PSI - Issue 13

Muhammad Zakir Sheikh et al. / Procedia Structural Integrity 13 (2018) 2120–2125 Muhammad Zakir Sheikh et al. / Structural Integrity Procedia 00 (2018) 000–000

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The experimental details can be found in [8]. The EOI tests were integrated with a Cranz-Schardin camera with the farming rate of 0.10 microseconds. The projectile impacts the glass plates on the side face instead of in the center of font or back face. The test arrangement is made so that the propagation of damage and stress waves in target plates in 100 × 100 mm face can be recorded by shadow-graph mode (transmission of light shadowgraph) and Photoelastic mode (using cross polarizers). The tests were conducted using steel cylindrical and spherical projectiles with the range of impact velocities from 270 m/s to 925 m/s. 3. Numerical Simulations of EOI Test 3.1. Finite element model The computational model for EOI tests on Starphire® soda-lime glass plates by [8] are modeled using ANSYS/Autodyn. The target plates of size 100 × 100 × 10 mm3 were edge impacted by namely two types of steel 4340 projectiles, spherical (Ø 16 mm) and cylindrical (Ø 30 mm and length of 23 mm). In current work, only the case of a spherically shaped projectile impact on soda-lime glass plates is studied. The half symmetric model is generated due to the nature of tests (normal impact of a projectile on target plates). Both the projectile and target plates are meshed using solid elements and the Lagrange formulation. The target plate is meshed with a uniform element size of 0.5 × 0.5 × 1.0 mm 3 for easy capturing the location of the longitudinal and transverse waves during simulations. The finer mesh was used in order to make sure that the results are not influenced by the element size. The finite element (FE) model of the projectile and target plate is presented in figure 2. The interaction between projectile and target is achieved by using the Lagrange/Lagrange interaction logic available in ANSYS/Autodyn. The projectile was filled with translational velocity using initial conditions and fixed boundary condition is applied on the top surface of the target.

Figure 2 FE model of the projectile and the target plate for EOI simulations.

3.2. Material model The EOI simulations on brittle soda-lime glass plates impacted by spherical steel 4340 projectiles employed Johnson Holmquist (JH-2) constitutive material model for target plates available in the standard material library of ANSYS/Autodyn. The JH-2 model is widely used by many researchers to simulate the ballistic behavior of brittle materials like glass. The strength of the brittle material is described as a smoothly varying function of intact strength ( � ∗ � , fractured strength ( �∗ � , strain-rate and damage through a dimensionless analytic function as described below: � ∗ � � ∗ �� ∗ � � ��� � � � �∗ � (1) �∗ � � ∗ � ��� � ∗ �� �∗ � (2) �∗ � ����� �� ∗ � � �� � � � �∗ � � ���� � (3) where , , and are the material constants. ∗ is the normalized pressure, ∗ is the normalized maximum tensile hydrostatic pressure, and �∗ is the effective plastic strain rate normalized by a reference strain rate of 1.0 s -1 . The accumulated damage ( D ) is the ratio of incremental plastic strain over currently estimated fracture strain. The effective strain is pressure dependent as expressed below: