Applied Science, Faculty of
Non UBC
Materials Engineering, Department of
DSpace
Polymers 16 (1): 31 (2024)
Jamora, Von Clyde
Rauch, Virginia
Kravchenko, Sergii G.
Kravchenko, Oleksandr G.
Automated fiber placement is a state-of-the-art manufacturing method which allows for precise control over layup design. However, AFP results in irregular morphology due to fiber tow deposition induced features such as tow gaps and overlaps. Factors such as the squeeze flow and resin bleed out, combined with large non-linear deformation, lead to morphological variability. To understand these complex interacting phenomena, a coupled multiphysics finite element framework was developed to simulate the compaction behavior around fiber tow gap regions, which consists of coupled chemo-rheological and flow-compaction analysis. The compaction analysis incorporated a visco-hyperelastic constitutive model with anisotropic tensorial prepreg viscosity, which depends on the resin degree of cure and local fiber orientation and volume fraction. The proposed methodology was validated using the compaction of unidirectional tows and layup with a fiber tow gap. The proposed approach considered the effect of resin bleed out into the gap region, leading to the formation of a resin-rich pocket with a complex non-uniform morphology.
Citation: Jamora, V.C.; Rauch, V.;Kravchenko, S.G.; Kravchenko, O.G.Effect of Resin Bleed Out onCompaction Behavior of the Fiber TowGap Region during Automated FiberPlacement Manufacturing. Polymers2024, 16, 31. https://doi.org/10.3390/polym16010031Academic Editors: PhuongNguyen-Tri, Ana Pilipovic´ andMustafa ÖzcanliReceived: 11 November 2023Revised: 1 December 2023Accepted: 7 December 2023Published: 21 December 2023Copyright: © 2023 by the authors.Licensee MDPI, Basel, Switzerland.This article is an open access articledistributed under the terms andconditions of the Creative CommonsAttribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).polymersArticleEffect of Resin Bleed Out on Compaction Behavior of theFiber Tow Gap Region during Automated FiberPlacement ManufacturingVon Clyde Jamora 1,*, Virginia Rauch 1, Sergii G. Kravchenko 2 and Oleksandr G. Kravchenko 11 Department of Aerospace and Mechanical Engineering, Old Dominion University, Norfolk, VA 23529, USA;vrauch.vmr@gmail.com (V.R.); okravche@odu.edu (O.G.K.)2 Department of Materials Engineering, The University of British Columbia, Vancouver, BC V6T 1Z4, Canada;sergey.kravchenko@ubc.ca* Correspondence: vonjamora@gmail.comAbstract: Automated fiber placement is a state-of-the-art manufacturing method which allows forprecise control over layup design. However, AFP results in irregular morphology due to fiber towdeposition induced features such as tow gaps and overlaps. Factors such as the squeeze flow andresin bleed out, combined with large non-linear deformation, lead to morphological variability. Tounderstand these complex interacting phenomena, a coupled multiphysics finite element frameworkwas developed to simulate the compaction behavior around fiber tow gap regions, which consists ofcoupled chemo-rheological and flow-compaction analysis. The compaction analysis incorporated avisco-hyperelastic constitutive model with anisotropic tensorial prepreg viscosity, which depends onthe resin degree of cure and local fiber orientation and volume fraction. The proposed methodologywas validated using the compaction of unidirectional tows and layup with a fiber tow gap. Theproposed approach considered the effect of resin bleed out into the gap region, leading to theformation of a resin-rich pocket with a complex non-uniform morphology.Keywords: process modeling; compaction; finite element analysis; automated fiber placement1. IntroductionHigh-throughput manufacturing processes for fiber-reinforced composites allow forcomplex layups with a lower processing cycle time [1,2]. Particularly, automated fiberplacement (AFP) is a robotic system that deposits pre-impregnated (prepreg) fiber towstrips at specified locations and enables tailored orientations [3–7]. For example, Wu et al.created a variable stiffness structure with a cut-and-restart functionality of an AFP machinein order to manufacture a prototype of an airplane fuselage [3]. However, depositioninduced AFP tow features, especially fiber tow gaps, inevitably lead to irregular, localnon-uniform morphology upon cure and compaction [8]. Manufacturing features, such asvoids and resin-rich regions, develop when plies neighboring to the gap tow sink into thegap and experience large non-linear deformation caused by the flow of liquid resin intothe empty space (Figure 1). Previous reports show that AFP manufacturing defects createdduring the early stages of cure before resin gelation can significantly affect the mechanicalproperties of the composites [8–10]. These regions with irregular morphology can serve asweak points and reduce the strength [11–13].Fiber tow gaps and overlaps can be restricted during manufacturing or allowedwithin a specific tolerance. However, imperfections in the cured composites propagatefrom these AFP deposition features within the preform and produce local non-uniformmorphology, such as ply thickness variations, waviness, and resin-rich pockets (Figure 1).These irregularities produced from AFP deposition features cannot be entirely avoidedand should be considered as a part of AFP-manufactured composites to properly predictPolymers 2024, 16, 31. https://doi.org/10.3390/polym16010031 https://www.mdpi.com/journal/polymersPolymers 2024, 16, 31 2 of 21the strength of composite structures [14,15]. Furthermore, microscopic features, such asfiber volume fraction redistribution, and mesoscopic features (ply thickness, waviness) arenot formed in isolation from each other and should be analyzed within a comprehensiveframework that considers their coupling [7,16,17].Polymers 2024, 16, x FOR PEER REVIEW 2 of 22 and should be considered as a part of AFP-manufactured composites to properly predict the strength of composite structures [14,15]. Furthermore, microscopic features, such as fiber volume fraction redistribution, and mesoscopic features (ply thickness, waviness) are not formed in isolation from each other and should be analyzed within a comprehen-sive framework that considers their coupling [7,16,17]. Figure 1. Schematics of gaps within a laminate and the effects of resin bleed out on the non-linear morphology. Prior to vitrification, resin changes from an incompressible viscoelastic liquid to a viscoelastic solid upon gelation. The compaction of AFP-deposited preform develops prior to composite gelation, wherein resin viscosity depends on the degree of cure and temperature [18,19]. At this stage, the deformation of the prepreg acts as a homogeneous medium, which is treated as a squeeze flow. In the case of AFP preform compaction, the squeeze flow develops when the fiber tow above the gap region is pushed inside of the void space during the compaction. However, resin bleed out through the fiber bed also occurs simultaneously (Figure 2a), causing the formation of resin-rich zones in the tow gap void and local fiber volume fraction variation in the composite [20]. Conventionally, the effect of resin bleed out in manufacturing of prepregs is considered insignificant, but in the case of AFP preforms with fiber tow gaps, it was shown to affect the waviness of the ply [21]. Figure 1. Schematics of gaps within a laminate and the effects of resin bleed out on the non-linearmorphology.Prior to vitrification, resin ch nges from an incompressible viscoela t c liquid to aviscoelastic solid upon gelation. The compaction of AFP-deposited preform developsprior to composite gelation, wh rein resin viscosity depends on the d gree of cure andtemperature [18,19]. A this stage, the deformation of the prepreg ac s as a homogeneousmedium, which is treated as a squ ez flow. In th case of AFP preform compaction, thesqueeze flow dev lops when th fiber tow above the gap region is pushed inside of tvoid space during the compaction. H wever, resin ble d out through the fiber bed alsooccurs simultaneo sly (Figure 2a), causing the formation of resin-rich zo es in the tow gapvoid and local fiber volume fraction variation in the composite [20]. Conventionally, theeffect of resin bleed out in manufacturing of prepregs is considered insignificant, but inthe case of AFP preforms with fiber tow gaps, it was shown to affect the waviness of theply [21].Recently, a hyper-viscoelastic material model was applied by Belnoue et al. to simulatethe squeeze flow deformation during compaction [7,22–25]. However, the research did notconsider the anisotropic viscosity of prepreg tape and its dependence on the fiber volumefraction. Furthermore, earlier studies did not consider the effects of the resin bleed outfrom the compacted prepreg into the gap region. The present study considers the effectof resin bleed out on the formation of non-uniform morphology around the region of thefiber tow gap. To model prepreg behavior around the internal void, like in the case ofdebulking, a negative internal pressure gradient can be considered inside of the void usingporous-cohesive elements [26]. Another approach is to consider the flow front filling thegap via a one-dimensional numerical model [27]. These studies represent a two-phasePolymers 2024, 16, 31 3 of 21modeling scheme where a region other than the composite is represented [21,27]. In thepresent work, a single-phase model was used and the effects of the resin bleed out intothe gap was shown to have a larger impact on the morphology of the composite prior toresin gelation.Polymers 2024, 16, x FOR PEER REVIEW 3 of 22 Figure 2. (a) Schematics of the bleed out in a unidirectional composite sample. (b) A unidirectional sample which shows a dashed red line dividing the transverse resin bleed, longitudinal resin bleed and the area of the unidirectional tow. Recently, a hyper-viscoelastic material model was applied by Belnoue et al. to simu-late the squeeze flow deformation during compaction [7,22–25]. However, the research did not consider the anisotropic viscosity of prepreg tape and its dependence on the fiber volume fraction. Furthermore, earlier studies did not consider the effects of the resin bleed out from the compacted prepreg into the gap region. The present study considers the ef-fect of resin bleed out on the formation of non-uniform morphology around the region of the fiber tow gap. To model prepreg behavior around the internal void, like in the case of debulking, a negative internal