Experimental and modelling study of interaction between friction and galling under contact load change conditions

The galling process remains one of the least understood phenomena in metal forming. The transfer of material from a work-piece onto the tool surface can cause an evolutionary increase in friction coefficient (COF) and thus the use of a constant COF in finite element (FE) simulations leads to progressively inaccurate results. For an aluminium work-piece, material transfer, which has history and pressure dependency, is determined by a dynamic balance between the generation and ejection of wear particles acting as a ‘third body’ abrasive element at the contact interface. To address this dynamic interactive phenomenon, pin-on-disc tests between AA6082 and G3500 were performed under step load change conditions. The COF evolutions, morphologies of the transfer layer and its cross-section were studied. It has been found that contact load change will disequilibrate and rebuild the dynamic balance and high load will increase the generation and ejection rate of third body and vice versa. Moreover, based on the experimental results, an interactive model was developed and presented to simulate the dynamic formation process of the aluminium third body layer under load change conditions, enabling multi-cycle simulations to model the galling distribution and friction variation.


Introduction
Galling is a form of surface damage due to adhesive wear between two or more sliding solids and is commonly found in metal forming operations resulting in work-piece material adhering to the tool surface [1,2]. This phenomenon occurs frequently in the forming of 'soft' materials such as aluminium sheet metal against steel tooling material, where after repeated operations, a transfer layer originating from the work-piece forms on the tool surfaces [3][4][5][6][7]. This transfer layer may lead to products with low surface quality and damage functional surfaces on the tools. Although the application of lubricant and coating can partly suppress aluminium transfer [5,[8][9][10][11], there is still no effective solution to prevent aluminium transfer during forming. To enable the prediction of galling distributions and friction evolutions within tools and to further predict tool life in multi-cycle loading conditions, there is a fairly urgent requirement to study and model the progress of aluminium transfer. Galling is a system response rather than a material property. It depends on contact conditions, such as counterpart material, surface roughness, sliding distance, contact pressure, and temperature, as well as the contact history, which cause numerous interrelationships and interdependencies. The transfer mechanism has been identified as wear particles that detach from the workpiece and transfer to the counterpart by either adhering as lumps or covering as loose wear particles [9,[12][13][14]. These transferred tribo-materials known as 'third bodies', to distinguish from the two original sliding bodies, are produced by mechanical and chemical interactions of the contact couple during sliding, and can be both macro/micro structurally and chemically different from the source material [14][15][16][17][18]. The chemical composition of the aluminium third body formed at room temperature with steel has been described in the literature as being a combination of aluminium-oxygen solid solutions and hydroxylated materials [19][20][21]. The initial surface roughness of the contact pair was found to be an important trigger for transfer where a high surface roughness may result in severe galling [4,13,[22][23][24]. The formation of a transfer layer with increasing sliding distance can be modelled as two states: 1) the initial running in state, where the mass of aluminium transfer layer gradually increases until stage (2) (S2); and 2) a critical level [13], namely the steady stage, which is characterised by a dynamic balance of the mass/volume [25], the thickness [22,23,26] and the galling area of the transfer layer [4,27]. It was also found that both the formation rate and the saturated volume of the transfer layers increase with increasing contact load [26]. In the early research by Bowden and Tabor [28], adhesive wear was described as the forming and breaking of adhesive junctions, which suggests that tangential stresses may be simultaneously generated with detachment and transfer of material fragments. For the sliding of aluminium against tool steels, the interaction between aluminium transfer wear and friction was commonly observed by the evolutions of both the coefficient of friction (COF) and transfer layer formation [2,5,8,22,23,29]. A holistic interactive study was suggested in the investigation of the relationship between friction and adhesive wear [30][31][32].
Adhesive wear, material transfer, and friction are the three main responses in the dry sliding contact between aluminium and tool steel. The evolution of adhesive wear is a significantly studied tribo-system response. The Holm-Archard equation and its variants have provided great flexibility for modelling wear volumes at the equilibrium state [25,30,[32][33][34][35][36][37], and the transition of wear evolution in the running in state was modelled by Yang [38,39]. Based on these adhesive wear models, the interaction between the responses of friction and transfer were modelled: A statistical model for describing the growth of third body particles or lumps and the generation of adhesion force has been developed [22]. Subsequently de Rooij et al. [23] proposed a model to predict material transfer phenomenon for a single asperity, in which the morphology variation and the interactive resisting force generated by a lump was modelled. The concept of solid third body was gradually applied into galling analysis to holistically investigate the three responses in the tribo-system between the original mating pairs and the transfer layer [25,40,41]. In the third body model [25], the formation of transfer layer was described as a competition between the generation and ejection of wear particles until a dynamic equilibrium is reached. However, although these physics-based models provide insights into the chemical and mechanical nature of galling, the complexities and lack of insight of dynamic forming processes limit their further industrial application.
On the other hand, modelling of the friction evolution caused by galling can be treated as a nonlinear dynamic problem in tribological modelling. Instead of understanding the sophisticated interactions between friction, wear, and transfer generations, dynamic models focus on accurate modelling of mechanical responses in order to model the correct operation of a system. The history and pressure dependencies of friction were addressed in many dynamic friction models [42,43] with several models even specifically designed for sheet metal forming [44][45][46][47][48][49][50][51]. However, these non-linear dependencies were always caused by lubrication, abrasive running in, and the start/stop of the tribosystem rather than galling. Although the interaction between friction and galling has been confirmed in the literature, there are few dynamic models developed to model the formation process of galling. In addition, the conditions of sheet metal forming also provide unique dynamic characteristics compared to other dynamic systems: 1) due to the sudden contact and detachment of tools, rapid change of contact load, or 'load jump', which widely exists in metal forming [52][53][54][55][56]; and 2) the shape complexity of forming tools combined with the flow of work-piece material generates uneven spatial and historical distribution of sliding distance and contact pressure, and thus leads to an uneven distribution of galling and friction 456 Friction 10(3): 454-472 (2022) | https://mc03.manuscriptcentral.com/friction on tools [57]. These characteristics provide challenges both to the existing friction/wear models as well as the previous study of galling mechanisms. Therefore, the development of a holistic model capable of predicting tool damage caused by load-change through the interaction of adhesive wear, material transfer, and friction is essential to accurately predict metal forming processes and significantly improve component quality.
In the present study, the dynamic effects of contact load on aluminum adhesive wear in the running in state are presented. Pin-on-disc tests between AA6082 pin and G3500 disc were performed at step load change conditions to explore the pressure and history dependencies of dynamic transfer mechanisms. Results that show the interaction between friction increase and aluminum transfer were analysed by COF evolutions and micrographics. The validity of an interactive friction model developed in the previous study [58] was investigated and verified to accurately model the tool damage caused by galling incorporating load changes as a driving variable. This model has enabled the prediction of galling area and COF variations under load changing conditions with the formation of an aluminium transfer layer over time.

