Advances in friction of aluminium alloy deep drawing

Broad use of lightweight aluminium alloy parts in automobile manufacturing, aerospace, electronic communication, and rail transit is mainly formed through deep drawing process. Deep drawing friction is a key boundary condition for controlling the forming quality of aluminium alloy parts. However, due to the oxidation and adhesion tendency of aluminium alloys, the tribological situations of aluminium alloy deep drawing (AADD) system is more complicated than those of traditional deep drawing of steel sheets. Therefore, the study of AADD friction is essential for manufacturing high-performance aluminium alloy parts. Herein, aiming to provide a valuable reference for researchers in related fields, a comprehensive review of AADD friction is provided, including friction mechanism, influencing factors, friction measurement, friction model, friction simulation, and lubrication-free friction control. Finally, a brief conclusion and several current challenges were discussed.


Introduction
Aluminium alloys are known to be the lightweight alloys that offer high specific strength and stiffness together with good weldability, machinability, and corrosion resistance [1].As the demand for lightweight industrial products continues to increase, aluminium alloys showed promising applications in automobile manufacturing, aerospace, electronic communications, and rail transit.Currently, aluminium alloy sheets are mainly formed through deep drawing process, not only because of its high machining efficiency, but also because that it enables manufacturing components with complex geometry.However, the surfaces of die and aluminium alloy sheets are not ideally smooth, and there are complex interactions at the contact interface during the deep drawing process, forming a multi-variable and time-varying tribological system.The friction between die and the aluminium alloy sheets plays a decisive role in controlling the ultimate quality of the sheets by affecting the material flow and the interface stress and strain distribution.Therefore, fully understanding the tribological behavior in deep drawing process is critical to improving the performance of aluminium alloy parts.
To reduce the lost time and manufacturing costs due to try-out and design changes of die, it is essential to establish friction models that accurately predict the actual deep drawing process in the early stage of product development.By quantifying the contributions of different factors of a tribological system to friction behavior, friction models can evaluate the robustness of an industrial production process.Using friction models to investigate possible scenarios corresponding to production conditions prior to the final design and machining of the die can contribute to determining a robust process window to obtain defect-free parts.However, the interface friction behavior in the deep drawing process changes with the variations of lubrication amount, lubrication distribution, and die www.Springer.com/journal/40544| Friction temperature, and it is difficult to guarantee the quality of parts during continuous production for a long time.This requires control and regulation of the friction to control the process.In 2018, Tatipala et al. [2,3] analyzed the influence of lubrication performance changes on the quality of the front door inner of a Volvo XC90 based on the lubrication amount and lubrication distribution data measured in production, which improved the prediction accuracy of the part forming performance.In 2020, Veldhuis et al. [4,5] studied the sensitivity of the process to temperature-induced frictional effects, and adjusted the blank holder force F H and ejection force in real time to adapt the process to the tribological system changes caused by die heating, thereby avoiding the fracture caused by the deterioration of friction conditions.Thus, building the link between the control systems based on friction models and the manufacturing technologies can realize stable process control to improve the quality of deep drawing parts and the overall production stability.
To study the important role of friction in sheet metal forming, some excellent review papers on metal forming friction have been published in recent decades.As early as 1986, Kalpakjian [6] outlined the importance and complexity of tribology in sheet metal forming.Subsequently, Kawai and Dohda [7] listed the friction test methods suitable for sheet metal forming, focusing on the influence of different factors on the lubrication mechanism.In 2003, Guo et al. [8] summarized the friction models commonly used in simulation of sheet metal stamping.In 2014, Meng et al. [9] divided the existing friction models into five categories based on the development of friction models in metal plastic forming, and the characteristics of various friction models and their application scopes were discussed in detail.In 2018, Seshacharyulu et al. [10] and Xu et al. [11] briefly introduced several devices to measure the coefficient of friction (COF) μ, and analyzed the influence of process parameters on the friction law by investigating the friction characteristics in sheet plastic forming.In 2018, Nielsen and Bay [12] took time as the boundary and summarized the important progress of friction modelling in the metal forming process  since Bowden and Tabor [13] put forward the adhesion theory.Li et al. [14] reviewed the friction mechanism and the influencing factors of friction characteristics in the stamping process.In 2020, Trzepiecinski and Lemu [15] classified and summarized the friction test apparatus of conventional sheet metal forming and incremental sheet forming in detail.Although these reviews analyzed sheet forming friction from multiple angles, they mainly targeted at traditional steel sheet forming and cannot fully reflect the complex tribological conditions in the aluminium alloy deep drawing (AADD) process.To date, review papers systematically elucidating AADD friction have not been reported.
Different from steel, aluminium alloys exhibit poor formability at room temperature due to lower tensile strength and elongation at break [16].In addition, when hard die is in contact with soft aluminium sheet, the surface of aluminium sheet will undergo severe plastic deformation, and the surface material will detach and transfer from the substrates.Aluminium chips are easy to adhere to die surface.Accompanied by the oxidation reaction that might occur, a transfer layer with complex compositions will be formed [17].Because of the significant adhesion between the die and the aluminium alloy sheet, the AADD system has unique friction characteristics.Therefore, a comprehensive review of AADD from friction mechanism to friction control will provide a valuable reference for researchers in related fields.
The organizational structure of this review is shown in Table 1.Section 1 introduces the background of AADD friction.Section 2 analyzes the friction behavior of AADD and its influencing factors.Section 3 reports the friction test methods of AADD.Section 4 summarizes the friction models of AADD, including empirical models based on friction test results and

AADD friction
The friction between the die and the aluminium alloy sheet affects the interface force, inhibits the material flow, and regulates the sheet deformation behavior during the deep drawing process.But friction is not an isolated state; it depends on the complex interactions of rough surfaces, and is affected by many factors such as deep drawing process parameters, die-sheet surface and material characteristics, and lubrication conditions.In Section 2, the influence of friction behavior on AADD is discussed, and the influencing factors of AADD friction are analyzed.