pressure gradient can be considered inside of the void us-ing porous-cohesive elements [26]. Another approach is to consider the flow front filling the gap via a one-dimensional numerical model [27]. These studies represent a two-phase modeling scheme where a region other than the composite is represented [21,27]. In the present work, a single-phase model was used and the effects of the resin bleed out into the gap was shown to have a larger impact on the morphology of the composite prior to resin gelation. The present treatise extends the use of a hyper-viscoelastic model by introducing the fiber volume-dependent anisotropic tensorial viscosity of the prepreg into the formulation of the viscous component [22,28,29]. This approach introduces the local fiber volume frac-tion as a coupling between the squeeze flow and resin bleed out. Resin bleed-out meas-urements were obtained from the unidirectional tape compaction experiments and used to predict the amount of resin bleed out around the tow gap region. In the present case, a single-phase model was developed based on sequential compaction flow analysis, which adds the influence of resin flow into fiber tow gaps without explicitly modeling the resin. First, the hyper viscoelastic finite element analysis (FEA) squeeze flow was performed and the tow gap volume decrease was predicted. Once the tow gap volume reached the resin bleed-out volume, the time of filling was predicted. To capture the presence of resin inside of the tow gap, internal pressure was introduced in the tow gap based on the predicted time of void filling. The interaction between the squeeze flow and resin bleed out was investigated and the predicted resin-rich pocket shape agreed closely with the experi-mental observations. The proposed sequential compaction flow methodology can be ex-tended to modeling various combinations of fiber tow gaps in AFP manufacturing to pre-dict fiber waviness, resin-rich regions, as well as ply thickness variation in the region around the fiber tow gaps. Figure 2. (a) Schematics of the bleed out in a unidirectional composite sample. (b) A unidirectionalsa ple hich sho s a dashed red line dividing the transverse resin bleed, longitudinal resin bleedand the area f t e i ir ti l tThe present treatise extends the use of a hyper-viscoelastic model by introducing thefiber volume-dependent anisotropic tensorial viscosity of the prepreg into the formulationof the viscous component [22,28,29]. This approach introduces the local fiber volumefraction as a coupling between the squeeze flow and resin bleed out. Resin bleed-outmeasurements were obtained from the unidirectional tape compaction experiments andused to predict the amount of resin bleed out around the tow gap region. In the present case,a single-phase model was developed based on sequential compaction flow analysis, whichadds the influence of resin flow into fiber tow gaps without explicitly modeling the resin.First, the hyper viscoelastic finite element analysis (FEA) squeeze flow was performed andthe tow gap volume decrease was predicted. Once the tow gap volume reached the resinbleed-out volume, the time of filling was predicted. To capture the presence of resin insideof the tow gap, internal pressure was introduced in the tow gap based on the predictedtime of void filling. The interaction between the squeeze flow and resin bleed out wasinvestigated and the predicted resin-rich pocket shape agreed closely with the experimentalobservations. The proposed sequential compaction flow methodology can be extended tomodeling various combinations of fiber tow gaps in AFP manufacturing to predict fiberwaviness, resin-rich regions, as well as ply thickness variation in the region around thefiber tow gaps.2. Sample Fabrication and Experimental Measurement2.1. Unidirectional Tow Compaction ExperimentsExperiments were performed on unidirectional samples with different geometriesdesigned to measure the tow spreading and to predict resin bleed out from the prepregduring compaction. The material used was tows of IM7/8552 (Hexcel, Stamford, CT, USA)with low tack behavior with a width of 6.57 mm and a thickness of 0.14 mm. To measurethe compaction of unidirectional tows in the early stages of manufacturing before resingelation, the first hold stage of the manufacturer’s cure cycle was used. This included a holdtemperature of 110 ◦C with that of an initial ramp of 3 ◦C/min. A pressure of 0.551 MPa(80 psi) was applied to the composite at a ramp of 0.034 MPa/min. Six configurations weremade for the unidirectional samples. The tow width and length were varied between one,Polymers 2024, 16, 31 4 of 21two, and four plies. This measured to be 0.14 mm, 0.28 mm, and 0.56 mm for the thicknessand the widths were 6.46 mm, 12.92 mm, and 25.84 mm, respectively. The length of thesamples was a constant 25.84 mm. Six samples were made for each of the configurationsand the experimentally measured results were averaged for each configuration.To analyze the tow spreading during cure, the thickness and width of the unidirectionalsamples were measured at 5, 15, 30, and 60 min into the hold stage by taking images of thetop x-y plane of the unidirectional samples using a digital microscope. At the end of thefirst isothermal stage of the cure cycle, the bleed-out resin was observed on the outside ofthe ply (Figure 2b). This resin was cut with a blade and its mass was measured. The imagestaken throughout the cure cycles were used to estimate the resin bleed out in fiber as wellas transverse to the fiber direction throughout the cure process.2.2. Compaction Experiments with an Embedded Fiber Tow GapA cross-ply configuration with an embedded tow gap was laid up and used to studythe compaction behavior around the region of the tow gap. The fiber tow stacking se-quence [0◦/90◦/0◦] was used with the centrally located 90◦ tow gap oriented in the ydirection. The width of the sample consisted of four fiber tows with 0◦ and two tows with90◦ layers (Figure 3). The overall dimensions of the fabricated sample before cure were25.15 mm × 25.15 mm × 0.40 mm. A hand roller was used to apply slight uniform contactforce to ensure proper contact in the layup. Once the top 0◦ layers were deposited, noadditional fiber spreading was observed and the 0◦ tows sank into the tow gap region inthe central location of the gap.Polymers 2024, 16, x FOR PEER REVIEW 4 of 22 2. Sample Fabrication and Experimental Measurement 2.1. Unidirectional Tow Compaction Experiments Experiments were performed on unidirectional samples with different geometries designed to measure the tow spreading and to predict resin bleed out from the prepreg during compaction. The material used was tows of IM7/8552 (Hexcel, Stamford, CT, USA) with low tack behavior with a width of 6.57 mm and a thickness of 0.14 mm. To measure the compaction of unidirectional tows in the early stages of manufacturing before resin gelation, the first hold stage of the manufacturer’s cure cycle was used. This included a hold temperature of 110 °C with that of an initial ramp of 3 °C/min. A pressure of 0.551 MPa (80 psi) was applied to the composite at a ramp of 0.034 MPa/min. Six configurations were made for the unidirectional samples. The tow width and length were varied between one, two, and four plies. This measured to be 0.14 mm, 0.28 mm, and 0.56 mm for the thickness and the widths were 6.46 mm, 12.92 mm, and 25.84 mm, respectively. The length of the samples was a constant 25.84 mm. Six samples were made for each of the configu-rations and the experimentally measured results were averaged for each configuration. To analyze the tow spreading during cure, the thickness and width of the unidirec-tional samples were measured at 5, 15, 30, and 60 min into the hold stage by taking images of the top x-y plane of the unidirectional samples using a digital microscope. At the end of the first isothermal stage of the cure cycle, the bleed-out resin was observed on the outside of the ply (Figure 2b). This resin was cut with a blade and its mass was measured. The images taken throughout the cure cycles were used to estimate the resin bleed out in fiber as well as transverse to the fiber direction throughout the cure process. 2.2. Compaction Experiments with an Embedded Fiber Tow Gap A cross-ply configuration with an embedded tow gap was laid up and used to study the compaction behavior around the region of the tow gap. The fiber tow stacking se-q ence [0°/90°/0°] was used with the centrally located 90° tow gap oriented in the y direc-tion. The width of the sample consisted of four fiber tows with 0° and two tows with 90° layers (Figure 3). The overall dimensions of the fabricated sample before cure were 25.15 mm × 25.15 mm × 0.40 mm. A hand roller was used to apply slight uniform contact force to ensure proper contact in the layup. Once the top 0° layers were deposited, no additional fiber spreading was observed and th 0° tows sank into the tow gap region in the central location of the g p. The same cure cycle was used to cure th tow gap sample, which was post-cured in the oven at 180 °C for tw hours. To observe he cross section of the fiber tow gap, the samples were cut and polished. To determine the ffects of the c mpaction on the cured morphology, the x-z plane of the samples wa analyzed u ing a Le ca DM6 upright micro-scope, and different ply features were measured, including the fiber angles in the top 0° tow, size, nd shape of the r sin-rich region, a well as ply thickness variations in the bot-tom 0° tow. Figure 3. Schematics of the manufactured fiber tow gap dimensions and stacking sequence. The dashed line indicates the 90º ply between the 0º plies in the laminate. Figure 3. Schematics of the manufactured fiber tow gap dimensions and stacki g eque ce. Thdashed line indicates the 90º ply between the 0º pli s in the laminate.The same cure cycle was used to cure the tow gap sample, which was post-cured in theoven at 180 ◦C for two hours. To observe the cross section of the fiber tow gap, the sampleswere cut and polished. To determine the effects of the compaction on the cured morphology,the x-z plane of the samples was analyzed using a Leica DM6 upright microscope, anddifferent ply features were measured, including the fiber angles in the top 0◦ tow, size, andshape of the resin-rich region, as well as ply thickness variations in the bottom 0◦ tow.3. Multiphysics FEA Simulation Framework for AFP Fiber Tow Preform CompactionThe interconnected nature of the cure and compaction process was studied via aunified process