The composite damage effects of explosion after penetration in plain concrete targets

Highlights

• In order to investigate composite damage effects of penetration and explosion of concrete, twelve groups of composite damage tests of explosion after penetration were carried out, in which the explosive-charges were placed at the end of the penetration tunneling hole.

• The initial damage effects caused by penetration, including apparent morphological damages and material damage, were studied, which can be characterized by the dimensionless impact coefficient.

• Two empirical formulas which describe the composite damage effects of explosion after penetration had been obtained through dimensional analysis and experimental data fitting. The accuracy and rationality of formulas to describe the relationship between the two dimensionless coefficients and the composite damage had been proved based on experimental data.

• The two dimensionless coefficients comprehensively reflects the influence of the following factors: the kinetic energy of projectile, the warhead shape factor, the diameter of the projectile, the detonation velocity and the mass of the explosive charge, and the material strength, which are the determined parameters of composite damage effects.

Abstract

To investigate the composite damage effects of explosion based on initial damage caused by penetration, a series of penetration and explosion tests were conducted on plain concrete at different impact velocities, charge masses, and charge locations. Before that, a dimensional analysis of explosion effects after penetration in a concrete slab was undertaken, in which the composite damage effects can be characterized by a dimensionless explosion coefficient and a dimensionless impact coefficient. In addition, the initial damage caused by penetration can be characterized by the dimensionless impact coefficient. Based on the experimental data and theoretical analysis, the physical relationships between the composite damage effects of explosion and the initial damage effects of penetration were revealed, and the regression equation of the final crater depth and radius caused by explosion was obtained, which is described by the dimensionless impact coefficient and the dimensionless explosion coefficient.

Introduction

Concrete protective structures are required to withstand intensive damage due to various types of warhead. Although there are lots of investigations on damage effects of penetration and explosion respectively, the research on composite damage effects of explosion after penetration remains sparse. Generally, the protective engineering structure may be destroyed by composite damage effects of penetration and explosion, which may not reduce its protective efficiency under one source of impact. The composite damage effects of penetration and explosion in plain concrete targets are a vital problem in impact engineering.

There have been many investigations of the damage to concrete under impact and explosion loads, and some formulae for target penetration and explosion have been put forward.

In terms of the penetration effects, the theory of spherical or cylindrical cavity expansion was widely used. Based on the continuous conditions on the boundary, the equation of state, and conservation equations, the expressions of the resistance to the projectile in the process of penetration were established. Combined with experimental data, semi-theoretical and semi-empirical formulae for penetration depth were obtained [1], [2], [3], [4], [5], [6], [7]. At the same time, penetration tests under various conditions, such as different sizes of projectiles and different concrete strengths, were conducted. Thus, many empirical formulae for penetration depth have been proposed [8]. Furthermore, to ascertain the dynamic behaviors of projectiles and targets under impact interaction, numerical simulation methods have also been widely used. In particular, given the development of meso‑mechanics, meso‑mechanical models that can describe the concrete mechanical behaviors more accurately were proposed [9,10]. Therefore, the thorough and mature research on the penetration effect of concrete can provide a solid foundation for the present study.

In the case of explosive effects, there has been much research on concrete structures subjected to external blast loading. When the distance between the charge and the target is large enough, the structure is typically simplified to a single degree of freedom system (SDOF) [11], [12], [13], [14], [15]. Besides, damage assessment methods, i.e., the pressure-impulse (P-I) diagram based on the relationship between air over-pressure and impulse, have been established and widely used in explosion damage analysis [16,17]. However, the initial damage effect of penetration is not considered in most of the internal explosion effects in the medium due to the complexity of composite damage effect of penetration and explosion. To research the internal explosion effects on concrete or geo-material, many representative numerical or theoretical models have been developed, such as the Harries model, the Grigorian model, the hydro-elasto-plastic model, the embedded crack model, the NAG-FRAG model, the HJC model, the TCK model, the BFRACT model, etc. Moreover, based on brittle failure theory, some researchers explored the formation and development of cracks in geological materials under the effects of shallow buried explosion [18]. They proposed a method with which to calculate the size and shape of explosion crater, which considered the characteristics of the medium, charge parameters, and burial depth. Some scholars conducted experimental investigations of the anti-penetration and anti-explosion performance of ultra-high-performance concrete (UHPC), while they did not report on the composite damage after penetration strike and internal explosion [19]. Wang [20] used the smoothed-particle hydrodynamics (SPH) method to research the explosion inside the reserved blast hole of concrete target, which can describe the damage process in the different irreversible deformation regions. Duan [21] conducted a series of experimental studies to examine the internal explosion of concrete. Based on dimensional analysis, they obtained a formula for calculating the critical buried depth, which considered the length-to-diameter ratio and specific energy of the charge.

Generally, the projectile can cause apparent material damage to the concrete target, which affects the effects of the explosion [22]. At present, the penetration process and explosion process are examined separately in most investigations. There have been many penetration-calculation formulae, and most work is aimed at how to improve the higher-order accuracy; however, the precision of explosion calculation formulae remains poor, since the problem of explosion is very complex, and is affected by multiple factors such as explosion source parameters, target medium parameters, the external environment, and so on. Furthermore, research into explosive effects of an attacking warhead on its target does not consider the influence of penetration damage within the target. In the article, a series of experimental and theoretical investigations were conducted considering the initial damage effect of penetration and the composite damage effect of the explosion. Specifically, concrete target-penetration tests were performed in the speed range of 450–700 m/s. After measuring initial damage data pertaining to penetration, the composite damage effects of explosion tests, in which the explosive-charges were placed at the end of the penetration tunneling hole, were conducted. Besides, the damage effects of penetration and explosion, including the depth and the radius of final crater, were studied by using numerical simulation methods and dimensional analysis. In addition, the influence of shell case on explosion effects may be enhanced or weakened, which depends on the thickness of the shell case and can be assessed by ammunition explosion test. Therefore, the physical model mainly considers the composite damage effects of explosion energy, and it was simplified without considering the influence of fragmentation.