Computational Methods and Experimental Measurements XII 909

Transcription

1 Computational Methods and Experimental Measurements XII 909 Modelling of a LPM filling process with special consideration of viscosity characteristics and its influence on the microstructure of a non-crimp fabric fiber bed M. Repsch, U. Huber & M. Maier Institut für Verbundwerkstoffe GmbH, Department Design and Analysis, University of Kaiserslautern, Germany Abstract Recently, in RTM process techniques, in-situ polymerizing thermoplastics are a promising alternative for conventional thermoset matrix systems. The advantages of these systems are given by a low initial injection viscosity in combination with a polymerization process during injection. This means that a fast mold filling is possible even for high fiber volume fractions. Additionally, the process steps of injection and curing are combined to one single step, which leads to a significant reduction in cycle time. From these advantages several problems arise for the simulation of a filling process, which is mainly based on Darcy s Law. The low initial viscosity causes high and inertia affected fluid velocities, violating the Darcy s Law restriction of a sufficient slow flow. With proceeding polymerization the viscosity characteristic is changing from an initial Newtonian to a visco-elastic flow behavior. The shear rate dependency of the fluid is additionally violating the restriction of a constant viscosity. The intention of this paper is to investigate high velocity and therefore inertia affected fluid flow in a non-crimp fabric fiber bed. Several fluids have been characterized by their rehological behavior. Based on these characterizations, flow experiments were executed to investigate the deviations between Darcy flow and fluid flow, which does not fulfill the restrictions. Additionally, the influence of visco-elastic fluid characteristic on the fiber bed microstructure was analyzed. Keywords: permeability, visco-elasticity, Newtonian, micro structure, Darcy s Law, high fluid velocity, viscosity characteristic, non-crimp.

2 910 Computational Methods and Experimental Measurements XII 1 Introduction Resin Transfer Molding (RTM) is an efficient process for the manufacturing of polymer composite structures. During RTM a liquid, low viscosity thermoset resin is injected into the mold cavity containing a pre-placed dry fabric preform. Due to quite low injection pressure applied in processing this technique it is expected to offer potential for cost reduction in the fabrication of large parts of complex shape. Recently in RTM an alternative to the use of thermoset resins has been developed by in-situ polymerizing thermoplastics. In general the process steps for this modified RTM technique are very similar. Due to polymerization of the thermoplastic during mold filling the flow behavior of the fluid changes from Newtonian to visco-elastic flow. This leads to a rising viscosity by a factor of 100 starting from an initial viscosity of 17 mpas [1]. In order to shorten the development process nowadays a simulation tool for designing molds as well as optimizing the process are absolutely necessary. These tools are mainly based on Darcy s law, which represents one of the most common used empirical equations to describe flow through porous medias. In its simplest formulation it takes the form: K f p v = (1) η x f In this formulation v denotes the fluid velocity respectively the flow front speed, η f represents the viscosity of the infiltrating fluid, K f stands for the permeability of a porous media and p/ x is representing the pressure gradient [2]. In general Darcy s Law is restricted to slow inertia free flow and a low viscosity Newtonian flow behavior of the fluid [3]. As described above these restrictions are not satisfied when using in situ polymerizing thermoplastics due to their non- Newtonian viscosity and inertia effects which are caused by the water like low initial viscosity. This significant difference in the fluid characteristic requires adapting the flow model for the simulation. In order to get information about the flow behavior of these thermoplastics flow experiments in unidirectional fiber beds were performed. For this application one-dimensional flow test is suited best, the exact test setup is described elsewhere [3]. This kind of experiments can be evaluated by the constant method. This method assumes that the permeability over the flow length is constant. Thus the following equation results directly by integration from Darcy s Law: K const m η = 2 p 0 (2) In this formulation denotes K const the permeability to be calculated, η represents the constant viscosity of the fluid used, p 0 stands for the constant injection

