Zr基非晶合金JH-2模型的构建及应用

张云峰; 罗兴柏; 刘国庆; 施冬梅

doi:10.11883/bzycj-2019-0377

Zr基非晶合金JH-2模型的构建及应用

doi: 10.11883/bzycj-2019-0377

陆军工程大学石家庄校区，河北石家庄 050000

详细信息

作者简介:
张云峰（1990－　），男，博士研究生，1193954881@qq.com

通讯作者:
刘国庆（1975－　），男，博士，副教授，13081106809@163.com

中图分类号: O346.5；TG139.8
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出版历程
- 收稿日期: 2019-09-29
- 修回日期: 2020-06-04
- 刊出日期: 2020-07-01

Construction and application of the JH-2 model for a Zr-based bulk metallic glass alloy

Shijiazhuang Campus, Army Engineering University, Shijiazhuang 050000, Hebei, China

摘要

摘要: 为构建Zr_62.5Nb₃Cu_14.5Ni₁₄Al₆非晶合金在高压、大应变、高应变率状态下的材料模型，采用根据实验数据理论推导和数值模拟对比反馈的方法，对材料的Johnson-Holmquist本构模型（JH-2模型）参数进行了研究：材料的静水压力-体应变关系通过平板冲击实验数据和理论推导得到；无损材料强度与应变、应变率的关系通过轴向压缩实验数据确定；材料损伤参数与破碎材料强度参数的关系通过平板冲击实验数据确定；破碎材料强度参数通过数值模拟与实验结果对比的反馈法得到。将材料模型应用于平板冲击和破片侵彻的数值模拟，通过数值模拟与实验结果对比的方式，验证材料模型的准确性。结果表明，平板冲击实验中，材料的自由面粒子速度曲线与数值模拟结果吻合度较高；破片侵彻实验中，破片对钢靶的侵彻深度、开坑孔径与数值模拟结果的一致性较好，构建的材料模型较准确反映了材料的动态力学特性。
- Zr基非晶合金 /
- JH-2模型 /
- 本构关系 /
- 大应变
Abstract: Zr-based bulk metallic glass is a type of glass alloy with many excellent properties, such as high strength and high hardness. With the increasing application of Zr-based bulk metallic glass alloys in military field, it is urgent to construct the mechanical models for these materials, including equations of state and constitutive relations. The Johnson-Holmquist constitutive model (JH-2 model) is the most widely used constitutive model to describe the response of brittle materials subjected to high pressures, large strains, and high strain rates. The parameters of the JH-2 model for the Zr_62.5Nb₃Cu_14.5Ni₁₄Al₆ bulk metallic glass alloy were determined by experimental and theoretical methods, as well as “back out” approaches from simulation data. The Hydrostatic pressure-volume strain relationship was developed by theoretical derivation from the results of plate-impact experiments. The results of axial compression tests were used to propose the relationship between the intact strength and strain, strain rate of the material. The relationship between the damage parameters and fracture strength of the material was determined by the plate-impact experiments. The plate-impact data were used to “back out” the fracture strength parameters as well. Numerical simulation results including plate impact and fragment penetration were provided to validate the accuracy and applicability of the developed model. The results show that the particle velocity curve of the freedom surface agrees well with the numerical simulation. The penetration depth and cavity radius obtained in the tests are in good agreement with the numerical simulation results, and the developed model can describe the dynamic properties of the material accurately.
- Zr-based amorphous alloy /
- JH-2 model /
- constitutive relation /
- large strain

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图 1 JH-2模型^[12]

Figure 1. Description of the JH-2 model^[12]

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图 2 材料的压力-体应变关系

Figure 2. Relation between pressure and volumetric strain for the material

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图 3 确定的材料归一化静水压力-等效破碎应变关系

Figure 3. Determined relation between normalized hydrostatic pressure and equivalent crushing strain for the material

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图 4 材料的应变率敏感性

Figure 4. Strain rate sensitivity of the material

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图 5 构建的无损材料强度模型和破碎材料强度模型

Figure 5. The intact strength and fractured strength models developed for the material

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图 6 不同冲击速度下，试样自由面速度的数值模拟结果与平板冲击实验结果的对比

Figure 6. Comparison of simulated impact-induced free-surface velocities in samples with those measured in flyer-plate impact tests at different impact velocities

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图 7 侵彻实验装置的布局

Figure 7. Layout of devices for penetration tests

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图 8 靶板横截面的数值模拟结果与侵彻实验结果的对比

Figure 8. Comparison of cross sections of targets between numerical simulation and penetration test results

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图 9 不同冲击速度下的侵彻深度和弹坑直径

Figure 9. Penetration depths and crater diameters at different impact velocities

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表 1 平板冲击实验数据^[24] 及相应计算结果

Table 1. Experimental data^[24] by plate impact tests and the corresponding calculation results

