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

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Abstract

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 the 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 adiabatic 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 −10° to the notch ligament and the other at −128° 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 failure 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 5×107/s respectively.

Key words: Failure-mode transition, shear bands, thermoviscoplasticity, numerical simulations.

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Authors and Affiliations

  1. Department of Engineering Science and Mechanics, MC.219, Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061, U.S.A.

    R.C. Batra & R.R. Gummalla

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  1. R.C. Batra
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  2. R.R. Gummalla
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Batra, R., Gummalla, R. Effect of material and geometric parameters on deformations near the notch-tip of a dynamically loaded prenotched plate. International Journal of Fracture 101, 99–140 (2000). https://doi.org/10.1023/A:1007504431357

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