Experimental characterization and modeling of the inter-ply sliding behavior of unidirectional prepreg in the preforming process

The inter-ply sliding behavior is one of the important factors affecting the quality of carbon fiber composite products. In this paper, the inter-ply sliding behavior of the unidirectional prepreg was investigated for the preforming process. The inter-ply sliding resistance of prepreg under different conditions was measured by the homemade measuring device and the lubricating effect of inter-ply resin was identified by the micromorphology. The effect of fiber orientation was quantified by the combined roughness. With the increase of sliding distance, the inter-ply sliding resistance initially increased significantly, and finally maintained a constant value. A phenomenological model of the inter-ply sliding resistance was developed to explain the effects of pressure, velocity, and fiber orientation. This model can accurately describe the inter-ply sliding behavior of prepreg, which can be used for numerical simulation and the optimization of preforming process.


Introduction
Fiber-reinforced polymer composites have been widely used due to their unique mechanical properties and designability [1][2][3]. Among them, carbon fiber reinforced composite has excellent mechanical properties and it has a high specific strength and specific modulus, which is widely used in aerospace manufacturing [4]. Compared with military aircraft, civil aircraft manufacturers have a strong desire to reduce manufacturing costs. Traditional hand lay-up manufacturing method is gradually being replaced by automated molding methods due to their time-consuming, high cost, and unstable quality. As a promising technology, the automatic placementpreforming method is being applied in the manufacturing process of airframe structures [5]. In this process, the prepreg flat sheets or small curvature sheets are first prepared by the automatic lay-up process. Then the sheets are bent into complex structural preform by mechanical force or vacuum pressure, and the preform is transferred to the autoclave for finally curing. This method improves production efficiency while ensuring product quality. Many aircraft manufacturers have already applied preforming technology in the manufacturing process of complex parts such as composite hat-stringer [6,7].
In the preforming process, inappropriate parameters may lead to defects such as wrinkles, which can affect the performance of the final product [8,9]. During this process, the inter-ply sliding behavior of prepreg has a significant effect on the quality of the preform [10][11][12][13]. The relative sliding of prepreg's layups can relieve the compressive stresses caused by bending. Excessive inter-ply slip resistance limits the sliding of prepreg and leads to the appearance of wrinkle defects. Therefore, researching the inter-ply slip behavior of prepreg is essential to avoid defects.
The Stribeck curve is widely used to investigate the inter-ply slip behavior of prepreg [14,15]. In this curve, a new variable the Hersey number is defined by viscosity, velocity and pressure [16,17]. In the hydrodynamic lubrication region of the Stribeck curve, the Hersey number is linearly related to the friction coefficient. Researchers have used the Hershey number to explain the inter-ply sliding behavior of prepreg [18][19][20]. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
However, some researchers believe that the friction coefficients deduced from the Stribeck curve cannot fully reflect the actual sliding behavior of prepreg. They derived various models for calculating the inter-ply slip resistance by considering the stress variation with the sliding distance.
Erland et al [21] studied the inter-ply sliding behavior of prepreg, proposed a bilinear fitting model, and analyzed the effect of molding conditions on the model coefficients, where the R 2 of the model fitting parameters is greater than 0.91. Wang et al [5] proposed a three-stage slip model taking temperature and pressure into account. which was in good agreement with the experimental results and the R 2 of the fitting values were greater than 0.98. But previous studies lacked analysis of the microscopic mechanism of the slip process and rarely considered the effect of layered fiber orientation. Fiber orientation is one of the main factors in composite design, especially for unidirectional prepreg. Dutta et al [22] studied the effect of fiber orientation on sliding resistance, and found that the resistance was greatly affected by fiber orientation. However, the current research is only the qualitative analysis and cannot quantify the impact of fiber orientation. Therefore, it is necessary to propose a reasonable index to quantify the effect of fiber direction on inter-ply sliding resistance to establish the model of inter-ply sliding resistance.
In this paper, the inter-ply sliding behavior of unidirectional prepreg under different conditions is investigated by the homemade measuring device. The effect of fiber orientation is quantified by the combined roughness and the mechanism of molding conditions is elucidated through sliding experiments. A phenomenological model of sliding resistance is established to characterize the inter-ply sliding behavior of prepreg with different velocities, normal pressures, and fiber orientations.