modeling approach in the form of a physics-based simulation that capturedthe chemo-rheological transformation of the resin, squeeze flow, and resin bleed out.Figure 4 shows a highly non-linear multivariable model in which chemo-rheological resinbehavior was used to determine the effective flow-compaction characteristics of the prepreg.Therefore, the proposed model was implemented in a commercially available FEA softwareABAQUS/Explicit 2021 (Dassualt Systemes, Vélizy-Villacoublay, France) using custom-built subroutines. The rheological and physical state properties, such as the degree ofcure, viscosity, fiber volume fraction, and fiber orientation, updated the in situ effectiveanisotropic viscosities of the fiber tow. The elements of the present model may be calibratedfor different elastic and rheological properties for different material systems. With a largenumber of factors involved in the model, future algorithms, such as smoothed-FEA andPolymers 2024, 16, 31 5 of 21machine learning, can be used to predict the deformation response of composites duringmanufacturing [30,31]. However, the present methodology is a more accessible approachfor the process modeling of composites [32,33].Polymers 2024, 16, x FOR PEER REVIEW 5 of 22 3. Multiphysics FEA Simulation Framework for AFP Fiber Tow Preform Compaction The interconnected nature of the cure and compaction process was studied via a uni-fied process modeling approach in the form of a physics-based simulation that captured the chemo-rheological transformation of the resin, squeeze flow, and resin bleed out. Fig-ure 4 shows a highly non-linear multivariable model in which chemo-rheological resin behavior was used to determine the effective flow-compaction characteristics of the pre-preg. Therefore, the proposed model was implemented in a commercially available FEA software ABAQUS/Explicit 2021 (Dassualt Systemes, Vélizy-Villacoublay, France) using custom-built subroutines. The rheological and physical state properties, such as the de-gree of cure, viscosity, fiber volume fraction, and fiber orientation, updated the in situ effective anisotropic viscosities of the fiber tow. The elements of the present model may be calibrated for different elastic and rheological properties for different material systems. With a large number of factors involved in the model, future algorithms, such as smoothed-FEA and machine learning, can be used to predict the deformation response of composites during manufacturing [30,31]. However, the present methodology is a more accessible approach for the process modeling of composites [32,33]. Figure 4. Coupled chemo-rheological and compaction model for predicting defect morphology in AFP-manufactured composites. 3.1. Chemo-Rheological Model of Thermosetting Prepreg The degree of cure and viscosity of resin govern the squeeze flow behavior of the prepreg during the compaction process [34]. No significant exothermic reaction was ob-served due to the small thickness [16]. The chemo-rheological model of resin provided the degree of cure, α, and the resin viscosity, µ. The modified autocatalytic resin kinetics model were used in the present work [35]: 𝑑𝛼𝑑𝑇 ൌ𝐴𝑒ି∆ாோ்𝛼௠ഀሺ1 െ 𝛼ሻ௡ഀ1 ൅ 𝑒஼ഀሼఈିሺఈ೎బାఈ಴೅்ሻሽ (1)where ∆𝐸 ൌ 66,500 ୎୫୭୪∙୏ is the activation energy, 𝐴 ൌ 153,000ଵୱ is a pre-exponential cure rate coefficient, and R is the gas constant. 𝑚ఈ ൌ 0.813 is the first exponential coef-ficient, 𝑛ఈ ൌ 2.74 is a second exponential coefficient, 𝐶ఈ ൌ 4.31 is a diffusion constant, 𝛼஼଴ ൌ െ1.684 is the critical degree of cure at T = 0 K, and finally, 𝛼஼் ൌ 0.005473 is a constant that governs the increase in the critical resin degree of cure with temperature, where 𝛼 is the degree of cure and 𝑇 is the imposed temperature. The initial degree of cure of the composite samples was measured using digital scanning calorimetry (DSC), which determined it to be 0.145. Figure 4. Coupled chemo-rheological and compaction model for predicting defect morphology inAFP-manufactured composites.3.1. Chemo-Rheological Model of Thermosetting PrepregThe degree of cure and viscosity of resin govern the squeeze flow behavior of theprepreg during the compaction process [34]. No significant exothermic reaction wasobserved due to the small thickness [16]. The chemo-rheological model of resin providedthe degree of cure, α, and the resin viscosity, µ. The modified autocatalytic resin kineticsmodel were used in the present work [35]:dαdT=Ae− ∆ERT αmα(1− α)nα1+ eCα{α−(αc0+αCT T)}(1)where ∆E = 66, 500 Jmol·K is the activation energy, A = 153, 0001s is a pre-exponential curerate coefficient, and R is the gas constant. mα = 0.813 is the first exponential coefficient,nα = 2.74 is a second exponential coefficient, Cα = 4.31 is a diffusion constant, αC0 = −1.684is the critical degree of cure at T = 0 K, and finally, αCT = 0.005473 is a constant that governsthe increase in the critical resin degree of cure with temperature, where α is the degree ofcure and T is the imposed temperature. The initial degree of cure of the composite sampleswas measured using digital scanning calorimetry (DSC), which determined it to be 0.145.As the resin cures, the viscosity increases exponentially. The function for the viscosityuses the degree of cure and temperature as shown in Equation (2):µ = µ∞ekiαeURT (2)where µ∞ = 83× 10−8 MPa·s is a viscosity constant, U = 49, 100 kJ is the activation en-ergy of the viscosity, and k1 = 25.49kJmol and k2 = −1.32 kJmol are temperature-independentconstants determined via the experimental data [36]. The applied temperature, the evo-lution of the degree of cure, and the viscosity is shown in Figure 5. The degree of curewas seen only reaching a 17% cure at the end of the hold stage, which means the resinremains in the viscous state during the experiment [37,38]. Upon gelation, the viscosity in-creases exponentially and the material develops solid viscoelastic properties. Therefore, theflow-compaction analysis was restricted to the first stage of the cure cycle, since the largenon-linear deformation and resin flow will develop prior to gelation. Also, the chemicalPolymers 2024, 16, 31 6 of 21and thermally induced shrinkages that develop prior to gelation will be relaxed due to theliquid resin state [39,40].Polymers 2024, 16, x FOR PEER REVIEW 6 of 22 As the resin cures, the viscosity increases exponentially. The function for the viscosity uses the degree of cure and temperature as shown in Equation (2): 𝜇 ൌ 𝜇ஶ𝑒௞೔ఈ𝑒௎ோ் (2)where 𝜇ஶ ൌ 83 ൈ 10ି଼ MPa ∙ 𝑠 is a viscosity constant, 𝑈 ൌ 49,100 kJ is the activation en-ergy of the viscosity, and 𝑘ଵ ൌ 25.49 ୩୎୫୭୪ and 𝑘ଶ ൌ െ1.32୩୎୫୭୪ are temperature-independent constants determined via the experimental data [36]. The applied temperature, the evolu-tion of the degree of cure, and the viscosity is shown in Figure 5. The degree of cure was seen only reaching a 17% cure at the end of the hold stage, which means the resin remains in the viscous state during the experiment [37,38]. Upon gelation, the viscosity increases exponentially and the material develops solid viscoelastic properties. Therefore, the flow-compaction analysis was restricted to the first stage of the cure cycle, since the large non-linear deformation and resin flow will develop prior to gelation. Also, the chemical and thermally induced shrinkages that develop prior to gelation will be relaxed due to the liquid resin state [39,40]. Figure 5. The applied temperature and the evolution of the degree of cure and viscosity using the thermo-rheological model. 3.2. Constitutive Squeeze Flow Model during Prepreg Fiber Tow Compaction When heated above the instantaneous glass transition temperature, the resin be-comes a viscoelsatic fluid, while rigid continuous fibers result in anisotropic viscous be-havior of the uncured prepreg. Specifically, the inextensible fibers lead to the axial viscos-ity being six orders of magnitude higher than transverse and shear viscosity [29]. There-fore, the constitutive model simulates the unidirectional material with transversely iso-tropic properties. The flow-compaction model incorporated visco-hyperelastic behavior to capture the contribution of the liquid resin and included an elastic part and a viscous part [41]. The elastic part was calculated from a hyperelastic potential energy equation, 𝜓, using the five invariants of the Cauchy–Green deformation tensor, C. 𝜎ො ൌ 𝜎ො𝑒 ൅ 𝜎ො𝑣 ൌ 2 ൬𝜕𝜓𝑒𝜕𝐶෠ ൅𝜕𝜓𝑣𝜕𝐶෠ሶ ൰ ൌ 2 ෍ሺ5𝛼ൌ1𝜕𝜓𝑒𝜕𝐼𝛼𝜕𝐼𝛼𝜕𝐶෠ ሻ ൅ 𝜎ො𝑣 ൌ 2𝐽 ൬𝐹ො ∙𝜕𝜓𝑒𝜕𝐶෠ ∙ 𝐹ො𝑇൰ ൅ 𝜎ො𝑣 (3)Figure 5. The a plied temperature and th evolution of the degree of cure and viscosity using thethermo-rheological model.3.2. Constitutive Squeeze Flow Model during Prepreg Fiber Tow CompactionWhen heated above the instantaneous glass transition temperature, the resin becomesa viscoelsatic fluid, while rigid continuous fibers result in anisotropic viscous behaviorof the uncured prepreg. Specifically, the inextensible fibers lead to the axial viscositybeing six orders of magnitude higher than transverse and shear viscosity [29]. Therefore,the constitutive model simulates the unidirectional material with transversely isotropicproperties. The flow-compaction model incorporated visco-hyperelastic behavior to capturethe contribution of the liquid resin and included an elastic part and a viscous part [41]. Theelastic part was calculated from a hyperelastic potential energy equation, ψ, using the fiveinvariants of the Cauchy–Green deformation tensor, C.σˆ = σˆe + σˆv = 2(∂ψe∂Cˆ+∂ψv∂.Cˆ)= 25∑α=1(∂ψe∂Iα∂Iα∂Cˆ) + σˆv =2J(Fˆ·∂ψe∂Cˆ·FˆT)+ σˆv (3)Through a push-forward operation, the stress becomes a function of the deformationgradient, Fˆ, and its Jacobian, J. The fiber direction was solved using the linear-elasticbehavior from the fiber instead of the homogenized composite since it is governed byinextensible fibers. The constitutive equation for the stress is given by Equation (4) [42].σe11 = 2µ f ε11 + λ f tr(ε) (4)where ε11 is the strain in the fiber direction and tr(ε) is the trace of the strain. The constantsµ and λ are related to the fiber material properties asµ f =E f2(1+ ν f) (5)λ f =µ f ν f(1− 2ν f) (6)Polymers 2024, 16, 31 7 of 21where E f = 168 GPa and ν f = 0.027 are the modulus of elasticity and Poisson’s ratio of theIM7 fiber, respectively.For the transverse and shear properties, a transversely isotropic neo-Hookean modelwas used to calculate the stress of the current configuration. The strain energy potentialused for the 2–3 plane for the stress is shown in Equation (7).