Zeitschrift Kunststofftechnik Journal of Plastics Technology

Transcription

1 Zeitschrift Kunststofftechnik Journal of Plastics Technology Wissenschaftlicher Arbeitskreis der Universitäts- Professoren der Kunststofftechnik archivierte, peer-rezensierte Internetzeitschrift des Wissenschaftlichen Arbeitskreises Kunststofftechnik (WAK) archival, peer-reviewed online Journal of the Scientific Alliance of Polymer Technology eingereicht/handed in: angenommen/accepted: Dipl.-Wi.-Ing. Teresa Möbius, Dipl.-Ing. Stephan Eilbracht, Dr.-Ing. Natalie Rudolph, Prof. Tim A. Osswald Polymer Engineering Center, Department of Mechanical Engineering, University of Wisconsin Madison Analyse zur Faserorientierung und Faser- Matrix-Separation bei einem Pressprozess mit kreisförmiger Fließfront Bei der Konstruktion von faserverbundverstärkten Kunststoffen spielt die Faserorientierung eine wichtige Rolle. Im Gegensatz zu kurzfaserverstärkten Kunststoffen können bei Langfasern die mechanischen Eigenschaften eines Bauteils gezielt eingestellt werden. Während des Fließprozesses können Effekte wie Faser-Matrix-Entmischung und Faser-Ansammlungen auftreten. Mit dieser Arbeit wird eine Analyse zum Einfluss verschiedener mechanischer Charakteristiken der Fasern und des Faser-Matrix-Gemisches auf die beiden Phänomene Faserorientierung sowie Faser- Matrix-Entmischung vorgestellt. Analysis of fiber orientation and fiber matrix separation in a compression molding process with an equi-biaxial flow front Fiber orientation plays a decisive role in the mechanical characteristics of fiber reinforced plastics. During the flow process of the matrix several phenomena such as fiber matrix separation and fiber jamming can occur. This paper focuses on the effects of fiber aspect ratio, fiber volume content, fiber flexibility, initial mold coverage and viscosity of the matrix material on fiber orientation, as well as on fiber matrix separation in a compression molding process with an equi-biaxial deformation. Within this study, a mechanistic fiber simulation model was used, as well as simple experiments with model fluids and fibers. Carl Hanser Verlag Zeitschrift Kunststofftechnik / Journal of Plastics Technology 9 (2013) 2

2 Analysis of fiber orientation and fiber matrix separation in a compression molding process with an equi-biaxial flow front T. Möbius, S. Eilbracht, N. Rudolph, T. A. Osswald 1 INTRODUCTION Over the last few years the importance of fiber reinforced plastics has increased and replaced metallic materials in multiple applications. The rising market share of fiber reinforced plastics is based on several mechanistic characteristics which are adjustable to the fiber s orientation. On the one hand, specific fiber orientation is beneficial for the final product; on the other hand, however, when the fiber orientation is uncontrollable, the performance could suffer. Another effect that can occur during polymer processing is fiber matrix separation. Thereby different fiber volume contents can be found in the final part with a fiber free region that can normally be found at the flow front. An example of this uncontrollable fiber orientation, as well as the occurrence of fiber matrix separation, is the flow process in compression molding. The work presented in this paper focuses on the effects of fiber aspect ratio, fiber volume content, fiber flexibility, initial mold coverage plus viscosity of the matrix material on fiber orientation as well as on fiber matrix separation in a compression molding process. The first effect was assessed by illustrations of the fibers in the mold and diagrams of fiber orientation; the second effect was analyzed using the Fiber-Matrix-Separation-Parameter (FMS-Parameter). This parameter is a function of the flow covered areas at a given time which do not contain any parts of fibers. The research was performed in two steps: the numerical and the experimental approach. For the simulations all the above-mentioned parameters have been verified, while in the experiments only the fiber aspect ratio, the fiber volume content and the viscosity of the matrix material were changed. The experimental set-up is based on a simple compression molding process. For the optical evaluation during the experiments, fiber suspensions were squeezed between two transparent PMMA sheets and the thereby obtained simple flow fields were recorded during the experiments. Journal of Plastics Technology 9 (2013) 2 101

