ADDRESSING VARIABILITY OF FIBER PREFORM PERMEABILITY IN PROCESS DESIGN FOR LIQUID COMPOSITE MOLDING. Hatice Sinem Sas

Transcription

1 ADDRESSING VARIABILITY OF FIBER PREFORM PERMEABILITY IN PROCESS DESIGN FOR LIQUID COMPOSITE MOLDING by Hatice Sinem Sas A dissertation submitted to the Faculty of the University of Delaware in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mechanical Engineering Summer Hatice Sinem Sas All Rights Reserved

2 ProQuest Number: All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. ProQuest Published by ProQuest LLC (2015). Copyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code Microform Edition ProQuest LLC. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, MI

3 ADDRESSING VARIABILITY OF FIBER PREFORM PERMEABILITY IN PROCESS DESIGN FOR LIQUID COMPOSITE MOLDING by Hatice Sinem Sas Approved: Suresh G. Advani, Ph.D. Chair of the Department of Mechanical Engineering Approved: Babatunde A. Ogunnaike, Ph.D. Dean of the College of Engineering Approved: James G. Richards, Ph.D. Vice Provost for Graduate and Professional Education

4 I certify that I have read this dissertation and that in my opinion it meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy. Signed: Suresh G. Advani, Ph.D. Professor in charge of dissertation I certify that I have read this dissertation and that in my opinion it meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy. Signed: James L. Glancey, Ph.D, P.E. Member of dissertation committee I certify that I have read this dissertation and that in my opinion it meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy. Signed: Rakesh, Ph.D. Member of dissertation committee I certify that I have read this dissertation and that in my opinion it meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy. Signed: Pavel Simacek, Ph.D. Member of dissertation committee

5 ACKNOWLEDGMENTS I would like to express my sincere gratitude to my advisor, Prof. Suresh G. Advani, for the continuous support, patience, and enthusiasm he has provided during my Ph.D. journey. I feel extremely lucky to have been mentored by someone with deep knowledge, solid experience and infinite motivation to learn, teach, investigate and invent. I would like to thank Dr. Pavel Simacek for his support and advice on process modeling and numerical simulation, and agreeing to serve on my dissertation committee. I acknowledge and give thanks to my other two committee members, Prof. James Glancey and Prof. Rakesh for generously devoting time to judge my work and providing insightful comments. I would also like to thank many colleagues who worked with me during my time in Delaware. I had the privilege to work with Jeffrey Lugo and Eric Wurtzel, and with Louis Agostino and Minyoung Yun. I was lucky to have Richard Readdy for his help in countless lab and LabVIEW problems. I want to express my gratitude to Dr. Volkan Eskizeybek for his valuable advice. Also, I am grateful for the support and friendship of the rest of my research group: Dr. John Gangloff, Thomas Cender, Jiayin Wang, Dr. Hang Yu, Hong Yu and Michael Yeager. I would also like to thank all of my office mates in Spencer007, CCM118 and CCM123 (The Pit). Thank you all for the good times and friendship that we share. iv

6 I would also like to thank the administrative staff of the Mechanical Engineering Department: Lisa Katzmire, Ann Connor and Letitia Toto and Center for Composite Materials: Corinne Hamed, Robin Mack, Penny O Donnell, Therese Stratton and Megan Hancock. I am thankful for your hard work and smiles. I would also like to thank all of my dear friends for making the bad times good, and the good times even better. I want to give special thanks to Sumeyra Yildirim, Deniz Ozdiktas, and Sezin Zengin for their friendship and support. Also, I am lucky to have Ozan Erol and Sinan Boztepe both as friends and colleagues in CCM. I am feeling lucky to have the chance to meet my dearest friend Sevil Buzcu. She made my Ph.D journey colorful and cheerful. We shared our moments for five years and we will continue to do so. I am also grateful to my friend Furkan Cayci for the perspectives he brought into my life. I am also thankful to him for his contribution to my research using his software skills that made this dissertation complete. I also want to thank Filiz Yesilkoy for not only being a best friend, but also being an inspiration and motivation for my studies and my life. She says, Life is all about asking the right question. and I know we will keep looking for questions together. Lastly, I would like to thank my family. Mom, Dad and my sister Senem, thanks for your unconditional love and endless support. I am deeply thankful to all of my family members for their support. I want to dedicate this dissertation to my grandmother who foresees my future in academia. We built this dream with her. I know she is watching me from heaven and will continue to send her blessings. Rumi says, Be grateful for whoever comes, because each has been sent as a guide from beyond. and I am grateful to everyone who touched my life. v

7 TABLE OF CONTENTS LIST OF TABLES... ix LIST OF FIGURES... x ABSTRACT... xv Chapter 1 INTRODUCTION Liquid Composite Molding Materials used in LCM Reinforcements Matrices The LCM Family of Processes The Resin Transfer Molding Vacuum Assisted Resin Transfer Molding Seemann s Composite Resin Infusion Molding Process Manufacturing Challenges in Vacuum Resin Transfer Molding Permeability variation Race-Tracking Modeling of LCM Processes Objective and Dissertation Outline PERMEABILITY MEASUREMENT TECHINIQUES Historical Background Analytical and Predictive Methods Numerical Methods Experimental Measurement Techniques Rectilinear Flow vi

8 2.4.2 Radial Flow Transverse and Three-Dimensional Flow Skew terms Introduction Methodology Results and Discussion Summary THROUGH THICKNESS PERMEABILITY Introduction Effective Permeability of Preform Stacks Unidirectional fabrics and their orientation Through-thickness permeability characterization Numerical Analysis Experimental Validation Results and Discussion Experimental Study Parametric Study Summary CHARACTERIZATION OF LOCAL VARIABILITY OF FABRICS Introduction Mathematical Implementation Experimentation Results and Discussion Characterization of permeability variation Characterization of the defects within a fabric Summary OPTIMIZED DISTRIBUTION MEDIA LAYOUT Introduction Flow Control Mechanisms for Flow Through Fibrous Domain vii

9 5.3 Methodology and Implementation Discrete Optimization Tree Search Algorithms Pedagogical Example Algorithm for Optimum DM lay-out Partition method Experimentation Results and Discussion Experimental Validation Complex Geometries Summary CONCLUSIONS, CONTRIBUTIONS AND FUTURE WORK Conclusions Contributions of this work Future Work REFERENCES Appendix A MATLAB SCRIPTS FOR DISTRIBUTION MEDIA OPTIMIZATION A.1 Scissors.m: Main m-file A.2 Rock.m: Evaluation of all race-tracking possibilities A.3 Paper.m: Finding the optimum region to place DM B REPRINT PERMISSION LETTERS B.1 EFFECT OF RELATIVE PLY ORIENTATION ON THE THROUGH-THICKNESS PERMEABILITY OF UNIDIRECTIONAL FABRICS B.2 FRACTAL CONCEPTS IN SURFACE GROWTH viii

10 LIST OF TABLES Table 2.1. Parameters for virtual experiment Table 2.2. Predicted permeability for the experiment Table 3.1. Experimental and numerical comparison of through-thickness permeability. Case 1 and case 2 of 0o and 5o refers to all six unidirectional layers being aligned along those angles respectively. In case 3, case 4 and case 5, the successive layers were rotated by 5o, 45o and 90o degrees respectively Table 4.1. Characterization of the roughness exponent Table 5.1. Properties of E-glass fabric, DM and corn syrup ix

11 LIST OF FIGURES Figure 1.1. Type of reinforcements... 2 Figure 1.2. Different fabric types: (a) E-glass-plain weave, (b) E-glass random mat, (c) Aramid twill weave, (d) Carbon twill weave... 3 Figure D reinforcement architectures (generated via TEXGEN [3])... 4 Figure 1.4. Schematic of RTM (left) and VARTM (right) steps (adapted from [1]).. 7 Figure 1.5. Schematic of SCRIMP steps... 9 Figure 1.6. Examples of (a) macro-void and (b) micro-void [27] Figure 1.7. Example of defects in the preform; (a) plain weave glass fabric, (b) 3D orthogonal glass fabric Figure 1.8. Thickness variation during vacuum infusion Figure 1.9. Race-tracking formation on the edges due to fray edges Figure Race-tracking examples: (a) Mid-layer of the preform with metal insert spatially in the middle, and Flow front profiles at the bottom of the preform at two different time steps with race-tracking along the metal insert for two same experimental configurations: (b) experiment 1, (c) experiment Figure Liquid Injection Molding Simulation (LIMS) Structure Figure Permeability map approach Figure 2.1. Flow front profile with xyz mold coordinate, x y z principle direction of the preform Figure 2.2. One-dimensional permeability characterization experiment to find the bulk permeability value in the direction of flow x

12 Figure 2.3. Schematic of radial flow front profiles: (a) isotropic (R1=R2), (b) anisotropic (R1 R2), (c) anisotropic with non-zero in-plane skew term (global coordinate frame doesn t coincides with principle directions of the preform) Figure D g/m 3 E-glass fabric Figure 2.5. Figure 2.6. Figure 2.7. Figure 2.8. Figure 2.9. Experimental set-up to monitor the resin flow at the top and bottom surfaces of the preform (left: schematic, right: picture of the set-up) (Left) An image of isotropic flow from an experiment. (Middle) The image after having the preceding flow image subtracted from it, filtered, and converted to binary. (Right) An ellipse is fitted to the edge of the resin flow front Algorithm for permeability prediction from experimental fill time of top and bottom surfaces Flow front profiles at the top (solid lines) and bottom (dash-dot lines) for different skew permeability at time equal to 700 seconds. The jagged flow fronts are numerical artifacts because of fairly coarse mesh Flow front profiles comparisons with assigned and predicted permeability values at the top and bottom surfaces Figure Flow front profiles at time seconds at the top and bottom: experimental, with predicted permeability and comparison Figure 3.1. Solid model of a unit cell and the corresponding cross-section of four unidirectional plies stacked on top of each other (a) All plies aligned along the y- axis (b) All plies are rotated by 10 degrees in the x-y plane with respect to the y- axis (c) Each successive ply is rotated by 10 degrees resulting in a stacking sequence of 0/10/20/30 with respect to the y- axis with the corresponding cross sections in the throughthickness direction, respectively Figure 3.2. Front and back side of the unidirectional fabric Figure 3.3. Representation of the orientation of the plies Figure 3.4. (a) The Gambit model with each successive layer rotated by five degrees. b) Gambit mesh of the model with 1,968,652 elements and 484,911 nodes. The cut-out shows the mesh density xi

13 Figure 3.5. (a) Periodic boundary conditions to evaluate the permeability in z- axis, (b) Evaluation of permeability in z-axis Figure 3.6. Figure 3.7. Figure 3.8. Figure 3.9. Figure 4.1. Figure 4.2. Figure 4.3. Figure 4.4. Figure 4.5. Figure 4.6. Experimental set-up: (a) Upper mold plate, (b) Lower mold plate, (c) Mold assembly, (d) Resin flow through preform Numerical through thickness permeability with different mesh element sizes for incremental rotation angle 5 o Effect on through-thickness permeability with increasing rotation angle of the successive ply. The unit cell was created using the square and hexagonal arrangement of the fiber tows in the unidirectional ply.. 63 Effect on through-thickness permeability with increasing rotation angle of the successive ply. The unit cell was created using the square and hexagonal arrangement of the fiber tows in the unidirectional ply.. 65 Radial injection and permeability tensor characterization: (a) Schematic of flow front in an anisotropic fabric at a time step with the principle direction x y -axes, (b) Radial injection inlet gate and resin propagation, (c) Permeability tensor. Kxy is non-zero as the principal axis do not align with the selected coordinate axis Flow front locations (height h(r, t)) at various times with system size L, and mean height (flow front position) h (a) Change of the interface width with time (logarithmic scales for both axes) for a fixed L value, (b) Growth of the interface width with different system sizes (L). Reprinted with permission from [143] Top: LIMS mesh and random permeability assignment, Bottom: flow front progression with time obtained via LIMS Assignment of the variation of the permeability of the defected zones: left: 25% defective sample, right: variation of permeability within the defective zone obtained from solution of Equation (4.5). Permeability is higher in the center of the zone and reduces to the values prescribed at the edges as described by the parameter Q in Equation (4.5) Flow through porous media experimental set-up with flow visualization xii

14 Figure 4.7. Resin flowing into a fibrous preform with 25 cent coins placed inside the fabric to simulate defective regions. On the left the defects were evenly distributed on the right the defects are randomly distributed. Measured experimental flow front profiles are also shown (flow front contours at Δt = 25 seconds) Figure 4.8. Characterization of the growth exponent: (a) Shape of flow front at a time instant, (b) Bell curves with three different standard deviations selected for the permeability values assigned in LIMS, (c) Change of the variance of the interface with time from the simulated experiment with permeability distributions shown in (b) Figure 4.9. Change in growth exponent, β with increasing percentage of defective zones (m) for different degree of defects, Q. A best fit functional relationship is also plotted Figure Change in roughness exponent, α with increasing percentage of defected zones, m, for different degree of defects, Q. A best fit functional relationship is also plotted Figure Defect tests via VARTM with 37.5% defect and flow front profiles (Δt = 25 seconds), left: quarters right: tacky tape to represent the defective zone Figure 5.1. Fill time contours for a VARTM and SCRIMP Figure 5.2. Figure 5.3. Tree search algorithms (a) example problem with two acceptable, H and T, nodes, (b) Breadth-first search: finds node H, (c) Depth-first search: finds node T Example to explain the methodology to determine the optimal DM design using the DFS discretization method Figure 5.4. Flow chart of the algorithm to obtain optimal DM Figure 5.5. Division of the domain with the built in k-means script in Matlab Figure 5.6. (a) 4th layer of the E-glass with metal insert placed in the center of the fabric, (b) Experiment layup under vacuum xiii

15 Figure 5.7. DM layout design (a) geometry with inlet/vent locations with 4 race-tracking possibilities along the insert edges creating 2 4 =16 different scenarios (b) 8 regions for placement of distribution media when using discrete optimization, and (c) optimum DM design which resulted in successful filling for all 16 scenarios Figure 5.8. Figure 5.9. Numerical Solution of flow front profiles of the top and bottom views for 4 different race-tracking scenarios with time steps 10 seconds apart, (a) with 95% of the top layer covered with DM, (b) with optimized DM design Experimental flow fronts with the optimized DM design with flow front locations in red 20 seconds apart. The background image of the experiment at 60 seconds, (a) Top and (b) Bottom Figure Optimized DM design of trailer geometry with 1024 different possible flow patterns Figure Void regions with full DM on top surface on the left hand side with optimized DM design on the right hand side for three representative scenarios from 1024 possible scenarios Figure Time contours with full DM on top surface on the left hand side with optimized DM design on the right hand side for three representative scenarios from 1024 possible scenarios Figure Pressure distribution at the instant resin reaches the vent with full DM on the left and with optimized DM design on the right for the three representative scenarios Figure Change in CPU time with mesh size for optimized DM design xiv

16 ABSTRACT In Liquid Composite Molding (LCM) processes, reinforcing glass, carbon or Kevlar fiber preforms are placed in a mold cavity and a liquid resin is introduced to cover the remaining empty space to form a composite by curing the resin. The fiber preform permeability plays a key role in the filling pattern of the mold, which dictates if there will be any voids (empty spaces) in the composite. Permeability tensor describes the resistance to fluid flow through the anisotropic fibrous porous media, which may not be spatially uniform. The variability in the permeability due to the variation in the preform or its placement in the mold can influence the filling pattern and hence the quality of the part being manufactured. The permeability map of a preform specifies the values of components of the permeability tensor at various locations of the preform. The overall objective of this dissertation is to investigate various approaches and tools to create a permeability map that will ensure filling to achieve manufacturing success despite the variability of the filling pattern, a requirement of robust process design. When unidirectional fabrics are used to manufacture composites, they are typically stacked on top of each other to build up the desired thickness. A slight misalignment during the stacking can change the through-thickness permeability dramatically and the flow pattern due to the creation of low-resistance pathways. Experimental characterization of the out-of-plane or through-thickness permeability of a series of unidirectional fabrics stacked in various orientations is investigated. Also, numerical simulations are conducted to predict the effect of change in fiber orientation xv

17 on the through-thickness permeability for unidirectional fabrics. Results demonstrate that the stacking sequence of the unidirectional fabrics influence the through thickness flow and hence the transverse permeability. Next, variation in the permeability value of the fibrous domain caused by the non-uniformity in fiber architecture is investigated. The time evolution and geometry of the rough interfaces of the fluid flow in porous medium are analyzed using the concepts of dynamic scaling and self-affine fractal geometry and is shown to belong to the Kardar-Parisi-Zhang (KPZ) universality class. Additionally, this characterization can be used to quantify the percentage of abnormalities within the preform from flow front profile analysis using KPZ formulation. Finally, a methodology is introduced to create a permeability map for a given mold geometry along with inlet and vent locations which will allow the mold to completely fill despite the variations in the preform and the flow disturbances caused due to its placement. The resin flow pattern can be manipulated with a tailored highly permeable layer (Distribution Media (DM)) layout to be placed on top of the preform as it does impact the flow patterns significantly. Thus, a predictive tool to design an optimal shape of DM, which accounts for the flow variability introduced due to race-tracking along the edges of the inserts is presented by adapting a discrete optimization algorithm. xvi

18 Chapter 1 INTRODUCTION 1.1 Liquid Composite Molding Polymer composite materials combine polymeric resin with reinforcing fibers to fabricate products that are lightweight of tailored stiffness and strength with improved fatigue life and corrosion resistance compared to traditional materials. There are various manufacturing methods to combine the reinforcement and matrix materials together. Injection molding, hand lay-up, filament winding, pultrusion, compression molding of sheet molding compound (SMC), prepreg vacuum bagging and autoclave curing and liquid composite molding (LCM) to name a few commonly employed processes. Selection of the manufacturing method is mainly based on the geometrical and structural properties constraints in addition to total volume and cost requirements. For example, one should use filament winding for making composite pressure tanks and pultrusion for long profiles such as poles and window frames. Moreover, the manufacturing method should result in desired design properties with low cost and cycle time. LCM is one of the most popular manufacturing method for its short cycle times, low cost, high quality and it can handle complex geometries. LCM is a class of processes in which the dry fiber preform in the shape of final product is placed in a mold and impregnated by the desired resin system. The types of materials and the common processes that belong to this family are described in the following sections. 1