ψe =12µ(I1 − 3)− µln(J) + 12λ(J − 1)2 + [β+ ζln(J) + κ(I4 − 1)](I4 − 1)− 12β(I5 − 1) (7)I1–I5 are the invariants of the Cauchy–Green strain tensor. The material constants, λ, µ,β, ζ, and κ, are material constants derived from the material constants of the homogenizedcomposites using Equations (8)–(11) [43]. The model uses the invariants of the Cauchy–Green strain tensor.λ =E22(ν+ nν2)m(1+ ν)(8)µ =E222(1+ ν)(9)β = µ− G23 (10)ζ =E22ν(1− n)4m(1+ ν)(11)κ =E11(1− ν)8m− λ+ 2µ8+β2− ζ (12)m = 1− ν− 2nν2 (13)n =E11E22(14)where E11 = 25 MPa and E22 = 1 Pa are the Young’s modulus in the fiber and transverse tothe fiber directions of the homogenized uncured composite to ensure the correct bendingstiffness and the stability of the FEA, respectively. ν = 0.01, and G23 = 1 MPa are thePoisson’s ratio and the shear modulus of the homogenized composite, respectively [41].The Cauchy stress tensor can then be derived by differentiating the strain energy potentialand pushing forward with a double multiplication of the deformation gradient provided byAbaqus [43]. Since the flow and the hyperelasticity constitutive equations are dependent onthe fiber direction, the fiber orientation is updated every step. A model assumed that thefiber orientation follows an affine motion based on the deformation gradient characterizedby the following equation [44]:→P =Fˆ·→p0∥∥∥Fˆ·→p0∥∥∥ (15)where→p is the fiber direction vector and→p0 is the initial fiber direction vector. The fiberdirection is used to inform the anisotropic component of the hyperelastic model, where itbecomes the variable for the function of stress based on the strain energy potential [24].The microscopic fibers suspended in resin show time-dependent behavior basedon the strain rate effects and resin viscous behavior. Research from Kelly [28] used themultiplicative decomposition of apparent viscosity to describe the squeeze flow. To quantifythe homogenized prepreg tape response, the proposed approach for the viscous term usesmultiplicative components that consist of strain- and strain rate-dependent terms [28,29,41].The strain dependent terms take into account the ply geometry and the strain rate describedas the resin behavior [41]. The viscous stress term followed the behavior as shown inEquation (16).σvij = ηrateij · ηplyij · ηmicroij ·.ˆεij (16)Polymers 2024, 16, 31 8 of 21where ηˆrate is a strain rate-dependent viscosity tensor component and.ˆε is the strain ratetensor. ηˆply is the term responsible for ply geometry and ηˆmicro is the phenomenologicalstrain-dependent term derived from micromechanical considerations at the micro level.During the curing, the fiber–resin system is assumed to act as a power-law viscousfluid. Previous work described the anisotropic viscosity of oriented discontinuous fiberssuspended in Newtonian fluid [29]. The same principles may be applied to continuousfiber with a finite length. Therefore, a tensorial viscosity approach was used to model theηˆrate term where the resin matrix follows a power-law behavior. Since the composite towis transversely isotropic, the in-plane directions (transverse to the fiber) were assumed tohave the same properties, while the fiber direction is assumed to be inextensible.In Nixon’s work [23], the strain rate term used phenomenological parameters that weredetermined experimentally. The proposed rate term for the current study uses effectiveproperties of the composite derived from the anisotropic viscosity as a function of thestrain rate, fiber volume fraction, and a power-law exponent using the following tensorcomponents [29].ηrate11 = ηresin2−m f√f1−√fm( LD)m+1.ϵ11m−1 (17)ηrate22 = ηrate33 = ηresin2m+1[1−√f]−m.ϵ22m−1 (18)ηrate23 = ηresin[1−√f]−m.γ23m−1 (19)ηrate12 = ηrate13 = ηresin2−m1−√f1−√fm .γ12m−1 (20)where f is the fiber volume fraction, L is the fiber length, D is the fiber diameter, and m = 0.5is the power-law exponent.The ply geometry term is derived from an analytical solution by Kelly [28] anddescribes the geometry and surface conditions of the ply. A frictionless boundary conditionwas assumed for the solution since the scope of the curing and compaction has the resin asa fluid. A solution to the work, rearranged by Belnoue et al. [41], was used in this study, asshown in the equations below.ηply11 = ηˆply12 = ηˆply13 = ηˆply23 = 1 (21)ηply22 = 2(w0h0)2e−4ε22 (22)ηply33 = 2(w0h0)2e−4ε33 (23)where w0 is the initial width of the ply, and h0, is the initial height of the ply.The micro term depends on the phenomenological parameters that govern the flowregimes between an incompressible solid to a compressible solid due to resin bleed out inthe fiber direction as a result of fiber locking during compaction [45].ηmicro11 = ηmicro12 = ηmicro13 = ηmicro23 = 1 (24)ηmicro22 = 2√χleε22 k( k√χ f eε22 − k)2+ 3 (25)Polymers 2024, 16, 31 9 of 21ηmicro33 = 2√χleε33 k( k√χ f eε22 − k)2+ 3 (26)where k is a stepwise function of the temperature, χl = 0.63 is the aspect ratio duringlocking, and χ f = 0.785 is the final aspect ratio based on the maximum packing fraction ofthe composite [46]. The packing in this case is interpreted as the fiber volume fraction.3.3. Finite Element Modeling of Compaction in Unidirectional Tows and Fiber Tow Gap SamplesThe proposed flow-compaction constitutive behavior was validated using the ex-perimental results from unidirectional fiber tows with varying widths and thicknesses(Figure 6a). The same geometry was modeled and simulated using FEA with the proposedvisco-hyperelastic behavior (Figure 6b). There were 60 to 200 C3D8T elements dependingon the width of the composite, with one element through the thickness for all configura-tions. The model was constrained in the z-direction to simulate the rigid tool used in theautoclave curing process. The strain was measured using the average deformation of thenodes on the top of the ply.Polymers 2024, 16, x FOR PEER REVIEW 9 of 22 𝜂௣௟௬ଶଶ ൌ 2 ൬𝑤଴ℎ଴ ൰ଶ𝑒ିସఌమమ (22)𝜂௣௟௬ଷଷ ൌ 2 ൬𝑤଴ℎ଴ ൰ଶ𝑒ିସఌయయ (23)where w0 is the initial width of the ply, and h0, is the initial height of the ply. The micro term depends on the phenomenological parameters that govern the flow regimes between an incompressible solid to a compressible solid due to resin bleed out in the fiber direction as a result of fiber locking during compaction [45]. 𝜂௠௜௖௥௢భభ ൌ 𝜂௠௜௖௥௢భమ ൌ 𝜂௠௜௖௥௢భయ ൌ 𝜂௠௜௖௥௢మయ ൌ 1 (24)𝜂௠௜௖௥௢మమ ൌ 2ඥ𝜒௟𝑒ఌమమ𝑘 ൭ቆ𝑘ඥ𝜒௙𝑒ఌమమ െ 𝑘ቇଶ൅ 3൱ (25)𝜂௠௜௖௥௢యయ ൌ 2ඥ𝜒௟𝑒ఌయయ𝑘 ൭ቆ𝑘ඥ𝜒௙𝑒ఌమమ െ 𝑘ቇଶ൅ 3൱ (26)ere k is a ste ise f ctio of t e te erat re, 𝜒௟ ൌ 0.63 is the aspect ratio during locki g, a 𝜒௙ ൌ 0.785 is the final aspect ratio based on the maximum packing fraction of the composite [46]. The packing in this case is interpreted as the fiber volume fraction. 3.3. Finite Element Modeling of Compaction in Unidirectional Tows and Fiber Tow Gap Samples The proposed flow-compaction constitutive behavior was validated using the exper-imental results from unidirectional fiber tows with varying widths and thicknesses (Fig-ure 6a). The same geometry was modeled and simulated using FEA with the proposed visco-hyperelastic behavior (Figure 6b). There were 60 to 200 C3D8T elements depending on the width of the composite, with one element through the thickness for all configura-tions. The model was constrained in the z-direction to simulate the rigid tool used in the autoclave curing process. The strain was measured using the average deformation of the nodes on the top of the ply. Figure 6. (a) The fully cured samples of the unidirectional experiments and the aspect ratio in order from left to right and labeled with the aspect ratio (𝜉ሻ: one ply thick (𝜉 = 1.0), two ply thick (𝜉 = 0.5), four ply thick (𝜉 = 0.25), two ply wide (𝜉 = 2.0), and four ply thick (𝜉 = 4.0) (b) Schematics of the unidirectional FEA models, where it was varied by the same aspect ratios. (b) Schematics of the unidirectional experiments, where the width and thicknesses were varied. Figure 6. (a) The fully cured samples of the unidirectional experiments and the aspect ratio in orderfrom left to right and labeled with the aspect ratio ( ξ): one ply thick (ξ = 1.0), two ply thick (ξ = 0.5),fo r ly t ick (ξ 0.25), t o ly i e (ξ 2.0), and four ply thick (ξ = 4.0) (b) Schematics of thei i , r it s aried by the sa e aspect ratios. (b) Schematics of thei irecti l ri ts, r t i t t ic esses ere varied.The tow gap configuration was used for understanding the effect of resin bleed outon the cured morphology around the gap region and used the same stacking sequenceand geometry as the experimentally manufactured composite (Figure 7). To incorporatethe initial sinking of the top 0◦ ply created via a manually applied roller during the layup,the initial slope was incorporated by connecting the bottom and top 0◦ plies at the middleof the gap. Symmetrical boundary conditions were used on the x-z plane of the 0◦ pliestowards the gap and one side towards of the y-z plane to reduce processing time. Tosimulate the tool, the bottom of the laminate model was constrained in the z-direction.The model consisted of 2088 C3D8RT elements to capture the non-linear deformation.Frictionless contact between the layers of 0◦ and 90◦ plies was used. Each ply had anominal 0.14 mm in thickness with five elements through the thickness. The models used adensity for the homogenized composite of 1590 kg/m3 with a mass scaling of 10 to reducethe amount of time to complete the FEA simulations. No significant rise in kinetic energywas found with the addition of the mass scaling. The material properties for both theIM7 carbon fibers and the 8552 resin were derived from the literature and are utilizedPolymers 2024, 16, 31 10 of 21in the subroutines [19,35,36]. Geometric non-linearity was activated for both models toaccommodate the large deformations during the compaction.Polymers 2024, 16, x FOR PEER REVIEW 10 of 22 The tow gap configuration was used for understanding the effect of resin bleed out on the cured morphology around the gap region and used the same stacking sequence and geometry as the experimentally manufactured composite (Figure 7). To incorporate the initial sinking of the top 0° ply created via a manually applied roller during the layup, the initial slope was incorporated by connecting the bottom and top 0° plies at the middle of the gap. Symmetrical boundary conditions were used on the x-z plane of the 0° plies towards the gap and one side towards of the y-z plane to reduce processing time. To sim-ulate the tool, the bottom of the laminate model was constrained in the z-direction. The model consisted of 2088 C3D8RT elements to capture the non-linear deformation. Fric-tionless contact between the layers of 0° and 90° plies was used. Each ply had a nominal 0.14 mm in thickness with five elements through the thickness. The models used a density for the homogenized composite of 1590 kg/m3 with a mass scaling of 10 to reduce the amount of time to complete the FEA simulations. No significant rise in kinetic energy was found with the addition of the mass scaling. The material properties for both the IM7 car-bon fibers and the 8552 resin were derived from the literature and are utilized in the sub-routines [19,35,36]. Geometric non-linearity was activated for both models to accommo-date the large deformations during the compaction. Figure 7. The schematics of the fiber tow gap model with boundary conditions, applied pressure The green plies indicate 0° and the blue ply indicates 90°. Internal resin pressure is applied to the gap in the middle of the 0° plies. 