Characterization of the interactions of two unequal co-rotating vortices

The interactions and merging of two unequal co-rotating vortices in a viscous fluid are investigated. Two-dimensional numerical simulations of initially equal-sized vortices with differing relative strengths are performed. In the case of equal-strength vortices, i.e. symmetric vortex pairs (Brandt & Nomura, J. Fluid Mech., vol. 592, 2007, pp. 413–446), the mutually induced strain deforms and tilts the vortices, which leads to a core detrainment process. The weakened vortices are mutually entrained and rapidly move towards each other as they intertwine and destruct. The flow thereby develops into a single compound vortex. With unequal strengths, i.e. asymmetric pairs, the disparity of the vortices alters the interaction. Merger may result from reciprocal but unequal entrainment, which yields a compound vortex; however other outcomes are possible. The various interactions are classified based on the relative timing of core detrainment and core destruction of the vortices. Through scaling analysis and simulation results, a critical strain rate parameter which characterizes the establishment of core detrainment is identified and determined. The onset of merging is associated with the achievement of the critical strain rate by ‘both’ vortices, and a merging criterion is thereby developed. In the case of symmetric pairs, the critical strain rate parameter is shown to be related to the critical aspect ratio. In contrast with symmetric merger, which is in essence a flow transformation, asymmetric merger may result in the domination of the stronger vortex because of the unequal deformation rates. If the disparity of the vortex strengths is sufficiently large, the critical strain rate is not attained by the stronger vortex before destruction of the weaker vortex, and the vortices do not merge.

Peak and Average Temperatures in Adiabatic Shear Band for Thermo-Viscoplastic Metal Materials

Gradient-dependent plasticity considering the microstructural effect is introduced into Johnson-Cook model to calculate the nonuniform temperature distribution in adiabatic shear band (ASB) and the evolutions of average and peak temperatures in ASB. Effects of initial static yield stress, strain-hardening coefficient, strain-hardening exponent, strain-rate parameter and thermal-softening parameter are numerically investigated. The calculated peak temperature in ASB considering both the plastic work and the microstructural effect is always greater than the average temperature calculated only using the plastic work. For much lower flow shear stress, the peak temperature approaches two times the average temperature. The occurrence of phase transformation in ASB is easier in metal material with higher initial static yield stress, strain-hardening coefficient, strain-rate parameter and thermal-softening parameter. At much lower flow shear stress or much higher average plastic shear strain, the phase transformation occurs more easily in material with a lower strain-hardening exponent. Traditional elastoplastic theory without the microstructural effect underestimates the peak temperature in ASB so that the experimentally observed phase transformations cannot be explained.

Correlation of Flow Stress With Strain Rate and Temperature During Machining

An idealized model of the orthogonal metal cutting process is used to determine the stresses, strain rates, and temperatures at the tool rake face for the machining of several materials under dry, unlubricated conditions, where a continuous chip is produced with an absence of a built-up edge. An attempt is made to correlate stress with strain rate and temperature using a temperature compensated strain rate parameter, and velocity modified temperature.