19 1.1.1 Materials used in LCM The process design of the LCM starts with the selection of the reinforcement and the resin system that can satisfy the design requirements Reinforcements High strength and high stiffness reinforcements are the load carriers of the composite materials and usually manufactured as continuous fibers. These continuous fibers can be put together in the form of rovings, yarns, strands and tows [1]. Different forms of yarns or tows (bundles of fibers) can be used to create fiber preforms. Fabric reinforcements are generated by weaving and stitching the tows as shown in Figure 1.1.(a) or from chopped fibers and strands (Figure 1.1.(b)). The architecture of the fabric also affects the characteristics of the reinforcement. In Figure 1.1.(a) two different weaving types are given: plain and twill. (a) (b) Unidirectional 0 0 Plain Twill Chopped Mat Figure 1.1. Type of reinforcements Glass, Aramid and Carbon are the most common type of reinforcement materials (Figure 1.2). Glass fiber is preferred for its tradeoff between mechanical properties and cost (Figure 1.2.(a) and Figure 1.2.(b)). Aramid fibers have excellent 2

20 damage tolerance with low density and high toughness (Figure 1.2.(c)). Carbon fibers have better mechanical properties but are more expensive than glass and aramid fibers. Based on the design criteria of the composite material, the selection of the reinforcement type is dictated by the tensile strength, tensile modulus, compression strength, density, impact strength, environmental resistance and cost. For example; for tensile strength and cost glass fiber; for tensile modulus and compression strength carbon; and for density and impact strength aramid fibers are preferred. (a) (b) (c) (d) Figure 1.2. Different fabric types: (a) E-glass-plain weave, (b) E-glass random mat, (c) Aramid twill weave, (d) Carbon twill weave Fiber tows can also be braided and/or woven to create a 3D reinforcement structure by orienting the tows in all three directions. The yarn in the through thickness direction improves the mechanical properties, delamination resistance and impact damage. Different types of 3D weave architectures are shown in Figure 1.3. Figure 1.3.(a) is an example of orthogonal weave where tows are placed vertically between the in-plane layers and promote the tensile strength by increasing the stiffness [2]. Figure 1.3.(b) is an example of an interlock weave in which the tows in the vertical direction have a pattern. 3

21 (a) Orthogonal (b) Angle interlock Figure D reinforcement architectures (generated via TEXGEN [3]) Matrices The matrix is the other component of the composite materials that holds and protects the fabrics. The matrix materials are resins that protect the fibers from abrasion, transfer the load between fibers and provide inter-laminar shear strength to the composite material. The resins can be classified as thermosets and thermoplastics. Thermoset resins are low viscosity liquids at room temperature but when mixed with a curing agent initiate a chemical reaction forming long molecular chains by cross-linking. Once they start to cross-link, the resin viscosity increases and as the resin approaches a gelation state, the viscosity becomes very large and resin cannot flow anymore. So the goal with thermoset resins is to ensure that they have reached their destination before they gel. Gelation time is the time that polymer chains start to form 3-dimensional network and when the resin viscosity starts to increase exponentially and ceases to flow. 4

22 Thermoplastic resins on the other hand are solid at room temperature and need to be heated to get them to flow. Their viscosity even in molten state is two to three orders of magnitude higher than thermosets. Hence, use of thermoset resins such as epoxy or vinylester is preferred for LCM processes The LCM Family of Processes LCM processes can be divided into two main groups: Resin Transfer Molding (RTM) and Vacuum Assisted Resin Transfer Molding (VARTM). RTM family of processes require two-sided rigid mold and resin is impregnated into the dry preform with positive pressure. VARTM needs one-sided mold surface and the other side is covered with nylon vacuum bag and the vacuum is applied to infuse the resin into the preform The Resin Transfer Molding RTM is the most traditional LCM process. The steps of the RTM process are shown on the left hand side of Figure 1.4. First the reinforcements are stacked to form the desired preform shape. The preform is placed in the mold cavity and the mold is closed. As the mold is closed and placed in a hydraulic press, the preform takes its final thickness and it is impregnated with the resin. The resin system is pushed into the dry preform by the resin injection unit that applies constant pressure or constant flow rate. After the resin completely wets the dry preform, the injection is closed and the resin is allowed to cure in the mold. Finally, the cured part in the final shape is removed from the mold [4]. The main advantages of the RTM process are good surface finish because of the two-sided rigid mold and high quality final products. The positive pressure from 5

23 the inlet enables the resin to fill the dry preform at higher speeds, which decreases the cycle time. Since the two-sided mold is kept closed via hydraulic press, mold deflection can be prevented under high-pressure fillings. By preventing the mold deflection the dimensional uniformity of the product can be satisfied [5,6]. Also, higher fiber volume composites can be manufactured with RTM due to higher inlet forces and rigid and stable mold cavity. The fiber content is described by the fiber volume fraction, vf; the ratio of the volume of the fibers/preform to the mold cavity. The mechanical properties of the composite material can be enhanced by increasing the fiber content [7,8]. The main disadvantage of the RTM is the high initial cost for the mold. This makes RTM more feasible for small-sized parts with high production rates. For large and complex part the mold cost might be a deterrent factor. The other disadvantage is the lack of resin flow monitoring during the impregnation process [9]. If there is a problem during the impregnation, it cannot be seen until the part is de-molded. This issue might yield an expensive and inefficient trial and error procedure. However, use of experimental and simulation tools to design the process can overcome the resin impregnation issues. Danisman et al. [10] lists a variety of experimental tools (sensors) to monitor the resin flow and cure cycle in closed RTM mold such as SMARTweave [11], dielectric [12], ultrasonic [13,14], fiberoptic [15], thermocouple [9], pressure transducer [16], and point- and lineal-voltage sensors [17,18]. The simulation tools can also help overcome these issues. Adapting the Finite Element/Control Volume approach in RTM simulations first implemented by Fracchia et. al [19] and following simulation tools are developed: RTM-FLOT [20], PAM-RTM [21], MyRTM [22] and LIMS [23]. 6

24 Resin Transfer Molding (RTM) Preform manufacturing: Vacuum Assisted Resin Transfer Molding (VARTM) Preform lay-up: Mold Closure: Inlet Vacuum bag Resin Injection: Resin injection Resin impregnates fibers and cures Vacuum pump Curing and De-molding: Cured part Figure 1.4. Schematic of RTM (left) and VARTM (right) steps (adapted from [1]) 7

25 Vacuum Assisted Resin Transfer Molding VARTM process is similar to the RTM process except VARTM has one-sided mold and a nylon transparent layer, vacuum bag, is placed on the other side. As shown schematically on the right-hand side of Figure 1.4, the process starts with preparing the preform by placing the layers of reinforcement in the final shape of the product. The preform is then placed on one-sided mold or a tool surface and the other side is sealed with a vacuum bag. The sealing between the mold surface and vacuum bag is achieved with a sealing tape. The vacuum pump, which is placed at the vent, is turned on to extract the air and creates the pressure gradient to invoke resin flow. The inlet is closed after the resin wets the preform and reaches the vent. The vacuum is maintained until the resin cures. Once the resin cures, the part is de-molded. VARTM process only needs a one-sided mold or a tool surface which reduces the cost by orders of magnitude and makes it possible to manufacture large structures such as wind blades. Thus, for large and complex parts VARTM becomes the manufacturers choice [24]. However, VARTM has limitations due to vacuum pressure. The maximum driving pressure is atmospheric pressure. This limit increases the fill time and the risk of fill time reaching the gelation time of the thermoset resin arises, especially for large parts. The fiber content that can be reached with VARTM is limited compared to RTM as the compaction of the preform is being achieved with atmospheric pressure [25]. Finally, the surface finish of the vacuum bag side is not as good as the mold-side Seemann s Composite Resin Infusion Molding Process Seemann Composites Resin Infusion Molding Process (SCRIMP) is a widely used patented version of Vacuum Assisted Resin Transfer Molding (VARTM) in 8

26 which a highly permeable layer (distribution media (DM)) is placed on top of the dry preform to distribute the resin with very low flow resistance to reduce the filling and hence the manufacturing cycle time [26]. The schematic in Figure 1.5 shows the steps of the SCRIMP. As DM is not part of the composite, a peel ply is placed between the preform and the DM and after the entire assembly cures, peel ply is used to separate the DM from the composite and discard it. Preform manufacturing Preform lay-up Distribution Media (DM) Peel Ply Curing and De-molding DM Peel Ply Cured part Mold Closure Resin Injection Vacuum bag Inlet Distribution Media Resin injection Resin impregnates fibers and cures Vacuum pump Figure 1.5. Schematic of SCRIMP steps 9

27 1.2 Manufacturing Challenges in Vacuum Resin Transfer Molding LCM enables tailoring of physical and mechanical properties and creating complex composite parts. The success of the process depends on the preforming, impregnation and curing, whereas impregnation is the most challenging part. Unsuccessful impregnation results in formation of macro- or micro-scale voids. Macro-scale voids are the large air pockets, dry spots that form due to problems in the flow front profiles (Figure 1.6.(a)) and micro-scale voids forms around the fiber tows due to trapped air (Figure 1.6.(b)). Any void that remain in the part after the part cures, damages the quality of the final part. Trapped air Dry spot cm (a) Macro-voids (b) Micro-voids Figure 1.6. Examples of (a) macro-void and (b) micro-void [27] Permeability variation Flow through porous media with Darcy s law is used to describe the movement of resin in the fibrous preform [28]. When using Darcy s law volume-averaged values are employed for flow variables such as resin velocity, pressure, and material 10

28 properties such as resin viscosity and fiber preform permeability. These averaged quantities are defined at any location by averaging them over a selected volume surrounding that region within the domain. However, these fabrics (for example ones in Figure 1.2) are rarely homogeneous and there can be statistically significant variation from one region to the next. As shown in Figure 1.7, these variations could also be due to defects in the fabric. This local non-homogenous architecture of the fabric can have a noticeable effect on the dynamics of resin flow behavior [29 33] cm cm (a) (b) Figure 1.7. Example of defects in the preform; (a) plain weave glass fabric, (b) 3D orthogonal glass fabric Most fabrics do have local variations caused by local changes in fiber orientation and due to change in fabric density [29]. During composite manufacturing many layers of fabrics are stacked together to build up a certain layer of thickness. When these layers nest, the nesting may not be uniform across the length of the fabric may also contribute significantly to permeability variations [30]. Endruweit and Ermanni [34] found that for a coarse 2x2 twill weave fabric made of thick fiber tows the variance of local permeability values was higher than for a fine 8-harness satin 11

29 weave fabric for the same fiber volume fraction, which could be explained by the intrinsic in-homogeneity of the fabric and the relatively high local variations of the fiber configuration. Quantitative evaluation of injection experiments, which is normally based on flow front tracking, implies averaging of local variations in material properties and measuring averaged global permeability values. While the experimentally determined permeability values characterize quasi-uniform materials, the accurate predictive description of global flow for non-uniform materials requires knowledge of the distribution of local properties. Another challenge during vacuum infusion is the change in the preform thickness during injection. In RTM resin impregnation is performed through the preform that is kept between two rigid molds. Assuming the mold design s stiffness stands the pressure of the resin and the preform, the preform will not be expanded or compacted during the filling. However, in VARTM one side of the mold is sealed with flexible nylon vacuum bag which will not be able to prevent the expansion of the preform during impregnation. As seen in Figure 1.8, the thickness of the preform changes as the resin propagates [35,36]. This variation arises because of the resin pressure decreases the compaction. However, this variations does not significantly affect the resin flow behavior during impregnation [37]. 12

30 vacuum bag flow front mold surface Figure 1.8. Thickness variation during vacuum infusion Race-Tracking Resin finds low resistance pathways when there are open channels: (i) between the mold and preform edges (Figure 1.9), (ii) along sharp bends in reinforcement and/or (iii) between preform and inserts in the mold (Figure 1.10.(a)). This fast movement of the resin along edges and surfaces is called race-tracking. The filling pattern can change significantly with the presence of race-tracking pathways in the mold (Figure 1.10). This potentially could allow the resin to reach the vent line before impregnating the entire preform which will result in a large dry spot or void within the part resulting in the part that needs to be discarded or re-worked [38 43]. In RTM, resin racing along the mold edges is more common than VARTM as the mold is a two-sided closed cavity. In VARTM, race-tracking will be more prominent along the boundaries of the inserts in the mold or around sharp bends. This can be seen in the experimental filling of the preform with a metal inset placed in the 4 th layer of an 8 layer preform. As seen in Figure 1.10.(a) the metal insert is placed in the middle of 0.5mx0.5m layer and from the flow front profiles at two different time steps for two experiments (Figure 1.10.(b) and Figure (c)) race-trackings took place along the 13

31 edges of the metal insert. The flow front profiles in Figure 1.10.(b) and Figure (c) are obtained from two different set of experiments with same process parameters. For the first experiment (Figure 1.10.(b)) race-tracking channel permeability is higher than the ones in the second experiment (Figure 1.10.(c)). Thus, the same part with the same process parameters may end up with significantly different filling patterns. Another issue with the race-trackings is their location can be predicted but their occurrence and the strength of the race tracking cannot be predicted. fray edges preform mold wall gap Figure 1.9. Race-tracking formation on the edges due to fray edges 14

32 metal insert race-tracking channels inlet line (a) (b) (c) Figure Race-tracking examples: (a) Mid-layer of the preform with metal insert spatially in the middle, and Flow front profiles at the bottom of the preform at two different time steps with race-tracking along the metal insert for two same experimental configurations: (b) experiment 1, (c) experiment Modeling of LCM Processes Modeling the LCM process will allow one to predict the filling pattern, fill time and the distribution of fluid pressure in the preform. Good understanding of these issues will allow one to improve the quality and reduce the cost of the composite [44]. Inlet/s and vent/s positions, permeability of the preform, injection rates are the factors that influence the filling [45]. Numerical simulations have been developed to optimize processing window and process design to improve manufacturing with LCM [46 51]. In LCM simulations, resin is modelled as a Newtonian fluid that flows in porous 15

33 media with averaged pore size. The mathematical description of the resin flow through porous media that models the physics is Darcy s law (Equation (1.1)) coupled with continuity equation (Equation (1.2)), as given below; v = K P (1.1) µ v = 0 (1.2) ( K P) = 0 (1.3) µ where v is the volume averaged resin velocity and P is the pore-averaged resin pressure, µ is the resin viscosity and K is the permeability tensor. The components of the symmetric, positively definite permeability tensor, K, as shown (in Cartesian coordinates) in Equation (1.4), represent how easily resin can flow in the corresponding direction; K xx K xy K xz K = [ K yx K yy K yz ]. (1.4) K zx K zy K zz Solution of those equations with the initial pressure and/or flow rate specified at the inlet gate for the fibrous domain enables the estimation of time to fill the mold, identification of the optimal locations for placement of gates and vents, and to find regions which may be susceptible to formation of dry-spots. Fracchia et al. [19], Bruscheke and Advani [52] and Trochu et al. [53] presented successful 2D resin impregnation models. Those models are practical for thin parts (for most of the 16

34 composite materials). There are other successful models for both isothermal and non-isothermal mold filling [49,50,54 61]. As the modeling tools are developed and improved, those tools are used to optimize the LCM process. If the objective is to have minimum fill time and/or avoid dry spots, various methodologies have been developed and reported [4,62,63]. In this dissertation, the numerical simulations of the flow through fibrous preform are performed via Liquid Injection Molding Simulation (LIMS), which was developed at the University of Delaware [23]. LIMS is a dedicated finite element/control volume based simulation of flow through porous media that is capable of analyzing both 2D and 3D flows. It has both a built in scripted language and a userfriendly graphical user interface that user can set and perform the simulations. It can also be called from Matlab as a function to be used for optimization routines. As represented in Figure 1.11, the program requires the mesh geometry, viscosity of the resin, permeability tensor, porosity/fiber volume fraction with boundary conditions and it provides the flow front locations with time, the last region to fill and the fill time along with pressure distribution and the success of the filling (location of dry spots, if any). The permeability values of the reinforcements are relatively low, so the resin flow is slow (low Re, Re<10). Therefore LIMS adopts the quasi-steady state assumption. At each step the pressure distribution is obtained from Darcy s Law (Equation 1.1) and the Continuity Equation (Equation 1.2). From the pressure distribution the flow front is advanced using the Darcy s Law (Equation 1.1) for resin velocity. Hence one can design gate and vent locations if the preform permeability map and the permeability tensor in the preform domain (Figure 1.12), are known with certainty and do not change from one part to the next. 17

35 Figure Liquid Injection Molding Simulation (LIMS) Structure K1 K 6 K 11 K 10 K 2 K 5 K 8 K 3 K 4 K 7 K 9 Figure Permeability map approach 18

36 1.4 Objective and Dissertation Outline Research objective of this dissertation is to develop a methodology to create a spatial distribution of the permeability tensor, called the permeability map for a given geometry (Figure 1.12), that will allow the mold cavity to fill from a gate and arrive last at the vent (which implies no voids) despite variability in the preform and flow disturbances around the mold walls, inserts and corners. The simulation output is the void area where the input is the geometry of the part along with the permeability map, location and strength of flow disturbances, location of gates and vents and the inlet pressure or flow rate boundary condition at the gates. The goal is to find a permeability map for a selected gate and vent location that will give at most a small void region despite flow disturbances and variability in preform permeability. In order to achieve this objective one needs; (i) to develop a characterization method for permeability, (ii) to be able to quantify the variability in the fabric due to manufacturing variability of textiles, (iii) to identify race-tracking and other issues of the fabric and their effect on permeability, replaced by, (iv) to develop optimization methods that create permeability maps despite variations to achieve successful filling. In this dissertation, after the introduction to LCM processes in Chapter 1, permeability measurement and characterization methods are presented in Chapter 2. Also, a methodology is introduced to characterize the six components of the permeability tensor with non-zero skew components. In Chapter 3, the 3D permeability characterization technique introduced in Chapter 2 is used to demonstrate that slight variation in orientation during lay-up can influence through thickness permeability variability dramatically and a permeability map should take this into consideration. 19

37 Chapter 4 introduces a technique to quantify variation in permeability of a fabric which will be taken into account when assigning a permeability map Chapter 5 presents the formulation of a methodology and development of optimization technique that will use the forward simulation allowing for variability in permeability to create a permeability map that will fill the mold without voids despite the variations and flow disturbances. The last chapter lists the conclusions and contributions with suggestions for future work. 20

