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The equation for prediction of the spring-in angle of a cylindrically orthotropic segment is shown to be independent of all material properties except for the anisotropic coefficients of thermal expansion and a stress-free state is insured for the corresponding unconstrained deformation. In contrast, the complete cylindrical geometry is shown to provide constraint to thermal deformation and thereby induce thermal residual stresses in the form of a moment. The method of superposition is demonstrated whereby traction-free conditions yield stress-free cylindrical elements with corresponding angular displacements at the element free boundaries. The first derivation of the spring-in equation is attributed to Radford, in contrast to the widely accepted view that the equation was first developed by Spencer et al. Finite-element methods, combined with the superposition approach, further validate the accuracy of the Radford equation for cylindrically orthotropic segments and explore its limitations for multiaxial composite laminates.

We present a Bayesian methodology to infer the elastic modulus of the constituent polymer and the fiber orientation state in a short-fiber reinforced polymer composite (SFRP). The properties are inversely determined using only a few experimental tests. Developing composite manufacturing digital twins for SFRP composite processes, including injection molding and extrusion deposition additive manufacturing (EDAM) requires extensive experimental material characterization. In particular, characterizing the composite mechanical properties is time consuming and therefore, micromechanics models are used to fully identify the elasticity tensor. Hence, the objective of this paper is to infer the fiber orientation and the effective polymer modulus and therefore, identify the elasticity tensor of the composite with minimal experimental tests. To that end, we develop a hierarchical Bayesian model coupled with a micromechanics model to infer the fiber orientation and the polymer elastic modulus simultaneously which we then use to estimate the composite elasticity tensor. We motivate and demonstrate the methodology for the EDAM process but the development is such that it is applicable to other SFRP composites processed via other methods. Our results demonstrate that the approach provides a reliable framework for the inference, with as few as three tensile tests, while accounting for epistemic and aleatory uncertainty. Posterior predictive checks show that the model is able to recreate the experimental data well. The ability of the Bayesian approach to calibrate the material properties and its associated uncertainties, make it a promising tool for enabling a probabilistic predictive framework for composites manufacturing digital twins., Comment: 33 pages, 13 figures, 3 tables

Numerical modelling is used to perform process simulations for thick-section composite laminates. Three forms of laminate are used to illustrate how thermal and cure gradients can be reduced by choice of thermal cycle. Low exotherm epoxy powders with the vacuum bag process have shown success in both glass and carbon fiber systems and the results presented in the present work show how the optimum thermal cycle can be determined. The three laminate geometries investigated in the present study included: a one-dimensional flat laminate, a three-dimensional flat laminate, and an axisymmetric section of the cylindrical root of a typical wind turbine blade. Further, energy efficient and cost-effective alternative heating methods are explored.

This work introduces both deterministic and Bayesian methodologies to simultaneously determine the elastic constants of the constituent polymer and the fiber orientation state in a short fiber-reinforced polymer (SFRP) composite based on a small number of experimental measurements of the composite properties. The ability of the Bayesian approach to calibrate uncertainties makes it a promising tool for enabling a probabilistic framework for composites manufacturing digital twins. The two methods that enable the reverse engineering of the orientation of the fibers and the in-situ polymer properties are compared. For the extrusion deposition additive manufacturing (EDAM) process and other SFRP composites processes (e.g. injection molding), extensive characterization efforts are currently required to develop composites manufacturing digital twins. To circumvent the extensive characterization required, Digimat© provides a suite of tools to reverse engineer material properties of SFRPs. However, Digimat© lacks a methodology to inversely determine the fiber orientation state and the constituent polymer properties simultaneously. To that end, this work presents both a deterministic and hierarchical Bayesian approaches to determine the polymer properties and the fiber orientation state simultaneously. The results indicate that both approaches provide a reliable framework for the reverse engineering process. The deterministic approach provides a more rapid, point estimate methodology, whereas the Bayesian approach provides a more comprehensive methodology that includes uncertainties in the reverse engineering process.

