PSI - Issue 14

Akhilesh Kumar Jha et al. / Procedia Structural Integrity 14 (2019) 416–428 Akhilesh Kumar Jha et al. / Structural Integrity Procedia 00 (2018) 000–000

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projectile greatly excels the yield stress of the projectile material. This is the hydrodynamic regime, for which the projectile can be treated as a fluid.

Nomenclature L Length of the bird V o T Velocity of shock U s

Initial impact velocity

Duration of impact (Squash up time)

ρ

Density of bird

Γo C o

Grueneisen coefficient

Speed of sound Material constant Young’s Modulus Poisson Ratio

s

E

ν

σ cy

Compressive yield stress Hydrostatic yield stress

P

E 1+ E 1- E 2+ E 2- G 12 X 1+ X 1- X 2+ X 2-

Young’s modulus along longitudinal fiber direction 1 Young’s modulus along transverse fiber direction 1 Young’s modulus along longitudinal fiber direction 2 Young’s modulus along transverse fiber direction 2 Tensile strength along fiber direction 1 Compressive strength along fiber direction 1 Tensile strength along fiber direction 2 Compressive strength along fiber direction 2 Shear stress at the onset of shear damage Energy per unit area for tensile fracture along fiber direction 1 Shear Modulus

S

G f G f

1+

1- Energy per unit area for compressive fracture along fiber direction 1 G f 2+ Energy per unit area for tensile fracture along fiber direction 2 G f 2- Energy per unit area for compressive fracture along fiber direction 2 α 12 Parameter in the equation of shear damage d 12 max Maximum shear damage σ yo Initial effective shear yield stress C Coefficient in hardening equation p Power term in hardening equation d max Maximum value of damage variable used in element deletion criterion ε max pl Maximum value of equivalent plastic strain for element deletion criterion ε max Maximum (Positive) principal logarithmic strain beyond which the element will get deleted ε min Maximum (Negative) principal logarithmic strain beyond which the element will get deleted The bird impact process can be considered as the hydrodynamic impact. The bird essentially behaves like a fluid during impacts; they do not bounce and the impact duration is approximated from the bird squash-up time. The squash up time is given by: � � � � � (1) The bird impact process can be classified into four stages, they are, Initial Impact Phase, Shock Propagation, Steady state flow and Pressure Decay phase as shown in Fig. 1. At the initial impact phase, the particles at the front end are