Effect of material and geometric parameters on deformations near the notch-tip of a dynamically loaded prenotched plate

We analyze plane strain thermomechanical deformations of a prenotched recta ngular plate impacted on one side by a prismatic body of rectangular cross- section and moving parallel to the axis of the notch. Both the plate and th e projectile are made of the same material. Strain hardening, strain-rate h ardening and thermal softening characteristics of the material are modeled by the Johnson-Cook relation. The effect of different material parameters, notch-tip radius, impact speed and the length of the projectile on the maxi mum tensile principal stress and the initiation and propagation of adiabati c shear bands at the notch-tip is analyzed. It is found that for high impac t speeds or enhanced thermal softening, two shear bands, one at -10 degrees to the notch ligament and the other at -128 degrees to it, propagate from the notch tip. Otherwise, only one shear band nearly parallel to the notch- ligament initiates at the notch-tip. The notch-tip distortion for high stre ngth materials is quite different from that for low strength materials. The maximum tensile principal stress occurs at a point on the upper surface of the notch-tip and for every set of values of material parameters and impac t speeds studied equals about 2.3 times the yield stress of the material in a quasistatic simple tension or compression test. We assume that the britt le failure occurs when the maximum tensile principal stress equals twice th e yield stress of the material in a quasistatic simple tension test and a s hear band initiates when the effective plastic strain at a point equals 0.5 . The effect of material and geometric parameters on the time of initiation of each failure mode is computed. It is found that for low impact speeds ( < 30 m/s) a material will fail due to the maximum tensile principal stress exceeding its limiting value, and at high impact speeds due to the initiati on of a shear band at the notch-tip. Results are also computed for a C-300 steel with material parameters given by Zhou et al. For an impact speed of 50 m/s, the shear band speed and the maximum effective plastic strain-rate before a material point melts are found to be 350 m/s and 5x10(7)/s respect ively.