The effective properties of composites are influenced by the time-dependent behavior of polymer matrices, which are very sensitive to changes in temperature. Improved plate and beam models are required to efficiently design, and simulate composite structures when the long-term performance of large anisotropic composite structures is the matter of interest. In this work, mechanics of structure genome (MSG) is used to construct linear thermoviscoelastic plate and beam models that can homogenize three-dimensional heterogeneous materials made of constituents with time- and temperature-dependent behavior. The formulation derives the transient strain energy based on integral formulation for thermorheologically simple materials subject to finite temperature changes with the restriction that the strain is small. The reduced time parameter is introduced to relate the time-temperature dependency of the anisotropic material by means of master curves at reference conditions. The new formulation has been implemented in SwiftCompTM, a general-purpose multiscale constitutive modeling code based on MSG. Experimental data and three-dimensional direct numerical simulations of thin-ply high-strain composites (TP-HSC) using a commercial finite element analysis (FEA) package are conducted to verify the accuracy of SwiftCompTM results. The paper also analyzes the relationship between the shift factor of the polymer matrix and the temperature dependencies of the effective beam properties.

The objective of this work was to develop a finite-element based computational model to investigate the complex three-dimensional load transfer from the known meso-structure of a prepreg platelet molded composite (PPMC) system with a layered planar morphology and deterministic orientation state, where platelets are aligned and staggered in each layer. Three-dimensional stress transfer was studied for the prediction of failure under tensile loading. A finite-element model was used for the analysis of the composite structure-property relationship. Variability of meso-structure geometry was shown to control the distributed tensile properties of a PPMC laminate. Platelet length-to-thickness and length-to-width ratios were found to control the composite effective strength. Experimental analysis was used to complement the results of theoretical studies. A PPMC meso-structure with deterministic orientation state of engineered morphology was found to provide enhanced effective tensile properties with reduced variability as compared to stochastic prepreg platelet meso-structure. The mechanisms leading to enhanced structural performance were (i) the improved hierarchical structure of the platelet system and (ii) the ability to define the fiber orientation state of the composite system.

The process simulation tool Additive3D has been developed in Abaqus© 2017 to model the Extrusion Deposition Additive Manufacturing (EDAM) process for fiber-reinforced thermoplastic composites. This additive manufacturing (AM) method encompasses material deposition processes where geometries are constructed layer by layer and the resulting layer properties are highly anisotropic. The goal is to predict final deformed shapes and residual stresses of printed geometries due to the printing process and the material anisotropy. The resulting design tool allows to assess the outcomes of the printing process based on the part geometry, the printing material and the position control parameters. Material properties were characterized, and validation experiments, without additional calibration, show an excellent agreement between modeled and measured part deformation states with relative deviations below 7%. Due to the physics-based nature of the developed simulation tools, the simulations can be extended to account for different part scales, printing materials and printing histories.

Simulation methods, particularly those implemented in commercially available software, for the prediction of flow and fiber orientation in polymer composites molding processes typically neglect the coupling between flow and orientation which presents as anisotropic viscosity due to reinforcing fibers. While several particular solutions have been performed for simple geometries, the application of tensor based anisotropic constitutive behavior presents solution difficulties; thus, any potential consequences of neglecting coupling have been accepted in favor of developing and implementing additional complexity to the orientation evolution models. Here, a simple model is presented by which flow and orientation analysis can be coupled through a scalar viscosity function such that minimal adjustment to existing solvers is required for implementation.

X-ray computed tomography (CT) analysis is used to measure the heterogeneous fiber orientation fields in a 20 cm 3 composite bracket made from prepreg platelet-based molding compound (PPMC). The as-molded mesostructure of the complete geometry is captured using material density gradients in 50 µm resolution CT scans without the need to resolve individual fibers. Fiber collimation and physical density gradients within intact platelets of this material system facilitates nondestructive assessment of average local fiber orientation at the component scale. Microscopy-based validation of the local orientation measurements indicate the accuracy that can be attained utilizing the density-based structure tensor CT analysis method. Local orientation field measurements for the complete geometry can be mapped into a “digital twin” model, for purposes such as experimental performance simulation and validation of molding process orientation state predictions. Composite designers, analysts, and material suppliers can employ this methodology to more confidently utilize PPMCs and morphologically similar composite material systems.

Prepreg platelet molding compounds (PPMCs) offer improved performance potential as compared to short-fiber composites and increased geometrical complexity as compared to continuous fiber composites. The increased adoption of PPMCs in automotive and aerospace applications necessitates the development of predictive tools for determining the final orientation state in complex geometries produced through molding flows. Due to the large geometric scale of platelets as compared to molded geometry scales, the orientation structure of PPMCs is spatially nonsmooth, thereby eliminating the requisite separation of scales utilized by typical molding simulation approaches. Additionally, the large fiber volume fraction and fiber length in platelets yield highly anisotropic flow behavior, as manifested in the resistance to stretching deformations along platelet fiber directions. Thus, the goal of this work is to present the development, implementation, and validation of a flow simulation approach for PPMCs accounting for fiber direction and platelet normal direction evolution with coupled anisotropic viscous behavior. The simulation approach is implemented using the smoothed particle hydrodynamics method. To validate the proposed approach, a pin bracket geometry is manufactured from a charge with the orientation state measured by computed tomography (CT). The final orientation state determined by the flow simulation predictions and by measuring the orientation state of the final bracket by CT is compared to validate the predictions.

The Bouligand structure in some arthropods is a hierarchical composite comprised of a helicoidal arrangement of strong fibers in a weak matrix. In this study, we focus on the Bouligand structure present in the dactyl club of the smashing mantis shrimp due to its exceptional capability to withstand repetitive high-energy impact without catastrophic failure. We carry out a combined computational and experimental approach to investigate the high damage resistance of the Bouligand structure through a biomimetic composite material. This is studied by performing specific fracture experiments on the helicoidal composites specimens, where it was found that crack twisting, driven by the fiber architecture, is the main fracture mechanisms. This crack twisting mechanism competes with other alternative mechanisms such as crack branching and delamination, delaying catastrophic failure. The main mechanism of crack twisting is studied through specifically designed specimens in which the crack propagation path is controlled. Further quantification of the toughening mechanisms and crack growth rate is analyzed with analytical and finite element models. The biomimetic helicoidal composites are shown to have improved fracture resistance as the crack twists mainly driven by the increase in crack surface area and fracture mode mixity. Our analysis allowed us to study the effect of crack front shape, stress distribution and energy dissipation mechanisms.

Mechanics of Structure Genome (MSG) is extended to provide a new two-step homogenization approach to predict the viscoelastic behaviors of textile composites. The first homogenization step (micro-homogenization) deals with determining the viscoelastic properties of yarns from fibers (assumed to be linear elastic) and matrix (assumed to be linear viscoelastic) using the MSG solid model. In the second homogenization step (macro-homogenization), the viscoelastic behaviors of textile composites are computed from the homogenized yarns and matrix properties using the MSG plate model. Representative volume element (RVE) analysis using a commercial finite element package at micro-scale is conducted to verify the accuracy of MSG micro-homogenization. The viscoelastic behaviors of textile composites at macro-scale using the MSG plate model are validated using experimental data. All the results are in good agreements. The proposed approach is applied to several commonly used woven composites to study the effects of different weave patterns on the viscoelastic behaviors.

The tensile strength of a discontinuous composite system consisting of aligned, unidirectional prepreg platelets is predicted by performing progressive damage analyses in a periodic representative volume element. Interlaminar and in-plane damage mechanisms are combined to yield failure characteristics of the meso-structure. The length-to-thickness ratio of the platelet was found to be the primary variable for control of system strength and failure mode. A critical platelet aspect ratio was determined as that ratio wherein system strength is maximized. Further, composite strength variability was shown to be vary inversely with aspect ratio, while attaining a minimum at the critical aspect ratio.

