A thermo-viscoelastic approach for the characterization and modeling of the bending behavior of thermoplastic composites

Currently, there is no established and cost-effective method for the bending characterization of continuous fiber reinforced thermoplastic composites. Isothermal mechanical testing techniques are time and labor-intensive and deliver information only about distinct points of the temperature-dependent property curves. In this study, Dynamic Mechanical Analysis (DMA) as well as novel rheometer-based bending experiments were performed to assess temperature-dependent and viscoelastic behavior. On the basis of the experimental results a new method was defined and validated for the efficient characterization of temperature-dependent elastic bending behavior via DMA. Furthermore a linear viscoelastic material model was derived from DMA experiments by means of time–temperature superposition. As the material behavior proved to be of a highly viscoelastic nature, a method was developed to calibrate a material model, the parallel rheological framework, implemented in Abaqus.     

A rate-dependent non-orthogonal constitutive model for describing shear behaviour of woven reinforced thermoplastic composites

A rate dependent constitutive model for woven reinforced thermoplastic matrix composites at forming temperatures is proposed in this work. The model is formulated using a stress objective derivative based on the fibre rotation. Nonlinear shear behaviour is modelled as a polynomial function and the rate dependence is described using a Cowper–Symonds overstress law formulated in terms of shear angle rate. The model parameters are determined by means of bias extension tests. The applicability of the material model is validated through a forming experiment.     

A mechanism-based multi-scale model for predicting thermo-oxidative degradation in high temperature polymer matrix composites

This paper describes a mechanism-based multi-scale model for life prediction of high temperature polymer matrix composites (HTPMC) under thermo-oxidative aging conditions. The multi-scale model incorporates molecular level damage such as inter-crosslink chain scission in a thermoset polymer due to thermo-oxidative aging of the polymer resin. The degradation of inter-laminar stress depends on remaining inter-crosslink density of thermo-set polymer in fiber/matrix interface region subjected to thermo-oxidative aging environment. The degradation of inter-laminar shear stress of thermo-oxidatively aged unidirectional IM-7/PETI-5 composite specimens at 300 °C was modeled using an in-house test-bed FEA code (NOVA-3D). A micromechanics based viscoelastic cohesive layer model was used to model delamination. The model is fully rate dependent and does not require a pre-assigned traction-separation law. Viscoelastic regularization of the constitutive equations of the cohesive layer used in this model not only mitigates numerical instability, but also enables the analysis to follow load-deflection behavior beyond peak failure load. The model was able to successfully simulate delamination failure in thermo-oxidatively aged unidirectional IM-7/PETI-5 composite, and the model predictions were verified using test data.     

Analysis of the thermomechanical shear behaviour of woven-reinforced thermoplastic-matrix composites during forming

Shear behaviour of a glass fibre/polypropylene composite is characterized over a wide range of strain rates and forming temperatures using the bias extension test. A temperature- and rate-dependent material model is here introduced to describe the observed behaviour. The model is based on a continuous approach and formulated considering a stress objective derivative based on the warp and weft yarns rotation. The effects of temperature and strain rate on the shear behaviour are analysed via bias extension test simulations. Temperature change in the sheet during forming was measured. This data is used to model cooling during forming. Isothermal and transient forming simulations were performed in order to show the effects of temperature and forming speed on the obtained shear angle distribution. It was found that at low forming speeds the assumption of isothermal forming is not valid anymore since the cooling of the sheet affects the shear behaviour.     

A progressive damage simulation algorithm for GFRP composites under cyclic loading. Part I: Material constitutive model

A life prediction algorithm and its implementation for a thick-shell finite element formulation for GFRP composites under constant or variable amplitude loading is introduced in this work. It is a distributed damage model in the sense that constitutive material response is defined in terms of meso-mechanics for the unidirectional ply. The algorithm modules for non-linear material behaviour, pseudo-static loading-unloading-reloading response, Constant Life Diagrams and strength and stiffness degradation due to cyclic loading were implemented on a robust and comprehensive experimental database for a unidirectional glass/epoxy ply. The model, based on property definition in the principal coordinate system of the constitutive ply, can be used, besides life prediction, to assess strength and stiffness of any multidirectional laminate after arbitrary, constant or variable amplitude multi-axial cyclic loading. Numerical predictions were corroborated satisfactorily by test data from constant amplitude fatigue of glass/epoxy laminates of various stacking sequences.     