3 Computational Methods and Experimental Measurements XII 911 pressure and m represents the ascending slope of the straight line through the origin of a diagram square of flow path over time [4]. This slope m is directly proportional to the permeability as can be seen easily from equation. (2). 2 Fluid characterization 2.1 Overview As a first step the fluid has to be characterized. The important parameters are the change in viscosity over time and temperature as well as the dependency of the viscosity on the shear rate. Due to handling difficulties of the in-situ polymerizing thermoplastic a replacement fluid has been chosen. The main requirement for this fluid is a similar characteristic as the polymerizing thermoplastic; especially a strong shear thinning property is needed. Additionally the fluid has to be curable to allow the preparation of micrographs of the impregnated fiber bed. Thus an epoxy system has been selected, which will be described more detailed later on. For reference experiments a commercially available vegetable oil has been chosen as Newtonian fluid. 2.2 Newtonian fluid Due to the strong temperature dependency of polymer fluids the measurements of the oil have were carried out at different temperatures. A temperature range from 20 C up to 27,5 C was defined, reflecting that all experiments were carried out isothermally at slightly changing room temperature. The viscosity of the vegetable oil is ranging from 0,055 Pas at 20 C to 0,036 Pas at 27,5 C. In order to verify the Newtonian behavior of the vegetable oil some measurements of the viscosity in dependence of the shear rate were performed. Since only a low momentum can be transferred at low shear rates it was not possible to measure directly the shear rate dependency of the vegetable oil. For this purpose the phase angle of the viscosity measurement was observed. The phase angle gives the ratio of the elastic fraction of the total viscosity of the fluid. In this case a phase angle of 90,6 was measured thus the fluid can be held as shear rate independent. 2.3 Viscoelastic fluid For the shear rate dependent flow an epoxy system (Ly113 / Hy97) from the Huntsmann Company was selected and characterized. Figure 1 shows the initial viscosity of the resin decreasing from 0,690 Pas at 20 C to 0,325 Pas at 27,5 C but at the same time the polymerization velocity is rising significantly. In contrast to the vegetable oil the higher initial viscosity of the epoxy resin with 690 Pas at 20 C allows measuring the shear rate dependency directly. So shear rates from 0,023 1/s to 225 1/s were measured. Figure 2 shows the results from these measurements. The first measurement of the viscosity was started

4 912 Computational Methods and Experimental Measurements XII 1200 s after mixing the single components of the resin. Then, the measurements were repeated in intervals of 1800 s to evaluate if the shear rate dependency of the viscosity is influenced by the ongoing polymerization. In the graphs in figure 2 the strong shear rate dependency on the viscosity at low shear rates is visible. But interestingly at shear rates lower than 0,1 1/s the viscosity is not dependent of the degree of polymerization. This effect occurs when the macromolecular chains only need one energetic level to keep their degree of orientation independently from the grade of polymerization. Viscosity [Pas] ,0 C 22,5 C 25,0 C 27,5 C Time [s] Figure 1: Viscosity evolution at different temperatures Viscosity [Pas] ,1 T1200 T3000 T4800 T6600 T8400 T10200 T ,01 0, Shear rate [1/s] Figure 2: Shear rate dependency of the epoxy resin.

5 3 High fluid velocities In order to examine inertia affected fluid flow experiments with high flow velocities were executed using the oil with Newtonian viscosity characteristic. The fiber volume fraction in these experiments was 26% by vol. using a noncrimp unidirectional fabric. The temperature was held constant during impregnation. The injection pressure was set to a constant level of 0,2 bar. Graph 2 in figure 3 shows a reasonable fit of the experiment with the straight line through the point of origin predicted by the theory. This match indicates that the fluid velocity with 0,0018 m/s is fulfilling the restriction of a sufficient slow flow. Afterwards the injection pressure was elevated to 0,5 bar to investigate the differences in flow behavior to the former experiment. The results from these experiments are shown in graph 1 of figure 3. It is obvious that the experimental values are differing from the straight line given by the assumption of the constant method. Up to a flow path of 0,17 m (0,03 m²) the fluid flow is inertia affected. At this point the deviation has its maximum. From this point onward the fluid flow is starting to become flow channel dominated. The flow channel effect is visible through the rising slope of the graph, which means an increased permeability of the fiber bed. The forming of flow channels will be demonstrated in section 5. 0,14 Computational Methods and Experimental Measurements XII 913 Length² [m²] 0,12 0,10 0,08 0,06 0,04 0,02 0, Time [s] 0,2 bar 0,5 bar Regr. 0,2 Regr. 0,5 Figure 3: Square of flow path over time at 0,2 bar and 0,5 bar injection pressure. 4 Visco-elastic flow Based on the reference permeability calculated from the 0,2 bar experiment the differences of Newtonian and viscoelastic flow are now quantified. For this

