Determination of lubricating behavior of resin during the sliding process of unidirectional prepreg

In this paper, the lubrication behavior of resin during the molding process of unidirectional prepreg materials was scrutinized using a custom-made device. The thickness of the resin between prepregs under various conditions was calculated using Inverse Hydrodynamic Lubrication (IHL) theory to elucidate the lubrication mechanism. This calculation was confirmed by examining the surface morphologies of the prepreg and employing Digital Image Correlation (DIC) techniques for validation. Furthermore, the effect of unidirectional fiber orientation on the process of inter-ply sliding was quantitatively analyzed through the combined roughness. The study showed that factors such as sliding velocity, normal pressure, and fiber orientation play a key role in the lubrication mechanism. The lubrication behavior of unidirectional prepreg transformed to mixed lubrication under specific conditions. The results in our study of the lubrication mechanism have significant implications for the refinement of molding process and the enhancement of numerical simulations of unidirectional prepregs.


Introduction
Over the past few decades, carbon fiber reinforced plastic (CFRP) has emerged as a highly promising material within the aerospace industry, primarily due to its exceptional lightweight properties and high-strength characteristics.Nonetheless, traditional CFRP manufacturing techniques such as hand lay-up have been limited due to their inefficiency, low-quality outcomes, and labor-intensive nature.In response to these limitations, automated molding methods such as hot press-forming have been introduced into the manufacturing process.During this process, prepreg sheets are fabricated through automated layup technologies, subsequently formed to designated shapes under applied pressure [1].However, some defects like wrinkling and fiber misalignments may be produced in this molding process, which can lead to reductions in the mechanical properties of the final product [2,3].Researchers believe that the behavior of inter-ply slipping plays a pivotal role in defect generation [4][5][6].Therefore, it is necessary to investigate the inter-ply slip behavior to minimize the occurrence of defects.
Currently, the Stribeck curve serves as a primary method for investigating the inter-ply slip behavior of prepregs [7][8][9][10], which defines the lubrication behavior by the ratio of the film thickness to the surface roughness.Many researchers hold that the inter-ply slipping behavior of prepregs conforms to the hydrodynamic lubrication behavior in the Stribeck curve [10][11][12].Within hydrodynamic lubrication, the friction coefficient of the prepregs is linearly correlated with the Hersey number, which is determined by the viscosity, velocity, and pressure.Zhang et al have investigated the lubrication of fabric prepreg, employing a hydrodynamic lubrication model to simulate prepreg interaction during manufacturing, highlighting the key role of resin viscosity, fiber orientation, and surface texture [11].Pasco et al conducted an in-depth analysis of the inter-ply slip of fabric and unidirectional prepregs, uncovering significant differences in lubrication behavior between these materials.Their study revealed that unidirectional prepregs adhere to a hydrodynamic lubrication model, where the friction coefficient increases with sliding velocity [10].
Nevertheless, some researchers argue that the inter-ply slipping behavior of prepreg cannot be ascribed to hydrodynamic lubrication mechanisms.Thije et al [6] have developed models for the slip formation of prepregs using a simplified Reynolds equation, thereby describing thickness variations of the fluid layer.They observed that lubrication transitions from the hydrodynamic lubrication to the mixed lubrication as slip velocity decreases.Rashidi A et al have conducted a series of investigations into the inter-ply slip behavior of fabric prepreg, utilizing a designed testing device to study the slip behavior between fabric prepreg layers and its influencing factors [13,14].Through calculations of the inter-ply resin thickness, they discovered that changes in conditions such as normal pressure could change the inter-ply slip behavior from hydrodynamic to mixed lubrication.Brunetière et al explored the lubrication behavior of carbon fiber tows, which evaluated the surface morphology of the samples and explored the lubrication behavior under different conditions [15].Their study found that hydrodynamic lubrication in carbon fiber tows only occurs under high sliding speeds (several meters per second), leading to the inference that mixed lubrication is the predominant state during the forming processes of composite.
An increasing number of researchers believe that the behavior of prepregs during the forming process is mixed lubrication.However, existing researches have centered on fabric prepregs or carbon fiber bundles, with an absence of investigation into the inter-ply resin thickness and lubrication behavior of unidirectional prepregs.Additionally, there is a lack of validation for the calculated results of resin thickness.Moreover, the fiber orientation is a significant characteristic of unidirectional prepregs.But there is a lack of quantitative evaluation of the effects on lubrication behavior.This study substantiated the key role of the resin in the process of inter-ply sliding using a custom-made device.The thickness of the resin layer between prepreg was determined through IHL theory.To validate the accuracy of calculations, the results were verified with surface morphology and the DIC system.The impact of unidirectional fiber orientation was characterized by the combined roughness.And lubrication behaviors of prepreg resin under different conditions were studied.

