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Prediction of Proper Temperatures for the Hot Stamping Process Based on the Kinetics Models

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Abstract

Nowadays, the application of kinetics models for predicting microstructures of steels subjected to thermo-mechanical treatments has increased to minimize direct experimentation, which is costly and time consuming. In the current work, the final microstructures of AISI 4140 steel sheets after the hot stamping process were predicted using the Kirkaldy and Li kinetics models combined with new thermodynamically based models in order for the determination of the appropriate process temperatures. In this way, the effect of deformation during hot stamping on the Ae3, Acm, and Ae1 temperatures was considered, and then the equilibrium volume fractions of phases at different temperatures were calculated. Moreover, the ferrite transformation rate equations of the Kirkaldy and Li models were modified by a term proposed by Åkerström to consider the influence of plastic deformation. Results showed that the modified Kirkaldy model is satisfactory for the determination of appropriate austenitization temperatures for the hot stamping process of AISI 4140 steel sheets because of agreeable microstructure predictions in comparison with the experimental observations.

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Notes

  1. In fact, the thermal history of the specimens was validated using the strategy in which the heat transfer coefficient of AISI 4140 steel and water was determined by trial and error in simulations so that the obtained cooling rates resulted in satisfactory hardness predictions of the Creusot-Loire equations comparing with the empirical results. Therefore, it can be declared that the averaged heat transfer coefficient obtained by this method (200 W/m2 K) acts in the similar way that the heat transfer coefficient changes with temperature and the latent heat of transformations are considered in simulations.

Abbreviations

m :

A material coefficient

p :

A material coefficient

t :

Time (s)

G :

The prior austenite grain size

T :

The absolute temperature (K)

Xn:

The normalized transformed austenite volume fraction

Acm:

The start equilibrium temperature of the cementite transformation (K)

Ae3 :

The start equilibrium temperature of the ferrite transformation (K)

Ae1 :

The start equilibrium temperature of the pearlite transformation (K)

B s :

The start temperature of the bainite transformation (K)

B nose :

The temperature below Ae1 at which the ferrite volume fraction reaches zero (K)

M s :

The start temperature of the martensite transformation (K)

C i :

The weight percentage of the element i

R :

The universal gas constant (J/mol K)

\( \bar{\varepsilon }_{\rm{a}}^{\rm{P}} \) :

The effective plastic strain in austenite

μ j i :

The chemical potential of the component i in the phase j (J/mol)

ΔG γMechanical :

The molar mechanical energy stored in austenite (J/mol)

σ :

The equivalent stress (Pa)

ɛ P :

The equivalent plastic strain

ρ s :

The density (kg/m3)

M :

The molar mass (kg/mol)

X F :

The volume fraction of ferrite

X P :

The volume fraction of pearlite

X B :

The volume fraction of bainite

X M :

The volume fraction of martensite

C F :

The equilibrium weight fraction of ferrite

C αγ :

The weight percentage of carbon in the gamma phase in equilibrium with the alpha phase

C γα :

The weight percentage of carbon in the alpha phase in equilibrium with the gamma phase

C cemγ :

The weight percentage of carbon in the austenite phase in equilibrium with the cementite phase

C cemα :

The weight percentage of carbon in the alpha phase in equilibrium with the cementite phase

ρ A :

The density of austenite (kg/m3)

ρ F :

The density of ferrite (kg/m3)

ρ P :

The density of pearlite (kg/m3)

ρ B :

The density of bainite (kg/m3)

\( \Delta t \) :

The time increment (s)

XnF(T):

The normalized ferrite volume fraction at the beginning of the time step of the temperature T

XnP(T):

The normalized pearlite volume fraction at the beginning of the time step of the temperature T

XnB(T):

The normalized bainite volume fraction at the beginning of the time step of the temperature T

XeF(T):

The equilibrium (max) ferrite volume fraction at the temperature T

XeP(T):

The equilibrium (max) pearlite volume fraction at the temperature T

XeB(T):

The equilibrium (max) bainite volume fraction at the temperature T

XnF′(T):

The normalized ferrite volume fraction at the end of the time step of the temperature T

XnP′(T):

The normalized pearlite volume fraction at the end of the time step of the temperature T

XnB′(T):

The normalized bainite volume fraction at the end of the time step of the temperature T

\( \Delta t_{{1\%X_{\text{F}} }} \) :

The time period between the austenite transformation start and formation of one volume percent of ferrite (s)

\( \Delta t_{{1\%X_{\text{P}} }} \) :

The time period between the austenite transformation start and formation of one volume percent of pearlite (s)

\( \Delta t_{{1\%X_{\text{B}} }} \) :

The time period between the austenite transformation start and formation of one volume percent of bainite (s)

\( T_{{1\%X_{\text{F}} }} \) :

The temperature of the formation of one volume percent of ferrite (K)

\( T_{{1\%X_{\text{P}} }} \) :

The temperature of the formation of one volume percent of pearlite (K)

\( T_{{1\%X_{\text{B}} }} \) :

The temperature of the formation of one volume percent of bainite (K)

Δt total :

The time period between the austenite transformation start and finish (s)

T finish :

The temperature of the end of the austenite transformation (K)

HVFP:

The hardness of ferrite + pearlite (Vickers)

HVB:

The hardness of bainite (Vickers)

HVM:

The hardness of martensite (Vickers)

HVN:

The total hardness (Vickers)

Vr:

The cooling rate at 700 °C (°C/s)

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Authors and Affiliations

  1. School of Metallurgy and Materials Engineering, College of Engineering, University of Tehran, P.O. Box 11155-4563, Tehran, Iran

    P. Samadian, M. H. Parsa & H. Mirzadeh

  2. Center of Excellence for High Performance Materials, School of Metallurgy and Materials Engineering, University of Tehran, Tehran, Iran

    M. H. Parsa

  3. Advanced Metal Forming and Thermomechanical Processing Laboratory, School of Metallurgy and Materials Engineering, University of Tehran, Tehran, Iran

    M. H. Parsa & H. Mirzadeh

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Correspondence to M. H. Parsa.

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Samadian, P., Parsa, M.H. & Mirzadeh, H. Prediction of Proper Temperatures for the Hot Stamping Process Based on the Kinetics Models. J. of Materi Eng and Perform 24, 572–585 (2015). https://doi.org/10.1007/s11665-014-1371-3

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