Experimental Measurements of sink terms for unsaturated flow during liquid composite molding

Transcription

1 Experimental Measurements of sk terms for unsaturated flow durg liquid composite moldg Fei Yan 1, Shil Yan *,1, Yongjg Li 1 and Dequan Li 1 1. School of Science, Wuhan University of Technology, Wuhan, Hubei, Cha Abstract: Simulation of the res flow process is an important method used to vestigate the unsaturated flow of liquid composite moldg (LCM), and establishment of the sk function is the primary premise of unsaturated flow fillg simulation durg LCM. In this study, an experimental facility for unsaturated flow under one-dimensional constant pressure was established and an experimental method to establish the sk function was proposed. A specific expression of the sk function was obtaed. This sk function was used to simulate the unsaturated mold fillg experiment. Variations of flow front position, unsaturated length, mold fillg time, and jection flow were compared. The established sk function and the simulation results were consistent with the experimental data. Keywords: LCM, constant pressure, unsaturated flow, permeability, sk function 1. Introduction Fiber fabrics LCM is often woven or stitched by fiber tow. The gap between fiber tows is at the millimeter level, and the gap side the fiber tow is at the micron level. Once res is impregnated to the dual-scale fiber preform, unsaturated flow would be generated because of different impregnation rates, thus makg existg theory misestimate mold fillg pressure and fail to predict mold fillg time accurately 1-4. Several scholars proposed the sk model to analyze this unsaturated flow behavior 5-7. This theory divides unsaturated flow to micro tra-tow flow and macro ter-tow flow among fiber fabrics, as shown Figure 1. Figure 1. Schematic representation of unsaturated flow. The proposed sk function was used to represent delay impregnation the unsaturated region The proposed sk function is tegrated to the equation of contuity to obta the control equation of macro flow. With the development of computg technology, sk theory has been the focus of considerable attention and is creasgly accepted by many scholars. Sk theory assumes that the volume change rate of res the fiber tow is not zero and the tra-tow gap is not filled completely. From the mass conservation equation, the followg expression can be derived: K ( p ) = S (1) µ where K is the permeability tensor, p µ is the pressure gradient, is the liquid viscosity, and S is the sk function. S represents the rate of unit volume change when res impregnates the fiber tow and is expressed as follows: ds S = εtow(1 ε gap) dt (2) gap where ε is the porosity between fiber tows (excludg porosity side the fiber tow), ε tow is the porosity side the fiber tow, S tow is the saturation side one fiber tow, and dt is the saturated rate side the fiber tow, which is recorded as S& tow. When S tow = 0, tra-tow gaps are not filled. When 0 < S tow < 1, several tra-tow gaps are filled. When S tow = 1, tra-tow gaps are filled fully. At this moment, S = 0 and the fiber preform is saturated completely. Equation (2) shows that S is the key factor couplg ter-tow and tra-tow flows. The sk rate of res to fiber tows can be obtaed after S is determed, thus enablg the simulation of the unsaturated flow of dual-scale fiber preform. In recent years, many calculation models were established to do numerical simulation base on the dual-scale flow behavior With this model, they traced the flow behavior side fiber tows. However, most existg research, sk function was acquired through unit cell simulation. Unit cell simulation can easily obta the sk function, but has high requirements on the accuracy of the unit cell. In actual circumstances, the simulation result often deviates from experimental result to a certa extent. Do to the heterogeneous fiber ply and the deformation which is caused by the pressure of the mold, unit cell can t represent the microstructure for fiber preform. Therefore, further experimental research on sk function is important to improve simulation accuracy, optimize mold design, and reasonably determe moldg pressure, mold fillg time, and jection port. tow Journal of Residuals Science & Technology, Vol. 13, No. 6,

