45钢柱壳爆炸膨胀断裂的SPH模拟分析

吴思思; 董新龙; 俞鑫炉

doi:10.11883/bzycj-2021-0172

45钢柱壳爆炸膨胀断裂的SPH模拟分析

doi: 10.11883/bzycj-2021-0172

吴思思^{1, 2,},
董新龙^{1, 2, ,},
俞鑫炉^{1, 2}

1.
宁波大学机械工程与力学学院, 浙江宁波 315211
2.
宁波大学冲击与安全工程教育部重点实验室，浙江宁波 315211

基金项目: 国家自然科学基金面上项目（11672143）；国家自然科学基金重点项目（11932018）

详细信息

作者简介:
吴思思（1996－　），女，硕士研究生，597108926@qq.com

通讯作者:
董新龙（1964－　），男，博士，教授，博士生导师，dongxinlong@nbu.edu.cn

中图分类号: O382
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出版历程
- 收稿日期: 2021-05-06
- 修回日期: 2021-06-03
- 网络出版日期: 2021-09-24
- 刊出日期: 2021-10-13

An investigating on explosive expanding fracture of 45 steel cylinders by SPH method

WU Sisi^{1, 2
,},
DONG Xinlong^{1, 2
, ,},
YU Xinlu^{1, 2}

1.
Faculty of Mechanical Engineering and Mechanics，Ningbo University，Ningbo 315211，Zhejiang，China
2.
Key Laboratory of Impact and Safety Engineering, Ministry of Education, Ningbo University, Ningbo 315211, Zhejiang, China

摘要

摘要: 金属柱壳爆炸膨胀断裂存在拉伸、剪切及拉剪混合等多种断裂模式，目前其物理机制及影响因素还不清晰。本文中采用光滑粒子流体动力学方法（smoothed particle hydrodynamics， SPH）对45钢柱壳在JOB-9003及RHT-901不同装药条件下的外爆实验进行了数值模拟，探讨柱壳在不同装药条件下发生的剪切断裂、拉剪混合断裂模式及其演化过程，模拟结果与实验结果一致。SPH数值模拟结果表明：在爆炸加载阶段，随着冲击波在柱壳内、外壁间来回反射形成二次塑性区，沿柱壳壁厚等效塑性应变演化呈凸形分布，壁厚中部区域等效塑性应变较内、外壁大；在较高爆炸压力（JOB-9003）作用下，柱壳断裂发生在爆轰波加载阶段，损伤裂纹从塑性应变积累较大的壁厚中部开始沿剪切方向向内、外壁扩展，形成剪切型断裂模式；而在RHT-901空心炸药加载下，虽然裂纹仍从壁厚中部开始沿剪切方向扩展，但随后柱壳进入自由膨胀阶段，未断区域处于拉伸应力状态，柱壳局部发生结构失稳，形成类似“颈缩”现象，裂纹从剪切方向转向沿颈缩区向外扩展，呈现拉剪混合断裂模式。拉伸裂纹占截面的比例与柱壳结构失稳时刻相关。可见，柱壳断裂演化是一个爆炸冲击波与柱壳结构相互作用的过程，不能简单将其作为一系列膨胀拉伸环处理。
- 柱壳 /
- 爆炸膨胀加载 /
- 断裂模式 /
- 光滑粒子流体动力学方法 /
- 45钢
Abstract: The expanding fracture of ductile alloy cylinder subject to the explosion includes multiple fracture modes, such as tensile, shear, and mixed tensile-shear fracture. The mechanism and the factors influencing the fracture processes are still enigmatic and far from understood. In this paper, the smoothed particle hydrodynamics (SPH) method is used to simulate the explosion experiment of 45 steel cylinders shell with different charges of JOB-9003 and RHT-901. The shear fracture, tension-shear mixed fracture modes and the evolution process of cylindrical shell with different charges are discussed. The simulation results are consistent with the experimental trend. The SPH results show that due to the propagation and reflection of shock wave between the inner and outer surfaces of cylinder during the loading stage of detonation wave, the distribution of equivalent plastic strain on wall-thickness of the cylinder is a convex shape, i.e. the strain in the middle of wall-thickness is larger than that of in the inner and outer walls; when loading by a higher explosive pressure (JOB-9003), the fracture cracks initiate from the middle of wall-thickness, and then develop to the inner and outer walls along the direction of maximum shear in loading stage, showingthe shear fracture mode. However, under the loading caused by charge RHT-901 with relatively low pressure, although the crack still starts from the middle of wall-thickness and propagates along the shear direction, the shear crack could not grow through the section of the wall completely in the loading stage; then the cylinder experiences the stage of free expansion, the stress state of unbroken zone changes into triaxial tensile stress state and the structural instability, similar to “necking” occurs in the unbroken zone. Consequently, the cracks turn from the shear direction to the necking zone along the radial direction, showing the mixed tensile-shear fracture mode. The proportion of tension and shear cracks is related to the occurrence time of structural instability. The results show that the explosion expanding-fracture process of a metal cylinders involves the interaction between shock wave and cylinder structure, and cannot be treated as that of a series of expansion rings.
- cylinder /
- explosive-expanding /
- fracture modes /
- smoothed particle hydrodynamics /
- 45 steel

