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

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

1.
国防科技大学理学院, 湖南长沙 410073
2.
中国人民解放军96901部队, 北京 100094

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
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- 被引次数: 0
出版历程
- 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

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

1.
College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073, Hunan, China
2.
96901 Unit of PLA, Beijing 100094, China

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

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。
- Kong-Fang模型 /
- 准静态实验 /
- 动态实验 /
- 平板撞击 /
- 侵彻实验
Abstract: The establishment of the dynamic mechanical model of rock materials and the determination of the relevant model parameters are of great significance to the studies of rock’s dynamic mechanical properties and related simulation calculation. Taking granite in Shandong Province as the experimental object, based on the Kong-Fang fluid elastic-plastic damage material model (KF model), the model parameters are classified into three categories, and the test scheme is then correspondingly determined. The basic strength parameters of the KF model were measured by quasi-static uniaxial compression and unconfined splitting tests. The strength-surface related material parameters were fitted by the results of the conventional triaxial tests under five different confining pressure conditions. In addition, the dynamic split Hopkinson pressure bar (SHPB) tests under several strain rate conditions were carried out to determine the strain-rate related parameters, of which the effectiveness were then verified by the dynamic split Hopkinson pressure bar-Brazilian disk (SHPB-BD) tests results. According to the principle of reverse impact and the Rankine-Hugoniot equation, the plate impact experiments with different impact stress levels were conducted by using a single-stage light gas gun, the state equation parameters in the KF model were fitted according to the impact Hugoniot results of rock samples. To verify the applicability of the material model and the experimentally measured parameter values, the simulation of a penetration process is furtherly conducted. The granite penetration tests were carried out by using a $\varnothing $30 mm caliber gun. The $\varnothing $20 mm bullets penetrated the $\varnothing $1200 mm×800 mm rock targets vertically, which was used to characterize the semi-infinite thickness condition, at an approximately designed speed of 670 m/s. To avoid accidental errors, combined with the high-speed photographic images, three effective penetrate results were obtained. The penetration depth and crater size of the target failure surface were directly measured and scanned by 3D scanner, the experimental average penetration depth, maximum and minimum diameters of the penetration craters were approximately 80.62 mm, 381.47 mm and 263.01 mm, respectively. Using the parameter values obtained from the laboratory experiments, the KF model is then implemented into LS-DYNA through a user-defined material model and used to simulate the penetration test of granite. According to the simulation result of damage distribution and cratering parameters of the target, the calculated penetration depth, maximum and minimum diameters of craters are 80.02 mm, 400 mm and 300 mm, respectively, so the errors between the calculated and the test results are less than 15%, which is acceptable in dynamic problems. The agreement between the numerical and experimental results provides a support to the application of the KF model and the relevant parameter values.
- Kong-Fang model /
- quasi-static experiment /
- dynamic experiment /
- plate impact /
- penetration experiment

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图 1 岩石试件的实物照片和显微图像

Figure 1. Photographs and micrographs of rock samples

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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)

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图 3 常规三轴实验

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

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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

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图 5 花岗岩a₁、a₂参数拟合结果

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

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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

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图 7 基于SHPB实验数据拟合得到的α、β、θ参数值

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

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图 8 利用SHPB-BD实验数据对α、β、θ值进行验证的结果

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

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图 9 拟合的花岗岩p_rock-μ_rock曲线

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

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图 10 侵彻实验装置布局图

Figure 10. Device layout diagram of penetration test

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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

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图 12 侵彻实验数值模型

Figure 12. Numerical model

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图 13 靶体损伤分布情况及成坑参数

Figure 13. Damage distribution and cratering parameters of target

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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

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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	f_t	劈裂拉伸强度	准静态劈裂实验
	f_c	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	a₁、a₂	强度面相关材料常数	准静态常规三轴实验
强度面相关参数	α、β、θ	应变率相关材料参数	SHPB/ SHPB-BD实验
状态方程相关参数	k₁、k₂、k₃	状态方程参数	平板撞击实验

