This study uses the unified strength theory to analyse the elastoplastic stage and plastic stage of a linear strain-hardening target material while considering the effects of the intermediate principal stress and the free lateral boundaries of the target. In this investigation, analytical solutions of the radial stress in the cavity wall are obtained, and a unified penetration model of the target material is built. On this basis, penetration resistance formulas and penetration depth formulas for rigid projectiles with various nose shapes penetrating into thick, finite-radius, metallic targets are deduced, the solutions of which are obtained by utilizing the Simpson method. Accordingly, the proposed method offers a broader scope of application and higher accuracy than previous methods. Through this method, a series of analytical solutions based on different criteria can be obtained, and the penetration depth ranges of targets under different striking velocities can be effectively predicted. Moreover, penetration processes under different conditions are numerically simulated using the software ANSYS/LS-DYNA to study the motion law of the projectiles and the dynamic response of the targets. From the theoretical and numerical approaches, a list of influencing factors for terminal ballistic effects are analysed, including the strength criterion differences, the strength parameter b, the striking velocity , the projectile nose shape, and the target radius-to-projectile radius ratio r_t/a. The results indicate that, as b changes from 1 to 0, the penetration depth D_max increases by 22.45%. Additionally, D_max increases by 40.76% when r_t/a changes from 16 to 4; hence, it cannot be calculated as an unlimited-size target anymore when r_t/a ≤ 16. In weapons field tests, the radius of the metallic target can be conservatively designed to be greater than 28 times the projectile radius to ignore the effect from the free lateral boundaries of the target.

中文翻译：

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刚性弹丸侵彻厚，有限半径金属靶的边界效应和动力响应研究

本研究使用统一强度理论分析线性应变硬化目标材料的弹塑性阶段和塑性阶段，同时考​​虑了目标的中间主应力和自由横向边界的影响。在这项研究中，获得了腔壁内径向应力的解析解，并建立了目标材料的统一渗透模型。在此基础上，推导了具有不同鼻形的坚硬弹丸渗透到厚的有限半径金属靶材中的耐穿透性公式和穿透深度公式，并利用辛普森方法获得了解决方案。因此，与先前的方法相比，所提出的方法提供了更广泛的应用范围和更高的准确性。通过这种方法，可以得到一系列基于不同准则的解析解，可以有效地预测不同打击速度下目标的穿透深度范围。此外，使用软件ANSYS / LS-DYNA对不同条件下的穿透过程进行了数值模拟，以研究弹丸的运动规律和目标的动态响应。从理论和数值方法上，分析了影响末端弹道的因素，包括强度标准差，强度参数。使用ANSYS / LS-DYNA软件对不同条件下的弹丸穿透过程进行了数值模拟，以研究弹丸的运动规律和目标的动态响应。从理论和数值方法上，分析了影响末端弹道的因素，包括强度标准差，强度参数。使用ANSYS / LS-DYNA软件对不同条件下的弹丸穿透过程进行了数值模拟，以研究弹丸的运动规律和目标的动态响应。从理论和数值方法上，分析了影响末端弹道的因素，包括强度标准差，强度参数。b，打击速度，弹头形状和目标半径与弹丸半径之比r _t / a。结果表明，当b从1变为0时，穿透深度D _max增加22.45％。此外，当r _t / a从16变为4时，D _max增加40.76％；因此，当r _t / a时，就不能再将其计算为无限制尺寸的目标 ≤16。在武器野外测试中，可以保守地将金属目标的半径设计为大于弹丸半径的28倍，以忽略目标自由横向边界的影响。