Recent advancements in the Additive Manufacturing (AM) Fused Filament Fabrication (FFF) approach are described with focus on the application to tooling and molds for composite materials and structures. A detailed summary of mechanical properties of printed parts for different composite material systems is presented and discussed. These material systems are comprised of discontinuous fiber-reinforced polymers characterized by fiber orientation dominantly parallel to the direction of the extrudate. An overview of the FFF process and its physical phenomena is given including the flow and resulting fiber orientation, the bond formation between adjacent beads and the thermomechanical solidification behavior of the deposited material. Based on reviewed research in these different phenomena, future research needs are discussed and desirable objectives are formulated.

The influence of anisotropic viscosity on fiber orientation evolution in classic squeeze flow is examined with a viscous fiber suspension of specified initial orientation state. The components of the anisotropic viscosity tensor for a well dispersed and collimated fiber suspension developed in micromechanical analyses earlier by one of the authors were combined in an orientation averaging approach to produce the effective suspension viscosity components for arbitrary orientation states. A coupled anisotropic viscosity constitutive relationship was numerically implemented into a displacement-based finite element code for nonlinear analysis of flow and fiber orientation. The numerical method was verified by agreement between predicted and observed responses for a single element subjected to canonical states of deformation. Evolution of fiber orientation during the deformation processes was confirmed by analytic predictions. This approach was validated by examining the squeeze flow of a fiber suspension studied earlier both analytically and experimentally. The present analysis was found to be in excellent agreement with experimental data and clearly demonstrated that evolution of fiber orientation and the resulting effective anisotropic viscosity tensor were essential to the correct predictions.The influence of anisotropic viscosity on fiber orientation evolution in classic squeeze flow is examined with a viscous fiber suspension of specified initial orientation state. The components of the anisotropic viscosity tensor for a well dispersed and collimated fiber suspension developed in micromechanical analyses earlier by one of the authors were combined in an orientation averaging approach to produce the effective suspension viscosity components for arbitrary orientation states. A coupled anisotropic viscosity constitutive relationship was numerically implemented into a displacement-based finite element code for nonlinear analysis of flow and fiber orientation. The numerical method was verified by agreement between predicted and observed responses for a single element subjected to canonical states of deformation. Evolution of fiber orientation during the deformation processes was confirmed by analytic predictions. This approach was validated by examining the squeeze flow of a fiber suspension stud...

Anisotropy caused by flow-induced fiber orientation of discontinuous fibers within the extrudate in the Extrusion Deposition Additive Manufacturing (EDAM) process gives rise to anisotropic shrinkage in printed parts and thereby, final part deformations. Three fiber orientation states, described by the second-order orientation tensor, were investigated to determine their influence upon final geometry. Two material systems were investigated including a short glass fiber-reinforced polyamide and a short carbon fiber-reinforced polyamide. A curvilinear geometry was modeled and printed virtually in the thermo-mechanical simulation, ADDITIVE3D©. The scale of the printed geometry was in the range of 300–400 mm and contained three semicircular geometry regions connected to linear regions, thereby inducing significant magnification of the spring-in deformation. The predicted deformation of the printed geometry for the three fiber orientation states and two material systems were compared. The deformation predicted for glass fiber-filled polyamide and carbon fiber-filled polyamide of the same fiber orientation states showed comparable deformations. The largest residual deformation was shown to correspond to the orientation tensor with the greatest degree of anisotropy.

The prediction of the bending moment–curvature and moment-angular rotation relationships for a collimated, fiber-reinforced thermoplastic prepreg in the melt state is the subject of this work. The central assumption of the developed relationship is that the fiber phase controls the deformed state of the composite and the local curvature rate of the fiber phase induces shearing strain rate in the viscous polymer. The corresponding shearing stresses are shown to retard the elastic deformation of the fibers when subjected to curvature-rate. Further, the developed models exhibit the characteristics of the traditional Voigt-Kelvin viscoelastic medium and thereby provide the rich family of corresponding viscoelastic solutions. The results illustrate how the constituent properties for reinforcing fiber and the thermoplastic polymer can be utilized to develop the desired composite constituent relationships necessary for simulation of thermoplastic hybrid forming.