Materials
Pin-on-disc tests were performed to determine the effect of contact load change at the running in state on aluminium adhesive wear in order to: 1) quantitatively measure its effect on the COF and galling area, and 2) to verify an interactive friction model. The flat pin was made of AA6082 aluminium alloy with a diameter of 2 mm, surface roughness (Ra) of (486 ± 35) nm and hardness of (115 ± 5) HV. The disc was made of G3500 cast iron with surface roughness (Ra) of (126 ± 19) nm and hardness of (209 ± 18) HV, which represented the tool material.

Testing methods
The pin-on-disc experiments were conducted at room temperature with a linear sliding speed of 50 mm/s and the radius of the wear track was 5 mm (Fig. 1). The flat contact between the pin and disc was selfaligned in less than ten laps. As shown by the test matrix in Table 1, the step change of contact load was characterized by stages with a certain sliding distance. Two conditions of contact load change, test 1 with load increase from 2 to 10 N and test 2 with load decrease from 10 to 2 N, were conducted. To obtain clear results of the effects of load change, the sliding distance of stage 1 (S1) was designed to reach approximately the middle of the running in state; and S2 to reach the equilibrium state. For S1, 200 laps of sliding distance under 2 N and 100 laps under 10 N were used. COF evolutions were recorded in real time with an acquisition rate of 160 Hz. Each test condition to generate the COF evolutions was repeated three times. The obtained COF data were smoothed and presented by average values with standard deviations (SDs) of the three repetitions in Figs. 2 and 3. In addition, a series of experiments conducted under constant load ( Table 2) were designed to compare the results with tests 1 and 2. In addition, to calibrate the tests, tests 4 and 6 were conducted to represent the morphology condition at the end of S1 in tests 2 and 1 respectively. Tests 5 and 7 were conducted under the constant loads of 2 and 10 N respectively and were completed at the equilibrium state enabling a comparison with the COF evolutions under load change conditions. The load effect on wear particles was studied by comparing tests 3 (2 N) and 6 (10 N).

