Description of Hot Compressive Stress-Strain Curves Using Transfer Functions

Abstract

Mathematical descriptions of true stress/true strain curves, experimentally obtained on cylindrical specimens under hot compressive conditions, are of great importance and are widely investigated. An additional black-box modelling approach using transfer functions (TF) is tested. For tested 51CrV4 steel, a TF of third order is employed for description of true stress (output) depending on the strain rate (input). Sets of TF coefficients are determined using numerical optimization techniques for each testing temperature and strain rate. To avoid scattering of TF parameters, time in Laplacian transformation is replaced with strain, while TF input is the strain rate. Obtained models cover deformations starting practically from zero to 0.7. Average absolute relative error for models based on TF of the third order and of the second order are 0.93% and 3.64%.

Keywords

• hot deformation
• transfer function
• Laplacian transformation
• numerical optimization