Materials and method Materials
The M21/UD194/IMA unidirectional prepreg (Hexcel, USA) was used in our experiment. The thickness of the prepreg is 0.187 mm.

Measurement of sliding resistance between prepregs
In the preforming process, the relative slide of prepreg occurred under high temperature and pressure. Commercial measuring devices cannot characterize this slip behavior under these conditions. Therefore, it is necessary to design a special device to investigate the inter-ply sliding behavior of prepreg.
As shown in figure 1, the inter-ply sliding resistance measuring device is composed of the pressurizing system, the heating system, the fixed fixture and the tensile testing machine (ETM 204C, Wance Testing Machine Co., Ltd). Normal pressure was applied through the air cylinder and monitored by the pressure sensors in real-time. The maximum experimental temperature of the heating system could reach 150°C, which completely covered the range of the preforming process. The fixture was designed by the pull-through principle [23,24]. The contact area of the prepreg remained constant during the experiment, which ensured the constant normal pressure. The contact area of the sample was 100 × 100 mm. The samples were fixed on the pressing plate and the sliding plate respectively. The tensile testing machine was connected to the sliding plate to measure the force value in the experiment. The sliding plate was composed of a thin metal, which could transfer the normal pressure and prevent uneven normal pressure of the prepreg. By adjusting the mode of the pressing plate and the sliding plate, the sliding resistance of the prepreg with different fiber orientations was measured. Figure 2 shows the installing methods with different fiber orientations, which includes the common fiber orientation like 0°/0°, 0°/90°, 90°/ 90°, 0°/45°, 90°/45°and 45°/45°. Before the experiment, the measuring device was heated to the required temperature. Normal pressure was controlled by adjusting the cylinder air intake. During the experiment, the prepreg on the sliding plate slid with prepregs on both sides of the pressing plate. Therefore, the inter-ply sliding resistance is: where, F f is the inter-ply sliding resistance of the prepreg. F is the force value measured by the tensile testing machine.
The inter-ply sliding experiments were carried out in different parameters of temperature (T ), normal pressure (P), sliding velocity (V) and fiber orientation. Experimental parameters are summarized in table 1.

Characterization of cross-section morphology
To avoid changes in the cross-sectional morphology of the sample during the process of preparation, the sample after experiment was directly encapsulated in epoxy resin and cured at 80°C for 48 h. The cross-sectional morphology of the sample was observed by the metallographic microscope (BX41M-LED, Olympus).

Characterization of the influence of fiber orientation on the prepreg
The fiber orientation of unidirectional prepreg is an important factor, which determines the processing difficulty and the performance of the product. Therefore, it is necessary to explore the influence of fiber orientation. Fiber  layers in the prepreg with different orientations have distinct roughness characteristics, so the combined roughness is used to quantify the effect of fiber orientation for the inter-ply sliding behavior. Among them, the roughness of single fiber layer is characterized by the root mean square average (R q ), which is more accurate than the arithmetic average roughness (R a ) [25,26]. The combined roughness of upper and lower surfaces can be calculated as follows [27,28]: where, R q,1 and R q,2 are the roughness of the fiber layers in different prepregs, R ¢ is the combined roughness. The sample had been removed from the surface resin before testing to obtain the fiber surface. The treatment steps were as follows: first, the prepreg sample was pasted on a plate. Then the edge of the sample was fixed to prevent fiber misalignment. At last, the surface of the sample was rinsed with acetone and gently wiped until all surface resin was removed. Figure 3 shows samples before and after treatment. The white light interferometer (Mahr LD130, Mahr Inc.) was used to measure the roughness of samples with different fiber orientations. This same treatment was applied to prepare samples without surface resin for the inter-ply sliding experiments.

