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Chemical shrinkage in thermosetting polymers drives residual stress development and induces residual deformation in composite materials. Accurate characterization of chemical shrinkage during curing is therefore vital to minimize residual stresses through process modeling and optimize composite performance. This work introduces a novel methodology to measure the pre- and post-gelation chemical shrinkage of an epoxy resin using three-dimensional digital image correlation (3D-DIC). Differential scanning calorimetry (DSC) is employed to calculate reaction kinetics and correlate chemical shrinkage with the degree of cure. Rheology experiments are conducted to quantify gelation and validate post-gelation. 3D-DIC post-gelation results show excellent agreement with rheology. Pre-gelation results show the effect of the in-situ curing in the proximity of constraints on the global strain behavior. This work introduced an innovative approach to characterize the chemical shrinkage of thermosets during curing, which will enable accurate residual stress prediction for enhancing thermoset composite performance and provide insight into the in-situ polymer behavior during processing.

Uncontrolled curing-induced residual stress and strain are significant limitations to the efficient design of thermoset composites that compromise their structural durability and geometrical tolerance. Experimentally validated process modeling for the evaluation of processing parameter contributions to the residual stress build-up is crucial to identify residual stress mitigation strategies and enhance structural performance. This work presents an experimentally validated novel numerical approach based on higher-order finite elements for the process modeling of fiber-reinforced thermoset polymers across two composite characteristic length scales, the micro and macro-scale levels. The cure kinetics is described using an auto-catalytic phenomenological model. An instantaneous linear-elastic constitutive law, informed by time-dependent material characterization, is used to evaluate the stress state evolution as a function of the degree of cure and time. Micromechanical modeling is based on Representative Volume Elements (RVEs) that account for random fiber distribution verified against traditional 3D FE analysis. 0/90 laminate testing at the macroscale validates the proposed approach with an accuracy of 9%.

During the manufacturing of composite structures, cure shrinkage of the thermoset matrix and differential thermal contraction mismatch between the matrix and fiber reinforcement cause the formation of residual stresses, which can result in a loss in structural durability. New multiscale computational process modeling is essential for linking material chemistry, processing parameters, residual stress evolution, and optimizing mechanical performance. This study establishes a new multiscale process modeling method to accurately predict residual stresses in a unidirectional carbon fiber/epoxy composite using molecular dynamics and finite element analysis simulation techniques. The results of this work demonstrate that process-induced residual stresses have a significant impact on the composite strength in transverse tension, out-of-plane shear, and in-plane shear, with a maximum reduction in strength of 35%. Moving forward, this method can be used as a design and optimization tool for future composite structures for specific engineering applications and can provide processing parameters that can maximize desirable composite properties and/or minimize composite manufacturing energy and cost.

It is well-known that all-atom molecular dynamics (MD) predictions of mechanical properties of thermoset resins suffer from multiple accuracy issues associated with their viscous nature. The nanosecond simulation times of MD simulations do not allow for the direct simulation of the molecular conformational relaxations that occur under laboratory time scales. This adversely affects the prediction of mechanical properties at realistic strain rates, intermediate degrees of cure, and elevated temperatures. An efficient method of correcting such MD predictions of elastic properties is proposed and demonstrated. The phenomenological approach is used to map the predictions of Young's modulus and Poisson's ratio for a DGEBF/DETDA epoxy system to the corresponding laboratory-based properties for intermediate degrees of cure and temperatures above and below the glass transition temperature. The approach uses characterization data from dynamical mechanical analysis temperature sweep experiments. The mathematical formulation and experimental characterization of the mapping are described, and the resulting corrections to the predicted elastic properties for various degrees of cure and temperatures are compared with the experiment. This mapping is particularly important to mitigate the strain-rate effect associated with MD predictions, as well as to accurately predict mechanical properties at elevated temperatures and intermediate degrees of cure to facilitate accurate and efficient composite material process modeling.

