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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.

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 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 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.

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.

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.

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.

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 .

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.

Structural integrity, durability, and thermal stability represent critical areas for adequately modeling the behavior of composite materials. Polymeric matrices are prone to have time-dependent behavior very sensitive to changes in temperature that influence the effective properties of the composite. This study extends mechanics of structure genome (MSG) to construct a linear thermoviscoelastic model that allows to homogenize three-dimensional heterogeneous materials made of constituents with time- and temperature-dependent behavior. The formulation models the transient strain energy based on integral formulation for thermorheologically simple materials and treats thermal expansion creep as inherent material behavior. An analytical three-dimensional thermoviscoelastic homogenization solution has been derived for laminates modeled as an equivalent, homogeneous, anisotropic solid. Three-dimensional representative volume element (RVE) analyses and direct numerical simulations using a commercial finite element software have been conducted to verify the accuracy of the MSG homogenization. Unlike MSG, the RVE method exhibits limitations to properly capture the long-term behavior of effective coefficients of thermal expansion (CTEs) when time-dependent constituent CTEs are considered. The analyses of the homogenized properties also reveal that the shift factor of the polymeric matrix drives the temperature dependencies of the effective CTEs and engineering constants of the heterogeneous composite material regardless of the structural scale.

Prepreg platelet molded composite (PPMC) is derived from compression molded pieces of chopped unidirectional prepreg tape. The properties of a stochastic PPMC arise from the meso-structure that develops during processing. This paper describes an integrated methodology for analysis of stochastic PPMC to develop process-structure-property relationships. Flow-induced fiber orientation distributions were predicted using an anisotropic viscous constitutive model implemented in a nonlinear, explicit finite element (FE) solver. The predicted orientation state was validated by CT-based orientation measurements and optical microscopy. A computational framework for simulation of tensile property distributions of a stochastic PPMC by progressive failure analysis is presented. The probabilistic simulation results were statistically validated against experimental data. A FE analysis was developed with an explicitly modeled platelet meso-structure wherein the platelets are treated as a homogeneous orthotropic medium using continuum damage mechanics to model the intraplatelet failure and a cohesive zone model for interlaminar disbonding. Panels were molded using partial charge coverage to induce flow alignment of the fibers. Tensile coupons were excised from the molded panels both along (parallel) and transverse (perpendicular) to the preferential fiber direction to compare the composite effective properties with those reported in the literature for planar random orientation states. The composite tensile properties were found to be strongly dependent on the global orientation state.

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.

An investigation into the effect of meso-structure variation on the dynamic properties of a plate made from unidirectional pre-impregnated discontinuous carbon fiber platelets was performed. A platelet generation code was implemented to make finite element models of flat plates comprised of platelets with random in-plane orientations. While the mode shapes were not particularly sensitive to orientation changes of the platelets, natural frequency was shown to have a frequency variance similar to a normal distribution for specific modes. Using the orientation tensor developed by Advani and Tucker [1], the local effective elastic properties were calculated and shown to have a correlation with natural frequency shifts. This method could be used in the future to inform modal tap testing results to determine local material properties of discontinuous fiber parts.

An efficient shell model based on mechanics of structure genome is introduced to predict manufacturing induced residual stress and deformation for composite laminates. This model utilize shell elements in commercial finite element codes to represent the composite laminate, which greatly reduces the computational cost compared with a direct numerical simulation (DNS) using 3D solid elements or accuracy loss compared with using smeared properties. In this study, a line through the thickness of the composite laminate is chosen to be the structure genome, separating the original 3D body into a 1D through the thickness analysis and a 2D shell analysis. Constitutive relations for the shell elements, considering the effect of residual stress and strain, are constructed. The tool is modeled using 3D elements with a relative coarse mesh and a contact interaction is applied between the tool and composite part, as commonly done in a DNS. Several case studies are presented with comparison between DNS and analysis using smeared properties.

Discontinuous Fiber Composites (DFCs) constitute a new class of highperformance molding compounds that enable the use of compression molding as the manufacturing process of complex components with high volume fraction of fibers. However, the use of DFCs is still limited, one reason being the lack of theoretical modeling and numerical analysis methodologies enabling their use at full potential. During compression molding, the polymeric resin is brought above its melting temperature and thus the material system consists in the cohabitation of a fluid and solid component. In this paper we adopted a macroscopic point of view that consists in depicting the material system as an open thermodynamic system through which the fluid can flow thus yielding a macroscopically compressible system for which a specific state, referred to as the compaction point, exists. The compaction point denotes the state at which no relative motion of fluid can occur with respect to the solid one and thus the thermodynamics system becomes incompressible. A stabilized mixed finite element method is presented that allows for the direct solution of the compaction problem in which all variables are treated as primary ones. This method yields a generalized saddlepoint problem that is known to be stable only for specific coupling of interpolation orders between the primary variables. Circumventing the latter is achieved via a stabilization procedure based on the use of the Algebraic Sub-Grid Stabilization (ASGS) method that yields a fully stable Galerkin weak mixed formulation for equalorder interpolation between all primary fields. This method proves beneficial to highlight the physical phenomena occurring in compression molding of fiber-reinforced media.

