Within this paper, the authors present a rapid method for residual cure stress analysis. The method uses a high-fidelity path-dependent cure kinetics analysis subroutine implemented in Abaqus to calibrate values for a linear elastic analysis. The path dependent model accounts for the tool-part interaction, forming pressure, and the changing composite modulus during the rubbery region of matrix curing during an arbitrary cure cycle. Results are used to calculate equivalent lamina-wise coefficients of thermal expansion (CTE) in 3 directions for a linear temperature analysis. The goal is to accurately predict distortions for large complex geometries with a single linear temperature load as rapidly and accurately as possible for use in an optimization framework. A carbon-epoxy system is studied. Simple parts are manufactured using unbalanced layups and out-of-autoclave methods. The resulting distortions are scanned with a 3D scanner and compared with simulation results for the same geometries. Further, a more complicated part is studied to compare the two methods using complex geometry. Results are presented and the accuracy and limitations of the rapid simulation method are discussed with particular focus on implementation in a numerical optimization framework.

In this paper a rapid method for residual cure stress analysis from composite manufacturing is presented. The method uses a high-fidelity path-dependent cure kinetics subroutine implemented in ABAQUS to calibrate a linear elastic model. The path-dependent model accounts for the tool-part interaction, forming pressure, and the changing composite modulus during the rubbery phase of matrix curing. Results are used to calculate equivalent lamina-wise coefficients of thermal expansion (CTE) in 3 directions for a linear temperature analysis. The goal is to accurately predict distortions for large complex geometries as rapidly as possible for use in an optimization framework. A carbon-epoxy system is studied. Simple coupons and complex parts are manufactured and measured with a 3 D scanner to compare the manufactured and simulated distortion. Results are presented and the accuracy and limitations of the rapid simulation method are discussed with particular focus on implementation in a numerical optimization framework. © The Author(s) 2021.

As polymeric resins are used as matrix in reinforced composites, understanding of their viscoelastic-viscoplastic response is critical for long-term performance design. However, during service life, thermosets are not in a thermodynamic equilibrium state, resulting in physical aging, which affects failure and viscoelastic (VE) properties, becoming a concern for industries. In this paper, an alternative methodology for testing and parameter determination for aging polymer, at different temperatures (TA) and times (tA), is proposed. The experimental data analysis was performed using a Schapery's type thermo-aging-rheologically simple VE model with constant coefficients in Prony series and the effect of temperature and aging included by two shift factors (aT, aA). Results showed that the shift factor can be presented as the product of shifts aT and aA. Furthermore, for short tA the change rate of the aA with tA does not depend on TA, whereas for long tA at high TA the rate increases. 

The effect of physical aging on the viscoelastic (VE) behavior of epoxy resin is investigated experimentally performing strain-controlled tests at various temperatures on specimens aged at different temperatures (TA) for different times (tA). The aging effect is analyzed using as a framework Schapery's type of thermo-aging-rheologically simple (T-A-R simple) VE model that contains aging-state and test-temperature dependent shift factor. Experiments show that in first approximation, the shift factor can be presented as the product of aging related shift factor aA and temperature related factor aT. It is found that for short aging times the change rate of the aging shift factor with tA does not depend on TA, whereas for long tA at high TA the rate increases. Shift factors alone are not able to explain differences in relaxation curves for almost “fully” aged specimens aged at different high TA, It is shown that a T-A-R complex VE model with two additional aging-dependent functions can describe the observed discrepancies. © 2021

Reliable accelerated testing routines involving tests at enhanced temperatures are of paramount importance in developing viscoelastic models for polymers. The theoretical basis, the time-temperature superposition (TTS) principle, is used to construct master curves and temperature-dependent shift factor, which is the necessary information to simulate the material response in arbitrary temperature and strain regimes. The Dynamic Mechanical and Thermal Analysis (DMTA) TTS mode, being one of the most promising approaches in terms of time efficiency and maturity of the software, is compared in this paper with macrotests at enhanced temperatures in their ability to give reliable master curves. It is shown, comparing simulations with test data for a chosen epoxy polymer, that none of the three DMTA TTS mode-based attempts used (at different temperature steps during frequency scanning) was successful in predicting the epoxy behavior in tests. On the contrary, using one-hour macrotests at enhanced temperatures gives a viscoelastic model with a very good predicting accuracy. Simulations were performed using an incremental formulation of the previously published VisCoR model for linear viscoelastic materials. 

