Carbon fiber reinforced composites have received growing attention because of their superior performance and high potential for lightweight systems. An economic method to manufacture the parts made of these composites is a sequence of forming followed by a compression molding. The first step in this sequence is called preforming that forms the prepreg, which is the fabric impregnated with the uncured resin, to the product geometry, while the molding process cures the resin. Slip between different prepreg layers is observed in the preforming step, and it is believed to have a non-negligible impact on the resulting geometry. This paper reports a method to characterize the interaction between different prepreg layers, which should be valuable for future predictive modeling and design optimization. An experimental device was built to evaluate the interactions with respect to various industrial production conditions. The experimental results were analyzed for an in-depth understanding about how temperature, relative sliding speed, and fiber orientation affect the tangential interaction between two prepreg layers. Moreover, a hydro-lubricant model was introduced to study the relative motion mechanism of this fabric-resin-fabric system, and the results agreed well with the experiment data. The interaction factors obtained from this research will be implemented in a preforming process finite element simulation model.

## Introduction

Carbon fiber reinforced plastics (CFRPs) have received growing attention because of the improved properties and performances of the materials, such as high specific modulus and specific strength, high damping capacity, good dimensional stability, excellent damage tolerance, strong corrosion, and fatigue resistance [1,2]. Replacing conventional metals with CFRPs in transportation industry leads to a weight reduction of vehicles and equipment systems, and thus improved fuel economy [35]. The most widely used CFRPs have woven structured fibers to improve the material properties and simplify the handling process by several well-developed textile technologies [6]. Current manufacturing process for the woven CFRP parts, especially in the automobile industry, however, still heavily relies on manual layout [7], hindering the potential of mass production of these composite parts.

In order to tackle this challenge, a process chain consisting of prepreg preforming and compression molding has been proposed [810]. The first step is to stack several layers of woven prepregs, i.e., laminates consisting of fabric woven by carbon yarns and uncured resin, in a proper yarn orientation; then, these two-dimensional (2D) plane laminates are heated in an oven and formed to a three-dimensional (3D) shape on a press during the preforming process; after this, the parts are cured so that the epoxy between the prepreg layers are hardened to achieve the designed shape permanently [11,12]. The preforming process, which replaces the hand laying method, greatly reduces the human labor cost and increases the production rate.

Currently, utilization of the preforming process requires numerous tests and prototypes with different parameters, such as temperature, fiber orientation, and forming rate, in order to produce a defect-free part via an optimized process [13]. The large material waste and long experimental period result in a high developing cost and a long product cycle, which hampers the wide utilization of woven CFRPs in practical application, especially in the automotive industry. Thus, numerical methods that can simulate the behaviors of woven composite materials during preforming [6,10,14,15] should be developed to resolve this problem.

Previous works showed that the pin-joint net approximation has been widely used to simulate the behavior of woven composites in the preforming process [1619]. This approximation focuses on the kinematic behavior of the materials with the assumption that the composites exhibit only a pure shear deformation. Therefore, the fibers rotate freely at the tow joints during the preforming process. This approach is computationally efficient. However, the ignorance of the mechanical properties of the fabric and the resin could lead to an inaccurate prediction, especially when the nonuniform deformation is a concern [20]. Furthermore, this approximation is incapable of predicting wrinkling due to the lack of bending stiffness, or optimizing the forming force and forming rate because of the simplifications mentioned previously.

As an alternative approach, the finite element method (FEM) draws a growing attention from both academic and industrial researchers. Preforming simulations that predict the fiber orientation, draw-in amount, and wrinkling behavior during the process have been documented in literatures [3,7,11,14,2024]. It should be noted that the fitness of a material model with proper material properties is essential for the proper utilization of these FEM models.

One the other hand, many experiments that study the material behavior have been carried out. The most widely adopted methods for characterizing the properties within one prepreg layer are: (1) the uniaxial tension test to determine the tensile modulus of the composites and (2) the bias-extension test to measure the shear modulus of the woven composites. The reliability and repeatability of these two tests have been validated by using different apparatus to study a set of similar materials [25]. However, it is still lack of a systematic study for the characterization of the interaction between two different composite prepreg surfaces, or between the prepreg surface and the metal tool surface, while this interaction surely affects the fiber orientation after preforming. For instance, the single-dome preforming simulation result from literature [11] showed that when the prepreg-tool friction coefficient was 0.3, the maximum predicted shear strain was 0.4. When the friction coefficient was changed to 0.1, more concentrated shear deformation distribution with a larger 0.5 maximum shear strain was predicted because of insufficient constraints to the prepreg in-plane deformation. This difference in the shear deformation distribution should lead to different predictions of the final product performances.