Influence of friction on AADD
Under F H , punch force F D , and friction force f, the aluminium alloy sheet will undergo large plastic deformation during the deep drawing process.The stress and strain states of different regions of sheet exhibit remarkable differences.This is illustrated in Fig. 1.The sheet deformation zone is mainly divided into nine regions: I, blank holder region; II, drawbead region; III, inner ring region; IV, die radius region; radius region, which affects the stress and strain states of different regions of sheet and the forming performance of parts.Bouchaâla et al. [18] studied the impact of friction on the wall thickness distribution of AA2198 deep drawing parts by contrasting the simulation and experimental results.Reddy et al. [19] investigated the effect of COF on the limit drawing ratio and limit strain of AA1100, and found that the limit drawing ratio and limit strain of the workpiece decrease with the increase of the COF.Folle and Schaeffer [20] showed that the COF in AA1100 deep drawing process is not a constant value, and the variations of COF affect the drawing force.Bellini et al. [21] analyzed the influence of friction on the forming properties of AA6060 discs.The deep drawing tests and simulations of AA6111 by Ma et al. [22] and AA 6061-T4 by Mohamed et al. [23] also confirmed that friction is a key factor affecting the thickness, forming limit, maximum thinning position, and failure modes of parts.

Influencing factors of AADD friction
As shown in Fig. 2, friction is a bridge linking the influencing factors of deep drawing system and the forming quality of parts.The unreasonable friction distribution will cause wrinkling, fracture, springback, and other defects.These can be attributed to the influence of different input factors on AADD friction.However, the difficulty of AADD frictional study lies in that as the input conditions vary, the proportion of different factors will change, and the law might also be completely opposite.

Process parameters
AADD friction has a strong correlation with temperature.So far, reports related to AADD friction have mainly focused on conventional cold deep drawing and hot deep drawing.Lu et al. [24,25] revealed the friction mechanism of AA7075 sheet at different temperatures.When the temperature is lower than 150 °C, plowing friction dominates; and when the temperature is higher than 300 °C, adhesive friction dominates.In the temperature range of 25-450 °C, Hanna [26] and Gali et al. [27] carried out the P20 and AA5083 friction test, respectively.Although the COF increases with the increase of temperature, there is a large difference of tendency between them.
The COF of the former only changes drastically at 200-300 °C, while the COF of the latter increases exponentially with the increase of temperature.In the 300-500 °C temperature range, the friction test of AA6061 by Liu et al. [28] and AA6111 by Dou et al. [29] also obtained similar changes.Although warm/hot deep drawing improves the forming properties of aluminium alloys, this operation may affect the microstructures and mechanical behaviors of aluminium alloys.Because the cryogenic temperature can significantly improve the strength and toughness of aluminium alloys, and the parts have good comprehensive performance.In the past seven years, the cryogenic temperature deep drawing of aluminium alloy sheet (Fig. 3) has received a massive amount of interest [1,[30][31][32][33][34].In contrast, there is a lack of research on cryogenic temperature AADD friction.In 2019, only Padmini et al. [35] conducted AA2024, AA6082, and AA7075 cryogenic temperature friction tests at −196 °C in liquid nitrogen, and found that cryogenic temperature environments can reduce COF and improve the tribological properties of aluminium alloys.
Fig. 2 Influencing factors of AADD friction on forming quality of parts.Under different contact pressures and velocities, AADD friction undergoes marked changes.The AA3004 dry friction test of Lin et al. [36] showed that under low pressures, increasing the drawing speed can reduce friction.When the pressure is large enough, the effect of drawing speed on friction is weakened.Under lubrication conditions, the friction tests of AA5023 by Ooki and Takahashi [37], AA6063 by Hwang and Chen [38], and AA5182 and AA6016 by Sabet et al. [39] showed that the larger the sliding speed, the smaller the COF.However, the AA6014 friction test of Steiner and Merklein [40] pointed out that the drawing speed is not related to friction under dry contact conditions, and the COF increases with the increase in contact pressure (the same conclusion as that reported in Refs.[25,28]).The drawing speed affects the friction under lubrication conditions, and the COF decreases with the increase of contact pressure (the same conclusion as that reported in Refs.[39,41,42]).Contrary to those reported in Refs.[25,28,40], the dry friction test of 1.2343/AA6016 by Domitner et al. [43] showed that the COF decreases with the increase of contact pressure.In the P20/AA7075 friction test conducted by Yang et al. [44], when the system is in a boundary lubrication condition, the influence of contact pressure and sliding speed on friction can be ignored.The friction test of Shi et al. [45] confirmed it.Due to the extremely complicated influence of the deep drawing process on the AADD friction, single conclusion cannot truly reflect the friction behavior of contact interface.

Surface characteristics
AADD friction is affected by the surface roughness, coating, and texture of sheets and tools.Aluminium alloy sheet is commercially available in three surface finishes, i.e., milling finish (MF), dull finish (DF), and electrical discharge texturing (EDT).Among them, MF has the lowest surface roughness, and EDT has the highest surface roughness [46].The surface morphologies of MF and EDT aluminium alloy sheets are shown in Fig. 4 [47].Under lubrication conditions, Keum et al. [48] found that when the surface roughness of aluminium alloy sheet is low, the COF decreases with the increase of surface roughness due to small cavity for storing lubricating oil.When the surface roughness of aluminium alloy sheet is high, the oil film ruptures due to surface asperity plastic deformation, and the COF increases with the increase of the surface roughness.Lemu and Trzepieciński [49] pointed out that the influence of tool surface roughness on friction depends on the friction conditions (dry or lubrication conditions).Under dry friction conditions, tools with low surface roughness may not necessarily reduce friction.Under lubrication conditions, the law is the same as that reported in Ref. [48].In addition, coatings can reduce AADD friction and forming force under dry conditions [50][51][52].Steiner et al. [53] conducted friction test between 1.2379-coated tools and AA5182, and the results showed that the lower the surface roughness of coated tools, the smaller the COF.Abraham et al. [51] further corroborated that the low surface roughness of coated tools is beneficial to reducing adhesive friction of AA5083.The aluminium alloy sheet is affected by the manufacturing process, and the surface roughness also has obvious orientation characteristics.Aktürk et al. [54] proposed that the COF is the smallest when sliding parallel to the rolling direction of AA6111 sheet.However, the conclusions of Liu et al. [55] and Saha et al. [56] are completely opposite to that reported in Ref. [54].Menezes et al. [57,58] believed that the COF is not relevant in the surface roughness, but is relevant in the surface texture of tool.Zabala et al. [59] analyzed the friction behavior between GGG70 tools with different polishing degrees and AA1050 sheets with different degrees of EDT textures under lubrication conditions.The results showed that the COF decreases with the increase of texture degree of aluminium alloy sheet and increases with the increase of tool roughness.Therefore, only combining specific tribological conditions can the influence of surface characteristics on AADD friction be correctly analyzed.

