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Effect of geometrical and process parameters on the quality of open moulded composite parts with sharp… Torres, Juan David 2015

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EFFECT OF GEOMETRICAL AND PROCESS PARAMETERS ON THE QUALITY OF OPEN MOULDED COMPOSITE PARTS WITH SHARP CORNERS:  A DECISION-BASED APPROACH  by  Juan David Torres   B.A. Sc., La Universidad del Zulia, 2008  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE  in  THE COLLEGE OF GRADUATE STUDIES  (Mechanical Engineering)   THE UNIVERSITY OF BRITISH COLUMBIA   (Okanagan)  May 2015   © Juan David Torres, 2015  ii Abstract  The use of autoclaves and ovens in modern composite manufacturing processes has shown a potential to greatly control the geometry and structural properties of composite materials. The use of such manufacturing tools has been supported by numerical tools and optimization/statistical methods, in order to further improve the quality of composite products. However, the costs associated with these advanced manufacturing techniques are not always acceptable for all Fiber Reinforced Composite (FRC) manufacturers. In particular, for large products with low production rates (e.g., marine and automotive industries), open moulding are preferred as they typically offer the best compromise between the quality of the part and manufacturing production cost. The quality of open-moulded parts, however, is highly dependent on the skill of the operator, hence resulting in possible variations in part properties, particularly for geometrically complex parts. This variation often causes out-of-specification products, resulting in costly trial and error approaches to minimize the product defects. The purpose of this thesis was to study the FRC process conditions that have a statistically significant effect on the generation of defects in open-moulded parts with sharp corner (i.e., small radius) features. Samples with different geometrical, material and process parameters were manufactured. Defects such as void content, corner fiber bridging, fabric formability, fiber misalignment and bending resistance of the material were evaluated through different characterization techniques. The statistical analysis of the data has provided new means to determine the contribution of each parameter to the final quality of the composite part. The results suggest that the part radius and part thickness both have  iii significant effects on the bending resistance of the FRC specimens. Also, it was observed that reinforcement orientation has a significant effect on the formability and surface defects around the part corners.   Finally, a novel Multiple Criteria Decision Making (MCDM) approach has been developed using “signal to noise” ratios with subjective and objective weighting, in order to identify the optimum design parameters for both aesthetic and structural properties of the open moulded FRC parts with sharp corners.    iv Preface  Portions of this thesis have been published as a part of the Society for the Advancement of Materials and Process Engineering (SAMPE) 2014 Conference in Seattle, WA as: J. Torres, B. Crawford, F. Islam, L. Bichler, A.S. Milani (2014) The Effect of Design Parameters on the Quality of Open  Moulded Fiber Reinforced Composites with Sharp Corners. SAMPE Tech Conference and Exhibition. Seattle, WA. Two journal articles are also under submission from parts of  Chapter 4.   v Table of Contents  Abstract ..................................................................................................................................... ii Preface...................................................................................................................................... iv Table of Contents ...................................................................................................................... v List of Tables ......................................................................................................................... viii List of Figures ........................................................................................................................... x Acknowledgements ................................................................................................................ xiii Dedication .............................................................................................................................. xiv Chapter 1: Introduction ....................................................................................................... 1  Thesis Objectives ...................................................................................................... 3 1.1Chapter 2: Literature Review.............................................................................................. 5  Composite Materials ................................................................................................. 5 2.12.1.1 Thermoset Matrix Composites .............................................................................. 6 2.1.1.1 Unsaturated Polyester Resins ........................................................................ 7 2.1.1.1.1 Effects of Processing Parameters on the Curing of UP Resins ................ 8 2.1.2 Manufacturing Methods for Composites ............................................................ 11 2.1.3 Open Moulding Techniques ................................................................................ 13 2.1.3.1 Wet Lay-up ................................................................................................. 13 2.1.3.1.1 Advantages of Wet Lay-up ..................................................................... 14 2.1.3.1.2 Disadvantages of Wet lay-up ................................................................. 14 2.1.4 Mechanical Properties of Angled Composites .................................................... 15 2.1.5 Defects Affecting Quality of Composites ........................................................... 21 2.1.5.1 Void Content ............................................................................................... 21 2.1.5.2 Defects on Angled Laminates ..................................................................... 24 2.1.6 Flexural Rigidity of Fibers .................................................................................. 24  MCDM Methods ..................................................................................................... 25 2.22.2.1 TOPSIS ............................................................................................................... 26 2.2.1.1 Weighting Method ...................................................................................... 28 2.2.2 Signal to Noise Ratio (S/N) ................................................................................ 29 Chapter 3: Experimental Methods and MCDM Procedure .............................................. 31  vi  Manufacturing of Test Coupons ............................................................................. 31 3.1 Experiment #1: Evaluation of Geometrical Parameters.......................................... 32 3.23.2.1 Quality Evaluation .............................................................................................. 33 3.2.1.1 Void Content Test ....................................................................................... 33 3.2.1.2 Curved Beam Strength (CBS) ..................................................................... 34 3.2.1.2.1 Digital Image Correlation for the CBS Test ........................................... 37 3.2.1.2.2 Finite Element Model (FEM) for the CBS Test ..................................... 39 3.2.1.3 Fiber Misalignment ..................................................................................... 41 3.2.1.4 Thickness Uniformity ................................................................................. 41 3.2.1.5 External Surface Defects............................................................................. 42 3.2.1.6 External Formability of Reinforcement ...................................................... 43 3.2.2 Multiple Criteria Decision Making (MCDM) Procedure ................................... 44  Experiment #2: Effective Flexural Rigidity Evaluation ......................................... 50 3.3 Experiment #3: Process Conditions Evaluation ...................................................... 51 3.4Chapter 4: Results and Discussion ................................................................................... 53  Experiment #1 Results: Influence of Geometrical Parameters ............................... 53 4.14.1.1 DIC for the CBS Test .......................................................................................... 53 4.1.2 Non-linear Response Evaluation via FEM ......................................................... 57 4.1.3 Sensitivity Analysis Results ................................................................................ 60 4.1.3.1 CBS Tests.................................................................................................... 60 4.1.3.2 Void Content ............................................................................................... 64 4.1.3.3 Fiber Misalignment ..................................................................................... 66 4.1.3.4 Thickness Uniformity ................................................................................. 68 4.1.3.5 Corner Bridging .......................................................................................... 70 4.1.3.6 External Formability of Reinforcement ...................................................... 74 4.1.3.7 External Surface Defects............................................................................. 76 4.1.3.8 Summary of Geometrical Parameters Effects ............................................. 77 4.1.4 MCDM Results and Discussions ........................................................................ 81 4.1.4.1 Structural Scenario Ranking ....................................................................... 84 4.1.4.2 Aesthetic Scenario Ranking ........................................................................ 85  Experiment #2 Results: Influence of Flexural Rigidity .......................................... 85 4.2 vii  Experiment #3 Results: Influence of the Cure ........................................................ 88 4.3Chapter 5: Conclusions and Future Work ............................................................................... 90  Conclusions ............................................................................................................. 90 5.1 Future Work ............................................................................................................ 93 5.2Bibliography ........................................................................................................................... 94 Appendices .............................................................................................................................. 99 Appendix A: ANOVA Experimental Results for Samples of Group 2 ............................. 99 Appendix B: DIC Qualitative Evaluations on Experimental Group 3 ............................. 101 Appendix C: Experimental Raw Data .............................................................................. 103   viii List of Tables   Table 3.1  Mechanical properties used for the reference FEM model; properties   extracted from........................................................................................................ 40 Table 3.2  Schematic of MCDM for the experimental methodology ..................................... 45 Table 3.3  Relative importance between criteria based on the MDL method ......................... 47 Table 3.4  Experimental matrix for flexural stiffness evaluation (Experiment #2) ................ 51 Table 3.5  Experimental matrix for Experiment #3 ................................................................ 52 Table 4.1  ANOVA results for the CBS response (α=0.05) ................................................... 61 Table 4.2  ANCOVA results for the CBS response (α=0.05) ................................................. 63 Table 4.3  ANOVA results for the void content response (α=0.05) ....................................... 64 Table 4.4  ANOVA results for the misalignment response (α=0.05) ..................................... 66 Table 4.5  ANOVA results for the thickness uniformity response (α=0.05) .......................... 68 Table 4.6  ANOVA results for the bridging response (α=0.05) ............................................. 70 Table 4.7  ANOVA results for the external formability response (α=0.05) ........................... 74 Table 4.8  ANOVA results for the surface defects response (α=0.05) ................................... 76 Table 4.9  Comparison between DIC results and optical imaging for samples   with 70° angle ........................................................................................................ 78 Table 4.10  Comparison between DIC results and optical imaging for select  samples with 40° angle ......................................................................................... 79 Table 4.11 Trends of the influence of significant design inputs on the quality  metrics; ranking of input variables are given in brackets in each  column; ‘No’ refers to statistical insignificance .................................................. 81 Table 4.12  Images corresponding to the best quality designs under different  quality metric criteria ........................................................................................... 81 Table 4.13  Relative importances between criteria based on the MDL method;  structural scenario ................................................................................................ 82 Table 4.14  Relative importances between criteria based on the MDL method;  aesthetic scenario ................................................................................................. 82 Table 4.15  Pearson's correlation results for criteria pairs; Rjk ............................................... 83   ix Table 4.16  Summary of weighting results under the combinative method  for each design scenario ....................................................................................... 83 Table 4.17  TOPSIS results using four design alternatives for a structural application ......... 84 Table 4.18  TOPSIS results using four design alternatives for an aesthetic application ........ 85 Table 4.19  Flexural rigidity values for the reinforcement material at different  orientations ........................................................................................................... 85 Table 4.20  Comparison for all quality metrics between -45 o/45 o and 0o/90o specimens (green marks indicate a statistically preferred condition) .................................... 86 Table 4.21  ANOVA results for the CBS response as a function of process conditions (α=0.05) ................................................................................................................ 88 Table A.1  ANOVA results for the CBS response (group 2) (α=0.05)................................... 99 Table A.2  ANOVA results for the void content response (group 2) (α=0.05) ...................... 99 Table A.3  ANOVA results for the formability response (group 2) (α=0.05) ........................ 99 Table A.4  ANOVA results for the thickness ratio response (group 2) (α=0.05) ................. 100 Table A.5  ANOVA results for the bridging response (group 2) (α=0.05) .......................... 100 Table A.6  Comparison between DIC results and optical imaging for samples  with 5 layers (group 3) ....................................................................................... 101 Table A.7  Comparison between DIC results and optical imaging for samples  with 3 layers (group 3) ....................................................................................... 102 Table A.8  Raw data for experiment #1 (geometry effect) ................................................... 103 Table A.9  Raw data for experiment #1 (geometry effect) (continued) ................................ 104 Table A.10  Experimental design alternatives for the MCDM (experiment #2) .................. 105 Table A.11  Raw data for experiment #2 (reinforcement orientation effect) ....................... 106 Table A.12  Raw data for experiment #3 (degree of cure effect) ......................................... 107   x List of Figures  Figure 2.1  UP polymerization reaction (Strong, 2008) ............................................................ 7 Figure 2.2  Conversion (cure) profile as a function of time under different temperatures. ...... 9 Figure 2.3  Gel time as a function of temperature for a UP resin under three  different initiator concentrations. ......................................................................... 10 Figure 2.4  Schematic of the change on the storage modulus based on the degree of cure of an UP resin. ......................................................................................... 11 Figure 2.5  Schematic of hand lay-up process ........................................................................ 14 Figure 2.6  Composite diagram indicating transverse direction in flat and curved parts ....... 15 Figure 2.7  Schematic of geometrical parameters used for the radial stress calculation  in a curved composite beam ................................................................................. 16 Figure 2.8  Theoretical radial stress versus different curvature radii  .................................... 19 Figure 2.9  CBS versus: a) Thickness (mm), b) R/t and maximum radial stress versus:  c) Thickness, d) R/t of the composite laminated beams ....................................... 20 Figure 2.10  Void content vs. shear, flexural, and tensile strengths ....................................... 22 Figure 2.11  Visual reference for void content in unidirectional samples .............................. 23 Figure 2.12  Euclidean distances from an ideal positive and negative solutions) .................. 27 Figure 3.1  Schematic of the master mould ............................................................................ 31 Figure 3.2  Sample geometry and input parameters used ....................................................... 32 Figure 3.3  The CBS test fixture used ..................................................................................... 