Effect of Material and Geometric Parameters on Deformations of a Dynamically loaded Prenotched Plate
We analyze plane strain thermomechanical deformations of a prenotched rectangular plate impacted on one side by a prismatic body of rectangular cross-section and moving parallel to axis of the notch. Both the plate and the projectile are made of the same material. Strain hardening, strain-rate hardening 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 maximum tensile principal stress and the initiation and propagation of shear bands at the notch-tip is analyzed. It is found that for high impact speeds or enhanced thermal softening, two shear bands, one at and the other at 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 strength 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 impact 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 brittle fracture occurs when the maximum tensile principal stress equals twice the yield stress of the material in a quasistatic simple tension test and a shear 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 initiation 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 5 x /s respectively.