This paper proposes a new experimental method to characterize the interaction between carbon fiber composite prepreg layers during the preforming process. The main focus of this method is to characterize the influence of temperature, sliding speed, and fiber orientation on the tangential interaction. Moreover, a hydro-lubricant interaction model is constructed to analyze the interaction between those layers. Comparison between the calculation and the experiment reveals the details of the fiber interaction, such as its strength and periodic pattern. Interaction factors obtained can be utilized in the FEM multilayer prepreg preforming process simulation [8,2628].

## Material Architecture

The carbon fiber composite prepreg studied in this paper was newly developed by Dow Chemical Company (Midland, MI). It has a 2 × 2 twill structure, as shown both by the real material photo and the texgen software [29] model in Fig. 1. The characteristic sizes of woven structure, i.e., yarn width, yarn gap, and yarn thickness, listed in Table 1, were measured by a microscope from the cross section of the material. The length of a single unit cell was then measured as 9.738±0.464 mm.

The reinforcements of this woven composite prepreg are the carbon fibers, and the matrix is the uncured resin. Previous observations during the tests revealed that the resin fully transformed from a solid state to a liquid state at about 50 °C, which was then set as the starting point in the viscosity test. During the preforming process, the highest temperature of the prepreg was controlled less than 80 °C; therefore, the highest temperature of the viscosity test was set at about 80 °C. Experimental data show that the viscosity of the resin monotonically drops 99.43% from 50 °C to 70 °C, and the viscosity change is less significant if the temperature increases beyond 70 °C.

## Experimental Apparatus for Interaction Characterization

Interactions in preforming occur at the interfaces between (1) prepreg and prepreg and (2) prepreg and tooling. Various tests have been performed by means of different lab-scale machines. Groves first applied a nonlinear low frequency oscillatory shear with a Rheometric dynamic spectrometer to measure the viscous shear behavior of prepreg–prepreg interaction at a certain temperature [30]. The test apparatus provided good results for steady-state or dynamic shear flows. However, this setup introduced strain hardening at larger strains because of an imposed steady shear, and it could not capture the effect of fiber orientation because in the Rheometric dynamic spectrometer machine, the relative motion is introduced by the rotation between the top and the bottom layers.

As an improvement, Scherer et al. utilized the pull-out experiment, subjected to a set of controlled pressure, temperature, and relative motion speed, to characterize the interaction of the prepreg layers, and used the shear stress to examine the interaction strength [31]. This “pull-out” test mechanism laid the foundation of the following tests. Murtagh et al. improved the test apparatus by fixating the fibers of each ply and imposing an interply relative motion between the prepreg and the tool surface [32]. The friction coefficient was calculated based on the ASTM D1894 standard. They also used the friction coefficient to simulate a more accurate forming process. It should be noted that it is convenient to use sufficiently long specimens to maintain a constant contact area of the surfaces when designing the pull-out test, as shown in Fig. 2. If the area varies, the normal force that compresses the materials should be adjusted accordingly throughout the entire process in order to maintain a relatively constant normal pressure [33].

The current research used the test apparatus shown in Fig. 3. The schematic of this apparatus is shown in Fig. 4. During the test, the top prepreg layer was clamped on the motion stage, which resembled the relative “pull-out” slip. The bottom prepreg was clamped on a stationary heating stage, which raised the temperature between the two prepreg surfaces. The motion stage has a size of 49.5 mm in width and 90.0 mm in length. The edges of the top prepreg layer were fixed on the side of the motion stage instead of the bottom to avoid any possible edge effect and to guarantee the surface-to-surface interaction during the entire test. A six degree-of-freedom force-torque sensor, with the capability of 1500 N in the x and y directions and 2000 N in the z direction, was mounted on the motion stage to record both the normal force and the tangential force caused by sliding at a sampling frequency of 250 Hz. In this test, the compression between the two layers was introduced by the displacement-control motion stage. Hence, the contact force varied during the test if the thickness of prepreg across the entire test stage changed. Interestingly, as shown in the following analysis, this variation should not affect the interaction factor, which is calculated through normalizing the in-plane tangential force by the contact force.