Material properties
AADD friction involves sophisticated elastoplastic deformation of the die-sheet surface.This is closely related to the mechanical properties, microstructures, and material transfer of the contact process.It can be seen from Fig. 5(a) that the surface hardness of aluminium alloys is significantly less than that of tool steel.The plastic deformation of aluminium pin tip gradually increases with the increase of sliding distance s u [17].The scratches during the friction process cause the aluminium alloy detachment from surface, which is easy to adhere to tool (Fig. 5(b)), forming a material transfer layer.The transfer layer on tool surface interacts with the oxide layer on sheet surface, which increases the friction between tool and sheet [43].Hu et al. [60] studied the formation mechanism of aluminium transfer layer on cast iron (CI) and the evolution of the friction system from transition state to steady state through the G3500/ AA6082 dry friction test.Wilson and Sheu [61] proposed that the effective hardness of sheet surface is substantially reduced due to plastic flow.The friction test of Keum et al. [48] indicated that with the increase of surface hardness of aluminium alloy sheet, the COF decreases slightly.Zhao et al. [62] discussed the dry friction mechanism of closed and open friction systems.In a closed system, AA5182 with higher yield strength and lower elongation shows higher adhesion.In an open system, since loose abrasive particles can be separated from the contact interface, adhesive friction is reduced.
Microstructure is another important factor affecting AADD friction.For this reason, Afshin and Kadkhodayan [63] determined the COFs of AA1050 and AA5052 sheets at different grain sizes by Coulomb friction test.The results showed that the COF increases with the increase of grain size.Lu et al. [24,25] established the AA7075 hard phase dissolutionprecipitation coupled friction evolution model (Fig. 6) by analyzing the role of hard phase of microstructure, oxides, and wear debris in friction process.In contrast, Kirkhorn et al. [64] analyzed the influence of tool steel microstructure on sheet forming friction.And they found that there is no direct link between the amount of carbide precipitation and the COF.Since the material properties directly affect the force and  | https://mc03.manuscriptcentral.com/frictiondeformation of contact interface, it is vital for the in-depth analysis of the AADD friction mechanism.

Lubrication
Lubrication can directly change the contact conditions of solid surface.It is an important means to reduce AADD friction.Lin et al. [36] and Keum et al. [48] studied the effect of lubricating oil viscosity on AADD friction.And the results showed that the COF decreases with the increase of lubricating oil viscosity.Yang et al. [44] further studied the influence of oil film thickness and concluded that the COF increases with the decrease of oil film thickness.Meiler and Jaschke [65] compared the lubricating properties of liquid lubricants and dry film lubricants.It is found that the dry film lubricant is evenly distributed on the surface of aluminium alloy sheet during deep drawing process, which is more beneficial to improving the friction conditions of contact interface and the formability of sheet.Because traditional liquid lubricants contain harmful ingredients.Dyja and Więckowski [66] developed a biodegradable liquid lubricant to reduce AA2024 friction.

Friction measurement
Under the complex influencing factors of deep drawing system, the friction phenomenon, law, and mechanism of AADD exhibit large uncertainties.For this, the development of friction measurement methods suitable for deep drawing is of great significance for studying the friction behavior and estimating the COF.Because of the different friction characteristics in different regions, it is currently impossible using a single friction test to characterize the ever-changing sheet forming conditions.Figure 7 summarizes the main friction measurement methods for three typical regions, including flange region, die radius region, and punch radius region.

In-situ friction measurement
The in-situ measurement technology (Fig. 7(a)) can obtain F H and tangential force T simultaneously by installing a force sensor on die surface, and directly determine the μ during the deep drawing process.The existing in-situ friction measurement methods include the probe sensor measurement method (Fig. 8(a)) and the three-axis force sensor measurement method (Fig. 8(b)) [67][68][69].The in-situ measurement can reflect the real COF of flange region, but the installation of sensors exists inherent limitations, and it cannot be installed in the radius region of die or punch.

Pin-on-disk tribometer
The rotary pin-on-disk tribometer (Fig. 7(b)) and the reciprocating pin-on-disk tribometer (Fig. 7(c)) are two common COF measurement methods.Wang et al. [70] improved the cylindrical pin to rectangular pin, which increases the contact area between the pin and disk, and reduces the possibility of the local eccentric load under a small contact area.Dong et al. [71] and Hanna [26] used a reciprocating pin-on-disk tribometer to study AADD friction and aluminium adhesion.Yang et al. [44] used a robot to measure the friction between the tool pin and the aluminium alloy sheet under variable contact conditions.Compared with the actual forming conditions, repeated contact between the pin and disk will change the friction conditions and affect the measurement results.

Strip drawing test
The strip drawing test (Fig. 7(d)) can simulate the friction behavior of flange region.The test uses upper and lower tool blocks, clamps the metal strip under F H , and slides the metal strip along tool surface through T. The calculation method of the μ is shown in Eq. ( 1).| https://mc03.manuscriptcentral.com/frictioncompared the strip drawing test results with the in-situ measurement results and found that the COF measurement results of the two methods are basically the same.Shi et al. [45] used a standard tensile testing machine to build a simple high-temperature strip drawing testing device.Liewald et al. [72] improved the traditional strip drawing test by drilling micro-holes in the tool block, and studied the effect of CO 2 lubrication on sheet deep drawing friction.Han [73] used tool steel and frictionless rollers to clamp the metal strip, and pulled it to slide relative to tool steel.Based on strip drawing test, Kirkhorn et al. [74] developed the strip sliding friction test (Fig. 7(e)) by using a linear motor.The COF calculation in Refs.[73,74] is shown in Eq. ( 2).Different from the actual forming process, strip drawing test does not consider the influence of tangential shrinkage of flange region.

