PSI - Issue 8

L. Landi et al. / Procedia Structural Integrity 8 (2018) 3–13 L. Landi et l. / Structural Integrity Procedia 00 (2017) 0 0 – 000

5

3

= ( − ) 1⁄

(1)

where: = + and = 2 In Børvik (2002a, 2002b) and Dey (2004):  v bl is the average value between the lowest v i that causes perforation and the highest v i that do not cause perforation during real penetration tests.  a, p are usually calculated through (1) with minimum square method from experimental penetration tests. In our opinion, the ballistic limit calculated as average value can lead to approximated formulation because of the large dispersion of experimental data due to the several non-linearity of the experiments. Landi and Amici (2016) shown that a better approximation of the ballistic limit can be found though a full minimum square method in order to calculate all parameters of the ballistic limit in (1): a, p and also v bl , where v i and v r are used as input data from real or virtual experiments. The difference between the two methods is not so large, however one can consider the full interpolation method more reliable than the one proposed by Børvik (2002a, 2002b) and Dey (2004). Concerning the calculation of the ballistic limit, it is fundamental to know that the different types of impact behaviour and damage, are strictly related to impact velocity and other physical parameters (material plasticity, target thickness,…). For this reason, the RI formula has a range of validity that is directly correlated with the physic of impact. In our opinion, the experimental and the numerical impact tests should be limited to velocity lower than 2.5 times than the estimated ballistic limit in order to have better results on regression. For a wider discussion on higher impact velocities and thicker plates see Landi and Amici (2016). This chapter describes the issues that can arise during numerical modelling physical behaviour of impact bodies. Due to its relative simplicity and big amount of material data, Johnson-Cook constitutive model is widely used on impact numerical simulations. Its formulation defines equivalent stress as component of equivalent plastic strain , temperature T and strain rate hardening ̇ . = ( + )(1 + c ln ̇ ∗ )(1 − ∗ ) (2) Where the so called homologous temperature is defined as: ∗ = ( − 0 ) ( − 0 ) ⁄ ሺ͵ሻ ̇ ∗ = ̇ ̇ 0 (4) These parameters are obtained experimentally with tensile tests as described by Dey (2004), also using the considerations by Dieter (1988), Bridgman (1964) and Earl (1976). 3. Characterization of material