A Micro-Epsilon TIM 160 infrared (IR) camera, calibrated with the same prepreg material using a Type K thermocouple, was also included in the system. It measured the surface temperature distribution and provided the average values of a selected area. During each test, temperature was adjusted until it could be maintained within ±1 °C variation from the desired value by carefully changing the power of the heating stage.

The design of the experiments takes various factors into consideration. These factors are listed in Table 2. The parameters are changed accordingly for comparison. For the fiber orientation effect, the motion speed was fixed at 10 mm/s. Each test was repeated for three times.

The most important parameter of the experiment is the surface temperature because it affects the viscosity of the resin in the composite. During the actual preforming process, the prepreg material was heated to 50–80 °C in a heating chamber and then placed in a press that is at room temperature. Thus, the temperature selected here ranges from room temperature (24 °C) to 80 °C.

During the preforming step that deforms a 2D sheet into a 3D part, the relative motion speed between the material layers varies at different locations, resulting in a different interaction strength between the prepregs because of the shear rate effect caused by the resin viscosity at the interfaces. Thus, relative motion speed should be one important factor. The selected speed values are 5, 10, and 15 mm/s, controlled by the motors of the equipment system.

Another parameter is the fiber orientation. In the industrial applications, prepreg layers with different fiber orientations are stacked together to optimize the performance of the product in all directions. Since the surface texture of the composite is anisotropic, which affects the hydrodynamic interaction between the fabric and the resin, it is also important to test the material interaction subjected to different fiber orientation combinations. Figure 5 illustrates two different combinations of fiber orientations studied in this paper.

## Test Procedure

After the test parameters were selected, the prepreg layers were clamped first. The bottom layer was always aligned with the sliding direction while the top prepreg layer was adjusted to a desired fiber orientation. Then, the bottom prepreg was heated to a specific temperature. The real-time temperature distribution and the average value of the targeted area marked by the white rectangular, as shown in Fig. 6, were obtained via the Micro-Epsilon TIM 160 IR camera mentioned in the Experimental Apparatus for Interaction Characterization section.

At the beginning of the test, the top motion stage wrapped with the prepreg layer was moved away from the bottom stage so that the IR camera could obtain the full field temperature image of the target area, i.e., the prepreg layer on the bottom heating stage (see Fig. 4 for the setup). Once the desired temperature was reached, the power of the heating stage was tuned so that the prepreg temperature could be maintained (±0.5 °C) for about 1 min. Then, the top prepreg was moved down and was set in contact with the bottom prepreg at the pressure around 10 kPa, which is estimated by the average forming force divided by the prepreg surface area measured in the previous double-dome benchmark tests [8].

The prepreg layers were then kept in contact without relative motion for about 30 s to allow the top prepreg to be heated up to the desired temperature range through thermal conduction. This time was determined by measuring the top prepreg temperature history with a k-type thermocouple. It was found that after contact, 30 s would be long enough for the top prepreg to reach to the same temperature as the one of the bottom prepreg. Then the motion stage started to slide at the desired speed. It should be noted that during sliding, though the motion stage would block partial view of the IR camera, the temperature distribution was well maintained at the desired values, because the temperature at any location of the specimen did not change significantly when the top stage passed by.

## Analysis of the Interaction Behavior

The interaction factor is defined in this work to indicate the intensity of the yarn-resin-yarn interaction between the two prepreg layers, which includes contact, friction between fiber/resin, viscous resistance in resin, stick/slip, and tack. For the convenience of the datum implementation in the simulations [32], the interaction factor is calculated according to the definition of the Coulomb friction, which is the tangential interaction force divided by the normal force. The results in Fig. 7 show that at the beginning of the test, large variations in the force components and the interaction factor value were observed. The reasons for this could include: (1) the starting point of the sliding was at the edge of the bottom prepreg, which was not in the uniform temperature region because the heating stage only provided a uniform field at the center and (2) during the first 30 s of the test, the two prepreg layers were in contact for heat conduction without relative motion. Thus, the prepregs were very tacky, resulting in a high initial interaction factor. Based on the steady temperature field measured with the IR camera image and the trend of the interaction factor curves, only the experimental data within the stable stage, which is the sliding distance ranging from 30 to 70 mm as indicated by the two vertical straight-line marks in Fig. 7, were utilized for the further analysis. For each test, the average and the standard deviation of the interaction factor were calculated as indicators for the interaction strength and its oscillation, respectively. The oscillation should reveal the strength of the stick-slip phenomenon caused by the viscous resin and the fabric texture during the relative sliding.