2 2. Experiment prciple and program 2.1 Experimental prciple From Equation (2), the sk function is a function related to the saturated rate. The specific form of the sk function can be obtaed as long as the relational expression of S & tow is determed. Therefore, S & tow was implemented dimensionless by takg the characteristic time as the fillg time (t ). Then, the dimensionless form of S& S & tow can be expressed as follows: ds dt ( ) t dτ tow tow = = (3) where τ is the dimensionless time, t is the characteristic time, and is the dimensionless saturated rate and is a function dτ related to S tow. Sk theory reveals that fluid impregnation to fiber tows can be viewed as sgle-scale saturation flow. Then, t is a function related to clearance pressure and viscosity. Therefore, the specific expression of the sk function can be obtaed after the expressions of t and are determed. dτ 2.2 Experimental program The basic parameters of the sk function can be calculated through the unsaturated flow experiment of constant pressure jection the one-dimensional plane. A set of visual digital acquisition systems was established (Figure 2) for the convenient observation of flow front position changes durg mold fillg. The experimental facility maly cludes a constant pressure power unit, flowmeter, pressure sensor, signal collector, mold, computer, rectifier, camera, and related valves and conduits. This experimental facility itially creased pressure through the air compressor and then controlled pressure at the air compressor exit through the constant pressure control valve to provide a stable pressure output. The other end of the constant pressure control valve was connected to a closed tank with mold fillg liquid. The entire mold fillg process can be viewed as a one-way flow along the length direction. From the previously discussed prciple, the mold should be made of 7075-T651 alumum alloy with excellent performance. The mold cavity should have a thickness of 4 mm, a width of 90 mm, and a length of 1,000 mm. The upper mold should be sealed with a 10 mm-thick organic glass and fixed with an alumum alloy framework to form an observation wdow. The time which the liquid flows from the front position to the preset position can be determed from this observation wdow. The dynamical system adopted the external connection of the Jaguar ZB-0.10 air compressor with pressure regulatg valve to control air compressor to ensure a constant pressure output. A closed tank with mold fillg liquid was connected to the exit of the air compressor. The pressure effect ensured that the liquid flowed out from the other end of the closed tank and was jected to the mold cavity through the NU.ER.T. flowmeter made by an Italian company. Five pressure sensors were set from the jection port along the length of mold. Pressure and flow variations at different measurement pots were converted to digital formation through an electric signal collector and stored a computer. A digital camera was set at the upper mold to record the entire mold fillg process. Figure 2. Experimental facility. In this study, triaxially stitched and unidirectional glass fiber fabrics were selected as fiber preforms. Low-viscosity vegetable oils were used as mold fillg liquid. The correlated experimental parameters are listed Table 1. Table 1. Experimental sample and correlated parameters. Sample Material Ply Injection pressure (kpa) Porosity Viscosity (Pa s) Journal of Residuals Science & Technology, Vol. 13, No. 6,

3 1 Triaxially stitched 2 Triaxially stitched 3 Unidirectional Glass fiber fabrics were cut to 9 cm 60 cm strips and layered the mold cavity accordg to a certa layerg mode. The organic glass panel and the alumum alloy framework of the mold were fixed with bolts and were connected to the air compressor, pressure sensor, flowmeter, and data acquisition system. Preloadg was adopted, and the pressure-regulatg valve was adjusted to the desired pressure. The tightness of the experimental facility was examed. Then, the valve was opened and data acquisition was updated after no voltage draage was detected. The test temperature and humidity were set 20 C and 60%. 3. Test method of sk function In the unsaturated flow experiment under constant pressure jection, a total of five different pressure test pots were set. In the experiment, the time which the saturated flow front reached at the test pots was selected as the study object. An unsaturated region was detected at the test pot at this moment (Figure 3). Figure 3. State of saturated flow front arrivg at the test pots. Figure 3 shows the state of saturated flow front arrivg at one test pot, where the red region is unsaturated region. From the characteristics of unsaturated flow, this red region is observed to have saturated and unsaturated flow fronts. Test pot 2 is the saturated flow front. Pressure at this pot is recorded as the itial tra-tow pressure P 0 and the time is recorded as t 0. The length of the unsaturated region can be observed the experiments. The positions of the saturated flow front were observed. The time which the unsaturated region is filled completely was recorded as t 1. Thus, the time which the liquid fills the tra-tow gaps of the unsaturated region can be expressed as t = t 1 t 0. The relationship between t and P 0 under different experimental samples is determed based on the time which the saturated flow front reaches test pots 1 to 5 to derive the variation laws of unsaturated flow time and ter-tow pressure durg the mold fillg process (Figure 4). Figure 4. Relationship between t and P 0 under sample 1. The relationships between t and P 0 under sample 1 are shown Figures 5. The black square pots denote the measured data of five test pots, and the red curve denotes the fittg results. For this experimental samples, the relationships between t and P 0 can be fitted A P = approximately by the function image of 0 t. The liquid impregnated to the fiber tows can be viewed as saturated flow. Given a constant pressure, viscosity is proportional to mold fillg time. Therefore, the relationship between t and P 0 can be expressed as follows: t aµ = (4) P0 Journal of Residuals Science & Technology, Vol. 13, No. 6,