Result and discussion
Effect of resin on sliding behavior of prepreg The surface resin affects the inter-ply sliding behavior of the prepreg. In this section, the influence mechanism of resin was investigated by comparing the inter-ply sliding behavior of the original sample and the sample without surface resin. Figure 4 shows the inter-ply sliding resistance curve of the untreated and treated sample. The sliding resistance of the sample without surface resin is significantly greater than the original sample, indicating that the resin greatly reduced the resistance. Figure 5 is the micromorphology of the sample cross-section after the experiment. In figure 5(A), fibers of upper and lower prepreg contact directly because of the absence of surface resin. Figure 5(B) shows that the resin layer is present between the fiber layers, which separates the fiber layer from different prepregs and prevents fibers contacting with each other. The sliding resistance mainly comes from the internal friction of the resin. The results indicate that fibers contact directly cause an elevated sliding resistance. The resin works as a lubricant and significantly reduces the sliding resistance.
Effect of temperature on inter-ply sliding behavior of prepreg The viscosity of the resin in prepreg is closely related to the temperature. In this section, the inter-ply sliding behaviors of prepreg at different temperatures were explored. As can be seen from figure 6(A), the inter-ply sliding resistance is extremely large at 25°C. The reason can be explained by the adhesion of the resin at room temperature. The resin between prepregs remains essentially solid at room temperature and is tightly bound together under normal pressure. When the experiment start, shear damage was occurred in the resin area between the prepreg, resulting in extreme resistance. Figure 6(B) shows the inter-ply sliding resistance behaviors of prepreg at different heating temperatures. With the increase of temperature, the trend of sliding resistance decreases at first and then increases. The viscosity of resin in the prepreg is relatively large at low temperature, which leads to the greater internal friction of the resin and the increase of the sliding resistance. The viscosity and the internal friction of resin decrease as the temperature raising, resulting in a decrease of sliding resistance. However, the inter-ply sliding resistance increases again with the higher temperature. When the viscosity of resin decreases with the increase of temperature, the resin is extruded due to the normal pressure. This phenomenon weakens the lubrication effect of the resin and increases the probability of the fiber collision between the prepreg, which lead to an increase in sliding resistance. It can be found that the temperature is an important factor affecting the inter-ply sliding resistance of prepregs. When the temperature is suitable, the inter-ply sliding resistance of the prepreg is minimal.
Effect of fiber orientation on inter-ply sliding behavior of prepreg Figure 7 shows the curve of inter-ply sliding resistance with different fiber orientations. The inter-ply sliding resistance of 0°/0°fiber orientation is the smallest, the sliding resistance of 0°/90°fiber orientation is the largest, and the resistance of 0°/45°fiber orientation is in between. Table 2 shows the surface roughness of the fiber layer and the combined roughness calculated by equation (2). It indicates that the roughness is minimum when the fiber orientation is 0°/0°and maximum when the fiber orientation is 0°/90°. Greater roughness means the fibers from the upper and lower prepreg are more likely to collide, resulting an increase in the sliding resistance.  To exclude the influence of fiber orientation, 0°/0°was selected as the fiber orientation of the sample in the following experiment.
Effect of normal pressure and velocity on inter-ply sliding behavior of prepreg Figure 8 shows the inter-ply sliding resistance curve of prepreg under different normal pressures and velocities. It shows that the sliding resistance is proportional to the normal pressure. When the normal pressure increases,  the resin is extruded or infiltrated and the lubrication of the resin is reduced. The increase in pressure also bonds the resin layer tighter. For the above reasons, sliding resistance increases with the increase of normal pressure.
With the increase of slip distance, the resistance increases rapidly at first. Then the amplitude of sliding resistance growth decreases after an inflection phase. Before the inflection phase, the increased of sliding resistance is proportional to the sliding velocity. After the inflection phase, the increase of sliding resistance is inversely proportional to the sliding velocity. This is related to the bonding time of resin layer, which can be explained by the mechanism of sliding behavior.
The mechanism of inter-ply sliding behavior The above results indicate that the inter-ply sliding resistance of prepreg increases with the increase of sliding distance. However, the sliding resistance cannot increase indefinitely. To investigate the whole process of sliding behavior, a long-distance sliding resistance experiment was carried out with normal pressure of 500N, temperature of 75°C, sliding velocity of 0.5 mm min −1 , and slip distance of 130 mm.
As can be seen in the figure 9, the inter-ply sliding behavior of prepreg can be divided into four phases. The first phase is the linear phase. The resin between prepregs is deformed by shear action and the sliding resistance increases linearly in this phase. The second phase is the yield phase. In this phase, the resin between prepregs  begins to soften and yield. The increase of sliding resistance decreases gradually. The third phase is the hardening phase. The inter-ply sliding resistance increases linearly again. At this phase, the interaction of resin/resin, resin/fiber, or fiber/fiber occurred between prepregs. The last phase is the equilibrium phase. In this phase, the generation of new interfaces between prepregs balance with the peeling of old interfaces, leading to a stable sliding resistance. The slip distance between the prepreg layers is generally short in the preforming process. Therefore, only the linear phase, yield phase, and hardening phase need to be considered in the inter-ply sliding major behavior. The boundary point between the linear phase and the yield phase is defined as the yield point. Sliding displacement and stress of this point are defined as the critical yield distance s .  t and H of the inter-ply sliding experiment. Due to the sliding distance of the linear phase being extremely short, s Y is normalized as 0.02 mm. Figure 10 shows the variation of the critical yield stress under different experimental conditions. It indicates that the critical yield stress is directly proportional to the normal pressure and sliding velocity, independent of the combined roughness. The critical yield stress reflects the initial bonding properties of the inter-ply resin. When resin layer starts to yield, the initial bonding interface is destroyed. The degree of bonding is proportional to the normal pressure, so the critical yield stress is proportional to the normal pressure. The mechanical behavior of the resin exhibits velocity dependence due to viscoelasticity, resulting in a critical yield stress  proportional to the sliding velocity. Therefore, the increase of stress is also proportional to the sliding velocity in the linear phase. Figure 11 shows the variation of the hardening coefficient under different conditions. It can be found that the hardening coefficient is proportionate to the normal pressure and the combined roughness, and inversely proportional to the sliding velocity. During the hardening phase, the disruption and formation of the resin interface between prepregs occur simultaneously. The inter-ply sliding resistance is increasing because the rate of new interface formation is greater than old interface destruction. Higher normal pressure means that the resin is more bonded and the old interface is more difficult to break, leading to a rise in the hardening coefficient. A higher combined roughness means that the fibers are more likely to contact, resulting in higher sliding resistance.
The sliding velocity determines the formation time of the resin interface. When inter-ply sliding velocity is lower, the time to from the resin interface between prepregs is longer. The entangling degree of molecules in the resin is stronger, which requires more energy to break the interface. This results in a greater increase in inter-ply sliding resistance at a low velocity.