Characterisation of galling
Surface morphologies of the cast iron disc were    observed and analysed by the scanning electron microscopy (SEM) with an in-situ focused ion beam (FIB) and the white light interferometry (WLI). The electron beam was performed at 10 kV and the secondary electron signals were collected. The crosssection was prepared by FIB operated at an energy of 30 kV and a probe current of 50 pA. The observation area was chosen as the central line of the wear track to minimise the effect of radius. The galling area fraction covering the cast iron was calculated based on the 3D surface plot generated by WLI. As the original surface is a Gaussian surface, asperities with height of  3 ≈ 500 nm above the mean surface were identified as the transfer layer, with  being the SD of the original cast iron surface. Particles with the major dimension smaller than 500 nm may be neglected by this standard. These smaller particles will be proved to have a very limited effect on the macro-scope galling area and hence are not included in the study.

COF evolution
The COF evolution under load increases from 2 to 10 N is shown in Fig. 2. The COF was low at the beginning (0.18) and gradually increased to approximately 0.3 at the end of S1. Immediately after the abrupt increase of contact load to 10 N, a rapid increase of COF to the value of 0.55 was observed with a steeper slope from 200 to 400 laps than that before 200 laps. Figure 3 demonstrates the results of COF under the load decrease condition from 10 to 2 N. Under 10 N, the COF began with a value of 0.2 and increased to approximately 0.42 at the end of S1. After the contact load decreased to 2 N, the increasing rate of COF had reduced between 100 laps to approximately 570 laps. It should be noted that the COF evolution experiences an unstable period after the decrease of contact load, which has a large fluctuation duration of approximately 500 laps as shown in Fig. 3. Comparing to the COF evolutions obtained under constant contact loads, the change of rate increase before and after load change are clearly presented. In Fig. 2, the COF curve of load change and constant load almost coincide in S1 under 2 N; they separate after 200 laps due to the rapid increase of COF caused by the load increase. The load change system reached its equilibrium at 400 laps, which is between the equilibrium distance of 2 N (780 laps) and 10 N (220 laps). In Fig. 3, in S1 under 10 N, the COF curve shows a rapid increase similar to the curve under the load of 10 N. The mismatch between curves of 10 N and 2-10 N at the initial 100 laps may be caused by system errors between different test batches. After a reduction of the rate increase of COF by decreasing the load, this system reached the equilibrium at a sliding distance of 600 laps, which is between the evolutions under 10 N (220 laps) and 2 N (780 laps). The initial COF and the saturated COF at equilibrium obtained from different conditions were close to the value of 0.18 and 0.55, respectively, and thus they can be considered as constants in the studied load range, which is independent of the contact pressure.   view of the transfer layers is presented by the SEM pictures in Figs. 5 and 6, which show that they were comprised of contact patches and loose wear particles.

