Theoretical model for a ductile porous projectile striking on an elastic target bar

• Behavior of ductile porous projectile impinging on a semi-infinite elastic bar is studied.
• Nonlinear relationship between density and plastic strain of projectile is obtained.
• The present model can be degenerated to previously developed models.
• Consideration of elastic effect of the target bar will reduce plastic deformation of projectile.
• Geometry and material parameters can affect deformation and energy of projectile.

As an extension of the Taylor model, in 2001 Lu et al. [13] made a study on the impact behavior of a flat-nosed cylindrical porous projectile in order to determine the dynamic yield stress of porous materials at a high strain rate. They assumed that the density of the compressed porous material was a linear function of the compressive strain, which was only suitable for small strain cases. In 2010, as another extension of the Taylor model, Yang et al. [16] proposed a theoretical model to study the flat-nosed solid cylindrical projectile impinging against a semi-infinite elastic bar along its axial direction, which provided a useful guide for the application of the output bar in a Hopkinson test system to obtain instantaneous deformation characteristics of the projectile. However, this investigation was only concerned with metal projectiles, where the density is a constant. The present paper is developed from both Lu׳s and Yang׳s models and an analytical model is proposed to study a ductile porous projectile impinging against a semi-infinite elastic bar. The compressibility of the porous projectile is incorporated and a nonlinear relationship is used between the density of the compressed porous projectile and strain. The plastic Poisson׳s ratio of the projectile can be either a constant or a function of the compressive plastic strain. For the case of constant value of plastic Poisson׳s ratio, the present model based on the first order Taylor series expression of the density ratio can be degenerated to the existing models. For the case that the plastic Poisson׳s ratio changes with the compressive plastic strain, attention is paid to the influence on the impact responses of the porous projectile, of the geometry and material properties of both the porous projectile and the target bar, and the initial impact velocity of the porous projectile. The results show that the non-dimensional material, geometry and initial velocity parameters have great effects on the compressive plastic strain and lengths of the deformed and undeformed sections of the projectile, the duration of impact-contact process and the energy partitioning between the projectile and the target bar. The present investigation provides a theoretical model for testing ductile porous materials.