Multivariable dependency of thermal shrinkage in highly aligned polypropylene tapes for self-reinforced polymer composites

Self-reinforced composites offer a unique combination of properties such as high specific strength, high impact resistance, and recyclability by incorporating highly aligned fibers within a random matrix of the same polymer. However, high temperatures will shrink the system to recover randomness in the aligned segments, compromising the composite thermal stability during processing as self-reinforced tapes are consolidated into the final composite through heating and pressure. Hence, the dynamic nonlinear multivariable (i.e., time, temperature, stress) shrinkage exhibited by self-reinforced polypropylene (SRPP) tapes was measured and modeled at the maximum shrinkage limit achieved in the proximity of the composite processing temperature [∼140 to160 °C]. At high stress (∼7.5 MPa) the thermal shrinkage of the SRPP tapes was reduced and a parallel creep mechanism was activated. The modeling, and prediction of the main factors governing the thermal shrinkage expand and diversify the dynamic design window for new SRPP composites.     

Experimental assessment of dual-scale resin flow-deformation in composites processing

In this paper we are concerned with the assessment of sub-models within a two-phase continuum mechanical FE framework for process modeling of composites manufacturing. In particular, the framework considers the inclusion of two deformation dependent models describing resin flow related to: (1) meso-scale wetting and compaction of individual plies and (2) overall preform deformation and macroscopic Darcian flow. Using micro-mechanical modeling, we model the physics of these sub-processes in relation to the recently developed Out-Of-Autoclave (OOA) prepergs. The models are placed in context with a compression–relaxation experiment, employed to study the preform deformations considered separated from other sub-processes. Finally, calibrations and model validations are carried out against the relaxation experiment to relate the FE framework to the mechanical response of the preform. Therefore, using the above experiment, parameter values out of the literature and those estimated from micrographs gave a fair agreement between the simulation and experiments.     

Development of viscoelastic/rate-sensitive-plastic constitutive law for fiber-reinforced composites and its applications Part II: Numerical formulation and verification

The viscoelastic/rate-sensitive plastic constitutive law to describe the non-linear, anisotropic/asymmetric and time/rate-dependent mechanical behavior of fiber-reinforced (sheet) composites were developed as discussed in Part I along with experimental procedures to obtain the material parameters for the woven fabric composite. Here, numerical formulations were developed. For verification purposes, finite element simulation results based on the proposed constitutive law were compared with experiments for the time-dependent springback in rate-dependent three point bending tests.     

Nanoreinforced polymer composites: 3D FEM modeling with effective interface concept

A computational study of the effect of structures of nanocomposites on their elastic properties is presented. The special program code for the automatic generation of 3D multiparticle unit cells with/without overlapping, effective interface layers around particles is developed for nanocomposite modeling. The generalized effective interface model, with two layers of different stiffnesses and the option of overlapping layers is developed here. The effects of the effective interface properties, particle sizes, particle shapes (spherical, cylindrical, ellipsoidal and disc-shaped) and volume fraction of nanoreinforcement on the mechanical properties of nanocomposites are studied in numerical experiments. The higher degree of particle clustering leads to lower Young’s modules of the nanocomposites. The shape of nanoparticles has a strong effect on the elastic properties of the nanocomposites. The most effective reinforcement is cylindrical one, followed by ellipsoids, discs, and last, spheres. Ideally random oriented and correlated microstructures lead to the same average Young moduli, yet, the standard deviation of Young modulus for correlated microstructure is nearly 4 times of that for fully random orientation case.     