Aluminium transfer layer analysis
The material transfer layer formation in the direction of sliding can be clearly observed in both WLI and SEM pictures from ploughing grooves and transfer tracks. Figure 5 shows the SEM and WLI topographies of the cast iron surface at the end of sliding under 2 N (S1(inc)) and later 10 N (S2(inc)) in the load increase test. In S1, small peaks with the average height of 1 μm were generated on the cast iron surface in the direction of sliding ( Fig. 5(a)). A slight transfer layer composed of transfer patches can be observed in the SEM picture at this stage ( Fig. 5(b)). The enlarged picture (Fig. 5(c)) shows the wear layer was formed by individual transfer lumps (dark coloured transfer patch surrounded by bright boundary) and wear particles (bright particles). The transfer lumps appear to be built in an ellipsoidal shape with the major dimension from 10 to 50 μm being aligned in the direction of sliding with micro-scale wear particles scattered around. Overlaps between lumps were rare although were observed in this stage. After sliding under S2 of 10 N, significant height increase of the transfer layer (average of 3 μm) can be observed in Fig. 5(d). Large transfer patches (dark coloured area with major dimensions from 50 to 300 μm in the direction of sliding) can be observed (Fig. 5(e)). It is shown from the enlarged view ( Fig. 5(f)) that, the dark coloured transfer patches were composed of large transfer lumps (major dimension approximately 100 μm). Boundaries between lumps and on the top of transfer patches can be observed, which indicates the formation process of either accumulating or overlapping of wear particles. Scattered small wear particles can also be observed around the transfer patches. Figure 6 shows the SEM and WLI topographies of the cast iron surface at the end of sliding under 10 N (S1(dec)) followed by 2 N (S2(sec)) in the load decrease test. In the WLI picture of S1 ( Fig. 6(a)), a large amount of high transfer layer was generated with an average height of approximately 2 μm. In the SEM picture ( Fig. 6(b)), transfer patches were formed in the direction of sliding with the size and pattern close to the observation of S2 (inc) but with low density and height. In the enlarged picture ( Fig. 6(c)), boundaries on the top surface of the transfer patches formed by overlapping and accumulation can also be observed, which is similar to S2 (inc). After sliding of S2, the height of the largest peaks was close to the condition of S1 (dec), but several small peaks in the range less than 1.5 μm grew at this stage ( Fig. 6(d)). In the SEM picture ( Fig. 6(e)), these layers of small peaks were observed as a bright transfer layer composed of small wear particles that covered the whole wear track. In the enlarged view ( Fig. 6(f)), a large transfer lump (major dimension of 80 μm) can be observed under the layer of small wear particles. This layer particularly accumulated in the edge area towards the direction of sliding as shown in Fig. 6(f) by a purple shadow.

Wear particle analysis
Pictures of wear particles generated under 10 N (test 6, Figs. 7(a)-7(d)) and 2 N (test 3, Figs. 7(e)-7(h)) were captured on the outer boundary of the wear track.  Under 10 N, large wear particles (with major dimensions between 50 and 300 μm) were generated; under 2 N, the single wear particles are small (with major dimensions less than 30 μm) and likely to cluster together (Figs. 7(f) and 7(g)).
Independent of contact load, certain shapes of single wear particles were observed throughout the tests and can be classified into two catalogues: 1) chip shape particles (Figs. 7(a), 7(b), and 7(h)) and 2) typical adhesive wear particles (Figs. 7(d)-7(g)). Chip shape, which may adhere on the counterpart but detach, is characterised by its ellipsoidal or semi-ellipsoidal outline with ploughing grooves or transfer layer on the top surface in the direction of sliding. For example, in Fig. 7(a), a chip-shape wear particle with contours of small transfer lumps can be observed; its former sliding direction can be inferred by both the direction of its outline major axis as well as the grooves and small transfer lumps. In Figs. 7(b) and 7(h), chip shape particles with relatively flat surfaces and shallow ploughing grooves in the direction of sliding when compared to Fig. 7(a) may indicate their top surfaces, shown in the pictures, were adhered on the cast iron surface instead of contacting the counterpart. In contrast, adhesive wear equiaxed particles present irregular shapes with rough regions of typical shear fracture [59]. For the small irregular wear particles observed at 2 N, the edges present a flake-like shape, which is more likely to accumulate together and form loss structures as shown in Figs. 7(d) and 7(f). In Fig. 7(d), a special cluster was observed, which was formed by a chip-shape wear particle in the middle clustered with adhesive wear particles. In Fig. 7(f), a rope-like cluster was formed with different size and type of small wear particle.  enable the observation of the historical formation process of the laminar transfer layers. In the enlarged view ( Fig. 8(b)), the boundary between the cast iron substrate and the transfer layer can be clearly observed in the cross-section area. The cross-section of the cast iron presents homogeneous properties with no clear deformation or crack being observed. In contrast, boundaries between wear particles gives an insight of the deformation history where the wear particle experienced plastic deformed from loose wear particles of irregular shapes shown in Fig. 7 into chip shape transfer lump during sliding. As shown in Fig. 8(b), transfer lumps may be crushed and accumulated compactly and leave small spaces at the edge (e.g., boundary 1 in Fig. 8(b)). Otherwise, lumps may accumulate loosely with large gaps formed between them, which were later filled by small wear particles (boundaries 2, 3, and 4 in Fig. 8(b)). A similar phenomenon can also be observed beneath the top surface in Fig. 8(c), where the boundaries between wear particles extended on the cross section and void spaces were formed by loose accumulation. A schematic diagram of the laminar structure of aluminum transfer layer is shown in Fig. 8(d), in which a sub-layer of fine wear particles can be observed at the bottom of the transfer layer.