38 Chapter 2 PERMEABILITY MEASUREMENT TECHINIQUES 2.1 Historical Background In 1856 Darcy conducted sets of water flow through sand beds experiments which was the first attempt to model fluid flow through porous domain [64]. He introduced the term permeability to quantify the ease of fluid flow in porous domain and developed an empirical relationship to relate the flow rate of water to the pressure drop across the sand column as follows Q = KA µ P x (2.1) where Q is the flow rate, µ viscosity of water, A is the cross-sectional area, P is the pressure gradient along the flow direction and K is the scalar that characterizes the permeability of the sand in the flow direction. Darcy developed the equation for homogeneous and isotropic porous domain with water flow in one-direction. In 1961 Liakopoulos [65,66] expanded the Darcy s empirical equation by introducing the permeability as a tensor. The permeability tensor (Equation 1.4) characterizes the ease of resin flow in porous domain in all three-directions. Symmetric, positively definite permeability tensor, K has orthogonal set of axes principle directions (which are the diagonal terms when the non-diagonal terms are zero). Figure 2.1 shows the mold coordinate (xyz) and the principle direction of x 21

39 the preform (x y z ). The permeability tensor in mold coordinate frame which is given in Equation 1.4 can be rotated by θ degree such that the mold coordinate axis coincides with the principle directions of the preform, in which case the diagonal permeability tensor, K in x y z coordinate frame can be expressed as; K = [ K yy 0 ] (2.2) 0 0 K zz K xx z flow front preform z x θ y x y injection point Figure 2.1. Flow front profile with xyz mold coordinate, x y z principle direction of the preform As mention in Chapter 1, in LCM processes the dry preform is placed into mold cavity and after the mold is closed and sealed, the resin is introduced into the mold to impregnate the porous fibrous media. Darcy s law is used to mathematically 22

40 describe the flow of resin into a closed mold containing fiber preform. However, how closely the mathematical model mimics the actual flow behavior depends on the fidelity of the material input data such as viscosity of the resin and the permeability values of the fabric placed in the mold. Hence it is important to characterize the permeability data accurately. Over the years, researchers have presented many different methodologies to characterize the permeability of the fabric. The overall approach to permeability characterization can be investigated under three broad categories (i) analytical and predictive methods, (ii) numerical methods and (iii) experimental methods. 2.2 Analytical and Predictive Methods As a mathematical model, Darcy s Law, relates the pore-averaged velocity with the pore-averaged pressure gradient with the permeability of the porous domain, K and the viscosity of the resin, µ (Equation (1.1)). Darcy s Law is a macroscopic model and the microscopic physical properties are averaged using continuum approach. Thus, the effect of the fiber volume fraction (namely porosity), tortuosity and capillary effects are lumped under permeability in Darcy Law [67]. Kozeny-Carman (KC) tried to establish a relationship between permeability and porosity by modeling the flow within a porous media as a series of cylinder capillary channels coupled with Carman s introduction of hydraulic channel [68]. The Kozeny-Carman equation can be expressed as; K = R f 2 4k 0 (1 v f ) 3 v f 2 (2.3) with R f is the fiber radius, k 0 is the Kozeny constant that empirically accounts for the tortuosity to be determined experimentally and v f is fiber volume fraction. 23

41 KC equation is a semi-empirical relation with k 0 empirical constant which is later proved not to be constant [69]. The KC model improvements are performed to estimate the permeability [70]. Ahn et al. [71] showed good agreement in permeability estimation for woven fabrics using KC, however, Gauvin et al [72] reported KC model is not sufficient for random mats. Also, unsuccessful experimental implementations are presented [73]. Thus, researchers suggest the introduction of the capillary model for the resin flow to improve the estimations. Gebart [74] developed a geometric model for permeability prediction. Set of analytical expressions are presented for an idealized unidirectional reinforcement with regular, parallel fibers. The expressions consists of Navier-Stokes equations both for flow along and perpendicular to the fibers. Solution for the flow along the fibers has the same form with KC formulation, however, for perpendicular flow includes the physical limit in terms of fiber volume fraction. Another predictive model is introduced by Bruschke [75]. The model consists of regular array of cylinders to represent the fiber tows. Close form solutions are derived for the upper and lower fiber volume fraction values for Newtonian fluids. Good agreement is obtained between closed form solutions and numerical models for mid-range fiber volume fractions. The limitation of Gebart and Bruschke models is that the physical model used to describe the system does not capture the structural details of real preform materials. The fiber preform usually used in LCM processes consist of woven or stitched fiber bundles known as tows or yarns, rather than of individual fibers and their geometric arrangements are usually more complex than the one assumed in analytic models. Since, predictive tools cannot represent the realistic geometrical arrangement, 24

42 experimental and numerical methods are more useful for permeability characterization. 2.3 Numerical Methods Numerical methods, as a tool to characterize the permeability, generally involves the solution of the Navier-Stokes equation for well-defined cell geometry for the preform. The solution involves either use of periodic boundary conditions or implementation of the Lattice-Boltzmann method. All methods impose a pressure drop across the porous domain and calculate the average flow through the unit cell or prescribe a flow rate along one face of the unit cell and calculate the pressure drop. The permeability of the unit cell is derived by using the Darcy s Law. Averaging of permeability in a unit cell is an example of homogenization method. Over the macro-scale, the equivalent homogeneous medium represents the average behavior of the heterogeneous medium. Mathematical theory of the homogenization method is established in several studies [76]. The numerical method solves the Navier-Stokes equation for the homogeneous medium, representative unit cell using the periodicity boundary condition [77]. The Lattice-Boltzmann Method (LBM) is based on microscopic models and mesoscopic kinetic equations. The methods models the fluid as set of particles that are moving and interacting on a lattice. From the discrete data of the particles, one can define the space and time aspects of the fluid flow. LBM has been used to investigate the porous media by several authors [78 81]. Koponen et al. [78] employed the nineteen velocity LB model to calculate permeability of three dimensional random fibrous structure generated by a growth algorithm in discretized space. Nabovati and Sousa [82] investigated the permeability 25

43 of sphere packs. Also Nabovati and Sousa [82] reported their work on fluid flow in three-dimensional random fibrous media simulated using the lattice Boltzmann method. The LBM overcomes the major limitation of the homogenization method. It is capable of simulating flow in realistic situations of complex fabric geometries and structure. However, Belov et al. [83]reported that the Lattice Boltzmann calculations are computationally intensive. But it can also incorporate the surface tension effects of the fluid very easily. The numerical solutions providing permeability data for the unit cell, may not accurately represent the permeability of the preform at the macro-scale. To perform an entire simulation within a preform with thousands of unit cells solving for Navier- Stokes equation may be a formidable computational challenge. Hence, experimental methods are used to determine the permeability coupled with phenomenological and numerical methods since the permeability changes with fiber orientation and fiber volume fraction; otherwise one would have to conduct many experiments for the same fabric to find the dependence on fiber orientation and volume fraction. 2.4 Experimental Measurement Techniques Permeability characterization experiments are performed by controlling either inlet pressure or injection flow rate and grouped according to the pattern of fluid flow through the preform: rectilinear, radial, transverse and three-dimensional. Each approach has its own advantages and disadvantages. 26

44 2.4.1 Rectilinear Flow In-plane permeability measurements are the most commonly reported in literature as they are straight forward. Rectilinear experimentation is an in-plane permeability measurement technique to characterize the permeability by conducting linear flow channel experiments [84 86]. The preform can be placed either in a RTM mold with one transparent side or a VARTM set-up. As the resin flows through the preform, linear flow front profiles are tracked with time, as shown in Figure 2.2. For an ideal experimentation, the flow front profiles will be linear and can be easily monitored. The experimental data is the flow front position with time. Then, time integration of one-dimensional Darcy s Law yields the solution of the flow front position with time, as given in Figure 2.2. In this equation, xf(t) is the flow front position at time t, K is the permeability of the preform in the flow direction, ΔP is the resin pressure drop along the flow, μ is the resin viscosity and φ is the preform porosity (defined as (1-vf)). From the slope of the best line fit of the plot of the square of the experimental flow front, the average bulk permeability of the fabric in the flow direction can be evaluated for that particular fiber volume fraction. 27

45 Filled region Preform x f (t): flow front location at time t t 1 Actual flow fronts Linear flow fronts used to find bulk permeability t 2 t 3 Figure 2.2. One-dimensional permeability characterization experiment to find the bulk permeability value in the direction of flow Rectilinear flow experiment is easy to conduct and the experimental data is easy to process and have high reproducibility [84,87,88]. However, appropriate equipment, such as visualization tools and sensors, might increase the initial cost which can be listed as a disadvantage. Another disadvantage arises due to the race-tracking issue (as introduced in Chapter 1) which invalidates the linear flow assumption and generates error in permeability data [42,89]. As mentioned before, this approach is used to determine the permeability component only in the flow direction. Set of experiments are required for characterization of all the six components of the permeability tensor. 28

46 2.4.2 Radial Flow Radial flow is another method for in-plane permeability characterization. The test fluid is injected through a gate which is a hole in the center of the fiber preform. The resin entering in the circular cutout in the middle of the preform spreads radially impregnating the preform in a circular or elliptical shape. The radius of this boundary is important during the data analysis. As seen in Figure 2.3, if the preform is isotropic the flow front profiles are circular and as the anisotropy of the preform increases the major minor axes ratios increases. The ellipses major and minor axes align with the principle direction of the preform and the ellipse is at an angle with respect to global coordinate frame if the principal axis of the preform do not coincide with the coordinate axis (as shown in Figure 2.3.(c)). Radial injection eliminates many of the disadvantages of the rectilinear flow [85,90 97]. However, flow front tracking requires visual monitoring through the transparent mold surfaces [98,99], fiber optic sensors [71], thermistors [100], pressure transducers [101], and ultrasound and electrical residence [102]. Then, data reduction schemes are required. Additionally data reduction schemes is more complex than the linear flow experimental data. Though, for isotropic preforms the analytical solution of the in-plane permeability can be calculated easily [103]; K = {R 2 f [2 ln(r f R 0 ) 1] + R 2 0 } 1 μφ t 4ΔP (2.4) where R f is the flow front radius at time t, and R 0 is the radius of the injection gate. Thus, using equation 2.4, permeability of isotropic preforms can be determined by measuring the pressure gradient and monitoring the circular flow fronts with time. Then, for the anisotropic fabrics Chan and Hwang [91] proposed an approach to determine the principle permeability components using the major and minor radius of 29

47 elliptical flow front profiles (Figure 2.3.(b)). This work is followed by Weitzenbock et al. [103,104] with the methodology to obtain the principle permeability components without the knowledge of the principle axes (Figure 2.3.(c)). Radial flow experimentation can be used to characterize in-plane permeability components. Moreover, the race-tracking issue doesn t occur in radial injection and doesn t affect the permeability evaluation. However, radial flow experiments are consistent with linear flow but result in different values for the same preform at the same fiber volume fraction. However, for a reliable in-plane permeability data Wang et al. [85] suggests conducting both linear and radial flow experiments. 30

48 (a) Isotropic flow front R 2 R 1 Injection point, R0 (b) Anisotropic flow front R 2 R 1 Preform y (c) Anisotropic flow front with non-zero in-plane skew term R 2 R 1 θ x Figure 2.3. Schematic of radial flow front profiles: (a) isotropic (R1=R2), (b) anisotropic (R1 R2), (c) anisotropic with non-zero in-plane skew term (global coordinate frame doesn t coincides with principle directions of the preform) 31

49 2.4.3 Transverse and Three-Dimensional Flow A variety of methods that have been used to experimentally characterize the in-plane preform permeability components are presented in the previous section. For thin parts only in-plane permeability is required which has three independent components either two principal values and the orientation of principal axes or two normal and one skew component. For thick parts, one must characterize through the thickness permeability as well [95,100, ]. There are two approaches for transverse permeability measurement; simultaneous measurement of three principle permeability components and independent measurements (separate experimentations for in-plane and transverse). Several researchers conducted transverse permeability studies [100, ]. One-dimensional channel flow apparatus is utilized to characterize this component with Darcy s Law [111]. Trevino et al. [112] developed a tool to evaluate the transverse permeability based on one-dimensional flow and discretized Darcy s Law. Wu et al. [113] includes the three-dimensional flow simulation to one-dimensional flow model using steady state flow profiles. Ahn et al. [71] presents a device that simultaneously measures the transverse permeability and capillary pressure. In order to model the three-dimensional resin impregnation, three-dimensional permeability characterization is required. Three-dimensional flow experiments are proposed to fully characterize both isotropic and anisotropic permeability with a single experiment. Traditionally, LCM parts are thin but there are practical resin flow problems seeking for three-dimensional permeability tensor [100]. A general methodology is presented by Woerdeman [110] for three-dimensional permeability tensor characterization from set of one-dimensional 32

50 flow experiments. The permeability data is derived from numerical solution of six nonlinear equations [114]. Whereas, Weitzenbock et al. [100] tracked the flow fronts using thermistors and mentioned the importance of the capillary pressure on the three-dimensional permeability characterization. Using the same measurement principle Ahn et al. [71]monitored the flow fronts using embedded fiber optic sensors which are placed inside the preform. Following that, Ballata et al. developed Smart Weave as another flow monitoring technique [115]. Gokce et al. [116] introduced a new experimental method, Permeability Estimation Algorithm (PEA). PEA processes flow front information during the experimentation and process with a numerical process model. Its limitation is being applicable only for VARTM process. Whereas, Breard et al. [117] used X-ray radiography to monitor the flow but the cost of the system requires expensive tooling. Nedanov et al. [114] presents a method to evaluate principle values of the three-dimensional permeability tensor. This method is based on visual monitoring of the in-plane flow front profiles. The shape and size of the in-plane flow front through the transparent membrane as well as the amount of fluid in the preform and elapsed time are recorded and allow for characterization of principle permeability in all three directions. Similar approach is used by Okonkwo et al. [118]. Instead of transparent plates, electrostatic sensors are placed on the top and bottom surfaces of 3-D radial injection mold is used and instead of an analytic solution, numerical simulation is utilized to characterize the permeability. Each of these experiment approaches has their disadvantages. The use of embedded sensors affects the pattern of flow and renders the experimental data unreliable. Weizenbock [100] observed that the flow front in the part of the mold 33

51 where the thermistors sensors had been placed was lagging behind compared with other undisturbed parts of the mold. Also since the sensors are normally embedded in the preform manually, this requires time and effort. Numerous experiments are usually required for reliable characterization of preform permeability and as such using embedded sensors will require extensive time and labor rendering the methods less efficient. And the method [117] that involves the use of X-ray spectroscopy to measure the flow front through the thickness is rather expensive. In case of Nedanov experiments [114], the results for through thickness could be unreliable as they used only one data point to find the transverse permeability which was when the arrival of the resin was recorded at the bottom. Also the size of the gate had an effect on the permeability calculations. The method developed by Okonkwo et al. [118] is applicable to non-conductive fabrics, e.g. cannot be implemented to carbon fibers. From the review of the existing experimental methods for permeability characterization of fibrous media shows that while traditional methods for in-plane permeability measurement are well developed the methods for transverse permeability measurement need further investigation. Hence the need for reliable and fast method to determine the components of the three-dimensional permeability tensor in a single experiment and use of simple equipment is desirable. 2.5 Skew terms For thin parts, only in-plane permeability (Kxx, Kxy, Kyy) are necessary. That requires three components either two principal values and the orientation of principal axes or two normal and one skew component (Kxy). Several methods to obtain these values were devised. For thick parts, particularly when flow media is used 34

52 on part surface, through the thickness permeability is needed as well and can be measured [ ]. Three-dimensional tensor contains not only this (normal) transverse permeability but also two additional skew components. These are, in practice, neglected as it is assumed that fabric layering produces symmetry needed to eliminate them. This assumption is somewhat questionable in the first place, but it becomes truly invalid when thick, three-dimensionally woven or braided reinforcements are concerned. The geometry of weave allows these terms to appear and acquire some significance for flow. So far, no methods have been developed to measure these terms for thick preforms and it remains uncertain how important they are for the manufacturing process. In this section, permeability tensor is investigated for thick 3-D woven fabrics, including the skew components via a multi-objective optimization algorithm coupled with Liquid Injection Molding Simulation (LIMS) tool. The effect of the skew components on the resin impregnation and the limitations on the importance of those terms are evaluated Introduction Three-dimensional fabric permeability tensor requires in addition to the transverse permeability, two additional out of plane skew components if the through thickness principal direction is not orthogonal to the plane of the fabric. Most researchers assume that the principal Kzz direction of the fabric coincides with the z-axis. This assumption may not be true for thick, three-dimensionally woven or braided textile fabrics as the ones shown in Figure 2.4. The geometry of the weave could be such that the principal Kzz direction may not be aligned with the normal direction of the preform plane. This will influence the resin flow pattern in a mold due 35

53 to the non-zero skew components (Kxz and Kyz not being equal to zero). So far, no methods have been developed to measure these terms for thick, unbalanced and braided preforms and it remains uncertain how important they are for the manufacturing process. Figure D g/m 3 E-glass fabric In this chapter a methodology is presented to determine these skew terms using radial flow experiments in an instrumented mold. Flow front profiles at the top and the bottom of the mold are used to construct the flow front pattern at the top and bottom of the preform respectively. Using a multi-objective optimization algorithm, the input values for the permeability tensor in the flow simulation program LIMS are varied until the flow front patterns at the top and the bottom of the mold in the simulation match with the experimental results. 36

54 2.5.2 Methodology To characterize the permeability, the fibrous preform is placed in the mold, which consists of transparent acrylic top and bottom surfaces connected via aluminum spacers and steel bolts. A resin injection hose is connected to the center of the bottom surface, and the resin is contained in a pressurized vessel. Two video cameras are placed and synchronized so as to capture images of the top and bottom surfaces of the mold simultaneously. The recorded images contain a timestamp in their file name. After recording the fiber volume fraction and viscosity, the resin is introduced into the mold under constant pressure from the pressurized tank. The experiment is recorded until the flow front reaches any edge of the mold. The experiment set-up is given in Figure 2.5. The fill times and flow front characteristics are determined experimentally via image-processing, an example of which is shown in Figure 2.6. The images captured during the experiment are input into a MATLAB script, which processes and analyzes them. The images are filtered and converted to binary, so that it only contains a white elliptical ring, which represents the progress of resin flow from the preceding image to the current one. The script iterates through each image to record the locations of pixels in the flow front. These pixel locations are provided as input to a MATLAB function that generates an ellipse for the flow front using a least squares fit method. Given a set of ideal images (distinct resin flow edges with no noise) taken from a virtual experiment so that the actual fill times were known, the approximated fill times from image processing were shown to have an average relative error of less than 2.0%. From the fitted ellipses, the script can also determine characteristics such as; the semimajor and minor diameters, the angle of rotation, and centroid location. 37