3 2 BASIC PRINCIPLES Effects such as fiber orientation, fiber matrix separation, and consequently fiber jamming are all phenomena that have already been noticed in sectors other than the composites industry. A classic example of suspension rheology, where a strong interaction between the fluid and the solid inclusions exists, is the historic log-jamming of the late 19th century. Figure 1 presents photographs that depict one such instance, when wooden logs jammed up in the St. Croix River, causing a separation between the matrix (water) and the solid inclusion or fibers (logs). While this particular case of separation between inclusions and matrix is extreme, with a viscosity that is extremely low and a rigid inclusion that is very high, the principle of fiber matrix separation is quite obvious. Jeffery was one of the first scientists who tried to describe mathematically the motion of particles in a viscous fluid. His work on Motion of Ellipsoidal Particles Immersed in a Viscous Fluid [1] was fundamental for future research. His so called Jeffery's Equation describes the orientation of a particle with time for a finite aspect ratio. Later, Mason et al. [2] proved that Jeffery's Equation can also be used for particles of a cylindrical shape if a correction factor is added to the aspect ratio. In 1984 Folgar and Tucker presented their work of Orientation Behavior of Fibers in Concentrated Suspensions [3], including a mathematical model, which is based on Jeffery's Equation. By adding a summation, and including a factor for fiber concentration, they took the phenomenon of fiber interaction into account. In 1987 Advani and Tucker [4] developed a tensor representation of the Folgar-Tucker Model. They used tensors instead of the single angles of the fibers and hence developed the possibility for a more accurate calculation of fiber orientation. This model is known as the Advani- Tucker Model. Another important step for the approximation of the fiber orientation was the development of the model for a flexible fiber. While former models assume rigid fibers, introducing flexible fibers allowed these models to take fiber bending into account. Yamamoto and Matsuoka [5] as well as Ross and Klingenberg [6] modified the model of a rigid fiber while Switzer [7] displayed fibers as chains of prolate spheroids connected through ball and socket joints. One of the newer works on describing fiber orientation, depending on flexible fiber suspensions, was developed by Wu and Aidun [8]. Currently, modeling flexible fibers as well as approximating the calculation for fiber orientation is still being modified. In addition to fiber orientation, fiber matrix separation plays an important role for the quality of a part. As shown in former works for example by Londoño et al. [9], an irregular fiber density distribution can occur in compression molded components such as ripped parts. Journal of Plastics Technology 9 (2013) 2 102

4 Figure 1: St. Croix River, Wisconsin, U.S.A [Courtesy, Wisconsin State Historical Society] Top: Logs floating along the St. Croix River (ca. 1885) Bottom: Log jam on the St. Croix River (ca. 1886) Schmachtenberg et al. [10] showed that a lower fiber density distribution is measurable within the region of the flow front of a compression molded part. This phenomenon was called fiber matrix separation and found to depend on the closing velocities of the press. Journal of Plastics Technology 9 (2013) 2 103

5 r l Möbius, Osswald et al. While this topic up until now was often investigated experimentally, the advancement of technology and increasing knowledge in the field now allows numerical simulation of this problem. Thus, a numerical model was developed [11] to analyze the behavior of a fiber as a function of time during the flow process. A model for flexible fibers was derived which defines fibers as beads connected by springs. Hence, phenomena such as fiber deformation and stretching, fiber jamming and mechanical interlocking as well as fiber matrix separation can be displayed. Within this model Londoño et al. investigated the fiber flow during the compression molding process with SMC. The simulation includes the placement of the charge in the mold between the upper and lower piston of the press and the decrease of the gap between the pistons during closing. The accompanied squeezing of the charge into its final position during mold filling and the curing of the resin, when the final fiber positions are defined, are additional steps. While Londoño and Eilbracht examined fiber and matrix behaviour for monoaxial elongation flow, the work presented here is focused on the analysis of fiber orientation and fiber-matrix separation with an equi-biaxial flow front in a compression molding process. Mechanistic Model The mechanistic model used in the presented work is based on the abovementioned work [11] and has been modified by Eilbracht et al. [12]. Figure 2 shows a schematic image of a flexible fiber, represented by beads connected with springs. The radius of a bead r, the distance between the beads d, and the total number of the beads n, which results in the length of a fiber l, are adjustable components of the simulation. Furthermore, the stiffness of the fiber is adjustable by changing the flexibility of the spring, thus resulting in a different bending behavior. Modeling the stretching and compression of a fiber is also possible. Figure 2: Model of a single fiber Journal of Plastics Technology 9 (2013) d

6 To predict the behavior of a fiber the forces are calculated for each bead. Figure 3 depicts the forces, which act on the bead. Figure 3: Forces that act on a bead [after [13]] While neglecting inertia force, a force balance can be generated: f d i + f xv ij + f d i xv i wall + f c i + f b i + f f ij + f l ij = 0 where f represents the hydrodynamic drag force, f xv represents the excluded volume forces acting between the beads v, while f is the excluded volume force between each bead and the wall; f c i is the connector force b between neighboring beads generated by the connecting springs, f i is the fiber bending force, f f ij ( 1 ) is the fiber friction force, and f l ij the hydrodynamic lubrication force between neighboring beads. The hydrodynamic drag force, also known as Stokes force, accounts for the fluid resistance (matrix) without including lubrication or long range effects. The excluded volume force keeps the beads from overlapping with each other or the wall. The connector force accounts for the reaction effects between adjacent beads i and j. In the flow process fibers bend due to viscous and dynamic forces. This phenomenon is described by the fiber bending force. The Coulomb friction forces acting between adjacent fibers are also considered. Londoño [13] used dimensional analysis to prove that the friction effects overpower the lubrication effects by several orders of magnitude. For that reason lubrication forces are neglected. Journal of Plastics Technology 9 (2013) ij xv i wall