Materials
The M21/UD194/IMA unidirectional prepreg (Hexcel, USA) was used in this paper.The prepreg thickness is 0.187 mm.Before use, the prepreg is frozen and sealed in a bag to prevent the resin in the prepreg change its properties because of curing.

The inter-ply slipping behaviors of prepregs in the hot-press forming process
The frictional characteristics of the prepreg are inherently tied to the sliding velocity.Hence, a prior analysis of the inter-ply sliding velocity of the forming process is imperative as a preliminary step in determining the experimental parameter range.
The preforming process was carried out as illustrated in figures 1(A)-(D).Initially, the prepreg was positioned onto the die, after which the blank holder was lowered to apply a consistent clamping force on the prepreg and initiate the heating process.To prevent any sagging of the prepreg during heating, the mold core was elevated to align flush with the mold on both sides.Once the temperature reached the predetermined set temperature and stabilized, the punch was lowered, pressing the prepreg into the desired shape.
In the flange section (Zone I, figure 1(C)), the blank holder applies pressure to the prepreg sheet and induces a rubbing motion between them.This frictional contact imparts tension to the prepreg sheet in the horizontal direction, ultimately enhancing the quality of the forming process.As for the crown (Zone III), both the punch and the core mold exert pressure on the prepreg sheet, effectively securing it in place.In the flange area (Zone I) and the web portion (Zone II), the prepreg sheet experiences in-plane slippage while undergoing the forming process.
At the corners marked as a and b in figure 1(E), the prepreg sheet experiences bending and deformation.As illustrated in the figure, the arc lengths of the outermost and innermost layers (designated as L O /L i and L O ¢/L i ¢) within the prepreg sheet are not equal.The variance between these arc lengths represents the intended slip distance.To illustrate, for the corner , a the inter-ply slip distance can be calculated as follows: where L D is ideal slip distance, mm; R o and R i are the radii of the outermost layer and the innermost layer respectively, mm.
Because the difference between the radius of the outermost layer and the innermost layer is the thickness of the prepreg sheet.Therefore, in the web (Zone II), the slip distance caused by the corner a is where T is the thickness of the prepreg sheet, mm.
As can be seen from figure 1(E), the outermost layer at the corner a is the innermost layer at the corner b in the hat stringer.Therefore, the slip distance of the prepreg sheet in the flange (Zone III) is: When the two corners are the same, the slip distance of prepreg sheet in the web is zero.The velocity of the inter-ply sliding in the web and flange is: where v is the velocity of inter-ply slip, mm min −1 ; t is the time of the hot press-forming process, min.Given the geometric characteristics and forming duration of the typical hat stringer, a velocity range of 0.1-1 mm min −1 was chosen for this investigation.Consequently, the experiments were conducted at three distinct velocities: 0.1 mm min −1 , 0.5 mm min −1 , and 1 mm min −1 .