55 Figure 2.5. Experimental set-up to monitor the resin flow at the top and bottom surfaces of the preform (left: schematic, right: picture of the set-up) The permeability tensor is evaluated by minimizing the difference between the experimental flow-fronts and the flow-fronts numerically predicted with six permeability components as variable parameters. The minimization uses Nelder-Mead simplex method. This method is designed to solve unconstrained multi-objective minimization/maximization problems. The method needs initial function values to form the initial simplex but does not require any gradient input. The method is a simplex-based method where a simplex, S, in n-space is defined as a convex hull of n+1 vertices. For example, a simplex in a 2D space is a triangle and in a 3-D space is a tetrahedron. The method begins with n+1 points (vertices of initial simplex) and function values at those points for n-variable optimization. The method then performs a sequence of transformations of the working simplex, S, aimed at decreasing the function values at its vertices. At each step, the transformation is determined by 38

56 y computing one or more test points, together with their function values, and by comparison of these function values with those at the vertices. This process is terminated when the working simplex, S, becomes sufficiently small that satisfies the assigned tolerance. For this study the generation of the new simplex algorithm is adopted from Mathews and Fink [17] a (x 2 )+b x y+c (y 2 )+d x+e y+f = x Figure 2.6. (Left) An image of isotropic flow from an experiment. (Middle) The image after having the preceding flow image subtracted from it, filtered, and converted to binary. (Right) An ellipse is fitted to the edge of the resin flow front. In this optimization routine the objective function is to minimize the residual sum of square of the experimental and numerical fill times of the filled nodes located at the top and bottom surface of the mold (Figure 2.7). The flow with initial permeability values is simulated via a numerical tool called Liquid Injection Molding Simulation, LIMS, which is a finite element/control volume based program that uses Darcy s law to describe the flow of resin inside a fibrous media and tracks the flow front during the impregnation process [45] with input values provided for the permeability and viscosity. LIMS then outputs the calculated node fill times, and the 39

57 computation is made to converge using the Residual Sum of Squares (RSS) method with the difference between the experimental fill times and the simulated fill times. This process is iterated by updating the input values for permeability until the LIMS fill times are sufficiently close to the experimental fill times. Those final input permeability values in LIMS are the permeability values for the fabric One of the main advantages of this method to characterize the permeability tensor is that it is inexpensive and easy to implement. Okonkwo et al. [118] proposed a similar algorithm, however the experiment involved a heavy mold with an expensive set of electric resistance sensors. The use of electric resistance sensors excludes the use of carbon fiber preforms, as carbon fiber is electrically conductive. The method described in this paper requires no sensors, as it uses image-processing as its primary means of calculating fill times. Also, the mold is relatively light and simple to set up and clean, while a senor-based experiment would require a more tedious clean-up process; if the resin is not completely cleaned off of the sensors, it could obstruct the sensors and the subsequent experiment could yield unreliable data. Other proposed methods have used embedded optical fiber sensors, which obstruct resin flow, leading to inaccurate data. Another benefit of this method is that K can be characterized in a single radial flow experiment, and the top and bottom surfaces of the mold are accounted for so as to allow one to determine all the six independent components of the three-dimensional permeability tensor. Weitzenböck et al. [93] proposed a method for measuring the permeability components in one radial flow experiment, however the resin was to be injected uniformly in the through-thickness direction. Therefore only in-plane components of K could be determined. 40

58 Figure 2.7. Algorithm for permeability prediction from experimental fill time of top and bottom surfaces Results and Discussion First, the methodology is tested with a parametric study of radial injection from the bottom center of the mold cavity injected under constant pressure. Figure 2.8 demonstrated the effect of non-zero skew terms; Kxy, Kxz and Kyz on the flow pattern. In Figure 6.a-c the magnitude of Kxy is increased while other two skew terms are zero to investigate its influence on the flow front. As expected increase in-plane skewness, Kxy, yields an increase in the in-plane rotation of the elliptical flow fronts. The center of the ellipses observed along the top and the bottom surfaces coincide and do not shift with the magnitude of Kxy. Nor do the ratios of the major and minor axes change, only the angle of the in-planar rotation increases with increasing Kxy. However, as the 41

59 other two skew terms, Kxz and Kyz are assigned a non-zero value, the center of the top ellipse in no longer coincident with the ellipse at the bottom surface. The shift between the two centers is proportional to the magnitude of the skew terms. As the Kxz value is increased the distance between the centers of the ellipse on the top surface and the bottom surface increases along the x-direction (Figure 2.8.d-f), similarly as the Kyz value is increased, the distance between the top and the bottom center increases in the y-direction (Figure 2.8.g-i). The numerical approach presented in Figure 2.7 is applied to the ellipses of Figure 2.8 in order to predict the permeability tensor just using the top and bottom ellipse flow front information. The maximum error between the assigned permeability and the predicted one is found to be 3.33 % Furthermore, the methodology is validated by assigning six non-zero permeability components in the LIMS simulation. The flow fronts on the top and bottom surface of this virtual experiment are used in the approach presented in Figure 2.9, to find the six components of the permeability tensor based on just this information as follows; the permeability tensor values on the left side in Table 2.1 are assigned into LIMS and resin arrival time are obtained with the developed image processing tool from the images of the top and bottom at different time steps. These arrival times are used as the experimental fill time (Ti,exp in Figure 2.7). Also, from the flow front profiles at the top and bottom the ratios of the in-plane permeability components and the angle between the principal directions and the global coordinate frame can be estimated. These estimations are assigned as the initial simplex. The algorithm converged to the assigned permeability values listed on the right side of Table 1 in about 6 hours of CPU time on a PC computer. In Figure 2.9, the flow front profiles are compared with the assigned and predicted permeability values for the top 42

60 and bottom surfaces. At time equal to 90 seconds the resin reaches the top for the first time and as it impregnates the top surface to form the ellipse, the center of the top ellipse is not coincident with the center of the ellipse at the bottom because of the non-zero Kxz and Kyz. This virtual experiment also shows the methodology can predict the six components of the permeability tensor accurately. Next, the methodology is applied to characterize the 3D glass fabric with 2627 g/m 2 areal weight. Three layers of 3D fabric are placed in the mold cavity with dimensions of 25.4 cm x 25.4 cm x 0.6 mm with 60% fiber volume fraction. Due to Newtonian behavior, colored corn syrup diluted with water with viscosity of 107 cp is used as simulated resin. The images with time stamps are analyzed via the image processing routine and the fill times at the bottom and top nodes are derived as the experimental data. Then the algorithm given in Figure 2.7 is implemented. Table 2.2 shows the results of predicted permeability components. From the predicted permeabilities, the Kxz component is seen to be negligibly small, but Kyz values is found to have effect on resin impregnation. In Figure 2.10, experimental flow front profiles are compared with the profiles obtained using the predicted permeability values provided in Table 2.2 at time equal to seconds. As it can be seen in the figure, the match between experimental and predicted profiles is quite good. The major and minor axes values are compared are also compared. For the top, experimental major and minor radius are m and m and the prediction data are m (9.09% error) and m (3.57% error), respectively. For the bottom, experimental major and minor radius are m and m and the prediction data are m (1.16% error) and m (1.96% error), respectively. 43

61 Kxz = Kyz = 0 (a) K xy = 1.0x10-11 (b) K xy =3.0x10-11 (c) K xy = 7.0x10-11 K xy = K yz = 0 δ x δ x δ x (d) K xz = 1.0x10-12 (e) K xz = 3.0x10-12 (f) K xz = 7.0x10-12 K xy = K xz = 0 δ y δ y δ y y (g) K yz = 1.0x10-12 (h) K yz = 3.0x10-12 (i) K yz = 7.0x10-12 x *For all simulations: K xx = 2.0x10-10 K yy = 1.0x10-10 K zz = 1.0x10-12 Figure 2.8. Flow front profiles at the top (solid lines) and bottom (dash-dot lines) for different skew permeability at time equal to 700 seconds. The jagged flow fronts are numerical artifacts because of fairly coarse mesh. 44

62 Table 2.1. Parameters for virtual experiment Parameter: Numerical value: Inlet pressure: 1.0 bar Fiber volume fraction of E-glass: 50% Viscosity of corn syrup 100 cp Assigned Permeability (m 2 ) Predicted Permeability (m 2 ) Percentage Error (%) Kxx 2.0x x Kxy 1.0x x Kyy 1.0x x Kxz 5.0x x Kyz 2.5x x Kzz 1.0x x δ Level Time(sec) y x Bottom Top Assigned Predicted Figure 2.9. Flow front profiles comparisons with assigned and predicted permeability values at the top and bottom surfaces 45

63 Table 2.2. Predicted permeability for the experiment Kxx Kxy Kyy Kxz Kyz Kzz 2.405x x x x x x10-12 TOP Experimental With predicted permeability Comparison BOTTOM a (x 2 )+b x y+c (y 2 )+d x+e y+f = y x Experimental With predicted permeability Comparison Figure Flow front profiles at time seconds at the top and bottom: experimental, with predicted permeability and comparison 46

64 2.5.4 Summary This work presents a methodology to characterize all the six independent components of a three dimensional second order permeability tensor. The approach employs a multi-objective optimization algorithm coupled with Liquid Injection Molding Simulation (LIMS) tool to calculate the permeability values. The effect of the non-zero skew components on the flow front progression and flow patterns is investigated through a virtual study to underline when the skew terms could change the nature of filling and influence the manufacturing process. 47

65 Chapter 3 THROUGH THICKNESS PERMEABILITY 3.1 Introduction When unidirectional stitched fabrics are used as reinforcement in composites, plies are typically stacked on top of each other to build up the desired thickness. Strength and stiffness requirements dictate the orientation of individual layers and the accuracy of angular alignment is limited. A pressure differential across the thickness is used to distribute the resin, either from a pre-impregnated fabric or injected from a resin source, to occupy all of the empty spaces between the fibers. This process is commonly modeled using Darcy s law, which describes flow of resin through porous media in which the flow rate is directly proportional to the applied pressure differential by the through-thickness permeability of the fabric. A different orientation between layers or even a slight misalignment during the stacking can change the through-thickness permeability dramatically due the change of resin pathways. In this chapter, characterization of the through-thickness permeability of a series of unidirectional fabrics stacked in various orientations is studied to address both the effect of stacking sequence and those of misalignment of the individual layers. Numerical simulations are conducted to predict the effect of change in fiber orientation on the through-thickness permeability. The results from the numerical model are compared with experimental measurements. Results show that averaging approach is not suitable to calculate the through-thickness permeability component when using unidirectional fabrics and that the stacking sequence of the unidirectional 48

66 fabrics may significantly influence the through-thickness permeability. Also, it has been shown that the effects of misalignments smaller than 5 degrees rotation between individual layers do not significantly modify the transverse flow. This chapter will analyze through-the thickness flow depending on relative orientation of individual reinforcement layers. It will show that such an averaging approach can result in large errors in calculation of the through-thickness permeability component when the preform consists of layers of unidirectional fabrics stacked in different desired fiber orientations. It will be shown both experimentally and by modeling, that the stacking sequence can significantly influence the through-thickness flow and hence the transverse permeability. This study will show that a limited misalignment less than 5 degrees rotation between the neighboring layers which can be attributed to inaccuracy of the layup process does not significantly modify the through the thickness permeability. A numerical study for a simplified model fabric is shown in Figure 3.1. Through-the-thickness direction is aligned with the z-axis. It is assumed that this is the principal direction of permeability and hence Kyz and Kxz are assumed to be zero. This is a reasonably valid approximation, as these components are usually insignificant. Figure 3.1 shows a solid model of three unit cells along with the corresponding crosssections. Each unit cell has four layers of unidirectional fabrics with different fiber orientation sequence in the in plane direction. In Figure 3.1.(a), all plies are aligned in the y-direction, while in Figure 3.1.(b), all plies are still aligned but rotated by 10 degrees with respect to the y axis in the x-y plane, and in Figure 3.1.(c) plies are rotated by 10 degrees with respect to the previous ply in the x-y plane as they are stacked on top of each other so the fiber orientation sequence with respect to the y-axis 49

67 will be 0/10/20/30 degrees. The change in orientation may arise from two sources: First, the design commonly requires that the unidirectional reinforcement is oriented with stacking sequence in pre-determined directions for desired strength and stiffness. This change of orientation from one layer to the next is usually in increments of 15 degrees or more even though several subsequent layers might have the same orientation. Second, the change in orientation may arise due to small unintentional misalignments. We address both these cases. Note that the cross-sectional area for the lay-up in Figure 3.1.(c) has a very different profile for through-thickness flow of the resin compared to no rotation and rotation of the plies by the same rotation degree (Figure 3.1.(a) and Figure 3.1.(b) respectively). Thus, the in plane orientation of unidirectional fabrics and their stacking sequence can create different pathways for resin flow in through-thickness direction resulting in different through the thickness permeability values (Kzz component). In this study the effect of the pathways formed by different in plane orientations of the plies on the through-thickness component of the permeability tensor are investigated. The simplified nature of the model is demonstrated by circular cross sections of the fiber tows and by the absence of stitching which (Figure 3.2) may actually form a very sparse weft layer. The only effect this stitching has in our model is that we do not allow any interpenetration of subsequent layers. 50

68 z z x y (a) x z z x y x (b) z z x y x (c) Figure 3.1. Solid model of a unit cell and the corresponding cross-section of four unidirectional plies stacked on top of each other (a) All plies aligned along the y- axis (b) All plies are rotated by 10 degrees in the x-y plane with respect to the y- axis (c) Each successive ply is rotated by 10 degrees resulting in a stacking sequence of 0/10/20/30 with respect to the y- axis with the corresponding cross sections in the throughthickness direction, respectively. 51

69 3.1.1 Effective Permeability of Preform Stacks Traditionally, the permeability tensor of a set of unidirectional plies stacked together to form the thickness of the composite is calculated by using the laminate analogy and the tensor transformation rules taking into account the orientation of the plies with respect to a coordinate system [119]. This approach serves reasonably well for two-dimensional (in-plane) permeability components, though some issues have been noted [123]. However, for the three-dimensional permeability tensor mainly the through-the-thickness component(s), this method has two major shortcomings. First, many models conclude that the permeability component (Kzz) in the thickness direction will be the same irrespective of the lay-up and the stacking sequence [124,125]. This is definitely not the case for unidirectional fabrics. It will be shown that, for example, 6 plies of unidirectional fabric that are all in the zero direction, their Kzz value will be very different from the same 6 plies if they have 0/90 sequence repeated three times. Physically this is true because the permeability depends on easy pathways for flow which will change in the thickness direction as one changes the orientation lay-up. Front Back mm Figure 3.2. Front and back side of the unidirectional fabric 52

70 The effect of ply-angle misalignment has been studied in detail on in-plane permeability of woven textiles components, but these studies have not addressed its effect on the through-thickness permeability component [34,123,126,119]. The relation between woven, random and stitched preforms and their effect on transverse permeability has been studied both numerically and experimentally [124,125,127,128,97,129,130]. Tahir M.A. et al. and Stylianopoulos, T. et al. stated that transverse/ through-thickness permeability is independent of in-plane fiber orientation [124,125]. Permeability studies for various preform configurations have measured the through thickness component along with other components of the permeability tensor [127,128,97,129]. Chen et al. [130] presented statistical analysis in terms of inter-fiber spacing for through thickness permeability only for disordered fiber arrays. For non-crimp fabric, Nordlund study [131] bears some similarity to our approach but concentrated on in-plane permeability components, while Drapier [132] did investigate the through-thickness permeability variations but dependent only on the stitching density. The change in the transverse direction with ply-angle misalignment is only investigated in terms of transverse matrix crack formation and propagation [133,134]. The effect of ply angles on the through-thickness permeability for unidirectional fabrics has not been addressed in the literature. By accurately measuring this permeability component, a much more accurate resin infusion prediction can be made in the through-thickness direction especially for processes such as Vacuum Assisted Resin Transfer Molding Processes (VARTM) in which a distribution media is placed on one side of the preform and in Out of Autoclave processing as the resin flow is mainly through the thickness and plays a key role in filling the empty spaces between the fibers [ ]. 53

71 3.1.2 Unidirectional fabrics and their orientation Experimental characterization is conducted for the unidirectional glass fabric with the areal density of 1397(+/-42) g/m 2. As seen from Figure 3.2, the stitching of the fabric (at the back) eliminates the nesting of the layers and because it is rather sparse it does not affect the unidirectional characteristic of the fabric. The layers are cut manually to stack up in desired orientations to build the required thickness. Figure 3.3 illustrates how each ply is rotated schematically to obtain the successive rotation of the plies with a picture of the corresponding fabric layer. Figure 3.3. Representation of the orientation of the plies 3.2 Through-thickness permeability characterization Numerical Analysis In this study the characterization of through-thickness permeability by numerical analyses is performed using the commercial software ANSYS Fluent Inc. [138], implementing a mesh generated by the software, ANSYS Gambit 2.4 [139]. The numerical study conducts a simulation of laminar viscous flow of resin through 54

72 the open regions of a unit cell of a preform created by stacking unidirectional fabric layers in desired orientations. The unit cell preform, composed of open regions and fiber tows, is represented in Figure 3.4. The fiber tows are modeled as a solid as the permeability of the fiber tows is usually five orders of magnitude smaller than the bulk permeability and can be neglected [140]. No slip boundary condition is applied on the fiber tow surfaces. The boundary conditions of the unit cell model are defined for each pair of parallel faces using the meshing software Gambit. An example of the numerical model of the unit cell is shown in Figure 3.4.(a), in which the successive unidirectional fiber layers are rotated by increments of 5 degrees. Thus the angular difference between fiber orientations of tows in two successive fabric layers is five degrees. The model was created with 6 layers for comparison with experimental results as we used six layers in our experiments. For numerical parametric studies we created a model with 10 layers of fabric in the through - thickness direction with 10 tows in the first layer of unidirectional fabric. In order to ensure equal spacing in successive rotated plies, additional fiber tows were introduced in the unit cell. The number of tows introduced will depend on the rotation angle as can be seen from Figure 3.1. The mesh for the corresponding sample is presented in Figure 3.4.(b). In order to ensure that the periodicity or periodic effect on all four faces (two x-z and two y-z (as defined in the Figure 3.4) is satisfied, the unit cell dimension in x and y - direction are incrementally increased until the through-thickness permeability values (Kzz) converges. For numerical convergence, the cell dimension along in plane direction (x and y direction) need to be increased as the rotation angle of the successive unidirectional layer changes. The unit cell for the case with the largest 55