The calculated interaction factor is nearly independent of the pressure variation. Take the data in Fig. 7 below as an example, the normal force changes with the sliding distance, while the measured tangential interaction force varies proportionally to the normal force. As a result, the interaction factor calculated by the Coulomb friction law is nearly constant during the test, except for some oscillations caused by stick-slip. This pressure-independence behavior was verified by other tests at different conditions. The results support the idea of using the displacement-controlled method to introduce the pressure in the experimental setup since the pressure varies around the desired 10 kPa value, which was likely due to the surface roughness of the specimens and does not affect the calculated interaction factor.

Periodical changes of the interaction factor are observed from the resulting plots, especially at 50 °C when the resin has the highest viscosity. Take the interaction factor at the 30–70 mm displacement steady-state stage shown in Fig. 8 as an example. In addition to the small oscillations caused by stick-slip, the plots from all three tests show consistent and noticeable peaks and valleys that have similar amplitude and phase, which suggests a good repeatability of the test results. The variation period of the interaction factor is about 10 mm, which is very close to the 9.74 mm length of the unit cell used for the prepreg representative volume element. This phenomenon will be further investigated by the hydro-lubricant interaction model in the Hydro-Lubricant Interaction Model section.

The interaction factors and the stick-slip strengths from three repeated tests under the same condition were averaged. The final results with respect to average stable stage temperature, relative motion speed, and fiber orientation combination are plotted in Fig. 9. Both the interaction and stick-slip strengths reach the peak values at 50 °C, which is the critical temperature when the resin fully transforms from the solid to the fluid state and shows the highest viscosity. Below 50 °C, the resin is in its solid state. It gradually becomes softer and tackier as temperature increases, which would lead to: (1) larger interaction factor because a stronger external force is needed to shear the resin in different layers under the relative sliding motion and (2) larger amplitude and higher frequency stick-slip because of the more frequent molecular chain mixing and interdiffusion, causing the tangential interaction force to fluctuate.

When the temperature is higher than 50 °C, the resin fully transforms to a viscous liquid state and acts like a “lubricant” between the two prepreg layers. At this stage, further temperature increase reduces the resin viscosity and enhances its lubricity during the sliding, resulting in a lower interaction factor, and less frequent stick-slip with a smaller amplitude.

In Fig. 9(a), a weak influence of relative motion speed on the interaction factor at temperatures below 50 °C was found. Similarly, it is not significant either at temperatures higher than 60 °C when the viscosity of the resin is greatly reduced. The interaction factor has a positive relation to the motion speed at about 50 °C, when the viscosity of the resin reaches the peak value.

For the fiber orientation effect, when temperature is higher than 50 °C, the interaction factor becomes larger with the 0/90/0/90 fiber orientation than that with the 0/90/−45/+45 orientation because the transverse fiber yarns in different layers are more likely to interlock each other with the 0/90/0/90 orientation, making it more difficult for the layers to slide. This also explains the fact that the stick-slip strength is generally larger if the fibers in both top and bottom layers are aligned with each other, especially at 50 °C when the resin viscosity reaches the peak value. However, when temperature is below 50 °C and the resin is in the solid state, the difference between two orientation combinations becomes less significant. This is mainly due to the fact that sheets are still in the solid states, and that the resin fills the surface “valleys” generated by the fiber yarns to flatten the prepreg. As a result, the orientation combination does not have a large effect compared to those at higher temperatures. An in-depth theoretical analysis is then needed for understanding the prepreg interaction mechanism at this condition.

