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

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Nomenclature A

yield stress (MPa) strain Hardening (MPa)

B D

external diameter of the projectile D 1 ,..,D 5 material parameters for Johnson-Cook failure model definition E PL equivalent plastic strain melting temperature (K) 0 room temperature (K) c, n, m non-dimensional coefficients for Johnson-Cook constitutive model h t thickness of the target m p initial mass of the projectile in grams (=10 -3 kg) m pl mass of the plug in grams (=10 -3 kg) v bl ballistic limit (m/s) v i initial velocity (m/s) v r residual velocity in m/s failure plastic strain ̇ 0 strain rate hardening reference (1/s) σ H hydrostatic stress (MPa) σ eq equivalent stress (MPa) σ * stress triaxiality (σ H/ σ eq )

1. Introduction

In the last few years, some international standards for safety of machine tools have been developed, such as the ISO 23125: 2010, improving the ballistic protection of safety guards. The uncontrolled projection of parts of work piece or tools can often cause very dangerous perforations of the guards, such as the one shown in Mewes (2000). In such way, specific experimental tests like the ones conducted in EU by Mewes (2000, 2011) have assured the possibility to write the appendices of ISO standards regarding safety guards design of machine tools. These tests are based on impact between a particular standardized projectile, which exemplifies an impacting fragment of variable size and energy, and a flat plate placed perpendicular to the trajectory of the projectile. The penetration or deep buckling of the target determines the non-suitability of a particular material of a given thickness, for the design and production of safety guards. For example, in the normative annex B of the ISO 23125, the standardized target is a 500 mm x 500 mm plate, clamped for 25 mm on each side with a standardized penetrator. Depending on the impact energy and the penetrator weight, one can choose between a very limited set of materials and thicknesses to fulfil the safety requirements. This paper is focused on the simulation of impacts with steel targets having a thickness of 3 mm, projectiles with mass in a range of 0.6-2.5 kg with impact velocities lower than 100 m/s. Several different constitutive/fracture steel models will be presented and the correlation between models and standardized result will be discussed. Other topics, such as influence of mesh, diameter of the target and proper setup of the virtual models has been discussed by Landi and Amici (2016).

2. The ballistic limit

Before introducing explicit FEM models, it is necessary to have a short introduction to the definition of ballistic limit and to the different models usable for material characterization. The ballistic limit is the velocity required by a projectile to completely penetrate a target, Landi and Amici (2016). In several studies, the ballistic limit (v r ) is calculated with regression of the formulas proposed by Recht and Ipson (1963) using experimentally measured initial (v i ) and residual (v r ) velocities of the projectile: