Numerical study on local contact conditions on rough surface under press hardening

The primary concern of press hardening for a manufacturer is productivity, which can deteriorate owing to wear. The harsh tribological behaviours, such as increasingly frictional force and severe wear, result in blank rupture, surface scratches, and shape deviation of the formed parts, which increases the cost and time required for maintenance. Furthermore, the harsh tribo-logical behaviours occur suddenly and develop unpredictably. To understand the mechanism behind the harsh tribological behaviours during consecutive stamping strokes, a dedicatedly tribological test that highly reproduced the press hardening conditions was conducted. A ﬁnite element (FE) simulation of the interface between the blank and the tool steel was established. The FE simulation mimicking the sliding process of the tribological test involved the real surface topography, which aimed to obtain the local contact conditions. The eﬀects of the nominal pressure and range of the friction coeﬃcient on the local contact conditions were studied. It was found that the local contact conditions in terms of contact pressure, contact area, and sliding distance diﬀered from the nominal values. The present FE simulation with a rough surface explores the possible length scale of the surface topography, where the calculated parameters may be the main factors af-Preprint


Introduction
The development of press-hardened parts in modern automobiles started with the research of Luleå University of Technology in the 1970s.In 1984, Saab Automobile first applied the press hardening technology to produce the side-impact beam of Saab 9000 series automobiles according to Billur and Boskovic (2019).Subsequently, major automobile companies gradually started using press-hardened parts as structural parts because they provide a higher strength with lighter weight and meet the present demand for energy saving and emission reduction.Typical procedures for press hardening are presented in Mori (2017).The boron steel sheet is heated to an austenite state (approximately 930 • C) in a furnace and then transferred to the die for stamping and cooling in the die closing stage.However, the severe wear in press hardening changes the topography of the contact interface, which causes sudden changes in the coefficient of friction (COF) and acceleration of the wear.These harsh tribological behaviours result in blank rupture, surface scratches, and shape deviation of the formed parts and then reduce the productivity and increasing the maintenance cost.
In recent years, the tribology of press hardening has attracted increasing attention.The tribological behaviours occurring at the interface between the workpiece and the die have been studied at elevated temperatures through a pin-on-disc test by Hardell et al. (2008).Research has shown that the formation of an intermetallic layer at the interface reduces the wear Hardell et al. (2010).The use of coated workpieces or surface engineering may significantly affect the wear mechanism.Hardell and Prakash (2010) reported that the severe adhesion is the predominant wear mechanism due to the formation of wear debris, transfer material, and the accumulation of the wear lumps on the tool surface.Pelcastre et al. (2013) found that the severe adhesion is related to the accumulation and compaction of wear debris, which may be attributed to the coating fracture during the sliding process under press hardening conditions.Further research by Pelcastre et al. (2016) outlines the effect of the microstructure of the coating on the tribological behaviours at elevated temperatures.Vergne et al. (2006) focused on the relationship of oxide scale and the friction coefficient in a hot rolling process.The creation and movement of the oxide debris were described using a phenomenological model based on microscopic observations of the wear features.In the process of continuous forming, Mozgovoy et al. (2018) reported that the oxide and die coating may break under repeated impact on the die surface, resulting in a mixed wear mechanism of three-body abrasion and adhesion.In addition, the die surface is hardened by plastic working during consecutive stamping, as described in Hernandez et al. (2014), and the elements in the coating gradually diffuse at high temperatures; thus, different microhardness layers are formed on the surface, as shown in Mozgovoy et al. (2019).Furthermore, a dense tribochemical layer is formed on the die surface under repeated impact, which can delay wear to a certain extent.This implies that the accumulation of adhesion increases in a complex high-temperature mechanical and chemical coupling field.Decrozant-Triquenaux et al. (2021) indicated that the formation of a tribolayer in the contact zone influences the tribological behaviour, and the stability of these layer depends on the surface roughness and chemical affinity of the contact pair.The analysis of the mechanism behind the tribological behaviours shows that the wear is the consequence of the frictional process, which composes with the interactions among the wear debris, surface treatment, adhesion development and surface topography.
Finite element (FE) simulations are widely used in metal-forming industries for feasibility analyses and parameter optimisation.Archard (1953) considers adhesive wear happens during the plastic deformation of the sliding spherical asperities and it is commonly employed for the wear prediction based on the parameter calibration by experiment.It is possible to determine where severe wear occurs, but the accurate prediction of the quantity during consecutive stamping strokes is difficult because the linear extrapolation of the wear quantity based on the number of strokes neglects the change in the contact interface, such as the movement of wear particles on the wearing surface, see Deng et al. (2019).This is beyond the scope of the FE simulation for industrial applications because, in the modelling, a perfectly flat surface is considered for efficiency.It is notable that the theoretically wear model developed on a single asperity, for example, Challen and Oxley (1979), or on statistical multi-asperities, for example, Greenwood and Tripp (1970), which substantially simplifies asperity conditions into statistical data, such as shape and height.However, the asperities at the interface of the press hardening may differ from batch to batch owing to manufacturing of the die surface, transport and storage of the workpiece, which decreases the practicability of the predictive model.Hol et al. (2012) presents a multiscale friction model for sheet metal forming simulation based on the surface change due to the flattening on asperities.The model calculates the real contact and then estimates the amount of asperities.Once the shear stress on the asperity is calculated, the frictional force owing to the ploughing and adhesion due to boundary lubrication in marco-scale can be obtained by means of a stochastic method Hol et al. (2015a).Afterwords, this model extends to mixed lubrication regime by the use of Reynolds equation for hydrodynamic stress Hol et al. (2015b).Venema et al. (2022) develops the method to hot stamping by employment of the high-temperature in the corresponding experiments.
In this study, an FE simulation mimicking the sliding process of the tribological test with real surface topography, was conducted and validated by a tribological test that reproduced the press hardening conditions in the laboratory.A rough surface with the waves due to grinding was employed, which represented a real die surface instead of the stochasticity of asperities.
An analysis of the local contact conditions occurring at the contact spot was performed.Furthermore, various COF and loads were used in the FE simulation as variables to correlate the local contact conditions and possible parameters related to the wear development.