35 Figure 3.4  CBS test geometrical considerations (ASTM D6415, 2007). .............................. 36 Figure 3.5  Typical response for multidirectional composite specimens ................................ 36 Figure 3.6  Fixture and calibration plate for DIC imaging ..................................................... 38 Figure 3.7  Speckle pattern used for DIC measurements on CBS test ................................... 39 Figure 3.8  Schematic of FEM model of CBS 4-point bending test for 40° sample ............... 40 Figure 3.9  Curved part with non-uniform surface geometry, as modified in the model ....... 41 Figure 3.10  Misalignment angle measurement on the curved specimens ............................. 41 Figure 3.11  Measurements of the total (white arrows) thickness on: a ) the corner  (Tc) and b) the flat region (Tf). ........................................................................... 42 Figure 3.12  (a) Top and (b) lateral views of a typical corner surface defect ......................... 43  xi Figure 3.13  (a) Design curvature, and (b) the actual reinforcement curvature at  the outer surface ................................................................................................. 43 Figure 3.14  Reference of ply orientation for a) 0o /90o degrees and b)-45o /+45o degrees .... 50 Figure 3.15  Cantilever bending tester used of the stiffness characterization of the               reinforcement ..................................................................................................... 50 Figure 4.1  Load vs. extension plot with DIC results, indicating: a) stage without failure,  b) first delamination on the upper region, and c) second delamination; specimen with a radius of 1/8”, part angle of 70° and 3 layers. ........................................... 54 Figure 4.2  Load vs. extension plot with DIC results, indicating: (a) stage without   failure, (b) first delamination on the lower region, (c) extension of the  first delamination and (d) second delamination on multiple regions;  specimen with a radius of 5/16”, part angle of 40° and 3 layers. ......................... 55 Figure 4.3  Load vs. extension plot: Three different runs under with variable maximum loads to evaluate repeatability on the curve for evaluation of the elastic  region in a specimen with a radius of 1/4”, part angle of 40° and 3 layers .......... 56 Figure 4.4  Stress distribution of the sample on the y. direction ............................................ 57 Figure 4.5  Force vs. displacement response from the FEM simulation ................................. 58 Figure 4.6  Cross-section of a sample manufactured with manual wet lay-up ....................... 58 Figure 4.7  Comparison of force vs. extension plot between an ideal (plain) inner surface and an internal surface with rough geometry .......................................... 59 Figure 4.8  Comparison of experimental force vs. extension plots for a specimen with a modified (plain) internal surface and the one with the original (rough) inner surface .................................................................................................................. 60 Figure 4.9  Main effect plots of CBS vs. (a) part angle in degrees, (b) corner radii in inch and (c) number of layers .......................................................................... 62 Figure 4.10  Main effect plot of  a) void content vs. corner radius in inch and  b) void content vs. corner angle ......................................................................... 65 Figure 4.11  Main effect plots of misalignment vs. (a) part angle in degrees, and  (b) corner radii in inch ....................................................................................... 66 Figure 4.12  Draping comparison between a) mould with 40° and b) mould  with 70° angle .................................................................................................... 67  xii Figure 4.13  Main effect plots of thickness uniformity vs. (a) part angle in degrees,  (b) corner radii in inch and (c) number of layers ............................................... 69 Figure 4.14  Main effect plots of bridging vs. (a) part angle in degrees,  (b) corner radii in inch and (c) number of layers ............................................... 71 Figure 4.15  Bridging effect plot for AB interaction; bridging values are in [mm] ............... 72 Figure 4.16  Comparison between bridging for (a) sample with 40°, 1/8” (b) sample with  70°, 1/8”  (c) sample with 5/16”, 40° and (d) sample with 5/16”, 70° .............. 73 Figure 4.17  Main effect plots of external formability vs. (a) part angle in degrees,  (b) corner radii in inch ....................................................................................... 74 Figure 4.18  CBS effects plot for the interaction AB ............................................................. 75 Figure 4.19  Main effect plots of surface defects vs. (a) part angle in degrees,  (b) corner radii in inch and (c) number of layers ............................................... 77 Figure 4.20  Effect plots for interaction between angle and layer orientations for  formability metric .............................................................................................. 87 Figure 4.21  Effect plot for interaction between angle, number of layers and  reinforcement orientation for the surface defects metric ................................... 88     xiii Acknowledgements   I would like to express my deepest gratitude to my supervisors, Dr. Abbas Milani and Dr. Lukas Bichler. Thank you for your professional guidance and support during these years.   Also, I would like to thank to the research group of the Composites Laboratory of UBC Okanagan, especially Mr. Bryn Crawford for all his support and kind help on all the activities related to this project. Moreover, I would like to thank Mr. Faisal Islam, Mr. Prabhakar Pal and Mr. Norberto Feito for all their help on the experiments developed during this research.  Last, I would like to recognize the help and support that I have constantly received from my friends and family over the years. Especially from my parents, sisters, cousins and my wife, thanks for being there in all difficult moments to offer the right word, advice and opportunities that let me achieve my goals.            xiv Dedication  To my wife Karol,  Gracias por estar siempre a mi lado y por tu amor incondicional, te amo.                           1 Chapter 1: Introduction  The concept of “composite material” refers to a material that is composed of two or more constituent materials, with properties different from the individual components. One important group of composite materials is fiber reinforced composites (FRCs), which are normally material systems comprised of a polymeric resin and the reinforcing fibers. FRCs have already demonstrated great advantages over traditional materials such as aluminum and steel, including higher specific strength, specific stiffness, and fatigue resistance. However, difficulties on maintaining part quality along with the lack of standard design rules, especially for parts with complex geometrical features such as sharp corners/curvatures, the full implementation of FRCs is still limited in a number of industries (Strong, 2008). The use of autoclaves and ovens in modern FRC manufacturing processes has enhanced the ability for some manufacturers to greatly control complex geometrical features and structural properties of curved composite parts. These manufacturing tools are also often supported by numerical tools and optimization methods to produce more robust products (Liu et al., 2005). However, the production costs associated with advanced manufacturing techniques are not suitable for all FRC manufacturers. Therefore, other cost-effective processes are currently considered in small-to-medium enterprises in the composite sector. In particular, for common engineering composites (e.g., Glass Fiber Reinforced Plastics (GFRPs)) with large product sizes and lower production rates, open moulding techniques offer the best compromise between the part quality and the manufacturing cost (Strong, 2008).  The term ‘quality’ is subjective and highly dependent on the application of the final product. For example, what is classified as a defect in an “advanced” composite may be acceptable for an “engineering” composite (e.g., non-aerospace applications). However, defect formation  2 mechanisms and contributing factors in advanced and engineering composite materials and processes are similar. Regarding open-moulded parts, quality is known to highly depend on the skill of the operator, hence resulting in a wide variation in product outcomes (Mazumdar, 2002). This variation occasionally results in parts with out-of-specification dimensions. Accordingly, optimization of the design and manufacturing process is associated with lengthy and costly trial-and-errors.  Mechanical properties of FRP composites such as shear and flexural strengths are known to be highly sensitive to the void content in composite materials (Liu et al. 2005).  Similarly, the bending resistance of parts is affected by the void content or dimensional distortions (Hubert and Poursartip, 2001). Other factors influencing the mechanical behavior of FRP composites are fiber misalignment and the volume fraction. Both of these factors are more pronounced in curved sections of parts (Hubert and Poursartip, 2001); (Potter et al. 2008); (Potter, 2009). The mechanical stress developed on curved parts under bending is highly dependent on the interlaminar properties (Lekhnitskii, 1968). Several investigations have been carried out exploring the effect of process parameters and geometrical conditions on the development of the aforementioned defects on advanced composite parts (Potter, 2009; Cauberhs and Hubert, 2011; Michel et al. 2013; Wisnom and Jones, 1996). These investigations have defined admissible thresholds variables for the control of defects in composites. However, a very limited portion of these previous works has considered the application of control strategies to statistically reduce the number of defects in open moulded parts.  3  Thesis Objectives 1.1 This thesis attempts to quantify (via statistical approach) the quality of open moulded parts with sharp corners. This knowledge could be used by industrial manufacturers in order to create quality-based guidelines for the design and manufacture of complex parts in open moulded FRP processes. The specific objectives of this thesis are to:  1. Define a characterization procedure for assessing the quality of hand lay-up open moulded samples with sharp corners. 2. Quantify the effect of different geometrical and process parameters on the ensuing quality of the open moulded parts. 3.  Propose a new methodology, based on statistical analysis and multiple criteria decision making, to arrive at desired design solutions for open moulded, sharp-cornered parts under conflicting quality metrics.  In chapter 2, a general summary of composite materials and their manufacturing processes relevant to this thesis are provided. The chapter also includes a review of Multiple Criteria Decision Making (MCDM) methods. Chapter 3 describes the experimental methods and the samples under different ranges of geometrical parameters. Characterization methods for common defects such as void content, bridging and fibre misalignment are described. Mechanical performance of the samples is also evaluated through a modification of the standard curved beam strength (CBS). A modified MCDM procedure for the evaluation of geometry influence is described. In Chapter 4, the statistical analysis of the obtained data is used to provide new means to determine the contribution of each design and process  4 parameter to the final quality of the open-moulded composite parts. Based on the statistical trends of the quality metrics, the results of the MCDM technique are also presented for the geometrical design case. In Chapter 5, conclusions and potential future work from the above experimental and optimization results are summarized.            5 Chapter 2: Literature Review  This chapter is divided into two main sections. First, Section 2.1 provides an overview of thermoset composites and their common manufacturing methods. A general description of the typical manufacturing defects that control the quality of curved composite parts is also discussed. Moreover, a brief discussion of the stress response of angled composite specimens under bending conditions is presented. Then, in Section 2.2, a general background on the use of Multiple Criteria Decision Making Techniques is presented.    Composite Materials 2.1 The concept of a “composite material” refers to every material that is composed of more than one solid element, where each element provides complementary properties (Strong, 2008). This concept includes a wide variety of different materials including: wood laminates, reinforced concrete and fiber reinforced plastics. Fiber reinforced composites are defined as a group of composite materials that are formed by a matrix that holds in place fiber reinforcements (Strong, 2008). The properties of a composite material are governed by the constituent elements of the composite. The matrix provides the shape to the structure and protects the embedded fibers; the reinforcement fibers provide strength and stiffness to the part and increase the mechanical properties in the direction coincident with the fibre orientation (Strong, 2008).  Fiber reinforced composites can be divided into two groups based to the nature of the matrix material. The first group corresponds to thermoplastic composites, which are comprised of composites with thermoplastic resins as the matrix material. Thermoplastics are usually in  6 solid state at the room temperature, and the resin has to be melted and softened prior to processing. As a result, the molding process temperatures for thermoplastic materials have to be above the melting point of the resin, in order for the resin to penetrate between fibers and form the desired mold shape. After filling the mold, and as the temperature decreases below the crystallization temperature, the composite part cures and is formed. In general, thermoplastic resins show better toughness and impact resistance than thermoset resins; however, the high viscosity and higher cost associated with thermoplastic materials create unique challenges. As a result, thermoset materials have found a more widespread use in many engineering applications of composites (Strong, 2008).  2.1.1 Thermoset Matrix Composites  In thermoset composites, the molecules of the polymer develop chemical bonds called crosslinks during the curing process. The formation of multiple crosslinks generates a significant increase in the molecular weight of the resin, which causes the melting point of the resin exceed the decomposition temperature of the matrix. As a result, thermoset resins cannot be melted or recycled. A key advantage of thermoset resins is their low viscosity, which allows the resin to penetrate the fibers of the reinforcement, even after the curing reaction has started. As a result, the time to properly impregnate the reinforcement and adopt the geometry of the mold is increased. Another advantage of this material is related to its elevated glass transition temperature, which allows the composite part to operate at temperatures above the curing temperature (Strong, 2008). Within thermoset resins, the unsaturated polyester (UP) is one of the most common resin materials used today due to its low cost when compared with other thermoset resins such as  7 epoxies or vinyl esters (25% less than vinyl esters and up to 50% less than epoxies) (Strong, 2008). 2.1.1.1 Unsaturated Polyester Resins  Unsaturated Polyester (UP) resins are created by polymerization through the combination of two monomers: 1) a glycol with an alcohol group (OH) and 2) diacids with a COOH group, as shown in Figure 2.1:  Figure 2.1 UP polymerization reaction (Strong, 2008)  When glycols react with diacids, the reactive groups of both monomers join to form a water molecule. During this reaction, the remaining oxygen in the glycol molecule bonds with Carbon of the acid, and creates an ester link. The active ends of the polyester molecule continue reacting with new glycol and diacid monomers, thus elongating the new molecule until the concentration of monomers is low enough to enable further reaction of the polyester  8 (Strong 2008). The term “unsaturated” refers to organic molecules, which contain carbon-carbon double bonds in the polyester from the diacid monomer.  The curing reaction of the composite is achieved via a cross-linking mechanism. Crosslinking starts with the organic peroxide initiator generating free radicals which reacts with the double bonds of the UP to create a new free radical in one of the carbon bonds. This bond subsequently reacts and creates further bonds with other polyester molecules. A traditional element often used to facilitate the reaction is styrene, an aromatic ring attached to a carbon-carbon double bond able that work as a reactive diluent on the resin. 2.1.1.1.1 Effects of Processing Parameters on the Curing of UP Resins  There are several factors which influence the reaction of UP resins. These factors include: curing temperature, amount of initiator and the chemical composition of the resin itself. From the practical consideration, two main factors that manufacturers readily control during the composites molding process are the curing temperature and the amount of the initiator. With the increase of the temperature in a UP curing reaction, the movement of molecules is increased resulting in a higher level of crosslinking. Several studies were carried out on the effect of temperature on the curing time of UP resins and the level of conversion of the double bonds (Huang and Leu 1992), (Delahaye et al., 1998) (Vilas et al., 2000).  The evaluation of the degree of conversion of carbon-carbon double bonds for UP resins with 1% of the initiator Methyl Ethyl Ketone Peroxide (MEKP) was developed by Vilas et al. (2000). The results from their differential scanning calorimeter tests indicated the different degrees of conversion under different ambient temperatures for UP resins, as shown in Figure 2.2.   9  Figure 2.2  Conversion (cure) profile as a function of time under different temperatures. UP resin with 1% MEKP (Vilas et al., 2000)     In Figure 2.2, the maximum degree of conversion was obtained at 80 °C. For average temperature conditions (typically 30 °C), the conversion rate reached a maximum of only 50%. Also, the higher curing temperature provided shorter curing times.  