7 3 METHODS AND RESULTS 3.1 Numerical Approach For the numerical approach several simplifications of the experimental design were made. First of all, a thin layer is examined instead of the whole mold charge. The result is a simplified compression molding process, Figure 4. Figure 4: Simulated thin layer of a charge The parameter R 1 represents the radius of the charge and R represents the radius of the mold cavity. Furthermore the parameter h describes the closing velocity of the pistons. The thickness of the layer of the charge is much smaller compared to the thickness of the charge. Therefore, the changes in the thickness in the x-y plane can be neglected in the simulation. The mechanistic model, explained above, is based on equations that describe fiber behavior during the flow process in simple flow fields. The geometrical changes are accounted for in these simplified equations ( 2 ) to ( 4 ), and are given in Cartesian coordinates [14]. u x u y u z 2 2 h x y x * cos cos 2 2 h( t) 2 x y 2 2 h x y x *sin sin 2 2 h( t) 2 x y = - h *z h() t 2 2 ( 2 ) ( 3 ) ( 4 ) Journal of Plastics Technology 9 (2013) 2 106

8 Several other simplifications were made in order to keep the computational time reasonable. These simplifications are as follows: To mimic the behavior of a thin layer in the mold, the total amount of fibers is kept between 91 and 2450 (equal to fiber volume content between 0.5 % and 6 %). The fibers are distributed randomly within the charge. The mold size is imitated; therefore interactions between fibers and walls are neglected. For the simulated fiber-fiber interaction simulations, friction forces are included while volume forces are excluded. The mold closing velocity h is kept constant. The simulations end when the given mold size radius is reached. The changes in thickness of the simulated thin layer are negligible compared to the large variations in the x-y-plane and is therefore kept constant. All simulations are based on an equi-biaxial flow field. Within this flow field the influence of the fiber aspect ratio, initial mold coverage, fiber volume content, fiber flexibility, and the viscosity of the matrix material was explored. In the first step of a simulation the charge is placed into the mold. Therefore, the configuration of the charge equals that one of a SMC - process. Different layers of the fibers are placed in the x-y-direction and fractionally in z-direction. A summary of the data complied in these simulations can be seen in Table 1 below. Initial mold coverage [%] Min Max Fiber volume content [%] Min Max Fiber aspect ratio [-] Min Max Fiber flexibility [-] Min Max Viscosity [CST] Journal of Plastics Technology 9 (2013) Min Max Range Table 1: Range of variations of simulation settings

9 Fiber Matrix Separation and FMS-Parameter With the help of the FMS-Parameter (see equation ( 5 )) and the illustrations of the fiber density distribution (see Figure 5) the influence of several factors can be quantified and visualized. ( 5 ) position flow front position no fiber square FMS Parameter *100% radius mold last time step The fiber density distribution itself could be visualized with the help of a MATLAB subroutine. Therefore, the mold was divided into 1296 squares. For each square the number of beads is counted and related to the volume of the cubic content. Hence the fiber density distribution is measured and displayed by different colors for each square. The color white represents the squares, which are not reached by the flow front yet. "Dark blue" represents low fiber volume content whereas "green" displays the average. "Red" represents three times higher fiber volume content than the average. Within the charge it allows to analyze fiber jamming and weak spots while at the flow front it is used to visualize fiber matrix separation. Mold size Flow front FMS-line Fiber density distribution Regions without beads/ fibers Figure 5: Fiber density distribution and FMS-line Fiber Orientation The fiber orientation distribution ψ was calculated by the position of each bead as a function of each time step. It was defined to quantify the orientation of the fibers between angles Φ of +90 and -90. The post processing of the fiber orientation was done in two steps: first, by using a MATLAB subroutine to create histograms for several time steps showing the influence of the modified parameters on the orientation of the fibers Journal of Plastics Technology 9 (2013) fiber volume fraction distribution [vol.-%]

10 [12] and second, by using the VMD-Player for a visual inspection of the simulated flow process, Figure 6. ψ Φ Figure 6: Fiber orientation Left: Quantification of fiber orientation Right: Illustration of fiber orientation during flow process 3.2 Results of Numerical Approach All simulations are based on the following parameter configuration: Fiber aspect ratio: Fiber volume content: 3 % Initial mold coverage: 36 % Viscosity: 1000 CST Fiber flexibility: 10-2 For the evaluation of the influence of each parameter on fiber matrix separation and on fiber orientation, one of these parameters was varied at a time, as will be described in the following sections, while the remaining parameters were kept unchanged. Fiber Matrix Separation Fiber Aspect Ratio The fiber aspect ratio is defined as length of the fiber divided by its diameter, L/D. Assuming a constant diameter, an increase in the fiber length results in a higher fiber aspect ratio. To analyze the influence of the fiber aspect ratio on the fiber matrix separation, two test sets were performed: one with initial mold coverage of 36 %, Figure 7, and the other with 68 %, Figure 8. In both sets, a range from 10 to 30 L/D was studied. The diagrams show the same trend: an Journal of Plastics Technology 9 (2013) 2 109

