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花岗岩Kong-Fang流体弹塑性损伤材料模型参数研究

聂铮玥 丁育青 宋江杰 彭永 林玉亮 陈荣

聂铮玥, 丁育青, 宋江杰, 彭永, 林玉亮, 陈荣. 花岗岩Kong-Fang流体弹塑性损伤材料模型参数研究[J]. 爆炸与冲击, 2022, 42(9): 091409. doi: 10.11883/bzycj-2021-0363
引用本文: 聂铮玥, 丁育青, 宋江杰, 彭永, 林玉亮, 陈荣. 花岗岩Kong-Fang流体弹塑性损伤材料模型参数研究[J]. 爆炸与冲击, 2022, 42(9): 091409. doi: 10.11883/bzycj-2021-0363
NIE Zhengyue, DING Yuqing, SONG Jiangjie, PENG Yong, LIN Yuliang, CHEN Rong. A study of parameters of Kong-Fang fluid elastoplastic damage material model for Shandong granite[J]. Explosion And Shock Waves, 2022, 42(9): 091409. doi: 10.11883/bzycj-2021-0363
Citation: NIE Zhengyue, DING Yuqing, SONG Jiangjie, PENG Yong, LIN Yuliang, CHEN Rong. A study of parameters of Kong-Fang fluid elastoplastic damage material model for Shandong granite[J]. Explosion And Shock Waves, 2022, 42(9): 091409. doi: 10.11883/bzycj-2021-0363

花岗岩Kong-Fang流体弹塑性损伤材料模型参数研究

doi: 10.11883/bzycj-2021-0363
基金项目: 国家自然科学基金(12072369,11902355)
详细信息
    作者简介:

    聂铮玥(1997- ),女,硕士,niezhengyue_97@163.com

    通讯作者:

    陈 荣(1981- ),男,博士,副教授,r_chen@nudt.edu.cn

  • 中图分类号: O347.3

A study of parameters of Kong-Fang fluid elastoplastic damage material model for Shandong granite

Funds: LIANG B, LIU T. Boundary effects of finite concrete targets subjected to impact projectiles [J]. Journal of Projectiles, Rockets, Missiles and Guidance, 2004, 24(4): 39-41. DOI: 10.3969/j.issn.1673-9728.2004.04.013.
  • 摘要: 岩石类材料的动态力学模型的建立及相应模型参数的确定,对岩石动态力学性能研究及相关仿真计算具有重要意义。以山东五莲地区花岗岩为例,基于Kong-Fang流体弹塑性损伤材料模型(KF模型),通过准静态单轴压缩、劈裂、常规三轴实验及动态分离式霍普金森杆压缩(split Hopkinson pressure bar,SHPB)实验对模型中的强度参数进行了确定,并利用基于分离式霍普金森杆的巴西圆盘(split Hopkinson pressure bar-Brazilian disk,SHPB-BD)实验对应变率相关参数的有效性进行了验证;同时,根据平板撞击实验结果对模型中的状态方程参数进行了拟合。利用实验获得的材料参数值,采用KF模型对花岗岩侵彻实验进行数值模拟,计算得到的弹体侵彻深度及成坑尺寸与实际实验结果误差均小于15%,验证了材料模型及参数值的适用性。
  • 图  1  岩石试件的实物照片和显微图像

    Figure  1.  Photographs and micrographs of rock samples

    图  2  花岗岩单轴压缩及劈裂实验

    Figure  2.  Typical view of uniaxial compression test (UCT) and splitting test (ST)

    图  3  常规三轴实验

    Figure  3.  A view of triaxial compression test (TXC, σ2=σ3)

