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中文摘要：
基于动力球型空腔膨胀理论和＂冲击成坑＋钻孔区＂两阶段侵彻模型,以截卵形弹头弹体为例,运用曲面积分,引入表征弹头形状和弹靶摩擦效应的量纲一系数、质量比和冲击因子,提出了综合考虑弹头形状变化、成坑区深度、弹靶摩擦阻力的混凝土和岩石靶体的刚性弹垂直侵彻深度的计算公式。该公式在相关参数取特殊值时,可退化为经典的侵彻深度计算公式。通过与8组不同弹头形状弹体冲击混凝土和岩石靶体的侵彻实验数据、已有10个（半）经验公式计算结果对比,验证了本文公式的适用性。并结合实验和参数影响分析,给出了混凝土和岩石靶体的弹靶摩擦系数和与冲击因子相关的不同弹头形状弹体成坑系数的建议值。
英文摘要：
Based on the dynamic spherical cavity-expansion theory and the two-stage penetration model consisting of cratering and tunneling,a dimensionless formula was proposed for normal penetration depth of rigid projectiles into concrete and rock targets by taking a truncated-ogive nose projectile as an example.In the proposed formula,the surface integration method was applied,and the mass ratio and the impact factor were introduced,as well as the dimensionless coefficients denoting the projectile nose geometry and the projectile-target friction effect,to consider the variation of projectile nose geometry,cratering depth,and tangential resistance on projectiles.And the proposed formula can be regressed to the classic penetration formulae in special cases.The proposed formula was validated by comparing the penetration depths predicted by the proposed formula with those predicted by the existing ten classic empirical and semi-empirical formulae as well as the experimental data from eight field shot tests of concrete and rock targets hit by projectiles with different nose geometries.Based on the tests and parametric analyses,the corresponding parameter values were recommended aiming to different nose projectiles,including the dynamic projectile-target frictional coefficient of concrete and rock targets,as well as the linear coefficient of cratering depth related to the impact factor.
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