Extrusion Deposition Additive Manufacturing (EDAM) is a technology where 3-D digital objects are manufactured extruding beads of molten material in a layer-by-layer basis. This technology offers the flexibility for processing pelletized material, and thus a semi-crystalline polymer highly-filled with carbon fiber has been used for printing. Significant technology improvements in the EDAM technology have been made recently, however, the design of the printing strategy is still mostly driven by empirical development. Hence, there is a need for simulation tools that capture the phenomena involved in the EDAM process to drive the development and optimization of this technology. Currently, one limitation of printed parts in terms of mechanical properties is the strength of the interface developed between printed layers. Therefore, the focus of this work is to couple the phenomena involved in the bonding process of adjacent layers to predict the degree of bonding, such as the temperature history, the melting and crystallization of the semi-crystalline polymer and the diffusion of polymer chains. The models utilized to describe these phenomena and their couplings were implemented in a UMATHT user subroutine in Abaqus to predict the evolution of the degree of bonding during the EDAM process. The effects of the couplings implemented in this approach are demonstrated by predicting the evolution of the degree of bonding throughout the simulation of the printing process of a geometry with sections that undergo different cooling and crystallization rates.

Constrained thermoset deformation has been shown to exhibit cure history dependence. The practical significance of this problem is due to the necessity to ensure dimensional stability and tolerance in composite structures especially with curvilinear geometry. During manufacturing of curved composite laminates, cure shrinkages produce so-called spring-in or spring forward effect, as a result of material thermo-elastic anisotropy. The residual cure deformation in a thermosetting composite laminate was considered by subjecting bi-lamina strip samples, composed of [0/904] plies, to cure cycles with different heating profiles. This allowed to separate and study different sources of shrinkage in thermosetting composites, namely chemical resin shrinkage, which occurs due to cross-linking reaction, and thermal shrinkage or expansion, result of applied change in temperature. The significant dependence of the residual strip deflection was found to relate to (i) interaction between chemical and thermal shrinkages and (ii) resulting resin cure strain rate, which affected elastic modulus development in the composite. The constitutive material model of composite during cure was developed and applied to reduce residual deformation during the manufacturer recommended cure cycle (MRCC) by enabling different interactions between thermal and chemical shrinkage. Consequently, the modified cure cycle (MCC) was proposed allowing to further reduce the amount of residual deformation in bi-lamina laminate prior to cooling. The presented approach of establishing the constitutive cure model of composite provides an insight of how to control the laminate final shape by selecting the parameters of the cure cycle. Consequently, cure cycle can be used to mitigate the adverse effects of the residual deformation on the performance of laminated composites.

An end-to-end process simulation has been created to predict the high pressure resin transfer molding (HP-RTM) process. Material properties such as fiber orientations and resin properties are mapped throughout the process so that a performance model can be run on a part as it is actually manufactured, not just as it is designed. A B-Pillar geometry was used as a demonstration part and showed a difference in residual deformation of almost 20% when the as-manufactured material properties were considered.

A multi-scale model for the response of a bi-material “thermostat”, consisting of a single unidirectional lamina of carbon/epoxy and an uncured layer of neat diglycidyl ether of bisphenol F (DGEBF) with curing agent, diethyltoluenediamine (DETDA), is developed in order to measure thermal strains during a prescribed, but arbitrary thermal history. Molecular modeling simulations provided the elastic modulus, coefficient of thermal expansion, glass transition temperature of DGEBF/DETDA as a function of degree of cure. Cure kinetic properties were determined with differential scanning calorimeter measurements. The model allowed separation of strains due to cure shrinkage and thermal expansion. Combining the molecular modeling predictions, cure kinetic measurements and “thermostat” deflection measurements, the complete polymer shrinkage phenomenon is determined over a prescribed thermal cycle. Furthermore, this work can provide a vehicle to develop cure cycles wherein the difference between instantaneous glass transition temperature and specimen temperature is controlled to provide optimum cure cycles for minimum cure shrinkage.