73 change in orientation (angle of 90 degrees from the adjacent ply) is studied for the determination of the dimensions that satisfies numerical convergence criteria. x z x z y y (a) Figure 3.4. (a) The Gambit model with each successive layer rotated by five degrees. b) Gambit mesh of the model with 1,968,652 elements and 484,911 nodes. The cut-out shows the mesh density After the mesh with boundary conditions is generated using Gambit as shown in Figure 3.4, it is exported to Fluent Inc. to be solved for the viscous flow within the unit cell under a prescribed pressure gradient across the layers of the fabric as in Figure 3.5.(a). The corresponding volumetric flow rates through the faces in the through-thickness direction are obtained and one-dimensional Darcy s law in the through the thickness direction is used to find the through-thickness permeability, as given in Figure 3.5.(b). The simulation results are presented and discussed in the results and discussion section. 56

74 x y z x y z Figure 3.5. (a) Periodic boundary conditions to evaluate the permeability in z- axis, (b) Evaluation of permeability in z-axis Experimental Validation For the experimental set-up, resin flow through fibrous preform is tracked radially within a mold in all three directions simultaneously, yielding all three permeability components from a single test [118]. During the experimentation of the resin transfer molding process, stack of fabrics is placed between two horizontal plates (top and bottom: 40 cm x 40 cm), as shown in Figure 3.6, that are separated by 6 mm each with 96 electrical sensors in a radial configuration. Located in the center of the bottom plate is an inlet hole, 6 mm in diameter, through which resin of known and constant viscosity, µ 0.1 Pa.s, is injected applying a positive pressure of P = 100 kpa. 57

75 (a) upper mold plate inlet (b) bottom mold plate (c) mold assembly (d) resin flow Figure 3.6. Experimental set-up: (a) Upper mold plate, (b) Lower mold plate, (c) Mold assembly, (d) Resin flow through preform Corn syrup is used as simulated resin because of its favorable characteristics; it is a Newtonian fluid and nontoxic. As the fluid flows through the fabric in all three directions, it wets the sensors, inducing a voltage drop that is subsequently recorded by a LabVIEW data acquisition system. By having two sets of planar sensors, which are separated by 6 mm in the z-direction, the flow can be tracked in the z-direction as well, yielding experimental data for the through-thickness component of the permeability tensor. A three dimensional numerical simulation of flow through anisotropic porous fibrous media called Liquid Injection Molding Simulation (LIMS) is used in which the permeability values are changed iteratively in a geometry, that is 58

76 identical to the experimental mold, with numerical sensors placed at the same locations as in the experiments until the residual sum of squares between the numerical and the experimental arrival times converges to a minimum [118]. The converged numerical values provide the three-dimensional permeability tensor for the fabric lay-up which includes the through-thickness value, which is the main focus of this study. 3.3 Results and Discussion Experimental Study Table 3.1 compares the numerical predictions with the experimental results for five separate lay-ups of 6 unidirectional fabrics: (1) All plies are aligned along y axis (zero degrees), (2) All plies are aligned and make an angle of five degrees with the y axis (3) Successive plies are rotated in increments of five degrees, (4) successive plies are rotated in increments of forty five degrees, and (5) successive plies are rotated in increments of ninety degrees. For each case, the experiment was repeated three times, from which the maximum standard deviation was observed to be 4.15 x10-12 m 2 for case 5 as shown in Table 3.1. As expected, the results for cases 1 and 2 are nearly identical as they should be. This can be attributed to the fact that there is no relative planar rotation of the plies with respect to each other. The planar permeability with respect to the fixed coordinate system of the mold may change between cases 1 and 2 and the skew permeability term (Kxy) should reflect the change - but the principal through-thickness permeability should not be affected which, was confirmed with the experiments. For case 3, the angle between successive layers was increased by five degrees and this did not influence the through-thickness permeability in any 59

77 significant way. This answers one of the issues targeted by this study: Is a small misalignment, such as caused by inaccurate lay-up, significant for the throughthickness flow. Hence one does not notice any significant change in permeability due to small misalignments. However, when we conducted the extreme case of 45-degree and 90-degree increment between successive layers, there is a sharp increase in transverse permeability, as one would expect due to lower resistance pathways straight across the thickness that increases the permeability dramatically. Numerical simulations at the unit cell level confirm this behavior. Additionally, in Figure 3.7 numerical convergence study is conducted for through thickness permeability values with increasing mesh density. Table 3.1. Experimental and numerical comparison of through-thickness permeability. Case 1 and case 2 of 0 o and 5 o refers to all six unidirectional layers being aligned along those angles respectively. In case 3, case 4 and case 5, the successive layers were rotated by 5 o, 45 o and 90 o degrees respectively. Case Kzzx10-11 (m 2 ) Experiment Angle 0 o Angle 5 Increment angle 5 o Increment angle 45 o Increment angle 90 o vf = 54 % Average Standard Deviation Numerical Results

78 Figure 3.7. Numerical through thickness permeability with different mesh element sizes for incremental rotation angle 5 o Parametric Study After the numerical model is validated with experiments as shown in Table 3.1, the effect of ply angle is further investigated using the numerical approach only. For this analysis ten layers of plies are stacked on top of each other to systematically predict the effect of planar rotation between successive unidirectional plies. In order to observe the effect of the cell configuration, for the numerical simulations the tows are modeled using both square and hexagonal grid configurations The permeability of a unit cell in which all ten plies were aligned along the same angle was calculated for various angles and it was found that the throughthickness permeability was not affected by changing the in-plane angle as long as the 61

79 unidirectional fibers in all ten layers were aligned in the same direction. This is physically necessary as long as the through-the-thickness direction constitute the principal direction of the permeability. In this case due to symmetry, this is true and this result verifies the fact. To explore the effect of the stacking sequence of ten layers on the throughthickness permeability, a numerical unit cell was constructed in which one could vary the fiber orientation of the unidirectional fabric in the successive layers by a fixed number of degrees. Permeability in a total of 14 different unit cells in which the angular in plane rotation of the successive plies was incremented by 0, 1, 2, 5, 10, 20, 30, 40, 45, 50, 60, 70, 80, and 90 degrees was predicted and is compared with zero rotation (all layers aligned in the same direction) using square grids in Figure 3.8. Figure 3.8 emphasizes the fact that larger the difference in the angular rotation of the successive ply, higher is the through-thickness permeability of the fabric. Obviously, a small change (such as one caused by lay-up inaccuracy) will only have a negligible effect. 62

80 Figure 3.8. Effect on through-thickness permeability with increasing rotation angle of the successive ply. The unit cell was created using the square and hexagonal arrangement of the fiber tows in the unidirectional ply. It is also clear that the rotation effect is a non-linear one, as the probability of higher permeability pathways increase with larger degree of rotations. Additionally those 14 unit cell configurations are repeated for hexagonal unit cells and no significant variations are observed with the square unit cells counterparts. As the stacking sequence of ply orientation may vary depending on mechanical property requirements, we explored if the order of the rotated plies would influence the permeability value. Figure 3.9 represents the effect of the order of the ply rotation. The first set of bars in Figure 3.9 shows the through-thickness permeability value for 12 plies in which each successive ply was rotated by 30 degrees. This configuration was compared with 12 layers where layers with the same orientation were grouped together (stacked as 0/0/30/30/60/60/90/90/120/120/150/150). These were also 63

81 compared with all plies aligned (no rotation) as the baseline case. This was repeated for 45-degree and 90-degree increment of the successive plies, with number of plies reduced to eight and six, respectively. By grouping the layers, the effective through the thickness permeability drops significantly, though it is always higher than the baseline case of the unidirectional sample with no rotation. This is shown in Figure 3.9. This result suggests the wider resin pathways are generated by successive rotation of the plies. As seen from the results when layers of zero and ninety degree are grouped together with a single angle change in the stack, the permeability of the assembly is closer to the permeability of unidirectional layers without any rotation (baseline case). The change in orientation between successive layers does influence the transverse through-thickness permeability value even if the average orientation of the stacked sequence is the same. Consequently, if a permeability value is to be determined from component permeability, the number of crossovers at certain angular difference (compared to total number of layers) should be taken into account. The commonly used averaging scheme to find the transverse permeability component does not account for this and will result in large errors in permeability predictions. 64

82 Figure 3.9. Effect on through-thickness permeability with increasing rotation angle of the successive ply. The unit cell was created using the square and hexagonal arrangement of the fiber tows in the unidirectional ply. 3.4 Summary The simplified numerical model that quantifies the effect of change of fiber orientation direction in the successive ply of a laminate formed with unidirectional fabrics on its through-thickness permeability has been created and compared with the experimental results. The comparison was favorable and the model was used to determine the dependence between the successive plies and through-thickness permeability. Note, however, that we did not allow any nesting in our model between the adjacent layers, as the stitching pattern essentially prevents it. For a different material this may not be true. The experimental and numerical results demonstrate that as the angle between successive plies increases, the permeability in the through-thickness direction 65

83 increases in a non-linear fashion. Small deviations from alignment (such as fivedegree rotation between successive plies) did not noticeably affect the throughthickness permeability, showing that lay-up inaccuracy is not significant; at least as far as through-thickness flow properties are considered. For higher angular rotation, experiment and model agree that the permeability increases significantly in strongly non-linear fashion. This may be explained by the architecture of the fiber layout. As the fiber alignment between plies decreases it changes the layout of empty spaces, creating lower resistance pathways between successive layers and increasing the bulk through-thickness permeability of the laminate. Second important finding is that the grouping and order of the rotated plies (stacking sequence) influences the through-thickness permeability value. Note that the determination of this grouping is not for processing engineers to decide. It is dictated by structural needs. The latter finding leads us to hypothesize that, in order to build a successful through-thickness permeability model based on the through-thickness permeability of unidirectional plies one must also account for the number and relative angle of layer contacts into the model. 66

84 Chapter 4 CHARACTERIZATION OF LOCAL VARIABILITY OF FABRICS 4.1 Introduction Local non-homogenous architecture of the fabric can have a noticeable effect on the dynamics of resin flow behavior. There is no available standard characterization method to characterize the fabric variation and defects from the observed variation in the flow front motion. Thus, the objective of this chapter is to present a quantitative way to characterize the local permeability variation of a fabric by monitoring the flow front movement. To study the effect of local permeability variations on the global permeability, de Parseval et al. [141] simulated one-dimensional flow with stochastic and regular local permeability variations. They observed that the global permeability is the spatial harmonic mean of the local permeability values. Padmanabhan and Pitchumani [31] performed stochastic analyses of non-isothermal injection processes based on simulation of one-dimensional flow. For a rectangular mold with linear injection gate, Sozer [32] simulated two-dimensional flow applying local random permeability variations to observe the effect of preform non-uniformity on mold filling. Random variations of the local permeability of up to +/- 35% were reported to have no significant effect on the flow pattern, while variations in a specific pattern caused a more significant effect on the mold filling results. Using a similar approach for studying global permeability variations, Desplentere et al. [33] assigned local permeability values for injection simulation not only randomly, but also imposed a 67

85 correlation between the properties of adjacent material zones along the principal flow direction. It was found that for random assignment of local permeability values to discrete material zones, the variation of global permeability values was influenced by the size of the zones. For correlated local permeability values varying only along the principal flow direction, the results for the global permeability were in agreement with the observations of de Parseval et al. [141]. Lundstrom et al. [142] determined nonuniform local permeability values from the dimensions of flow channels with variable widths between the fiber tows. For a completely random distribution of the local permeabilities, they found that the global permeability decreased with the maximum variation at the unit cell level, while for a correlated distribution, the global permeability could either increase or decrease. The current state of the art to measure permeability of a fabric in a certain direction assumes that the fabric is uniform and hence the permeability is spatially uniform. Those assumptions allow one to conduct a one-dimensional experiment as shown in Figure 2.2 and from the flow rate pressure drop relationship obtain an averaged value of permeability in that direction. If one wants to find the principal permeability values in the plane of the fabric, one would conduct a radial experiment and from the elliptical spreading domain and the flow rate pressure drop relation one can calculate the in-plane permeability tensor as shown in Figure 4.1 [118]. Quantitative evaluation of injection experiments, which is normally based on flow front tracking, implies averaging of local variations in material properties and measuring averaged global permeability values [29,30,34]. While the experimentally determined permeability values characterize quasi-uniform materials, the accurate 68

86 predictive description of global flow for non-uniform materials requires knowledge of the distribution of local properties. (a) (b) (c) Figure 4.1. Radial injection and permeability tensor characterization: (a) Schematic of flow front in an anisotropic fabric at a time step with the principle direction x y -axes, (b) Radial injection inlet gate and resin propagation, (c) Permeability tensor. K xy is non-zero as the principal axis do not align with the selected coordinate axis In this chapter, emphasis will be on the characterization of the variation of the permeability within the fibrous preform. The goal is to determine the variability of the preform before it is used in the manufacturing process and measure the permeability with its variations so it could be included in the process design. This characterization will be based on the mathematical descriptions derived from surface growth equations and interface/flow front analysis. 69

87 4.2 Mathematical Implementation In order to generate a model to characterize the local variation of the fabric and preform, the surface growth equations that provide mathematical description for disorderly surface growth in random media is adopted [143]. Growth phenomena can be divided into two groups based on the driving factors: local interactions and non-local interactions. Examples of local interactions are spreading of fire and fluid flow in porous media, whereas examples for non-local ones are formation of the snowflakes and metallic dendrites [144]. The local growth can be formulated by what is known as the Kardar-Parisi-Zhang (KPZ) equation: h(r, t) t = ν 2 h(r, t) + λ 2 [ h(r, t)]2 + F + η (4.1) where h(r, t) is the height of the variable which depends on position and time as shown in Figure 4.2 for fluid flow through porous media, ν and λ are constants, F is the driving force and η is the white noise in the system. Figure 4.2. Flow front locations (height h(r, t)) at various times with system size L, and mean height (flow front position) h 70

88 Thus, the flow through porous media can be defined as local interaction on the macro scale in which certain universality can be obtained. Then, the surface growth in random media forms self-affine shapes of interfaces. In order to define that selfaffinity the local height h(r, t) is obtained as the flow front propagates, then interface width, w(l, t) which is the variance of the h(r, t) on a flat surface over the inlet gate length, L, can be defined as w(l, t) = 1 L (h(i, t) h (t)) 2 (4.2) where h(i, t) is the local height at a specific location and h (t) is the averaged value of the h(i, t) (Figure 4.2). w sat w sat (L 4 ) w sat (L 3 ) w sat (L 2 ) w sat (L 1 ) L increases (a) (b) Figure 4.3. (a) Change of the interface width with time (logarithmic scales for both axes) for a fixed L value, (b) Growth of the interface width with different system sizes (L). Reprinted with permission from [143] 71

89 Typical plot of time evolution of the interface width has two regions (in Figure 4.3.(a)). First, interface width w(l, t) increases linearly with time in logarithmic scale until the cross-over time, t x. The slope in the first region characterizes the timedependent dynamics of roughening, β and is called the growth exponent. Then at time t x it reaches saturation point when the variance, w(l, t) reaches its saturation point, w sat (L). As seen in Figure 4.3.(b), the saturation point, w sat (L) increases with system size, L. Thus, self-affinity of the interfaces can be defined under the universality class of KPZ using the following power law relationship [145]. w(l, t)~t β F w (Lt 1/γ )~ { tβ for t t x L α for t t x (4.3) with F w is a scaling function. β is the growth exponent and α is the roughness exponent. The roughness exponent, α characterizes the roughness of the saturated interfaces at different system sizes, L, (in Figure 4.3.(b)) with the relationship given in Equation (4.3). Moreover, cross-over time, t x is dependent on the system size, L as follows: t x ~L α/β (4.4) where α/β is called dynamic exponent, γ. For phenomena such as paper burning, fluid flow through fibrous media and two-phase viscous flows, the interface fluctuations can be measured experimentally or numerically to determine the exponents α and β. For example- for flow through fibrous porous media as the resin front advances the fluctuations of the flow front 72

90 shape can be visualized and recorded at different time steps as seen in Figure 2.2 and using the flow front shapes with time data in Equation (4.2) and Equation (4.3) one can determine the growth exponent, β and roughness exponent, α. For different applications, the exponents may be different; however, there is universality/consistency of those exponents despite the randomness of the medium [ ]. Thus, the above theory could be used for the characterization of the morphology and the dynamics of the growth/propagation of the resin through the fibrous preform. A conclusion can be formed from the investigation of the three exponents listed above, α, β, and γ in terms of the variation of the permeability values within the fabric via the monitoring of the interface/flow front position data with time. These values can then serve as the indicator of the homogeneous nature of the fabric from manufacturing viewpoint. By monitoring the flow front progression as the resin impregnates the fibrous media, we will describe the flow-front progression in 1D flow, measuring the (h(i, t)) values and calculating w(t, L) using Equation (4.2) at a series of time steps and then determine the exponents α and β using Equation (4.3). These exponents are directly related to the permeability variations/defects of the fibrous preform. To correlate the fabric permeability variation with the two exponents α β we need to simulate the effect of a series of known permeability distributions on flow front progression variations which will allow us to calculate the exponents using Equation (4.2) and Equation (4.3). The flow with known permeability disturbances/distribution is simulated using Liquid Injection Molding Simulation, LIMS [23,149]. In LIMS, every element in the finite element mesh can be assigned its own permeability. Thus by populating the elements with a selected permeability 73

91 distribution, the effect of that distribution on flow front variation can be tracked to measure h(x, t) and evaluate w(t, L) (Equation (4.2)) at each time step. Equation (4.3) can then be used to find the three exponents. This could be repeated for various selected permeability distributions to establish a correlation between the coefficients and the variations in the permeability distributions. As shown in Figure 4.4, in the LIMS mesh a distribution of permeability values with a selected standard deviation with upper and lower limits are generated and assigned randomly to each element in the mesh mimicking the variation one may expect due to manufacturing of such fabrics. The one-dimensional flow is simulated by introducing the resin along one edge of the mold. LIMS can capture the variations in the flow front as the flow progresses from the inlet to the vent. Figure 4.4 shows an example of LIMS simulation results in flow front interfaces at different time steps. Thus, those flow front locations are used to obtain the interface width in Equation (4.2), which will be then be used for the calculations of the exponents stated in Equation (4.3). 74