6 914 Computational Methods and Experimental Measurements XII purpose experiments with a fiber volume fraction of 50% have been carried out. An injection pressure of 1,5 bar was applied, the epoxy resin mentioned in section 2.3 was used as fluid. Figure 4 shows a diagram of a representative experiment. The square of flow path over time is displayed, additionally the straight line delivered by Darcy. Again, up to a flow length of 0,17 m (0,03 m²) inertia affected flow can be observed. It can be seen that the curve progression up to 0,17 m (0,03 m²) is not a continuous enlargement of the following section. The following region is dominated by an accelerated flow in the inter tow space. This is expressed by a further increase of the deviation of the experiment from the straight line with a maximum at 0,24 m (0,06 m²) in flow length. The forming of flow channels will be shown in section 5 by the microstructural investigation. The last part of the curve is mainly influenced by a rising viscosity resulting from the viscoelastic viscosity characteristic due to decreasing shear rates with increasing flow length, which also means decreased flow speed. 0,12 0,10 Length² [m²] 0,08 0,06 0,04 0,02 0, Time [s] 1,5 bar Regr. 1,5 Figure 4: Square of flow path over time for a visco elastic injection. 5 Micro structural investigation The aim of the micro structural analysis was to investigate the influence of the fluid flow on the non-crimp fabric bed. The samples used for the investigation are produced with the same set of parameters as for the visco-elastic flow mentioned in section 4. After the impregnation is finished the injection pressure is held constant during the whole curing process to avoid changes in bundle and filament distribution by relaxation on a lower curing pressure. To analyze these influences polished cross-section cuts have been prepared from the plates impregnated by the epoxy resin. From these samples micrographs were taken to analyze at first the mesoscopic distribution of bundles, the forming of micro

7 Computational Methods and Experimental Measurements XII 915 channels inside the fiber bed and the distribution of the filament inside one bundle itself. The pictures in figure 5 are taken at a flow length of 15 mm, 115 mm, 265 mm and 365 mm respectively. From picture (a) it can be seen that the bundle distribution at the beginning of the flow path is nearly homogeneous. Picture (b) and (c) show the forming of micro channels supporting an accelerated fluid flow. It can be assumed that the main stream flows in these flow channels and impregnates the bundles transversally. Picture (d) shows the bundle distribution to be nearly homogeneous. In contrast to picture (a) taken at the beginning of the flow area the bundles are no longer that compact. One reason for this effect could be the slower flow speed and thus a relocation of the flow from the inter tow to the intra tow space possibly supported by capillary effects. (a) 15 mm (b) 115 mm (c) 256 mm (d) 365 mm Figure 5: Micrographs from different positions over the flow length. 6 Conclusion Inertia affected and visco-elastic flow plays an important role during the impregnation process in RTM. It can be stated that flow channel driven and

8 916 Computational Methods and Experimental Measurements XII therefore transversal impregnation of bundles is one of the most important mechanisms for transfer molding processes. From this arises the need to understand and to investigate the role of the microstructure during the process. One aim of this project is to detect the impregnation mechanisms on a micro structural level to achieve a more accurate flow simulation on a macroscopic scale. References [1] Eder, R.H.J, Cyclics Thermoplastics- Properties and Processing, IVW Schriftenreihe Band 25, pp , 2001 [2] Darcy, H.P., Les Fontaines Publiques de la Ville Dijon, Victor Dalmont, Paris, 1856 [3] Huber, U., Zur methodischen Anwendung der Simulation der Harzinjektionsverfahren, Dissertation University Kaiserslautern, 2001 [4] Flemming, M., Ziegmann, G. & Roth, S., Faserverbundbauweisen Fertigungsverfahren mit duroplastischer Matrix, Springer-Verlag: Berlin and New York, 1999