The Bladder Assisted Composite Manufacturing (BACM) technique allows fabrication of complex hollow composite geometries. However, traditional bladder manufacturing methods require multiple steps and a master geometry which increases the cost and the manufacturing time. Hence, additively manufactured bladders are presented as an alternative solution to bladders manufactured through traditional methods. The use of printed bladders is demonstrated by consolidating and curing a composite part made out of an aerospace grade composite prepreg material, IM7/8552. Bladders are additively manufactured using the Fused Deposition Modeling (FDM) technique with Thermoplastic Polyurethane (TPU). Based on the results of a thermomechanical investigation of the TPU, a two-step curing cycle for manufacturing a composite part with IM7/8552 prepreg was designed. The part consolidation achieved with this method was characterized by measuring void content and comparing it to the void content in a sample cured in a standard autoclave process. The low void content achieved with the BACM method demonstrated the potential of this technology for providing bladders for short production runs or prototyping.

The stochastic prepreg platelet molded composite (PPMC) occurs when the orientation and arrangement disorder of platelets are determined by the uncontrolled molding conditions. The understanding of composite structure-property relationship is essential for the engineering applications of PPMCs. Computational analysis of the structure-property relationship in a PPMC with stochastic meso-scale morphology is herein performed under uniaxial tension conditions. The virtual distributions of tensile properties are obtained from the in-silico tensile tests based on the progressive failure analysis in the full-sized stochastically generated PPMC coupons. The developed analysis allows investigation of how the PPMC meso-structure details, such as platelet geometry and system morphology, define the variability in PPMC effective tensile properties.

SUMMARY: The reinforcement potential of cellulose nanocrystal (CNC) additions on an idealized 2-dirmensional (2-D) fiber network structure consisting of micron sized fiber elements was investigated. The reinforcement mechanism considered in this study was through the stiffening of the micron sized fiber elements via a CNC-epoxy coating. A hierarchical analytical modeling approach was used to estimate the elastic properties spanning three different structural features; i) micromechanics for CNC-epoxy properties, ii) laminate theory for fiber elements coated with CNCepoxy, and iii) a 2-D network model for an assembly of interconnected fiber elements. The extent to which CNCepoxy coating can stiffen a fiber element was dependent on the CNC volume fraction, CNC-epoxy layer thickness, CNC alignment, CNC aspect ratio, and the original stiffness of the fiber element. Calculations suggest there is a potential for CNC additions to stiffen network structures, the extent to which is strongly depending on the initial fiber element stiffness. Incorporation of limited experimental observations into the model and fiber element properties typical of fibers used in paper products, however, suggests that the enhancement of CNCs on a wood fiber element and thus on the network structure, may be limited.

An experimental investigation of a newly proposed through-thickness reinforcement approach aimed to increase interlaminar toughness of laminated composites is presented. The approach alters conventional methods of creating three-dimensional fiber-reinforced polymer composites in that the reinforcing element is embedded into the host laminate after it has been cured. The resulting composite is shown to possess the benefits of a uniform surface quality and consolidation of the original unreinforced laminate. This technique was found to be highly effective in suppressing the damage propagation in delamination double-cantilever beam (DCB) test samples under mode I loading conditions. Pullout testing of a single reinforcing element was carried out to understand the bridging mechanics responsible for the improved interlaminar strength of reinforced laminate and stabilization and/or arrest of delamination crack propagation. The mode I interlaminar fracture of reinforced DCB samples was modeled using two-dimensional cohesive finite-element scheme to support interpretation of the experiments.

Characterization of Carbon Nanotube (CNT) dispersion in a polyimide matrix and its effect on nanocomposite mechanical properties is presented in this paper. CNT bundle aspect ratio, measured by voltage-contrast scanning electron microscopy, is determined to be the quantitative measurement of dispersion and is found to decrease with increase in nanotube concentration. The reduction of CNT bundle aspect ratio with concentration is shown to explain the less effective reinforcement observed in composites as CNT concentration is increased beyond the electrical percolation concentration. It is shown that increase in CNT concentration beyond percolation concentration does not yield proportional improvement in elastic modulus because CNT aspect ratio systematically decreases as concentration increases. A modified Cox micromechanical model that accounts for the actual nanotube bundle aspect ratio as a function of concentration, nanotube waviness and orientation is shown to predict the observed nanocomposite elastic modulus dependence upon concentration.

Composite materials are widely used in industry due to their superior material properties and light weight. However, shear failure can occur at the interface between the fibers and polymer matrix when a tensile force stretches the matrix more than the fibers. Repairing the damaged composite material appears to be cost effective but still remains a challenge despite extensive research. Laser induced water breakdown plasma, which is generated by the strong interaction between nanosecond laser and water, is proposed in this work to etch the surface layer of a carbon fiber reinforced composite sample. It is found that the polymer layer can be effectively removed by the plasma while the carbon fiber remains almost intact. The dependence of the etching depth on the laser power density, laser focus position, and the number of shots are also investigated in this work. The maximum possible etching depth is around 350 μm with 50 laser shots at laser power density of 70 GW/cm2.

