# A recent study br Acknowledgments We are thankful to the Uni

Acknowledgments
We are thankful to the University of Guilan Research Council for partial support of this work.

Introduction
It is significant to predict the mass, number and velocity distribution of BAD generated by RHA subjected to penetration of EFP by the thickness of target and the impact velocity of EFP, and obtaining the mass of BAD generated by RHA and EFP accurately is the basement of the prediction [[1], [2], [3], [4], [5],30].
The A-T model established by Alekseevskii [10] and Tate [[11], [12], [13], [14]] has achieved good results in penetration problem. Many scholars [[15], [16], [17], [18], [19], [20], [21], [22]] have developed A-T model, but the main part of the penetrator is slender and equal cross section cylindrical rod, and they do not consider the small length-diameter ratio and the variable cross section. Alekseevskii [10], Tate [[11], [12], [13], [14]], Rosenberg [15], and Grace [16,17] neglected the influence of the axial length of mushroom in penetration process when studying the long rod penetration. Li [2] and Zhang [3] neglected the influence of the axial length of mushroom in penetration process when studying the normal penetration of EFP into steel target. Rosenberg [27] pointed out that shapes of plug block are different when penetrating the finite thickness target with different penetrator nose shapes. Zhang [3] considered that the plug had two shapes, namely cylinder and frustum of a cone and the angle between generatrix and bottom is 45° when studying the normal penetration of EFP into steel target, and the latter was chosen as combining with the specific research object. Held [23,24] gave the radial crater growth model neglecting the strength of jet. Li [2] neglected the strength of EFP and applied the Held model [23,24] directly when analyzing the behind armor effect of EFP, so it A recent study is inconsistent with the actual situation. The theoretical studies on the behind armor effect are all based on the penetrator whose main part is slender and equal cross section cylindrical rod [25,26]. The studies about behind armor effect of EFP mostly focus on numerical simulations and experiments [[4], [5], [6], [7]], while the variable cross-section characteristic of EFP has not been considered in the theoretical study about BAD generated by target subjected to penetration of EFP. The penetration theory derived by penetrator whose main part is slender and equal cross section cylindrical rod cannot be directly applied to EFP, since EFP has the characteristic of variable cross-section. And the influence of the axial length of mushroom in penetration process cannot be ignored, since the EFP has a small length-diameter ratio. The shape of plug produced by the finite thickness target is uncertain, since the shape of EFP nose is irregular. The strength of EFP cannot be ignored like a jet, since the stand-off distance of EFP is so long (up to 1000 times the diameter of the charge) and the velocity of EFP is much slower than jet. And theoretical mass of BAD generated by finite thickness RHA subjected to normal penetration of EFP based on the above existing theories may lead to a large error.
So based on our previous work [30], combined with theoretical analysis, numerical simulation and experimental data, variable cross-section characteristic and strength of EFP are taken into consideration, then the relationship between the mass of BAD generated by RHA and EFP and the thickness of RHA and the impact velocity of EFP are obtained when the axial length of mushroom and the shape of plug are different. Finally, whether the axial length of mushroom need to consider and which shape of plug is suitable are decided.

Theoretical model
The laser high-speed photography and the equivalent numerical simulation model of the typical EFP were both introduced in details in Ref. [30]. It can be found from Refs. [9,30] that EFPs have variable cross-section characteristic, and their cross section radius vary at different axial positions. Therefore, variable cross-section is a key characteristic of EFP, and the effect of variable cross-section characteristic on crater radius by penetration mechanism is needed to analyze.