Comparing Three Equations Used for Modeling the Tensile Flow Behavior of Compacted Graphite Cast Irons at Elevated Temperatures

Abstract

A comparison between three constituent relationships used to approximate the plastic part of a tensile test curve was performed on compacted graphite cast iron (CGI) samples at temperatures between room temperature and 873 K (600 °C). The investigated relationships were the Hollomon, Ludwigson, and Voce equations. The investigated CGI materials were alloyed with four different amounts of molybdenum, and each chemical composition was cast with three different solidification rates. The two coefficients in the Hollomon equation \( \sigma_{\text{H}} = K_{\text{H}} \times \varepsilon^{{n_{\text{H}} }} \) showed a temperature dependence, where the strength coefficient KH was temperature stable for temperatures up to 573 K (300 °C) and the strain-hardening exponent nH showed a maximum value at about 473 K (200 °C). Both coefficients were affected by an altered metal matrix and by increased nodularity, and they showed a slight increased value with reduced pearlite interlamellar spacing. Ludwigson added an exponential term \( e^{{K_{\text{L}} + n_{\text{L}} \times \varepsilon }} , \) including two new coefficients to the Hollomon equation, to adjust and improve the approximation. The main purpose of KL was to adjust the stress value at zero plastic strain and was affected little by the metal matrix constituents and microstructure features. The value of nL was greatly dependent on the total plastic strain in which small plastic strains resulted in larger nL values, whereas large plastic strains resulted in smaller values. The deformation behavior was similar for all samples; hence, the total plastic strain also had a large influence on whether the adjustment term was positive or negative as a consequence of how nH was chosen. Compared with the Hollomon and Ludwigson equations, the Voce equation \( \sigma_{\text{V}} = \sigma_{S} - \left( {\sigma_{S} - \sigma_{1} } \right)e^{{n_{\text{V}} \times \varepsilon }} \) included coefficients representing an initial stress value σ1 and a saturation stress value σS. The initial stress values and the saturation stress values showed great linear correlations with yield strength values at 0.2 pct elongation and ultimate tensile strength, respectively. The values of both these coefficients were reduced with increasing temperature but had a plateau or even a slight increase between about 473 K and 573 K (200 °C and 300 °C). nV was reduced constantly with increasing temperature and was affected by the total plastic strain values in the same way as nL. The overall best approximation of the stress values was made by the Ludwigson equation followed by the Hollomon equation and last by the Voce equation. The downside with the Ludwigson equation was that the correction term either could be positive or negative, which made it harder to use as a general equation to approximate stress values, compared with the Hollomon and Voce equations.