σ_x/GPa	μ	p/GPa	p^*	σ/GPa	σ_i/GPa	σ_f/GPa	D	$\varepsilon_x^{\rm{total}} $	$\varepsilon_x^{\rm{elastic}} $	$\varepsilon_x^{\rm{plastic}} $	$\varepsilon_x^{\rm f} $	$\varepsilon_x^{\rm f} $
5.97	0.043	4.84	1.27	1.69	2.94	1.00	0.65	0.041	0.034	0.007	0.011	0.007
6.76	0.046	5.56	1.46	1.81	3.07	1.04	0.62	0.044	0.034	0.010	0.016	0.011
7.57	0.054	6.22	1.64	2.03	3.18	1.07	0.55	0.051	0.034	0.017	0.031	0.021
8.88	0.059	7.42	1.95	2.19	3.37	1.12	0.52	0.055	0.034	0.022	0.041	0.027
10.05	0.060	8.54	2.25	2.26	3.53	1.16	0.54	0.057	0.034	0.023	0.042	0.028

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表 2 Zr_62.5Nb₃Cu_14.5Ni₁₄Al₆非晶合金轴向压缩实验数据^[24]

Table 2. Experimental data of axial compression for Zr_62.5Nb₃Cu_14.5Ni₁₄Al₆ amorphous alloy^[24]

编号	设备	σ/GPa	p/GPa	σ^*	p^*	$\dot \varepsilon $/s^-1
1#	Instron 5982	1.26	0.43	0.48	0.11	0.000 4
2#	Instron 5982	1.30	0.43	0.48	0.11	0.001
3#	Instron 5982	1.34	0.45	0.20	0.12	0.002
4#	Instron 5982	1.26	0.42	0.47	0.11	0.003
5#	Instron 5982	1.28	0.43	0.47	0.11	0.004
6#	Instron 5982	1.37	0.46	0.51	0.12	0.010
7#	SHPB	1.45	0.48	0.54	0.13	1 755
8#	SHPB	1.46	0.49	0.54	0.13	1 964
9#	SHPB	1.51	0.50	0.56	0.13	2 783
10#	SHPB	1.75	0.58	0.65	0.15	3 129
11#	SHPB	1.64	0.55	0.61	0.14	3 410
12#	SHPB	1.87	0.62	0.70	0.16	6 378

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表 3 计算参数及误差

Table 3. Parameters and errors

编号	B	M	D₁/10⁻³	D₂	误差/%	编号	B	M	D₁/10^-3	D₂	误差/%
1#	0.1	0.5	4.8	2.704	4.2	9#	0.3	0.1	3.6	2.838	3.9
2#	0.2	0.5	4.2	2.663	4.1	10#	0.3	0.2	3.6	2.793	3.8
3#	0.3	0.5	3.6	2.606	3.9	11#	0.3	0.3	3.6	2.741	3.8
4#	0.4	0.5	3.0	2.520	4.2	12#	0.3	0.4	3.6	2.679	3.9
5#	0.5	0.5	2.4	2.372	4.2	13#	0.3	0.5	3.6	2.606	3.9
6#	0.6	0.5	1.9	2.060	4.9	14#	0.3	0.6	3.7	2.521	4.0
7#	0.7	0.5	1.5	0.929	12.3	15#	0.3	0.7	3.7	2.418	4.4
8#	0.8	0.5	0.003 5	5.281	139.6	16#	0.3	0.8	3.8	2.295	4.8

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表 4 Zr_62.5Nb₃Cu_14.5Ni₁₄Al₆非晶合金材料常数

Table 4. Parameters of the JH-2 model for Zr_62.5Nb₃Cu_14.5Ni₁₄Al₆ amorphous alloy

ρ₀/(kg·cm⁻³)	ν	HEL/GPa	K₁/GPa	K₂/GPa	K₃/GPa	β	D₁	D₂
6.76	0.37	5.54	110.9	−871.7	20 930	1.0	0.003 5	2.83

p_HEL/GPa	σ_HEL/GPa	T/GPa	A	B	C	M	N	$\sigma _{{\rm{fmax}}}^{\rm{*}}$
3.8	2.7	0.57	0.83	0.3	0.033	0.25	0.34	1.0

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表 5 数值模拟中铜材料参数

Table 5. The parameters of copper in the simulations

ρ₀/(kg·cm⁻³)	G/GPa	σ_y/MPa	冲击状态方程参数
ρ₀/(kg·cm⁻³)	G/GPa	σ_y/MPa	Γ₀	c₁/(m·s⁻¹)	S₁
8.93	47.7	120	2.02	3940	1.489

Steinberg-Guinan强度模型参数
σ_max/MPa	β	n	dG/dP	(dG/dT)/(kPa·K⁻¹)	dY/dG
640	36	0.45	1.35	−17 980	0.003 396

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表 6 数值模拟中45钢的材料参数

Table 6. The parameters of 45 steel in the simulations

ρ₀/(kg·cm⁻³)	强度模型参数
ρ₀/(kg·cm⁻³)	A/MPa	B/MPa	C	N	M
7.85	780	730	0.0083	0.307	0.804

K/GPa	损伤模型参数
K/GPa	D₁	D₂	D₃	D₄	D₅
157.9	0.05	3.44	−2.12	0.002	0.61

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