11 increasing fiber aspect ratio causes increasing FMS-Parameters. In addition, the absolute values of the FMS-Parameters are higher for the smaller mold coverage of 36 %. The effect of more pronounced fiber matrix separation at a higher fiber aspect ratio can be described with the increasing probability for mechanical interlocking, resulting in the entanglement of longer fibers. At the same mold coverage rate the intermolecular forces can be assumed as constant. Figure 7: FMS-Parameter - influence of fiber aspect ratio with initial mold coverage of 36 % Figure 8: FMS-Parameter - influence of fiber aspect ratio with initial mold coverage of 68 % Journal of Plastics Technology 9 (2013) 2 110

12 This effect is comparable to the increase in viscosity with increasing molecular weight. The higher the molecular weight, the longer the fibers and the more often mechanical interlocking occurs. Due to this interlocking and the resulting friction, the viscosity is increased and the polymer flow is slower than a polymer with shorter chains. In the case of the increasing fiber aspect ratio, the higher mechanical interlocking slows down the effect of entrainment of the fibers by the matrix system. The outcome of this is a higher fiber matrix separation at the flow front. This effect is schematically displayed by fiber density distribution illustrations, Figure 9. Figure 9: Fiber density distribution at the last time step for different fiber aspect ratios (with initial mold coverage of 36 %) Left: Fiber aspect ratio of 10 Right: Fiber aspect ratio of 30 By observing the fiber density distribution for different fiber aspect ratios it is conspicuous that there is a small visual difference for the completely filled mold (mold coverage of 100 %). The fibers with a fiber aspect ratio of 10 are equably spread over the whole mold, while for a fiber aspect ratio of 30, a formation of spots with a higher density - fiber jamming - has occurred. Fiber Volume Content Figure 10 shows the influence of fiber volume content on fiber matrix separation. For this work a range between 0.5 % and 6 % fiber volume content was analyzed. It can be seen that there is a trend between these two parameters. With increasing amount of fibers per unit of volume there is a smaller band without fibers at the flow front, which corresponds to a smaller FMS-Parameter. Journal of Plastics Technology 9 (2013) 2 111

13 Figure 10: FMS-Parameter - influence of fiber volume content This effect can be based supposably on intermolecular forces and drag forces. With a higher amount of fibers per unit of volume, the forces increase. If one fiber is dragged by the matrix system a chain reaction can take place, so that the following fiber is dragged and so on. Thus, the fiber matrix separation decreases with higher fiber volume content. The possibility of mechanical interlocking depends on the fiber volume content since the characteristic properties of the fibers are not varied. Figure 11 illustrates that the fiber density distribution is very different for the examples with 0.5 % and 6 % fiber volume content. While the higher fiber volume content features a uniform fiber density distribution at the last time step, the distribution for 0.5 % is very irregular and fiber jamming spots are visible. This can be presumably explained by a lesser possibility for intermolecular forces between the fibers itself and less dragging of fibers with the matrix. The hindrance of fibers by others can eventually play an additional role. It is obvious that the placing of the fibers in time step one plays an important role, too. This effect is described in chapter 4 in greater detail. Journal of Plastics Technology 9 (2013) 2 112

14 Figure 11: Fiber density distribution for different fiber volume contents Left: Fiber volume content of 0.5 % Right: Fiber volume content of 6 % Initial Mold Coverage For completeness of the results, the influence of the initial mold coverage on the FMS-Parameter was determined and additional simulations were performed. The range of the initial mold coverage was analyzed between 20 % and 72 %. In a former project the influence of the initial mold coverage on the FMS- Parameter has been already partly analyzed. Additional simulations show the same results. With increasing initial mold coverage, the FMS-Parameter decreases as was expected in these analyses. Figure 12 displays these results. With higher initial mold coverage the distance between the borders of the completely filled mold and the FMS-lines decreases. Due to this it can be deducted that the possibility, and the time available, for fiber matrix separation decreases as well. Hence, the fiber matrix separation decreases with increasing initial mold coverage. The effect of fiber bending can be assumed as constant for all reviewed initial mold coverage and thus should not have an influence. The fiber density distribution at the last time step is different for each fulfilled simulation. Considering the 20 % and 72 % initial mold coverage, there is a big discrepancy. Figure 13 shows that there is a much higher fiber density in the center of the mold for the 20 % initial mold coverage as compared to 72 % initial mold coverage. This effect can be explained due to each having the same fiber volume content, but with different initial mold coverages. Placing the fibers in the smaller area in the center of the mold favors the flow of the matrix system out of the initially covered mold area during the closing process and hence higher fiber matrix separation. Journal of Plastics Technology 9 (2013) 2 113