This paper presents a hybrid rule of mixtures for calculating the complete set of effective three-dimensional thermoelastic properties of a composite laminate when it is approximated as an equivalent, homogeneous, anisotropic solid. The laminate can be made of generally anisotropic layers with arbitrary layup sequence. This hybrid rule of mixtures is based on the exact solution obtained using the recently discovered mechanics of structure genome. Since mechanics of structure genome minimizes the loss of accuracy for homogenization, the three-dimensional thermoelastic properties obtained using the mechanics of structure genome-based hybrid rule of mixtures will be the most accurate one could obtain for composite laminates. The results of the hybrid rule of mixtures are compared with several other representative methods for predicting thermoelastic properties of composite laminates.

The cure history dependent residual deformation in a thermosetting composite laminate was investigated using bi-lamina strip sample with [0/904] stacking-sequence. The samples were subjected to cure cycles with different heating profiles. Significant dependence of the residual strip deflection was found to relate to (i) the interaction of thermal expansion and cure shrinkage of resin and (ii) dependence of resin modulus development on cure strain rate. The lamina constitutive model was proposed to include cure induced shrinkage and composite hardening during cure. The model was calibrated following the single and multiple ramps cure cycles and applied to a number of two hold stage cure cycles with constant maximum temperature. The heating ramp of the cure cycle was varied allowing decreasing the residual deformation at ambient conditions after cure. The presented methodology can be applied for designing the cure cycle to reduce the amount of residual deformation in composite materials from manufacturing.

The thermal expansion behavior of polymer carbon nanotube (CNT) nanocomposites was investigated, and a micromechanical model was proposed to explain the highly nonlinear dependence of the coefficient of thermal expansion of the nanocomposite with CNT content for the CNT/polyimide nanocomposite. The microscopic analysis of CNT/polyimide matrix showed homogeneous dispersion of bundles composed of CNTs. Therefore, the proposed model to predict the thermal expansion behavior of the nanocomposite considered a random, homogeneous distribution of CNT bundles with a hierarchical arrangement of helical CNTs within the polymeric matrix. The CNT bundle morphology influenced the thermal expansion response of the nanocomposite through (i) bundle volume fraction and (ii) degree of helicity, affecting thermo-mechanical properties of the bundle. The effective, homogenized, properties of CNT bundles were determined by the elasticity based solution of the layered cylinder model. Bundle effective properties were used in the micromechanical model implementing the homogenized strain rule of the mixture expression to predict the thermal expansion behavior of nanocomposite in a wide range of CNT volume contents. The proposed micromechanical analytical model was found to correlate closely with the experimental results for polyimide/CNT nanocomposite films as measured using a digital image correlation method.

Effects of water on epoxy cure kinetics are investigated. Experimental tests show that absorbed water in an uncured bisphenol-F/diethyl-toluene-diamine epoxy system causes an increase in cure rate at low degrees of cure and a decrease in cure rate at high degrees of cure. Molecular simulations of the same epoxy system indicate that the initial increase in cure rate is due to an increase in molecular self-diffusion of the epoxy molecules in the presence of water. Effects of water on the glass transition temperature (Tg) of the crosslinked thermoset are also studied. Both experiments and simulations show that water decreases Tg. Both types of results indicate that Tg effects are small below 1% water by weight, but that Tg depression occurs much quickly with increasing water content above 1%. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017