High-temperature tribometer
To reproduce the sliding process under press-hardening conditions in the laboratory, a high-temperature tribometer device was developed, as shown in Figure 1.The tribological test rig involved a pair of tool steel pins, which were loaded against the workpiece strip surfaces (one from each side) and subsequently slid along the length of the strip.The tool steel pin was mounted on a moving assembly driven by a ball screw to swipe along the strip.The configuration allowed the easy replacement of the dedicated pin.The normal load on the tool steel pin was applied using a pneumatic bellows.
The heating of the strip was achieved via the Joule effect by passing a current through the strip up to a maximum temperature of 930 • C and then decreasing to 750 • C. The designed temperature history was consistent with the measurement in the production line, as discussed in Deng et al. (2017).
The test conditions are presented in Table 2, which represents the typical contact conditions in press hardening, as reported by Deng et al. (2017).
The positive pressure and tensile force of the friction pin were simultaneously recorded to calculate the Coulomb coefficient of friction (COF).The pin was made of QRO90 and the strip of 1.6 mm was made of boron steel, as shown in Table 1.The pin surface was spherical, and the nominal pressure was determined by the load and worn area after sliding.This designation was to achieve a high pressure based on Hertzian initial point-contact configuration.
The pin surface was ground to a roughness in the range of 0.35-0.4µm (Ra), which range was measured from a die of press-hardening.The strip surface was employed as delivered, which Ra was about 1.16 ±0.16 µm.

Finite element modelling of contact pair under mesoscopic contact pair
The workpiece (blank) and stamping tool surfaces were wavy for a scale length of a few millimetres.The topography of the surface is affected by several factors, such as grinding of the die surface, transport and storage of the workpiece.Roughness is defined as the arithmetic height of asperities on   respectively.The present FE simulation was established using the commercial FE software LS-DYNA.In general, the blank surface is rougher than the tool surface, but the roughness, surface orientation, and skewness depend on several uncertainties, such as manufacturing, transport and storage.To avoid uncertainty, both the tool and strip surfaces were modelled by a sinusoidal profile with an amplitude of 10 um based on the profile measurement mentioned above.As a primary study focusing on the apparent observation of tribological behaviours, the surface orientation in the FE simulation was perpendicular to the sliding direction of the strip.The present model mimicked the clean surface and no scale or wear debris was considered.The tool pin was QRO90 steel, and the strip was 22MnB5 boron steel.The material parameters used in the FE simulation, such as mechanical parameters, heat capacity, and thermal expansion, were the same as those in Deng et al. (2017).For the boron steel strip (blank), a thermal mechanical coupling constitutive model of an elastic-plastic model based on the von Mises yield criterion was adopted to simulate the flow behaviour at elevated temperatures, and the effect of phase transformation during the press hardening processes was calculated with good validation Åkerström (2006).QRO90 was modelled by an elastic-plastic constitutive model with different yield stresses at elevated temperatures provided by the supplier.The FE simulation included 19404 nodes and 16500 hexahedral solid elements, which were densely arranged on the contact surface, and at least 12 elements were contained along the wave profile.The size of the solid element used in the present model was 0.02 mm on the contacting surface but it increased to 0.1 mm along the thickness direction for computational efficiency.The FE simulation included a loading process followed by a sliding process, which ensured that the prescribed load in the pin constantly influenced the entire sliding process.The movement was restricted to three directions applied at the bottom of the tool steel part.A force was applied at the top of the blank part at a prescribed velocity.The contact algorithm adopted the penalty function method in the present simulation, according to Hallquist (2006).The initial temperatures of the blank was defined as 930 • C and then decreased to 750 • C before the sliding process by defining a scaled heat convection.The tool parts were 40 • C.These values were consistent with the tribological test, which was measured using the actual press hardening production, see Deng et al. (2017).To explore the correlation between the contact conditions and tribological behaviour, the test parameters of the FE simulation covered the main range of nominal contact conditions, as shown in Table 3.The FE simulation was performed using an implicit scheme because the inertia effect exceeded the scope of the study.Sliding distance in the contact spot accumulated on the node at each time step.In order to study the effect of various load on the local contact conditions respectively,