It is well-known that all-atom molecular dynamics (MD) predictions of mechanical properties of thermoset resins suffer from multiple accuracy issues associated with their viscous nature. The nanosecond simulation times of MD simulations do not allow for the direct simulation of the molecular conformational relaxations that occur under laboratory time scales. This adversely affects the prediction of mechanical properties at realistic strain rates, intermediate degrees of cure, and elevated temperatures. An efficient method of correcting such MD predictions of elastic properties is proposed and demonstrated. The phenomenological approach is used to correct the predictions of Young’s modulus and Poisson’s ratio for a DGEBF/DETDA epoxy system for intermediate degrees of cure and temperatures above and below the glass transition temperature. The approach uses characterization data from dynamical mechanical analysis temperature sweep experiments. The mathematical formulation and experimental characterization of the correction is described, and the resulting corrections to the predicted elastic properties for various degrees of cure and temperatures are compared with experiment. This correction is particularly important to mitigate the strain-rate effect associated with MD predictions, as well as to accurately correct predicted mechanical properties at elevated temperatures and intermediate degrees of cure to facilitate accurate and efficient composite material process modeling.

Rapid reaction kinetics often produce drastic changes in the thermo-chemo-mechanical characteristics of thermoset polymers over short time periods. Thus, it is a major challenge to quantify material properties over the entire spectrum of cure states at relevant temperatures with both efficiency and accuracy. This work presents a novel characterization technique as a function of the cure state of a difunctional epoxy with amine curing agent through off-stoichiometry mixing formulations that serve as proxies for the intermediately crosslinked polymer. Mass density, cure kinetics, and elastic and strength properties are characterized across four mixing ratios, and relative cure/crosslinked states of off-stoichiometry cases are quantified. Essential to this unique approach is the capability to eliminate time dependence resulting from reaction kinetics on characterizing intermediate crosslinking states. The procedure reported herein facilitates efficient and accurate measurement of properties of curing epoxies for building and validating computational process modeling frameworks developed for optimizing material performance.

Thermoset resin-based composite materials are widely used in the aerospace industry, mainly due to their high stiffness-to-weight and strength-to-weight ratios. A major issue with the use of thermoset resins in fiber composites is the process-induced residual stresses that are formed from resin chemical shrinkage during the curing process. These residual stresses within the composite material ultimately result in reduced durability and residual deformations of the final product. Polybenzoxazine (PBZ) polymer resins have demonstrated near-zero volumetric shrinkage during the curing process. Although the low shrinkage of PBZ is promising in terms of reduced process-induced residual stresses, little is known about the physical causes. In this work, Molecular Dynamics (MD) simulations are performed with a reactive force field to predict physical properties (gelation point, evolution of network, mass density, volumetric shrinkage) and mechanical properties (Bulk modulus, Shear modulus, Young's modulus, Poisson's ratio, Yield strength) as a function of crosslinking density. The MD modeling procedure is validated herein using experimental measurements of the modeled PBZ resin. The results of this study are used to provide a physical understanding of the zero-shrinkage phenomenon of PBZ. This information is also a critical input to future process modeling efforts for PBZ composites.

Thermoplastic Matrix Composites (TMC) are shown to have a considerable commercial interest in cutting-edge industries due to their superior mechanical and chemical properties and the resistance to high temperatures. During the processing, TMCs are subjected to a wide range of elevated temperatures involving different cooling and heating cycles which result in the development of internal residual stresses in the matrix. In semicrystalline polymers such as PEEK, formation of crystalline regions during the processing causes shrinkage in the matrix leading to generation of additional residual stresses. Optimization of materials, manufacturing and design of components reduces development cycle time and cost for future hightechnology applications of TMCs. It has been shown that manufacturing of TMCs has a huge impact on the microstructure of these material, which in turn control the in-service performance. Since the thermo-mechanical properties of composite materials are defined by phenomena at multiple length scales, to have precise estimation of these residual stresses, a computational approach is required to combine simulation tools at multiple length scale. In this study, a multiscale approach has been introduced based on the Integrated Computational Material Engineering (ICME) which integrates Molecular Dynamics (MD) and Finite Element Analysis (FEA) to predict the induced residual stresses during processing. In the first step, thermoelastic properties of semicrystalline PEEK are determined as function of crystallinity content at different processing temperature at nanoscale using MD and micromechanics modeling. In the next step, the evolution of thermo-elastic properties during the crystallization is achieved using computational and experimental data. These results will be used to estimate the induced residual stresses of composites at higher length scales. This two-scale approach will allow us to virtually characterize material properties and predict the residual stress state of composites during manufacturing as a function of processing parameters and investigate the effect of temperature and temperature history on semi-crystalline PEEK thermal-mechanical properties.