Galling area calculation
The results of the galling area at various stages under the load increase and decrease conditions are shown in Fig. 9. It was found that galling area fraction, which is defined by the area of cast iron covered by aluminium transfer layer, is a reliable and feasible parameter of measuring the formation process of a transfer layer as well as modelling the contact area between solid aluminium and its transfer layer. The galling area starts from zero at the beginning and gradually increases to a pressure-dependent saturated value with the tribo-system reaching its equilibrium [4,27]. The saturated galling areas obtained under constant contact load of 2 and 10 N are plotted in Fig. 9 and compared with results obtained from load change tests. In Fig. 9(a), S1 stopped before equilibrium and showed a galling area of 15.6%, which is lower than the saturated value (34.3%) under the same load of 2 N. After sliding at S2 under 10 N when the system reached equilibrium, a final galling area of 71.4% was obtained, which is almost equal to the saturated galling area under constant load of 10 N (70.2%). In Fig. 9(b), S1 stopped before equilibrium under 10 N and showed a galling area of 49.5%. This value is lower than the saturated galling area under a constant load of 10 N (70.2%) but greater than the saturated galling area under a constant load of 2 N (34.3%). After sliding at S2 under 2 N, the system reached equilibrium, and a galling area of 41.1% was obtained. This value is lower than the galling area achieved at S1 but still greater than the saturated galling area under a constant load of 2 N. Figure 10 shows the angular maps of COF evolution from tests 1 and 2. The x-axis is set as the angle from 0° to 360° corresponding to a cycle of rotation of the cast iron disc. Number of laps were plotted in the y-axis. An acquisition rate of 160 Hz was set to generate approximately 100 points per lap. The coloured bar shows the COF. These angular maps show a spatial and historical distribution of aluminium lumps along the wear track. As the COF increase stems from aluminium transfer, a red spot in the angular maps of COF evolution indicates high COF points where a cluster of aluminium patches or wear particles were accumulated at a certain angle on certain laps on the cast iron surface.

COF angular map
2 and 10 N presented different features on the angular maps. As shown in Fig. 10(a) from 0 to 200 laps and Fig. 10(b) from 100 to 350 laps, high COF points generated under 2 N presented a dense but | https://mc03.manuscriptcentral.com/friction short period, which always lasts less than 10° rotation angle. Comparing to Fig. 10(a) from 200 to 550 laps and Fig. 10(b) from 0 to 100 laps, high COF points generated under 10 N present a sparse pattern with a relatively long period. This can be caused by: 1) 2 N was likely to generate small and dense transfer lumps, which is illustrated by SEM micrographics (Figs. 5 and 6), and 2) the small inertia of the weight of 2 N made it easy to generate a signal by a small disturbance on the wear track.
When an individual lump was formed, it was likely to survive and accumulate more wear particles and finally formed a large transfer patch [13,29]. This phenomenon can be illustrated with the angular maps by chains of high COF points formed in the direction of the axis of laps, such as area 1 in Fig. 10(a), which is a cluster of lumps that were initially formed at approximately 45 laps in the angle of 95° under 2 N, grown under 10 N at the same degree until the end of the test. This survival feature is the most common characteristic of the galling phenomenon and can be observed all over the angular maps. Instead, some lumps may not survive during the whole sliding progress. As shown in Fig. 10(a) in area 2, there is a zone of high COF formed at 120 laps from the angle of 110°-250°. This zone disappeared (or known as healing) under 2 N load condition but regenerated at the 10 N load condition, which indicates that lumps may be ejected as wear particles but regenerated by secondary transfer based on the former transfer patches. Also, these mechanisms can continuously be observed through load changes. As shown in area 1 in Fig. 10(a) and area 3 in Fig. 10(b), continuous red lines can be observed from increase and decrease of contact load.