15 Figure 12: FMS-Parameter - influence of initial mold coverage Figure 13: Fiber density distribution for different initial mold coverages Left: Initial mold coverage of 20 % Right: Initial mold coverage of 72 % Viscosity Figure 14 presents the influence of viscosity on the FMS-Parameter. From this figure a trend can be seen for the analyzed range between 1000 and CST: with higher viscosity of the matrix the FMS-Parameter decreases. The outlier at CST can be explained by the position of the fibers in time step one (see chapter 4). Journal of Plastics Technology 9 (2013) 2 114

16 Figure 14: FMS-Parameter - influence of viscosity For a low viscosity such as 1000 CST, the flow of the matrix is advanced and hence the fiber matrix separation. In comparison to that, a high viscosity of the matrix system results in a high flow resistance and the entrainment of the fibers is most likely created by drag forces. Figure 15 displays the fiber density distribution. These illustrations show the effect of entrainment of the fibers for a high viscosity and hence an entrainment of the fibers from the center. With a lower viscosity an equal distribution is gained at the end of the flow process Carl Hanser Verlag, München Nicht zur Verwendung in Intranet- und Internet-Angeboten sowie elektronischen Verteilern. Möbius, Osswald et al. Figure 15: Fiber density distribution for different viscosities Left: Right: Viscosity of 1000 CST Viscosity of CST Journal of Plastics Technology 9 (2013) 2 115

17 Fiber Flexibility Figure 16 illustrates the influence of fiber flexibility on fiber matrix separation. A range from 10 0 to 10-4 for the fiber bending flexibility was analyzed. The changing of the fiber flexibility influences the bending behavior of a fiber and therefore the possibility of mechanical interlocking. The scale at the y-axis ranges between 24 % and 30 %; a comparatively small variation. By including the inaccuracy of the FMS-Parameter in these results, a trend is not predictable. As investigated in a former project for the case of mono-axial elongational flow [12] it seems that there is an influence of the fiber bending flexibility on the fiber matrix separation. Higher fiber flexibility may result in a better reaction of the fibers during fiber-fiber interactions and result in less fiber matrix separation at the flow front. Fiber orientation is taking place with a mono-axial flow front and hence fiber-fiber interactions. With more fiber-fiber interaction, the possibility for a reaction on this phenomenon rises and therefore the influence of the fiber flexibility on the fiber matrix separation. In case of an equi-biaxial elongation flow front these effects cannot be verified. The formation of a circular flow front combined with the flow of the fibers without any orientation results in less fiber-fiber interaction, as well as less entanglement of other fibers than would be seen in a mono-axial flow front. In principle there is a negligible influence of fiber flexibility and fiber matrix separation in the case of the observed two-dimensional equi-biaxial elongation flow. Figure 16: FMS-Parameter - influence of fiber flexibility In addition, for this case, the fiber density distributions also show almost no difference, Figure 17. The viewable divergence of fiber jamming can be reduced Journal of Plastics Technology 9 (2013) 2 116

18 due to the placing of fibers by the random generator right at the beginning of the simulations in time step one. Figure 17: Fiber density distribution for different fiber flexibilities Left: Fiber flexibility of 10 0 Right: Fiber flexibility of 10-4 Since the results of the influence of the fiber flexibility on fiber matrix separation are inconclusive, more work needs to be done in the future. Fiber Orientation Histograms of the fiber orientation were created for each time step of each simulation. As an example, Figure 18 illustrates the case of an initial mold coverage of 36 %, a fiber volume content of 3 %, a fiber aspect ratio of 23.75, a fiber flexibility of 10-2, and a viscosity of 1000 CST, at the beginning of the squeezing, in the middle of the flow process and at the end of flow. Therewith the change of orientation during the mold filling can be followed. The fiber orientation illustrations in Figure 18 give a visual presentation of the fiber orientation during the flow process for the same case and at the same time steps. As expected, the equi-biaxial flow field maintains the initially random fiber orientation distribution. Furthermore, the fiber-matrix separation is clearly visible. Journal of Plastics Technology 9 (2013) 2 117