Thus, the results suggest that the curing conversion rates and the time were sensitive to temperature conditions. For low temperature curing conditions, a post curing process was necessary to increase the degree of conversion in UP resins (Delahaye et al., 1998).  The variation of the gel time is also affected by the amount of initiator used on the reaction of UP resin. This is illustrated in Figure 2.3 for different amounts of initiator (Vilas et al., 2000).  10  Figure 2.3  Gel time as a function of temperature for a UP resin under three different initiator concentrations. (Vilas et al., 2000)   Figure 2.3 shows the influence of the amount of initiator on the decrease of the gel time on the UP resin system. The more MEKP was added, the shorter the gel time was.  Also, the addition of a higher percentage of initiator contributed significantly to the degree of conversion of the resin. The degree of cure of UP resins has an influence on its mechanical properties. The work by Shah Mohammadi et al. (2013) confirmed the effect of the curing temperature on the elastic modulus of an UP resin. These results are illustrated in Figure 2.4 for parts cured at 20, 30 and 40 ⁰C.   11  Figure 2.4 Schematic of the change on the storage modulus based on the degree of cure of an UP resin. (Shah Mohammadi et al., 2013)  Figure 2.4 schematically illustrates a difference in the modulus of elasticity of the resin under different degrees of cure. Thus, the change in the degree of cure of the resin will modify the properties of the composite material, especially those properties that are strongly influenced by the matrix conditions (e.g., transverse modulus). 2.1.2 Manufacturing Methods for Composites  The selection of an appropriate manufacturing process for composite materials is a challenging task. The engineering and business aspects of the material, and part process must be considered. The most important parameters include:  Production rate: Depending on a given application and customer requirement for product delivery, the selection of the manufacturing process with respect to the production rate considers the type of resin, type of molding operation and the part size.  12  Performance target of the composite material: The general mechanical properties targeted for composite materials are governed by different principles depending on whether the parts are used in advanced or general engineering applications. Parameters such as fiber architecture, length, orientation and content directly influence the mechanical properties of the composites. These parameters can also restrict the selection of the optimum manufacturing process.  Size: For small sized products, the use of closed moulds and injection processes is preferred. For large parts, the use of open moulds offers optimal balance between the manufacturing costs and the achievable production rates.  Shape: Depending on the geometry of the part, proper manufacturing method must be selected. For example, for complex geometries hand lay-up is preferred, while for simple cylindrical parts filament winding is used.  Cost: Depending on the market and the product application, cost may preclude the use of complex technologies. For example, the use of autoclaves to fabricate high quality components can be justified only in situations where economic profitability can be achieved.  Once these parameters are decided upon, the manufacturer needs to select the type of resin for the composite material. Thermoset resins have advantages such as the low viscosity of the resin, which helps the fibers to get properly soaked in resin and create a better bonding between layers. Also, a process where solidification of the resin is associated with a chemical reaction may reduce the energy costs associated with melting and cooling processes. On the other hand, the main disadvantage of thermoset resins is their long curing reaction time,  13 which eliminates the possibility of using this kind of materials in applications with high production rates (e.g., in the automotive industry).   2.1.3 Open Moulding Techniques  Traditional open moulding techniques are performed with a single mould and without the application of matching tools. Open moulds are commonly used for manufacturing of parts of diverse sizes and geometries. The deposition of fibers and resin into the mold is a manual process. Therefore, variations in the fiber orientation of pre-impregnated parts (prepregs), spray lay-up or wet lay-up are often considered. The experimental part of this thesis focused on the use of the wet lay-up to create angled composite parts. As a result, the following section reviews the wet lay-up open moulding process. 2.1.3.1 Wet Lay-up  One of the basic methods used in composite manufacture is the wet lay-up process. This process consists of a manual placement of the thermoset liquid resin in combination with the desired reinforcement material. The fibers must be fully wetted by the resin, and subsequent layers are placed on top of the reinforcement material until the desired thickness is obtained. Also, pressure is applied to the composite with a roller for better compaction of the fabric layers, as illustrated in Figure 2.5. The resin is typically left for extensive periods of time at room temperature to achieve a total consolidation of the material (Mazumdar, 2002).   14  Figure 2.5 Schematic of hand lay-up process (Mazumdar, 2002)  2.1.3.1.1 Advantages of Wet Lay-up  In spite of being one of the earliest composite manufacturing methods, wet lay-up is still widely used in the engineering composite industries mainly due to the following advantages (Mazumdar, 2002):  It requires a low capital investment in equipment.  Various geometries, sizes and fiber orientation configurations can be quickly prepared.  The use of fibers and thermoset liquid resins is less expensive than the use of advanced materials (e.g., prepregs). 2.1.3.1.2 Disadvantages of Wet lay-up  The use of manual processes provides a limited control of the manufacturing conditions and thus the main disadvantages of wet lay-up process are:  15  It is a labor intensive process and provides limited control over manufacturing conditions.  It is economically viable only for large structures with a low requirement on mechanical properties.  It has a poor consistency in sample quality.  The absence of pressure systems reduces the possibility to obtain ideal fiber/resin ratios on the parts (between 60 to 70%) (Mazumdar, 2002).  2.1.4 Mechanical Properties of Angled Composites  It is widely known that composite materials have deficiencies in their transverse direction (Figure 2.6), and frequently fail in this direction. The transversal, or “through the thickness” properties of composites are mainly governed by the matrix properties, which has just a fraction of the material properties in coordinates coincident with the orientation of the reinforcement (Kedward et al. 1989), (Cui et al. 1995).      Figure 2.6  Composite diagram indicating transverse direction in flat and curved parts  Transverse direction. . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . . . Curved region Transverse direction.  16 Equation 2.1 Depending on the part geometry, composite parts can be exposed to transverse loads in real world applications. In particular, angled composite beams under pure bending experience such loads. When pure bending is applied on angled composites, radial stresses develop in the curvature region, leading to a failure due to delamination or matrix cracking. The theoretical solution for the calculation of the radial stress on a curved beam with cylindrical anisotropy under flexural loads was developed by Lekhnitskii (1968). The following expression (Equation 2.1) was obtained for cylindrically anisotropic homogeneous curved beams under pure bending through classical elasticity theory:  𝝈𝒓 =𝑴𝑹𝒐∗𝒃∗𝒈[𝟏 −𝟏−𝒄𝒌+𝟏𝟏−𝒄𝟐𝒌(𝒓𝑹𝒐)𝒌−𝟏−  𝟏−𝒄𝒌−𝟏𝟏−𝒄𝟐𝒌𝒄𝒌+𝟏 (𝑹𝒐𝒓)𝒌+𝟏]    Where, 𝑀 corresponds to the applied moment, 𝑏 is the width of the specimen and 𝑅𝑖  represents the inner curve radius (Figure 2.7)    Figure 2.7  Schematic of geometrical parameters used for the radial stress calculation in a curved composite beam (Kedward, 1989)  The radial location 𝑟 corresponding to the maximum stress is given by Equation 2.2:  17 Equation 2.2  𝑟 = [(𝑘+1)(1−𝑐𝑘−1)𝑐(𝑅𝑖𝑅𝑜)𝑘(𝑘−1)(1−𝑐𝑘+1)] 12𝑘  Where,                                                                                                  𝒈 =𝟏−𝒄𝟐𝟐−𝒌𝒌+𝟏 (𝟏−𝒄𝒌+𝟏)𝟐𝟏−𝒄𝟐𝒌+𝒌𝒄𝟐𝒌−𝟏(𝟏−𝒄𝒌−𝟏)𝟐𝟏−𝒄𝟐𝒌                                         The dimensionless parameters k and c can be calculated from Equations 2.4 and 2.5, respectively: 𝑘 = (𝐸𝜃𝐸𝑟)1/2                                                                                                         𝑐 =𝑅𝑖𝑅𝑜  Where, 𝑅𝑜 and 𝑅𝑖 represent the corresponding outer and inner curvature radii, and 𝐸𝜃 and 𝐸𝑟 are the effective elastic modulus on the tangential and radial directions, respectively. Other approximate expressions for maximum radial stresses have been reported in the literature. Kuhn (1956) used Equation 2.6 to calculate radial stresses in curved composite parts: 𝜎𝑟 =3𝑀2∗𝑏∗𝑡∗𝑅𝑚 Where Rm is the mean radius, and t is the thickness of the part. This expression was developed assuming that the location of the maximum load was coincident with the mean Equation 2.5 Equation 2.6 Equation 2.3 Equation 2.4  18 radius Rm.  An approximation for determining the location of the maximum radial stress was developed by Mabson and Neil (1988): 𝜎𝑟,𝑚𝑎𝑥 =12𝑀𝑏∗𝑡3∗ [𝑅𝑚 − (𝑅𝑖 ∗ 𝑅𝑜)1/2] Kedward (1989) combined equations 2.6 and 2.7 into Equation 2.8.  𝜎𝑟,𝑚𝑎𝑥 =3𝑀2∗𝑏∗𝑡∗(𝑅𝑖∗𝑅𝑜)1/2 The error generated when using equations 2.6, 2.7 and 2.8 versus the classical elasticity method, was minimal for Equation 2.8 (Kedward, 1989) when 𝑅𝑖 and 𝑅𝑜 had similar values. The current ASTM standard D6415 for the evaluation of stresses in curved parts, suggests the use of Eq. 2.2 and Eq.2.8 for the calculation of radial stress; however, the use of the simplified solution (Eq.2.8) provides a more accurate approximation when the ratio 𝐸𝜃/𝐸𝑟 decreases and the ratio 𝑅𝑖/𝑅𝑜 increases.  The above expressions show a dependency of radial stress on the curvature of the part. By evaluating the stress response using Equation 2.2 for a constant moment and thickness (but variable curvature radius), Figure 2.8 shows that the radial stress is expected to decrease as the design radius increases. The observed increase in stress is higher for curvatures with a radius ≤ 5/16”.  Equation 2.7 Equation 2.8  19  Figure 2.8 Theoretical radial stress versus different curvature radii (the vertical dashed lines show the region tested experimentally in this research; Chapter 3)  Avalon et al. (2010) evaluated the effect of part radius, part thickness and the use of resins enhanced with vapor-grown carbon nano-fibers on the failure mode of curved composite specimens under bending loads. The experimental results from four-point bending tests on curved beam samples indicated that there was no effect of the number of plies, radius or type of additives used on the radial stress response. A similar experiment was carried out by Hao et al. (2012), where carbon/epoxy unidirectional specimens were evaluated and the influence of the part thickness and radius on parameters such as curved beam strength and radial stress via Eq. (2.2) was calculated. The results are presented in Figure 2.9.   0510152025303540450   1/8   1/4   3/8   1/2   5/8   3/4   7/8 1 1  1/8Radial Stress (N/mm^2)Design Radius (in) 20  Figure 2.9 CBS versus: a) Thickness (mm), b) R/t and maximum radial stress versus: c) Thickness, d) R/t of the composite laminated beams (Hao et al., 2012)  The results in Figure 2.9 reveal the influence of the radius and the part thickness on the curved beam strength (CBS) and stress response of the tested composite. From Figures 2.8a and 2.8b, it can be observed that the composite CBS increased with every increase in the radius and part thickness, with the most significant increase resulting from the variation of the part thickness. On the other hand, Figures 2.9c and 2.8d show the effect of part thickness and radius on the maximum radial stress. The results indicate that the maximum radial stress decreased with an increase in the part thickness and radius. This effect was attributed to the high susceptibility of the material to flaws and process induced defects on specimens with bigger sizes. Such phenomena are described in the composite manufacturing industry as “size effects”. The presence of size effects influencing the quality of composite materials has been explored by Zweben, (1994), Wisnom and Jones (1996) and Hitchon (1978). All these studies have  21 reported a trend indicating the decrease of the mechanical properties such as tension, bending, short beam shear and in-plane transverse tension with an increase in the size of the composite parts. In 1996, an experimental study developed by Wisnom and Jones explored size effects on curved laminates by developing samples with different numbers of plies. A drop on the interlaminar tensile stress from 109MPa (in specimens with 16 plies) to 61MPa (in specimens with 64 plies) was observed. This reduction was associated with the presence of voids in the specimens with higher number of plies.  2.1.5 Defects Affecting Quality of Composites  Potter (2009) has comprehensively discussed the origin of defects in the composite materials. His study classified possible sources of variability in the final quality of composite parts. Defects in composite materials have multiple origins. For example, the mechanical properties of composite part can be affected by fiber alignment. The tensile properties of the reinforcement dominate the tensile properties of the composite. Hence, inappropriate alignment could reduce the tensile strength of the material in a specific direction. Nevertheless, next to fiber placement/geometrical defects, void content was described as the most significant quality parameter affecting the mechanical performance of composite parts. 2.1.5.1 Void Content   The presence of voids is often observed in composite parts independently of the manufacturing process (Guo et al. 2006). Formation of voids in composites is attributed to several reasons, including entrapped air during the manufacturing process, moisture absorbed by the reinforcement material and volatiles that are not released from the resin during the  22 cure reaction. If hydrostatic pressure of the resin system is not sufficient to expel the entrapped air, voids will form (Campbell et al., 1994). The presence of packed fibers impregnated with high-viscosity resins is also known to limit the resin flow, which enables further growth of the voids (Guo et al., 2006; Liu et al. 2005; Hagstrand et al., 2003).  The presence of voids critically affects various mechanical properties. Depending on the specific composite applications, the maximum admissible levels of voids vary from 1% to 5% of the total volume of the part. Most of the characterization works previously developed have reported reduced flexural, tensile and interlaminar shear strength (ILSS) with an increase of void content (Olivier et al., 1994; Guo et al., 2006; Liu et al., 2005; Hagstrand et al., 2003). Since the void content is dependent of the hydrostatic pressure of the resin, the application of external compacting pressure during the resin consolidation of the part has demonstrated to effectively reduce the void content in the composite. The relation between void content, mechanical properties and compaction pressure can be observed in Figure 2.10 from the results reported by Liu et al. (2005).  Figure 2.10 Void content vs. shear, flexural, and tensile strengths (Liu et al., 2005)  23 Figure 2.10, shows a reduction of about 20% in the flexural, shear and tensile strength of the composite with a variation of voids between 0.5 and 3.3%. At the same time, it is evident that the applied pressure significantly reduced the porosity levels in the part.   Typically, void content is evaluated by standard methods that measure the void fraction based the total volume through resin matrix burn-off or chemical digestion. However, the use of microscopy imaging in the void content analysis provides additional information related to the size and location of the voids. For instance, Purslow (1984) made the following key observations: - Volatiles present in the resin can contribute to ~0.5% of void content. The resulting voids are circular with a diameter of  ~10μm. - Air pockets may develop between plies. These may contribute to ~1%. These pockets usually are form near misaligned fibers. The dimension of the void is equivalent to the fiber diameter and the length is  ~100μm. Purslow (1984) also provided a void content diagram (Figure 2.10) as a qualitative visual reference for his results.     Figure 2.11 Visual reference for void content in unidirectional samples (Purslow, 1984)    24 2.1.5.2 Defects on Angled Laminates  An experimental research carried out by Hubert and Poursartip (2001) on angled composite parts identified defects that are likely to occur in hand lay-up products. Thickness variation in corner regions of concave molds was observed and related to resin flow towards the lower regions of the mold. Also, difficulties in proper compaction of fabric in the corners, which created a higher void content in corner regions was reported. Their study also described the effect of fiber orientation on the final draping capacity of the material. The reinforcement fiber orientation was difficult to control in regions with sharp curvatures. Similar results were reported for out of autoclave materials prepared by Cauberghs and Hubert (2011). Most of the experimental works previously carried out evaluated qualitatively the manufacturing defects in high value advanced composite materials. However, there is only limited literature on the defect formation in general ‘engineering composites’.   2.1.6 Flexural Rigidity of Fibers  Pierce (1930) proposed an experimental method to measure the stiffness of textile materials in order to establish a parameter that could define the capacity of the fibers to drape over a desired shape. The proposed method consisted of the combined measurements of the fabric weight and its bending length. The measurement of flexural rigidity was used as a reference to evaluate the draping capacity of textiles, as well as reinforcement materials used in composites (Behre, 1961), Dahlberg (1961), (Grosberg, 1966). Recent experiments have evaluated the relation between the fabric properties and the flexural rigidity. Parameters such as fabric density, fibers dimensions and modulus of were seen to  25 influence the flexural stiffness of the composite (Yuksekkaya et al. 2008). For angled composite parts, the flexural rigidity of the fibers could potentially represent a key parameter to help manufacturers obtain premium quality parts.   