## Hydro-Lubricant Interaction Model

The woven fibers form a certain texture of surface topography. It is well known that textures affect the interaction of textured surfaces [3436]. A hydrodynamic model developed based on the work reported in Refs. [37] and [38] was utilized to simulate and study the woven prepreg–prepreg interaction mechanism. In this model, the top and bottom woven fabrics were aligned to the same direction with 0/90/0/90 fiber orientation for 2D simplification to ease the prepreg surface modeling and increase the calculation speed. And they were treated as rigid solid because (1) they were firmly stretched in the fiber matrix, so that the vertical deformation was minimal and (2) the normal load was low. Then the relative movement of the interface can be considered by the general lubrication system illustrated in Fig. 10, where P0 is the external force, U is the relative motion speed, h0 is the minimum resin thickness between the two prepreg layers, A is the fiber yarn width, and B is one half of the yarn thickness. This system is formed with two solids separated by a continuous fluid film. In the simulation, the solid geometry was determined based on the cross section of the 2 × 2 twill prepreg, as shown in Fig. 1(b). The single warp yarn cross section was idealized as an elliptical shape, while the cross section of the weft yarn on top of the two warp yarns was modeled as a plane tangent to two half elliptical shapes. It was assumed that, in the simulation, the upper layer would move with respect to the lower one. The fluid film thickness h at any given location was described by Eq. (1), where hg was the height variation along the surface profile
$h=h0+hg$
(1)
In this hydro-lubricant model, the one-dimensional transient Reynolds equation for an incompressible Newtonian fluid flow is utilized, as shown in Eq. (2), where η is the viscosity of the resin at the motion condition
$∂∂xh312η∂p∂x=U2∂h∂x+∂h∂t$
(2)
Assuming bottom surface is infinitely large while the top surface is made up with ten unit cells, the corresponding boundary conditions are
$p0=0$

$px0=0$

$∂p∂xx0=0$
(3)

where 0 and x0 are the positions of the two ends for the top surface, respectively, in the tangential direction.

The tangential interaction force due to fluid shear deformation is calculated from Eq. (4) for a Newtonian fluid
$Wf=∫ηUh+∂p∂xh2dx$
(4)
The normal force acting on the fabric layers is obtained by integrating the pressure along the entire surface in the following equation:
$W=∫pxdx$
(5)
By gathering Eqs. (1)(5), given the relative motion speed, the normal contact force between the two layers, the woven fabric structure parameters, such as the yarn width and the yarn thickness, and the resin viscosity at the given test condition, the tangential interaction force, as well as the interaction factor, can be calculated. The iteration error control criteria for the pressure, load, and film thickness convergence within the numerical calculation are listed in Eqs. (6)(8), respectively
$Errpressure=∑1iPik+1−Pik∑1iPik≤0.001%$
(6)

$Errload=W−P0AP0A≤0.1%$
(7)

$Errthickness=h00−h0th0(0)≤0.1%$
(8)

Given the condition that the resin fully transferred to the liquid state at 50 °C, and that the viscosity of the resin dropped rapidly after 70 °C, the interaction behaviors at 50, 60, and 70 °C were analyzed by this model for the relative motion speed set at 10 mm/s. The comparison of numerical and experimental results is shown in Fig. 11, where the average, maximum, and minimum values of the interaction factor are plotted. At 50 °C, the numerically calculated interaction factor is significantly larger than the experimental one because the continuity assumption is not valid. In the simulation, the resin layer behaves like a continuous fluid with high viscosity, while in the experiment, the resin may only partially melt, so there is still an interface where friction takes place between top and bottom prepregs. It should be noted that at this interface which breaks the continuity assumption in the simulation, the friction should be lower. Moreover, in the numerical calculation, the prepreg fiber is assumed to be rigid for simplification. In the experiment, on the other hand, the highly viscous resin at this temperature leads to large fluid shear stress, deforming the prepreg fiber, changing the surface profile and in return reducing the interaction. At 60 °C, the numerical results agree very well with the experimental ones because the viscosity falls in a reasonable range, and the continuity assumption is valid since the resin fully melts. At the 70 °C condition, the numerical predictions are slightly smaller than the experimental result. A larger interaction factor in the experiment is due to the direct contact between two woven fabrics. It was found that at this condition, the minimum film thickness would reach 0.06 mm during the calculation because the viscosity of the resin becomes very small. The minimum film thickness is in the same order of the 0.012 mm half-yarn thickness variation; thus, in the real tests, two woven fabric surfaces may contact each other at some positions, resulting in a boundary-mixed-hydrodynamic lubrication cycling.