Results and discussion
This section focuses on the numerical results in conjunction with the experimental observations to analyse the local contact conditions related to the tribological behaviour.The mean COFs obtained from the experiment were 0.81 and 0.56 with the nominal pressure of 16 and 48 M P a respectively.
The quantitative and qualitative of the tribological behaviours based on the tribological test was presented in the study Deng et al. (2017).

The effect of load
The extreme conditions, which were obtained in the FE simulation during the loading and the sliding process, are presented in In the loading process, a linear relationship between the calculated and nominal pressures was obtained.However, a steeper gradient between the nominal load and calculated pressure was obtained during the sliding process because of the impact effect between the contact pairs.When the load was increased from 30 M P a to 48 M P a, the calculated pressure increased slightly.A higher load resulted in more deformation in terms of the larger contact area and more elastic energy dissipated in the bulk material.Greenwood and Tripp (1970) found that the real contact area is strictly proportional to the applied load, and it is extremely small compared to the nominal contact area.Venema et al. (2022) reported the fractional real contact area in the press hardening was approximately 5 % of the nominal contact area when a load of 20 M P a was applied.Theoretically, the real contact area is correlated with the distribution of deformed asperities.
In fact, the oxide layer or tribofilm on the surface probably covers the initial asperity ( see Mozgovoy et al. (2019)), and neglecting the squeezing of neighbouring asperities increased the complexity.Figure 4 (b) presents the contact area due to the deformation of the surface waviness under different loads, where the nominal contact area was 4.5 × 10 −6 m 2 .In fact, it was sensitive to the size of the contacting element Deng et al. (2017).A certain number of contacting nodes produce a reaction force based on the penetrated depth, which is the main characteristic of the penalty method Hallquist (2006).A marginally higher load could be balanced by deeper penetration of the identical node because a constant penalty scaling factor was used.The reason for the non-proportion between the loads and the calculated contact areas was that the same number of contacting nodes may produce variable contact pressures.The contact areas during the sliding process were larger than those in the loading process under all employed loads because an enlarged deformation of the contact pair was required to dissipate the energy of the impact during the sliding.
Owing to their dissimilar mechanical properties, the blank and tool steels exhibited different deformations during the test.QRO90 (the tool steel) exhibited no plastic deformation in the FE simulation because its yield stress was approximately 900 M P a at 500 • C as specified by the supplier.During the sliding process of the FE simulation, the contact pressure increased with the COF under both nominal pressures of 16 M P a and 48 M P a, as shown in Figure 6 (c).The calculated contact pressures during the sliding process were higher than those during the loading process.Figure 6 (d) presents a drastic increase in the plastic strain in the case of 48 M P a, which was measured on the contact spot in the bank.In the case of 16 M P a, the slope between the plastic strain and COF was gentle because a higher pressure caused increased plastic deformation.A strong correlation between the contact pressure and plastic strain was obtained.The high value of the plastic strain accumulated in the blank may result in fracture.The effect of COF on the contact pressure and plastic strain implied that an optimised lubricity scheme controlling the COF at a low value may significantly decrease the fracture and material transfer.

Comparison of the frictional behaviour in the FE simulation and the tribological test
To validate the FE simulation with the tribological test, nominal pressures of 16 M P a and 48 M P a were employed, where the COF corresponded to experimental result of 0.81 and 0.56, respectively.The analysis of the tribological behaviours in the experiment was presented in the study Mozgovoy et al. (2018).Wear is a progressive material transfer due to the relative motion of the contact surfaces during the stamping process, and the energy dissipated by friction is directly proportional to the volume of wear (Ramalho and Miranda (2005)).The friction work, calculated as the production of the normal force and the sliding distance occurring in the surface node, is presented in Figure 9, where the friction was accumulated after the relative motion of the sliding over one wavelength.According to Fouvry et al. (2003), the friction energy    proposed by Archard and Hirst (1956), is widely used in the metal forming simulation so as to predict when and where the unacceptable wear occurs.
This model was initially developed on asperities, but nominal contact conditions are typically substituted for the prediction, for example, Deng et al.