MCDM Methods    2.2 The design stage of composite parts often deals with the consideration of multiple conflicting criteria. This means that the ideal design solution for one evaluation parameter could be in conflict with the ideal solution of other parameter. For this reason, the decision of the optimum design solution is not a simple selection process and requires the use of Multiple Criteria Decision Making (MCDM) techniques to systematically evaluate multiple possible solutions. MCDM techniques can be classified into two principal groups: 1) compensatory and 2) non-compensatory methods.  In the case of non-compensatory techniques, each attribute is considered equally important and there is no trade-off between criteria, meaning that the higher evaluation of one alternative on a specific criterion is not affected by the evaluation of different parameters. Some examples of this approach include techniques such as Maximin, Maximax, Conjunctive, Disjunctive, Lexicographical (Hwang and Yoon, 1995) and Elimination by aspects (Tversky, 1972). The second group of the MCDM techniques corresponds to the compensatory techniques, in this case an alternative that is slightly less favourable under one evaluation criteria might end up being and optimum solution, if it represents a superior alternative for one or more other attributes. Some of the methods in this category include the Simple Additive Weighting (Fishburn, 1967), Weighted Product Method, ELECTRE, PROMETHEE, Analytic Hierarchy Process (AHP) and Technique for  26 Order Preference by Similarity to Ideal Solution (TOPSIS) (Hwang and Yoon, 1981). The application of non-compensatory techniques generally is more specific and requires proactive ‘attitude-oriented’ decisions by the decision maker, while compensatory techniques have demonstrated to be fairly simple and effective in achieving valid results in a wide range of applications (Hwang and Yoon, 1995). In this thesis, the TOPSIS compensatory method was used for data analysis. 2.2.1 TOPSIS  Proposed by Hwang and Yoon (1981), the application of TOPSIS has been proven to be an effective tool for the design selection and decision making in diverse engineering fields (Davoodi et al. 2011; Jee and Kang, 2000). This MCDM technique is based on the principle that the optimum solution corresponds to an alternative that is the most similar with respect to an ideally positive solution (an imaginary alternative with the best possible score on each and every single attribute) and additionally, is more dissimilar to the ideally negative solution (an imaginary alternative with the worst possible score on each and every single attribute). In other words, by considering a number of n attributes to evaluate and compare a series of m alternatives in an n-dimensional space, the optimum solution will correspond to the attribute that offers the shortest Euclidean distance to the ideal positive scenario and the longest distance to the worst case scenario (Hwang and Yoon, 1981). This concept is graphically described in Figure 2.12.    27  Figure 2.12 Euclidean distances from an ideal positive and negative solutions (Yoon and Hwang, 1995)  In Figure 2.12, as an example, the alternatives A1, A2 and A3 are evaluated with respect to two attributes. Alternative 2 (A2) is the optimum solution based on the TOPSIS principle, since this alternative has the shortest distance from the ideal positive solution and the longest distance from the ideally negative solution. An additional detail to observe from this example is that A2 is the optimum solution even though it is outranked by A1 on attribute 2. This shows the nature of a compensatory MCDM method such as TOPSIS, where the low performance of an alternative under one attribute is allowed to  be compensated with the good scores under the rest of attributes, providing an “overall” best solution.      28 2.2.1.1 Weighting Method  The correct application of TOPSIS and many other MCDM techniques depends on the weighting methodology. The assignment of weights defines the level of importance of each of the evaluation attributes in the given application. Weighting techniques are divided in three different groups: subjective, objective and combinative methods.  Subjective weighting methods correspond to the group in which the preference between attributes for a specific application merely relies on the decision maker (DM). This preference can be based on the design requirements or previous experience (Jahan et al. 2011). Methods such as weights from ranks, ratio weighting and Digital Logic are examples of the subjective weighting techniques (Stillwell et al., 1981; Saaty, 1980; Farag, 1997).  The Digital Logic (DL) approach is a useful method to establish weights based on comparisons between multiple evaluation criteria. According to the opinion of the expert, the attributes are compared by pairs assigning a score of 1 to the more favorable attribute and 0 to the less favorable. After all the attributes have been compared, the weights are given by a number of positive decisions (1) obtained per attribute. A Modified Digital Logic (MDL) weighting technique was proposed by Dehghan-Manshadi et al. (2005), based on the same principle of the original DL method, but this time three different scores (1, 2, or 3) on every pair-wise comparison between attributes were allowed. Namely, the least convenient attribute receives a value of 1 instead of 0. In this way, no attribute is totally removed from the weighting considerations. The method also creates the possibility to establish comparisons with ‘equal’ importance sate (in which case both attributes receive a score of 2), and finally the preferred attribute gains a score of 3.   29 The subjective methods have a possible degree of uncertainty that arises from the capacity of judgement of the DM. On the other hand, objective methods evaluate the importance of the attributes solely based on the nature of the measured data. These methods are important when there is no decision maker or when it is difficult to obtain reliable subjective weights. Some examples of such methods include the Mean Weight method, Entropy, and Criteria Importance Through Inter-criteria Correlation (CRITIC) (Diakoulaki et al., 1995). The general principle of the CRITIC method is to provide a higher level of importance to the criteria that have less correlation with the rest of attributes. In 1995, Djakoulaki et al. noticed that one of the principal sources of errors in data comes from the level of inter-dependency between parameters. For this reason the use of Pearson’s correlations between parameters was suggested to determine the weighting value of attributes.  The use of objective methods sometimes presents significantly different results with respect to the DM’s opinion (Jahan et al. 2011). For that reason, a method that could combine both objective and subjective approaches is often deemed more effective in order to obtain an ideal solution.  An example of combinative methods was proposed by Jahan et al. (2011), by combining the use of the DL as a subjective method and the Entropy and CRITIC as objective methods. This approach enabled more balanced importance for all the previously obtained weights and clearly overcame the limitations of using just one weighting method. 2.2.2  The Use of Signal to Noise Ratio (S/N) in Optimization   The use of Signal to noise (S/N) in experimental optimization techniques was introduced by Taguchi (1990). The S/N metric results in a ratio where the signal represents the mean or the desired value, and the noise corresponds to the standard deviation obtained from repeated  30 measurements. Taguchi recommended using the S/N since it measures the quality characteristics of the data with respect to a desired target. The calculation of the S/N ratio is given by Equation 2.9:  𝑆/𝑁 = −10 ∗ 𝐿𝑜𝑔(𝑀𝑆𝐷)  Where MSD is the mean squared deviation, calculated according to the quality nature of the corresponding attribute; that is, depending of the evaluation parameter there is a specific expression for criteria with different characteristics: the “higher the better” (benefit attributes), “the lower the better” (cost attributes) or “the target is best” (for calibration problems). The use of this concept for data treatment could represent an advantage for experiments with limited control and high noise in their outcomes. By replacing the average value by the S/N through test repeats, an outcome with a higher repeatability (robustness) would receive priority in ranking analyses.           Equation 2.9   31 Chapter 3: Experimental Methods and MCDM Procedure   This chapter provides an overview of the procedures that have been employed during the manufacture of curved test specimens and their quality evaluations, as well as the implementation of a new S/N Multiple Criteria Decision Making method. Quality evaluations for open moulded samples mainly included the use of optical imaging techniques for the measurement of fiber misalignment at sharp corners, fabric formability, and surface defects. In addition, the mechanical performance of test specimens was evaluated using the Digital Image Correlation (CIC) and Curved Beam Strength (CBS) tests.   Manufacturing of Test Coupons 3.1V-shape composite samples were prepared using unsaturated polyester resin (Envirez™) with 1% initiator (methyl ethyl ketone peroxide) and E-glass fibers (142oz 3 WEAVE®)  heavy tri-axial fabric; the fibers were laid on the mold in warp direction along part length. All samples were fabricated using the wet lay-up process using horizontal female molds, as shown in Figure 3.1. After demolding, the obtained curved beams were trimmed at the edges to eliminate undesired irregularities, and then sectioned in 2.5cm wide sub-samples using a conventional band saw (Figure 3.2). The sub samples were used for the destructive and non-destructive evaluation of the curved beam’s properties.   Figure 3.1 Schematic of the master mould  32  Using the same master mould, the analyses of geometry, lay-up orientation, and process parameters were classified into three different experimental groups. The procedures for each experimental group are presented in the following sections.  Experiment #1: Evaluation of Geometrical Parameters 3.2 The first set of experiments was performed with the objective of exploring the influence of the part geometry on the final quality of the composite part. Thus, samples were fabricated in four master moulds (one master mould per radius level) using a fiber orientation of 0/90° at room temperature (25°C) with the following geometrical features.   Corner Radius: 1/8”, 3/16”, 1/4” and 5/16”.  Part angle: 40⁰, 50⁰, 60⁰ and 70⁰.  Number of layers: 3 and 5.   Figure 3.2 Sample geometry and input parameters used  These parameters were chosen based on a literature review of historical design ranges for open moulded parts. Typically, the mould design recommendations avoid sharp corners with  33 the radii of curvature lower than 0.08” (Mazumdar, 2002). Using the open moulding hand lay-up technique, 64 sample configurations were manufactured with four corner radii, four part angles, and two different numbers of layers, and two repeats of each configuration.  3.2.1 Quality Evaluation  The quality of open moulded parts was evaluated through quantitative measurements of: void content, curved beam strength, fiber misalignment, thickness uniformity, external surface defects and reinforcement formability. In these evaluations, statistical methods such as Analysis of Variance (ANOVA) and Analysis of Covariance (ANCOVA) were implemented as outlined below.  3.2.1.1 Void Content Test  The method for quantifying the void content in the fabricated samples was based on the ASTM D2734 standard. This standard relates the density of the cured sample to a calculated theoretical value based on fiber and matrix densities. With the use of a MDS-300 specific gravity tester, the value of the density of each trimmed specimen and its mass were measured. Subsequently, in order to determine the corresponding mass of the resin and the fibers, each sample was placed in a furnace following the ASTM 3171 test for matrix decomposition at 565 ⁰C. Once the resin was burned off, the mass of the fibers was determined and the theoretical density was obtained using Equation 3.1:   34 𝑻𝒅 = 𝟏𝟎𝟎(𝑹𝑫+𝒓𝒅)                                                                                                                                        Where, 𝑇𝑑 was the theoretical density value, R and r were the weight fractions of the resin and reinforcement, respectively; the densities of the resin and reinforcement were represented by D and d, respectively. Finally, the theoretical density of the specimen was compared with the measured value (𝑀𝑑) to obtain the final void content as expressed in Equation 3.2: Void content = 100(𝑇𝑑−𝑀𝑑)𝑇𝑑  3.2.1.2 Curved Beam Strength (CBS)  The bending strength of the samples was evaluated using a modified version of the ASTM D6415 standard for flexural testing of curved beams.  Specifically, the fixture specified in the original standard was customized (Figure 3.3) to accommodate different dimensions and geometries of sample configurations based on the previously defined geometrical inputs. Equation 3.1 Equation 3.2  35  Figure 3.3 The CBS test fixture used  According to ASTM D6415, the distance between upper supports should be 75 mm. However, the modified fixture had a separation of 22mm. This modification was made to use the same bar separation for all the geometries examined in this research. Additionally, the roller bearing system was replaced with two rigid polished bars lubricated with mineral oil (to reduce error induced by friction).  By definition, the CBS value corresponds to the moment per unit of width of the composite specimen at the first delamination point. Since one of the parameters to evaluate in the present work was the number of layers (i.e., variation of thickness), the part resistance to the moment applied was expected to be highly sensitive to this variable. The CBS value from each test configuration was calculated using (ASTM D6415, 2007):                                                                                                                                          𝐂𝐁𝐒 = (𝐏𝟐𝐰∗𝐜𝐨𝐬 (∅)) ((𝐝𝐱𝐜𝐨𝐬(∅)) + (𝐃 + 𝐭)𝐭𝐚𝐧 (∅) )                                                                                                                                                Where P corresponded to the applied force at the point where the first failure was detected; in this work, it was identified from the first kink appearing in the force-displacement curve obtained by an Instron 5969 load frame; t was the part thickness, w was the width, ∅ was the Equation 3.3   36 specimen’s flat surface angle relative to the horizontal line (Figure 3.4), 𝑑𝑥 was the horizontal distance between centers of the fixture bars of diameter D.   Figure 3.4 CBS test geometrical considerations (ASTM D6415, 2007).  The expected typical response from the standard test for curved beam samples is presented in Figure 3.5. The presence of different kinks in such progressive sequence of delamination events can help to clearly identify the location of the maximum load needed for Equation 3.3 (i.e., at the onset of first delamination).   Figure 3.5 Typical response for multidirectional composite specimens (ASTM D6415, 2007)   37 In the experiments performed in this research, two factors were expected to introduce inaccuracy during the CBS tests. First, the presence of high void levels in the samples due to the nature of the wet lay-up manufacturing process. Second, the non-uniform geometry of the test samples which can randomly vary across different sample surfaces (e.g., random surface roughness at different locations of the part). Recognizing these limitations, and to gain a deeper understanding of the underlying composite behavior, a complementary imaging technology known as Digital Image Correlation (DIC) was employed to relate the macro-level CBS measurements to the local failure mode of each part with a particular geometry. In addition, an auxiliary finite element model (FEM) of the test was established to understand some non-linear behavior (as opposed to Figure 2.5) that was seen for a few geometrical configurations. The employed DIC and FE modeling methods are described in detail in the following sub-sections. 3.2.1.2.1 Digital Image Correlation for the CBS Test  DIC has demonstrated to be a useful tool in the characterization of complex deformations of composites (Dridi et al., 2012; Lomov, et al., 2008; Komeili, 2014), and to arrive at new levels of understanding of composites behaviour. For instance, a recent application of DIC to analyze 2D strain fields in composite brackets subjected to four-point bending revealed that the initial cracks develop in regions where “interlaminar” strain evolves (Hao et al., 2012).  The 3D digital image correlation in the present research was carried out using a Q-400 System®. The principle acting in the DIC is the use of stereoscopic vision camera system with two or more different perspectives of a single object. Then, a reconstruction of 2D or 3D  38 images was performed (Bhatti, 2008; Pan et al., 2009;”Q-400 DIC and ISTRA4D training,” 2011). In order to determine the location of the cameras with respect to the specimen, a calibration process was performed. Calibration plates with pre-established dimensional references (Figure 3.6) were placed in front of the cameras. Once the calibration plate was focused in both cameras, the software automatically determined their relative position.    Figure 3.6 Fixture and calibration plate for DIC imaging      Next, a speckle pattern was sprayed on the surface of the test sample to be analyzed, as seen in Figure 3.7. This pattern provided a unique visual reference on the specimen, and allowed the software to track the location of specific points on the sample surface. Calibration  Plate Camera 2 Camera 1  39  Figure 3.7 Speckle pattern used for DIC measurements on CBS test  The DIC strain measurement process started with the collection of images during the CBS test. For this phase, a PIP counter attached to the Instron® machine was used. The PIP counter was used during live CBS tests as a reference system for the experimenter to externally trigger a specific point/event (e.g., matrix cracking) via the observations in camera images and register it in the load vs displacement curve for further data analysis. Subsequently, the group of images was post-processed and the area of interest (corner region) was divided into facets and space regions. The location of these facets was tracked on every image, and the local positions were captured by the DIC software. Subsequently, mapping the strain field on the specimens was achieved via the software calculations.  