弹体侵彻干砂的数值模型

李杰; 李猛深; 李宏; 施存程

doi:10.11883/1001-1455(2015)05-0633-08

摘要: 基于砂粒的不可压缩性假设，利用球形空腔动态收缩模型和广义Mises强度准则推导了干砂的孔隙压密演化方程；根据Hugoniot冲击突跃条件和Grüneisen系数，推导了干砂考虑孔隙演化影响的状态方程；根据关联流动法则，得到了大变形时砂的弹塑性应力应变关系；基于动力有限元计算平台，采用上述模型分析了弹体高速侵彻干砂的作用过程。结果表明，该模型能够表征高速侵彻时砂的孔隙演化对应力应变状态的反向影响，能够较准确地反映高速侵彻作用下干砂的动力响应过程。

关键词:

Abstract: Assuming that sand grains are incompressible, a compaction equation for porous dry sand was derived by applying the dynamic systolic model of a spherical cavity and the generalized Mises strength criterion. Based on the Hugoniot jump condition and the Grüneisen parameter, the equation of state for dry sand was given by considering porous compaction. According to the associated flow rule, the elasto-plastic stress-strain relationships of dry sand under large deformation were obtained. By means of the dynamic finite element computing method, the above models were used to analyze the penetration process of dry sand by a projectile. The results show that the models can reflect the reverse influence of sand pore evolution on the stress-strain state in the high-velocity penetration process, and can accurately describe the dynamic response of dry sand under high-velocity penetration.

Key words:

图 1 砂的孔隙演化等效模型

Figure 1. An equivalent model of pore evolution for sand

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图 2 加卸载时砂的孔隙演化曲线

Figure 2. Pore evolution curves for sand under loading and unloading conditions

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图 3 弹体尺寸

Figure 3. Projectile dimensions

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图 4 弹靶的有限元模型片段

Figure 4. Parts of the finite element models for the projectile and target

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图 5 一质量80.3 g的弹体侵彻速度与侵彻深度的关系

Figure 5. Velocity varied with penetration depth for a projectile with the mass of 80.30 g

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图 6 靶体在不同时刻的压力场

Figure 6. The pressure fields of the target at different times

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表 1 砂的侵彻深度计算值与实验结果

Table 1. Test and computed results for penetration depths of sand

m/g	v_{p, 0}/(m·s^-1)	H_e/m	H_c/m	$\frac{{\left\| {{H_{\text{c}}} - {H_{\text{e}}}} \right\|}}{{{H_{\text{s}}}}}$ /%
80.30	674	1.37	1.04	24.1
81.20	716	1.28	1.37	7.0
80.96	673	1.33	1.04	21.8
81.05	649	1.26	0.96	23.8
80.86	640	1.27	0.93	26.7
81.11	645	1.26	0.95	24.6
81.15	641	1.28	0.93	27.3
81.00	664	1.24	1.01	18.5
81.25	692	1.36	1.24	8.8
80.75	682	1.29	1.15	10.8
80.42	661	1.30	1.00	23.1
80.30	678	1.37	1.10	19.7
81.10	666	1.47	1.01	31.3

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