红砂岩的HJC本构模型的参数，建立了大口径分离式霍普金森压杆动态压缩试验的有限元模型对参数进行验证。结果表明:红砂岩在围压环境下，内部裂纹的扩展方向和程度受到限制，使得裂纹难以快速贯通，从而峰值应力随着静水压力和的增加而增加；红砂岩在不同气压的加载下，存在明显率效应现象，动态抗压和劈拉强度与平均应变率呈现正相关，通过抗压强度因子和抗拉强度因子的研究分析，动态拉伸峰值应力的率效应现象更为明显；确定的HJC本构模型参数在LS-DYAN中可以较好地模拟红砂岩在动态冲击的损伤失效过程，在未达到最大峰值应力时，数值模拟结果与试验的结果应力-应变曲线基本一致。确定的致密、高强度的红砂岩参数可为红砂岩的动态力学性能的研究和工程应用提供参考。
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关键词:
- 红砂岩 /
- Holmquist-Johnson-Cook（HJC）本构 /
- LS-DYNA /
- 霍普金森压杆
Abstract: Rock materials are widely used in protective engineering and various civil engineering structures such as tunnels, and the research on their dynamic mechanical properties is of great significance. The red sandstone from a stone mine in Jinan, Shandong Province, is taken as the research object. Triaxial testing machines and split Hopkinson pressure bar (SHPB) devices were used to study the mechanical properties of red sandstone under different confining pressures and strain rates, respectively. Based on the static and dynamic mechanical tests, the parameters of the Holmquist-Johnson-Cook constitutive model for red sandstone were calibrated. Using the calibrated parameters of the HJC constitutive model for red sandstone, a finite element model for the dynamic compression test of the large-diameter split Hopkinson pressure bar was established, and verification was conducted by comparing the numerical simulation results with the test results in terms of the failure mode of red sandstone and the corresponding stress-strain curve. The results show that: Under the confining pressure environment, the propagation direction and extent of internal cracks in red sandstone are restricted, making it difficult for cracks to penetrate rapidly. Thus, the peak stress increases with the increase of hydrostatic pressure. Under loading with different air pressures, red sandstone exhibits an obvious rate effect. The dynamic compressive and splitting tensile strengths are positively correlated with the average strain rate. Through the research and analysis of the dynamic increase factor for compressive strength and dynamic increase factor for tensile strength , the rate effect of the dynamic tensile peak stress is more significant. The calibrated HJC constitutive model parameters can well simulate the damage and failure process of red sandstone under dynamic impact in LS-DYNA. Before reaching the maximum peak stress, the stress-strain curves from the numerical simulation results are basically consistent with those from the test results. The calibrated parameters for dense and high-strength red sandstone can provide a reference for the research on the dynamic mechanical properties of red sandstone and its engineering applications. -
图 3 TAW-2000微机控制岩石三轴试验机
Figure 3. TAW-2000 microcomputer-controlled rock triaxial testing machine
图 7 静态压缩下红砂岩的压应力与应变变化关系
Figure 7. The relationship between compressive stress and strain of red sandstone under static compression
图 8 静态劈裂下红砂岩的拉应力与位移变化关系
Figure 8. The relationship between tensile stress and displacement evolution of red sandstone under static splitting
图 10 红砂岩在压缩中的四个典型阶段
