Metallurgical and Materials Transactions B

, Volume 44, Issue 2, pp 332–343 | Cite as

Experimental Characterization of Heat Transfer Coefficients During Hot Forming Die Quenching of Boron Steel



The heat transfer coefficient (HTC) between the sheet metal and the cold tool is required to predict the final microstructure and mechanical properties of parts manufactured via hot forming die quenching. Temperature data obtained from hot stamping experiments conducted on boron steel blanks were processed using an inverse heat conduction algorithm to calculate heat fluxes and temperatures at the blank/die interface. The effect of the thermocouple response time on the calculated heat flux was compensated by minimizing the heat imbalance between the blank and the die. Peak HTCs obtained at the end of the stamping phase match steady-state model predictions. At higher blank temperatures, the time-dependent deformation of contact asperities is associated with a transient regime in which calculated HTCs are a function of the initial stamping temperature.

List of symbols

Latin symbols


Specific heat (J kg−1 K−1)


Microhardness (MPa)


Heat balance deficit (–)


Knudsen number (–)


Martensite start temperature (K)


Temperature (K)


Stamping temperature (K)


Dimensionless surface roughness ratio (–)


Dimensionless gap thickness ratio (–)


Peak-to-valley surface roughness (m)


Thickness (m)


Effective gap thickness (m)


Martensite fraction (–)


Temperature jump distance (m)


Heat transfer coefficient (W m−2 K−1)


Thermal conductivity (W m−1 K−1)


Mean asperity slope (rad)


Stamping pressure (MPa)


Regularization parameter (–)


Time (seconds)


FE model coordinate (m)

Greek symbols


Heat flux (W m−2)


Accommodation coefficient (–)


Density (kg m−3)


RMS surface roughness (m)


Thermocouple response time (seconds)







Bottom die


Contact spot


Die (top and bottom)


Air gap


Maximum value


Mean free path






Top die


Usibor 1500P® blank





The authors wish to thank Professor M.M. Yovanovich of the University of Waterloo for his assistance with the thermal contact conductance models and Professor R. Liu of Carleton University for her help with the high temperature microhardness measurements. The authors also acknowledge the support of Honda R&D Americas, Cosma International and the Promatek Research Centre, ArcelorMittal, the Natural Sciences and Engineering Research Council (NSERC) of Canada, and the Initiative for Automotive and Manufacturing Innovation (IAMI) program of the Ontario Research Fund.


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Copyright information

© The Minerals, Metals & Materials Society and ASM International 2012

Authors and Affiliations

  1. 1.Department of Mechanical and Mechatronics EngineeringUniversity of WaterlooWaterlooCanada

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