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图 1 数值计算SPH模型

Figure 1. SPH model with different explosive charges

下载: 全尺寸图片幻灯片

图 2 JOB9003炸药加载下柱壳膨胀断裂过程

Figure 2. Expanding fracture process of the explosively-driven cylindrical shell by JOB9003 charge

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图 3 柱壳外表面径向膨胀速度

Figure 3. The radial expanding velocity of the outer surface of cylindrical shell

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图 4 RHT-901空心炸药作用下不同R/h的柱壳膨胀断裂过程模拟结果

Figure 4. Simulation results on fracture process of the cylindrical shell with different R/h under RHT-901 charge

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图 5 JOB-9003炸药加载下45钢柱壳的爆炸压力、膨胀及断裂演化过程

Figure 5. The explosive pressure, expanding deformation and fracture for 45# steel cylindrical shellwith JOB-9003 charge

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图 6 RHT-901加载下5 mm壁厚柱壳的爆炸压力、膨胀及断裂过程

Figure 6. Explosive pressure, expanding deformation and fracture for 45 steel cylindrical shell (h = 5 mm) with RHT-901 charge

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图 7 RHT-901加载下4 mm壁厚柱壳的爆炸压力及断裂演化过程

Figure 7. Explosive pressure, fracture process for 45 steel cylindrical shell (h= 4mm) with RHT-901

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表 1 实验柱壳、加载条件及爆炸膨胀断裂实验结果^[8]

Table 1. 1The fracturecharacteristics and failure modes of 45 steel cylindersunder different explosive conditions and geological parameters^[8]

炸药	药柱尺寸		试样尺寸		爆炸膨胀断裂实验结果
炸药	外径R/mm	内径r/mm	内径R/mm	壁厚h/mm	$ {\varepsilon }_{\mathrm{c}} $	$ {t}_{\mathrm{c}}/ $µs	$ {\varepsilon }_{\mathrm{f}} $	$ {t}_{\mathrm{f}}/ $µs	$ \dot{\varepsilon }/{\mathrm{s}}^{-1} $	断裂模式
JOB-9003（实心）	20	0	20	4	0.40	7.5	1.31	19.5	7.1×10⁴	纯剪切
RHT-901(空心)	30	20	30	4	0.24	8.8	0.43	15.4	2.9×10⁴	拉剪混合
RHT-901(空心)	30	20	30	5	0.18	7.8	0.37	15.8	2.5×10⁴	拉剪混合

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表 2 45钢柱壳本构参数数值^[25]

Table 2. Constitutive parameters of 45 steel^[25]

Johnson-Cook模型						Gr$ \ddot{\mathrm{u}} $neison状态方程
A/MPa	B/MPa	n	m	C	$\dot{ {\varepsilon }_{0} } /{\mathrm{s} }^{-1}$	c/(m·s⁻¹)	s	$ {\gamma }_{0} $
350	600	0.307	0.804	0.07	2×10^-4	4600	1.49	$ 2.17 $

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表 3 炸药JWL本构方程相关参数^[26]

Table 3. JWL EOS parameter of thecharges^[26]

炸药	A/GPa	B/GPa	ω	R₁	R₂	E₀/（GJ·m⁻³）	p_cj/GPa	ρ/（kg·m⁻³）	D/（m·s⁻¹）
JOB-9003	842.0	21.81	0.28	4.6	1.35	1.0	35	1884	8740
RHT-901	503.0	9.065	0.35	4.3	1.10	7.6	27	1658	7800

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表 4 SPH数值模拟与实验结果比较

Table 4. Comparison betwwen SPH simulation and experimental results

炸药	内径R/mm	壁厚h/mm	方法	$ {\varepsilon }_{\mathrm{c}} $	t_c/µs	$ {\varepsilon }_{\mathrm{r}} $	t_r/µs	$ {\varepsilon }_{\mathrm{f}} $	t_f/µs	$ \dot{\varepsilon } $$ /{\mathrm{s}}^{-1} $	断裂模式
JOB-9003	20	4	实验	0.40	7.5			1.31	19.5	7.1×10⁴	双向剪切
JOB-9003	20	4	模拟	0.37	7.3	0.37	7.3	1.07	17.2	7.1×10⁴	双向剪切
RHT-901	30	4	实验	0.24	8.8			0.43	15.4	2.9×10⁴	拉剪混合
		4	模拟	0.30	13.1	0.31	13.5	0.41	17.3	2.7×10⁴	拉剪混合
		5	实验	0.18	7.8			0.37	15.8	2.5×10⁴	拉剪混合
		5	模拟	0.21	11.9	0.23	12.8	0.30	16.1	2.1×10⁴	拉剪混合

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