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Engineering model for estimating parameters of fragments forming at penetration of periodic string system into massive barrier

Belyaev V.P., Goloveshkin V.A.

#### Abstract:

The model for estimating parameters of fragments forming at high-velocity penetration of periodic string system into a massive barrier is suggested in papers [1,2]. Since the model itself and used mathematical relations that describe correlation of stress tensor and environment settings are approximate (as a criterion of destruction), mathematical accuracy is not always justified. The goal of this paper is a development of a simple engineering model for calculating the process of interaction that allows estimating size, speed and energy of fragments knocked out of the barrier. The hypothesis of incompressibility and ideal plasticity is accepted to describe mechanical properties of colliding object and barrier. It means that estimations require only knowledge of density and yield strength of material. The problem of collision is considered in 2-dimensional approximation assuming of flat deformed condition. It is assumed that the speed of the colliding object has the order of km/s. The result of solution, besides mechanical properties of materials, is determined by following geometrical attributes of system: string diameters, distance between centers of the strings. The process of interaction is divided into two stages. At the first stage the material spreading on the string occurs. The biggest splinter corresponds to the end of the first stage. Then the inertial motion remains in the colliding objects’ material. The result of this motion is a series of smaller splinters. Their mass increases, while speed and energy decrease. The research of solutions in papers [1,2] has been undertaken. Simple mathematical equations are built based on identified asymptotics of indicated solutions. These formulas allow estimating size and energy of forming splinters as well as depth of penetration (in the value range of initial parameters that has practical interest) without considerable loss of accuracy. The comparative calculations are accomplished and they show adequate accuracy of suggested model.

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