    图  4  常规三轴实验花岗岩试件应力-应变曲线

    Figure  4.  Stress-strain curves of rock samples in TXC tests

    图  5  花岗岩a1a2参数拟合结果

    Figure  5.  Fitting results of parameters a1 and a2 of granite

    图  6  花岗岩SHPB、SHPB-BD实验应力-应变曲线

    Figure  6.  Stress-strain curves of SHPB and SHPB-BD tests of granite samples

    图  7  基于SHPB实验数据拟合得到的αβθ参数值

    Figure  7.  Parameter values of α, β and θ fitted by SHPB tests data

    图  8  利用SHPB-BD实验数据对αβθ值进行验证的结果

    Figure  8.  Validation of α, β and θ values by SHPB-BD tests data

    图  9  拟合的花岗岩prockrock曲线

    Figure  9.  Fitting curve of plate impact data of granite samples

    图  10  侵彻实验装置布局图

    Figure  10.  Device layout diagram of penetration test

    图  11  花岗岩靶体弹坑照片及三维扫描图

    Figure  11.  Photos and 3D scanning results of cratering failure on the impact surfaces of granite targets

    图  12  侵彻实验数值模型

    Figure  12.  Numerical model

    图  13  靶体损伤分布情况及成坑参数

    Figure  13.  Damage distribution and cratering parameters of target

    图  14  弹体的侵彻深度和加速度时程曲线

    Figure  14.  History curves of penetration depth and acceleration of projectile

    表  1  KF模型参数的分类及实验确定方法

    Table  1.   Parameter classification and experimental determination method of KF model

    分类参数物理意义确定方法
    材料基本强度参数ft劈裂拉伸强度准静态劈裂实验
    fc单轴压缩强度准静态单轴压缩实验
    E弹性模量
    υ泊松比
    强度面相关参数a1a2强度面相关材料常数准静态常规三轴实验
    αβθ应变率相关材料参数SHPB/ SHPB-BD实验
    状态方程相关参数k1k2k3状态方程参数平板撞击实验
    下载: 导出CSV

    表  2  花岗岩的基本强度参数值

    Table  2.   Basic strength parameters of granite

    试件fc /MPaE/GPaυ试件ft /MPa
    UCT-1125.08838.0760.310ST-17.714
    UCT-2133.20641.820.352ST-26.9
    UCT-3128.96938.8430.318ST-38.12
    UCT-4133.80239.5340.498ST-46.887
    UCT-5133.77240.7590.259ST-57.409
    KF模型参数值130.967±3.85639.806±1.4970.347±0.091KF模型参数值7.406±0.532
    下载: 导出CSV

    表  3  不同围压条件下试件的轴向峰值强度、偏压力与静水压力

    Table  3.   The strength, deviatoric pressure and hydrostatic pressure of rock samples under different confining pressures

    试件围压/MPa轴向峰值强度/MPa静水压力/MPa偏应力/MPa
    10-110256.220 92.073246.220
    20-120327.341122.447307.341
    30-130385.384148.461355.384
    30-2393.095151.032363.095
    30-3390.809150.270360.809
    40-140437.691172.564397.691
    40-2440.422173.474400.422
    40-3444.189174.730404.189
    50-150482.936194.312432.936
    50-2485.975195.325435.975
    50-3495.950198.650445.950
    下载: 导出CSV

    表  4  SHPB、SHPB-BD实验的平均应变率及相应的$\eta_{\rm c} $$\eta_{\rm t} $

    Table  4.   Average strain rates and corresponding $\eta_{\rm c} $ and $\eta_{\rm t} $ values obtained from SHPB and SHPB-BD experiments