BUT in die radius
The BUT apparatus (Fig. 7(f)) is mainly used to simulate the friction behavior of die radius region.The force of the strip in BUT test is shown in Fig. 10(a), where T 1 is the tensile force, T 2 is the back tension, γ is the contact wrap angle, q is the average contact pressure, and R is the radius of roller [75].From the perspective of force balance, Eq. ( 3) can be established.
where w is the width of metal strip.
After integration, the μ is calculated as Considering the influence of R, the metal strip thickness t, and bending deformation force T b , Eq. ( 5) can be rewritten as Han [73] and Sanchez [76] developed a BUT device with γ = 90°.Fratini et al. [77] used a lever to provide T 2 on the basis of Saha and Wilson [78], which greatly simplifies the structure of BUT device.Bay et al. [79,80] designed a heatable BUT device with a temperature  [82] set up microchannels for the circulation of volatile media on die radius inserts, which expand the application range of BUT devices.Similar to the problems in strip drawing test, the BUT test does not consider the effect of sheet tangential shrinkage on friction.

BUT in punch radius
As shown in Fig. 7(g), BUT test in punch radius shares the same principle as BUT test in die radius.The difference is that one end of metal strip is fixed, and the other end slides around the roller surface under T 1 .The COF calculation method is the same as that of Eq. ( 5).Trzepiecinski [83] used the BUT device to study the variation of punch radius friction with relative elongation of sheet.Since the traditional method needs to calculate the friction force indirectly by measuring the strain of the metal strip, Hao et al. [84] designed "L" and "U" shapes' friction test devices that can directly measure the friction force.

Compound friction test
As shown in Fig. 7(h), the compound friction test is a method for measuring the deep drawing friction that has emerged in recent years.It combines the strip drawing test with BUT test, and can measure the COF of flange region and radius region at the same time.The compound friction test device designed by Dilmec and Arap [85] is shown in Fig. 11.The metal strip is divided into two sections: One section is located in the flange friction region, the other section is located in the radius friction region, and the middle is connected by a force sensor.The test can only be carried out at a very low speed.Evin and Tomáš [86] could complete the friction measurement of flange region and radius region by stretching the metal strip at one time, which not only increases the stretching speed, but also gets closer to the actual forming conditions.But they are not compared with the strip drawing test results or the BUT test results, so the accuracy and reliability of the compound friction test need to be further verified.

AADD friction model
Friction is one of the most important boundary conditions of AADD.However, the analysis in Section 2 shows that the COF in deep drawing is constantly changing due to many factors.In order to deeply study the internal mechanism of AADD friction,

Single-factor
The single-factor friction model is a simple mathematical induction of the law of a single influencing factor.In 2020, based on the H13/AA6111 reciprocating friction test results under boundary lubrication conditions, Dou et al. [29] characterized the relationship between the v, the normal load F H , and the μ, as shown in Eq. ( 7).Keum et al. [48] summarized the laws of five influencing factors through BUT test, and established a friction model considering v, sheet surface roughness and hardness, lubricating oil viscosity, and die radius.

Multi-factor
In order to study the interaction between different influencing factors under complex working conditions, it is necessary to establish a multi-factor coupled friction model.In 2019, Dou and Xia [87] built a friction model with comprehensive load and velocity effects.Klocke et al. [88] coupled the temperature in model, and further refined the friction model related to process parameters.To evaluate the effect of tool coating thickness h(t) variation on the total friction μ(t) evolution, Zhou et al. [89] developed the interactive friction model (Eq.( 8)) according to the results of the ball-on-disk friction test.
where μ a (t) is the initial friction, μ p (t) is the plowing friction when h(t) = 0, and κ 1 and κ 2 are the model parameters.In order to describe the evolution process of the contact interface from boundary lubrication to dry friction μ d (t), based on the Arrhenius equation, Yang et al. [44] established the interactive friction model (Eq.( 9)) in 2021.The contribution of boundary friction μ l (t) and μ d (t) to μ(t) is characterized by the ratio between the non-lubricated area and the lubricated areaξ.
The composition of the friction model proposed by Tamai et al. [90] is similar to that reported in Ref. [44], including a mixed lubrication part and a dry friction part.Hu et al. [60] developed a friction model related to aluminium transfer in pin-on-disk friction test.The model μ(t) can be decomposed into aluminium-CI contact friction μ Al-CI and aluminium-aluminium contact friction μ Al-Al , where ( ) f t is the normalized transfer area.
Compared with that of the single-factor friction model, the friction behavior represented by the multi-factor friction model is closer to the real forming conditions.

Macro-scale
The macro-scale friction model analyzes the friction mechanism of specific internal parameters and specific forming conditions.Based on Tabor's adhesive friction theory [91], Leu [92] established an extended friction model related to real contact area fraction α and strain hardening index n in three-dimensional (3D) stress element in 2009.
  where α = tanh(3p/σ u ), p is the normal pressure, and σ u is the maximum tensile stress.It can be seen from Fig. 13 that the extended model improves the distortion of μ tending to infinity when the Tabor model is close to the adhesion state (α ≈ 1) [91].Because the surface morphology of the die-sheet affects the real contact area A c , Ramezani and Ripin [93] believed depends on the normal load F N and root mean square rate of surface height m 2 , where erf is a function, E is the equivalent modulus, A n is the nominal contact area, and the extended friction model is transformed into Eq.(12).
In order to capture the friction response between AA6111sheet and D2 tool steel, Gearing et al. [94] proposed the friction evolution equation related to p, s u , and hardening/softening function, as shown in Eq. (13).(13) Among them, ŝ is the slip resistance function, μ 1 is the conventional coefficient of Coulomb friction at low pressures, s  is the interface sliding limit under high p, and p cr is the critical pressure.Figure 14 shows that under solid lubricant boric acid, the friction model exhibits good agreement with the experimental results.
In addition, Wilson et al. [95] established a friction model from thick film and thin film to mixed and boundary lubrication states by judging the oil film thickness during deep drawing.In thick and thin On the basis of this model, Darendeliler et al. [96] and Yang [97] introduced Wilson and Sheu's [61] semi-empirical equations about effective hardness, α, and dimensionless strain rate.The τ f in the mixed and boundary lubrication states are modified.Başpınar and Akkök [98] analyzed the application scopes of Sojoudi and Khonsari [99] and Wilson et al. [95], and pointed out that a single friction model cannot cover the wide range of internal and external conditions.
The combination of different models can not only improve the prediction accuracy, but also expand the scope of application.The macro-scale friction model establishes the link between specific forming parameters and overall friction effect, but ignores the effect of local topography changes and contact condition differences on deep drawing friction.

