Penetration of common ordinary strength water saturated concrete targets by rigid ogive-nosed steel projectiles

• Spherical cavity-expansion approximation models are developed for the penetration analysis of brittle materials.
• The new spherical cavity-expansion approximation models only require material properties from laboratory scale material tests and no prior depth of penetration data.
• The new spherical cavity-expansion approximation models are employed to model the penetration of water saturated ordinary strength R30A7 concrete.
• Model predictions are shown to be in reasonably good agreement with corresponding experimental data.

In this paper, we employ a dynamic spherical cavity-expansion solution for use with the spherical cavity-expansion approximation to analyze the penetration of common ordinary strength water saturated concrete targets by small scale rigid ogive-nosed projectiles with normal impact. To do this, we first obtain a quasi-static spherical cavity-expansion model for the radial stress at the cavity surface of a plastic–cracked–elastic material. Next, we add on a target inertia based term to the quasi-static radial stress at the cavity surface to obtain an approximate expression for the dynamic radial stress acting at the surface of the spherical cavity. This spherical cavity-expansion solution is employed with spherical cavity-expansion approximation based penetration models that previously required prior depth of penetration data to obtain the quasi-static target resistance function. With the newly proposed penetration models, a description of the common ordinary strength water saturated concrete material is based on a linear pressure–volumetric strain relation and a pressure dependent shear strength plasticity envelope with a tensile cutoff and is obtained from laboratory scale material tests; therefore, no prior depth of penetration data are required. Analytical model predictions obtained with the newly proposed model for final depth of penetration as a function of striking velocity, along with analytical models for acceleration, velocity and displacement as a function of time, are shown to be in good agreement with the corresponding experimental penetration data.