4 The value of coefficient a can be determed accordg to the experimental data. From Equation (4), the relationship between saturated rate and saturation should be determed to derive the specific expression of the sk function. From the defition of sk terms, the expression of sk flow the same region when t = t 0 can be written as follows: Q Kgap P = ( + )da A µ l Q (5) Ω b where Q is the sk flow representg the flow rate of liquid from ter-tow to tra-tow gap; Q K is the flow rate at t 0; gap is the l ter-tow permeability, which can be obtaed through experiments; and b is the length of the unsaturated flow front. Q at t 0 can be S & tow and Q have the followg relationship: calculated. From the physical significance of the saturated rate, Q S& tow = = (6) tf where V tf is the volume of tra-tow pores. Substitutg Equation (5) to Equation (6), dt V S & tow at t 0 can be obtaed. Given that the mold fillg liquid is compressible, the impregnated volume of fiber tows at t 0 is equal to all liquid volume the unsaturated region mus the ter-tow pores and is expressed as follows: Vt = Vf Vgap = Vf ε gapv (7) bulk where V t is the impregnated volume of fiber tows at t 0; V f is the total liquid volume the unsaturated region, which can be tested by data processg software; V bulk is the total volume of unsaturated region; V gap is ter-tow pores the unsaturated region; and ε gap is ter-tow porosity, which can be measured by experiments. The related results are shown Table 2. Sample Table 2. Related physical parameters fabrics. Material Inter-tow permeability (m 2 ) Inter-tow porosity Triaxially stitched Triaxially stitched Unidirectional Intra-tow porosity From the defition of saturation, tra-tow saturation ( S tow ) can be expressed as follows: S (8) where S tow is the tra-tow saturation the unsaturated region at t 0; V t is the impregnated tra-tow volume at t 0; and V tow is the volume of fiber tows, which can be calculated. In summary, Q, S & tow, and S tow the unsaturated region at t 0. were acquired by usg the same method, dτ and S tow can be obtaed. Their relationship can be disclosed through curve fittg. From polynomial nonlear fittg, dτ can be expressed as follows: 2 3 b cstow ds tow es tow dτ = (9) Integratg Equation (9) to Equation (2), the specific expression of the sk function can be expressed as follows: S P (1 ) aµ tow V = V t tow { b cs ds es } = εtow ε gap + tow + tow + tow (10) where ε tow and ε gap are the tra-tow and ter-tow porosities, respectively; P 0 is the tra-tow itial pressure; S tow is the saturation; and a, b, c, d, and e are constant coefficients, which can be obtaed through fittg of the experimental data. Constants under the three experimental samples obtaed from fittg of the experimental data are listed Table 3. Sample 1 2 Material Table 3. Coefficients of the sk function. Injection pressure (kpa) a b c d e Triaxially stitched 70 4,125, Triaxially stitched 100 4,358, Journal of Residuals Science & Technology, Vol. 13, No. 6,

5 3 Unidirectional 70 7,647, The table shows that the coefficient a of samples 1 and 2 are close to each other, whereas that of samples 2 and 3 differ significantly. Coefficient a represents the sk time side the tra-tow. The fiber tows of samples 1 and 2 have the same stitched structure; thus, their coefficients have a similar value. The other coefficients show that the sk function of fiber is related to its knittg structure. The same fabric has the same sk function, whereas fabrics with different geometric structures have significantly different sk functions. 4. Simulation analysis 4.1 Comparison of unsaturated flow The specific expression of the sk function and all physical parameters used to solve the control equation have been acquired previously. A comparative analysis of the accuracy of the sk function and the experimental data was implemented by combg the fite element solvg programs that have compiled. Given that the sk function was established through the constant pressure jection experiment the one-dimensional plane, sample 1 was taken as the control group to verify the accuracy of the calculation model. Under the same jection conditions, whether the simulation results were consistent with the experimental data was verified. The commercial software ANSYS was used for preprocessg, and a model was established accordg to the actual size of the mold cavity for the purpose of meshg and determg boundary conditions. The model adopted triangle unit discretion and cluded 540 discrete units and 310 nodes. Flow velocity was defed on the left node of the model, and the other side of mold was determed as the exit. The upper and lower ends were closed terfaces. The pressure distribution along the flow front position under sample 1 is shown Figure 5. The dotted le denotes the simulated results of saturated flow. The accompanyg curve denotes the simulated results of unsaturated flow. Each curve represents the pressure distributions when flow front reaches test pots 2 to 5. Figure 5 shows that the pressure distribution curves at different times all deviate toward the left to a basically equal extent because of the jection port. The calculation model did not consider the surface tension between fibers and the effect of capillary pressure, thus matag the constant pressure gradient between and side fiber tows. Figure 5. Pressure distribution when the saturated flow front reaches pots 2 to 5. The relationships between flow and time under sample 1 are shown Figures 6(a) and 6(b). Figure 6(a) shows the simulated result, and Figure 6(b) shows the experimental result. Notably, the simulated and experimental results have basically the same shape. A comparison of their vertical coordates shows that the simulated result is smaller than the experimental result durg the early mold fillg stage. This fdg is determed by the characteristics of the algorithm. In the simulation, impregnation side the fiber tow was considered at the begng of flow. Durg mold fillg, the liquid impregnates the large ter-tow pores, causg a delayed impregnation of the liquid side the fiber tow. Journal of Residuals Science & Technology, Vol. 13, No. 6,

