PSI - Issue 8

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

7

5

= 2 3 √ ( 12 + 22 + 32 ) − ( 1 2 + 2 3 + 3 1 ) + +3( 12 2 + 22 3 + 32 1 )

(7)

One must not forget that in FEM explicit simulation, excessive mesh distortion usually causes failure of the solution if Lagrange or ALE formulation of the element is used. So, in order to solve this convergence problem, erosion of elements it is usually used without taking care about its possible strong influence or results. A wider discussion on how to properly set element erosion can be found in Landi and Amici (2016). If a JC model is used for the simulation of a given material (see equation 2 and 5), very reliable results for a wide variation of testing parameters is expected (e.g. variation of plate thickness, impact velocity and projectile mass). On the other side, a lot of different tests have to be performed to fully implement those JC or equivalent models, see Bao and Wierzbicki (2005). The standardized tests usually have a limited variation of parameters; since they have to be usable outside the research laboratories, it is of great relevance to define a simplified material model usable for specific testing. For example, the equivalent plastic strain model is definitely simplistic, and it has been already employed in conditions of poor knowledge of the data on the material or of the physical conditions of impact. There is no doubt on the advantage of having a single parameter to define the fracture, but on the other hand it causes a poor adaptability of this parameter at the variation of the impact conditions. This drawback implies that recalibrating the threshold value is necessary whenever the behavior of impact is modified by variation of parameters. As already done for the fracture limit, it is possible to define simplified procedure for the definition of the constitutive JC model. Taking into account different general non-alloy steels such as the one on Børvik (2002a) and Dey (2004) or the ones on Rusinek (2008) and Kpenyigba (2013), very similar to the standardized ones for machine tools, it is possible to see that the main differences on constitutive JC models are related to the parameters A, B and n of equation (2). Parameters c and m are not often retrieved through laboratory experiments. Landi and Amici (2016) used for a DC01 steel the parameter retrieved by other authors for Weldox 460E, Børvik (2002a) and Dey (2004), taking into consideration that:  The constitutive law of a generic non-alloy steel from the strain rate has not an important dependence by the steel used (i.e. the c parameter is not so variable with the alloy steel)  Moreover, the strain rate hardening ̇ ∗ has not a wide variation since the impact velocities are lower than 400 m/s. In safety guards design the impact velocities are less than 100 m/s (less than 60 m/s for heavier projectiles) Due to the high hardness of the projectile in standardized tests, it can be assumed rigid during the simulation. The main proprieties of the material used to define its FEM model are reported in table 1.

Table 1. Mechanical proprieties of the projectile steel Propriety Min Yield strength [MPa] 1900 Tangential modulus [MPa] 1500 Density [kg/m3] 7850 Young Modulus [MPa] 204000 Poisson ratio 0.33

3.1 First model of a general non-alloy DC01 steel

The target material is steel called DC01 in the standard EN 10130. Its mechanical proprieties are defined on Table 2.