This manuscript presents the analysis of the curing process of thermoset polymers to predict the cure-induced residual stresses at the micro-scale level. A phenomenological cure kinetics model is used to describe the polymerization process, while an instantaneous linear-elastic constitutive law is used to predict residual stress. The computational model leverages higher-order structural theories derived from the Carrera Unified Formulation. A ten-fiber randomly packed repeating unit cell is virtually cured using the proposed higher-order method. The predicted stress state is shown to agree with reference results based on 3D finite element analysis while achieving a multi-fold reduction in the computational effort.

The transverse tensile strength of composites is susceptible to size effects. Therefore, it is paramount to develop length-scale specific physical test procedures to validate computational models that estimate the transverse composite response using micromechanics. To this end, a computational process modeling and virtual mechanical testing framework are presented in this study to predict the transverse response of composite microstructures subjected to processing conditions. Informed by a comprehensive material dataset, the numerical model is shown to reliably predict the process-induced residual stress generation in composite microstructures and accurately evaluate its influence on their transverse strength prediction. A novel procedure to fabricate thin composite laminates from a single ply of carbon fibers and characterize their transverse tensile response is presented to validate the numerical model. The results show excellent agreement with the virtual test predictions. This study highlights the importance of length-scale specific testing to minimize the influence of size effect on the transverse composite strength.

The curing of adhesives in wind turbine blades is a cost and time-intensive manufacturing step. Bondlines are critical to the structural integrity of the blade, but substantial variation in bondline thickness can result in different thermal histories and even degradation of the adhesive due to its exothermic reaction. Models to predict the thermal behavior of adhesive bondlines during the curing step, taking manufacturing conditions and variation in thickness into account, are needed to minimize cure times while avoiding excess temperature. In this study, a finite element model capable of tracing the thermal and conversion histories of the adhesive was developed. Standard heat transfer equations were coupled with cure kinetics in the model through user subroutines, and the cure kinetics were characterized and validated experimentally. A 2D cross-section model of a wind turbine blade was created to simulate the adhesive curing cycle in a manufacturing setting. This model was used to highlight critical aspects of the curing cycle and test methods to shorten the cycle time while maintaining the integrity of the bond. Several improvement methods and their potential cycle time savings were investigated, such as implementing individual heating and cooling zones for each adhesive area and additional spar cap heating/cooling.

The prediction of thermo-mechanical properties of a thermoset resin at different stages of cure is a complex process. An Integrated Computational Material Engineering (ICME) approach is used to predict the properties of a EPON828/Jeffamine D230 system. The proposed framework integrates two length scales - nano and microscale. Molecular Dynamics (MD) is used to predict the volume shrinkage and mechanical properties of the epoxy resin as a function of the progressing crosslink density at room temperature using the Reactive Interface forcefield (IFF-R). The predicted resin properties show good agreement with the literature, proving that IFF-R can be reliably used for this purpose. Once characterized, the predicted properties are used to further predict the effects of cure shrinkage and property transformation on the bulk-level composite residual stresses. P. P. DESHPANDE

In this work, Molecular Dynamics (MD) simulations are performed to predict the physical properties (gelation point, mass density, volumetric shrinkage) and mechanical properties (Bulk modulus, Shear modulus, Young’s Modulus, Poisson’s ratio) of a PolyBenzoxazine (PBZ) resin system as a function of crosslinking density. The molecular models are developed using the Reactive Interface Force Field (IFF-R). The results obtained from MD are in good agreement with the experimental data.

