Deformation and Recrystallization Behavior of the Cast Structure in Large Size, High Strength Steel Ingots: Experimentation and Modeling

Abstract

Constitutive modeling of the ingot breakdown process of large size ingots of high strength steel was carried out through comprehensive thermomechanical processing using Gleeble 3800^® thermomechanical simulator, finite element modeling (FEM), optical and electron back scatter diffraction (EBSD). For this purpose, hot compression tests in the range of 1473 K to 1323 K (1200 °C to 1050 °C) and strain rates of 0.25 to 2 s⁻¹ were carried out. The stress-strain curves describing the deformation behavior of the dendritic microstructure of the cast ingot were analyzed in terms of the Arrhenius and Hansel-Spittel models which were implemented in Forge NxT 1.0^® FEM software. The results indicated that the Arrhenius model was more reliable in predicting microstructure evolution of the as-cast structure during ingot breakdown, particularly the occurrence of dynamic recrystallization (DRX) process which was a vital parameter in estimating the optimum loads for forming of large size components. The accuracy and reliability of both models were compared in terms of correlation coefficient (R) and the average absolute relative error (ARRE).

Appendix

Arrhenius-type model[31] is used to describe the relationship between flow stress, deformation temperature and strain rate during high temperature deformation. It is given by

$$ \dot{\varepsilon } = AF\left( \sigma \right){ \exp} \left(- \frac{Q}{RT} \right) $$

(A1)

Generally, F (σ) is in the form of power function or exponential function or hyperbolic sine function as listed below:

$$ \begin{aligned} F \, \left( \sigma \right) = \sigma^{{n_{1} }} \,\left( {\alpha \sigma { < }0. 8} \right) \hfill \\ F \, \left( \sigma \right) \, = \, exp \, (\beta \sigma ) \, \left( {\alpha \sigma { > 1}. 2} \right) \hfill \\ F \, \left( \sigma \right) \, = \, \left[ {sinh \, \left( {\alpha \sigma } \right)} \right]^{n} \left( {{\text{for all }}\sigma } \right) \hfill \\ \end{aligned}, $$

(A2)

where, A, n _1, n, α and β are the material constants, with α = β/ n ₁ .

In order to find the constants, the value of F (σ) is put into Eq. [A2] which gives the relationship of low-level stress (ασ < 0.8) and high-level stress (ασ > 1.2).

$$ \begin{aligned} \dot{\varepsilon } &= B\sigma^{{n_{1} }} \hfill \\ \dot{\varepsilon }& = B' {\exp} \big(\beta \sigma\big) \hfill \\ \end{aligned} $$

(A3)

B, B, and $n_{1}$ are material constants which are independent of deformation temperatures. These constants can be calculated by taking logarithm on both sides of Eq. [A3].

$$ \begin{aligned} \ln \sigma = \frac{{{ \ln }\dot{\varepsilon }}}{{n_{1} }} - \frac{{{ \ln }B}}{{n_{1} }} \hfill \\ \sigma = \frac{{{ \ln }\dot{\varepsilon }}}{\beta } - \frac{{{ \ln }B'}}{\beta } \hfill \\ \end{aligned} $$

(A4)

Plotting graphs of lnσ vs ln $\dot{\varepsilon }$ and σ vs ln $\dot{\varepsilon } ,$ by the linear regression method gives the values of $n_{1 }$and β. The values are calculated using the average values of slope of parallel lines from different temperatures. Putting these values, value of α= β/ n ₁ can be found.

In order to calculate the value of Q, logarithm on both sides of Eq. [A2] of the function is taken for all values of stress and then assuming it as independent of temperature gives,

$$ \ln \left[ {\sinh \left( {\alpha \sigma } \right)} \right] = \frac{1}{n}{ \ln }\dot{\varepsilon } + \frac{Q}{nRT} - \frac{1}{n}{ \ln }A $$

(A5)

$ln\dot{\varepsilon }$ and 1/T are considered as two independent variables. Differentiating the above equation gives,

$$ n = \left. {\frac{{\partial { \ln }\dot{\varepsilon }}}{{\partial \ln \left[ {\sinh \left( {\alpha \sigma } \right)} \right]}}} \right|_{T} $$

(A6)

$$ Q = \left. {nR\frac{{\partial \ln \left[ {\sinh \left( {\alpha \sigma } \right)} \right]}}{{\partial \left( {\frac{1}{T}} \right)}}} \right|_{{\dot{\varepsilon }}} $$

(A7)

(T and $\dot{\varepsilon }$ taken as independent variables).

Using these equations, plots of ${ \ln }[\sinh \left( {\alpha \sigma } \right)] - { \ln }\dot{\varepsilon }$ and ${\text{ln}}[\sinh \left( {\alpha \sigma } \right)] - \left( {\frac{1}{T}} \right)$ can be generated and subsequently the value of n and Q can be found using regression analysis of experimental results. The value of the constant lnA can be found from the intercept of ${ \ln }[\sinh \left( {\alpha \sigma } \right)] - { \ln }\dot{\varepsilon }$ plots.