Effect of degree of cure on irreversible (viscoplastic) shear strain development in layers of glass fibre/ epoxy resin (LY5052 epoxy resin) [+45 °/−45 °]s laminate is studied performing a sequence of constant stress creep and viscoelastic strain recovery tests. For fixed values of degree of cure in range from 79.7% to 100%, the viscoplastic strains were measured as dependent on time and stress and Zapa's integral representation was used to characterize the observed behaviour. It is shown that at all degrees of cure the viscoplastic behaviour can be described by Zapa's model with parameters dependent on degree of cure. It is shown that for degree of cure lower than 80% the viscoplastic strains grow much faster and are much more sensitive to the increase of the applied shear stress. These irreversible strains developing in the final phase of the curing can significantly alter the residual stress state in the composite structure.

Stress relaxation and strain recovery phenomena during curing and changed thermal conditions are analyzed using a viscoelastic model developed for thermorheologically complex materials (VisCoR). By making several simplifying assumptions regarding the material behavior, the incremental form of the VisCoR model is reformulated to a version describing thermorheologically simple material and presented in one-dimension for simplicity. The model (called VisCoR-simple) is used to analyze material behavior under various conditions, including stress relaxation behavior at varying temperatures and time scales; tensile loading and unloading tests at high temperatures; stress build up and “frozen-in” strains during curing and following cool-down and strain recovery during the next step of heating. Furthermore, the differences between the so-called “path-dependent” model, which is a linear elastic model with different elastic properties in glassy and rubbery regions, and the presented viscoelastic model are studied. The path-dependent model is an extreme case of the viscoelastic model presented. The importance of considering viscoelasticity when considering temperature and curing effects on polymers and the shortcomings of the path-dependent model are revealed and discussed. © The Author

A thermo-rheologically complex linear viscoelastic material model, accounting for temperature and degree of cure (DoC), is developed starting with series expansion of the Helmholtz free energy and systematically implementing simplifying assumptions regarding the material behavior. In addition to the temperature and DoC dependent shift factor present in rheologically simple models, the derived novel model contains three cure and temperature dependent functions. The first function is identified as the rubbery modulus. The second is a weight factor to the transient integral term in the model and reflects the current temperature and cure state, whereas the third function is under the sign of the convolution integral, thus affecting the “memory” of the material. An incremental form of this model is presented which, due to improved approximation inside the time increment, has better numerical convergence than most of the similar forms. Parametric analysis is performed simulating stress development in a polymer, geometrically constrained in the mold during curing and cool-down. The importance of using proper viscoelastic model is shown, and the role of parameters in the model is revealed and discussed. 

The present contribution is toward the systematic characterization and development of a one-dimensional incremental viscoelastic (VE) model for thermo-rheologically complex materials (called “VisCoR”) for the prediction of residual stresses and shape distortions in composites. Traditionally, models that have been developed for this purpose within the composites industry are based on incremental linear elastic methods. While these methods are robust, they fall short in predicting exact behaviour of large composite parts and high temperature composites where relaxation effects also play a vital role in the final shape of the part. Moreover, these models also do not consider the dependency of stresses on temperature and degree of cure. Although viscoelastic models have been formulated, they are not in an incremental form (which is suitable for Finite Element (FE) simulations), hence requiring higher computational efforts. The presented model is an incremental form and requires lesser computational cost and characterization efforts and most importantly takes into account the effect of temperature and degree of cure. Preliminary studies indicate that the incremental 1D viscoelastic model can accurately model VE stress relaxation behaviour when compared to exact solutions.