3.2.1.2.2 Finite Element Model (FEM) for the CBS Test  Throughout the CBS experiments, it was observed that specimens with an angle of 40° and three layers, had a non-linear elastic region on the CBS curves. Therefore, a finite element model of the four point bending test was created in ABAQUS® for a specimen with 40° (angle), 5/16” (radius) and 3 layers. The analysis was performed in order to study the origin of the non-linear behavior. A schematic of the model is shown in Figure 3.8.  40  Figure 3.8 Schematic of FEM model of CBS 4-point bending test for 40° sample  The model was created with the use of a deformable composite solid with three different layers of 1.67mm thickness. The main assumption considered in this model was a hard contact on the ‘normal’ direction between master and slave elements. Also, frictionless ‘tangential’ contact between the supports and the part were assumed.  The properties of the material were obtained from the literature (Kachlakev and McCurry, 2000) for similar experiments with fiberglass woven fabrics and UP resin (Table 3.1). In addition, the internal surface of the part in contact with the fixture bars was modeled to have a ribbed surface, in order to mimic the internal surface finish of the open moulded composite samples with rough surface (Figure 3.9).  Table 3.1 Mechanical properties used for the reference FEM model; properties extracted from (Kachlakev and McCurry, 2000) Tensile modulus (E11,E22) Tensile modulus (E33) Poisson's ratio(13,23) Poisson's ratio (12) Shear Modulus (13,23) Shear Modulus (12) Tensile strength 20.7 GPa 6.89 GPa 0.26 0.3 2.65 GPa 1.52 GPa 600 MPa     41  Figure 3.9 Curved part with non-uniform surface geometry, as modified in the model  3.2.1.3 Fiber Misalignment  With the help of optical imaging and the Omnimet® BUEHLER software, the average deviation of fibers from the vertical direction was measured for each sample. The misalignment was defined as the average of inclination angle of the external-layer fibers with respect to the vertical plane, as shown in Figure 3.8.            Figure 3.10 Misalignment angle measurement on the curved specimens                       3.2.1.4 Thickness Uniformity   Due to the shape and orientation of the female molds (Figure 3.2), the resin was expected to flow down towards the corner features of the samples during manufacturing, therefore  42 generating resin-rich zones (Mazumdar, 2002). This may lead to significant differences between the thickness of the composite sample in flat sections and those adjacent to the corners. An optical microscope was used to measure the cross-sectional thickness at the flat section of each sample, as well as at the corner section. The ratio between these two values was defined as “thickness ratio”. Similarly, resin rich zones between layers were measured (Figure 3.11). Bridging was calculated from the average of all the distances between layers in the corner of each sample.  Figure 3.11 Measurements of the total (white arrows) thickness on: a ) the corner (Tc) and b) the flat region (Tf). Thickness ratio defined by Tf /Tc; the layer bridging is defined by the distance between layers in the corner (yellow arrow).  3.2.1.5 External Surface Defects  During the manufacturing process, corner areas were seen to be prone to surface porosity under certain sample configurations (Figure 3.12). As a result, the surface defects were quantified using the Omnimet® BUEHLER software. This software was used to determine the total area of the corner and the size of the area containing surface porosity.  Tc Tf a) b)  43      Figure 3.12 (a) Top and (b) lateral views of a typical corner surface defect  3.2.1.6 External Formability of Reinforcement  Due to the high flexural stiffness of the fabric reinforcement, the capacity of the fibers to drape into the desired curvatures was affected by the sample geometry. Thus, a formability parameter was developed by calculating the ratio between the target radius (defined by the mold shape) and the actual radius of the outer reinforcement layer (measured with the use of optical imaging (Figure 3.13).  Figure 3.13 (a) Design curvature, and (b) the actual reinforcement curvature at the outer surface (notice the resin rich region in the corner area)     44 3.2.2 Multiple Criteria Decision Making (MCDM) Procedure  The measurements and statistical analysis of the above discussed quality parameters (also listed in section 3.2.1) can provide useful information for open -moulding design conditions yielding overall higher quality FRP parts (i.e., with less defects). However, as will be shown in the results in Chapter 4, there are conflicts among different quality measures (e.g., higher part angles may cause less surface defects, but increase the fiber bridging defect).  For this reason, a MCDM approach was employed in order to obtain the best overall solutions considering all the measured quality variables based on two holistic application scenarios: (1) design for structural purposes, and (2) design for aesthetic purposes. TOPSIS MCDM was implemented with signal to noise (S/N) ratios and combinative weighting techniques. The procedure for the proposed MCDM method is as follows:  Step 1: Linear Normalization of the Raw Data The response values for each specific quality criterion (listed in section 3.2.1) were divided by corresponding maximum value according to Equation 3.4:  𝑦𝑖𝑗 =𝑥𝑖𝑗𝑥𝑗∗⁄   Where, 𝑥𝑖𝑗 corresponded to the measured j-th quality parameter (decision criterion; j=1 to n) under the i-th (i= 1 to m) design configuration alterative (see Table 3.2) 𝑥𝑗∗ is the corresponding maximum value among all configurations under the j-th parameter.  Equation 3.4  45 Table 3.2 Schematic of MCDM for the experimental methodology   Quality Criteria  Design Alternatives 1. CBS 2. Void Content   1. 40°, 5/16”, 3 layers x11 x11 x21 x21 x11 x11 2. 50°, 5/16", 3 layers x12 x12 x22 x22 x12 x12      x1j x1j x2j x2j x1j x1j  Weights W1 W2 Wi  Step 2: S/N Values The corresponding Mean Squared Deviation (MSD) for each criterion was calculated according to the characteristic type of quality parameter being evaluated. For the “higher the better” attributes the corresponding expression was: 𝑀𝑆𝐷𝑗 = ∑1𝑦𝑘𝑗2⁄𝑛′𝑛′𝑘=1  Where, 𝑦𝑘 corresponded to the normalized values for one specific combination of inputs (calculated in step 1) under given quality criterion, where n’ was the number of repeats per test (in this thesis n′=2).  For the “lower the better” characteristic, the corresponding MSD was obtained from: 𝑀𝑆𝐷𝑗 = ∑𝑦𝑘𝑗2𝑛′𝑛′𝑘=1  Also, for parameters where a target value (m) was desired, the MSD was obtained from Equation 3.7 as follows: Equation 3.5 Equation 3.6 ...𝑖𝑡ℎ ...𝑗𝑡ℎ  46 𝑀𝑆𝐷𝑗 = ∑(𝑦𝑘𝑗−𝑚)2𝑛′𝑛′𝑘=1    Once the MSD values of each of the attributes were calculated, the S/N ratio was obtained by substituting the corresponding MSD value in Equation 3.8.                                                                         𝑺/𝑵𝒋= −10 ∗ 𝐿𝑜𝑔(𝑀𝑆𝐷𝑗)                               Equation 3.8  Step 3: Subjective Weights Calculation (Modified Digital Logic)  The outcomes obtained from the Modified Digital Logic (MDL subjective weighting method) were based on two different application scenarios: (1) design for structural purposes, and (2) design for aesthetic purposes. Based on each design premise, pair-wise comparisons were performed between quality metrics. The purpose of the comparisons was to determine which of the input (design) parameters was more relevant with respect to the target (structural or aesthetic) performance measure. The parameters that were assumed to be more important received a score of 3, while the less important parameters received a score of 1. For situations where both parameters are deemed to be equally important, both received a score of 2. The schematic of pairwise comparisons for the structural and aesthetic scenarios are shown in Table 3.3 (note that only the assigned score values by the DM could change from one scenario to another; as will be shown through results in Chapter 4).   Equation 3.7  47 Preference designation  between attributes  Table 3.3 Relative importance between criteria based on the MDL method  Attributes Number of possible decisions 1 2 … Misalignment 1 1  CBS 3   Void content  3  …         The total number of pairwise decisions to be made by the DM was: 𝑁 = 2𝑛(𝑛 − 1)  Where, n was the number of attributes. Once all the comparisons were scored, the total number of positive decisions per attribute, 𝑁𝑝𝑗 , is found and the final subjective weight for each attribute (𝑊𝑠𝑗) is determined by:  𝑊𝑠𝑗 =𝑁𝑝𝑗𝑁   Step 4: Objective Weights Calculation (CRITIC) The Pearson correlation coefficient concept was employed to establish the level of interdependency between attributes. Considering two different attributes, j and k, the correlation between them was obtained using the Pearson’s product moment correlation as: 𝑅𝑗𝑘 =∑ (𝑥𝑖𝑗−?̅?𝑗)(𝑥𝑖𝑘−?̅?𝑘)𝑚𝑖=1√∑ (𝑥𝑖𝑗−?̅?𝑗)2 ∑ (𝑥𝑖𝑘−?̅?𝑘)2𝑚𝑖=1𝑚𝑖=1 Where, as before m was the number of design alternatives (possible geometry input combinations), 𝑥𝑖𝑗 corresponded to the response of each design alternative under attribute j. Equation 3.9  Equation 3.10  Equation 3.11   48 ?̅?𝑗 was the average from all the 𝑥𝑖𝑗’s. Similarly, 𝑥𝑖𝑘 corresponds to the response of each design alternative under the k-th attribute and  ?̅?𝑘 is the average value from all the 𝑥𝑖𝑘.  Then, total objective weight (𝑊𝑜𝑗) for each attribute was determined using Equation 3.12:  𝑊𝑜𝑗 =∑ (1−|𝑅𝑗𝑘|)𝑚𝑖=1∑ (∑ (1−|𝑅𝑗𝑘|)𝑛𝑘=1 )𝑚𝑖=1  Step 5: Calculation of the Total Combinative Weights   Following the methodology proposed by Jaham et al. (2011), the total combinative weight for each of the attribute was obtained via: 𝑊𝑗 =(𝑤𝑜𝑗∙𝑤𝑠𝑗)1/2∑ (𝑤𝑜𝑗∙𝑤𝑠𝑗)1/2𝑛𝑗=1   Step 6: Weighted Normalized Ratings and TOPSIS Ideal Solutions   With the use of the combined weights 𝑊𝑗, and the total responses expressed in S/N ratios in the decision matrix, the weighted normalized rankings, 𝑣𝑗 ,  were calculated using Equation 3.14:  𝑣𝑗 = 𝑤𝑗 ∙ 𝑟𝑖𝑗   Once the  𝑣j  values were found, the ideal positive and the ideal negative solutions were determined. At this point, the imaginary best and the worst design combinations for each attribute were identified. Since all types of the signal to noise ratios in quality evaluations were to be maximized, the positive ideal solution (𝑣𝑗+) corresponded to the highest 𝑣𝑗  score Equation 3.12 Equation 3.13 Equation 3.14  49 obtained under each attribute, while the negative ideal solution (𝑣𝑗−) corresponded to the lowest 𝑣𝑗  score.  Step 7: Separation Distances The corresponding Euclidean distances of each of the design solutions should be calculated for both the ideal positive and ideal negative solutions. The distance with respect to the positive ideal solution (𝑆𝑖+) was calculated as: 𝑆𝑖+ = √∑ (𝑣𝑗 − 𝑣𝑗+)2𝑛𝑗=1    Similarly, the distance to the negative ideal solution (𝑆𝑖−)  was obtained as:   𝑆𝑖− = √∑ (𝑣𝑗 − 𝑣𝑗−)2𝑛𝑗=1    Finally, the relative degree of similarity with respect to the positive ideal solution was obtained using:  𝐶𝑖+ =𝑆𝑖−𝑆𝑖++𝑆𝑖− The term 𝐶i+ provided a useful tool to help the DM to evaluate and rank different design options. The alternative with the highest 𝐶𝑖+ value corresponds to the best design solution.    Equation 3.15 Equation 3.16 Equation 3.97  50  Experiment #2: Effective Flexural Rigidity Evaluation 3.3 Following the same manufacturing procedure described in Section 3.2, specimens with          -45o/+45o fiber orientation were prepared, as shown in Figure 3.14.                                                                           (a)                                         (b) Figure 3.14 Reference of ply orientation for a) 0o /90o degrees and b)-45o /+45o degrees  The differences between fabric flexural rigidity for different orientations of the reinforcement were measured using the procedure described in the standard ASTM D1388 for stiffness of fabrics using a cantilever bending tester (Figure 3.15).  Figure 3.15 Cantilever bending tester used of the stiffness characterization of the reinforcement  For this group of experiments, samples were manufactured only with the 1/8” radius geometry.  Under this design radius, a 23 full factorial design was established considering two levels for the following inputs: part angle (40⁰, 70⁰), ply orientation (-45o/+45 o, 0 o /90 o) and 0⁰ 90⁰ -45⁰ +45⁰ Fabric bending under its own weight  51 the number of layers (3, 5). In total, 16 samples were manufactured for the eight possible combinations of parameters considering two repeats per condition, as described in Table 3.4. All the quality metrics previously discussed in Experiment #1 were evaluated for this group of samples, except the misalignment parameter (this parameter was excluded since the experiment itself considers a main change in the fiber orientation).  Table 3.4 Experimental matrix for flexural stiffness evaluation (Experiment #2) Sample Angle Ply Orientation Number of Layers 1 40⁰ -45/+45 3 2 40⁰ 0/90 5 3 40⁰ -45/+45 3 4 40⁰ 0/90 5 5 70⁰ -45/+45 3 6 70⁰ 0/90 5 7 70⁰ -45/+45 3 8 70⁰ 0/90 5     Experiment #3: Process Conditions Evaluation 3.4 A third set of specimens was manufactured to evaluate the effect of resin curing on the critical geometrical condition according to the results obtained from Experiment 1. Thus, specimens with a part angle of 70° and a radius of 1/8” were fabricated with the following variables:  Number of layers: 3 and 5 layers.  Amount of initiator (MEKP): 1% and 2% of MEKP.    Post curing of specimens: no post-cure and a post curing cycle of 1.5 hours at 90 ⁰C.  52 Similar to the experimental design in Experiment #2, for the total possible combinations between the above variables, 16 samples were manufactured. The specimens were evaluated only for their CBS test using the procedure previously described in section 3.2.1.2. The experimental matrix for Experiment #3 is presented in Table 3.5. It is worth adding that it is well known that the part thickness is a critical factor defining the thermal history of resin and hence interacting with other process parameters to define the final cure state (Strong, 2008). Table 3.5 Experimental matrix for Experiment #3 Sample Post Curing Radii Number of Layers 1 Yes 1% 3 2 Yes 1% 5 3 Yes 2% 3 4 Yes 2% 5 5 No 1% 3 6 No 1% 5 7 No 2% 3 8 No 2% 5     53 Chapter 4: Results and Discussion  This chapter provides the results of the novel multi-criteria, statistical characterization procedure developed in Chapter 3 for the evaluation of mechanical properties of open moulded curved samples with woven reinforcements and varying geometries and process conditions. The analysis of the CBS specimens is also related to a simplified finite element model to explore the reasons for the observed non-linear trends for particular geometries. Results of the MCDM and statistical analyses are discussed by closely relating the quantified quality measures to the design parameters. All the raw data values for this section have been included in Appendix C.  Experiment #1 Results: Influence of Geometrical Parameters 4.1  4.1.1 DIC for the CBS Test   The results obtained using the DIC approach for real time deformation studies on the CBS tests are presented first. In general, the load vs. extension curves exhibited a response similar to the classical behavior described earlier in Figure 3.6. One example of such material behavior under CBS test is presented in Figure 4.1 for the configuration  1/8” (corner radius), 70⁰ (angle), and 3 layers.   54  Figure 4.1 Load vs. extension plot with DIC results, indicating: a) stage without failure, b) first delamination on the upper region, and c) second delamination; specimen with a radius of 1/8”, part angle of 70° and 3 layers.   As Figure 4.1 shows, the first delamination in the sample (between states (a) and (b)) corresponded to the separation in the upper space between reinforcement layers, with a maximum load of approximately 400N. As can be seen in Figure 4.1(a), this region contained micro-voids which likely have contributed to the initiation of the first failure. Also, a second delamination was observed in the lower region of the cross-section between layers, with a maximum load of approximately 300N. Both failure events are clearly visible in the load vs extension curves as kinks corresponding to material’s sudden failure once the inter-laminar resistance is reached.  It was observed that for geometry configurations with a part angle of 40°, the load vs extension curves exhibited a unique response, which deferred from the classical (linear) (400) (300)  55 response in standard CBS test. The results obtained for sample with 5/16” (radius), 40⁰ (angle) and 3 layers, are shown in Figure 4.2.   Figure 4.2 Load vs. extension plot with DIC results, indicating: (a) stage without failure, (b) first delamination on the lower region, (c) extension of the first delamination and (d) second delamination on multiple regions; specimen with a radius of 5/16”, part angle of 40° and 3 layers.   The results indicate that the failure in this sample occurred after point (b), where the first delamination appeared to originate at the voids surrounding the lower reinforcement layer of the specimen. There was no DIC indication of failure in the non-linear region before point (a) in Figure 4.2. In order to further understand the source of this non-linear regime observed in the above CBS test, an additional sample was prepared and evaluated 3 times under the non-linear region (note that the same sample was loaded and unloaded). The results of this test are provided in Figure 4.3.   56  Figure 4.3 Load vs. extension plot: Three different runs under with variable maximum loads to evaluate repeatability on the curve for evaluation of the elastic region in a specimen with a radius of 1/4”, part angle of 40° and 3 layers  Figure 4.3 shows the results of the three repeat runs of the CBS test for a same specimen of with a radius of 1/4”. It can be observed that the curves overlapped and it confirmed the earlier observation that no failure was recorded in the DIC images. Thus, the observed non-linear behavior is not associated with failure in the composite layers and the material remains elastic/undamaged (since the three re-loadings overlapped). Next, the FE model developed in Chapter 3 was run for this test scenario to explore other potential sources of non-linearity for the observed global behavior.    