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Friction  2022, Vol. 10 Issue (2): 316-334    doi: 10.1007/s40544-021-0504-6
Research Article     
Multiscale friction model for hot sheet metal forming
Jenny VENEMA1,*(),Javad HAZRATI2,Eisso ATZEMA1,David MATTHEWS3,Ton van den BOOGAARD2
1 Tata Steel, Research & Development, CA Ijmuiden 1970, the Netherlands
2 Nonlinear Solid Mechanics, Faculty of Engineering Technology, University of Twente, Enschede 7522 NB, the Netherlands
3 Laboratory for Surface Technology and Tribology, Faculty of Engineering Technology, University of Twente, Enschede 7522 NB, the Netherlands
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The accurate description of friction is critical in the finite element (FE) simulation of the sheet metal forming process. Usually, friction is oversimplified through the use of a constant Coulomb friction coefficient. In this study, the application of an existing multiscale friction model is extended to the hot stamping process. The model accounts for the effects of tool and sheet metal surface topography as well as the evolution of contact pressure, temperature, and bulk strain during hot stamping. Normal load flattening and strip drawing experiments are performed to calibrate the model. The results show that the model can relatively well predict friction in strip draw experiments when the tool surface evolution due to wear is incorporated. Finally, the application of the formulated multiscale friction model was demonstrated in the FE simulation of a hot-stamped part.

Key wordstribology      wear      friction      hot stamping      friction model     
Received: 15 October 2020      Published: 17 January 2022
Corresponding Authors: Jenny VENEMA     E-mail:
About author: Jenny VENEMA. She received her Ph.D. degree in mechanical engineering from University of Twente, the Netherlands, in 2019. Since 2005, she has been a principal researcher in the application department at Tata steel. Her research interests are tribological aspects during forming processes of steel.|Javad HAZRATI. He received his Ph.D. degree in biomechanics from Eindhoven University of Technology, the Netherlands, in 2013. He is currently an assistant professor in nonlinear solid mechanics, University of Twente, the Netherlands. His research interests include friction and wear in material forming and modeling manufacturing processes related to material deformation.|Eisso ATZEMA. He received his Ph.D. degree from the University of Twente in 1994, specialising in applied mechanics used in forming technology. He has been working in forming technology at Tata Steel looking at supporting customers in processing the steel.|David MATTHEWS. He received his Ph.D. degree in applied physics and mathematics from the University of Groningen, the Netherlands, in 2008. Following nine years in industry as a principal researcher at Tata Steel, he is now an associate professor in surface design and engineering at the University of Twente, the Netherlands. His research interests surround the design and manufacture of surfaces for a wide range of applications and environments.|Ton van den BOOGAARD. He received his Ph.D. degree in mechanical engineering from the University of Twente in 2002. Since 2012, he has led the Chair Nonlinear Solid Mechanics and was appointed a full professor in 2015 at the same university. His research interests include mechanics of forming processes, computational material modelling, and process optimization.
Cite this article:

Jenny VENEMA,Javad HAZRATI,Eisso ATZEMA,David MATTHEWS,Ton van den BOOGAARD. Multiscale friction model for hot sheet metal forming. Friction, 2022, 10(2): 316-334.

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Fig. 1 Schematic of experiments: (a) normal load test, (b) HFT, and (c) hot stamping of top hat.
Fig. 2 Optical cross-sections of coating at (a) reference state and (b) after normal loading; confocal measurement (0.3 mm × 0.3 mm) of sheet surface for (c) reference state, (d) after loading including fractured particles, and (e) after loading without fractured particles. Normal load experiments are performed at 700 °C and contact pressure of 20 MPa.
Fig. 3 (a) Height distribution curves of undeformed and deformed surfaces (after normal loading) used to determine fractional real contact area (at 20 MPa contact pressure and 500 °C); (b) fractional real contact area (upper bound points) versus temperature at 5, 10, and 20 MPa contact pressure.
Fig. 4 Confocal measurements (2 mm × 2 mm) of strip surface at 700 °C and 5 MPa: (a) after heat treatment, (b) tool plows through hills and flattens profile, and (c) secondary plowing by adhesive wear on tool.
Fig. 5 Confocal measurements (2 mm × 700 μm) at 45°: (a) clean die radius, (b) die radius after 5 strokes, and (c) die radius after 50 strokes.
Fig. 6 Framework of multiscale friction model.
Fig. 7 Confocal measurements (1 mm × 1 mm): (a) sheet topography after heat treatment, (b) texture of clean tool, and (c) worn topography measurement tool at 650 °C after 10 strip draw tests.
PHS44-10T + 13,500-1.73ln(ε˙) + 188.617 × 10-51.8188106
Table 1 Substrate material parameters.
ε˙ = 0.01) and (b) yield strength versus coating temperature.
Fig. 8 (a) Stress-strain curves for substrate material model at different temperatures (ε˙ = 0.01) and (b) yield strength versus coating temperature.
Table 2 Coating material parameters.
Fig. 9 Schematic of normal loading model.
Fig. 10 Fractional real contact area versus temperature determined from experiments (dots) and predicted by model (gray line) at 5, 10 (left), and 20 MPa (right); red squares and blue circles represent upper and lower bounds of real contact area, respectively.
Fig. 11 COF versus temperature predicted by model and measured from experiments for clean and worn tools.
Fig. 12 (a) Schematic of contact patches and (b) geometric characteristics of elliptical paraboloid fitted on asperities.
Timsit and Pelow3.940.81
Clean tool90.812 × 10-3
Worn tool4.80.811 × 10-5
Table 3 Parameters of interfacial shear strength power law.
Fig. 13 Interfacial boundary shear strength for clean and worn tools.
Fig. 14 Wear mode diagram.
Fig. 15 (a) COF versus shear factor for attack angles of 25° and 35°; (b) COF versus attack angle for shear factors of 0.2 and 0.6.
Fig. 16 COF versus displacement from experiment at 700 °C: first sample calculation with clean tool and last sample calculation with worn tool.
20 °C950 °C
HTC (mW/(mm2·K))0.0200.145
Table 4 Heat transfer coefficient (HTC): heat transfer to surrounding.
0 MPa1 MPa2 MPa3 MPa20 MPa
HTC (mW/(mm2·K))
Table 5 HTC: heat transfer to tool with pressure dependency scaling factor.
PHS230Max (0.0102T2 - 29T + 21,500 + 215ln(ε˙); 500)-0.326ln(ε˙) + 0.0103T + 3.258.617 × 10-53.52101012
Table 6 Abspoel van Liempt flow stress parameters of substrate material.
600 °C0.650.580.78
700 °C0.720.810.88
Table 7 r values (Lankford coefficients) at various temperatures.
Fig. 17 Friction metamodel for clean die, punch, die with moderate wear, and die with severe wear: (a) cross-section at constant strain of 0 and (b) cross-section at constant temperature of 700 °C.
Fig. 18 COF after 50 mm of drawing for (a) clean die (1st product), (b) die with moderate wear (5th product), and (c) die with severe wear (50th product).
Fig. 19 Experiment and simulation results of (a) minimum thickness and (b) draw-in.
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