Relation between friction, wear, and aluminium transfer layer
The aluminium transfer layer has a significant influence on friction, wear, and surface topography of the aluminium-cast iron tribo-system. The mechanism in this system is identified as a combination of adhesion and abrasion by the observation of transfer patches and ploughings caused by severe adhesive wear and plastic deformation as shown in Figs. 5 and 6. Friction and wear is generated by the direct contact between solid aluminium and cast iron at the beginning. Contact junctions as initial transfer were formed, which may break by shearing inside the soft aluminium asperities and result in subsequent attachment of aluminium to the cast iron surface, and simultaneously generate friction and wear. Transfer patches can also be formed by adhesion of loose wear particles, which contributed to friction and wear by shearing and pressing. As a result, this initial aluminium-cast iron contact generated a COF of 0.18 (shown in Figs. 2 and 3)   www.Springer.com/journal/40544 | Friction tended to deform plastically, be compressed, and agglomerated into large wear particle clusters (Fig. 7), which may adjust to the velocity difference and partly reduce friction and wear at the interface [60,61]. However, friction may be increased due to stronger bonds between self-contact aluminium and thus gives a high self-mated COF [32]. Also, it should be noted that, although the asperities of aluminium lumps were subjected to a flattening process, and reached stable structures with a pressure-dependent height and galling area, the integral surface roughness increased due to the material transfer and increased the contribution of ploughing friction. Experimental results of COF increasing show that the mixture of adhesive and ploughing friction may play a dominant role in determining friction than simple mechanical interaction. As shown in the COF evolutions in Figs. 2 and 3, COFs were increased to and maintained at 0.55 when the material transfer reached the equilibrium.
The wear rate at the contact interface follows a general adhesive wear model where the initial contact between rough cast iron and aluminium generates a high wear rate on solid aluminium. This wear rate reduced significantly after the soft aluminium transfer layer is formed and gradually polished during the running in stages, which limits ploughing and abrasion. The wear rate finally became constant when the equilibrium was achieved and can be predicted by the Archard's equation [38,39].

Effect of sliding distance
In the aluminium-cast iron system, the formation of the aluminium transfer layer is related to the increasing sliding distance. At the initial stage of sliding, adhesive and abrasive wear are highly active and were observed by the high initial wear rate. Combined with the effects of external force of shearing and pressure, as well as the high adhesion characteristic of aluminium against steel [32,62], the loose wear particles are intended to transfer onto the counterpart by two main methods: 1) transfer against rough surface and 2) transfer by adhesive bonding [29,63]. These initial transfers may trigger secondary transfer by adhering and accumulating loose wear particles on the formed lumps, and further building multi-layer structures as shown in Figs. 5-8. Instead of infinite growth, the formation of aluminium transfer layer will reach a critical condition. In a single lump scale, an aluminium lump may reach a critical size and shape, and be mechanically stable rather than breakdown [23]. However, this mechanical stability may be broken by detachment and ejection. As observations show clear boundary and void spaces between the transfer layer and the cast iron substrate (Fig. 8), as well as the detachment of integral aluminium lumps once adhered on the cast iron surface (Fig. 7), a firm bond between aluminium and cast iron may not always exist. In a macroscopic view, the generation and ejection of loose wear particles and transfer lumps may be active along sliding; attachment and detachment of loose wear particles onto and from the material transfer layer may also exist [6,30,34,64,65]. As revealed by the angular map of COF (Fig. 10), transfer patches were gradually accumulated at certain positions on the wear track by initial transfer and may trigger secondary transfer at the same position. Some transferred lumps may not survive during sliding, but the rough transfer patches they leave can still trigger a further secondary transfer. Eventually, a pressuredependent steady state was reached as the COF, and wear rate and the galling area become stable. As the equilibrium was achieved, the interface morphology and the volume of transfer layer would become unchanged. Redundant wear particles were ejected out of the contact and a dynamic equilibrium of transfer layer was maintained.