Model of inter-ply sliding behavior
Based on the characteristic of the curve in figure 9, the relationship between sliding distance and stress in different phases can be defined as: From the above equation, the relationship between sliding distance and stress can be described as long as the yield point, hardening point, and hardening parameter are determined. It can be concluded from the above results that the inter-ply sliding resistance is related to normal pressure, sliding velocity, and fiber orientation at the same temperature. Among them, the effect of fiber orientation can be expressed by the combined roughness. Therefore, the parameter of the yield point, the hardening point and H can be established as [5]: The parameter of equation (11)- (13) are obtained by nonlinear fitting on experimental results. The fitting results are shown in table 4. The R 2 of fitting results are greater than 0.95, indicating that the selected model and fitting parameters match well with the experimental data. Table 5 and figure 13 show the experimental results and model curves of inter-ply sliding resistance under different conditions. The R 2 of fitting results under different conditions is greater than 0.96. The results make known that the model curves are close to the experimental results, indicating that this model can describe the inter-ply sliding behavior under different normal pressures, velocities, and fiber orientations.

Conclusion
In this paper, the inter-ply sliding behavior of prepreg under different temperatures, velocities, normal pressures and fiber orientations were investigated by the homemade measuring device. The model of inter-ply sliding resistance was established by analyzing the mechanism of prepreg sliding behavior.
Following conclusions are achieved: (1)The resin in the prepreg works as a lubricant and can obviously reduce the inter-ply sliding resistance of the prepreg. Temperature, sliding velocity, pressure and fiber orientations have a significant effect on the interply sliding behavior of prepreg. (2)Due to the different behavior of resin layer, the major inter-ply sliding behavior of prepreg in the preforming process can be divided into the linear phase, the yielding phase and the hardening phase. The effect of fiber orientation was quantified by combined roughness.
(3)A phenomenological model was established according to characteristics in different phases of sliding behavior, which could describe the inter-ply sliding behavior under different normal pressures, sliding velocities and fiber orientations. The results of model calculation are consistent with the experimental results, verifying the correctness of the modeling and indicating that the model can be used for the prediction and numerical simulation of the resistance in the preforming process.
Theoretically, the temperature of the prepreg remains constant during the preforming process. However, this is not always guaranteed, especially for the preforming process of complex structures. Hence, the main next step is to establish a model of inter-ply sliding resistance considering the effect of temperature for simulating the preforming process of complex structures.

Data availability statement
No new data were created or analysed in this study.