92 : random permeability values i: numer of elements Inlet (constant flow rate) LIMS simulation Figure 4.4. Top: LIMS mesh and random permeability assignment, Bottom: flow front progression with time obtained via LIMS Additionally to characterize the physical defects of the fabric, the variation of the permeability is assigned based on the solution of the Poisson s equation with Dirichlet boundary condition as stated in Equation (4.5). K = Q in Ω, where K = K base on Ω (4.5) 75

93 On the boundaries the permeability is assigned as the global (constant) permeability and the defect/high permeability is placed in the middle and reduces towards the edges as controlled by the parameter Q, which represents the size of the defect. As Q increases, the variation of the permeability in the zone increases. Then, Equation (4.5) is solved to obtain the variation of the permeability for the defected zone (as shown in Figure 4.5), which represents the permeability data for the defected zone. In Figure 4.5, the preform is divided into 4 x 4 equal to 16 zones of which four zones are randomly selected as defective zones. In these defective zones, permeability values are defined by the solution of Equation (4.5) and rest of the zones are assigned constant permeability value equal to Kbase. This analysis can be used to determine the extent of the defect within the fibrous domain. Figure 4.5. Assignment of the variation of the permeability of the defected zones: left: 25% defective sample, right: variation of permeability within the defective zone obtained from solution of Equation (4.5). Permeability is higher in the center of the zone and reduces to the values prescribed at the edges as described by the parameter Q in Equation (4.5). 76

94 4.3 Experimentation Once the correlation between fabric permeability variation and flow front variation is established with a series of LIMS simulations, one can experimentally determine the three exponents for an actual fabric and using the correlation determine the variability in permeability of the preform. In order to visualize the movement of the flow front through the fibrous medium with time, the one-dimensional test set up as shown in Figure 4.6, is created. After the preform is placed on the acrylic table it is sealed with a vacuum bag and the resin at atmospheric pressure is introduced from one end through a line gate while drawing a vacuum at the other end. The resin impregnates into the preform due to the pressure gradient of one atmosphere and the flow front movement is captured via the flow visualization camera system along with the time stamp. Due to its Newtonian characteristic, corn syrup with dark cloth dye and water is used as the simulated resin to create a clear contrast between the dark resin front and the white fibrous porous media. Using the set-up, the goal is to measure the variations at the flow front and use the KPZ evaluation scheme to determine the growth exponents which have been correlated to the permeability variation with the use of numerical simulations. This allows us to directly relate the variations of the flow front to the variation in the permeability of the porous media and identify the presence of defective zones in the preform. To validate identification of the defective zone and its quantification within the fiber preform, 25 cent coins were placed within the fibrous media to simulate the defective zones. The presence of coin within the layers will increase the permeability in that zone due to imperfect fit. Eight layers of plain weave E-glass fabric (Figure 1.2.(a)) were used as a preform with in-plane permeability value, Kbulk equal to 8.43e- 77

95 11 m 2. The resin was introduced from the line gate with the vacuum applied at the other end. From Figure 4.7, the effect of randomly distributed and evenly distributed defects can be observed on the progression and variation of the flow front profiles. Figure 4.6. Flow through porous media experimental set-up with flow visualization 78

96 Figure 4.7. Resin flowing into a fibrous preform with 25 cent coins placed inside the fabric to simulate defective regions. On the left the defects were evenly distributed on the right the defects are randomly distributed. Measured experimental flow front profiles are also shown (flow front contours at Δt = 25 seconds) 79

97 4.4 Results and Discussion Characterization of permeability variation To correlate the growth exponent to the permeability variation, the growth exponent, β for three different permeability data sets as shown in Figure 4.9.(b) with standard deviation for each distribution is shown in Figure 4.9.(c) were generated. The values from each distribution set were assigned randomly to elements of the LIMS mesh. Figure 4.8.(a) show flow front fluctuations for three different permeability distributions shown in Figure 4.8.(b). Figure 4.8.(c) plots the change in the interface width w(t) on a logarithmic scale with time (As given in Equation (4.3), the slope of the log(w(t)) vs log (t) where t >> t x, will provide the exponent β. The LIMS time and position data is transferred to a MATLAB script that calculates the w(t) and generates the plots. As it can be seen from the plot in Figure 4.8.(c) the slope β is the same for all the three different standard deviations. Its value is 0.77 ± 0.03 which matches with the value reported in the fluid through fluid flow example analyzed in random domain work [16]. These tests are repeated for different mesh sizes, different permeability ranges, different inlet pressure values and β value was found to be invariant. 80

98 (a) (b) (c) Figure 4.8. Characterization of the growth exponent: (a) Shape of flow front at a time instant, (b) Bell curves with three different standard deviations selected for the permeability values assigned in LIMS, (c) Change of the variance of the interface with time from the simulated experiment with permeability distributions shown in (b) In order to calculate surface roughness exponent, β, the simulated experiments with LIMS are repeated for different inlet gate sizes, L (Figure 4.4) and the saturation of the interface width is recorded. Using the relationship provided by Equation (4.3) which states w sat (L)~L α, α is the slope of the plot log (w sat ) vs log (L). The calculations are performed for both anisotropic and isotropic fibrous porous media. For anisotropic case, the permeability from the permeability distribution is only assigned to the permeability component in the flow direction and the permeability component in the perpendicular direction is held constant at 1.0e-12 m 2. For the isotropic case the perpendicular and parallel permeability components are equal for the same element and randomly assigned to each element. The results for α are tabulated 81

99 in Table 4.1 and for both anisotropic and isotropic cases change is observed with different standard deviation values under the permeability range values of 1.0e-14 to 1.0e-8 m 2. The α values are observed to decrease for both isotropic and anisotropic cases as the standard deviation for the generated permeability distribution function increases. Thus this decrease enables one to characterize the variation within the preform in a quantitative manner. Higher the value of α, lower will be the permeability variation within the preform. Thus the Kardar-Paris-Zhang (KPZ) equation that models the surface growth on random media can be adopted to characterize the variation of the permeability within the preform. Table 4.1. Characterization of the roughness exponent Standard Deviation (m 2 ) α (Anisotropic ) ) K = 1.0e 12 m 2 K = 1. e 11to 1e 9 m 2 α (Isotropic ) K = K = 1.0e 11 to 1e 9 m 2 2.0e e e Thus, the characterization of the local variation in the preform can be determined by the change in the roughness exponent, α which is related to the standard deviation in the fabric permeability variation but with no change in growth exponent, β. 82

100 4.4.2 Characterization of the defects within a fabric To characterize how the roughness exponent α and growth exponent β are related to the size of the defect Q and the percent of the defect, m a numerical study was performed via LIMS to obtain β and α at 4 different Q values (100, 75, 50 and 25) and for 65 different percentages of defect, m, from 1% to 65%. For each Q and m value the numerical analysis is repeated 5 times and the average value is used. The domain was divided into 100 zones and for each Q and m value, defective zones are randomly located and permeability variation in that zone is assigned using Equation (4.5) with K base value of 1.00e-10 m 2. The results are presented in Figure 4.9 and Figure 4.10 for β and α, respectively, and an exponential fit with the equation is obtained for each Q value. Thus through these set of simulations, strength of the defect, Q and percentage of the defect, m are related to the growth, β and roughness, α exponent. The analysis are not performed for m values larger than 65 % because a region that has over 65% defects can be detected visually and does not need to be analyzed. Also we found that the exponents calculated for regions over 65% were not reliable as they showed very large degree of fluctuations. 83

101 Figure 4.9. Change in growth exponent, β with increasing percentage of defective zones (m) for different degree of defects, Q. A best fit functional relationship is also plotted 84

102 Figure Change in roughness exponent, α with increasing percentage of defected zones, m, for different degree of defects, Q. A best fit functional relationship is also plotted. Using the data presented in Figure 4.9 and Figure 4.10, which provide the growth exponent and roughness exponent, respectively, a constitutive equation to describe Q and m as functions of β and α, was formulated as shown below; Q(β, α) = 125. ln(β. α) (4.6) m(β, α) = ln(β) ln(α) (4.7) It was hypothesized that if there was a large variation in the permeability value in a small region, one could capture that with change in the growth and roughness exponents. To explore this, two types of experiments were conducted in which the 85

103 local change in permeability was introduced by (i) placing 25 cent coins and (ii) tacky tape within the preform respectively as shown in Figure The goal was to relate the change in exponent value with the percentage of the porous media in which the permeability change was significant. The experiments are performed by placing quarters and tacky tape at the center of the zone. In Figure 4.11, 48 quarters and 48 tacky tape pieces are randomly placed in total of 128 zones which represents a preform with 37.5% defective zones for both cases. As shown in Figure 4.11, the flow front profiles with time intervals of 25 seconds are obtained via VARTM set-up (Figure 4.6). Those profiles are used to obtain β and α values. For defects introduced with coins the β and α values were and respectively, and for defective zones due to tacky tapes, the β and α values are and , respectively. When these values were substituted in Equation (4.7), the percentage of defective zones calculated was 36.78% and 35.72% for the coins and tacky tape respectively which was not far from the assigned 37.5%. 86

104 Figure Defect tests via VARTM with 37.5% defect and flow front profiles (Δt = 25 seconds), left: quarters right: tacky tape to represent the defective zone. 4.5 Summary In this study the variation of the preform permeability is characterized via KPZ formulations. Besides the growth exponent β belonging to the universality class of KPZ equations, by using roughness exponent α one can determine the variation of the permeability within the preform by recording the variations in the flow front profiles. Additionally, this study enables the determination of the percentage of defects within a preform, which is useful information to reduce variability due to material defects in composites processing. 87

105 Chapter 5 OPTIMIZED DISTRIBUTION MEDIA LAYOUT 5.1 Introduction The flow patterns during filling may vary from part to part due to the variability associated with the material, part geometry, and lay-up of the assembly, which may result in race-tracking channels. The process is considered as reliable and robust only if the resin completely saturates the preform despite changing filling patterns caused by flow disturbances. 5.2 Flow Control Mechanisms for Flow Through Fibrous Domain The resin flow pattern can be manipulated with a tailored DM layout as it does impact the flow patterns significantly. The continuous DM layout over the entire part surface works well for very simple geometries with no to little potential for race-tracking along the edges. In this study we address complex cases, which require placement of an insert within the assembly, which will introduce race-tracking along its edges, and hence uniform placement of DM over the entire top surface will fail to yield a void free part. We introduce a methodology using a predictive tool to design an optimal shape of DM, which accounts for the flow variability introduced due to race-tracking along the edges of the inserts. This iterative approach quickly converges to provide the placement of DM on selective areas of the preform surface that ensures complete filling of the preform despite the variability. This approach has been 88

106 validated with an experimental example and will help mitigate risk involved in manufacturing complex composites components with Liquid Molding. In order the show the effect of the DM placement on top of the preform, a numerical simulation via Liquid Injection Molding Simulation (LIMS) [23] (See Section 1.3 for LIMS introduction) for VARTM and SCRIMP are performed and time contours are compared (Figure 5.1). The simulation is performed for the cross-section of the preform in the through-thickness direction. The fill time with the VARTM is 751 seconds and for the same configuration with the DM on 95% of the top layer reduces the fill time to 378 seconds. The use of DM decreases the fill time because the resin first flows through the DM layer and then resin is infused in the through thickness direction [150,151]. Thus, SCRIMP eliminates the disadvantage of VARTM in terms of fill time. However, SCRIMP might yield formation of voids (especially at the leading edge of the flow front) and for complex geometries and parts containing impermeable inserts [152]. 89

107 inlet vent Distribution Media VARTM t fill = 751 sec SCRIMP t fill = 378 sec Figure 5.1. Fill time contours for a VARTM and SCRIMP 5.3 Methodology and Implementation First, given the part geometry along with insert locations, one must identify all possible race-tracking locations within the part and create possible scenarios, which take into account all possible permutations of race-tracking that may occur during the impregnation process. To determine a single optimal layout of DM for all these possible scenarios, a discrete optimization method is adopted. Discrete zones are generated by dividing the surface of the preform (where one places the DM) into a finite number of regions. Optimal solution finds the regions where one should place the DM such that for all scenarios the resin will arrive at the vent last after having impregnated the entire preform. Mathematically, this is done by prescribing the cost function that will minimize the region with no empty region or voids in the mold. Evaluation of the cost function is performed with an existing numerical simulation 90

108 called Liquid Injection Molding Simulation (LIMS) [45] which simulates the flow in any complex geometry in Liquid Molding. LIMS output provides the empty region after each fill based on the inputs of preform and DM permeability, race-tracking strengths along the edges and predefined inlet and vent locations Discrete Optimization Gradient descent method is a first-order algorithm to find a local minimum of a function. The method starts with an initial guess of the solution and the gradient of the function at that point is evaluated. The solution is stepped in the negative direction of the gradient and the process is repeated until the algorithm converges to a zero gradient. This method works for the objective functions for which the gradient can be evaluated. If the variables used in the objective function are only a finite or discrete set of values, discrete optimization should be applied. The discrete optimization problem can be defined as a set, S of finite possibilities that satisfies the objective function. The objective function provides local minimum, xopt for all elements of the set S, f(x opt ) f(x) for all x S (5.1) Discrete optimization can be used for different problems such as VLSI layouts, robot motion planning, test pattern generation, and facility location [153] Tree Search Algorithms The search of the optimal solution with discrete optimization consists of computationally expensive problems. As Koft [154] states there are two parameters that indicate the complexity of the searches: the branching factor of the problem space and the depth of the solution to the problem. The branching factor represents the 91

109 number of the new states that are generated and analyzed at each depth. The depth of the search is the distance between the initial node and goal node/s. There are two basic tree search algorithms; breadth-first search (BFS) and depth-first search (DFS). In Figure 5.2.(a), a sample tree layout is given and there are two goal nodes satisfying the objective function, H and T. BFS expands all the states one step away from the initial state until a goal state is reached and converges to node H, before node T (Figure 5.2.(b)). DFS explores a path all the way to a leaf before backtracking and exploring another path. Therefore, only path of nodes from the initial node to the current node must be stored in order to execute the algorithm. DFS will find the node T, before the node H (Figure 5.2.(c)) [155]. Figure 5.2. Tree search algorithms (a) example problem with two acceptable, H and T, nodes, (b) Breadth-first search: finds node H, (c) Depth-first search: finds node T As the BFS converges, the solution at the minimum depth is found (Figure 5.2.(b)). When a DFS succeeds, the solution may not be at the minimum depth (Figure 92

110 5.2.(c)). Thus, for a large tree, BFS may have large memory requirements and DFS convergence may take a long time to reach the solution, goal node. For the solution for DM layout design the minimum depth is not a concern but the memory is. So, DFS is adopted by generating regions on the preform which represents the finite solution set and the cost function is the unfilled area. Different race-tracking (RT) scenarios yield different unfilled regions and our goal is a DM layout design that results in a successful filling without voids for all possible race-tracking scenarios. Thus, the approach adopted is to first investigate all possible RT scenarios and implement the DFS algorithm to find a DM layout solution for the worst filling RT scenario defined by largest unfilled region. Then, this updated DM layout solution is used for the remaining cases of the RT scenarios and new worst filling RT scenario is identified. If this new worst filling satisfies the acceptable tolerance, the algorithm stops. If not, the DM layout is updated (superimposing on the DM layout from the previous iteration). This procedure is repeated until the layout satisfies the filling of the mold within an acceptable tolerance for all permutations of RT cases with the DFS algorithm. This methodology is explained in more details in the next sub-section with an example problem Pedagogical Example In Figure 5.3, a pedagogical example is presented to explain the methodology. For specified inlet and vent locations, three different race-tracking options are identified, the permutations of which could result in 2 3 =8 different race-tracking scenarios (Figure 5.3.(a)). In the first step, all possible eight scenarios are simulated without the use of DM with LIMS and the worst case of filling is identified by the maximum percentage of unfilled region (dry spots or voids) by halting the simulation 93

111 when the resin arrives at the selected vent. Unfilled region is calculated from the percentage of number of empty nodes to total number of nodes. For this example Case 8 resulted in largest unfilled region (14.1%- worst case), as shown in Figure 5.3.(a). The methodology suggests finding the DM layout for the worst case Case 8 first. DM layout solution is found by dividing the domain into six areas and conducting six separate simulations with DM placed in each of the six regions on top of the preform successively and the percentage of unfilled region is recorded for each placement as shown in Figure 5.3.(b). As seen from Figure 5.3.(b), by placing the DM on the bottom right corner provides the best filling option (0.1% void) out of the six configurations and this DM configuration will result in successful mold filling. Mold filling is considered to be successful even when the dry region is typically below a tolerance limit usually about 1 to 2%. This is because even after the resin reaches the vent if one allows the resin to bleed for a short time before closing the vent it may reduce the dry region to less than 1% and in some cases if the void is close to the vent, it will be flushed out with the resin. Next, this DM layout that provides successful fill for Case 8 is applied to the remaining seven scenarios and it is found that the Case 1 which has no race tracking along any edge has one of the largest unfilled region (11.5%) as shown in Figure 5.3.(c) and is the worst case out of the remaining seven. In order to find a successful filling solution for Case 1, the DM design from the previous solution is retained and the approach to conduct six simulations with an additional DM patch placed in each of the six areas successively is repeated and the resulting unfilled area percentages are recorded. It should be noted that the 5 th configuration represents placement of 2 layers of DM on the bottom right corner. The best filling solution for the Case 1 results in 7.3% voids, which is greater than the 94

112 tolerance (Figure 5.3.(d)). Therefore, the successive placement of DM in the six regions is repeated for Case 1 while retaining both the DM patches placed in the earlier trials (Figure 5.3.(e)). This trial results in zero voids and successful filling for the case in which the DM is placed in the middle of the top half while maintain the two DM layers from the previous trials as shown in Figure 5.3.(e). Finally, the updated design, which resulted in no voids for Case1, is used to perform mold filling simulation for the remaining seven cases and the results are shown in Figure 5.3.(f), which shows that the worst case scenario is Case 8 with void region of 0.5% which is within the tolerance limit. Thus, this represents the final DM layout design which will provide successful resin impregnations for all 8 scenarios possibly expected during manufacturing with the specified locations for the gate and vent. For this example and for this gate and vent location we were successful in finding the DM layout, which worked for all 8 cases. However, if this was not the case, one would continue with this algorithm of adding a region and testing the cases until all six regions were covered with DM. After covering all the regions if still one could not find a solution, then the number of regions is increased from six to eight (or ten or twelve) and the algorithm is repeated. If the gate and vent location are changed, one would expect the DM design to change as well. 95