19 ψ ψ Φ ψ ψ Φ ψ ψ0.50 Figure 18: Fiber orientation and fiber flow during the flow process Left: Middle: Right: First time step Time step at 50 % flow process Last time step Φ The arrows mark the same fibers at the different process steps. It can be seen, that there is no global, but a slight local fiber orientation most likely caused by fiber-fiber interactions. All simulations have shown the same results. 3.3 Experimental Approach To visualize the results of the numerical approach, several experiments were performed to investigate the simple flow process of fiber suspensions. The fiber suspensions used consist of silicone oil and carbon fibers. Within these experiments silicone oil as a matrix material was chosen to mimic a thermoset resin in a hot mold. Thereby three grades with different viscosities of the silicon oil XIAMETER PMX-200 Silicone Fluid were used: 1000 CST, CST and CST. Additionally four different lengths of Tenax -A HT C124 fibers were used for the experiments: 3 mm, 6 mm, 12 mm and 25 mm. The combinations of these different lengths of the fibers and the different viscosities of the silicone oil plus the examined fiber volume contents result in an experimental design of 19 experiments. In Table 2 the range of variation of the experimental settings are summarized. Journal of Plastics Technology 9 (2013)

20 Fiber volume content [%] Min Max Fiber aspect ratio [-] Min Max Fluid viscosity [CST] Journal of Plastics Technology 9 (2013) Min Max Range Table 2: Range of variation of experimental settings The weighing of the required amounts of both materials was done with a HR-60 scale, A&D Engineering, Inc., San Jose, CA, USA. To guarantee the homogeneity of the mixture, it was stirred multiple times a day for three days at room temperature. A few drops of water were added to the mixture to disperse the hairlines, which hold the fiber bundles together. Figure 19 shows the set-up of the experiments. To perform the experiments a Tetrahedron MTP-14 Compression/Lamination Press, Tetrahedron Associates, Inc., San Diego, CA, U.S.A with a piston size of 14 inch x 14 inch, was used. All experiments were run with the same characteristic parameters: a temperature of 25 C and a closing velocity of 5 mm/s. The set-up is based on a simple compression molding breadboard construction [15]. Figure 19: Experimental set-up Frames with transparent PMMA sheets were screwed on the plungers of the press to allow the optical study during experimentation. The charge was placed in the center of the mold and squeezed uniformly to the outsides by closing the press. Thereby, a circular flow front was enforced. For the material, black carbon fibers and transparent silicone oil was chosen to enhance the contrast, Figure 20.

21 Figure 20: Application of the charge Several pictures were taken during the experiment, at the beginning right after placing the charge into the mold and at the end of the experiment. To compare the flow behavior of the experiments, videos were taken additionally. For a better contrast between the fibers and the silicone oil a light source was installed on the opposite side of the camera. As mentioned before, the influence of the parameters fiber aspect ratio, fiber volume content and viscosity of the matrix material on fiber orientation and fiber matrix separation were analyzed. During the flow process, a visual inspection was performed. An image analysis was not conducted, as the measurement methods are too inaccurate. Furthermore, destroying the delivered fiber bundles could not been done equally. Hence, the fiber volume content was not consistent over the whole charge. 3.4 Results of Experimental Approach The following results were gathered from the experiments: in regards to fiber orientation the results agreed with the simulation. Only local, no global fiber orientation was observed. The fiber orientation is independent of the analyzed configurations. A small alteration between the fibers, when one fiber hinders another one in its flow process, was observable. This interaction is displayed for the case of a fiber volume content of 2 %, a fiber length of 6 mm (fiber aspect ratio of ) and a viscosity of 1000 CST exemplarily, Figure 21. Journal of Plastics Technology 9 (2013) 2 120

22 Figure 21: Fiber-fiber interaction and fiber orientation during the flow process ((1): right after placing of the charge to (4): squeezed charge); blue dotted circle: fiber orientation, red dashed circle: fiber-fiber interaction Additionally, the fiber matrix separation and the forming of fiber jamming and weak spots was visible, Figure 20. The same effects were observed in both experiments and simulations: Higher fiber aspect ratio results in more fiber matrix separation, Higher fiber volume content results in less fiber matrix separation and Higher viscosity results in less fiber matrix separation. Furthermore, an additional effect was observed. The fiber flow as well as the fiber orientation and the fiber matrix separation take place in two steps. First, an uncontrolled flow occurs, in the time period between placing the charge in the mold and the squeezing process. Secondly, a flow with an enforced circular flow front takes place, Figure 22. The flow of the material during the first period depends on the matrix system and on the placement of the fibers with irregular fiber density distribution. A higher matrix percentage enhances the flow of the matrix system. While the moving of the pistons enforces a circular flow front, a slight undefined flow direction is observable, if the charge is not placed in a perfect circular shape. Journal of Plastics Technology 9 (2013) 2 121