Because of composite materials’ inherent heterogeneity, the field of micromechanics provides essential tools for understanding and analyzing composite materials and structures. Micromechanics serves two purposes: homogenization or prediction of effective properties and dehomogenization or recovery of local fields in the original heterogeneous microstructure. Many micromechanical tools have been developed and codified, including commercially available software packages that offer micromechanical analyses as stand-alone tools or as part of an analysis chain. With the increasing number of tools available, the practitioner must determine which tool(s) provides the most value for the problem at hand given budget, time, and resource constraints. To date, simple benchmarking examples have been developed in an attempt to address this challenge. The present paper presents the benchmark cases and results from the Micromechanical Simulation Challenge hosted by the Composites Design and Manufacturing HUB. The challenge is a series of comprehensive benchmarking exercises in the field of micromechanics against which such tools can be compared. The Level I challenge problems consist of six microstructure cases, including aligned, continuous fibers in a matrix, with and without an interphase; a cross-ply laminate; spherical inclusions; a plain-weave fabric; and a short-fiber microstructure with “random” fiber orientation. In the present phase of the simulation challenge, the material constitutive relations are restricted to linear thermoelastic. Partial results from DIGIMAT-MF, ESI VPS, MAC/GMC, finite volume direct averaging method, Altair MDS, SwiftComp, and 3D finite element analysis are reported. As the challenge is intended to be ongoing, the full results are hosted and updated online at www.cdmHUB.org .

A simulation framework for extrusion deposition additive manufacturing (ADDITIVE3D) is presented in this chapter that shows promising results for capturing the physics-based phenomena that occur in the extrusion deposition printing process. By simulating the full physics of the manufacturing process and using this information to describe the state of the printed geometry, the outcomes of the printing process and consequences in performance can be predicted before the physical print begins. This manufacturing-informed performance can be used to drive design decisions and anticipate the success or failure of a given print. Unsuccessful and unfavorable designs can be discovered in silico without expending material, machine time, and operator effort. ADDITIVE3D offers designers and machine operators access to the ability to utilize the full multi-physics simulation capability for the EDAM process in a stand-alone fashion, requiring no expertise in FEA software or computer programming. The machine type (machine card) defines the processing conditions that govern applicable bead geometry, ambient conditions, print bed boundary conditions, compaction mechanism, and interpretation of the event series. The event series information contains the part specific information for the print including both the time-dependent bead location and the printing options available on the specified machine. The goal of ADDITIVE3D and the simulation workflow presented herein is to bring the power of simulation to the additive manufacturing community. The integrated nature of the ADDITIVE3D workflow also presents a platform for leveraging machine learning to further explore material, machine, and part design.

A commercially available thermoset polymer liquid coating reinforced with ceramic particles was applied on the surface of an additively manufactured carbon fiber reinforced thermoplastic composites to improve its surface characteristics for composite mold application. The mold demonstrated herein was fabricated via material extrusion additive manufacturing (MEAM) and served for the fabrication of autoclave-cured laminated composite structures. Test specimens used in this investigation were additively manufactured with Polyphenylene Sulfide (PPS) reinforced with 50% by weight of carbon fiber. Following the printing process, the surface of the specimens was finished in a numerical controlled milling machine. The effect of machining parameters such as the surface speed and the chip load on the surface roughness was investigated. The machining parameters that yielded the lowest surface roughness were used to machine the specimens used in this work. Following machining, an approximately 10 μm thick coating based on a thermoset resin reinforced with ceramic particles was applied on the surface of flat specimens via the liquid spray coating technique and cured at elevated temperature. Surface characteristics relevant to molds used in composite manufacturing such as surface roughness, abrasion resistance, hardness, friction, and vacuum integrity were assessed for the coated and noncoated specimens. The results showed that the coating decreased the abrasion wear index by about 89%, decreased the vacuum loss by about 95%, and lowered the static and kinetic friction by about 40% and 38%, respectively, compared to the non-coated printed material. However, the coated surface did not improve hardness nor roughness of the surface.