Micro-scale
The tool-workpiece (die-sheet) surface is nominally flat, but due to the presence of rough and uneven asperities at the micro level, contact only occurs at certain points, as shown in Fig. 15(a).The deep drawing friction is caused by shearing and plowing after tool asperities are pressed into the workpiece surface.The micro-scale friction calculation is inseparable from the force of tool asperity and the [106] calculated the frictional force vector F acting on a single elliptical parabolic asperity in 2019.The expression is similar to that of the macroscopic friction model (Eq.( 14)).Equation ( 15) is composed of the plowing part pl c p A n and adhesive part sh c Â  Among them, p pl is the real contact pressure, A c is the real contact area, τ sh is the interface shear stress, n is the unit normal vector, and t is the unit tangential vector.This model studies the variation of frictional force with size, ellipticity, and orientation angle of asperity, but ignores the influence of material accumulation at the front end of asperity, as shown in Fig. 17 where Hol et al. [108,113] and Karupannasamy et al. [114] calculated the μ of a single cylindrical or elliptical parabolic asperity sliding across the workpiece surface during the deep drawing process on the basis of Challen and Oxley [111,112].The micro-scale contact and friction model studies the force deformation process and friction mechanism of the die-sheet asperity, and explains the interface interaction at the micro level, which helps to analyze the friction response changes caused by local contact differences.

Multi-scale
The micro-scale friction model can more realistically and accurately reflect the friction characteristics of deep drawing.However, the model is too cumbersome to be applied to the calculation of large-scale sheet metal forming.For this reason, it is necessary to adopt appropriate methods to expand the model   Greenwood and Williamson (GW model) [115].However, the GW model is based on Hertzian elastic contact theory.It cannot calculate the plastic deformation of asperities.Pullen and Williamson [116] assumed that the asperities on non-contact surface rise uniformly, and the problem was solved by volume conservation and energy conservation.Inspired by Pullen and Williamson [116], Westeneng [117] derived a plastic contact model that replaces the peak height distribution with the ( ) z  in 2001.Since the Westeneng model [117] can describe asperity deformation of any shape and is closer to the real forming conditions, it has been developed rapidly in the past ten years [107,108,113,114,[118][119][120][121][122].The contact between smooth tool surface and rough sheet surface is shown in Fig. 19(a).The sheet surface in the model is identified by bars of equal width.Given the surface height distribution ( ) z  W and p, the energy conservation and volume conservation equations (Eqs.( 20) and ( 21), respectively) are combined using statistical methods to obtain the uniform rising of non-contact surface U L and the mean plane of rough sheet surface d L .Then the α can be calculated by Eq. (22).
Among them, B = 2.8 representing the hardness factor, 1 3 S  following the Von Mises yield criterion, ω is the indentation coefficient, ζ is the energy required to flatten the contact bar, χ is the energy required to lift the non-contact bar, ψ is the energy required to shear bar with relative motion, η is the roughness durability parameter, and z is the surface height.Furthermore, the interface sliding test shows that sliding contact induces junction growth, which promotes the A c of die-aluminium alloy sheet interface to further increase [123][124][125].This is because the increase in the subsurface volume strain of sheet material leads to a substantial decrease in hardness of asperities.The α needs to be combined with the influence of this effect [61,126,127].
After the A c is obtained through the cross-scale contact model, the multi-scale friction model is used to realize the calculation of deep drawing friction from micro-scale to macro-scale.At present, there are two methods for establishing multi-scale friction models: direct accumulation and statistical transformation [107,108,113,114,[118][119][120][121][122].The direct  15)- (18).The cumulative f is divided by normal load F N to calculate macro-scale μ.
The statistical transformation method is based on the distribution function of die surface asperities t ( ) s  , die surface asperity density ρ t , nominal contact length l nom , nominal contact width b, distance between sheet surface and average plane of die asperities δ, and the maximum height of die asperities G max .Using statistical methods, the asp W ( ) Compared with single-scale friction model, multi-scale model fully characterizes the friction evolution process of interface from micro-scale to macro-scale.Solving the shortcomings that micro-scale model is difficult to calculate on large-scale and macro-scale model cannot distinguish local differences.However, multi-scale model is still based on a lot of simplifications and assumptions.And there is a big gap between multi-scale model and actual friction contact.How to improve the calculation efficiency and calculation accuracy of model under the condition which is as close to the engineering practice as possible.It has become an urgent problem to be solved in the research of multi-scale friction model.

AADD friction simulation
As the demand for aluminium alloy parts continues to increase, simulation must be used for quality control and problem analysis in the early stage of product development and later production.In simulation of deep drawing process, the COF of the entire area is usually assumed to be constant according to Coulomb's law, which is significantly different from the real forming conditions of AADD, causing serious calculation errors.Currently, there are two main pathways to solve this problem: constant COF simulation based on COF sub-domain setting and variable COF simulation based on the development of friction model.The two methods have their own advantages.The constant COF simulation contributes to inversely solving the tribological conditions favorable to AADD.The variable COF simulation contributes to improving the prediction accuracy of AADD performance.Section 5 clarifies the characteristics and applications of the two simulation methods in turn.