4. Results 4.1. Experimental Quantification of Resin Bleed Out in Unidirectional Prepreg Tows Six configurations with six samples each of the unidirectional composites were com-pacted and cured in the first 90 min of the cure cycle (Figure 5) A tow aspect ratio in uni-directional tow was introduced based on the number of tows in the width and through the thickness: 𝑁௪𝑁் ൌ 𝜉 (27)where Nw is the number of plies in the tow width (transverse of the fiber direction), NT is the number of tows through the thickness of the composite, and 𝜉 is the geometric aspect ratio. For example, a sample with a thickness of four tows and a width of one tow had 𝜉 = 0.25. The experimental samples and corresponding simulations used the proposed fiber tow aspect notation. Resin bleeds out of the porous fiber bed when heat and pressure are applied [47]. This resin bleed out is a complex process which depends on resin viscosity, local fiber volume fraction, applied autoclave pressure, and pressure distribution throughout the laminate. In the present study, a phenomenological approach was proposed which con-sidered the amount of resin bleed out as a function of time for the given cure cycle. The experimental results of unidirectional tow compaction demonstrated that resin bleed out Figure 7. The schematics of the fiber tow gap model with boundary conditions, applied pressure Thegreen plies indicate 0◦ and the blue ply indicates 90◦. Internal resin pressure is applied to the gap inthe middle of the 0◦ plies.4. Results4.1. Experimental Quantification of Resin Bleed Out in Unidirectional Prepreg TowsSix configurations with six samples each of the unidirectional composites were com-pacted and cured in the first 90 min of the cure cycle (Figure 5) A tow aspect ratio inunidirectional tow was introduced based on the number of tows in the width and throughthe thickness:NwNT= ξ (27)where Nw is the number of plies in the tow width (transverse of the fiber direction), NT isthe number of tows through the thickness of the composite, and ξ is the geometric aspectratio. For example, a sample with a thickness of four tows and a width of one tow hadξ = 0.25. The experimental samples and corresponding simulations used the proposed fibertow aspect notation.Resin bleeds out of the porous fiber bed when heat and pressure are applied [47]. Thisresin bleed out is a complex process which depends on resin viscosity, local fiber volumefraction, applied autoclave pressure, and pressure distribution throughout the laminate.In the present study, a phenomenological approach was proposed which considered theamount of resin bleed out as a function of time for the given cure cycle. The experimentalresults of unidirectional tow compaction demonstrated that resin bleed out develops at theinitial stages of the manufacturing process where the flow was considered separately in thelongitudinal and transverse to the fiber directions. The amount of resin that came out inthe respective directions were cut from the composite and weighed. The mass loss in eachdirection was calculated as a ratio of the measured resin mass.The average bleed-out mass per unit of surface area, based on the initial dimensions,was measured. While the mass loss for the transverse resin weighs more, when thecorresponding area is considered, the resin flowing longitudinally along the fiber directionwas responsible for a larger fraction of mass loss per surface area. Longitudinal bleedout occurred through the surface as normal to the fibers, while transverse flow occurredon the side of the prepreg tape—no transverse flow occurred due the tool surface onthe bottom and the release film on top. Greater resin loss in the longitudinal directioncorresponds to the higher permeability in the fiber direction compared to permeability in thetransverse direction [48]. The single tow configuration (ξ = 1.0) shows that the longitudinaldirection bleeds out more resin mass per unit area, with a coefficient ρP(L) = 0.400 mg/mm2,compared to the transverse direction, with a mass loss coefficient ρP(T) = 0.0198 mg/mm2 at90 min into the cure cycle. The area of resin around a single tow (Figure 2b) was measuredPolymers 2024, 16, 31 11 of 21transversely and longitudinally over time and used as a scale to estimate the mass loss overtime per unit area over time (Figure 8). Functions representing the mass loss coefficientover time in longitudinal, ρP(L)(t), and transverse, ρP(T)(t), directions were based on thelogistic curve functions in Equation (28). Note that only the transverse resin bleed out waspresent around the surface area of the gap (Figure 3).ρP(T)(t) =A(T)11+ e A(T)2−tA(T)3 (28a)ρP(L)(t) =A(L)11+ e A(L)2−tA(L)3 (28b)where A(T)1 = 0.0195 mg, A(T)2 = 33.542 min, and A(T)3 = 3.10 min are transverse fittingparameters and A(L)1 = 0.0293 mg, A(L)2 = 43.881 min, and A(L)3 = 11.78 are the longitudinalparameters.Polymers 2024, 16, x FOR PEER REVIEW 11 of 22 develops at the initial stages of the manufacturing process where the flow was considered separately in the longitudinal and transverse to the fiber directions. The amount of resin that came out in the respective directions were cut from the composite and weighed. The mass loss in each direction was calculated as a ratio of the measured resin mass. The average bleed-out mass per unit of surface area, based on the initial dimensions, was measured. While the mass loss for the transverse resin weighs more, when the corre-sponding area is considered, the resin flowing longitudinally along the fiber direction was responsible for a larger fraction of mass loss per surface area. Longitudinal bleed out oc-curred through the surface as normal to the fibers, while transverse flow occurred on the side of the prepreg tape—no transverse flow occurred due the tool surface on the bottom and the release film on top. Greater resin loss in the longitudinal direction corresponds to the higher permeability in the fiber direction compared to permeability in the transverse direction [48]. The single tow configuration (𝜉 = 1.0) shows that the longitudinal direction bleeds out more resin mass per unit area, with a coefficient ?̅?௉ሺ௅ሻ = 0.400 mg/mm2, com-pared to the transverse direction, with a mass loss coefficient ?̅?௉ሺ்ሻ = 0.0198 mg/ m2 at 90 min into the cure cycle. The area of resin around a singl tow (Figure 2b) was measured transversely and longitudinally over time and used as a scale to estimate the mass loss over time per unit area over time (Figure 8). Functions representing the mass loss coeffi-cient over time in longitudinal, ?̅?௉ሺ௅ሻሺ𝑡ሻ, and transverse, ?̅?௉ሺ்ሻሺ𝑡ሻ, directions were based on the logistic curve functions in Equation (28). Note that only the transverse resin bleed out was present around the surface area of the gap (Figure 3). ?̅?௉ሺ்ሻሺ𝑡ሻ ൌ 𝐴ሺ்ሻଵ൭1 ൅ 𝑒஺ሺ೅ሻమି௧஺ሺ೅ሻయ ൱ (28a)?̅?௉ሺ௅ሻሺ𝑡ሻ ൌ 𝐴ሺ௅ሻଵ൭1 ൅ 𝑒஺ሺಽሻమି௧஺ሺಽሻయ ൱ (28b)where A(T)1 = 0.0195 mg, A(T)2 = 33.542 min, and A(T)3 = 3.10 min are transve se fitting pa-rameters and A(L)1 = 0.0293 mg, A(L)2 = 43.881 min, and A(L)3 = 11.78 are the longitudi al parameters. Figure 8. An estimated mass loss fraction over time of the fiber tow gap using experimental data from unidirectional experiments. 00.010.020.0300.10.20.30.40.530 50 70 90Transverse areal mass bleed out (mg/mm2) Longitudinal areal mass bleed out (mg/mm2)Time (min)LongitudinalTranverseFigure 8. An estimated ma loss fraction over time of the fiber tow gap using experimental datafrom unidirectional experiments.The experimental data shows that the resin begins flowing between 20 and 30 mininto the cure cycle before plateauing due to decreased permeability and increased viscosity.The resin mass loss data was also used to quantify the fiber volume fraction as a functionof the through-thickness strain. An average initial value of the fiber volume fraction of0.55 was derived from thermogravimetric (TGA) analysis [49]. The initial weight of theresin was determined using the matrix volume fraction based on TGA analysis, and theknown densities of the matrix and the fiber was determined via the rule of mixtures. Thechange in width and length and the known initial volume of a single unidirectional tow(ξ = 1.0) was used to calculate the through-thickness strain, ε33 over time. This allowedto fit the fiber volume with respect to the compaction strain as shown in Figure 9 as anexponential plateau:Vf (ε33) = Vf0 + B1 ∗ e(−B2ε33) (29)where B1 = 0.0673 and B2 = 0.0084 are fitting parameters, ε33 is the strain in the com-paction direction, and Vf0 is the initial fiber volume fraction. The fiber volume fractionrapidly increased at the early stages of compaction and plateaus as the permeability de-Polymers 2024, 16, 31 12 of 21creased and resin viscosity increased. Furthermore, the resin bleed out present at thebeginning of the cure cycle influenced the squeeze flow via the evolution of the fibervolume fraction, which affects the anisotropic apparent viscosity in Equations (17)–(20).The fiber volume fraction formulation was measured for the prescribed cure cycle andmaterial system. The same methods can be recreated with different temperature profilesand composite materials. With the resin bleed out and the development of the fiber volumefraction for the current cure cycle established, a single-phase model was made wherethe resin is not explicitly modeled. Modeling the flow of resin explicitly can be achievedwith a higher resolution model. However, this would require computationally expensiverepresentative volume elements to model the microscopic behavior. The present analyticalequation allows for an adequate estimate of the evolution of the fiber volume fraction.Polymers 2024, 16, x FOR PEER REVIEW 12 of 22 The experimental data shows that the resin begins flowing between 20 and 30 min into the cure