113 RT cases (a) Case1 Case2 Case3 Case4 4.9% void 1.9% void 0.2% void 4.9% void Case5 Case6 Case7 Case8 inlet Case8 Worst case vent Generate 6 regions no void 1.9% void %2.3 void 14.1% void (b) Worst case % void 16.9% void 5.2% void 9.7% void 0.1% void 9.5% void Best filling Tolerance Tolerance (c) 6 5 Case1 Case2 Case3 Case4 2 3 RT cases % void 7.5% void 5.3% void 11.5% void Worst case Case5 Case6 Case7 Case8 Case1 Worst case no void 7.5% void 4.4% void 0.1% void (d) % void 8.3% void 28.0% void 9.1% void 10.2% void 7.3% void Best filling Tolerance Tolerance (e) Case void % 3.9% void 24.0% void no void 6.9% void 7.5% void Best filling Tolerance Tolerance (f) Case1 Case2 Case3 Case4 2 3 RT cases no void no void no void no void Case5 Case6 Case7 Case8 no void %0.2 void no void %0.5 void Figure 5.3. Example to explain the methodology to determine the optimal DM design using the DFS discretization method 96

114 5.3.3 Algorithm for Optimum DM lay-out In the previous section, the methodology uses six regions to seek the optimal solution. However, one may not converge to a solution with the given regions. Thus, the adapted algorithm is developed not only to find an optimized DM layout for all possible RT scenarios for a given region but also to be able to update the number of the regions, if necessary. In Figure 5.4, the flowchart of the algorithm is presented. First, the domain is divided into 2n regions and solution is sought as explained in the pedagogical example. At the end of the Discrete Optimization (DO) routine the filling of the best case is selected and if that filling still has higher percentage of voids than the prescribed tolerance limit; the number of DM regions is increased by 1 and DO is repeated until the voids percentage is within the tolerance limit. If the number of DM regions (m) is equal to the regions of the domain (2n) and still the voids percentage is more than the tolerance limit, then the number of regions in increased by a factor of 2 and the entire cycle is repeated as shown in Figure

115 Figure 5.4. Flow chart of the algorithm to obtain optimal DM Partition method The presented methodology optimizes DM layout on a discrete domain. The discrete domain is generated by dividing the domain, the top surface of the preform where the DM is to be placed, into finite number of regions. This is accomplished by Matlab built in k-means++ algorithm [156]. The k-means clustering is a partitioning 98

116 method. The coordinates of the domain forms the data set and clustering divides the data into k clusters and indexes the cluster. The objective is to have the points in the same cluster being as close as possible to each other and as far as possible from points in other clusters. It is an iterative method that minimizes the sum of the distances from each object to its cluster centroid. Figure 5.5 presents an example region for the given domain. 2 regions 4 regions 6 regions 8 regions Figure 5.5. Division of the domain with the built in k-means script in Matlab 5.4 Experimentation After the optimum DM layout is obtained via the proposed algorithm, one can experimentally test the design. In order to visualize the movement of the flow front through the fibrous medium with time and observe the filling of the preform, the same test set up in Figure 2.2 except the additional camera system that monitors the bottom layer is used. After the preform along with a steel insert is placed on the acrylic table, it is sealed with a vacuum bag and resin at atmospheric pressure is introduced from one end through a line gate while drawing a vacuum at the other end. The resin propagates within the preform due to the pressure gradient of one atmosphere and the flow front movement is captured via the flow visualization camera system along with the time stamp. 99

117 In this experiment due to its Newtonian characteristic, corn syrup with dark cloth dye and water is used as the simulated resin to create a clear contrast between the dark resin front and the white glass fibrous porous media. The experiments are carried out using 8 layers of 50cmx50cm Plain Weave E-glass and distribution media made of polypropylene. The impermeable metal 1mm thick square metal insert (20 cm x 20 cm) is placed in the center of the 4 th layer (Figure 5.6.(a)). After adding the remaining 4 layers of fabric, the DM layer is placed on the top and the preform is sealed and vacuum is applied (Figure 5.6.(b)). Using the set-up, the flow front positions along the top and the bottom are recorded with time stamps. Possible race tracking can occur along the insert edges as the preform may not completely close the gap around the insert. The material properties of the resin, fiber preform and the DM were measured and are listed in Table 5.1 [157]. (a) (b) Figure 5.6. (a) 4th layer of the E-glass with metal insert placed in the center of the fabric, (b) Experiment layup under vacuum 100

118 Table 5.1. Properties of E-glass fabric, DM and corn syrup Parameter: Numerical value: Density of E-glass: 2500 [kg/m 3 ] Fiber volume fraction of E-glass: 50% Permeability of E-glass: Kxx=8.32e-11 [m 2 ] Kyy=5.88e-11 [m 2 ] Kzz=3.49e-12 [m 2 ] Density of DM: 946 [kg/m 3 ] Fiber volume fraction of DM: 15% Permeability of DM: 3.46e-09[m 2 ] Viscosity of corn syrup 100 [cp] 5.5 Results and Discussion Experimental Validation The methodology presented in section 2 was applied to the mold geometry presented in Figure 5.7 to find the DM layout to be placed on top of the preform so no voids are created. The mesh representing the preform domain is shown in Figure 5.7.(a) with the line inlet at the left side and vent on the right side with 4 race-tracking possibilities along the four edges (2 4 = 16 scenarios). Then the algorithm presented in Figure 5.4 is executed for placement of DM. The algorithm was not successful in finding a DM layout which would result in percentage of voids below the prescribed limit with 2 regions, 4 regions and 6 regions (Figure 5.5), respectively, but the algorithm converged to a successful filling solution with 8 regions as shown in Figure 5.7.(b). The algorithms finds the optimal DM layout design given in Figure 5.7.(c) as a C-shape DM layer to be placed on the left side of the preform that provides successful 101

119 filling for all 16 different possible scenarios. To arrive at an optimum layout for this geometry, the algorithm executed LIMS simulations of 16 scenarios four times to arrive at use of 8 regions and then had to execute 5 iterative LIMS simulations for the placement of DM on 8 defined regions. Thus the total number of simulations executed to arrive at the optimal DM layout were 104 (64+40) in 18 minutes on a PC computer with the tolerance of 2% voids (unfilled volume). RT4 RT1 insert RT2 RT3 inlet vent 8 regions 1 layer DM No DM (a) (b) (c) Figure 5.7. DM layout design (a) geometry with inlet/vent locations with 4 race-tracking possibilities along the insert edges creating 2 4 =16 different scenarios (b) 8 regions for placement of distribution media when using discrete optimization, and (c) optimum DM design which resulted in successful filling for all 16 scenarios. Manufacturing using the convectional way by covering nearly the entire preform (95%) with DM (leaving 5% gap at the end so the resin does not short circuit the flow path and reach the vent through the DM which will result in large regions of voids within the part. Figure 5.8 shows the resin flow front patterns along the top and the bottom of the part in 4 of the possible 16 scenarios that can occur due to permutations of race-tracking effects along the edges of the insert. These results are 102

120 contrasted with the tailored DM design which do not result in any voids for all 16 scenarios. Use of DM on 95% of the top layer decreases fill time but as it can be seen from the flow front profiles at the bottom (Figure 5.8.(a)) that large voids do form for this DM layout. Simulations with the optimized DM design clearly show that successful filling without entrapping any voids despite different flow front profiles (Figure 5.8.(b)). Use of tailored DM design also saves DM material as one does not need to cover the entire top of the mold with DM. 103

121 Top view Race-tracking channels Void Void Void Void Bottom view (b) With optimized Distribution Media Void Void Top view Bottom view Figure 5.8. Numerical Solution of flow front profiles of the top and bottom views for 4 different race-tracking scenarios with time steps 10 seconds apart, (a) with 95% of the top layer covered with DM, (b) with optimized DM design 104

122 The design is also tested experimentally to validate it. Figure 5.9 shows the flow front progression at the top and bottom of the preform at time intervals of 20 seconds. The experimental fill time is 221 seconds. The numerical fill times are in the range of 183 seconds to 273 seconds. The experimental flow front profiles show uniform flow front lines as the corn syrup reaches the vent and the filling is complete without voids. However, the profiles do not exactly match with any of the 16 numerical scenarios, though they are close. This can be explained by several factors. First and most importantly, the assigned of the race-tracking strength value for the simulations is not exactly known value but is an estimate. The strength of the racetracking is the ratio of permeability along the race-tracking line to preform permeability in the direction of the race-tracking line. For the simulations this value is kept at a very high value, 1000, so the DM design will work for smaller race-tracking strength values as well. Second, there are additional deviations between numerical model and the experiment, related to inaccurately determined material properties [48,158]. However, the flow pattern is reasonably captured despite these discrepancies and the proposed solution is able to fill the mold for all scenarios even if the times do not exactly match. 105

123 Void Void (a) Top view (b) Bottom view Figure 5.9. Experimental flow fronts with the optimized DM design with flow front locations in red 20 seconds apart. The background image of the experiment at 60 seconds, (a) Top and (b) Bottom Complex Geometries The proposed methodology is tested with a complex geometry with corners and edges. As seen in Figure 5.10, an optimized DM design is presented for a trailer of a truck. For this geometry there are 10 different RT channel possible whose permutations will yield 1024 different scenarios. The algorithm is used with defined inlet and vent locations and DM layout solution is sought that considers all 1024 scenarios and converges to the DM design that provides successful filling for all 1024 cases. For this geometry the convergence is tested with 2, 4, 6, 8, 10, 12 and 14 regions, respectively, and the algorithm convergences to the design given in Figure 5.10 with 14 regions. 106

124 vent inlet inlet vent 10 RT channels Dividing into regions DM No DM DM design algorithm Figure Optimized DM design of trailer geometry with 1024 different possible flow patterns If the entire top surface is covered with the DM, in 886 scenarios out of 1024 the unfilled volume will be more than 1% with the maximum unfilled volume being 20%. If the optimized DM design is used, in all 1024 cases the void fraction is less than 1%, the largest being 0.79%. Figure 5.11 shows void regions for the three representative examples out of 1024 for the case of entire top surface being covered by the DM on the left hand side and with the optimized DM design on the right hand side that is free of voids. Figure 5.12 presents the time contours comparison for fully covered DM situation and the optimized DM design for the same three scenarios. The fill time in the optimized DM case is slightly higher but it is robust enough to provide successful filling despite the variability introduced from possible race-tracking. The lowest and the largest fill time for full DM case was 3710 and 3458 seconds where as for the designed DM case, the fill time was and 8413 respectively from all

125 scenarios. Additionally, Figure 5.13 gives the pressure distribution data at the time when the resin reaches the vent location for full DM and DM layout design. Besides the improvement in the filling the DM design also provides uniform pressure along the preform that yields uniform volume fraction and uniform material properties. void filled Figure Void regions with full DM on top surface on the left hand side with optimized DM design on the right hand side for three representative scenarios from 1024 possible scenarios 108

126 Time (sec) vent location void Figure Time contours with full DM on top surface on the left hand side with optimized DM design on the right hand side for three representative scenarios from 1024 possible scenarios 109

127 Pressure (Pa) Figure Pressure distribution at the instant resin reaches the vent with full DM on the left and with optimized DM design on the right for the three representative scenarios In order to examine the effect of mesh size on the DM design and CPU time four mesh sizes starting with 0.05 m element size and halving it 3 times was investigated. Except for the first coarse mesh, the rest of the meshes converged to the same DM design but the CPU time increased exponentially with finer mesh size with tolerance of 5% unfilled area. For all those 4 cases, the algorithm converged when the domain is divided into 2 regions and 34 ( ) LIMS simulations are performed for each case. However, for the very coarse mesh (mesh size 0.05 m) required tolerance is not satisfied with the C shape DM design as for the other cases and convergence to the DM design is achieved when the domain is divided into 14 regions which make the CPU time needed for the very coarse mesh the largest. Hence it is 110

128 important to ensure that the mesh is fine enough to obtain DM design convergence with fewer numbers of divisions. Figure Change in CPU time with mesh size for optimized DM design 5.6 Summary In this study a methodology is introduced to design an optimum distribution media layout that makes the process robust by successful filling for all possible disturbances caused by different race-tracking scenarios around inserts. Depth First Search, a tree search, algorithm is adopted via discretization of the domain into finite regions to arrive at the DM design. The algorithm is demonstrated with an example and an experimental validation is presented. 111

129 Chapter 6 CONCLUSIONS, CONTRIBUTIONS AND FUTURE WORK 6.1 Conclusions In conclusion, this work has focused on various perspectives of permeability characterizations which will bring the results of flow simulations closer to what is observed in manufacturing practice First, the dissertation study introduces a new methodology to characterize the permeability tensor with non-zero skew terms via a single experiment. The available permeability characterization techniques are discussed. Besides the lack of consistency in most of the techniques, they mainly focus on the characterization of the in-plane permeability components. However, the transverse permeability of the preform gains importance especially for thick 3D fabrics. Additionally, the weaves in the through thickness direction results in non-zero skew terms in the thickness direction. A new methodology is introduced that records the flow fronts on the top and bottom surface of the mold and with image processing uses these flow front profiles with a multi-objective simplex optimization routine to find the six components of the permeability tensor from one experiment. This work enables the understanding of the effect of the non-zero skew components on the flow front progression and flow patterns through a virtual study to underline when the skew terms could change the nature of filling and influence the manufacturing process. Then, the dissertation work investigates the through thickness permeability characterization of uni-directional fabrics. During preparation of the preform using 112

130 uni-directional fabrics, the fabrics are stacked on top of each other which might cause misalignments. Also, design requirements might necessitate different degree of rotation for each unidirectional fabric layer. Under this section of the work the effect of those misalignments and degree of rotation of the layers with respect to each other on the transverse permeability component of the preform is studied. At first a numerical analysis is performed to model the change in the through thickness permeability with fiber orientation using Gambit and Fluent. The numerical model assumes the fiber tows are solid and impermeable and the laminar flow of the resin occurs between the fiber tows. The work is followed by experimental characterization of the permeability tensor using the electrostatic sensor embedded RTM mold plates to record the resin arrival time. Numerical and experimental through thickness permeability comparisons are reported to have good match. This study concludes that the averaging approach to estimate the through thickness permeability of the unidirectional fabrics when adjacent layers are rotated is not valid. The rotation in the layup sequence does influence the transverse permeability. For example two 0 and two 90s (0/0/90/90) will have a different through thickness permeability than 0/90/0/90 layup. A significant change in through thickness permeability is observed for misalignments larger than five degrees of rotation between individual layers. The misalignment of the unidirectional fabrics between individual fabric layers are showed to generate new pathways in through the thickness direction for resin flow and these pathways are correlated with the change in the through thickness permeability. Another factor affecting the dynamics of the resin flow behavior is the nonhomogeneity of the permeability of the fabric. The characterization of the variation of 113

131 the permeability due to local non-homogeneous architecture of the preform lacks standardization. A quantitative way to characterize the permeability variation within the fabric by monitoring the flow front profiles of the resin impregnation with time is introduced. The flow front profiles are processed using Kardar-Parisi-Zhang formulation (KPZ). KPZ formulation requires the evaluation of two parameters; growth exponent and surface roughness by evaluation the variance of the flow front profiles. A major finding is the growth exponent falls into the universality class of KPZ equations and roughness exponent can be used as parameter to quantify the permeability variation in the preform. Moreover, the KPZ model is utilized to determine the percentage of local defects in the preform, which can be a tool to characterize the quality of the preform. Finally, a methodology to optimize the distribution media layout is presented. The optimized design for successful filling of the dry preform should not only work for a single manufacturing scenario, it should also ensures successful filling for all possible manufacturing scenarios caused by different disturbances within the domain due to race-tracking. The algorithm adapts the Depth First Search, a tree search algorithm, with domain discretization. The introduction of the methodology is followed by experimental validation and application of the approach for a complex part which should prove useful in manufacturing of large complex parts containing inserts in VARTM. This methodology saves DM material and also provides more uniform pressure reducing thickness variations in the part. 6.2 Contributions of this work Some of the unique contributions of this work are summarized below. 114

132 First, the characterization of the permeability tensor with non-zero skew terms with a single experiment is achieved. This approach enables the characterization of the six components with a single radial injection experiment. The data reduction part involves image processing to convert the set of flow front images with time stamps into the fill time for predefined mesh geometry. Another improvement with this study is the quick convergence to the optimized permeability tensor because of the optimization algorithm adopted coupled with seamless interaction between LIMS and Matlab. Second, the through thickness permeability of the unidirectional fabric is investigated. The original contribution related to this work is the invalidation of the averaging approach to determine the permeability in the through thickness direction for plies rotated with respect to each other. Due to new pathways it has been showed that the through thickness permeability tends to increase exponentially as the relation rotation angle increases. Third, the characterization of the variation of permeability within the preform is studied for the first time. Using the growth exponent, the universality of the Kardar- Parisi-Zhang formulation is validated for the resin flow thorough porous media. Moreover, the roughness exponent is found to indicate the randomness of the permeability value in the preform. Then, the formulation is utilized to develop a correlation between growth and roughness exponents, and percentage of defects and strength of the defects. This correlation suggests that for the growth exponent and roughness exponent obtained from a single linear injection experiment for a fabric can be used to characterize the randomness, namely quality, of the fabric. 115

133 Finally, with the methodology introduced to generate and optimize the permeability map using distribution media of the preform for successful filling of the preform is the first attempt to obtain a solution that is valid for all possible disturbances and variations unlike previous studies. Also, the adaptation of the Depth First Search algorithm is a novel idea to enhance the computational efficiency and find optimal and automated solutions for optimum permeability map generation along with location of inlets and vents for a specified geometry with variations in the permeability characterized. 6.3 Future Work Following the current dissertation study, the new permeability tensor characterization can be improved with more experimental validation with various 3D fabrics. The convergence of the methodology is compared with virtual experimentation, but one can use the other permeability measurement techniques to compare the permeability data. Also, the adapted simplex algorithm is a direct search method, which doesn t require the gradient calculation but this slows down the convergence. The algorithm can be compared with other approaches, such as neural network training, in terms of convergence performance and speed. In order to improve the through thickness permeability study, the experimentation can be performed on unidirectional fabrics with different tow size, areal weight, material and/or fiber volume fractions. The numerical solution as a validation tool can be also tested not only with circular tows but also at different aspect ratios. The stitching can also be added as a parameter and its effect can be investigated. In the numerical part the tows are modeled as solid walls with no permeability. This assumption can be modified using multi-scale models or 116