3.7  57 4.1.2 Non-linear Response Evaluation via FEM  The obtained FEM stress distribution in the transverse direction of the specimen with 5/16” (radius), 40⁰ (angle) and 3 layers is presented in Figure 4.4.    Figure 4.4 Stress distribution of the sample on the y. direction                           Figure 4.4 shows that the maximum stress location during the CBS test simulation was coincident with the failure region observed in the DIC results (Figure 4.2). In the FE models, the load vs. extension curves of the sample were also obtained from the summation of the vertical reaction forces on points “a” and “b”. These points correspond to the upper support of the 4 point bending test fixture (Figure 3.3). The resultant force vs. extension plot is shown in Figure 4.5.  b “ a      Y    X  58  Figure 4.5 Force vs. displacement response from the FEM simulation   Figure 4.5 suggest that the displacement for the specified geometry is ideally linear, although it is contrary to the observed experimental response of the load vs. extension curve in Figure 4.2 for the same configuration. Hence, in the next step of analysis, a modification was made in the composite part FE model considering the surface finish of the open side during open-moulding. The actual difference between the two surfaces of the open moulded specimen is also presented in Figure 4.6. The magnitude of roughness on the open surface was in the range of 2mm.  Figure 4.6 Cross-section of a sample manufactured with manual wet lay-up   0204060801001201401600 1 2 3 4Force (N) Extension (mm) Force vs Displacementideal sampleOpen Side Mould Side  59 Figure 4.6 shows that in the open side, the architecture of the reinforcement defines the surface of the part. This open side surface was the one in contact with the lower support in the four point bending fixture during the CBS experiment. Figure 4.7 shows the force vs. extension curve for a modified specimen in the FE model (with a rough texture in the open side) when compared to the ideal specimen with no roughness (plain surface)   Figure 4.7 Comparison of force vs. extension plot between an ideal (plain) inner surface and an internal surface with rough geometry  From Figure 4.7, the results suggest that the internal surface of the specimens can be the main cause of non-linearity seen in the response of specimens with 40⁰ (angle) and 3 layers. In order to confirm this conclusion obtained from the FEM, a complementary experimental test was performed. Two specimens with 5/16” (radius), 40⁰ (angle) and 3 layers were evaluated under the CBS test. One of the specimens was polished until the inner surface of the specimen was plain. The results of the corresponding CBS tests are presented in Figure 4.8.  0204060801001201401600 1 2 3 4 5Force (N) Extension (mm) w/ internal textureIdeal Inner Surface 60  Figure 4.8 Comparison of experimental force vs. extension plots for a specimen with a modified (plain) internal surface and the one with the original (rough) inner surface    From the results seen in Figure 4.8, it can be concluded that the inner surface of the open-moulded part was the main source for the non-linear response in the specimens with 40° (angle) and 3 layers. Also, the results of the tests show that the maximum failure load for both specimens was about 80N. This suggests that the CBS failure load was “independent” of the texture of the internal surface.  4.1.3 Sensitivity Analysis Results  This section provides the results of the statistical tests corresponding to the quality parameters described in Section 3.2.1. 4.1.3.1 CBS Tests  Table 4.1 summarizes the ANOVA results of the measured CBS values with respect to the design inputs.  01020304050607080900 2 4 6 8Force (N) Extension (mm) Plain inner surfaceOriginal inner surfaceFailure Point  61 Table 4.1 ANOVA results for the CBS response (α=0.05) Factors  Sum of Squares  Degree of Freedom SSMean F-value P-value Percentage Contribution of SSMean Significance Angle (A) 168046 3 56015 6.955 0.001 4.77% Significant Radius (B) 53646 3 17882 2.220 0.105 1.52% Insignificant No. of layers (C) 1028820 1 1028820 127.736 0.000 87..62% Very high AB 135302 9 15034 1.867 0.094 1.28% Insignificant AC 29932 3 9977 1.239 0.312 0.84% Insignificant BC 32433 3 10811 1.342 0.278 0.92% Insignificant ABC 247931 9 27548 3.420 0.005 2.35% Very Low Error 257736 32 8054  --  -- 0.69% --  The results in Table 4.1 suggest that the corner radius (factor B) was not significant in controlling the CBS of the curved parts. On the other hand, the part angle (factor A) and the number of layers (factor C) have a strong statistical significance (see the p-values in Table 4.1). The third-order interaction term (ABC) indicated some statistical relevance, however with a less percentage contribution when compared to the significant main factors. Number of layers has controlled the CBS values by 88%, followed by the part angle at ~5% contribution. The corresponding main error plots of each parameter are also presented in Figure 4.9.   62   Figure 4.9 Main effect plots of CBS vs. (a) part angle in degrees, (b) corner radii in inch and (c) number of layers (note: vertical bars denote 0.95% confidence intervals; CBS values are in [N.mm/mm])   The difference between mean values due to the part angle (Factor A) change was statistically relevant, presenting a decrease in the CBS response for every increase of the part angle (Figure 4.9a). In contrast, increasing the radius increased the CBS, which supports the theoretical trend in Figure 2.7; i.e., as the part radius increases, the maximum radial stress decreases, hence increasing the CBS capacity (note that in Eq. 2.1 radial stress is highly dependent of part radius). However, the latter effect was not statistically significant in Figure 4.9(b) given the large level of random errors. The CBS values were seen to be very highly dependent on the number of reinforcement layers (Figure 4.9c), where specimens with 5 layers had a significantly higher average CBS value than parts made with 3 reinforcement layers. This effect can be explained theoretically via thickness correlation to the part’s mechanical strength. As described in Section 3.2.1., the CBS parameter represents a a) b) c)  63 measurement of flexural moment per unit of specimen width. Composite parts with a higher number of layers (i.e., greater thickness) are expected to have a higher CBS strength. The thickness of the corner region was not dependent of the number of layers of the part only: the experimental observations indicate that the part angle also affected the ‘actual’ thickness of the corner area. Due to of fiber bridging and formation of resin rich area (this will be discussed in more detail in section 4.1.3.4) the actual thickness increased. As a result, ‘thickness’ here in open-moulding represents a variable that cannot be directly/fully controlled, but can be measured in the experiment for each sample; statistically, such a variable is called a ‘covariant’ or ‘concomitant’ variable (Montgomery, 2009). The dominant influence of the thickness in the CBS response can override the net effect of part radius and part angle effect. In order to remove the effect of the thickness covariance, an Analysis of Covariance or ANCOVA (Montgomery, 2009) was performed. A summary of the ANCOVA results is presented in Table 4.2. Table 4.2 ANCOVA results for the CBS response (α=0.05) Factors Sum of  Squares Degree of  Freedom SS Mean F-value P-value Percentage  Contribution  of SS Mean Significance Thickness (A) 1004971 1 1004971 79.802 0.000 85.59% Significant Radius (B) 347184 3 115728 9.190 0.000 9.86% Significant Angle (C) 59297 3 19766 1.570 0.209 1.68% Insignificant BC 189583 9 21065 1.673 0.123 1.79% Insignificant Error 591883 47 12593  --  -- 1.07%  --  The results in Table 4.2 suggest that the part radius next to thickness was a relevant parameter for the CBS (as opposed to Table 4.1). This result suggests that the nuisance effect of the thickness in the ANOVA analysis may have affected the correct statistical evaluation  64 of the effect of the radius parameter. In addition, the part angle in ANCOVA presented no statistical significance. This result suggests that the significant effect of angle seen in Table 4.1 was highly dependent of the corner thickening (i.e., through factor interaction). 4.1.3.2 Void Content   The results of the ANOVA analysis for the void content response are presented in Table 4.3. Table 4.3 ANOVA results for the void content response (α=0.05) Factors  Sum of Squares  Degree of Freedom SSMean F-value P-value Percentage Contribution of SSMean Significance Angle (A) 3.481 3 1.160 2.436 0.083 17.34% Insignificant Radius (B) 10.033 3 3.344 7.020 0.001 49.99% Very high No. of layers (C) 0.017 1 0.017 0.035 0.853 0.25% Insignificant AB 4.894 9 0.544 1.141 0.364 8.13% Insignificant AC 1.068 3 0.356 0.747 0.532 5.32% Insignificant BC 1.726 3 0.575 1.208 0.323 8.59% Insignificant ABC 1.958 9 0.218 0.457 0.892 3.26% Insignificant Error 15.245 32 0.476 -- -- 7.12% --  The results in Table 4.3 indicate that the part radius had the highest impact to the void content, with a total contribution of ~ 50%. The second most important parameter was the part angle (A) with a 17.34% contribution (generally, tighter part angle would result in a higher void content (Figure 4.10b)); however, the level of error relative to this effect has been so high such that there was no statistical significance for Factor A in Table 4.3 (p-value>5%). The number of layers had a negligible contribution on the variation of the void content in the samples. The main effect plots of the radius and part angle are presented in Figure 4.10.   65    Figure 4.10 Main effect plot of  a) void content vs. corner radius in inch and b) void content vs. corner angle (note: vertical bars denote 0.95% confidence intervals; void content is given in percentage values)   The results in Figure 4.10a show that specimens with a radius of 1/8” had a notably higher void content. There was no statistical difference between specimens with radii of 3/16”, 1/4” and 5/16”. It can be hence concluded that for radius over 1/8”, the modification of this geometrical parameter would be ineffective to control void content at sharp corners.   a) b)  66 4.1.3.3 Fiber Misalignment  The results of the ANOVA analysis for the fiber misalignment are presented in Table 4.4. Table 4.4 ANOVA results for the misalignment response (α=0.05) Factors  Sum of Squares  Degree of Freedom SSMean F-value P-value Percentage Contribution of SSMean Significance Angle (A) 81.7 3 27.2 6.6 0.001 34.13% High Radius (B) 62.6 3 20.9 5.0 0.006 26.22% High No. of layers (C) 5.3 1 5.3 1.3 0.268 6.64% Insignificant AB 51.2 9 5.7 1.4 0.242 7.15% Insignificant AC 24.5 3 8.2 2.0 0.139 10.29% Insignificant BC 6.1 3 2.0 0.5 0.694 2.51% Insignificant ABC 56.0 9 6.2 1.5 0.191 7.78% Insignificant Error 132.9 32 4.2  --  -- 5.26% --  The results in Table 4.3 show that the part angle (34.13%) and radius (26.22%) have had significant effects on the fiber misalignment on the curvature areas of the parts. The corresponding trends for part angle and radius are also presented in Figure 4.11.      Figure 4.11 Main effect plots of misalignment vs. (a) part angle in degrees, and (b) corner radii in inch (note: vertical bars denote 0.95% confidence intervals; void content is given in percentage values) a) b)  67 Figure 4.11(a), shows that fiber misalignment is seen to gradually increase for every increase of the part angle. Also, Figure 4.10(b) shows that only specimens with a part radius of 5/16” had statistically different results when compared with parts of the smaller radii. These results can be related to the relative movement of the reinforcement material during the consolidation process of the part. In parts with low corner angles, the geometrical restriction provided by the mold on the fabric against its bending is high (Figure 4.12a). As a result, the reinforcement preserves its original position due to the high normal force and thereby friction force from the mould. For open moulded specimens with 70° angle (i.e., less sharp corners), the distortions are more significant. In this case, the mould provides a reduced restriction to the fibers and hence their relative movement can occur during draping, thus generate fiber misalignment (Figure 4.12b).    Figure 4.12 Draping comparison between a) mould with 40° and b) mould with 70° angle    Normal force of the mould     Friction force        a) b)  68 4.1.3.4 Thickness Uniformity  The ANOVA analysis results for thickness uniformity are presented in Table 4.5.  Table 4.5 ANOVA results for the thickness uniformity response (α=0.05) Factors  Sum of Squares  Degree of Freedom SSMean F-value P-value Percentage Contribution of SSMean Significance Angle (A) 0.082 3 0.027 3.098 0.041 8.28% Significant Radius (B) 0.559 3 0.186 21.163 0.000 56.53% Very High No. of layers (C) 0.061 1 0.061 6.933 0.013 18.52% High AB 0.149 9 0.017 1.879 0.092 5.02% Insignificant AC 0.048 3 0.016 1.818 0.164 4.86% Insignificant BC 0.009 3 0.003 0.335 0.800 0.89% Insignificant ABC 0.096 9 0.011. 1.207 0.325 3.22% Insignificant Error 0.282 32 0.009  --  -- 2.67% --  Table 4.5 shows that the variation of all the design factors had a significant contribution to the thickness uniformity of the parts. The results also suggest that the most important parameters were the curvature radius (56.53%) and the number of layers (18.36%). The part angle had a lower contribution of 8.28%. The main effect plots for the part angle, radius, and number of layers are presented in Figure 4.13.  69    Figure 4.13 Main effect plots of thickness uniformity vs. (a) part angle in degrees, (b) corner radii in inch and (c) number of layers (note: vertical bars denote 0.95% confidence intervals)   Figure 4.13(a) suggests that a more uniform thickness can be obtained for parts with a high angle (70°). Also, more uniform samples are observed in cases with high radius (1/4” and 5/16”) (Figure 4.13(b)). Figure 4.13(c) shows a more uniform thickness for specimens with less number of layers.       a) b) c)  70 4.1.3.5 Corner Bridging The ANOVA analysis results for corner bridging response are presented in Table 4.6. Table 4.6 ANOVA results for the bridging response (α=0.05) Factors  Sum of Squares  Degree of Freedom SSMean F-value P-value Percentage Contribution of SSMean Significance Angle (A) 2541695 3 847232 40.185 0.000 36.80% Very High Radius (B) 1315908 3 438636 20.805 0.000 19.05% High No. of layers (C) 505941 1 505941 23.998 0.000 21.98% High AB 2274753 9 252750 11.988 0.000 10.98% Significant AC 45117 3 15039 0.713 0.551 0.65% Insignificant BC 516331 3 172110 8.163 0.000 7.48% Low ABC 444816 9 49424 2.344 0.037 2.15% Low Error 674658 32 21083 -- -- 9.16% --  The results in Table 4.6 suggest that all the input design parameters and some of their interactions had a statistical impact on the bridging quality metric. The main effect plots for angle, radius and number of layers are shown in Figure 4.14.  71  Figure 4.14 Main effect plots of bridging vs. (a) part angle in degrees, (b) corner radii in inch and (c) number of layers (note: vertical bars denote 0.95% confidence intervals)  In Figures 4.14(a) and (b), the results indicate a decrease of bridging with the increase of the part angle and radius. Also, the lowest extent of bridging was seen in specimens with less layers of reinforcement. The presence of higher bridging under tighter radius was expected. Under reduced dimensions in a corner, the reinforcement layers could not fully drape into pre-defined concentric geometries; instead, they altered their curvatures, creating higher spaces between layers (bridging). Meanwhile, in Table 4.6 it was observed that the interaction between two geometrical design parameters (radius and part angle) was also important. The latter notion is further scrutinized in Figure 4.15.  a) b) c)  72   Figure 4.15 Bridging effect plot for AB interaction; bridging values are in [mm] (note: the curves have been slightly shifted in x-axis for better visibility)   The interaction plot in Figure 4.15 indicates the differences between bridging values for different combinations of part angle and part radius. For example, the tightest radii (1/8” and 3/16”) have induced significantly high bridging only on samples with a part angle of 40°. Figure 4.16 shows a visual comparison for these two conditions.        73   Angle 40° 70° Radius 1/8"   5/16"     Figure 4.16 Comparison between bridging for (a) sample with 40°, 1/8” (b) sample with 70°, 1/8”  (c) sample with 5/16”, 40° and (d) sample with 5/16”, 70°    In Figure 4.16(a), for a part angle of 40° it was observed that the upper layer draped into the curvature radius of the mold. The reduced space made the subsequent layers to separate from the previous one and form under a similar radius, thus producing high distance between the layers. On the other hand, for the 70° specimens (Figure 4.16(b)), the layers could not conform to the geometry of the mold. The parallel reinforcement layers draped to a radius higher than that of the mould. This condition has produced a lower distance (less bridging) between the layers, thus developing an external brittle area in the part corner due to the absence of reinforcement fibers.  a) b) c) d) Higher bridging  74 4.1.3.6 External Formability of Reinforcement  The ANOVA analysis results for the formability parameter are included in Table 4.7. Table 4.7 ANOVA results for the external formability response (α=0.05) Factors  Sum of Squares  Degree of Freedom SSMean F-value P-value Percentage Contribution of SSMean Significance Angle (A) 1.052 3 0.35076 42.008 0.000 42.37% Very High Radius (B) 1.111 3 0.37027 44.344 0.000 44.73% Very High No. of layers (C) 0.001 1 0.00054 0.064 0.801 0.07% Insignificant AB 0.591 9 0.06568 7.966 0.000 7.93% Significant AC 0.033 3 0.01097 1.313 0.287 1.33% Insignificant BC 0.025 3 0.00845 1.012 0.400 1.02% Insignificant ABC 0.115 9 0.01276 1.528 0.180 1.54% Insignificant Error 0.267 32 0.00835  --  -- 1.01% --  From Table 4.7, parameter A (part angle) and B (part radius) have the most relevant effect on the external formability response. Also, a statistically significant response was observed for the interaction parameter AB. The trends corresponding to the part angle and part radius are shown in Figures 4.17(a) and 4.17(b), respectively.   