cycle before plateauing due to decreased permeability and increased viscos-ity. The resin mass loss data was also used to quantify the fiber volume fraction as a func-tion of the through-thickness strain. An average initial value of the fiber volume fraction of 0.55 was derived from thermogravimetric (TGA) analysis [49]. The initial weight of the resin was determined using the matrix volume fraction based on TGA analysis, and the known densities of the matrix and the fiber was determined via the rule of mixtures. The change in width and length and the known initial volume of a single unidirectional tow (𝜉 = 1.0) was used to calculate the through-thickness strain, 𝜀ଷଷ over time. This allowed to fit the fiber volume with respect to the compaction strain as shown in Figure 9 as an exponential plateau: 𝑉௙ሺ𝜀ଷଷሻ ൌ 𝑉௙బ ൅ 𝐵ଵ ∗ 𝑒ቀି஻మఌయయ ቁ (29)where 𝐵ଵ ൌ 0.0673 and 𝐵ଶ ൌ 0.0084 are fitting parameters, 𝜀ଷଷ is the strain in the com-paction direction, and 𝑉௙బ is the initial fiber volume fraction. The fiber volume fraction rapidly increased at the early stages of compaction and plateaus as the permeability de-creased and resin viscosity increased. Furthermore, the resin bleed out present at the be-ginning of the cure cycle influenced the squeeze flow via the evolution of the fiber volume fraction, which affects the anisotropic apparent viscosity in Equations (17)–(20). The fiber volume fraction formulation was measured for the prescribed cure cycle and material sys-tem. The same methods can be recreated with different temperature profiles and compo-site materials. With th resin bleed out and the development of th fiber volume fraction fo the current cure cycl established, a single-phase model was made where the re in is not xplicitly m d led. Modeling the flow of resin explicitly can be achieved with a higher resolution model. However, this would require computationally expensive representative volume elements to model the microscopic behavior. The present analytical equation al-lows for an adequate estimate of the evolution of the fiber volume fraction. Figure 9. The fiber volume fraction plotted with respect to the strain. 4.2. Modeling and Validation of Compaction Behavior in Unidirectional Tows The compaction results of the unidirectional tows showed that the thicker samples display more tow spreading in comparison to the tows with a higher width. For a config-uration of a single tow (𝜉 = 1), the maximum compaction strain was shown to be 0.053 at 90 min into the cure cycle. The largest compaction strain, ε33 = 0.137, was found for the four tows arranged in the thickness direction (𝜉 = 0.25), while the smallest strain ε33 = 0.012 was found for the four tows arranged in the width direction (𝜉 = 4.0). The range in the Figure 9. The fiber volume fraction plotted with respect to the strain.4.2. Modeling and V l dation of Compaction Behavior in Unidirectional TowsThe compaction results of the unidirecti nal t s showed t at the thicker samplesdisplay more tow spreading in comparison to the tows with a higher width. For a configu-ration of a single tow (ξ = 1), the maximum compaction strain was shown to be 0.053 at90 min into the cure cycle. The largest compaction strain, ε33 = 0.137, was found for the fourtows arranged in the thickness direction (ξ = 0.25), while the smallest strain ε33 = 0.012 wasfound for the four tows arranged in the width direction (ξ = 4.0). The range in the observedcompaction strain shows the importance of the tow geometry, and more specifically, thethickness of the ply, on the squeeze flow behavior.The undeformed and deformed configuration of the unidirectional models are shownin Figure 10. The baseline configuration for the unidirectional models with one ply (ξ = 1.0)shows the thickness decreased and the tow spread at the Y-direction (transverse to thefibers). The modeling results in terms of the through-thickness compaction strains werecompared with the experimental measurements to validate the proposed flow-compactionmodel. The same trend between the experimental and numerical results demonstrated thatthe transverse spreading increased, with more plies through the thickness, and decreasedwith more tows across the width.The through-thickness strains, ε33, in the FEA models of unidirectional tows werequantified using the average displacement on the top y-x surface and the known initialthicknesses. Figure 11a shows the rapid decay of the through-thickness strain, ε33, at30 min into the hold stage with respect to the aspect ratio. The tow thickness during thecompaction simulations and the experimental measurements followed a non-linear visco-hyperelastic curve and decreased with the aspect ratio (Figure 11b). Both the experimentaland modeling prediction of compaction agreed closely that up to 90 min of the hold stagewas observed, and deviation was noticed at the end of the hold stage. The inclusion ofupdated fiber volume fraction as a function of the compaction strain (Equation (29)), due toresin bleed out, resulted in improved accuracy of the tow compaction strain (Figure 11a).Polymers 2024, 16, 31 13 of 21Polymers 2024, 16, x FOR PEER REVIEW 13 of 22 observed compaction strain shows the importance of the tow geometry, and more specif-ically, the thickness of the ply, on the squeeze flow behavior. The undeformed and deformed configuration of the unidirectional models are shown in Figure 10. The baseline configuration for the unidirectional models with one ply (ξ = 1.0) shows the thickness decreased and the tow spread at the Y-direction (transverse to the fibers). The modeling results in terms of the through-thickness compaction strains were compared with the experimental measurements to validate the proposed flow-com-paction model. The same trend between the experimental and numerical results demon-strated that the transverse spreading increased, with more plies through the thickness, and decreased with more tows across the width. Figure 10. Undeformed and deformed configuration of tows from compaction simulation: a one-tow wide and thick composite (𝜉 = 1.0), a four-tow thick composite (𝜉 = 0.25), and a four-tow wide composite (𝜉 = 4.0). The through-thickness strains, ε33, in the FEA models of unidirectional tows were quantified using the average displacement on the top y-x surface and the known initial thicknesses. Figure 11a shows the rapid decay of the through-thickness strain, ε33, at 30 min into the hold stage with respect to the aspect ratio. The tow thickness during the com-paction simulations and the experimental measurements followed a non-linear visco-hy-perelastic curve and decreased with the aspect ratio (Figure 11b). Both the experimental and modeling prediction of compaction agreed closely that up to 90 min of the hold stage was observed, and deviation was noticed at the end of the hold stage. The inclusion of updated fiber volume fraction as a function of the compaction strain (Equation (29)), due to resin bleed out, resulted in improved accuracy of the tow compaction strain (Figure 11a). Figure 10. Undeformed and deformed configuration of tows fro compaction simulation: a one-towwide and thick composite (ξ = 1.0), a four-tow thick composite (ξ = 0.25), and a four-tow wide composite(ξ = 4.0).Polymers 2024, 16, x FOR PEER REVIEW 14 of 22 (a) (b) Figure 11. (a) Comparison of compaction strain in tows with different aspect ratios. (b) Compaction strain evolution during cure time in tows with different aspect ratios. 4.3. Squeeze Flow Simulation of Layup with Embedded Tow Gap To further validate the proposed compaction constitutive model, the region around the fiber tow gap was analyzed. The initial undeformed configuration of the fiber tow gap model is shown in Figure 12a, which demonstrates the layup compaction during the sim-ulation. The initial FEA simulation did not consider coupling between the squeeze flow and resin bleed out, which is discussed in the following section. The top ply sank into the fiber tow gap, creating a curvilinear triangular void near the edge of the 90° ply. Early in the cure cycle (before 13 min), the gap closed rapidly until the autoclave pressure reached 0 1 2 3 4Tow aspect ratio ( )00.020.040.060.080.10.120.140.160.18ExperimentalWith Variable VfWithout Variable V fFigure 11. (a) Comparison of compaction strain in tows with different aspect ratios. (b) Compactionstrain evolution during cure time in tows with different aspect ratios.Polymers 2024, 16, 31 14 of 214.3. Squeeze Flow Simulation of Layup with Embedded Tow GapTo further validate the proposed compaction constitutive model, the region aroundthe fiber tow gap was analyzed. The initial undeformed configuration of the fiber towgap model is shown in Figure 12a, which demonstrates the layup compaction during thesimulation. The initial FEA simulation did not consider coupling between the squeeze flowand resin bleed out, which is discussed in the following section. The top ply sank into thefiber tow gap, creating a curvilinear triangular void near the edge of the 90◦ ply. Early inthe cure cycle (before 13 min), the gap closed rapidly until the autoclave pressure reachedthe maximum 0.541 MPa (80 psi). After the initial gap closure, the gap volume decreasedslowly until the end of the isothermal hold stage. Tow spreading was observed at the edgeof the 90◦ ply.Polymers 2024, 16, x FOR PEER REVIEW 15 of 22 the maximum 0.541 MPa (80 psi). After the initial gap closure, the gap volume decreased slo ly until the end of the isothermal hold stage. Tow spreading was observed at the edge of the 90° ply. The simulation results with only squeeze flow were compared to the experimentally manufactured sample with the fiber tow gap. The micrograph of the area of interest showed the morphology due to the fiber tow gap in Figure 12b, in which the top 0° ply sank in o the gap. The resin-rich region was fo med because of r si bl ed out from the adjacent plies. The experimental size of the resin-rich region was significantly larger (0.811 mm in length) compared to the one predicted from squeeze flow analysis (0.227 mm in the closed gap), as shown in Figure 12. A much steeper slope in the top 0° ply was more pronounced in the simulation than in the physical piece. The explanation for this discrep-ancy in the predicted and observed tow morphology is due to resin bleed out, which pro-vides the support against the sinking to a 0° ply. This result illustrates that resin bleed out must be considered to capture the cured defect morphology. (a) Polymers 2024, 16, x FOR PEER REVIEW 16 of 22 (b) Figure 12. (a) The effect of including internal pressure on the size of the void region. (b) The geometry of the resin rich region around the initial tow gap in cured composite. 