Adiabatic shear banding in a thick-walled steel tube |
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Authors: | R C Batra D Rattazzi |
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Affiliation: | (1) Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0219, USA, US |
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Abstract: | We analyze the initiation and propagation of adiabatic shear bands in a thick-walled 4340 steel tube with a V-notch in the middle. The material is modeled as strain hardening, strain-rate hardening and thermal softening. The deformations
are assumed to be locally adiabatic and the effect of inertia forces is considered. Two different loadings, i.e., torsional,
and combined torsional and axial pressure are considered. In each case, the load generally increases linearly from zero to
the final value, is kept steady there for some time, then decreases to zero and is kept at zero; thus a finite amount of energy
is input into the body. For the combined loading, the magnitude of the torsional loading pulse is kept fixed and the effect
of varying the magnitude of the axial pressure preload is investigated. A shear band first initiates in the element adjoining
the notch tip and propagates radially inwards. By recording the time when a shear band initiates at the centroids of different
elements we determine its speed of propagation in the radial direction to vary from approximately 50 m/s at the instant of
its initiation in an element abutting the notch tip, to nearly 90 m/s by the time it reaches the innermost surface of the
tube; the speed also depends upon the overall loading rate, and whether or not the loading is multiaxial. The drop in the
torque required to twist the tube at the initiation of a shear band is not as sharp as that in a thin-walled steel tube. We
compute the distance through which a shear band propagates as a function of the energy input into the body and thus ascertain
the energy required to drive a shear band through a unit distance.
We also study torsional deformations of a thick-walled CR-300 steel tube, model its thermal softening by a relation proposed
by Zhou et al. and use material properties derived from their data. In this case, the speed of a shear band initiating from
an element abutting the notch tip is found to vary between 750 m/s and 1,000 m/s at different points on a radial line through
the notch tip; this agrees with that observed by Zhou et al. in their experiments on single-notched plates. |
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