It is shown, using thermodynamically consistent linear viscoelastic material model that accounts for properties dependence on test temperature and cure state parameters, that for rheologically simple materials the cure and temperature related reduced times and shift factors are the same for all viscoelastic compliances, relaxation modulus, and Poisson’s ratio as well as for the storage and loss modulus. A necessary condition for that is that the cure and temperature parameters are affecting the reduced time only. This means that the Poisson’s ratio of polymeric materials, which for simplicity is often assumed constant, in fact exhibits a small dependence on time which is affected by temperature and state of cure. In this work, the evolution of the viscoelastic Poisson’s ratio of the commercial LY5052 epoxy resin is studied in relaxation test subjecting the specimen to constant axial strain. Specimens at several cure states are studied and Poisson’s ratio, defined as the lateral and axial strain ratio, is shown to evolve from 0.32 to 0.44 over time. Moreover, the data confirm that the cure state-dependent reduced time controlling the Poisson’s ratio development leads to the same shift functions as those identified in DMTA tests for storage modulus. The latter measurements also confirmed that the total shift can be considered as a sum of two shifts in the frequency domain, which means that function for reduced time calculation can be written as a product of two functions: one dependent on the test temperature and another one dependent on the cure state.

The aim of the presented work is to investigate the relationship between the rubbery modulus and the degree of cure for partially to fully cured LY5052 epoxy resin. In particular, this work experimentally tests an existing model defined in shear modulus by redefining into the elastic tensile modulus. Experiments were performed in a Dynamic Mechanical and Thermal Analysis (DMTA) machine in the frequency domain. After the model is tested, super-master curves generated using time-temperature-cure superposition are normalized using the model so that the rubbery modulus made independent on the state of cure, which further simplifies the super-master curves. This results in a unique master curve that describes the viscoelastic behavior of the LY5052 epoxy resin for the given conditions. This consequently could help formulate simplified models to predict viscoelastic behaviour and also develop better experimental methodologies to characterize them.

The Poisson's ratio of a solid under deformation is classically defined as the negative of the ratio between the lateral or transverse strain and the axial strain. Ideally for an elastic material, the Poisson's ratio is assumed to be a constant. However, for viscoelastic materials like polymers and polymer matrix composites this is also likely influenced by various factors like time [1], temperature, degree of cure and also on the strain. In this work, the evolution of the viscoelastic Poisson's ratio of the commercial LY5052 epoxy resin is studied under uniaxial tension subject to constant deformation stress relaxation testing. Measurements of the Poisson ratios are performed using contact extensometers and strain gages. Samples at five different cure states are manufactured and investigated. The relaxation testing is performed by loading the samples to 0.5% longitudinal strain and monitoring the relaxation behavior over a period of 24 hours per cure state. Poisson's ratio is observed to evolve from 0.32 to 0.44 over time depending on the cure state. Moreover the data indicates that the individual Poisson's ratio curves can be shifted horizontally following time-cure superposition. The shift functions used for this horizontal shifting are similar to those identified for DMTA tests for storage modulus under identical conditions. Following horizontal shifting, master curves that show the evolution of Poisson's ratio over time can be created for a particular reference cure state. This similarity of the shift functions in both micro-scale DMTA testing and macro-scale relaxation testing is an indicator of the validity of the shift factors. The observation is used to further develop a viscoelastic model which identifies the total shift function as the product of the temperature and cure shift functions. 

In this work, we investigate the relationship between the rubbery modulus and the degree of cure for partially to fully cured LY5052 epoxy resin. In particular, this paper experimentally tests an existing model formulated for shear modulus by redefining for in the tensile storage modulus. Experiments to characterize viscoelastic behaviour were performed in a dynamic mechanical and thermal analysis (DMTA) instrument in the frequency domain. Master curves are then created from DMTA using general time–temperature–cure superposition. The master curves are then normalized using the model so that the master curve does not depend on the properties in the rubbery region. This results in a unique master curve that describes the viscoelastic behaviour of the LY5052 epoxy resin for the given conditions. Once the relationship between the rubbery modulus and the degree of cure has been established, the amount of experimental characterization can be reduced. This could lead to the development of simplified experimental methodologies and simplified models to characterize the viscoelasticity of low molecular weight resins like the LY5052 epoxy resin system.