The morphological features of carbon nanotube (CNT) polymer composites and their influence on the effective modulus are evaluated. The considered features include bundle formation from the helical sub-bundles made of individual CNTs. The formation of bundles is considered as a result of agglomeration of individual nanotubes above and below onset of percolation and is related to electrical conductivity. The proposed geometrical model yields a bundle diameter that agrees closely with that of the experimentally measured by voltage-contrast method and scanning electron microscopy analysis of polyimide nanocomposites. The proposed micromechanical analytical model includes the helical structure of a bundle and provides close agreement of the effective Young's modulus of nanocomposite over a wide range of CNT content. It is shown that considering the helical structure of CNT bundles and its effect on bundle modulus is vital for predicting the effective modulus of CNT-polymer nanocomposite.

Failure mechanisms in amorphous polymers are usually separated into two types, shear yielding and crazing due to the differences in the yield surface. Experiments show that the yield surface follows a pressure modified von Mises relation for shear yielding but this relation does not hold during crazing failure. In the past different yield conditions were used to represent each type of failure. Here, we show that the same damage model can be used to study failure under shear yielding and crazing conditions. The simulations show that different yield surfaces are obtained for craze and shear yielding if the microstructure is included explicitly in the simulations. In particular the breakdown of the pressure modified von Mises relation during crazing can be related to the presence of voids and other defects in the sample.

Compaction deformations in a thermoplastic composite system molded from chopped prepreg platelets were analyzed to obtain statistical distributions of local distortions that define the final consolidated meso-structure. This study provides an insight into and allows quantification of the intrinsic geometric variability of the composite meso-structure that controls the variability of the effective composite mechanical properties. A two-phase viscoelastic finite element model was utilized to treat the behavior of molten prepreg platelets, which were assumed to be incompressible and inextensible in the fiber direction during processing. A two-step simulation procedure with discretely modeled platelets and platelet-to-platelet contacts is proposed. The analysis begins with a drop simulation of the uncontrolled material deposition followed by a 3D finite element analysis of the preform compaction and bulk material flow. The proposed model provides a method for generating a composite meso-structure ab initio starting from a statistical sampling of the initial conditions for platelet deposition. The predicted platelet thickness distribution, intra-platelet fiber waviness and out-of-plane platelet undulations were found to be in good agreement with experimental measurements. An estimate of the volume of resin pockets was inferred from the compaction simulation.

The increase in accessibility of fused filament fabrication (FFF) machines has inspired the scientific community to work towards the understanding of the structural performance of components fabricated with this technology. Numerous attempts to characterize and to estimate the mechanical properties of structures fabricated with FFF have been reported in the literature. Experimental characterization of printed components has been reported extensively. However, few attempts have been made to predict properties of printed structures with computational models, and a lot less work with analytical approximations. As a result, a thorough review of reported experimental characterization and predictive models is presented with the aim of summarizing applicability and limitations of those approaches. Finally, recommendations on practices for characterizing printed materials are given and areas that deserve further research are proposed.

For the practical compression molded glass-mat thermoplastics (GMTs), it is important that the flow pattern in squeezing of circular disks with initial alignment, from manufacturing or prior flow, usually develops into an elliptical shape due to fiber-orientation-induced anisotropic flow. However, prior predictive engineering tools have always provided unsatisfactory isotropic flow results. This challenging anisotropic flow prediction problem has been addressed in this work. Based on the orientation averaged fourth-order viscosity tensor, the Favaloro-Pipes model for an orientation informed isotropic viscosity is proposed and implemented to simulate the natural anisotropic flow behavior in GMT compression molding simulation.

Prepreg platelet molding compounds (PPMCs) are utilized in a growing number of composite applications where parts with complex geometry require both a moderate degree of processability and performance. In collaboration with Boeing Commercial Airplanes, a research group at Purdue University has developed a comprehensive framework for the analysis of process-structure-property-performance relationship of PPMC material systems. The research team focused on non-destructive inspection, multi-scale performance analysis, and molding flow simulation utilizing a complementary set of commercial and research tools that aid in design and understanding of PPMC materials and structures. The lessons learned from each approach about required degree of orientation information, variability in fiber orientation state, variability in performance, and best practices for modeling PPMC systems should be utilized wherever possible and added to as inspection and simulation technologies improve.

