Scaling effect of long-rod projectiles penetrating into geological material targets

Abstract

As the penetration velocity increases, the scale effect observed in scaled experiments on concrete and rock-like brittle media becomes increasingly pronounced, necessitating a re-examination and revision of the corresponding penetration similarity laws. This paper presents a quantitative investigation of the scale effect associated with long-rod projectiles penetrating geological brittle materials, such as rock and concrete. Based on a dynamic strength model for brittle materials that incorporates the effects of hydrostatic pressure and strain-rate strengthening, we establish a penetration resistance model, a penetration depth prediction model, and a method for determining the model parameters. This framework enables a quantitative description of the "scale effect" in rigid projectile penetration, achieving a prediction error of less than 15% across the entire range of projectile sizes considered. The results demonstrate that, during the rigid penetration phase, both penetration resistance and penetration depth exhibit significant scale effects. The penetration resistance is primarily composed of a strength term and a hydrostatic pressure term, with the strain-rate enhancement of the strength term being the principal cause of the scale effect. At a constant impact velocity, the relationship between the scale effect on penetration depth and the geometric scaling factor λ can be accurately described by a power-law function, where the exponent characterizes the magnitude of the scale effect. Within the range of impact velocities investigated herein, this scale-effect exponent varies from 0.275 to 0.042. Furthermore, the influences of target parameters—including material strength, bulk modulus, and strain-rate sensitivity—as well as projectile parameters—such as density, length-to-diameter ratio, and nose shape coefficient—on the penetration scale effect are systematically analyzed. The findings of this study can be employed to interpret the results of scaled penetration tests and to guide practical ammunition engineering design.