    试件动态压缩强度/MPaηc平均应变率/s−1试件动态劈裂拉伸强度/MPaηt平均应变率/s−1
    SHPB-1159.3241.21783SHPB-BD-141.3955.589138
    SHPB-2142.9251.091105SHPB-BD-237.3635.045135
    SHPB-3160.9941.229102SHPB-BD-345.4566.138133
    SHPB-4156.4551.19585SHPB-BD-445.5486.150135
    SHPB-5164.4341.256122SHPB-BD-552.4047.076187
    SHPB-6180.4031.377144SHPB-BD-652.6547.110183
    SHPB-7145.8911.114168SHPB-BD-749.9346.742187
    SHPB-8140.9331.076187SHPB-BD-849.2256.647188
    SHPB-9212.7901.625230SHPB-BD-965.3208.820241
    SHPB-10260.6961.991325SHPB-BD-1054.1907.317245
    SHPB-11158.4811.210258SHPB-BD-1170.3009.492239
    SHPB-12177.9771.359292SHPB-BD-1260.4368.160243
    SHPB-13215.6941.647360SHPB-BD-1348.5136.550155
    SHPB-BD-1461.3728.287199
    SHPB-BD-1571.1129.602210
    下载: 导出CSV

    表  5  花岗岩平板撞击实验结果

    Table  5.   Plate impact test results of granite samples

    实验w/ (m∙s−1)up,Cu (m∙s−1)up,rock /(m∙s−1)prock /GPaus,rock/ (m∙s−1)μrock
    G-1298.249170.887212.8063.1035430.2810.039
    G-2298.586171.614212.7793.1175454.7830.039
    G-3296.200175.154208.6233.1835681.9060.037
    G-4364.353210.768258.9693.8565543.8860.047
    G-5362.860210.444257.6383.8495563.6310.046
    G-6370.399217.718261.5403.9885677.5820.046
    G-7420.639247.273297.0024.5535708.8490.052
    G-8425.834247.173302.2484.5525607.3880.054
    G-9424.120246.701300.7694.5425623.7060.053
    G-10536.010308.458381.7715.7435601.4030.068
    G-11527.022302.785375.6085.6325582.9550.067
    G-12536.027312.243370.8795.8175840.6220.063
    下载: 导出CSV

    表  6  花岗岩KF模型参数拟合结果

    Table  6.   Fitting results of KF model parameters of granite

    强度参数状态方程参数
    fc/MPaft/MPaE/GPaa1a2/MPa −1υαβθk1/GPak2/GPak3/GPa
    130.9677.40639.8060.360.09/fc0.3470.063.471.8345.0021413.751−12037.857
    下载: 导出CSV

    表  7  弹体材料参数[28]

    Table  7.   Parameters of the projectile’s material[28]

    基本力学指标JC本构模型参数
    密度/
    (kg∙m−3)
    洛氏硬度
    HRC
    抗拉强度/
    MPa
    延伸率/
    %
    截面收缩率/
    %
    屈服强度A/
    MPa
    硬化系数B/
    MPa
    硬化指数n 应变率敏感
    系数c
    温度软化
    系数m
    7830451380125812698100.479 0.041
    下载: 导出CSV

    表  8  花岗岩靶成坑参数现场测量及三维扫描结果

    Table  8.   Direct measurement and 3D scanning results of crater parameters of granite targets

    试验子弹着角/(°)侵彻速度/(m∙s−1)侵彻深度/mm侵彻弹坑最大直径/mm侵彻弹坑最小直径/mm
    现场测量三维扫描现场测量三维扫描现场测量三维扫描
    靶1−3.563875.0576.29310327.98245248.36
    靶2−3.566772.1972.48430408.24275283.00
    靶3−1.567396.0091.73410402.60265261.67
    下载: 导出CSV

    表  9  实验和数值模拟得到的花岗岩靶侵彻结果比较

    Table  9.   Comparison of penetration results obtained from penetration test and numerical simulation

    方法侵彻深度/mm侵彻弹坑最大直径/mm侵彻弹坑最小直径/mm
    实验80.62±10.46381.47±49.60263.01±14.75
    数值模拟80.02400.00300.00
    误差/%−0.754.8614.07
    下载: 导出CSV
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  • 收稿日期:  2021-08-26
  • 修回日期:  2022-01-26
  • 网络出版日期:  2022-04-06
  • 刊出日期:  2022-09-29

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