PSI - Issue 37

Theodosios Stergiou et al. / Procedia Structural Integrity 37 (2022) 250–256 T. Stergiou et al. / Structural Integrity Procedia 00 (2019) 000 – 000

254

5

Fig. 4: Projectile ’s deceleration as function of normalised nose length.

Knowing the projectile ’s deceleration allows an estimation of the force acting on it during penetration. Yet, the discontinuity in the projectile ’s velocity-drop behaviour as a function of the projectile ’s half-angle inhibits the use of a global formulation for the force. To this aim, the normalised quantity /ℎ was identified to combine the two regions into one and enable the projectile ’s deceleration expression, and, consequently, the reaction force, using a global formulation. Fig. 4 illustrates the projectile ’s deceleration response with changes in the ratio /ℎ . The projectile deceleration is linear to /ℎ in the logarithmic scale, taking the form = 1 ( ℎ ) − 2 , (1) where 1 = 1 ms −1 /μs , 2 = 0.64 are the fitting parameters. Acquiring the expression for the projectile ’s deceleration provides an insight into the form of the local work required for complete penetration of the projectile into the thin target. Intuitively, the resistance to penetration can be expressed by the product of the projectile mass, , and , while the work is given as the product of the resisting force and the path of resistance. It was identified that the contribution of the projectile ’s shank section in the overall resistance was negligible, since friction played a minor role in the penetration of the thin target. The resistance path can then be assumed to extend only for the length of the projectile ’s nose and, therefore, the work term can be written as = 1 ( ℎ ) − 2 . (2) Eq. (2) estimates the local work done in eroding and penetrating the target. It is customary that work formulations are expressed in terms of the target resistance (Woodward and Cimpoeru, 1998; Taylor, 1948; Thomson, 1955), while there is a controversy on the magnitude of this quantity. Rosenberg and Dekel (2020) performed an analysis and identified that the target-resistance term in the work expressions should be taken as the yield strength at ≈ 0.27 and ̇ ≈ 10 4 ⁡ s -1 , where and ̇ are the plastic strain and plastic strain rate, respectively. In Eq. (2), a relation for the effective target resistance, , that is exerted by the target to the projectile can be extracted by equating the right hand part of Eq. (2) to the work required to open a hole in the target (ductile hole enlargement) equal to the cross sectional area of the projectile, ,