Finite element model for compression after impact behaviour of stitched composites

A finite element (FE) model using coupling continuum shell elements and cohesive elements is proposed to simulate the compression after impact (CAI) behaviour and predict the CAI strength of stitched composites. Continuum shell elements with Hashin failure criterion exhibit the composite laminate damage behaviour; whilst cohesive elements using traction-separation law characterise the laminate interfaces. Impact-induced delamination is explicitly modelled by reducing material properties of damaged cohesive elements. Computational results have demonstrated the trend of increasing CAI strength with decreasing impact-induced delamination area. Spring elements are introduced into the model to represent through-thickness stitch thread in the composite laminates. Results in this study validate experimental finding that CAI strength is improved when stitching is incorporated into the composite structure. The proposed FE model reveals good CAI strength predictions and indicates good agreement with experimental results, making it a valuable tool for CAI strength prediction of stitched composites.     

Finite element modeling of post-fire flexural modulus of fiber reinforced polymer composites under constant heat flux

In this study, a simple 1D finite element model was developed to predict the temperature evolution and post-fire mechanical degradation of glass fiber reinforced polymers (FRPs) subjected to constant heat fluxes, including 35 kW/m², 50 kW/m², 75 kW/m², and 100 kW/m². A temperature-dependent post-fire mechanical property model was proposed and implemented. The calculated temperature and residual mechanical moduli showed good agreement with the experimental data. By properly selecting the parameters of the model, an effective strategy was demonstrated to design FRP structure with enhanced durability.     

A micromechanics-based incremental damage model for carbon black filled rubbers

This paper is to develop a simple micromechanics-based model taking account of progressive damaging for carbon black (CB) filled rubbers. The present model constitutes of the instantaneous Young's modulus and Poisson's ratio characterizing rubber-like material, a double-inclusion (DI) configuration considering the absorption of rubber chains onto CB particles, and the incremental Mori-Tanaka formula to compute the effective stress–strain relations. The progressive damage in filled rubbers is described by the DI cracking, which is represented by the remaining load–carrying capacity. The present predictions are capable of embodying the well-known S-shaped response of filled rubbers, and also verified by the comparison with the experimental and analytical results. Moreover, strain localization effect is clearly demonstrated by finite element method (FEM) simulations, and reaches a decisive interpretation to the complicated synergic micro-mechanisms between hard fillers and soft phase in such flexible composites.     

A combined optical-thermal model for near-infrared laser heating of thermoplastic composites in an automated tape placement process

A combined optical-thermal model is presented for near-infrared laser heating of carbon fibre reinforced thermoplastic composites in an automated tape placement process. For the first time a three dimensional ray tracing model is presented for a near-infrared laser tape placement process which captures the unique anisotropic scattering behaviour of the composite. Predicted irradiance distributions on the composite are subsequently applied to a 2D non-linear finite element thermal model. It is shown that a shadow is present in the process and causes a significant drop in temperature prior to the consolidation zone. The effect of various source and surface model simplifications was also studied. The modelled temperature profiles agree well with experimental data. Substrate fibre orientation was investigated and found to have only a small influence on the temperature history.     

A progressive damage simulation algorithm for GFRP composites under cyclic loading. Part II: FE implementation and model validation

The FE implementation of FADAS, a material constitutive model capable of simulating the mechanical behaviour of GFRP composites under variable amplitude multiaxial cyclic loading, was presented. The discretization of the problem domain by means of FE is necessary for predicting the damage progression in real structures, as failure initiates at the vicinity of a stress concentrator, causing stress redistribution and the gradual spread of damage until the global failure of the structure. The implementation of the stiffness and strength degradation models in the principal material directions of the unidirectional ply was thoroughly discussed. Details were also presented on the FE models developed, the computational effort needed and the definition of final failure considered. Numerical predictions were corroborated satisfactorily by experimental data from constant amplitude uniaxial fatigue of multidirectional glass/epoxy laminates under various stress ratios. The validation of predictions included fatigue strength, stiffness degradation and residual static strength after cyclic loading.     