Inter-ply sliding device
Illustrated in figures 2(A)-(B), the inter-ply slip device was comprised of a pressurizing system, a heating system, and a fixture.secured to both sides of the central fixture.These samples make contact with the adjacent specimens on the left and right fixtures, maintaining a consistent contact area of 100 mm by 100 mm throughout the experiment.The device, based on the pull-through principle, was designed with reference to the device by Rashidi and other researchers [7,14,16], while incorporating modifications that expanded the test area to mitigate edge effects, thereby improving the accuracy of our results.The device employed a flexible metal plate, which connected to a tensile testing machine (ETM 204C, Wance Testing Machine Co., Ltd).The flexible metal plate served to transmit the cylinder's normal force evenly, thereby preventing any non-uniform pressure distribution within the fixture.
Figure S1 showcases the viscosity measurements of the prepreg material, obtained through a rotational rheometer.Analysis of the data reveals that the prepreg's viscosity reaches its minimum between 75 °C and 110 °C.In light of the observed viscosity trends and considering the prepreg's behavior under actual production conditions, we determined 75 °C to be the most appropriate experimental temperature.

Calculation of resin thickness in prepreg
This paper employed the IHL theory to calculate the thickness of the resin between prepreg [13,[17][18][19].Throughout the slip process, the resin filling the space between the two prepreg interfaces can be considered an isothermal and incompressible viscous fluid.Given the exceedingly thin nature of this resin layer between the prepreg, its thickness was estimated using a simplified one-dimensional Reynolds equation: where, h is the thickness of the fluid, m; p is the hydrostatic pressure, Pa; h is the viscosity of the fluid, Pa•s; v r is the velocity in the y direction, m/s.After integrating of equation (1), it may be rewritten as: where, h 0 is the minimum thickness of resin in the y direction, m.Pressure is applied to the prepreg through the fixture, and the resulting pressure distribution curve is illustrated in figure 3. Examination of the curve reveals that pressure initially increases, then decreases.At the central point of the fixture, the pressure remains constant.These observations indicate the presence of specific points on the pressure curve where the first derivative is zero (point A) and the second derivative is zero (point B). / ¶ ¶ = As the viscosity h and velocity v r are not zero, it can be obtained: By quadratic integration of equation ( 6), it can be obtained: / ¶ ¶ = Because the thickness gradient of the resin is obviously not zero, it can be obtained: Substitute equation (10) into equation (7), it can be obtained: So, h A can be expressed as: Substituting equation (11) into equation (7), the relationship between resin thickness and pressure can be obtained: According to equation (13), the thickness of the resin can be calculated as long as the first derivative of the pressure, viscosity, and slip velocity are determined.

Determination of pressure in prepregs
Pressure and its distribution are crucial parameters for calculating the resin thickness.In this study, the finite element simulation was employed to obtain the pressure values.Within the finite element simulation process, the prepreg was represented by the DefGen UMAT subroutine, which was developed by the Bristol Composites Institute [20,21].
The finite element simulation involved modeling both the fixture and the prepreg separately, as depicted in figure 4(A).The fixture was represented as steel: an elastic modulus of 190 GPa and a Poisson's ratio of 0.3.The material parameters for the prepreg were derived from M21 properties, which were integrated into the DefGen UMAT subroutine.The fixture had dimensions of (100 × 100 × 20) mm, while the prepreg measured (150 × 110) mm, with the long side oriented in the Y-axis direction.
The boundary conditions for the finite element simulation are outlined in figure 4(B).A normal force with a value of 500 N was applied at the center of the fixture as the normal pressure.All degrees of freedom on the lower surface of the prepreg was constrained, while the upper surface was unconstrained.The fixture was allowed one degree of freedom in the Z-axis direction, perpendicular to the prepreg surface.

Characterization of surface morphology of sample after slip
The surface morphologies of the prepregs under various conditions were examined using a scanning electron microscope (SEM, JCM-6000 Plus, JEOL Ltd).To maintain the unchanged surface morphology of the prepregs during both preparation and observation of the sample, the experimental samples were stored at room temperature for 50 days.