23 Figure 22: Divergence of equi-biaxial flow front The points below are limitations of these experiments: The disbandment of the fiber bundles is not guaranteed, hence there was an override on the fiber matrix separation. The focus was on a circular flow front, while right after placing the charge into the mold other shapes were observable, which influenced the later results. Blowing air influences the flow of the fibers as well. The fiber aspect ratio influences the orientation of the fibers in z-direction. This point was not included in the results. Due to the distortion of the construction, the pistons did not have an exactly parallel arrangement. Nevertheless, they were constructed to be stiff and the same distance at the end of the processes for each experiment was replicated by including distance pieces between the pistons itself. The material properties in the experiments did not exactly match the ones chosen for the simulations; however, the same trends were visible. In summary, the experiments agreed with the expected results, but these must be carefully adapted to real processes. 4 CONCLUSIONS AND DISCUSSION A compression molding process with an equi-biaxial elongation flow was simulated in this work. It was simplified to a two-dimensional problem. The influence of several parameters on the fiber orientation and fiber matrix separation during this process was analyzed. The following parameters were considered: fiber aspect ratio, initial mold coverage, fiber volume content, fiber flexibility, and the viscosity of the matrix system. All analyzed parameters have no influence on the global fiber orientation; however, a slight diversification of the local fiber orientation is visible. This Journal of Plastics Technology 9 (2013) 2 122

24 insignificant difference can be explained by fiber-fiber interaction during the flow process when one fiber hinders another one in its flow process. A positive trend is determined for the influence of the fiber aspect ratio on the FMS-Parameter; with increasing fiber aspect ratio, the fiber matrix separation increases as well and hence the FMS-Parameter. This effect can be described with the increasing possibility for mechanical interlocking and therefore more entanglements of longer fibers. A rising initial mold coverage results in a decreasing FMS-Parameter since the flow distance and time for fiber matrix separation are decreasing. Increasing fiber volume content results in the same trend as increasing initial mold coverage: the FMS-Parameter gets smaller. This effect can be explained by the rising of the intermolecular forces and drag forces with a higher amount of fibers per volume percent. When analyzing the influence of the fiber flexibility, no trends were observed. Here, the analyzed range of fiber flexibility and the resulting FMS-Parameter were too small while taking the inaccuracy of the parameter into account. The influence of the viscosity of the matrix material was analyzed. The result was not surprising, as a higher viscosity results in a lower fiber matrix separation. This effect is most likely explainable by the entrainment of the fibers during the flow process. The inaccuracy of the FMS-Parameter has to be taken into account for all results, since the placing of the fibers in time step one plays a significant role for the fiber flow during the compression molding process. As the amount of fibers at the flow front directly influences the FMS-Parameter, the usage of a small number of fibers and small fiber volume content can influence results greatly. Figure 23 illustrates an example. It is observable that fibers that are orientated perpendicular to the flow direction (see left figure) result in a smaller FMS-Parameter than fibers that are orientated in flow direction (see right figure). To illustrate the influence of fiber placing on the FMS-Parameter, one simulation was run five times with new fiber placement for each run. The following parameters were chosen for all of them: initial mold coverage of 36 %, fiber volume content of 3 %, fiber aspect ratio of 23.75, fiber flexibility of 10-2 and viscosity of the matrix material of 1000 CST. The resulted values of the FMS-Parameter including the standard error bars are shown for each example, Figure 24. Journal of Plastics Technology 9 (2013) 2 123

25 Figure 23: Inaccuracy of FMS-Parameter: two cases of fiber orientation Left: Right: Fibers orientated perpendicular to the flow direction Fibers orientated in flow direction Figure 24: Comparison of FMS-Parameters for different samples of fiber placement The FMS-Parameters range from to % with a maximum total difference of 6.03 %, and an average FMS-Parameter value of %. While deducting trends out of the diagrams shown in chapter 3, the inaccuracy of the FMS-Parameter values must be considered. To minimize the influence of the fiber placement, five cycles for each point of interest should be compiled to determine an explicit dependency. Furthermore, fiber placing in the center of the mold influences the fiber density distribution. The formation of weak spots is just as likely as the formation of weak spots within a three times higher fiber density distribution as the initial fiber volume content. Journal of Plastics Technology 9 (2013) 2 124

26 A simple compression molding process was carried out to obtain the experimental data. For a better visual control, the pistons of the press were extended with two PMMA sheets. The influence of the parameters fiber aspect ratio, fiber volume content and viscosity of the matrix material on fiber orientation and fiber matrix separation were analyzed. Within the possibilities of the visual control, the same effects were seen as for the simulations: no global fiber orientation was taking place, but a slight local alteration because of fiberfiber interactions. Furthermore, it was visible that the fiber flow, fiber orientation, and hence the fiber matrix separation take place in two steps: first an indefinite flow in the time period between placing the charge in the mold and the squeezing process; secondly, a flow with an enforced circular flow front. Acknowledgement The authors would like to thank Prof. Dr.-Ing. habil. Prof. E.h. Dr. h.c. W. Hufenbach, director of the Institute of Lightweight Engineering and Polymer Technology of the TU Dresden for his support during Ms Möbius research and while writing this article. Journal of Plastics Technology 9 (2013) 2 125