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表 2 花岗岩的基本强度参数值

Table 2. Basic strength parameters of granite

试件	f_c /MPa	E/GPa	υ	试件	f_t /MPa
UCT-1	125.088	38.076	0.310	ST-1	7.714
UCT-2	133.206	41.82	0.352	ST-2	6.9
UCT-3	128.969	38.843	0.318	ST-3	8.12
UCT-4	133.802	39.534	0.498	ST-4	6.887
UCT-5	133.772	40.759	0.259	ST-5	7.409
KF模型参数值	130.967±3.856	39.806±1.497	0.347±0.091	KF模型参数值	7.406±0.532

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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
10-1	10	256.220	92.073	246.220
20-1	20	327.341	122.447	307.341
30-1	30	385.384	148.461	355.384
30-2		393.095	151.032	363.095
30-3		390.809	150.270	360.809
40-1	40	437.691	172.564	397.691
40-2		440.422	173.474	400.422
40-3		444.189	174.730	404.189
50-1	50	482.936	194.312	432.936
50-2		485.975	195.325	435.975
50-3		495.950	198.650	445.950

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

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/MPa	η_c	平均应变率/s⁻¹	试件	动态劈裂拉伸强度/MPa	η_t	平均应变率/s⁻¹
SHPB-1	159.324	1.217	83	SHPB-BD-1	41.395	5.589	138
SHPB-2	142.925	1.091	105	SHPB-BD-2	37.363	5.045	135
SHPB-3	160.994	1.229	102	SHPB-BD-3	45.456	6.138	133
SHPB-4	156.455	1.195	85	SHPB-BD-4	45.548	6.150	135
SHPB-5	164.434	1.256	122	SHPB-BD-5	52.404	7.076	187
SHPB-6	180.403	1.377	144	SHPB-BD-6	52.654	7.110	183
SHPB-7	145.891	1.114	168	SHPB-BD-7	49.934	6.742	187
SHPB-8	140.933	1.076	187	SHPB-BD-8	49.225	6.647	188
SHPB-9	212.790	1.625	230	SHPB-BD-9	65.320	8.820	241
SHPB-10	260.696	1.991	325	SHPB-BD-10	54.190	7.317	245
SHPB-11	158.481	1.210	258	SHPB-BD-11	70.300	9.492	239
SHPB-12	177.977	1.359	292	SHPB-BD-12	60.436	8.160	243
SHPB-13	215.694	1.647	360	SHPB-BD-13	48.513	6.550	155
				SHPB-BD-14	61.372	8.287	199
				SHPB-BD-15	71.112	9.602	210

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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)	u_p,Cu (m∙s⁻¹)	u_p,rock /(m∙s⁻¹)	p_rock /GPa	u_s,rock/ (m∙s⁻¹)	μ_rock
G-1	298.249	170.887	212.806	3.103	5430.281	0.039
G-2	298.586	171.614	212.779	3.117	5454.783	0.039
G-3	296.200	175.154	208.623	3.183	5681.906	0.037
G-4	364.353	210.768	258.969	3.856	5543.886	0.047
G-5	362.860	210.444	257.638	3.849	5563.631	0.046
G-6	370.399	217.718	261.540	3.988	5677.582	0.046
G-7	420.639	247.273	297.002	4.553	5708.849	0.052
G-8	425.834	247.173	302.248	4.552	5607.388	0.054
G-9	424.120	246.701	300.769	4.542	5623.706	0.053
G-10	536.010	308.458	381.771	5.743	5601.403	0.068
G-11	527.022	302.785	375.608	5.632	5582.955	0.067
G-12	536.027	312.243	370.879	5.817	5840.622	0.063

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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
f_c/MPa	f_t/MPa	E/GPa	a₁	a₂/MPa ⁻¹	υ	α	β	θ	k₁/GPa	k₂/GPa	k₃/GPa
130.967	7.406	39.806	0.36	0.09/f_c	0.347	0.06	3.47	1.83	45.002	1413.751	−12037.857

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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
7830	45	1380	12	58	1269	810	0.479	0.04	1

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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
试验	子弹着角/(°)	侵彻速度/(m∙s⁻¹)	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	−3.5	638	75.05	76.29	310	327.98	245	248.36
靶2	−3.5	667	72.19	72.48	430	408.24	275	283.00
靶3	−1.5	673	96.00	91.73	410	402.60	265	261.67

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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±10.46	381.47±49.60	263.01±14.75
数值模拟	80.02	400.00	300.00
误差/%	−0.75	4.86	14.07

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