A family of analytic solutions for the prediction of interlaminar stresses in angle-ply laminates has been developed and is presented in a unified form and as a unique set of solutions. The uniqueness of the formulation is demonstrated for the class of thermomechanical states of deformation for which the solutions are valid. These are shown to be limited to the specific cases wherein only two in-plane stress components and one interlaminar stress components are nonzero. Interlaminar shear stress in the angle-ply laminate subjected to thermomechanical loading conditions of uniaxial extension, uniform temperature change, and anticlastic bending is shown to make up the family of solutions in the unified formulation. Further, these are shown to comprise the complete set of the solutions and the conditions which control the limitations of this family of solutions are articulated.

The significance of the free-edge singularities in angle–ply laminates and due to fiber terminations is explored and results are compared to that of a singularity due to the presence of a crack in the same region. A new dimensionless ratio, Δ is defined to compare the intensity of the singularities and the ratio shows that the stress field due to a crack of finite size is approximately twice that generated by free-edge singularities and 1.5 times as intense as the field generated by fiber terminations. For a range of material properties studied, it was found that the free-edge singularity was shown to effectively disappear as the ply angles decrease below ±15° or increase above ±85° and the fiber termination singularity was surprisingly insensitive to material properties. The results of this study suggest that singularities due to cracks dominate the stress field in the free-edge as compared to singularities at lamina discontinuities in equivalent media and fiber terminations.

We present a model to study the effect of the spatial distributions in fiber volume fraction on the failure initiation location in the open hole off-axis tensile. These variations are introduced with a micromechanical enhancement dehomogenization process. Good agreement is obtained between our predicted failure locations and experimental results by considering a failure criterion based on the effective shear strain in the matrix. The predicted failure angle distribution is in good agreement with the experimental results when the variability in the fiber volume fraction is included in the simulations.

An approximate elasticity solution for prediction of the displacement, stress and strain fields within the m-layer, symmetric and balanced angle-ply composite laminate of finite-width and subjected to uniform axial extension was developed earlier [4] . In the present paper, the authors have extended that solution to treat thermal stresses and deformations induced by a uniform change in laminate temperature. The results have revealed not only the complex fields within the laminate, but also inter-relationships between the lamina axial and shearing coefficients of thermal expansion and the effective laminate coefficients of thermal expansion. Further, the solution is shown to recover laminated plate theory predictions for thermally induced fields at interior regions of the laminate, thereby confirming the boundary layer nature of the interlaminar phenomena for the thermoelastic case. Finally, the results exhibit the anticipated response in congruence with the mechanical solution of Ref. [4] and the thermoelastic results satisfy the conditions of self-equilibration necessary for the finite-width laminate subjected to free thermal deformation. Integration of the stress σx over the laminate cross-section in the y–z plane is shown to converge to zero as the number of Fourier terms is increased. While the exact solution for mechanical loading is known to exhibit singular behavior, non-convergence of the interlaminar shearing strain is also seen to occur at the intersection of the free edge and planes between lamina of +θ and −θ orientation under thermal loading. The analytical results show excellent agreement with the finite-element predictions for the same boundary-value problem.

A computationally efficient method for determining the microscopic strain field within the separate phases of heterogeneous medium consisting of collimated, continuous fibers within an isotropic matrix is presented with the goal of providing one of the essential links in a multi-scale analysis of a composite structure which relates structural loading and deformations at the macro-scale to the state of strain within the fiber and matrix phases at the micro scale. The model utilizes a conventional influence function formulation and considers thermo-mechanical deformations.

The future development of polymer composite materials with nanotubes or nanoscale fibers requires the ability to understand and improve the interfacial bonding at the nanotube–polymer matrix interface. In recent work [Strus MC, Zalamea L, Raman A, Pipes RB, Nguyen CV, Stach EA. Peeling force spectroscopy: exposing the adhesive nanomechanics of one-dimensional nanostructures. Nano Lett 2008;8(2):544–50], it has been shown that a new mode in the Atomic Force Microscope (AFM), peeling force spectroscopy, can be used to understand the adhesive mechanics of carbon nanotubes peeled from a surface. In the present work, we demonstrate how AFM peeling force spectroscopy can be used to distinguish between elastic and interfacial components during a nanoscale peel test, thus enabling the direct measurement of interfacial energy between an individual nanotube or nanofiber and a given material surface. The proposed method provides a convenient experimental framework to quickly screen different combinations of polymers and functionalized nanotubes for optimal interfacial strength.