ADIABATIC SHEAR BANDING IN A THICK-WALLED STEEL TUBE

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 mater ial is modeled as strain hardening, strain-rate hardening and thermal softening. The deformations are assumed to be locally adiabatic and th e 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 zer o and is kept at zero; thus a finite amount of energy is input into th e body. For the combined loading, the magnitude of the torsional loadi ng pulse is kept fixed and the effect of varying the magnitude of the axial pressure preload is investigated. A shear band first initiates i n 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 radia l direction to vary from approximately 50 mis at the instant of its in itiation 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 dep ends 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 i nitiation of a shear band is not as sharp as that in a thin-nailed ste el tube. We compute the distance through which a shear band propagates as a function of the energy input into the body and thus ascertain th e energy required to drive a shear band through a unit distance. We al so study torsional deformations of a thick-walled CR-300 steel tube, m odel its thermal softening by a relation proposed by Zhou et al. and u se material properties derived from their data. In this case, the spee d of a shear band initiating from an element abutting the notch tip is found to vary between 750 mis and 1,000 mis at different points on a radial line through the notch tip; this agrees with that observed by Z hou et al. in their experiments on single-notched plates.