4.4. Effect of Resin Bleed Out during Compaction of Layup with Embedded Tow Gap The squeeze flow simulation of the fiber tow gap was used to track the changes in the gap volume. The size of the void in squeeze flow analysis was shown to rapidly de-crease because of top ply sinking, where the void volume quickly dropped from 0 to 13 min and then plateaued. However, it is evident that resin bleed out occurs simultaneously with the squeeze flow in the early stages of the cure cycle (see Figure 8), which slows down the volume of the gap from decreasing. In order to capture the coupling between the two phenomena, the squeeze flow, and the resin bleed out, the following procedure was used. The volume of the bled-out resin was estimated using the following equation: 𝑉ோ௘௦ሺ𝑡ሻ ൌ ?̅?௉ሺ்ሻሺ𝑡ሻ ∙ 𝑆𝐴ீ௔௣𝜌௥ (30)where the density of resin, 𝜌௥, was 1100 g/cm3; 𝑆𝐴ீ௔௣ is the initial surface of the fiber tow gap volume VGap(t), which changes during the compaction; and ?̅?௉ሺ்ሻ is the experimen-tally determined resin bleed-out areal density for the prescribed cure cycle, as given by Equation (28a). Over time, the volume of the gap region, VGap(t), is expected to close, as a result of ply sinking and squeeze flow, while at the same time, the volume of the bled-out resin is in-creasing, VRes(t). Once the volume of the bled-out resin reaches the volume of the tow gap void where the resin-rich region is formed. The time of gap filling with resin was predicted to occur from the squeeze flow simulation at tfill = 26 min (Figure 13). On the other hand, the estimated experimental volume of the resin pocket in the micrograph is shown as a horizontal line in Figure 13. The volume of the resin-rich pocket was found from a micro-graph in Figure 12b and corresponded to the volume of resin in the gap at a slightly later time of 29 min, which indicates the progressive filling and coupling between the squeeze flow and resin bleed out. The following method was used to describe this flow coupling effect. A pressure, matching the autoclave pressure, was applied on the internal surfaces of the closing gap to capture the presence of bled-out resin as it fills the void. Furthermore, to simulate the progressive filling of the gap, the internal void pressure was activated gradually in Figure 12. (a) The effect of including internal pressure on the size of the void region. (b) The geometryof the resin rich region around the initial tow gap in cured composite.Polymers 2024, 16, 31 15 of 21The simulation results with only squeeze flow were compared to the experimentallymanufactured sample with the fiber tow gap. The micrograph of the area of interest showedthe morphology due to the fiber tow gap in Figure 12b, in which the top 0◦ ply sank intothe gap. The resin-rich region was formed because of resin bleed out from the adjacentplies. The experimental size of the resin-rich region was significantly larger (0.811 mm inlength) compared to the one predicted from squeeze flow analysis (0.227 mm in the closedgap), as shown in Figure 12. A much steeper slope in the top 0◦ ply was more pronouncedin the simulation than in the physical piece. The explanation for this discrepancy in thepredicted and observed tow morphology is due to resin bleed out, which provides thesupport against the sinking to a 0◦ ply. This result illustrates that resin bleed out must beconsidered to capture the cured defect morphology.4.4. Effect of Resin Bleed Out during Compaction of Layup with Embedded Tow GapThe squeeze flow simulation of the fiber tow gap was used to track the changes in thegap volume. The size of the void in squeeze flow analysis was shown to rapidly decreasebecause of top ply sinking, where the void volume quickly dropped from 0 to 13 min andthen plateaued. However, it is evident that resin bleed out occurs simultaneously withthe squeeze flow in the early stages of the cure cycle (see Figure 8), which slows downthe volume of the gap from decreasing. In order to capture the coupling between the twophenomena, the squeeze flow, and the resin bleed out, the following procedure was used.The volume of the bled-out resin was estimated using the following equation:VRes(t) =ρP(T)(t)· SAGapρr(30)where the density of resin, ρr, was 1100 g/cm3; SAGap is the initial surface of the fiber towgap volume VGap(t), which changes during the compaction; and ρP(T) is the experimen-tally determined resin bleed-out areal density for the prescribed cure cycle, as given byEquation (28a).Over time, the volume of the gap region, VGap(t), is expected to close, as a result ofply sinking and squeeze flow, while at the same time, the volume of the bled-out resin isincreasing, VRes(t). Once the volume of the bled-out resin reaches the volume of the towgap void where the resin-rich region is formed. The time of gap filling with resin waspredicted to occur from the squeeze flow simulation at tfill = 26 min (Figure 13). On theother hand, the estimated experimental volume of the resin pocket in the micrograph isshown as a horizontal line in Figure 13. The volume of the resin-rich pocket was foundfrom a micrograph in Figure 12b and corresponded to the volume of resin in the gap at aslightly later time of 29 min, which indicates the progressive filling and coupling betweenthe squeeze flow and resin bleed out.The following method was used to describe this flow coupling effect. A pressure,matching the autoclave pressure, was applied on the internal surfaces of the closing gapto capture the presence of bled-out resin as it fills the void. Furthermore, to simulatethe progressive filling of the gap, the internal void pressure was activated gradually inpartitioned regions 1–4, as shown in Figure 12a, until the predicted moment in time, tfill,when the gap void is supported by the resin. The internal pressure was enabled, startingfrom the symmetrical end of the model, which was selected based on the proximity of thevoid surfaces in that region. The pressure was activated at 6, 12, 18, and 24 min, respectively.To capture the stress relaxation effects in the viscoelastic liquid resin, the applied pressurefollowed a linear decrease over 25 min (Figure 12a). The time was selected to correspondto the overall time of filling of the tow gap region. With the addition of the pressure, theinitial sinking of the fiber tow gap was slowed. With the incorporation of the couplingbetween squeeze flow and resin bleed out, the void filling was predicted to occur at alater time than in squeeze flow analysis (28 min compared to 26 min), which was closerto the moment corresponding to the predicted time of filling (at 29 min), based on thePolymers 2024, 16, 31 16 of 21experimental size of the resin-rich pocket (Figure 13). In conjunction with the change inthe fiber volume fraction, the resin bleed out was calibrated to the specific material andcure history. The sequential analysis and modeling method presented was calibrated forthe current configuration but can be used on other defect features.Polymers 2024, 16, x FOR PEER REVIEW 17 of 22 partitioned regions 1–4, as shown in Figure 12a, until the predicted moment in time, tfill, when the gap void is supported by the resin. The internal pressure was enabled, starting from the symmetrical end of the model, which was selected based on the proximity of the void surfaces in that region. The pressure was activated at 6, 12, 18, and 24 min, respec-tively. To capture the stress relaxation effects in the viscoelastic liquid resin, the applied pressure followed a linear decrease over 25 min (Figure 12a). The time was selected to correspond to the overall time of filling of the tow gap region. With the addition of the pressure, the initial sinking of the fiber tow gap was slowed. With the incorporation of the coupling between squeeze flow and resin bleed out, the void filling was predicted to occur at a later time than in squeeze flow analysis (28 min compared to 26 min), which was closer to the moment corresponding to the predicted time of filling (at 29 min), based on the experimental size of the resin-rich pocket (Figure 13). In conjunction with the change in the fiber volume fraction, the resin bleed out was calibrated to the specific material and cure history. The sequential a alysis and modeling method prese ted was calibrated for the current configuration but can be used on other defect features. Figure 13. The measured volumes of the model, a theoretical mass flow volume, and the experi-mental gap volume measured from the micrograph. 4.5. Evaluation of Morphology and Fiber Volume Fraction in Cured Layup with Fiber Tow Gap With the bled-out resin providing structural support against the sinking ply above the tow gap, the final morphology of the fiber tow gap model with the internal void pres-sure is shown in Figure 12a. When comparing the two FEA models (squeeze flow with and without the effect of resin bleed out) at 13 min, the void pressure applied prevented the ply from sinking too rapidly. The out-of-plane waviness for the top 0° ply, during the hold stage (45 min), was more gradual and developed over a larger distance, which matched the experimental observation. The out-of-plane angle measured in the top 0° ply is shown in Figure 14, where the simulation captured the evolution of waviness along the length of the gap; however, the experimental results were not as steep as the modeling prediction. The size of the predicted resin-rich region from the coupled simulation had a length of 0.946 mm (compared to the 0.227 mm without the internal void pressure), which agreed with the experimental size of 0.811 mm. The thickness variation in the bottom 0° Figure 13. The measured volumes of the model, a theoretical mass flow volume, and the experimentalgap volume measured from the micrograph.4.5. Evaluation of Morphology and Fiber Volume Fraction in Cured Layup with Fiber Tow GapWith the bled-out resin providing structural support against the sinking ply above thetow gap, the final morphology of the fiber tow gap model with the internal void pressureis shown in Figure 12a. When comparing the two FEA models (squeeze flow with andwithout the effect of resin bleed out) at 13 min, the void pressure applied prevented theply from sinking too rapidly. The out-of-plane waviness for the top 0◦ ply, during the holdstage (45 min), was more gradual and developed over a larger distance, which matchedthe experimental observation. The out-of-plane angle