Verification of changes of resin thickness between prepregs
Figure 5 illustrates the resin within the prepreg effectively separating the fiber layers.This behavior of the prepreg differs from traditional Coulomb friction and aligns with the principles of fluid lubrication.Identifying the thickness of the resin layer during prepreg slip is crucial for characterizing the specific lubrication type.In this study, the thickness of the resin between the prepreg layers during the slip process was investigated using a digital image correlation system (DIC system, VIC-3D SYSTEM, Correlated Solutions, Inc.).
The DIC system (figure 6(A)) is capable of capturing alterations in speckle patterns on the sample's surface, providing data on displacement, strain, velocity, and other parameters.As depicted in figure 6(B), this paper utilized the DIC system to measure the gap between the fixture under varying conditions, indirectly determining the thickness changes of the inter-ply resin to validate the calculation results.Before testing, the inter-ply slip device and DIC system were calibrated with a level to prevent any errors caused by tilting.Reference points were marked on the fixture, and the DIC system (figure 6(C)) was employed to measure the distance between these reference points.If the thickness of the resin varies under different conditions, the distance between the reference points changes accordingly.
Four groups of reference points were marked on the fixture.The positions of reference points are shown in figure 7.With each slip of 0.1 mm, the DIC system captures a set of images.During image processing, the DIC system's software established a spatial coordinate system based on the images of the calibration plate, ensuring precise and accurate measurements.
The coordinate value of the reference point could be obtained through DIC system software processing, and the distance of the reference point could be calculated.Due to the stop block in the z-axis direction (figure 8), there was no additional error in the distance in the z-axis direction in each experiment.The distance in the z-axis direction was composed as follows: where d z is the distance in the z-axis direction; d f is the distance of fixture; t p is the thickness of prepreg.
According to equation (14), the difference in point distance corresponded to the variation in prepreg thickness at different sliding velocities, in other words, it represented the change in resin thickness between the prepreg layers.In the measurement experiments conducted using the DIC system, three sets of samples were measured under each experimental condition, and the average value was subsequently calculated.

Determination of surface roughness of prepreg fibers
To establish the lubrication form of the resin between prepregs during the inter-ply slip, it is essential to determine the roughness of prepreg under various conditions.Before measurements, the prepreg's surface was prepared by removing the surface resin to expose the fiber surface.The following steps were undertaken for sample preparation: The prepreg was affixed to the fixture, and the sample's surface was cleansed with acetone until the epoxy resin had been entirely removed, as illustrated in figure 9.For roughness measurement, a white light interferometer (Mahr LD130, Mahr Inc.) was utilized.The dimensions of the prepreg samples with the matrix removed are (35 × 20) mm.Measurements were conducted on three samples in each direction, and the results are presented as average values.
The calculation method of combined roughness of upper and lower surfaces of prepreg is shown as follows [22,23]: where R a,1 and R a,2 are the roughness of upper and lower surfaces, μm; R a ̅ ¢is the combined roughness, μm.

Effect of resin on the behaviors of inter-ply slip
Following the fluid-lubricated theory, it was essential to investigate the impact of the resin in the prepreg on the slip behavior.Thus, under identical conditions, the inter-ply slip was tested on both the prepreg sample and the prepreg sample with the resin removed.Figures 10(A) and (B) display the prepreg sample and the corresponding specimen with the resin removed, respectively.Figure 10(C) shows the inter-ply slip resistance between the prepreg sample and the treated sample in 75 °C and 0.5 mm min −1 .It can be seen that the inter-ply slip resistance of the treated sample is much greater than the prepreg sample.The results demonstrate that, at the selected experimental temperature of 75 °C, the resin serves a lubricating function, substantially diminishing the frictional resistance among prepreg layers.