Constant COF simulation
The constant COF simulation is easy to perform and can be realized by using commercial software such as ABAQUS, ANSYS, LS-DYNA, DEFORM, and DYNAFORM.This method mainly includes the following four steps: (1) Different COFs in different contact areas are set; (2) the forming performance metrics are set to be tested, such as thinning, wrinkling, and cracking; (3) the simulation results are compared, analyzing the influence of COF on forming performance metrics; and (4) the best forming tribological conditions are inversely solved.For this reason, Bouchaâla et al. [18,128] set up different COF in three contact areas of sheet-punch, sheet-holder, and sheet-die, taking the wall thickness reduction rate as test metrics, using the orthogonal test studied the effect of COF on the wall thickness distribution of two aluminium-lithium alloys (AA2198 and AA2090), and determined the COF combination with the smallest wall thickness reduction.In order to improve the quality of AA6182 deep drawing, Shivpuri and Zhang [129] studied the friction distribution optimization design to reduce the risk of wrinkling and cracking in 2009.The division of deep drawing contact area is more detailed, as shown in Fig. 20(a).Based on constant COF simulation, the optimal design of friction distribution is obtained.In addition, constant COF simulation can also be used to study the influence of friction on AADD forming limit, wall thickness uniformity, failure mode, and failure location [19,22].Although constant COF simulation has the above applications and advantages, it does not consider the dynamic response of COF during deep drawing www.Springer.com/journal/40544| Friction process, and the simulation results cannot be directly applied to the engineering practice.

Variable COF simulation
In variable COF simulation, the COF changes in real time, and it is based on the empirical friction model and theoretical friction model, as shown in Section 4. Compared with the constant COF simulation, the simple empirical friction model can be realized through custom settings in commercial software, while the complex theoretical friction model requires the user to write a special program.The empirical friction model that fits the influence of pressure and speed can be input into software, which can directly simulate the variable COF of AADD, such as AA6016, AA6111, and AA5052.Comparing the measurement results of the thickness distribution and springback obtained by simulation and experiment, variable COF simulation results improve the overall prediction accuracy of deep drawing parts [29,87,130].Zhou et al. [89] proposed a Knowledge Based Cloud Finite Element (KBC-FE) simulation technique.By combining the interactive friction model established by Eq. ( 8) with the conventional finite element simulation, the life prediction of coated tool in multi-cycle loading AA5754 can be realized.The macro-scale friction model is established based on Eqs. ( 12)-( 14), which integrates the influence of internal material parameters and external forming conditions.Integrating the friction model into the finite element program can simulate variable COFs from μ d (t) to different lubrication states [93,94,96].The stress distribution of AA6061 sheet after V-bending in dry friction state is shown in Fig. 20(b).Based on multi-scale friction model established by steel, Wiklund et al. [131,132] extended it to AA6016 deep drawing simulation, demonstrating the application potential of multi-scale friction model in AADD variable COF simulation.
In the past decade, with the help of multi-scale friction models that systematically consider the state from boundary friction to mixed lubrication, Hol et al. [108,113,118], Shisode et al. [107,121,122], and Karupannasamy et al. [114] used an in-house software Dieka developed by University of Twente to conduct deep drawing simulation on several typical parts, such as cross-die, top-hat, and cup, and verified the accuracy of multi-scale friction models by comparing with the experimental results.These models provide theoretical support for the large-scale application of TriboForm software.TriboForm can describe the COF dependence of contact pressure, v, plastic strain, and temperature under the given combination of material, surface topography, coating, lubricant type, and amount parameters, and creates a friction model that fits the actual production for the tribological system.References [39,133,134] have shown that the TriboForm friction model is applied to deep drawing simulation of AA5182, AA6016, AL6-OUT, etc., which improves the prediction accuracy of F D , draw-in, major strain, thickness, and springback.This demonstrates its effectiveness in AADD variable COF simulation.Since 2016, there is an extensive collaboration on friction modelling between Volvo cars [135][136][137][138][139][140][141][142], Mercedes-Benz cars [133,143], Ford cars [144], Renault cars [145], Opel cars [5,146], and TriboForm engineering.The involved automotive panels are Volvo's inner door, front door ringframe, A-pillar reinforcement panel, and fender, Mercedes-Benz's door-outer and front fender, Ford's hood inner panel, Renault's trunk lid inner part, and Opel's spare wheel well.The forming simulations and experimental measurements of Volvo XC90 inner door (Fig. 21) indicate that the simulation results based on the TriboForm friction model are in good agreement with the experimental measurement results compared with those of the constant COF simulations [137].This is also confirmed by the simulation and experimental results of Ford Transit aluminium hood inner panel (Fig. 22(a)) and Mercedes-Benz aluminium front feeder (Figs.22(b) and 22(c)) [133,144].However, in 2018, van Beeck et al. [147] pointed out that the prediction accuracy under deep drawing and tensile loading conditions is less because the TriboForm friction model does not consider complex deformation modes.In 2022, Zabala et al. [130] developed a new TriboZone friction model based on the TriboForm friction model.This model can assign TriboForm friction models to different regions of the die to evaluate the influence of local roughness on the deep drawing of AA6016 fender, as shown in Fig. 23.The results showed that TriboZone and TriboForm friction models predict similar results, with local roughness having a moderate impact on AADD.The variable COF simulation developed on the basis of friction model can more realistically reflect the whole process of AADD forming, which contributes to shortening the development cycle and reduce the production cost.