Effects of load changing
Another important characteristic of the transfer layer formation process is its pressure dependency, which simultaneously affects the wear rate and transfer rate of the tribo-system. The effect of pressure on wear rate is well modelled by the Archard's equation and its derivations [25,30,[33][34][35][36] where the contact load increase will lead to a rapid wear rate increase, which can be observed in experiments as large quantities and size of wear particles were generated after load increased (Figs. 5-7) [66][67][68]. In addition, large aluminium lumps will be formed from large wear particles under high contact load, which increase both the transfer area and surface roughness and thus increase the possibility of secondary transfer and, furthermore, increase the transfer rate. Under constant loads, the effect of load is concluded as: 1) the saturated galling area increases with contact pressure increase, and 2) the duration of the transfer layer formation process is shortened by increasing contact pressure. Schematic illustrations of the mechanisms under contact load change are shown in Fig. 11. In the load increase condition (test 1), in S1 under 2 N, small wear particles were generated under a low wear rate, which led to a slow formation process of the transfer layer. The formed transfer layer had low height and small transfer patch (Fig. 5) and was unlikely to trigger further transfer, which caused the slow increase of COF in this stage (Fig. 2). In the S2 under 10 N, with higher energy input on the contact, the detachment of aluminium became more severe. The wear particle size dramatically increased and led to a wear rate increase. Large wear particles were likely to adhere on the initial transfer patches formed at 2 N by secondary transfer processes as shown in Fig. 10. Large transfer lumps were built and gradually accumulated loose wear particles and finally formed a dense transfer layer (Fig. 5). The galling area and COF experienced a steep increase in this stage and finally, the tribosystem reached equilibrium with a saturated condition under 10 N, which is indicated by the equality of the saturated galling areas in Fig. 9(a).
In the load decrease condition (test 2), in S1 under 10 N, combined with a high wear rate, large wear particles were generated immediately and a relatively dense transfer layer with a galling area of 49.5% at the end of S1 was rapidly formed (Figs. 5(b) and 9(b)). Consequently, COF experienced a rapid increase under 10 N. The COF began at 0.2 and increased to 0.42 within 100 laps of sliding. After a load of 2 N was applied, small wear particles were generated, which gradually replaced the large particles generated under 10 N by ejection, and eventually dominated the transfer on cast iron surface. The transfer of small wear particles was more likely to be triggered by the large aluminium lumps formed under 10 N through the www.Springer.com/journal/40544 | Friction mechanism of secondary transfer which caused a complete change of the morphology of the transfer layer (Fig. 6) with a galling area of 41.1% ( Fig. 9(b)) at the end of S2. This drop of galling area indicates a self-healing process occurred after the load change. In galling phenomenon, healing is reflected by removal of the formed transfer layer and reset of a new stable surface. When the contact load changed from high to low, the transfer layer might experience a process of self-mating to the low contact load, which led to a morphology change with the reduction of the galling area. This process may include recovery of the elastic deformation inside of the transfer lumps formed at high contact load [52], polishing/flattening the high asperities of aluminium lumps, accumulating small wear particles and ejection of unstable large transfer lumps. The increase of COF was largely reduced under S2, and due to the active evolution of the morphology, pronounced oscillations of COF were recorded during this healing process (Fig. 3). From friction measurements, it was found that the healing process under the contact load of 2 N when dropped from 10 N, required approximately 470 laps sliding distance over the cast iron surface. The final galling area at equilibrium was between the saturated galling area of 2 and 10 N, which indicates some of the aluminium lumps formed under high contact load may survive.
The change of contact load will lead to a rapid change of source rate (   s ), which will simultaneously rise or reduce the ejection rate (   e ) and further influence the instantaneous volume of the transfer layer (   i ). At the load increase condition, in S1 under 2 N,   i gradually increases towards the equilibrium with the converging of   s and   e to a constant at a relatively low rate. When the load of 10 N is applied, this running in process is replaced by a faster process of converging where   s jumps to a high value due to the rapid wear rate increase and is followed by an increase of   e . When      s e , the equilibrium (   i = 0) occurs. At the load decrease condition, in S1 under 10 N,   s begins at a high level and thus generates an initial steep increase of   e . After load decreases to 2 N,   s and   e are reduced to a low rate generated at 2 N and finally reach the equilibrium slowly. Based on the results and discussions, three conclusions can be drawn: 1) an increase of contact load will result in an increase of the source rate, the formation rate of transfer layer and the saturated galling area and vice versa, and 2) if the decrease of the saturated galling area caused by the decrease of the corresponding contact load was lower than the already formed galling area, the galling area will decrease by self-healing process. Otherwise, the galling area will continue to increase. 3) COF will continue increasing under any contact load until a saturated value; the rate of increase depends on the contact load.