Calculation of resin thickness during the inter-ply slip
As per equation (13), the viscosity of the resin is one of the essential parameters needed to calculate the thickness of the resin.Figure 11, obtained from the supplier, illustrates the resin's viscosity-temperature relationship, demonstrating a viscosity of approximately 191.36 Pa•s at the experimental temperature of 75 °C.Figure 12 presents the resin pressure distribution within the prepreg as simulated by finite element analysis, indicating the presence of edge effects.To improve the accuracy of our findings, we chose the pressure distribution at the midpoint parallel to the Y-axis as the basis for our calculations concerning the prepreg.
Equation (13) can be treated as a cubic equation, with the first derivative of resin pressure considered as the independent variable and the thickness of the resin as the dependent variable.A program utilizing the Newton-Raphson method was developed using Anaconda3 software to solve the equation.The iteration was initiated with a starting point of 5 × 10 -5 m, and the tolerance value for the iteration was set at 10 -15 m.
Figure 13 illustrates the variations in the calculated thickness of the inter-ply resin layer across different sliding velocities.It is evident from the figure that the resin layer thickness escalates as the sliding velocity increases.This trend is a consequence of the intensified hydrodynamic effect at elevated velocities, which augments the volume of resin infiltration and thus the layer's thickness [14,17].To simplify the calculation  process, an average value for the resin thickness across various positions was computed, with the corresponding results summarized in table 1.

Verification of the trend of resin thickness variation
The inter-ply slip experiment employed the pull-through method, as depicted in figure 14(A).This approach involved embedding the prepreg with a smaller area into the prepreg with a larger area under normal pressure.As the smaller prepreg moved forward, it pushed the resin of the larger prepreg, causing it to accumulate ahead.Figure 15 displays SEM images of resin accumulation at different velocities.It's evident that resin accumulation gradually increases as the velocity decreases.This suggests that at lower sliding velocities, more resin is pushed out, resulting in a greater volume.Essentially, the slower the velocity, the deeper the embedded depth of the prepreg.Since, under the same temperature and pressure, the thickness of the fiber layer in the same prepreg can be considered constant, different embedding depths indicate different resin thicknesses between prepregs.A deeper embedding depth means a thinner resin layer between prepregs.This observation aligns with the morphology of resin in SEM images and confirms the direct proportionality between resin thickness and velocity, consistent with the calculation results.
Figure 16 illustrates the difference in resin thickness measured by the DIC system and the theoretical calculations at different sliding velocities.VD0.1-0.5 represents the difference in thickness between 0.1 mm min −1 and 0.5 mm min −1 , while VD0.5-1 represents the difference in thickness between 0.5 mm min −1 and 1 mm min −1 .The proximity of the difference in resin thickness measured by the DIC system to that calculated theoretically indicates that the IHL theory is effective in calculating resin thickness during the inter-ply slip   process.It also confirms that resin thickness is directly proportional to sliding velocity.This substantiates the accuracy of the theoretical calculations for IHL theory.
As presented in table 2, the roughness of the prepreg was computed using equation (15).The relationship between resin thickness and lubrication behavior can be defined by equation ( 16) [21]: where h̅ is the average thickness of the resin, μm; Λ is the film thickness ratio.Typically, lubrication behavior is classified as hydrodynamic lubrication when Λ > 3. When 1 < Λ < 3, it's considered mixed lubrication.The finite element simulation images depicting prepreg pressure under varying normal pressures (0.01,0.05 and 0.1 MPa) are illustrated in figure S2.The calculation results illustrating prepreg theoretical thicknesses under different normal pressures are presented in figure S3 and summarized in table S1.Table 3 illustrates the calculated results of the film thickness ratio at different slip velocities and normal pressure.The film thickness ratio is influenced by both slip velocity and fiber orientation.As per the tabulated data, when the normal pressure is maintained at 0.05 MPa and the velocity at 0.1 mm min −1 , the film thickness ratios for the 0°/45°and 0°/90°orientations are less than 3. Similarly, with a normal pressure of 0.1 MPa and slip velocities of 0.1 mm min −1 and 0.5 mm min −1 , the film thickness ratios for the 0°/45°and 0°/90°orientations remain below 3.These results suggest that the intermediate resin region operates under mixed lubrication under some conditions.Hence, the lubrication behavior of resin in unidirectional prepreg cannot be solely classified as hydrodynamic lubrication.In mixed lubrication, there is a probability of fiberto-fiber collisions within the prepreg, contributing to increased friction.