Figure 4.17 Main effect plots of external formability vs. (a) part angle in degrees, (b) corner radii in inch (note: vertical bars denote 0.95% confidence intervals)  Figure 4.17(a) shows that the increase of the part angle decreased the capacity of the material to properly drape onto the mould curvature. On the other hand, better formability results were a) b)  75 obtained for every increment in the radius size, as indicated in Figure 4.17(b). The interaction plot of factor AB is shown in Figure 4.18.   Figure 4.18 CBS effects plot for the interaction AB (note: the curves have been slightly shifted in x-axis for better visibility)  The above interaction plot denotes that formability remains constant in specimens with a radius of 5/16”. Nevertheless, a progressive decreasing trend is observed with every reduction in the angle value. For larger angles, the effect to different radii is more pronounced. On the contrary, parts with 40° angle present comparably a good formability capacity for all the levels of part radius. The decrease of the part radius showed a negative impact on the formability only for specimens with a part angle higher than 40°.       76 4.1.3.7 External Surface Defects  The ANOVA results corresponding to analysis of the external surface defects are presented in Table 4.8. Table 4.8 ANOVA results for the surface defects response (α=0.05) Factors  Sum of Squares  Degree of Freedom SSMean F-value P-value Percentage Contribution of SSMean Significance Angle (A) 6381543 3 2127181 20.12215 0.000 35.50% Very High Radius (B) 2600065 3 866688 8.19847 0.000 14.46% High No. of layers (C) 1710395 1 1710395 16.17955 0.000 28.54% High AB 4799723 9 533303 5.04480 0.000 8.90% Significant AC 304252 3 101417 0.95936 0.424 1.69% Insignificant BC 878538 3 292846 2.77019 0.058 4.89% Insignificant ABC 2295282 9 255031 2.41248 0.032 4.26% Very Low Error 3382829 32 105713  --  -- 1.76% --  From Table 4.8, all the geometrical conditions studied in the experiments showed a significant influence. The most relevant parameter was the part angle (35.5%) followed by the number of layers (8.90%). The statistical trends for the part angle, radius, and number of layers are presented in Figure 4.19.   77  Figure 4.19 Main effect plots of surface defects vs. (a) part angle in degrees, (b) corner radii in inch and (c) number of layers (note: vertical bars denote 0.95% confidence intervals)  In Figure 4.19(a), the results show that specimens had less surface defects for parts with angles between 40° to 60°. The 70° angle was statistically the worst condition. Also, lower surface defects are clearly found in specimens with large part radius and large number of layers.  4.1.3.8 Summary of Geometrical Parameters Effects  By comparing the above presented set of ANOVA results, it can be stated that the design parameters having statistical contribution on different quality metrics are not completely commensurate. For example, the part angle and number of layers were found to have a a) b) c)  78 significant effect on the CBS response, but not on the void content response. In the case of part radius, a positive trend was observed in the CBS values with every size increase. Nevertheless, only samples with 1/8” radius were seen to have a higher void content. In the same relation, a summary of qualitative evaluation of the obtained results from the DIC tests and optical imaging is presented in Tables 4.9 and 4.10.  Table 4.9 Comparison between DIC results and optical imaging for samples with 70° angle   79 Table 4.10 Comparison between DIC results and optical imaging for select samples with 40° angle  As suggested by images in Tables 4.9 and 4.10 (for specimens with corresponding 40° and 70° angles), the failure mechanism in the CBS test samples was mainly associated with matrix cracking originating at the voids. These results show the relation between the level of porosity in the samples and part failure. However, the presence of voids is not affected by the geometrical parameters and is randomly distributed among all groups of specimens, except at radius of 1/8”. As a result, it is not possible to make a full correlation between void content and CBS. In turn, this suggests that in actual design practices it is necessary to consider all the quality metrics. The following overall design guidelines may be helpful to GFRP designers in this regard.  A general design guideline/chart for GFRP manufactures: As mentioned above from a practical application perspective, it is important to establish the impact of design decisions on the quality performance. This is summarized in Table 4.11, where the qualitative significance  80 between each design input and the quality outcome is described. The orientation of arrows indicates the trend of the input parameter providing a desirable output result. Values in brackets indicate the rank of corresponding variables in each column. The notation ‘N/A’ refers to the cases where the input variable showed no statistically significant effect on the output variable in the overall results (considering the hand lay-up process had large random errors). Regarding the output characteristics, the void content, fiber misalignment, and surface defect metrics are of the ‘the lower the better’ type (i.e., defect-type metrics), whereas the CBS was the mechanical strength and hence ‘the higher the better’. In the case of bridging, formability, and thickness ratio all are of ‘the higher the better’ type.  In Table 4.12, the optimum design configurations have been visualized based on the results of Table 4.11 for each metric. For instance, the thickness uniformity metric (Table 4.5) suggested that the corner radius played the most important role, followed by the number of layers and the part angle. Also it was noted that the best thickness uniformity ratio was obtained when the part angle was large, the corner radius was small, and the number of layers was low.   81 Table 4.11 Trends of the influence of significant design inputs on the quality metrics; ranking of input variables are given in brackets in each column; ‘No’ refers to statistical insignificance   Table 4.12 Images corresponding to the best quality designs under different quality metric criteria   4.1.4 MCDM Results and Discussions  The data in Tables 4.11 and 4.12 suggest the presence of conflicting results between different quality metrics for design of GFRP parts with sharp corners. For example, surface defects and bridging follow some inconsistent trends against changes in design factors. While both of these metrics are positively influenced by increasing the radius of curvature of the part, higher part angles cause less surface defects but increase the bridging. This type of a conflict represents a typical scenario of multiple criteria decision making (MCDM) that engineers frequently face in design of complex FRP parts.  Void Surface ThicknessContent Defect Ratio2 2(3) N/A 1 (3) N/A 231 3 2 3 3 1(2 )N/A 2 1 1 1BridgingCBS MisalignmentRadius (B)No. of layers (C)Angle (A)1(3) N/AFormability2N/A 40⁰ 40⁰ 40⁰ 70⁰ 40⁰ 40⁰5/16" 5/16" 5/16" 5/16" 5/16" 5/16" 5/16"N/A 5 layers N/A 5 layers 3 layers N/A N/AAngleRadiusN of layersVoid ContentCBS MisalignmentSurfaceDefectsThickness UniformityB t inputcombinationBridging Formability 82 The application of MCDM methodology in this section was aimed to assist designers to make a final choice regarding the geometrical parameters of curved parts, given the conflicts among quality metrics. Two different scenarios have been considered. These scenarios were created merely based on the potential type of application for open-moulded parts: structural applications (e.g., a GFRP boat hull), and aesthetic application (e.g., GFRP architectural cladding). In both scenarios, the subjective weighting (i.e., via the DM’s input and experience through the MDL method - section 2.2.1.1) and the corresponding objective weighting (through CRITIC method in section 3.2.2) have been implemented.  The summary of the obtained MDL (subjective) weights per scenario are presented in Table 4.13 and Table 4.14.  Table 4.13 Relative importances between criteria based on the MDL method; structural scenario   Table 4.14 Relative importances between criteria based on the MDL method; aesthetic scenario  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21Misalignment 1 1 2 2 3 1 10 0.125CBS 3 3 3 3 3 3 18 0.225Void content 3 1 3 3 3 2 15 0.188Bridging 2 1 1 3 2 1 10 0.125Surface defects 2 1 1 1 2 1 8 0.1Thickness ratio 1 1 1 2 2 1 7 0.088Formability 3 1 2 3 3 3 12 0.15Positive DecisionsWeightsStructural ScenarioNumber of possible decisions1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21Misalignment 3 2 1 1 1 1 9 0.107CBS 1 1 1 1 1 1 6 0.071Void content 2 3 1 1 1 1 9 0.107Bridging 3 3 3 1 2 1 13 0.155surface defects 3 3 3 3 3 2 17 0.202thickness ratio 3 3 3 2 1 1 13 0.155Formability 3 3 3 3 2 3 17 0.202Aesthetic ScenarioNumber of possible decisionsWeightsPositive 83 Next, the objective weights were obtained through the CRITIC technique, which as described in section 3.2.2 accounts for Pearson’s correlations between decision attributes. The results of the Pearson’s correlation factors are given in Table 4.15.  Table 4.15 Pearson's correlation results for criteria pairs; Rjk Criteria CBS Void Content Misalignment Bridging Surface Defects Thickness Uniformity Formability CBS 1 -0.022 -0.324 0.275 -0.346 -0.119 0.213 Void Content -0.022 1 -0.012 0.355 0.195 -0.121 -0.091 Misalignment -0.324 -0.012 1 -0.333 0.343 0.037 -0.451 Bridging 0.275 0.355 -0.333 1 -0.363 -0.558 0.245 Surface Defects -0.346 0.195 0.343 -0.363 1 0.428 -0.598 Thickness  Uniformity -0.119 -0.121 0.037 -0.558 0.428 1 0.039 Formability 0.213 -0.091 -0.451 0.245 -0.598 0.039 1  Table 4.15 shows that the highest correlation was present between the formability and surface defect measures (Rjk = 0.598). As a result, these two quality measures should be assigned lower objective weights for the MCDM analysis.  A summary of the final weights from the combinative method (equation 3.12) is presented in Table 4.16.   Table 4.16 Summary of weighting results under the combinative method for each design scenario     Misalignment CBS Void content Bridging Surface Defects  Thickness ratio Formability Ws Structural 0.125 0.225 0.188 0.125 0.1 0.088 0.15 Ws Aesthetic 0.107 0.071 0.107 0.155 0.202 0.155 0.202 Wo  CRITIC  0.145 0.151 0.168 0.125 0.12 0.151 0.14 Wc Structural 0.136 0.186 0.179 0.126 0.111 0.116 0.146 Wc Aesthetic  0.127 0.106 0.137 0.142 0.159 0.156 0.172  84 In Table 4.16, the results suggest that initially the weighting values were strongly influenced by the DM opinion from the subjective method. However, after including the objective CRITIC weights, the combinative weights present a different preference order. For example, for the structural scenario, the DM assigns an equal importance to bridging and misalignment measures (each 0.125). But the inclusion of the CRITIC weights modified this assignment, providing a higher relevance to the misalignment quality metric than to fiber bridging.  4.1.4.1 Structural Scenario Ranking   Four possible set of design parameters were considered based on the general guideline results in Table 4.12.  A summary of the scores and the corresponding TOPSIS ranking for each of these structural design options is presented in Table 4.17.   Table 4.17 TOPSIS results using four design alternatives for a structural application  Alternatives Angle Radius N of layers Ranking Score  Design 1 40 5/16" 5 layers 1 0.695  Design 2 70 5/16" 5 layers 2 0.557  Design 3 70 5/16" 3 layers 3 0.510  Design 4 70 1/8" 3 layers 4 0.320  The results indicate that from a structural application perspective, the most desired solution is given by the combination of a part angle of 40°, a radius of 5/16” and five fabric layers.  The most important quality parameters for this approach according to the weights presented in Table 5.4 are CBS and the void content of the samples. Hence, the samples with the higher number of layers and higher radius represent the best solution among the different alternatives.   85 4.1.4.2 Aesthetic Scenario Ranking  Under the aesthetic application scenario, quality parameters such as formability, thickness ratio and surface defects received the highest weights in the combinative method in Table 4.16. The results obtained from the selected possible solutions for the aesthetic scenario are presented in Table 4.18.   Table 4.18 TOPSIS results using four design alternatives for an aesthetic application Alternatives Angle Radius N of layers Ranking Score Design 1 40 5/16" 5 layers 1 0.652 Design 2 70 5/16" 3 layers 2 0.564 Design 3 70 5/16" 5 layers 3 0.540 Design 4 70 1/8" 3 layers 4 0.361         In Table 4.18, the optimum solution was coincident with the structural approach best result. It also corresponded to the case with a 40° angle, a 5/16” radius and 5 layers. However, the second best solution now was obtained for a specimen with 3 layers.    Experiment #2 Results: Influence of Flexural Rigidity 4.2 A comparison of the measured flexural rigidity of the tested glass fabric (Figure 3.15) was made in Table 4.19 for 0o/90 o (weft/warp) and -45o /+45 o fabric orientations.   Table 4.19 Flexural rigidity values for the reinforcement material at different orientations Fabric bending/draping  angle Flexural Rigidity  (μjoule/m) 0o /90o 17284 -45o /+45o 1227   86  In Table 4.19, the values of the flexural rigidity change significantly with the orientation of the fibers under a defined curvature; this result indicates that a change in the reinforcement orientation may improve the draping capacity of the reinforcement material (Pierce, 1930).  Next, new set of samples were prepared to represent the two different draping orientations (0o/90 o and -45o /+45o). Subsequently, all ANOVA analyses were repeated to evaluate the quality metrics (results are provided in Appendix A). A general comparison of the quality of parts made via these two reinforcement orientation options is provided in Table 4.20.    Table 4.20 Comparison for all quality metrics between -45 o/45 o and 0o/90o specimens (green marks indicate a statistically preferred condition) Fabric Draping Angle Void  Content  CBS Surface Defects Bridging Thickness  Ratio Formability -45o/+45 o -   - -  0o/90o - - -   -    The response obtained for the ‘void content’ presented no “statistical” differences between the two groups of samples. On the other hand, the ‘CBS’ metric (which would be the most relevant to structural applications) had statistically significant improvement for the -45o /+45o specimens. This observation was attributed to the increase of the corner thickness in the specimens, and can be further supported by the results of parameters such as bridging and thickness tatio (Table 4.20) where specimens in the -45o /+45o configuration were less uniform (corner thickening).  The results indicate that among the four quality parameters that would be considered more relevant for aesthetical applications, two (surface defects and formability) exhibited greater  87 sensitivity in response with the change of the material orientation from 0o/90o to -45o/+45o, and the other two (bridging and thickness ratio) were less sensitive. The interaction effect plots for the formability and corner surface defects are also presented in Figures 4.20 and 4.21, respectively.   Figure 4.20 Effect plots for interaction between angle and layer orientations for formability metric   In Figure 4.20, the results suggest that the samples with a lower flexural rigidity (-45o/+45o) had no statistically significant change between two part angle levels (40° and 70°) for the critical radius of 1/8”. At both angles, the formability index of (-45o/+45o) reinforcement orientation was fairly high (close to 0.9). This means that the flexural rigidity of the fibers can serve as a direct control factor for optimizing the formability metric. Similarly, the surface defect results (Figure 4.21) showed that no defects were found with the reinforcement at (-45o/+45o) orientation, regardless of the number of layers or the part angle.   88  Figure 4.21  Effect plot for interaction between angle, number of layers and reinforcement orientation for the surface defects metric   Experiment #3 Results: Influence of the Cure 4.3 The results presented in this section were obtained for the CBS quality metric analysis under a constant geometry and draping orientation, but different resin cure/process parameters, as explained in Section 3.4. The summary of the results of the ANOVA analysis for this group of experiments is shown in Table 4.21. Results in Table 4.21 suggest that none of the evaluated process parameters on these experiments had an effect on the response obtained from the CBS. Table 4.21 ANOVA results for the CBS response as a function of process conditions (α=0.05) Factors  Sum of Squares  Degree of Freedom SSMean F-value P-value Percentage Contribution of SSMean Significance No. of  layers (A) 122605.0 1 122604.0 32.758 0.000442 73.00% Very High Initiator % (B) 3180 1 3180.0 0.850 0.383608 1.82% Insignificant Post-curing (C) 6838.2 1 6838.2 1.827 0.213447 4.07% Insignificant AB 87.4 1 87.4 0.023 0.882362 0.01% Insignificant AC 3298.8 1 3298.8 0.881 0.375299 1.96% Insignificant BC 1127.9 1 1127.9 0.301 0.598015 0.67% Insignificant ABC 871.9 1 871.9 0.233 0.642277 0.52% Insignificant Error 29941.7 8 3742.7  --  -- 17.83% --  89  A qualitative evaluation of the failure of the specimens for the CBS test under this group of experiments is included in Appendix B.  The failure of the samples was related to the presence of voids in the matrix and interface areas. Any possible direct effect of the resin cure properties on the CBS performance of the material was not detected under the selected experimental conditions. Namely, the amount of initiator (1-2%) and the post-curing cycle have not been significant enough to show statistical differences in the wet lay-up open moulded specimens. This effect could be increased by increasing the temperature in the initial curing stage. As previously demonstrated by Vilas et al. (2000), the degree of cure of unsaturated polyester resins is highly sensitivity to the curing temperature. However, the effect of thermally induced defects (e.g. significant spring-in or residual stresses) must also be considered as a possible outcome during the application of extra heat in curing stages of parts.             