Bond behavior of superelastic shape memory alloys to carbon fiber reinforced polymer composites

In this research pull-out specimens were tested to investigate the bond behavior of superelastic NiTi (Nitinol) SMA wires to carbon fiber reinforced polymers (CFRP). A total of 45 pull-out specimens were tested monotonically up to failure. The test parameters considered include the wire diameter and embedment length. A digital image correlation (DIC) system was used to identify the onset and propagation of debonding. Based on the experimental observations two debonding mechanisms were observed: complete debonding after the onset of martensitic transformation of SMA wire, and complete debonding before the onset of wire transformation. The former mechanism predominated, while the latter mechanism governed for larger diameter wires with shorter embedment lengths. A 3-D non-linear finite element model (FEM) was developed to predict the pull-out behavior. A cohesive zone model (CZM) was used to model the interface. A parametric study was conducted using the FEM to quantify the parameters of the cohesive zone model. The results demonstrate that the proposed modeling approach can be used to characterize the bond behavior of superelastic SMA wires embedded in FRP composites.     

Micromechanical simulation of tensile failure of discontinuous fiber-reinforced polymer matrix composites using Spring Element Model

The micromechanical damage and strength of discontinuous fiber-reinforced polymer matrix composites was simulated by the Spring Element Model (SEM), and SEM was compared with Periodic Unit-Cell (PUC) simulation to clarify the potential of SEM. Tensile failure simulations indicate that SEM can be effectively used to predict the strength of long discontinuous fiber reinforced composites. The transition between matrix cracking mode and fiber breaking mode is also discussed to clarify the fiber length at which SEM can be used to predict strength. In addition, the strengths predicted with SEM are compared with the results of experiments on long discontinuous fiber-reinforced thermoplastic composites.     

Comparison between voxel and consistent meso-scale models of woven composites

The applicability of voxel meshes to model the mechanical behavior of woven composites at the mesoscopic scale is studied and compared to consistent Finite Element (FE) meshes. The methods are illustrated by mechanically modeling a Representative Unit Cell (RUC) of a composite made of four layers of glass fiber plain weave fabric embedded in an epoxy matrix. Mesh convergence is studied to determine the minimum element size necessary to obtain a correct yarn volume fraction. The comparison between both methods is based on (i) homogenized macroscopic elastic properties, (ii) local stress fields, and (iii) first damage prediction. Even if a good agreement is obtained for the elastic properties, the stress concentrations due to the steplike shape of voxels induce significant differences between both methods in terms of first damage prediction.     

Post buckling analysis of the shape memory polymer composite laminate bonded with alloy film

As a new kind of smart materials, shape memory polymer composites (SMPCs) are being used in large in-space deployable structures. However, the recovery force of pure SMPC laminate is very weak. In order to increase the recovery force of a SMPC laminate, an alloy film was bonded on the surface of the laminate. This paper describes the post bulking behavior of the alloy film reinforced SMPC laminate. The energy term associate with this in-plane post buckling have been given .Based on the theorems of minimum energy, a mathematical model is derived to describe the relation between the strain energy and the material and geometry parameters of the alloy film reinforced SMPC laminate. The finite element model (FEM) is also conducted to demonstrate the validity of the theoretical method. The relation between the recovery force and the material geometry parameters were also investigated. The presented analysis shows great potential in the engineering application such as deployment of space structures.     

Mechanical properties of hybrid composites using finite element method based micromechanics

A micromechanical analysis of the representative volume element of a unidirectional hybrid composite is performed using finite element method. The fibers are assumed to be circular and packed in a hexagonal array. The effects of volume fractions of the two different fibers used and also their relative locations within the unit cell are studied. Analytical results are obtained for all the elastic constants. Modified Halpin–Tsai equations are proposed for predicting the transverse and shear moduli of hybrid composites. Variability in mechanical properties due to different locations of the two fibers for the same volume fractions was studied. It is found that the variability in elastic constants and longitudinal strength properties was negligible. However, there was significant variability in the transverse strength properties. The results for hybrid composites are compared with single fiber composites.