134 homogenization to encounter the tow permeability. Furthermore, the numerical approaches introduced for characterization of the permeability tensor with single experiment and for the through thickness permeability can be adopted to different material characterizations, such as thermal conductivity. The characterization of the randomness work is the first attempt to quantify the permeability variation in the preform using a mathematical model. The work on randomness characterization proved that the growth exponent values for the flow through porous media falls in the universality class of the KPZ formulation and it is shown that the surface roughness can be used as a parameter to characterize the randomness. This study can be further improved by the extension of the numerical and the experimental work with wider variety in the dimensions and the standard deviations of the preform domain. Additionally, the KPZ formulation is adapted for the crystal structure radial domain. Thus, an investigation of the radial flow using the same methods would be useful. Also, similar study can be used to investigate the variation of the thermal conductivity. The optimization of the LCM filling process is achieved using optimized distribution media layout, which is experimentally validated for a single preform with a metal insert and tested numerically for complex parts. This validation can be extended with more experimental and numerical samples. The adapted algorithm converges to a local minimum, so the uniqueness of the methodology can be tested. The numerical solution with a complex geometry yields a more uniform pressure distribution along the preform. This finding can be experimentally validated. Finally, this methodology can be implemented for different problems, such as robot motion planning and factory layout. 117

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149 MATLAB SCRIPTS FOR DISTRIBUTION MEDIA OPTIMIZATION 132

150 A.1 Generation of the regions: regioning.m % generates the region#.txt files: % needs the nodes, elements, p (2p number of regions) function zones = regioning (nodes, elements, p) x_cord = nodes(:,2); %x coordinates y_cord = nodes(:,3); %y coordinates N = elements(:,3:6); %element connectivity % x_elem, y_elem x and y coordinates from element connectivity x_elem = [x_cord(n(:,1)) x_cord(n(:,2)) x_cord(n(:,3)) x_cord(n(:,4))]; x_elem = mean(x_elem,2); % x-cord center of the element y_elem = [y_cord(n(:,1)) y_cord(n(:,2)) y_cord(n(:,3)) y_cord(n(:,4))]; y_elem = mean(y_elem,2); % y-cord center of the element % generate regions zones = p*2; %number of zones X = [x_elem y_elem]; [IDX] = kmeans(x, zones); regions = [IDX elements(:,1)]; for i = 1:zones reg = regions(regions(:,1)==i,2); fname = sprintf('region%d.txt',i); fid = fopen(fname,'wt'); fprintf(fid, '%d\n',reg); end fclose all; % plot the regions Y = [IDX x_elem y_elem]; figure hold on for i = 1:zones sub_y = Y(Y(:,1)==i,:); plot(sub_y(:,2),sub_y(:,3),'o','color',rand(1,3),'marker',... '.','MarkerSize',20) end end % Regioning ends A.2 Scissors.m: Main m-file % Hatice Sinem Sas % Main % ROCK.m : Runs all possible race-tracking possibilities and return the % worst case % PAPER.m: finds DM desing working for the worstcase tic % define variables load('nodes.mat'); % node matrix 133

151 load('elements.mat'); % elements matrix - doesn't have DM on it. load('rts.mat'); % RTs matrix-includes all possible racetrackings - from allrts.dmp load('channel.mat'); % to place 1D elements to the inlet and/orvent location. remove for node vent cases n = length(nodes); % number of nodes m2d = length(elements); % number of 2D elements mchannel = length(channel); % ATTENTION m1d = length(rts); opt = max(rts(:,1)); Kxx = 8.32e-11; Kyy = 8.32e-11; h_preform = 5e-3; %thickness of the preform vf = ; %fiber volume fraction of the preform elements(:,9) = Kxx; elements(:,11) = Kyy; elements(:,7) = h_preform; elements(:,8) = vf; elementsmain = elements; KDM = 3.5e-9; % DM permeability h_dm = 1e-3; % thickness of 1-layer DM vfdm = ; % fiber volume fraction of KRT = Kxx.*1000; % ractraking permeability AreaRT = h_preform.*sqrt(12*krt); vfrt = ; % vol. fraction for 1D elements KDM1 = (h_preform*kxx+h_dm*kdm)/(h_preform+h_dm); KDM2 = (h_preform*kxx+2*h_dm*kdm)/(h_preform+2*h_dm); vfdm1 = (h_preform*vf+h_dm*vfdm)/(h_preform+h_dm); vfdm2 = (h_preform*vf+2*h_dm*vfdm)/(h_preform+2*h_dm); %% Generate the possibility matrix C = cell(opt,1); [C{:}] = ndgrid([true, false]); %// Generate N grids of binary values p = cellfun(@(x){x(:)}, C); %// Convert grids to column vectors p = [p{:}]; putrt = cell(2^opt,opt); for j = 1: 2^opt for i = 1:opt putrt{j,i} = RTs(RTs(:,1) == i,:); RTput{j,i} = putrt{j,i}.* p(j,i); end end pause(0.5); for i = 1 : 2^opt RTcase(:,:,i) = cell2mat(rtput(i,:)'); end pause(0.5); 134

152 %% empty_percentall = 100; %initial assignment r = 0; % first run, counts the RUN l = 0; % first loop, counts the LOOP % % generates the region#.txt files: p =1; zones = regioning(nodes, elements, p); % Regioning ends % while empty_percentall>= 5.01 r = r+1; % function call to [index, NEN] = ROCK(r, elements, channel, nodes, m2d, mchannel,rtcase, n, opt,areart, vfrt, KRT); worstcase = index(1); empty_percentall = NEN(worstcase,1)/n*100; % send the element and RT data to the PAPER.m fname = sprintf('run_%d_case_%d.dmp',r,worstcase); dummy = importdata(fname, ' ', n+7); elementdm = dummy.data(1:m2d,:); RTDM = dummy.data(m2d+mchannel+1:end,1:7); empty_percent = empty_percentall; while (empty_percent >= 5.00) l = l+1; % index for the next loop if l > zones p = p+1; l = 1; elements = elementsmain; zones = regioning(nodes, elements, p); r =1; [index, NEN] = ROCK(r, elements, channel, nodes, p, RTs, m2d, mchannel,rtcase, n, opt,areart, vfrt, KRT); worstcase = index(1); empty_percentall = NEN(worstcase,1)/n*100; % % send the element and RT data to the PAPER.m fname = sprintf('run_%d_case_%d.dmp',r,worstcase); dummy = importdata(fname, ' ', n+7); elementdm = dummy.data(1:m2d,:); RTDM = dummy.data(m2d+mchannel+1:end,1:7); empty_percent = empty_percentall; end [indexdm, NENDM] = PAPER( l, worstcase, elementdm, channel, nodes, RTDM, m2d, mchannel, n, zones); % [ indexdm, NENDM ] = PAPER( l, worstcase, elementdm, nodes, RTDM, m2d, n, zones); empty_percent = NENDM(indexDM,1)/n*100; %update elementzdm fname = sprintf('loop_%d_%d_%d.dmp',l,worstcase,indexdm); dummy = importdata(fname, ' ', n+7); elementdm = dummy.data(1:m2d,:); 135

153 DM_design = zeros(zones*2,1); DM_design(l) = indexdm; end elements = elementdm; end toc %prints the CPU time %% A.3 Rock.m: Evaluation of all race-tracking possibilities % Hatice Sinem Sas, Feb % Generate the.dmp files of all possible race-trackings function [index, NEN] = ROCK(r, elements, channel, nodes, m2d, mchannel, RTcase, n, opt, AreaRT, vfrt, KRT) % Generate the.dmp files for drum = 1:2^opt % loop to write all the.dmp files fname = sprintf('run_%d_case_%d',r,drum); filename = sprintf('%s.dmp',fname); o = fopen(filename, 'w'); fprintf(o,'# \r\n'); fprintf(o,'number of nodes : %5.0f \r\n',n); fprintf(o,' Index x y z\r\n'); fprintf(o,'===================================================\r\n'); for i = 1: n % loop to write node data fprintf(o,'%6.0f %12.6f %12.6f %12.6f \r\n',nodes(i,:)); end % loop to write DM data (if any) RTmatrix = RTcase(:,:,drum); RTmatrix(RTmatrix(:,1)==0,:)=[]; m1d = length(rtmatrix); % number of race-tracking elements : fprintf(o,'number of elements : %5.0f \r\n',m2d+mchannel+m1d); fprintf(o,' Index NNOD N1 N2 (N3) (N4) (N5) (N6) (N7) (N8) h(a) Vf Kxx Kxy Kyy Kzz Kzx Kyz\r\n'); fprintf(o,'========================================================== ===================================================================== ===============================================\r\n'); for i = 1: m2d % loop to write 2D elements data fprintf(o,'%6.0f %4.0f %6.0f %6.0f %6.0f %6.0f %32.6f %15.6f %15.4e %15.4e %15.4e \r\n',elements(i,:)); end for i = 1:mchannel %loop to generate 1D elements for inlet and/or vent fprintf(o,'%6.0f %4.0f %6.0f %6.0f %32.6e %15.6f %15.4e \r\n',channel(i,:)); 136

154 end if m1d ~=0 RTmatrix(RTmatrix(:,1)==0,:)=[]; m1d = length(rtmatrix); % number of race-tracking elements : RTelements = zeros(m1d,7); RTelements(:,1) = [1:m1d]+m2d+mchannel; RTelements(:,2) = 2; RTelements(:,3) = RTmatrix(:,2); % node 1 for 1D element connectivity RTelements(:,4) = RTmatrix(:,3); %node 2 for 1D element connectivity RTelements(:,5) = AreaRT; RTelements(:,6) = vfrt; RTelements(:,7) = KRT; for i = 1:m1d fprintf(o,'%6.0f %4.0f %6.0f %6.0f %32.6e %15.6f %15.4e \r\n',rtelements(i,:)); end end fprintf(o,'resin Viscosity model NEWTON\r\n'); fprintf(o,'viscosity : fclose(o); fclose all; 0.1\r\n'); end % Generate lb file Pin = e+005; %inlet pressure value for j = 1:2^opt fname = sprintf('run_%d_simulate_%d.lb',r,j); fid2 = fopen(fname,'w+'); fprintf(fid2,'proc simu\r\n'); fprintf(fid2,'do\r\n'); fprintf(fid2,'solve\r\n'); fprintf(fid2,'exitif SOFILLFACTOR(1436) > 0.9\r\n'); fprintf(fid2,'loop WHILE ((SONUMBEREMPTY() > 0) AND (SONUMBERFILLED() > 0))\r\n'); fprintf(fid2,'endproc\r\n'); fprintf(fid2,'\r\n'); fprintf(fid2,'read "run_%d_case_%d.dmp"\r\n',r, j); for i = 1:41 % inlet node numbers fprintf(fid2,'setgate %d, 1, %d \r\n',i, Pin); end fprintf(fid2,'\r\n'); fprintf(fid2,'call simu\r\n'); fprintf(fid2,'\r\n'); fprintf(fid2,'print "%d # empty nodes =", sonumberempty\r\n', j); fprintf(fid2,'\r\n'); fprintf(fid2,'setouttype "tplt"\r\n'); %fprintf(fid2,'setouttype "dump"\r\n'); fprintf(fid2,'write "run_%d_case_res_%d.tec"\r\n',r, j); %fprintf(fid2,'write "case_res_%d.dmp"\r\n', j); fclose all; 137

155 end % Run the lb files NEN = zeros(2^opt,2); % number of empty nodes for j= 1: 2^opt fname = sprintf('run_%d_simulate_%d.lb',r,j); filename = sprintf('load run_%d_simulate_%d.lb',r,j); lims(3,6,2000); % set time-out to 2000 ms lims(3,3,50); lims(1,1); lims(5,1,'setoutputlevel 2'); lims(5,1,'setmessagelevel 0'); lims(5,1,filename); lims(5,1,fname); output = 'ini'; pause(0.5); while ~isempty(output) output = lims(4,1,350); end lims(5,1,'print sonumberempty'); pause(5.0) lims(2,1) pause(5.0) filename2 = sprintf('run_%d_case_res_%d.tec',r,j); result = importdata(filename2, ' ', 3); emptynodes = result.data(1:n,6); % fill factors of the nodes NEN(j,1) = numel(emptynodes(emptynodes<0.9)); %number of empty nodes filltime = result.data(1:n,5); % fill times of the nodes NEN(j,2) = max(filltime); fclose all; end % Worst case index = find(nen(:,1) == max(nen(:,1))); %index array can have more than one elememts index = index(1); % index of one of the worst case f2name = sprintf('run_all_%d.mat',r); %stores all data save(f2name) fclose all; end A.4 Paper.m: Finding the optimum region to place DM function [ indexdm, NENDM ] = PAPER(l, worstcase, elementdm, channel, nodes, RTDM, m2d, mchannel,n, zones) if ~isempty(rtdm) m = RTDM(end,1); else m = length(elementdm)+mchannel; end 138

156 m1d = length(rtdm); Kxx = 8.32e-11; Kyy = 8.32e-11; KDM = 3.5e-9; vf = ; vfdm = ; h_preform = 5e-3; h_dm = 1e-3; KRT = Kxx.*1000; % ractraking permeability AreaRT = h_preform.*sqrt(12*krt); KDM1 = (h_preform*kxx+h_dm*kdm)/(h_preform+h_dm); KDM2 = (h_preform*kxx+2*h_dm*kdm)/(h_preform+2*h_dm); vfdm1 = (h_preform*vf+h_dm*vfdm)/(h_preform+h_dm); vfdm2 = (h_preform*vf+2*h_dm*vfdm)/(h_preform+2*h_dm); elements = elementdm; for drum = 1:zones % loop to write all the.dmp files fname2 = sprintf('region%d.txt',drum); data = importdata(fname2); data = data(:); data = data(~isnan(data)); data = sort(data); fname = sprintf('loop_%d_%d_%d',l,worstcase,drum); filename = sprintf('%s.dmp',fname); o = fopen(filename, 'w'); fprintf(o,'# \r\n'); fprintf(o,'number of nodes : %5.0f \r\n',n); fprintf(o,' Index x y z\r\n'); fprintf(o,'===================================================\r\n'); for i = 1: n % loop to write node data fprintf(o,'%6.0f %12.6f %12.6f %12.6f \r\n',nodes(i,:)); end if elementdm(data(1), 9) == KDM1 elementdm(data, 7 ) = (h_preform+2*h_dm); elementdm(data, 8 ) = vfdm1; elementdm(data, 9 ) = KDM2; elementdm(data, 11 ) = KDM2; else elementdm(data, 7 ) = (h_preform+h_dm); elementdm(data, 8 ) = vfdm2; elementdm(data, 9 ) = KDM1; elementdm(data, 11 ) = KDM1; end fprintf(o,'number of elements : %5.0f \r\n',m); fprintf(o,' Index NNOD N1 N2 (N3) (N4) (N5) (N6) (N7) (N8) h(a) Vf Kxx Kxy Kyy Kzz Kzx Kyz\r\n'); fprintf(o,'========================================================== 139

157 ===================================================================== ===============================================\r\n'); for i = 1: m2d % loop[ to write 2D elements data fprintf(o,'%6.0f %4.0f %6.0f %6.0f %6.0f %6.0f %32.6f %15.6f %15.4e %15.4e %15.4e\r\n',elementDM(i,:)); end for i = 1:mchannel fprintf(o,'%6.0f %4.0f %6.0f %6.0f %32.6e %15.6f %15.4e \r\n',channel(i,:)); end if ~isempty(rtdm) for i = 1:m1d fprintf(o,'%6.0f %4.0f %6.0f %6.0f %32.6e %15.6f %15.4e \r\n',rtdm(i,:)); end end fprintf(o,'resin Viscosity model NEWTON\r\n'); fprintf(o,'viscosity : 0.1\r\n'); elementdm = elements; end fclose(o); fclose all; % Generate lb file Pin = e+005; for j = 1:zones fname = sprintf('loop_%d_simulate_%d.lb',l,j); filename = sprintf('load loopd_%d_simulate_%d.lb',l,j); fid2 = fopen(fname,'w+'); fprintf(fid2,'proc simu\r\n'); fprintf(fid2,'do\r\n'); fprintf(fid2,'solve\r\n'); fprintf(fid2,'exitif SOFILLFACTOR(1436) > 0.9\r\n'); fprintf(fid2,'loop WHILE ((SONUMBEREMPTY() > 0) AND (SONUMBERFILLED() > 0))\r\n'); fprintf(fid2,'endproc\r\n'); fprintf(fid2,'\r\n'); fprintf(fid2,'read "loop_%d_%d_%d.dmp"\r\n', l, worstcase,j); for i=1:41 fprintf(fid2,'setgate %d, 1, %d \r\n',i, Pin); end fprintf(fid2,'\r\n'); fprintf(fid2,'call simu\r\n'); fprintf(fid2,'\r\n'); fprintf(fid2,'print "%d # empty nodes =", sonumberempty\r\n', j); fprintf(fid2,'\r\n'); fprintf(fid2,'setouttype "tplt"\r\n'); %fprintf(fid2,'setouttype "dump"\r\n'); fprintf(fid2,'write "loop_%d_%d_%d_res.tec"\r\n', l,worstcase,j); %fprintf(fid2,'write "case_res_%d.dmp"\r\n', j); fclose all; end 140

158 fclose all; NENDM = zeros(zones,2); for j= 1:zones fname = sprintf('loop_%d_simulate_%d.lb',l,j); filename = sprintf('load loop_%d_simulate_%d.lb',l,j); lims(3,6,2000); % set time-out to 2000 ms lims(3,3,50); lims(1,1); lims(5,1,'setoutputlevel 2'); lims(5,1,'setmessagelevel 0'); lims(5,1,filename); lims(5,1,fname); output = 'ini'; while ~isempty(output) output = lims(4,1,350); end lims(5,1,'print sonumberempty'); pause (2.0); lims(2,1) pause(2.0); filename2 = sprintf('loop_%d_%d_%d_res.tec',l,worstcase,j); result = importdata(filename2, ' ', 3); emptynodes = result.data(1:n,6); NENDM(j,1) = numel(emptynodes(emptynodes<0.9)); filltime = result.data(1:n,5); NENDM(j,2) = max(filltime); fclose all; end %Worst case indexdm = find(nendm(:,1) == min(nendm(:,1))); %index array can have more than one elememts indexdm = indexdm(1); % index of one of the worst case f2name = sprintf('all_loop_%d.mat',l); save(f2name) end 141

159 REPRINT PERMISSION LETTERS 142

160 B.1 EFFECT OF RELATIVE PLY ORIENTATION ON THE THROUGH- THICKNESS PERMEABILITY OF UNIDIRECTIONAL FABRICS 143

161 144

162 145

163 146

164 147

165 148