Abstract The early stage of penetration of a rigid projectile into a target is denoted as the entrance stage. It begins when the nose tip impacts the target surface and the projectile starts its penetration into the target. The entrance stage is characterized by an increasing contact area between the projectile and the target which yields an increasing resistance and deceleration. This is the more difficult and less studied part of the penetration process. The present paper is focused on the entrance stage aiming at clarifying the interaction behavior during this early stage penetration and contributing to this less investigated problem. The literature survey indicates that the depth of the entrance stage is rather unclear and different researchers define the entrance stage depth differently. All definitions relate this depth to the projectile diameter. The shape of the deceleration curve is examined, and the linear deceleration-depth relationship assumed by the widely used spherical cavity expansion (SCE) approximation is criticized. This paper examines these definitions and postulates a new rational definition which agrees well with test data. A new analytical solution that is based on the SCE approximation is developed for the initial stage of penetration of a rigid projectile into a concrete medium. This modified spherical cavity expansion solution (denoted as SCEM) considers the variation of the “projectile-target” contact area with time, which is typical to the projectile entrance stage. Comparing the deceleration time histories of the new solution with the experimental data and with the DISCS model analysis results shows very good agreement, and the difference between the proposed analytical model and the commonly assumed deceleration-depth linear relationship is demonstrated. Characteristics of the entrance stage are analyzed and features like the embedment duration and the effect on the final penetration depth are examined.

中文翻译：

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高速刚性卵形机头弹丸嵌入混凝土目标

摘要 刚性弹丸穿透目标的早期阶段称为进入阶段。当机头尖端撞击目标表面并且弹丸开始穿透目标时，它就开始了。进入阶段的特点是弹丸和目标之间的接触面积增加，从而产生增加的阻力和减速度。这是渗透过程中难度较大且研究较少的部分。本论文侧重于入口阶段，旨在澄清早期渗透期间的交互行为，并为这个较少研究的问题做出贡献。文献调查表明，入口阶段的深度尚不清楚，不同的研究人员对入口阶段的深度定义不同。所有定义都将此深度与弹丸直径相关联。检查了减速曲线的形状，并批评了广泛使用的球腔膨胀 (SCE) 近似所假设的线性减速-深度关系。本文检验了这些定义，并提出了一个新的合理定义，该定义与测试数据非常吻合。针对刚性弹丸穿透混凝土介质的初始阶段，开发了一种基于 SCE 近似的新解析解。这种改进的球腔膨胀解决方案（表示为 SCEM）考虑了“弹丸-目标”接触面积随时间的变化，这是弹丸进入阶段的典型特征。将新解的减速时间历程与实验数据和 DISCS 模型分析结果进行比较，显示出非常好的一致性，并且证明了所提出的分析模型与通常假设的减速深度线性关系之间的差异。分析了入口阶段的特征，并检查了嵌入持续时间和对最终渗透深度的影响等特征。