This study presents a finite element (FE) based virtual test procedure to investigate the effect of the manufacturing process on the transverse composite response. Computational models of the composite microstructures are generated and analyzed in commercial FE solver Abaqus supplemented by user-written subroutines. Several realizations of the composite microstructure with random fiber arrangement are analyzed assuming appropriate initial stress state and material definitions. The virtual test procedure is established to define the evolution of process-induced in-situ matrix properties through direct and inverse process modeling approaches. Subsequently, the composite microstructures are virtually tested in transverse tension to predict the transverse composite properties by implementing progressive damage models. In order to quantify the effect of manufacturing on the transverse composite response, predictions from the two approaches are compared to a third case which assumes an initial stress-free state and neglects the effect of processing conditions on the in-situ matrix properties. Variations of ±5% in average strength and 18% in standard deviations are observed with respect to ideally cured RVEs. It is established that process modeling in necessary to optimize the residual stress state and improve composite performance.

Polymer Matrix Composites (PMCs) have been the subject of many recent studies due to their outstanding characteristics. For the processing of PMCs, a wide range of elevated temperatures is typically applied to the material, leading to the development of internal residual stresses during the final cool-down step. These residual stresses may lead to net shape deformations or internal damage. Also, volumetric shrinkage, and thus additional residual stresses, could be created during crystallization of the semi-crystalline thermoplastic matrix. Furthermore, the thermomechanical properties of semi-crystalline polymers are susceptible to the crystallinity content, which is tightly controlled by the processing parameters (processing temperature, temperature holding time) and material properties (melting and crystallization temperatures). Hence, it is vital to have a precise understanding of crystallization kinetics and its impact on the final component's performance to accurately predict induced residual stresses during the processing of these materials. To enable multi-scale process modeling of thermoplastic composites, molecular-level material properties must be determined for a wide range of crystallinity levels. In this study, the thermomechanical properties and volumetric shrinkage of the thermoplastic Poly Ether Ether Ketone (PEEK) resin are predicted as a function of crystallinity content and temperature using molecular dynamics (MD) modeling. Using crystallization-kinetics models, the thermo-mechanical properties are directly related to processing time and temperature. This research can ultimately predict the residual stress evolution in PEEK composites as a function of processing parameters.

The effect of residual stress build-up on the transverse properties of thermoset composites is studied through direct and inverse process modeling approaches. Progressive damage analysis is implemented to characterize composite stiffness and strength of cured composites microstructures. A size effect study is proposed to define the appropriate dimensions of Representative Volume Elements (RVEs). A comparison between periodic (PBCs) and flat (FBCs) boundary conditions during curing is performed on converged RVEs to establish computationally efficient methodologies. Transverse properties are analyzed as a function of the fiber packing through the nearest fiber distance statistical descriptor. A reasonable mechanical equivalence is achieved for RVEs consisting of 40 fibers. It has been found that process-induced residual stresses and fiber packing significantly contribute to the scatter in composites transverse strength. Variation of ±5% in average strength and 18% in standard deviation are observed with respect to ideally cured RVEs that neglect residual stresses. It is established that process modeling is needed to optimize the residual stress state and improve composite performance.

This paper proposes a novel experimental investigation based on 3D printing to validate numerical models for biomechanics simulations. Soft elastomeric materials have been used in Polyjet multi-material 3D printer to mimicking arteries affected by atherosclerotic plaque. The nonlinear mechanical properties of five digital materials are characterized and used as an input for finite element (FE) modeling. Pressurized air is applied to the internal cavity of the printed model to reproduce the internal blood pressure in the artery. Digital Imaging Correlation is adopted to measure the displacement and deformation. A 1D linear higher-order FE model based on the Carrera Unified Formulation is compared to 3D nonlinear FE solutions.

Microscale computed tomography scans of fiber-reinforced composites reveal that fibers are most often not strictly parallel to each other but exhibit varying degrees of misalignment and entanglement. One characteristic of this entanglement is the degree to which fibers stay together as clusters. In this study, a method for identifying and isolating fiber clusters was established, and scans of two different composite microstructures were analyzed. To identify clusters, fiber center points of the first cross-section were triangulated, and the variation of the perimeter and area of triangles along the fiber direction was used to identify fiber triads which stay together. A filtering process eliminated fiber triads not part of a larger cluster. Geometric properties of the clusters such as cluster orientation, radius of gyration, cluster density, and volume fraction were calculated and compared. The metrics revealed fundamental differences between the two samples, suggesting that clusters have origins in manufacturing.