90 Chapter 5: Conclusions and Future Work  This chapter presents a summary of the key results obtained in this thesis along with the research limitations and potential future work direction. For practical application purposes, the findings of this research may be categorized into two general production stages: i) pre-production (design) stage based on the characterization of open moulded curved parts with the goal of targeting individual and general quality requirements through mould geometry variations, and ii) post-production stage (i.e. for cases where the mould shape has been finalized and only reinforcement configuration and/or processing conditions may be altered to resolve a part quality issue).  Conclusions 5.1 The findings for the pre-production stage were:   The surface quality of the open-side of the composite brackets has an impact on the response of the Curved Beam Strength (CBS).  For example, non-linear behavior was observed under specific geometrical conditions. The use of a modified four point bending test in conjunction with digital image correlation provided an alternative technique to identify the deformation of composite parts with non ASTM configurations.  The main failure mechanism observed at the corner area was related to the nucleation of cracks at voids (i.e., stress concentration zones).    91   The level of voids in the open moulded samples was not significantly affected by the geometrical conditions investigated.   The CBS of the material increased as the thickness of the part increased. The radius of the corner had a significant impact on the mechanical performance of the part. Formation of resin rich zones did not have a detrimental impact on the interlaminar resistance of the composite.  The geometrical parameters evaluated in this research (i.e. corner radius, angle, and number of layers) provided statistically optimum design configurations for individual quality metrics. These solutions (summarized in Tables 4.11 and 4.12) may be used as an initial guide for designers in order to achieve specific quality requirements.  The use of S/N ratio in the MCDM method was a useful technique to enhance the significance of data analysis and results obtained through experiments.  The use of statistical analysis for MCDM was an effective method to narrow down the design alternatives. This procedure identified the best design configuration based on statistically relevant observations.  The findings for the post-production stage were:   Misalignment of the fibers did not significantly influence the interlaminar properties of curved open moulded specimens under bending. The modification of the layup orientation to -45°/45° with respect to the forming direction significantly reduced the  92 flexural rigidity of the fibers, hence generating better draping properties which also improved aesthetic quality of the final part.  Process conditions related to post-curing or the increase of the initiator had no effect on the mechanical properties of the composite parts tested.  Research Limitations: This research was limited by the lack of previous testing standards applicable to open moulded composite parts. Further, the samples were manufactured using open moulding wet lay-up technique for one material configuration (i.e. woven fiberglass and UP resin). Hence, the obtained results may not be necessarily applicable to all composite parts manufactured using different materials and process conditions. In addition, the evaluation of curing parameters was carried out without the use of high temperature during the initial curing process. This condition could modify the results obtained in this experimental work regarding the statistical effect of degree of cure as presented in Section 4.3.        93  Future Work 5.2 This research provided insights and experimental work provided background on the effect of design parameters and process conditions on the quality of open moulded fibre reinforced parts. The focus of this research was to explore the preferred design scenarios based on geometrical conditions and process parameters that can yield the highest quality in sharp corner areas. In doing so, the MCDM was used to identify possible conflicts among design criteria and arrive at an overall optimum solution. However, in order to establish a better knowledge applicable to industry, several follow-up investigations could be carried out. For example:   Evaluate other composite materials with different resin (e.g. epoxies and thermoplastic resins) and fiber architectures (e.g. twill and unidirectional weaves) configurations in order to create a design database for fabric reinforcements and resins commonly used in the composite industries.  Apply the presented methodology to other manufacturing processes such as resin transfer moulding and vacuum bagging, in order to study the differences and specific solutions for each manufacturing process.  Study the influence of additional additives for UP resins (e.g. inhibitors, fillers, and promoters) on the mechanical response of composite parts with sharp corners.  Include the study of spring-in as an additional quality metric, especially in manufacturing processes with high temperature conditions.  94 Bibliography   American Society for Testing and Materials. (2007). 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A case study on dimensional change of glass fiber reinforced polymers: a combined effect of cure progression and thermo-viscoelastic behaviour. 19th International conference on composite materials. Montreal. Stillwell, W., Seaver, D.A., & Edwards, W. (1981). A comparison of weight approximation techniques in multiattribute utility decision making. Organizational Behavior and Human Performance, 28, 62-67.  98 Strong, A. (2008). Fundamentals of composites manufacturing, Materials, Methods and Applications. Dearborn, Michigan: Society of Manufacturing Engineers. Taguchi, G. (1990). Introduction to Quality Engineering. Tokyo. Asian Productivity Organization. Tversky, A. (1972). Elimination by aspects: A theory of choice. Psychological Review.  79(4), 281-299. Vilas, J., Laza, J., Garay, M., Rodriguez, M., & Leon, L. (2001). Unsaturated Polyester Resins Cure: Kinetic, Rheologic, and Mechanical-Dynamical Analysis. I. Cure kinetics by DSC and TSR. Journal of Applied Polymer Science, 79, 447-457. Wisnom, M. R., & Jones, M. (1996). Size effects in interlaminar tensile and shear strength of unidirectional glass fibre/epoxy. Journal of reinforced plastics and composites, 15:2. Yoon, K., & Hwang, C.-L. (1995). Multiple attribute decision making. An Introduction. Sage Publications, Inc. Yuksekkaya, M., Howard, T., & Adanur, S. (2008). Influence of the fabric properties on fabric stiffness for the industrial fabrics. Tekstil ve Konfeksiyon, 18(4), 263-267. Zweben, C. (1994). Is there a size effect in composites? Composites, 25, 451-454.                 99 Appendices Appendix A: ANOVA Experimental Results for Samples of Group 2   Table A.1 ANOVA results for the CBS response (group 2) (α=0.05) Factors  Sum of Squares  Degree of Freedom SSMean F-value P-value Percentage Contribution of SSMean Significance Angle (A) 12940 1 12940 1.587 0.243 1.41% Insignificant No. of layers (B) 599767 1 599767 73.544 0.000 69.02% Very High Ply Orient. (C) 70959 1 70959 8.701 0.018 8.17% Significant AB 15699 1 15699 1.925 0.203 1.81% Insignificant AC 25548 1 25548 3.133 0.115 2.94% Insignificant BC 42078 1 42078 5.160 0.053 4.84% Insignificant ABC 36761 1 36761 4.508 0.066 4.23% Insignificant Error 65242 8 8155  --  -- 7.51% --   Table A.2 ANOVA results for the void content response (group 2) (α=0.05) Factors  Sum of Squares  Degree of Freedom SSMean F-value P-value Percentage Contribution of SSMean Significance Angle (A) 2.614 1 2.614 1.277 0.291230 5.86% Insignificant No. of layers (B) 9.080 1 0.186 4.436 0.068283 20.36% Insignificant Ply Orient. (C) 1.563 1 0.061 0.764 0.407623 3.50% Insignificant AB 12.044 1 0.017 5.884 0.041485 27.01% Very Low AC 1.645 1 0.016 0.804 0.396139 3.69% Insignificant BC 0.968 1 0.003 0.473 0.511155 2.17% Insignificant ABC 0.305 1 0.011. 0.149 0.709413 0.07% Insignificant Error 16.376 8 2.047  --  -- 36.72% --   Table A.3 ANOVA results for the formability response (group 2) (α=0.05) Factors  Sum of Squares  Degree of Freedom SSMean F-value P-value Percentage Contribution of SSMean Significance Angle (A) 0.281 1 0.281 58.975 0.000059 28.32% Significant No. of layers (B) 0.006 1 0.006 1.198 0.305576 0.60% Insignificant Ply Orient. (C) 0.176 1 0.176 36.795 0.000301 17.71.% Significant AB 0.001 1 0.001 0.038 0.850590 0.02.% Insignificant AC 0.488 1 0.488 102.259 0.000008 49.09% Significant BC 0.001 1 0.001 0.099 0.761036 0.05% Insignificant ABC 0.004 1 0.004 0.907 0.368713 0.44% Insignificant Error 0.038 8 0.005  --  -- 3.82% --  100 Table A.4 ANOVA results for the thickness ratio response (group 2) (α=0.05) Factors  Sum of Squares  Degree of Freedom SSMean F-value P-value Percentage Contribution of SSMean Significance Angle (A) 0.101 1 0.101 8.717 0.018359 17.67% Significant No. of layers (B) 0.013 1 0.013 1.125 0.319837 2.28% Insignificant Ply Orient. (C) 0.306 1 0.306 26.299 0.000898 53.27% High AB 0.011 1 0.011 0.912 0.367453 1.85% Insignificant AC 0.002 1 0.002 0.193 0.672052 0.04% Insignificant BC 0.020 1 0.020 1.754 0.221975 3.55% Insignificant ABC 0.027 1 0.027 2.342 0.164496 4.75.% Insignificant Error 0.093 8 0.011  --  -- 16.19.% --   Table A.5 ANOVA results for the bridging response (group 2) (α=0.05) Factors  Sum of Squares  Degree of Freedom SSMean F-value P-value Percentage Contribution of SSMean Significance Angle (A) 4227846 1 4227846 15.187 0.004564 33.61% Significant No. of layers (B) 3595 1 3595 0.013 0.912319 0.03% Insignificant Ply Orient. (C) 4267983 1 4267983 15.331 0.004447 33.93% Significant AB 773881 1 773881 2.779 0.134014 6.15% Insignificant AC 354 1 354 0.001 0.972416 0.00% Insignificant BC 1070330 1 1070330 3.845 0.085552 8.51% Insignificant ABC 9001 1 9001 0.032 0.861768 7.15.% Insignificant Error 2227102 8 278388  --  -- 17.70.% --  101 Appendix B: DIC Qualitative Evaluations on Experimental Group 3 Table A.6 Comparison between DIC results and optical imaging for samples with 5 layers (group 3)   % Initiator Post-cured Optical imaging DIC first failure ObservationsnoFailure between layers 2-3, crack propagationfrom voids on the same region.nonoFailure between layers 2-3, high prescenceof voids in the corner region.1212Failure between layers 1-2, crack propagation from voids located in the same region.noFailure between layers 1-2, high void contentin the same region.Failure between layers 2-3. Largevoid in the same region2 yesFailure between layers 1-2, no significantdifferences between layers.1 yesFailure between layers 1-2, high void contentin the same region.1 yesFailure between layers 1-2 regardless of significant defect between layers 3-4.2 yes 102 Table A.7 Comparison between DIC results and optical imaging for samples with 3 layers (group 3)   % Initiator Post-curedFailure between layers 1-2. Cracks propagated from voids in the same region.Failure between layers 1-2. Simultaneousresin rupture in lower resin rich area.1 noFailure between layers 1-2. Regardless of voidcontent between layers 2-3.DIC first failure Observations1 noFailure between layers 1-2. Crack propagationfrom void on the left side.Optical imaging2 no21 yes2 yesFailure between layers 1-2. Cracks propagated from voids in the same region.2 yesFailure between layers 1-2. Cracks propagated from voids in the same region.1 yesFailure between layers 1-2. Cracks propagated from voids in the same region.noFailure between layers 1-2. Not signifcant void level observed on the corner area. 103 Appendix C: Experimental Raw Data Table A.8 Raw data for experiment #1 (geometry effect) Specimen  Number Angle Radius Number of  layers CBS (N*mm/mm) Void Content (%) Misalignment (Degrees) Bridging (mm) Surface defects (mm^2) Thickness  ratio Formability 1 70 1/8" 3 layers 205.576 2.858 5.780 504.420 2701.344 1.022 0.335 2 70 1/8" 3 layers 188.728 2.082 3.670 576.050 1888.417 0.978 0.340 3 60 1/8" 3 layers 367.887 2.087 4.180 590.450 743.077 0.503 0.467 4 60 1/8" 3 layers 294.694 1.672 11.230 302.425 1606.887 0.982 0.410 5 50 1/8" 3 layers 208.610 3.034 4.440 820.870 12.987 0.780 1.000 6 50 1/8" 3 layers 334.163 0.757 5.960 777.665 0.000 0.713 0.755 7 40 1/8" 3 layers 321.654 2.565 1.280 979.280 76.206 0.744 0.984 8 40 1/8" 3 layers 227.493 3.185 4.950 1353.710 0.000 0.695 1.000 9 70 3/16" 3 layers 260.505 0.922 3.820 590.449 377.779 0.654 0.741 10 70 3/16" 3 layers 212.312 0.106 5.480 547.246 461.410 0.694 0.686 11 60 3/16" 3 layers 164.908 0.965 0.460 748.862 293.988 0.759 0.866 12 60 3/16" 3 layers 178.274 0.141 4.150 662.755 874.469 0.943 0.728 13 50 3/16" 3 layers 322.357 1.971 5.920 846.069 324.195 0.547 0.933 14 50 3/16" 3 layers 320.467 0.495 8.840 1036.886 24.494 0.594 0.912 15 40 3/16" 3 layers 246.194 0.930 5.300 1730.079 45.732 0.446 0.961 16 40 3/16" 3 layers 360.954 2.799 1.500 1627.335 83.617 0.467 1.000 17 70 1/4" 3 layers 305.932 1.066 7.930 620.690 1178.454 1.003 0.713 18 70 1/4" 3 layers 337.892 2.143 5.860 677.215 1793.753 0.946 0.680 19 60 1/4" 3 layers 239.417 0.743 9.300 734.885 0.000 0.713 0.930 20 60 1/4" 3 layers 246.429 1.139 6.870 849.905 0.000 0.736 0.962 21 50 1/4" 3 layers 302.512 1.159 5.770 633.655 757.787 0.918 0.904 22 50 1/4" 3 layers 236.579 1.678 1.660 980.605 113.231 0.721 0.979 23 40 1/4" 3 layers 203.634 3.119 8.030 1152.095 1130.369 0.787 1.000 24 40 1/4" 3 layers 247.018 1.783 5.610 518.820 1139.278 0.975 1.000 25 70 5/16" 3 layers 171.015 0.689 5.030 633.653 277.408 0.915 1.000 26 70 5/16" 3 layers 250.210 1.869 2.780 619.520 543.090 0.939 1.000 27 60 5/16" 3 layers 139.414 1.250 3.550 749.447 76.863 0.840 1.000 28 60 5/16" 3 layers 235.617 1.161 5.220 561.647 39.961 0.895 1.000 29 50 5/16" 3 layers 261.041 1.699 2.910 604.850 0.000 0.925 1.000 30 50 5/16" 3 layers 387.469 1.299 2.020 532.844 0.000 0.937 1.000  104 Table A.9 Raw data for experiment #1 (geometry effect) (continued) Specimen  Number Angle Radius Number of  layers CBS (N*mm/mm) Void Content (%) Misalignment (Degrees) Bridging (mm) Surface defects (mm^2) Thickness  ratio Formability 31 40 5/16" 3 layers 411.508 0.797 1.680 633.653 0.000 0.863 0.551 32 40 5/16" 3 layers 519.138 1.912 2.680 648.533 0.000 0.843 0.622 33 70 1/8" 5 layers 368.144 2.881 10.880 727.593 769.950 0.618 0.722 34 70 1/8" 5 layers 278.452 2.485 7.010 662.580 828.847 0.835 0.809 35 60 1/8" 5 layers 350.997 1.537 3.170 957.903 69.233 0.634 0.958 36 60 1/8" 5 layers 286.266 1.479 7.610 943.510 71.821 0.693 1.000 37 50 1/8" 5 layers 430.804 1.951 6.470 1015.285 0.767 0.742 0.659 38 50 1/8" 5 layers 434.114 2.246 4.870 1202.500 0.748 0.678 0.595 39 40 1/8" 5 layers 602.427 3.050 -2.380 2073.770 33.711 0.550 0.758 40 40 1/8" 5 layers 836.388 2.020 1.340 2138.580 0.000 0.900 0.776 41 70 3/16" 5 layers 397.716 1.263 6.390 705.797 496.242 0.644 0.735 42 70 3/16" 5 layers 678.961 0.446 7.140 777.665 92.395 0.606 0.903 43 60 3/16" 5 layers 693.142 2.140 3.120 1095.019 92.363 0.595 1.000 44 60 3/16" 5 layers 532.006 2.666 7.270 979.650 553.507 0.600 1.000 45 50 3/16" 5 layers 447.433 0.972 2.790 1117.337 18.988 0.635 0.782 46 50 3/16" 5 layers 464.146 1.881 4.760 864.072 8.713 0.572 0.742 47 40 3/16" 5 layers 500.778 2.771 2.020 1864.955 17.795 0.533 1.000 48 40 3/16" 5 layers 415.299 0.943 3.070 1310.509 0.000 0.593 1.000 49 70 1/4" 5 layers 439.730 1.016 4.850 613.030 2213.091 0.841 1.000 50 70 1/4" 5 layers 444.990 2.276 7.370 642.540 303.137 0.836 1.000 51 60 1/4" 5 layers 412.638 1.528 7.450 864.758 119.616 0.777 0.987 52 60 1/4" 5 layers 723.921 0.663 4.690 691.708 0.000 0.782 1.000 53 50 1/4" 5 layers 471.744 1.815 6.010 915.150 0.000 0.780 0.960 54 50 1/4" 5 layers 616.329 0.663 3.760 900.453 0.000 0.744 1.000 55 40 1/4" 5 layers 822.223 2.094 2.300 780.278 0.000 0.875 1.000 56 40 1/4" 5 layers 582.917 1.378 2.230 743.005 0.000 0.850 1.000 57 70 5/16" 5 layers 387.759 1.151 1.160 727.405 86.768 0.796 1.000 58 70 5/16" 5 layers 449.982 1.475 5.040 655.895 148.856 0.882 1.000 59 60 5/16" 5 layers 572.053 0.877 2.990 813.913 99.401 0.795 1.000 60 60 5/16" 5 layers 464.715 0.980 3.690 749.125 37.960 0.870 1.000 61 50 5/16" 5 layers 672.915 1.029 1.530 784.865 17.603 0.773 0.551 62 50 5/16" 5 layers 802.862 1.497 2.900 871.272 0.000 0.830 0.622 63 40 5/16" 5 layers 531.492 0.877 2.940 691.367 0.000 0.814 0.722 64 40 5/16" 5 layers 710.719 1.060 1.030 655.444 20.717 0.827 0.809  105   Table A.10 Experimental design alternatives for the MCDM (experiment #2)  Design Configurations        Specimen  Number Angle Radius Number of  layers CBS (N*mm/mm) Void Content (%) Misalignment (Degrees) Bridging (mm) surface defects (mm^2) thickness ratio Formability 1 70 1/8" 3 layers 205.576 2.858 5.78 504.42 2701.344 1.022 0.335 2 70 1/8" 3 layers 188.728 2.082 3.67 576.05 1888.417 0.978 0.340 3 70 5/16" 3 layers 171.015 0.689 5.03 633.65 277.408 0.915 1.000 4 70 5/16" 3 layers 250.21 1.868 2.78 619.52 543.089 0.939 1.000 5 70 5/16" 5 layers 387.759 1.151 1.16 727.41 86.768 0.796 0.959 6 70 5/16" 5 layers 449.982 1.475 5.04 655.89 148.856 0.882 1.000 7 40 5/16" 5 layers 531.492 0.877 2.94 691.37 0 0.814 1.000 8 40 5/16" 5 layers 710.719 1.059 1.03 655.44 20.717 0.827 1.000   106  Table A.11 Raw data for experiment #2 (reinforcement orientation effect)  Input Parameters       Specimen  Number Angle Number of  layers Reinforcement  Orientation CBS (N*mm/mm) Void Content (%) surface defects (mm^2) Bridging (mm) Thickness ratio Formability 1 70 3 0/90 205.576 4.858 2701.344 504.420 1 0.335 2 70 3 0/90 188.728 4.064 1888.417 576.050 0.978 0.340 3 70 3 -45/+45 168.034 2.483 0.000 1400.000 0.572 1.000 4 70 3 -45/+45 255.631 2.369 0.000 2857.000 0.592 0.837 5 70 5 0/90 368.144 6.640 769.950 727.590 0.617 0.391 6 70 5 0/90 278.452 7.229 828.847 662.580 0.835 0.418 7 70 5 -45/+45 869.556 7.350 0.000 1014.500 0.616 0.882 8 70 5 -45/+45 600.119 5.523 0.000 1293.314 0.639 1.000 9 40 3 0/90 175.961 2.473 76.206 979.280 0.744 0.984 10 40 3 0/90 174.909 6.467 0.000 1353.710 0.695 1.000 11 40 3 -45/+45 251.328 2.578 0.000 1957.415 0.484 0.861 12 40 3 -45/+45 192.688 5.963 0.000 3400.000 0.376 0.756 13 40 5 0/90 521.634 4.458 33.711 2073.770 0.549 0.958 14 40 5 0/90 715.579 3.593 0.000 2138.580 0.901 1.000 15 40 5 -45/+45 693.007 3.999 0.000 2610.120 0.403 0.957 16 40 5 -45/+45 664.149 4.516 0.000 2747.270 0.423 0.809     107  Table A.12 Raw data for experiment #3 (degree of cure effect)  Input Parameters  Specimen  Number Number of  layers Initiator % Post-curing CBS (N*mm/mm) 1 5 1 n 466.597 2 5 2 n 279.769 3 5 1 y 329.243 4 5 2 y 322.258 5 5 1 n 294.883 6 5 2 n 371.554 7 5 1 y 228.997 8 5 2 y 252.049 9 3 1 n 168.286 10 3 2 n 149.782 11 3 1 y 184.022 12 3 2 y 100.956 13 3 1 n 165.428 14 3 2 n 114.137 15 3 1 y 120.377 16 3 2 y 141.762   

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