Prepreg platelet molding compounds (PPMCs), formed by slitting and cutting prepreg tape, are used to produce complex parts with moderate structural performance while maintaining good processing characteristics associated with compression molding. The fiber orientation state in the final part is driven by the processing (i.e. the initial orientation state of the preform and the flow). Then, the fiber orientation distribution within the structure determines its mechanical performance. However, there can be significant part to part variability for these systems which is accommodated through reduced design allowables. A recently developed molding simulation methodology predicts the final fiber orientation state given the initial conditions. Yet, the variability of the initial orientation state caused by preform deposition can contribute significantly to the variability in part microstructure, particularly for low flow processes. The method for anisotropic flow and fiber orientation analysis was employed to analyze the molding of a bracket geometry. Initial orientation states were stochastically generated. The predicted orientation state was transferred to a structured mesh to perform a structural analysis and obtain the part stiffness. The predicted stiffness was used as a metric to assess the ability to predict variability caused by stochastic initial conditions. The resulting predicted stiffness and variability were consistent with mechanical testing.

A methodology for predicting residual cure deformation and stresses in composite laminates during cure is proposed. The technique employs an unbalanced cross-ply strip denoted as a “bi-lamina” strip to measure the in situ development of chemical and thermal shrinkage deformation during a specified thermal cycle. The constitutive model of the composite material was developed based on self-consistent micro-mechanical homogenization with variable resin thermo-mechanical material properties during the cure cycle. The resin properties were determined as a function of cure and temperature using different experimental techniques, including differential scanning calorimetry, digital image correlation, rheometry and dynamic mechanical analysis. The predicted bending deflection profiles of the strip agreed closely with experimental observations. The proposed methodology can be used to validate the material model of the resin and composite during the cure cycle.

Interlaminar reinforcement may be achieved in a composite laminate by the insertion and bonding of stiff rods through the thickness. It is experimentally shown in the paper that increased aspect ratio (AR) of through-thickness rods significantly elevates mode I maximum delamination fracture resistance of a laminate. This effect is explained through the analysis of rod/laminate interfacial stress transfer. Lower interfacial shear stresses occur for interlaminar rods of greater AR for equivalent bridging traction against opening delamination. Thereby, a larger AR allows the rod to develop a greater closure force prior to the rod debonding from the laminate. Further, these results show that this approach for interlaminar reinforcement is best applied to laminates of thickness-to-rod diameter ratio sufficient to allow for insertion of high aspect ratio reinforcement rods.

A method for measuring chemical shrinkage and coefficient of thermal expansion during cure and post-gelation is presented based on digital image correlation to record the in situ stress-free strain field in a thermosetting polymer. An independent determination of the resin cure kinetics was required to relate the chemical shrinkage strain and coefficient of thermal expansion to the degree of cure. The changes in the coefficient of thermal expansion were observed from the initial heating to final cooling of the sample. The results obtained are shown to compare favorably with results previously found by other techniques. The proposed method provides a simple and reliable procedure to measure the evolution of thermo-chemical shrinkage properties of the resin during the cure cycle.

Unidirectional, prepreg platelet-based molding systems have gained considerable attention for manufacturing parts with moderate performance and processability metrics. A numerical study of squeeze flow, using a recently developed technique for coupled flow simulation and fiber orientation analysis, has been performed to investigate the effects of the platelet morphology on the processing of prepreg platelet based composite molding systems. Two competing effects have been shown to drive the processability of such a material: (i) increasing extensional viscosity due to increasing platelet length and (ii) increasing apparent viscosity due to increasing uniformity of orientation distribution. By adjusting the platelet dimensions, the above phenomena have been isolated in the numerical simulations to demonstrate their relative importance on the processability of platelet based molding systems.