AADD friction control
During the AADD process, due to its adhesion tendency, it is easy to form aluminium "accumulation" on die surface, which deteriorates the tribological conditions www.Springer.com/journal/40544| Friction of AADD.Therefore, in traditional deep drawing process, lubricating oil is used to separate die and sheet to reduce friction and avoid wear.However, most of the industrial lubricants contain harmful ingredients, and the disposal of lubricant waste has caused serious environmental problems.The cleaning before each operation also greatly reduces the production efficiency.In the context of global advocacy of environmental protection, effective utilization of resources, and sustainable development, the development of lubrication-free method suitable for AADD has become an urgent problem to be solved.Section 6 reviews the application of solid lubrication, surface texture, coating modification, and composite treatment methods in controlling AADD friction.
Solid lubrication overcomes the inherent shortcomings that lubricating oil pollutes the environment, and die and part need to be cleaned after deep drawing.It can replace lubricating oil to be used under severe conditions such as high temperatures, low temperatures, vacuum, and heavy loads.Solid lubricants can be divided into soft metals, metal compounds, inorganic substances, and organic substances according to the types of raw materials.Typical materials used as solid lubricants include layered materials such as graphite and molybdenum disulfide, soft metals such as lead and silver, and polymer materials such as polytetrafluoroethylene and nylon.Although solid lubricants have great potential to replace lubricating oils, there are few results in studying their control of AADD friction.In 2017, only Ghiotti et al. [148] studied the effect of three different solid lubricants on the deep drawing friction behavior of AA6016 sheets under high-temperature conditions of 300-400 °C.The prepared solid lubricants include Pulve BND 60A based on boron nitride, Pulve D18A based on molybdenum disulfide, and Bonderite L-GP Aquadag based on graphite.The surface topographies and  scanning electron microscopy (SEM) cross-sections of sheet are shown in Fig. 24.High-temperature friction tests showed that the graphite lubricant has the best performance and can maintain a low COF over a long stroke range, while boron nitride and molybdenum disulfide lubricants are easily peeled off the matrix, which is not suitable for high-temperature forming of AA6016 sheets.The applicability of solid lubrication in different aluminium alloys and deep drawing process remains to be further explored.
Surface texture design is an important approach to controlling AADD friction.On the one hand, the textured cavity can capture aluminium chips to avoid scratches.On the other hand, it can store lubricants to reduce friction.According to different preparation methods, it can be divided into laser surface texturing (LST), discharge surface texture, hammered surface texture, milled surface texture, and photochemical surface texture.Commonly used patterns are circle, ellipse, triangle, wedge, square, and channel; the main parameters include size, depth, spacing, and density.
References [54,[149][150][151][152] have confirmed the positive effect of die or sheet surface texture in reducing AADD friction.However, some researchers have challenged this view.Flegler et al. [153] and Hu and Hu [154] believed that the preparation of texture on die or sheet surface is not only difficult to alleviate adhesion between aluminium and die, but also increases the interface COF of AADD.In addition to the controversial friction control effect, the texture cannot maintain structural stability during long-term use due to wear and aluminium adhesion, and the friction control function is greatly restricted.The proper resolution of the above issues is related to whether surface texture can be applied to mass production of AADD.
It is well-known that coating can be used as a separation layer between die and sheet, so that die can adapt to complex and time-varying tribological conditions.And it can extend the service life of die while improving the forming quality of part.In the AADD process, due to excellent wear resistance and lubricating properties of carbon-based coating, it has received a great deal of attention from researchers [50,52,53,62,71,[155][156][157][158].Hydrogenated amorphous carbon (a-C:H)-based coatings, also known as diamond-like (DLC) carbon coatings, are carbon-based coatings commonly used by AADD.Due to its unique net-like carbon structure, the coating combines the advantages of diamond and graphite, with high hardness and wear resistance.The application of a-C:H coating significantly reduces the COF of AADD and the adhesion transfer of aluminium alloy material in a dry forming process, and realizes the stable production of high-quality aluminium alloy parts without lubricating oil.However, high-temperature friction tests show that the friction properties of a-C:H coatings are temperature-dependent.The anti-friction effect decreases with the increase of temperature.Tetrahedral amorphous carbon (ta-C)-based coating is another commonly used carbon-based coating with similar functional effects to a-C:H coatings.The difference is that when the ta-C coating is in contact, a graphite-like transfer layer is formed at the interface.As a result, the lubricating performance of ta-C coating is better than that of a-C:H coating, and the anti-wear effect is better.On the basis of ordinary carbon-based coatings, the developed tungsten-doped carbon-based Friction 12(3): 396-427 (2024) | https://mc03.manuscriptcentral.com/frictioncoatings can further reduce the adhesion of AADD [71].In recent years, in order to minimize the adhesion and friction of AADD, composite coatings with soft lubricating phase embedded in hard coatings have gradually emerged, such as micro-arc oxidation/graphite nanocomposite coatings, self-lubricating NC/NiBN, and NC/WC:C composite coating [159,160].In addition, the applicability of some conventional coatings has also been verified, and the results show that except for Cr coatings, TiCN, CrN, and TiN coatings are not suitable for AADD [155,161].Compared with solid lubrication, coating modification is a universal surface treatment method.The application research on AADD is more comprehensive and systematic, and its effectiveness has also been confirmed by production practice.
The composite treatment method refers to the friction control method of any combination of three lubrication-free methods of solid lubrication, surface texture, and coating modification.The existing AADD composite treatment method includes surface texture + solid lubrication and surface texture + coating modification.In 2019, Maldonado-Cortés et al. [162] discussed the synergistic effect of microchannel texture and TiO 2 nanoparticles (NPs).The microchannel textures of two orientations on die surface are shown in Fig. 25(a).The results of different combinations of ring-on-block test are shown in Fig. 25(b).It can be seen from Fig. 25 that compared with the die surface without any treatment, microchannel texture or TiO 2 NPs can greatly reduce the COF.Among them, the microchannel texture parallel to the sliding direction has the best friction reducing effect, and the synergistic effect of microchannel texture and TiO 2 NPs will increase or decrease the COF.Tenner et al. [163] studied the friction properties of AADD with rectangular or linear textured ta-C coatings, and the results showed that their friction increasing effect was significant.Contrary to the expected results, linear textured ta-C coatings not only does not reduce friction, but also the COF is higher than that of rectangular texture ta-C coating.Inspired by hydrophobic plants, Tillmann et al. [164] proposed five biomimetic textures of deposited CrAlN coatings, as shown in Fig. 26, which can provide references for AADD friction control.Low friction is not always beneficial to AADD.For example, the punch radius region requires a high COF to avoid cracking.Therefore, the development of a surface composite treatment method that controls local friction characteristics is of great interest to obtain high-quality AADD parts.