Interactive friction model
An interactive friction model was established to predict evolutions of COF and galling area considering the interdependent relationship between friction and galling wear for this aluminium-cast iron tribo-system [58], as expressed in Eqs. (1)- (8).
As the aluminium transfer layer is formed on the surface of cast iron, the contact condition at the interface transforms from aluminium-cast iron contact to the combination of aluminium-cast iron contact and aluminium-aluminium contact, leading to the COF gradually increasing from   Al CI (0.18) to   The model parameters of the above equations can be determined according to the calibration of experimental results under constant load conditions against predicted results made by the interactive friction model, as shown in Table. 3. The experimental results of load change tests, i.e., load increase and decrease, are then compared with the modelling results and close agreements of COF evolution and galling area are achieved, as shown in Fig. 12. The formation rate of the transfer layer directly affects the evolutions of COF and galling area. Rapid changes of COF and galling area evolutions are modelled for both an increasing ( Fig. 12(a)) and decreasing ( Fig. 12(b)) contact load condition. In Fig. 12(a), the modelling results show the rapid increase of COF and galling area under load increase condition from 2 to 10 N, which reaches the steady state earlier than under a constant load condition of 2 N. In Fig. 12(b), the modelling results show a decrease of the changing rate of COF evolution and a reduction of galling area caused by a decrease of contact load from 10 to 2 N. These modelling results are compared with results modelled under constant loads, between which the effects of load change are clearly presented. Experimental results are presented in scatter diagrams with SDs showing a good agreement being observed, which proves that the developed interactive model is sufficiently robust to predict friction evolution and galling wear under load change conditions.
To study the effect of contact load change, a series of modelling conditions were designed. Two stages of load with nine conditions were set: in S1, the load gradually decreased from 10 to 2 N with a sliding distance of 200 laps; in S2, the load increased from 2 to 10 N with a sliding distance of 600 laps. The modelling results of COF and galling area are shown in Fig. 13. In Fig. 13(a), the variation of the rate increase of COF evolutions caused by contact load change before and after load changing can be observed, where high contact load will lead to an increased rate of COF and vice versa. Finally, with continuous sliding, the COF evolutions converge to the saturated COF of 0.55 at the steady state. Figure 13(b) presents the load changing effect on the evolution of the galling area. According to galling area evolution, not only the rate increase but also the saturated galling area are affected by load change. In tests 1-4, due to the high contact load at S1, the galling areas generated at S1 were already greater than the saturated galling areas of the contact load of S2, which leads to self-healing processes in S2. From tests 6-9, as the saturated galling areas of S2 are not reached by S1, the final galling areas were dependent on the saturated galling area of the contact load under S2. Test 5 with a constant contact load of 6 N through two stages separates these two groups.  Table 4. Clear changes of the increasing rate of COF and galling area before and after load change can be observed with contact load of S2 gradually increasing from lower to higher than S1.

Conclusions
In this paper, experiments with a step change of contact load were conducted between AA6082 and G3500 to investigate the galling conditions experienced in metal forming operations. It has been found that rapid changes in the contact load result in rapid changes in the evolutions of transfer layer formation and COF. It was also found that the pressure and history dependency of transfer layer and COF which was discovered under constant load condition was also applicable for load change conditions. In addition, a new phenomenon was found in this study, where the formed transfer layer may partly survive after a reduction in contact load and thus affect the final galling area. A mechanical-based model for predicting galling area and COF evolution under load changing conditions has been described in the paper and showed reasonable agreement when compared to the experimental results. This model could therefore be used to predict tool damage caused by galling in aluminium metal forming processes, in which the multi-cycle operations with long sliding distance and rapid load changes are common. As galling is one of the most significant tool damage phenomena in aluminium forming, the successful modelling of dynamic galling will improve the prediction of tool life and assist in identifying critical failure locations on tools.
The obtained findings are summarised as follows: 1) The transition state of aluminium-cast iron tribosystem is determined by the competition between the generation and ejection of loose wear particles or third body at the interface. When equilibrium is achieved, the generation rate decreases and achieves dynamic equilibrium with the increasing ejection rate.
2) Contact load change will disequilibrate and rebuild the dynamic balance between generation and ejection of wear particles or third body. High load will increase the generation rate and ejection rate of third body and vice versa.
3) In the running-in period, the saturation level and formation of the transfer layer are pressure dependent, where a high contact pressure will reduce the transition period and increase the saturation transfer volume at the steady state and vice versa.
4) The decrease of contact load may lead to a period of self-healing of the morphology where a series of secondary transfer mechanisms were triggered and a mixed transfer layer of aluminium lumps and fine equiaxed particles were formed, which resulted in interactive oscillations of COF evolution and a partial decrease of galling area.
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