Figure 1 :
Figure 1: Schematic of the tribometer test

Figure 2 Figure 2 :
Figure2shows the FE simulation of the mesoscopic contact pair, which mimics the sliding process of the tribological test.The surface profile of the stamping tool after grinding is shown in Figure3, obtained using an interferometer, ZYGO 7300.The surface waviness and irregular concave and convex shapes above (roughness) are represented by dashed and bold lines, Strategy 2: various COFs with load=16 M P a and 48 M P a 0.1-0.9two parametric strategies were performed in the simulation.Strategy 1 employed a range of pressures from 1 M P a to 48 M P a in the FE simulation, which covered the main pressure during the stamping process.The variables of different pressures mimicked the pressure distribution occurring at the interface between the blank and the tool.A constant COF of 0.56 as measured from the tribological test with 48 M P a was applied in the FE simulation.In a real production line, COF might be in a narrow range owing to the use of lubricants (Azushima et al. (2012)) or surface engineering (Liu et al. (2020)).In contrast, the COF is affected by process parameters, such as temperature, velocity, and pressure (Okonkwo et al. (2012), Mozgovoy et al. (2013), Hernandez et al. (2014), Mozgovoy et al. (2018)).Furthermore, the COF is sensitive to the change in the surface topography where adhesion develops (Mozgovoy et al. (2019), Decrozant-Triquenaux et al. (2021)).It is necessary to understand the effects of various COFs on the local contact conditions to attain the optimised target of the lubricity scheme.Strategy 2 employed a constant COF in the range 0.1-0.9 in conjunction with two nominal pressures was used in the FE simulation, wherein the range of COF was thought to mimic the most frictional behaviour from dry to lubricated conditions.

Figure 3 :
Figure 3: Surface profile of a press hardening tool Figure 4.According to Figure 4, (a) the local contact pressures in the FE simulation were higher than the nominal loads, owing to the surface topography.Comparably, a normal loading test with a nominal pressure of 5 M P a reported by Venema et al. (2017) indicates plastic deformation and fracture of asperities on the surface.
shows the plastic strain of the blank at the contact spot during the loading and sliding processes.In general, the plastic strain increased with the load.The gradient became sharper during sliding.The maximum plastic strain attained 0.18 when the sliding blank was under a load of 48 M P a.The boron steel blank exhibited brittle fracture behaviour with different cooling processes owing to multiphase microstructures as reported byGolling et al. (2016), and a low fracture strain of approximately 0.1 was observed.This implies that fracture may occur during the sliding process of the tribological test, which could be regarded as the initiation of the material transfer, affecting the following wear process.The increased loads caused longer sliding distances, as shown in Figure4(d), because sufficient deformation eliminated the gap between counter bodies.In the load range from 1 M P a to 20 M P a, the sliding distance that occurred on the tool surface was lower than that on the blank surface because the blank was much softer at elevated temperatures compared to the tool steel.When the load was larger than 30 M P a, apparent deformation occurred in both counterparts, and the difference in the siding distance decreased.

Figure 5 Figure 4 :Figure 5 :
Figure5shows the shear stress of the blank surface during the sliding process, where data were extracted from the contact node.A positive value indicates the push stress, and a negative value represents the resistance stress, indicating the stick-slip phenomenon as the vibration in the tribological test.Actually, the fluctuated shear stress due to the surface

Figure 7 Figure 6 :
Figure7presents results comparable to those of the tribilogical test (tribo) and FE simulation (FEM).The statistical COF was extracted from the stable sliding period without initial loading in both the tribological test and FE simulation.Under a pressure of 48 M P a, the FE simulation was in good agreement with the tribological test in terms of the mean and stan-

Figure 7 :Figure 8 :
Figure 7: Statistical comparison of COFs obtained from the triblogical test and the FE simulation Figure 9: (a) Sampling positions (geometric exaggeration); (b) friction work in the surface waviness

Figure 11 :
Figure 11: Contact pressure on the tool-steel part during the sliding process

Figure 12 :
Figure 12: Broken strip obtained in the case with a flat pin surface, 20 M P a

Table 1 :
Chemical constituents of the materials used in the press hardening experiment

Table 2 :
Experimental parameters in the tribological test

Table 3 :
Test parameters in the FE simulation