High strain rate constitutive equation for metallic materials

The yield stress and flow stress increase significantly with strain rate. High speed Forming and Machining operation gives rise to strain rates varying from 10 to 10^ per second. A number of research work have been reported in which various techniques have been described for strain rates sensitivity. One of the reported technique 1 was based on high speed compression of small cylindrical specimens with tool steel projectile. The deformation was recorded with a high speed camera operating at 500,000 frames per second. The equipment is very expensive and the processing of the picture for data is very tedious and subjected to human error.\ud \ud The present study was aimed at using a similar technique of high speed compression without having to use any high speed photographs. From known initial and final dimension of the specimen together with the mass and the impact speed of the projectile, the deformation is simulated using a finite-difference technique based on an assumed dynamic constitutive equations. By iterative computation the constants of the constitutive equations are established and give close agreement between the experimental and simulated results in terms of the final dimensions of the cylindrical test specimens.\ud \ud Finally the principal aim of this investigation was to establish high strain rate constitutive equations for commercially pure Copper, Mild steel and Stainless steel, and compare the results with those obtained using more sophisticated and expensive equipment.This principal objective has been achieved and high strain rate constitutive equations have been determined for strain rates ranging between 103 to 10^ per second