For the interaction at 60 °C, the numerical calculations with the relative motion speed of 5 mm/s and 15 mm/s were then performed. The experimental and numerical results for the average, maximum, and minimum interaction factors are plotted together with the 10 mm/s ones in Fig. 12. The interaction model results agree well with the experimental ones in general. However, the speed effect is slightly more significant than that found in the experiments because of the hydrodynamics assumption between rigid surfaces in the model, which is sensitive to sliding speed. However, in the real experiment, other factors can also contribute to the speed effect. At low speed, there could be sufficient time for the resin to mix and interdiffuse, so that the resin is tackier and tends to stick the two surfaces together, thus increasing fluid resistance to motion. At high speed, the interaction force may increase because of the viscous friction, so that the in-plane elastic deformation of the fiber increases correspondingly, which in return flattens the surface and reduces the interaction in the real materials.

Finally, with this hydro-lubricant model, the periodic interaction factor variation demonstrated in Fig. 8 was investigated. The fast Fourier transformation was applied to both experimental and numerical results. The results for 60 °C and 10 mm/s condition are demonstrated in Fig. 13, showing that all the experimental and numerical curves have the first-order length frequency of about 0.1/mm, which means that the interaction factor changes in the period of about 10 mm. This phenomenon is dominated by the size of the prepreg unit cell, which has a 2 × 2 twill element of 9.74 mm side length. However, for the higher order frequencies, the numerical result agrees less with the experiment ones, especially in terms of amplitude. This might be explained by the fact that the viscoelasticity of the real material can absorb high frequency vibration energy during sliding.

The comparison between the modeling and experiment results demonstrates that under certain preforming conditions, which are 60 °C temperature and 5–15 mm/s motion speed for the woven composites tested here, the interaction between two composite prepreg layers can be explained by the hydro-lubricant mechanism and predicted via the proposed numerical method. The elastic deformation of the fabric and the resin mixing with interdiffusion at various deformation rates and temperatures should be considered in the future work in order to model the prepreg–prepreg interaction more accurately and predict the interaction behavior subjected to wider conditions.

## Conclusions

This paper reports the characterization of the interaction between the uncured prepreg–prepreg subject to relative sliding by means of experiment and simulation methods. The main focus has been paid on studying the influence of several factors, such as temperature, relative motion speed, and orientation on the interaction. Major findings can be concluded in the following two aspects:

1. (1)

A displacement-controlled apparatus was built for this work. Interfacial temperature, relative motion speed, and fiber orientation were three key factors that were studied. Periodical changes of interaction factors were identified in the interface temperature ranging from 50 °C to 70 °C, and both the average interaction factors and standard deviation were calculated to understand the interaction strength and the stick-slip phenomenon. Results show that at 50 °C, both interaction factor and stick-slip reach the highest strength due to the highest viscosity melting resin and reduces accordingly when temperature is higher.

2. (2)

A numerical interaction model was developed based on the hydrodynamic lubricant theory for the woven composite prepreg. This model is capable of directly simulating the interaction between the prepreg layers given the basic resin viscosity, prepreg weave pattern, and the process parameters. A good agreement between the simulated and experimentally obtained data was found in the temperature range from 60 °C to 70 °C. A periodicity of about 10 mm was recognized from the frequency plot, which is in good agreement with the geometry of prepregs. The model can help explain the stick-slip mechanism of the woven prepreg–prepreg interaction and predict the interaction factor for the temperature of around 60 °C and the sliding speed from 5 to 15 mm/s.

The experimental value of interaction factor can be further used as the input for the preforming simulation model reported in Ref. [8], which is believed to have a notable effect on the in-plane kinematic behavior of the woven composite prepreg. Moreover, this test method can also be applied to test different composite prepregs if new materials are developed for utilization in the similar preforming process.

## Acknowledgment

This work was supported by a subcontract from the Ford Motor Company with funding from the Office of Energy Efficiency and Renewable Energy (EERE).

## Funding Data

• U.S. Department of Energy (DE-EE0006867).

• China Scholarship Council (No. 201506680012).

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