Conclusions and perspectives
In conclusion, we first analyzed the important role of friction in AADD and its influencing factors.The main regions to control friction are flange region, die radius region, and punch radius region.The influencing factors include process parameters, lubrication conditions, surface characteristics, and material properties.Then, according to the divided main friction regions, friction measurement methods for As stated above, a significant progress in AADD friction has been achieved over the past few decades.However, there are still a few great challenges.The first challenge is lack of systematic research on cryogenic temperature AADD friction.It is well-known that the strength and toughness of aluminium alloys generally increase at cryogenic temperatures.The elongation at break in liquid nitrogen (−196 °C) is even 100% higher than that at room temperature.As a transformative technology different from traditional cold and hot forming, cryogenic temperature AADD has gradually drawn much attention since 2015.However, cryogenic temperature AADD friction is rarely mentioned in previously published papers.This is mainly because the accuracy of temperature control of cryogenic medias, such as liquid nitrogen, liquid argon, and liquid helium, is not high.Cryogenic medias are difficult to provide a stable cryogenic environment.And force sensors are unable to function normally under these conditions.Therefore, it is necessary to develop a new COF measurement method suitable for cryogenic temperature AADD.On this basis, the development of AADD friction model, friction simulation, and friction control will also face significant transformations.
The second challenge is the insufficient development of AADD theoretical friction model and variable COF simulation.At present, there are few theoretical friction models based on aluminium alloys, and the existing ones mainly focus on macro-scale friction models.But micro-scale friction models and multiscale friction models are almost all based on steel.Due to significant differences between aluminium and steel, it is obviously unreasonable to directly apply the friction model based on steel to AADD.At least, the relevant material properties need to be replaced with aluminium alloys.In addition, the grain size and oxides affect the mechanical properties of aluminium alloys at the micro level.The aluminium chips produced by friction adhere to die surface and change the geometry of asperities.The accurate calculation Fig. 26 (a-e) Biomimetic textures; (f) its reference surface.Note: R z , R z (x), and R z (y) are the total mean roughness, mean roughness at the x axis, and mean roughness at the y axis, respectively.Reproduced with permission from Ref. [164], © Elsevier Ltd. 2017.
Friction 12(3): 396-427 (2024) | https://mc03.manuscriptcentral.com/friction of COF is inseparable from these factors.Until now, they have not been well integrated into the AADD friction model.Because of various deficiencies in the theoretical friction model of AADD, the development of variable COF simulation is greatly restricted.
The third challenge is how to improve the reliability and stability of lubrication-free AADD friction control.Studies have shown that reasonable friction distribution design in AADD is essential for improving the forming limit of parts, maintaining a uniform wall thickness, and avoiding wrinkling and cracking defects.In the lubrication-free method, solid lubrication and coating mainly contribute to "friction reduction", whereas different surface texture can achieve both "friction reduction" and "friction increase".The combination of the three further strengthens the surface texture regulatory effect.However, the reality has proved that these friction control methods are fragile.They are prone to failure due to breakage under severe deep drawing conditions, and large-area coating, texture processing, and manufacturing costs are high.How to balance the above contradictions and prepare a stable, long-lasting, and wear-resistant surface has become the central issue that AADD lubrication-free technology needs to break through in the future.
To address the aforementioned challenges, more continuous efforts and more cooperation especially with researchers working in the fields of tribology, material science, mechanics, physics, and chemistry are required.All in all, it is an inevitable trend of sustainable development for high-performance aluminium alloys to replace conventional steel.AADD friction is a key boundary condition for controlling the forming quality of parts.Its friction law, test method, friction model, and friction control researches show great application potential.The progress and development in this field will continue to attract global attention.

Fig. 1
Fig. 1 Stress and strain states of AADD: I, blank holder region; II, drawbead region; III, inner ring region; IV, die radius region; V, straight wall region; VI, punch outer radius region; VII, punch outer flat region; VIII, punch inner radius region; and IX, punch inner flat region.

Fig. 3
Fig. 3 AADD at cryogenic temperatures.Reproduced with permission from Ref. [34], © The Korean Institute of Metals and Materials 2021.

Fig. 12
Fig. 12 Classification and construction methods of sheet metal deep drawing friction model.

Fig. 13
Fig. 13 Extended friction model based on Tabor model: (a) variation of μ with p/σ u when n is different; (b) variation of μ with n when p/σ u is different.Reproduced with permission from Ref. [92], © Elsevier B.V. 2008.

Fig. 14
Fig. 14 Variation of interface shear stress τ sh of AA6111/D2 with s u and friction model fitting under boric acid lubricated under (a) low p; (b) high p.Reproduced with permission from Ref. [94], © Elsevier Science Ltd. 2001.
. To make up for this shortcoming, Shisode et al.[107] improved the calculation accuracy of model by introducing a stacking factor in 2021.Challen and Oxley[111,112] conducted a slip line field analysis on the deformation of soft flat materials under hard wedge-shaped asperity.The cutting friction coefficient μ cutting , plowing friction coefficient μ plowing , and wear friction coefficient μ wear are described as a function of attack angle θ of wedge-shaped asperity and the shear coefficient f c , as shown in Eqs.

Friction 12 ( 3 )
: 396-427 (2024) | https://mc03.manuscriptcentral.com/friction from micro-scale to macro-scale.Multi-scale friction model has emerged.The evolution processes of sheet surface morphology during deep drawing are shown in Fig. 18.It can be seen that under normal load and sliding friction, the flattening of the sheet asperities leads to an increase in the macroscopic A c .At present, the method of establishing multi-scale friction model is as follows: (1) The process parameters and material properties are input; (2) the flattening model of sheet asperities with the normal load is established; (3) the sliding flattening model of sheet asperities is established; (4) the indentation depth of tool asperities on the sheet surface is calculated; (5) the friction force of single asperity F friction is calculated; and (6) the macroscopic COF is calculated.In deep drawing process, constructing a cross-scale contact model to solve the A c is the basis for calculating the multi-scale friction model.The cross-scale contact model for predicting the flattening behavior of rough surfaces mostly continues the pioneering work of

Fig. 19
Fig. 19 Contact surface recognition and simplification: (a) smooth tool surface in contact with rough sheet surface; (b) contact patches; (c) contact volume; and (d) asperity geometry.Note: δ is the distance between sheet surface and average plane of die asperities.Reproduced with permission from Ref. [108], © Elsevier Ltd. 2014.

Fig. 21
Fig.21 Forming simulations and experimental measurements of Volvo XC90 inner door: (a) wrinkle and fracture of inner door in production; (b) major strain difference between simulations and experimental measurements; and (c) part shape difference between simulations and experimental measurements.Reproduced with permission from Ref.[137], © IOP Publishing Ltd 2016.

Fig. 25
Fig. 25 Surface texture + NP composite treatment method: (a) texture perpendicular to sliding direction (left) and texture parallel to sliding direction (right); (b) average COFs of all texture and NP combinations.Reproduced with permission from Ref. [162], © Elsevier B.V. 2019.

Table 1
Organizational structure of this review.