Figure 10. The four typical stages of red sandstone under compression
图 12 红砂岩动态压缩应力-应变曲线
Figure 12. Dynamic compressive stress-strain curve of red sandstone
图 13 红砂岩动态劈裂应力-时间曲线
Figure 13. Mohr-Coulomb criterion relationship curve of red sandstone
图 14 不同应变率下抗压强度因子拟合曲线
Figure 14. Fitting curves of compressive strength factor under different strain rates
图 15 不同应变率下抗拉强度因子拟合曲线
Figure 15. Fitting curves of tensile strength factor under different strain rates
图 18 红砂岩在不同应变率下的归一化强度
Figure 18. Normalized strength of red sandstone under different strain rates
图 20 SHPB动态压缩试验的有限元模型图
Figure 20. Finite element model diagram of SHPB dynamic compression test
图 21 动态压缩实验与模拟的红砂岩动态断裂图对比
Figure 21. Comparison of dynamic fracture patterns between experimental and simulated dynamic compression tests
图 22 不同应变率下动态压缩实验与模拟的应力-应变曲线对比曲线图
Figure 22. Comparative stress–strain curves of dynamic compression experiments and simulations under various strain rates
表 1 红砂岩静力学参数
Table 1. Static mechanical parameters of red sandstone
岩石种类 密度ρ/(g·cm−3) 单轴抗压强度fc/MPa 抗拉强度T/MPa 弹性模量E/GPa 泊松比v 红砂岩 2.40 119.5 4.74 33.7 0.25 
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表 2 三轴围压试验结果
Table 2. The triaxial compression tests Results
编号 围压σ3/MPa 偏应力σ1-σ3/MPa 平均偏应力/MPa 平均主应力/MPa 10-1 10 168.4 166.0 176.0 10-2 10 163.6 20-1 20 206.4 194.0 214.0 20-2 20 181.5 30-1 30 230.0 227.2 257.2 30-2 30 224.3 40-1 40 253.6 258.4 298.4 40-2 40 263.2
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表 4 红砂岩在不同应变率下抗拉强度和强度因子计算数据表
Table 4. Data table of tensile strength and strength factor of red sandstone under different strain rates
加载状态 气压/MPa 平均应变率/s−1 拉伸峰值应力/MPa 抗拉强度因子$ {\lambda }_{\text{t}} $ 静态劈裂 / 10−5 4.74 1.000 动态劈裂 0.2 47 11.37 2.399 0.3 56 15.29 3.226 0.4 75 25.15 5.306 0.5 86 25.71 5.424 0.6 101 27.85 5.876 0.65 136 33.17 6.998
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表 3 红砂岩在不同应变率下抗压强度和强度因子计算数据表
Table 3. Data table of compressive strength and strength factor of red sandstone under different strain rates
加载状态 气压/MPa 平均应变率/s−1 压缩峰值应力/MPa 抗压强度因子$ {\lambda }_{\text{c}} $ 静态压缩 / 10−5 119.50 1.000 / 2×10−5 125.20 1.047 / 10−4 127.90 1.070 动态压缩 0.2 75 131.88 1.104 0.3 108 146.33 1.225 0.4 127 147.40 1.233 0.5 167 179.90 1.505 0.6 190 202.69 1.696 0.65 258 226.91 1.899
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表 5 红砂岩在不同应变率下归一化强度计算数据表
Table 5. Calculation Data Table of Normalized Strength of Red Sandstone under Different Strain Rates
加载状态 平均应变率/s−1 无量纲静水压力p* 无量纲等效应力σ* 归一化强度 静态压缩 10−5 0.333 1.000 1.0000 2×10−5 0.349 1.048 1.0048 10−4 0.357 1.070 1.0069 动态压缩 75 0.368 1.104 1.0099 108 0.408 1.225 1.0195 127 0.411 1.233 1.0201 167 0.502 1.505 1.0362 190 0.565 1.696 1.0446 258 0.633 1.899 1.0518
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表 6 红砂岩 HJC 本构参数
Table 6. The HJC constitutive parameter of Red Sandstone
ρ /(g·cm−3) fc/MPa G/GPa T/MPa A B N C Smax Emin 2.40 119.5 13.484 4.74 0.234 1.832 0.80 0.00182 7.0 0.01 pcrush/MPa μcrush plock/GPa μlock K1/GPa K2/GPa K3/GPa D1 D2 39.83 0.00177 1.211 0.0449 23.78 64.36 150.24 0.03872 1.0
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