6 Figure 6(a). Flow variation of sample 1 (simulation). Figure 6(b). Flow variation of sample 1 (experiment) The flow front positions under sample 1 at different times are shown Figures 7, 8, and 9. In Figure 7, the length of the simulated unsaturated region when t = 4.3 s is 4 cm and the length of the experimental unsaturated region is 4.5 cm. Thus, the lengths of the simulated and experimental unsaturated regions are similar to each other. The simulated unsaturated flow front position is at 12 cm, whereas the tested position is at 8.5 cm. Durg the early stage of jection, pressure creased slowly and the actual pressure gradient was smaller than the theoretical value; thus, the liquid flowed slowly. As mold fillg contued, this difference was offset gradually. When t = 65 s, the simulated flow front position is 42 cm, which is consistent with the experimental result (40 cm) (Figure 8). Position of flow front Unsaturated zone Figure 7. Simulated results under sample 1 when t = 4.3 s. Figure 8. Flow front position of sample 1 when t = 66 s. Journal of Residuals Science & Technology, Vol. 13, No. 6,

7 Figure 9. Flow front position of sample 1 when t = 120 s. The simulated and experimental results at 120 s of mold fillg are shown Figure 9. The unsaturated flow fronts of the simulated and experimental results were at 56 and 58 cm, respectively. It was noticed that the shape of the simulated unsaturated flow front at different times is straight, whereas the shape of the experimental unsaturated flow front is arched or different. Durg the simulation, the given boundary conditions are equal pressures at the left nodes. Vertically, the nodes have the same saturation, thus resultg the straight shape of the simulated unsaturated flow front. 5. Conclusions From the experiment and dimensionless analysis, this study deduces and establishes the expression of the sk function and derives the followg conclusions: (1) The experimental results show that the sk function and constant coefficients of same fabric are close, whereas the constant coefficients of different fabrics differ significantly. This fdg dicates that the geometric shape of fabrics is the ma fluencg factor of unsaturated flow durg LCM. (2) The simulated flow durg the early stage is significantly different from the experimental result because pressure creases slowly a certa period of the actual mold fillg process. As mold fillg contues, the simulated flow curve is consistent with the experimental data. (3) The pressure distribution curves at different times all deviate toward the left to a basically equal extent because of the jection port. (4) The flow front position durg mold fillg is consistent with the experimental result, which can be used to predict the mold fillg process accurately. Establishg the sk function based on the experiment provides a new idea for the simulation of unsaturated flow durg LCM and guides engeerg applications. Acknowledgements This work was supported by the National Science Foundation of P.R. Cha, Grant No References [1] S. Amico and C. Lekakou, Flow through a two-scale porosity oriented fibre porous medium. Transport Porous Med. Vol. 54, 35 53(2004) [2] W. B. Young and S. F. Wu, Permeability measurement of bidirectional woven glass fibers. J. Compos. Mater. Vol. 14, (1995) [3] J. Breard, Y. Henzel and F. Trochu, Analysis of dynamic flows through porous media. Part I: comparison between saturated and unsaturated flows fibrous reforcements. Polym. Composite. Vol. 24, (2003) [4] F. D. Dungan and A. M. Sastry, Saturated and unsaturated polymer flows: Microphenomena and modelg. J. Compos. Mater. Vol. 36, (2002) [5] C. M. Lekakou and G. Bader, Mathematical modellg of macro and micro filtration res transfer mouldg(rtm). Compos. Part A. Vol. 29, 29-37(1998) [6] Y. Wang, M. Moatamedi and S. M. Grove, Contuum dual-scale modelg of liquid composite moldg processes. J. Compos. Mater. Vol. 28, (2008) [7] H. Tan and K. M. Pillai, Fast LCM simulation of unsaturated flow dual-scale fiber mats usg the imbibition characteristics of a fabric-based unit cell. Polym. Composite. Vol. 31, (2010) [8] T. Centea and P. Hubert, Modellg the effect of material properties and process parameters on tow impregnation out-of-autoclave prepregs. Compos. Part A. Vol. 43, (2012) [9] X. Chen and T. D. Papathanasiou, On the variability of the Kozeny constant for saturated flow across unidirectional disordered fiber arrays. Compos. Part A. Vol. 37, (2006) [10] P. Simacek, V. Neacsu and S. G. Advani, A phenomenological model for fiber tow saturation of dual scale fabrics liquid composite moldg. Polym. Composite. Vol. 31, (2010) [11] G. Bechtold and L. Ye, Influence of fibre distribution on the transverse flow permeability fibre bundles. Compos. Sci. Technol. Vol. 63, (2003) [12] J. Slade, K. M. Pillai and S. G. Advani, Investigation of unsaturated flow woven braided and stitched fiber mats durg mold-fillg res transfer moldg. Polym. Composite. Vol. 22, (2001) Journal of Residuals Science & Technology, Vol. 13, No. 6,

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