27 Literature [1] Jeffery, G. B. The Motion of Ellipsoidal Particles Immersed in a Viscous Fluid Proceedings of the Royal Society of London. Series A, Vol. 102 (1922) [2] Mason, S. G.; Manley, R. ST. J. [3] Folgar, F.; Tucker, C. L.: Particle Motions in Sheared Suspensions: Orientations and Interactions of Rigid Rods Proceedings of the Royal Society of London. Series A, Vol. 238 (1956) Orientation Behavior of Fibers in Concentrated Suspensions Journal of Reinforced Plastics and Composites, Vol. 3 (1984) [4] Advani, S. G.: Prediction of Fiber Orientation during Processing of Short Fiber Composites PhD-Thesis, Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, 1987 [5] Yamamoto, S.; Matsuoka, T. [6] Ross, R. F.; Klingenberg, D. J. A method of dynamic simulation of rigid and flexible fibers in a flow field Journal of Chemical Physics, Vol. 98 (1993) Dynamic simulation of flexible fibers composed of linked rigid bodies Journal of Chemical Physics, Vol. 106 (1997) [7] Switzer, L. Simulating Systems of Flexible Fibers PhD-Thesis, Department of Mechanical Engineering, University of Wisconsin-Madison, 2002 [8] Wu, J.; Aidun, C. K. [9] Londoño-Hurtado, A.; Hernández-Ortiz, J. P.; Osswald, T. A. A method for direct simulation of flexible fiber suspensions using lattice Boltzmann equation with external boundary force International Journal of Multiphase Flow, Vol. 36 (2010) Mechanism of Fiber Matrix Separation in Ribbed Compression Molded Parts Polymer Composites, Vol. 28 (2007) Journal of Plastics Technology 9 (2013) 2 126

28 [10] Schmachtenberg, E.; Lippe, D.; Skrodolies, K. [11] Londoño-Hurtado, A.; Osswald, T. A. [12] Eilbracht, S.; Londoño-Hurtado, A.; Osswald, T. A. Faser-Matrix-Entmischung während des Fliesspressens von SMC Journal of Plastics Technology, Vol. 6 (2005) Modeling of Fiber Jamming Phenomena during Processing of Fiber Reinforced Composite Parts Key Engineering Materials Vol. 425 (2010) Fiber Orientation and Fiber-Matrix Separation Phenomena during Compression Molding Proceedings of the ANTEC 2010, Orlando, USA [13] Londoño-Hurtado, A. Mechanistic models for fiber flow PhD-Thesis, Department of Mechanical Engineering, University of Wisconsin-Madison, 2009 [14] Baird, D. G.; Collias, D. I. [15] Ufer, J; Brostowitz, N.; Londoño-Hurtado, A.; Ziegmann, G.; Osswald, T. A. Polymer Processing Principles and Design. John Wiley & Sons, New York, 1998 Experimental Study of Fiber-Matrix Separation and Fiber Density Distributions in Fiber Suspensions Proceedings of the ANTEC 2010, Orlando, USA Keywords: fiber orientation, fiber matrix separation, fiber jamming, computer simulation, flexible fiber Journal of Plastics Technology 9 (2013) 2 127

29 Autor/author: Dipl.-Wi.-Ing. Teresa Möbius Dipl.-Ing. Stephan Eilbracht Dr.-Ing. Natalie Rudolph Prof. Tim A. Osswald Department of Mechanical Engineering, University of Wisconsin Madison, 1513 University Avenue, Madison, WI Herausgeber/Editor: Europa/Europe Prof. Dr.-Ing. Dr. h.c. Gottfried W. Ehrenstein, verantwortlich Lehrstuhl für Kunststofftechnik Universität Erlangen-Nürnberg Am Weichselgarten Erlangen Deutschland Phone: +49/(0)9131/ Fax.: +49/(0)9131/ Adresse: ehrenstein@lkt.uni-erlangen.de Verlag/Publisher: Carl-Hanser-Verlag Jürgen Harth Ltg. Online-Services & E-Commerce, Fachbuchanzeigen und Elektronische Lizenzen Kolbergerstrasse Muenchen Tel.: 089/ Fax:089/ Adresse: harth@hanser.de -Adress: t.moebius@ilk.mw.tu-dresden.de Website: Tel.: +49(0)351/ Fax: +49(0)351/ Amerika/The Americas Prof. Prof. h.c Dr. Tim A. Osswald, responsible Polymer Engineering Center, Director University of Wisconsin-Madison 1513 University Avenue Madison, WI USA Phone: +1/ Fax.: +1/ Adresse: osswald@engr.wisc.edu Beirat/Editorial Board: Professoren des Wissenschaftlichen Arbeitskreises Kunststofftechnik/ Professors of the Scientific Alliance of Polymer Technology Journal of Plastics Technology 9 (2013) 2 128