measured in the top 0◦ ply is shownin Figure 14, where the si ulation captured the evolution of waviness along the length ofthe gap; however, the experimental results were not as steep as the mod ling prediction.The size of the predicted resin-rich region from the coupl d simulati n h d a length of0.946 mm (compared to the 0.227 mm without the internal void pressure), which agreedwith the experimental size of 0.811 mm. The thickness variation in the bottom 0◦ ply isshown in Figure 15. The measured thickness in the micrograph was found to increasefrom the left of the reference line towards the center of the composite. In comparison, thenumerical model followed a curve which had the thickest part at the reference line anddecreased in both directions. The resulting morphology can be utilized in further analysisof the composite, such as through progressive damage analysis, to compare with fabricatedlaminates in the future [50].Polymers 2024, 16, 31 17 of 21Polymers 2024, 16, x FOR PEER REVIEW 18 of 22 ply is shown in Figure 15. The measured thickness in the micrograph was found to in-crease from the left of the reference line towards the center of the composite. In compari-son, the numerical model followed a curve which had the thickest part at the reference line and decreased in both directions. The resulting morphology can be utilized in further analysis of the composite, such as through progressive damage analysis, to compare with fabricated laminates in the future [50]. Figure 14. The out-of-plane fiber waviness in the top 0° ply. Figure 15. The bottom 0° ply thickness variation. Figure 14. The out of-plane fiber waviness in the top 0◦ ply.Polymers 2024, 16, x FOR PEER REVIEW 18 of 22 ply is shown in Figure 15. The measured thickness in the micrograph was found to in-crease from the left of the reference line towards the center of the composite. In compari-son, the numerical model followed a curve which had the thickest part at the reference line and decreased in both directions. The resulting morp ology can be utilized in further a alysis of the composite, such as through progressive damage an lysis, to compare with fabricated laminates in the future [50]. Figure 14. The out-of-plane fiber waviness in the top 0° ply. Figure 15. The bottom 0° ply thickness variation. Figure 15. The bottom 0◦ ply thickness variation.Predictions of the variable volume fraction of the 90◦ ply is shown in Figure 16a. Amicrograph of the center 90◦ ply from the cured sample was discretized into rectangularsections where the fiber volume fraction, Vf, was quantified. The micrograph showed a Vfrange of 0.40–0.57 with a resin-rich region in the top corner that had a Vf of about 0.10. FEAsimulations predicted Vf to a range from 0.60 to 0.70. This study did not consider the initialdistribution of the local fiber volume fraction that can account for some of this variation.Polymers 2024, 16, 31 18 of 21Polymers 2024, 16, x FOR PEER REVIEW 19 of 22 Predictions of the variable volume fraction of the 90° ply is shown in Figure 16a. A micrograph of the center 90° ply from the cured sample was discretized into rectangular sections where the fiber volume fraction, Vf, was quantified. The micrograph showed a Vf range of 0.40–0.57 with a resin-rich region in the top corner that had a Vf of about 0.10. FEA simulations predicted Vf to a range from 0.60 to 0.70. This study did not consider the initial distribution of the local fiber volume fraction that can account for some of this var-iation. Figure 16. (a) The distribution of the fiber volume fraction in the fiber tow gap simulation of the 90° ply. (b) The micrograph based measurement of the fiber volume fraction of the 90° ply. 5. Conclusions The interconnected multiphysics framework, which incorporated chemo-rheological and coupled flow-compaction analyses, was developed to simulate the compaction of AFP prepreg preform in order to predict complex morphology around the region of deposited fiber tow gap. Anisotropic tensorial prepreg viscosity was used to capture tow spreading during the cure cycle. The deformation in unidirectional and fiber tow gap samples was observed to be a result of the coupling between the squeeze flow and resin bleed out. Resin bleed out was quantified by measuring the volumetric flux of the resin from unidirectional prepreg tape. The bled-out resin was found to fill the void in the samples with a single fiber tow gap. To capture this phenomenon in simulation, sequential compaction-flow analysis was proposed and validated. The multi-physics modeling approach connects the squeeze flow simulation with the effect of resin bleed out through the evolution of void closure in the simulation. As the first step, squeeze flow simulation is used to predict the evolution of the gap and estimate the time at which the void is filled with resin. At the second step, the calculated time of void filling was used to activate the internal pressure inside of the void. Instead of modeling the resin explicitly, a one-phase model was pro-posed, which considers the effect of resin bleed out via the activated internal void pres-sure. The void pressure is activated progressively to simulate the void filling with resin based on measured resin bleed-out behavior in unidirectional tows. By restricting early sinking of the top ply into the gap, the proposed modeling approach resulted in the cured Figure 16. (a) The distribution of the fiber volume fraction in the fiber tow gap simulation of the 90◦ply. (b) The micrograph based measurement of the fiber volume fraction of the 90◦ ply.5. ConclusionsThe interconnected multiphysics framework, which incorporated chemo-rheologicaland coupled fl w-compaction analyses, was developed to simulate the ompaction of AFPprepreg preform in order o predict complex morphology around t region of depositedfiber tow gap. Anis tropic tensorial pre r g viscosity was used to capture tow spreadingduring the cure cycle. The def rmation in un direc ion l and fiber tow gap samples wasobserved to be a result of the c upling between th squeeze flow and resin bleed out. Resinble d out was quantified by measuring the volumetric flux of the resin from unidirectionalprepreg ape. The bled-out resin was found t fill the void in the samples with a s ngle fibertow gap. To capture this phenomenon in simulation, sequential compaction-flow nalysiswas proposed and validated. The multi-physics modeling approach connects the squeezeflow imulation with the effect of resin bleed out t rough the evolution of void closure inthe simulation. As the first step, sque ze flow simulation is used to predict the evolution ofthe gap and esti ate the time at which the void is filled with resin. At the sec nd step, t ecalc lated time of void filling was used to activate t e internal pressure inside of the void.Instead of modeling the resin explicitly, a one-phase model was proposed, which considersthe effect of resin bleed out via the activated internal void pressure. The void pressureis activated progressively to simulate the void filling with resin based on measured resinbleed-out behavior in unidirectional tows. By restricting early sinking of the top ply intothe gap, the proposed modeling approach resulted in the cured morphology that capturedthe non-uniform morphology more accurately around the initial tow gap region.The modeling framework demonstrated that morphological features develop due tothe coupled manufacturing phenomena and cannot be considered in isolation from eachother. The phenomena include the chemo-rheology of the resin and visco-hyperelasticity ofthe laminate in the early stages of curing. The compaction strain was connected to the localfiber volume fraction via tensorial viscosity and it allowed us to consider the interactionbetween resin bleed out and squeeze flow. The initial deposition gap regions developinto the non-uniform morphological features in the composite, which includes the non-uniform ply thicknesses, fiber waviness, resin-rich regions, and the fiber volume fractionvariation. Moreover, the proposed multi-physics modeling framework can be adoptedto accommodate various material systems with different chemo-rheological properties.Polymers 2024, 16, 31 19 of 21The proposed sequential modeling approach has been used to predict cured morphologyin more complex layups with spatially distributed, staggered fiber tow gaps [51]. Theproposed modeling approach can be used to decouple the effect of various effects on thecure morphology in AFP composites, including the material uncertainty, such as initialfiber volume fraction and fiber orientation distributions.Author Contributions: Conceptualization, S.G.K. and O.G.K.; Methodology, V.R., S.G.K. and O.G.K.;Software, O.G.K.; Validation, V.C.J., V.R. and O.G.K.; Formal analysis, V.C.J.; Investigation, V.C.J.,V.R. and S.G.K.; Resources, S.G.K. and O.G.K.; Data curation, S.G.K. and O.G.K.; Writing—originaldraft, V.C.J. and V.R.; Writing—review & editing, V.C.J., S.G.K. and O.G.K.; Visualization, V.C.J.;Supervision, O.G.K.; Project administration, O.G.K.; Funding acquisition, O.G.K. All authors haveread and agreed to the published version of the manuscript.Funding: This researched has been funded by the NSF Scholarship in STEM (Award # 1833896) andthe Rao V. Arimilli and V. Laskshmi Graduate Award in Mechanical and Aerospace Engineering.Institutional Review Board Statement: Not applicable.Data Availability Statement: The data presented in this study are available on request from thecorresponding author. The data are not publicly available due to the proprietary model.Acknowledgments: Von Clyde Jamora acknowledges Old Dominion University Composite Modelingand Manufacturing group for their support of the study.Conflicts of Interest: The authors declare no conflict of interest.References1. Lukaszewicz, D.H.-J.A.; Ward, C.; Potter, K.D. The engineering aspects of automated prepreg layup: History, present and future.Compos. Part B Eng. 2012, 43, 997–1009. [CrossRef]2. Peeters, D.M.; Lozano, G.G.; Abdalla, M.M. Effect of steering limit constraints on the performance of variable stiffness laminates.Comput. Struct. 2018, 196, 94–111. [CrossRef]3. Wu, K.C. Design and analysis of tow-steered composite shells using fiber placement. 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process modeling
compaction
finite element analysis
automated fiber placement
Effect of Resin Bleed Out on Compaction Behavior of the Fiber Tow Gap Region during Automated Fiber Placement Manufacturing
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