Process-induced variabilities in fiber-reinforced polymer composite (FRPC) microstructures result in large scatters in the experimentally measured composite properties which lead to conservative designs and unnecessary manufacturing cost. Processing conditions such as cure temperature and time combined with low thermal conductivity impose spatially varying thermal histories that influence cure evolution and property development in composite during manufacturing. Additionally, irregular and off-axial fiber architectures introduce thermo-mechanical constraints which lead to residual stress generation, damage accumulation during curing, and in-situ matrix properties. Complete understanding of the process-induced variation in the fiber and matrix at the microscale is necessary to identify sources of scatter in bulk composite mechanical properties and eventually optimize the manufacturing process. The objective of the proposed study is to establish the processing-microstructure-property correlation to improve predictions and reduce processing times of FRPCs using experimental techniques and computational modeling. Statistical descriptors are developed to study process-induced variation in the fiber microstructures. Micro-CT scans of aerospace- and automotive-grade laminates are analyzed. The effect of processing conditions on the two microstructures is investigated; qualitative and quantitative comparisons of the statistical metrics are made. Micro-Raman spectroscopy is successfully employed to generate a 3D map of the degree of cure variation in a partially cured epoxy sample. This technique will be further explored to quantify the process-induced degree of cure variation in a composite laminate. Finally, a finite element (FE) based process modeling computational framework is developed to virtually study the process-induced variations in the composite microstructure. The process-induced variability in fiber and matrix will be correlated to residual stress generation, damage accumulation during cure, and bulk composite properties through process modeling simulations of virtually reconstructed microstructures.

An Integrated Computational Material Engineering (ICME) approach is employed to predict the thermo-mechanical properties of thermoset polymers at different stages of cure. The framework integrates Molecular Dynamics (MD) at nanoscale and Finite Element Methods (FEM) at microscale. MDis used to predict the volume shrinkage and mechanical properties of an epoxy resin as a function of the crosslink density at room temperature using the Interface Forcefield (IFF). The predicted resin properties show good agreement with the literature values, showing that IFF can be reliably used for this purpose. Once characterized, the predicted properties can be used to further predict the effects of cure shrinkage on bulk-level composite residual stresses.

To predict the effect of the cure cycle on the thermo-mechanical properties of thermoset polymers, a two-scale method is implemented within the Integrated Computational Material Engineering (ICME) approach. Molecular Dynamics (MD) is employed to predict the resin volume shrinkage as a function of the degree of cure at the corresponding curing hold temperature using the Interface Forcefield (IFF). The predicted resin shrinkage values show good agreement with the literature, showing that MD, using IFF, can be reliably used for this purpose. Once computed, the shrinkage values can be used to predict the effects of shrinkage on bulk-level composite residual stresses induced by curing.

This article details the modeling of EPON862/DETDA epoxy system using Molecular Dynamics to predict the volumetric shrinkage as a function of crosslinking density. The ‘fix bond/react’ command in LAMMPS is used to virtually simulate the curing of the epoxy. The results for the shrinkage showed a good agreement with other modeling data in literature.

This paper addresses the effects of defects occurring during the manufacturing process on mechanical performance of Polymer Matrix Composites (PMCs). Damage accumulation during cure and subsequent in-service performance are studied by using randomly packed Repeating Unit Cell (RUC) representative of unidirectional fiber ply material or a textile fiber tow, at the microstructural level. Computations are carried out using the Finite Element (FE) method within the commercial code ABAQUS in which constitutive models are implemented via user-written subroutines. The transition from a continuum to damage and failure is determined by using the Bažant-Oh crack band model. Results are presented for RUCs that are first subjected to curing and subsequently to mechanical loading in the transverse direction. The analysis shows the differences in both the cured RUC transverse strength, S , and stiffness, E , when cure induced damage and imperfections such as presence of voids, fiber contact, imperfect fiber/matrix bonding and presence of matrix pockets are considered.