PSI - Issue 23

Petr Opěla et al. / Procedia Structural Integrity 23 (2019) 221 – 226

222

Petr O pěla et al. / Structural Integrity Procedia 00 (2019) 000 – 000

2

1. Introduction

The mathematical description of the experimentally achieved hot-flow-curve dataset represents a highly-nonlinear approximation task. These curves represent a flow stress change under various thermo-mechanical conditions (i.e. strain, strain rate and deformation temperature) – see Fig. 1. In order to deal with this approximation issue, so-called flow stress models are usually utilized – see the overview composed by Gronostajski (2000). In addition to the known approaches, so-called intelligent algorithms, intensively studied in the last decades, offer a solution enhancement or even perspective alternatives of these models, Darwish (2018). The aim of the submitted research is to approximate the hot-flow-curve dataset of the AlSi1MgMn aluminium alloy. The dataset has been acquired via set of uniaxial compression tests by the Gleeble 3800 at the temperature levels of 723 K, 773 K and 823 K and the strain rate levels of 0.5 s − 1 , 1 s − 1 , 5 s − 1 and 10 s − 1 , with the true strain up to 0.6.

Fig. 1. Schematic illustration of the thermo-mechanical influence on the hot-flow-curve course.

2. Flow curve approximation In order to approximate the course of the flow stress, σ (MPa), of the investigated alloy under the different true strain, ε (-), strain rate, ̇ (s − 1 ) and temperature, T (K), the flow stress model derived by Cingara and McQueen (1992) and its high-strain modification Opěla et al . (2016) were used in the following form of Eq. 1 and 2, respectively:

c

   

   

  

   





exp 1 

 





  

 

(1)

p

p





p

p

s

   

   

  

   









exp 1 

ss p ss        





  

(2)

p





p

p

These equations contain five parameters: peak strain, ε p (-), peak stress, σ p (MPa), steady-state stress, σ ss (MPa) (see Fig. 1), hardening and softening exponents, c (-) and s (-). Each introduced parameter is dependent upon the temperature and strain rate. Experimental values of these auxiliary variables can be achieved via previously described methodology Opěla et al. (2018) . So, a precise approximation via models 1 and 2 is conditioned by a high accuracy approximation of the mentioned parameters. The parameter-approximation task has been solved by two different ways.