Conclusions
The lubrication behavior of the inter-ply resin in unidirectional prepreg materials significantly influences the frictional forces and processing characteristics during composite manufacturing.This paper established the  pressure distribution of resin through finite element analysis, delineating the compressive state of the prepreg.The theoretical thickness of the resin was computed utilizing Inverse Hydrodynamic Lubrication theory under varying conditions.Validation of theoretical thickness was innovatively conducted using Digital Image Correlation systems in conjunction with surface morphology analysis.Results demonstrated an increase in resin thickness with sliding velocity duo to the hydrodynamic effect.Furthermore, a combined roughness parameter was introduced to quantitatively analyze the effect of unidirectional prepreg fiber orientation on lubrication behavior.At excessive normal pressure, lower velocity, and specific layup angle, the possibility of fiber collision increases, thus modifying the lubrication behavior and augmenting inter-ply sliding resistance.These results are expected to guide process optimization and finite element modeling in the molding of unidirectional prepregs.Subsequent studies aim to extend these results to diverse types of prepregs and different temperatures, thus expanding the applicability of our research methods in the field of composite materials.

Figure 1 .
Figure 1.(A)-(D) Deformation of the prepreg during the process of hot press-forming (I: blank holder; II: Die; III: Punch; IV: core mold; V: industrial camera); (E) analysis of inter-ply slip of hat stringer preforms.

Figure 2 (
C) illustrates the prepreg specimen configuration within the experimental apparatus.Specimens positioned on the left and right fixtures are 140 mm in length and 100 mm in width, with 20 mm at each end designated for fixture attachment.Two prepreg samples, each 150 mm long and 110 mm wide, are

Figure 2 .
Figure 2. (A) Schematic diagram of the inter-ply slip device; (B) Picture of the device; (C) The fixture of prepreg.

Figure 4 .
Figure 4. (A) Models in finite element simulation; (B) boundary conditions in finite element simulation.

Figure 6 .
Figure 6.(A) The DIC system; (B) image collection using the DIC system; (C) schematic diagram of measurement process of DIC system.

Figure 7 .
Figure 7. Reference point on the fixture.

Figure 8 .
Figure 8. (A) Schematic diagram of reference point measurement; (B) the composition of the distance in the z direction.

Figure 14 (
Figure14(B) displays the surface morphology of the larger prepreg after the inter-ply slip experiment, illustrating a noticeable accumulation of resin on its surface.Figure15displays SEM images of resin accumulation at different velocities.It's evident that resin accumulation gradually increases as the velocity decreases.This suggests that at lower sliding velocities, more resin is pushed out, resulting in a greater volume.Essentially, the slower the velocity, the deeper the embedded depth of the prepreg.Since, under the same temperature and pressure, the thickness of the fiber layer in the same prepreg can be considered constant, different embedding depths indicate different resin thicknesses between prepregs.A deeper embedding depth means a thinner resin layer between prepregs.This observation aligns with the morphology of resin in SEM images and confirms the direct proportionality between resin thickness and velocity, consistent with the calculation results.Figure16illustrates the difference in resin thickness measured by the DIC system and the theoretical calculations at different sliding velocities.VD0.1-0.5 represents the difference in thickness between 0.1 mm min −1 and 0.5 mm min −1 , while VD0.5-1 represents the difference in thickness between 0.5 mm min −1 and 1 mm min −1 .The proximity of the difference in resin thickness measured by the DIC system to that calculated theoretically indicates that the IHL theory is effective in calculating resin thickness during the inter-ply slip

Figure 12 .
Figure 12.The pressure distribution of prepreg under normal pressures.

Figure 13 .
Figure 13.Theoretical thickness of resin between prepreg at different velocities.

Figure 14 .
Figure 14.(A) Schematic diagram of resin accumulation on the surface of prepreg; (B) Image of resin accumulation on prepreg surface after experiment.

Figure 16 .
Figure16.The difference between theoretical calculation and DIC system measurement of resin thickness at different velocities.

Table 1 .
The average theoretical calculated thickness of resin.

Table 2 .
Surface roughness of fiber layer in prepreg.

Table 3 .
Theoretical thickness of resin and film thickness ratio at different sliding velocities.