Nanomechanical characterisation of unidirectional fibre reinforced composites at the fibre matrix level

The use of bottom-up multiscale methods has become the privileged approach to predict the deformation and failure of fibre-reinforced polymer composites. The development of accurate computational multi-scale models relies on the proper description of the individual components of the composite ply. The determination of the local properties of these constituents is challenging, dependent on the specific local curing conditions and generation of heterogeneities, and accurate data are scarce for the interfaces and interphases [1]. The matrix is usually described based on continuum models, yet this may lead to inaccurate prediction of the local strain field around fibres. These challenges limit the accuracy of composite model predictions, even for unidirectional (UD) composites loaded in transverse compression, where the macroscopic deformation response is dictated by the matrix [2]. In this study, we propose a combined experimental and numerical approach to characterise the constituents of a carbon fibre-reinforced UD composite. The measurement and prediction of the matrix response at the fibre/matrix level is of particular interest, as matrix size effects may exist at this scale. Nanoindentation is used to determine the properties of the matrix in confined volumes in-between fibres. Care is taking to deconvolute artefacts resulting from the test procedure and the data treatment on possible size effects. Transverse compression tests on UD specimens are conducted inside a scanning electron microscope (SEM) allowing the use of micro digital image correlation (DIC). The objective is to quantify the local strain field with an accuracy as small as a few tens of nano-metres. The DIC strain maps are confronted with FEA results using a model enriched by the nanoindentation measurements

Nanoscale digital image correlation at elementary fibre/matrix level in polymer–based composites

Multiscale mechanical modelling aims at predicting the failure of composites from the fibre/matrix level up to the component scale. Existing frameworks are limited by the lack of reliable experimental data and by an incomplete understanding of the submicron deformation and failure mechanisms. A novel digital image correlation (DIC) method has been developed for the characterisation of the nanoscale mechanical response in composites, based on latest advances in surface patterning. Indium has been deposited on unidirectional composites leading to a dense, homogeneous speckle with particle diameter around 15 nm. The specimens were subjected to transverse compression in a scanning electron microscope, while minimising distortion effects. Strain concentration areas, like submicron shear bands and fibre–matrix interphases, were successfully captured for two systems: a carbon fibre-reinforced thermoset and a glass fibre-reinforced thermoplastic. DIC results were compared with alternative experimental data, obtained by atomic force microscopy, and with finite element simulations based on a conventional elastoplastic model

Modelling of size-dependent plasticity in polymer-based composites based on nano- and macroscale experimental results

A number of experimental evidences indicate that the local response of polymer matrices near fibres is inadequately represented by classical continuum models relying on the bulk polymer behaviour. This results from size-dependency associated to large plastic strain gradients, complex interphase behaviour and/or changes of polymer structure. Classical multiscale models require artificial tuning of the properties to provide realistic macroscale predictions. We demonstrate that an unprecedented modelling approach based on a micromorphic theory is able to capture such size effects in long-fibre composites. The model is identified via nano digital image correlation strain fields and validated by predicting the strengthening found in transverse compression of UD composites, not captured by classical models. Micro-shear bands are properly regularised by the model, thus correctly handling the size-dependent plasticity and softening effects. The improved prediction of the strain localisation pattern in the matrix opens avenues to more accurately model interfacial failure and damage processes

Visco-Plastic Behaviour of a Polymer Matrix at the Fibre Diameter Length Scale: a Finite Element Mesoscale Model Relying on Shear Transformation Zone (STZ) Dynamics

Polymeric glasses exhibit complex behaviour when subjected to deformation below the glass transition temperature. Uniaxial stress-strain curves typically include post-yield strain softening, strain hardening, and non-linear unloading. In addition, the deformation and failure responses are sensitive to the rate of deformation, pressure, and temperature. Sophisticated (visco-)elastic-(visco-)plastic continuum constitutive models have been developed to simulate the large strain deformation of (glassy) polymers; they generally give excellent fits to uniaxial stress-strain curves. However, they require the calibration of a large number of mostly phenomenological parameters, give limited insights into failure, and struggle to accurately predict the response for more complicated loading states and histories. At the opposite scale, molecular dynamics (MD) simulations have been used to elucidate the discrete molecular deformation mechanisms leading to the heterogeneous inelastic behaviour of polymeric glasses. The results of MD calculations suggest that plastic deformation of polymeric glasses is caused by thermally activated molecular rearrangements and conformational changes of a collection of polymer chains parts. The use of a mesoscale numerical model based on the activation of shear transformation zones (STZs) offers a convenient approach to bridge continuum and molecular dynamics simulations, which are typically limited to small length and time scales. We have used the implementation by Homer and Schuh [1] of Argon’s STZ theory [2] to develop a mesoscale finite element model for polymeric glasses. It is assumed that the elementary deformation mechanism giving rise to macroscopic plastic deformation in a polymeric glass is a pure shear deformation of an STZ; this corresponds to a change in molecular conformational state. Plastic deformation is governed by these changes and their interaction with the surrounding (visco-)elastic matrix. The mesoscale STZ framework requires the calibration of only five parameters and successfully predicts the complex large deformation response of glassy polymers, including creep and non-linear unloading [3]. In this contribution, we will summarise the key building blocks of the mesoscale framework and discuss a possible route for model calibration. In addition, we discuss the role of the visco-elastic matrix on the model predictions. These insights can be used to simulate the time- and temperature-dependent visco-plastic deformation and failure response of a fibre-reinforced polymer composite matrix at the fibre-diameter length scale

Major trends in the elasto-visco-plastic behaviour of highly cross-linked epoxy resins

Highly cross-linked thermosetting polymers, widely used as matrices for advanced polymer-based fibre-reinforced composites, have suffered from a lack of in-depth mechanical characterisation. The assumption is that their overall mechanical response is inherently similar to that of high glass transition temperature (Tg) amorphous thermoplastics, except for a lower ductility and a better creep resistance [1]. However, multi-scale test strategies have increasingly been used to improve the understanding of the deformation and failure of epoxies in order to feed computational models. The main motivation driving these studies is the recognition that a micro-scale level understanding of the deformation mechanisms of these materials is necessary to accurately predict the failure of the corresponding composites structures [2]. This is particularly important for loading conditions where plastic flow within the matrix is dominant such as overall shear or creep. However, these studies mostly limit themselves to the analysis of the elastic modulus and of the yield point, highlighting the remaining knowledge gap about the post-yield visco-plastic response of epoxies. The purpose of this work is two-fold. First, in order to supplement the scarcity of accurate experimental data, we establish master trends for the entire stress-strain response of highly cross-linked epoxies, hence providing a basis for first-level modelling attempts. Additionally, we unravel trends within the stress-strain response that can be correlated to one or several physico-chemical or molecular structure parameters. For this purpose, a vast database of the elasto-visco-plastic properties resulting from tension and/or compression tests performed on seven different epoxy systems is gathered. Parameters such as rate sensitivity, softening, re-hardening and activation volumes are carefully extracted as it has been shown that they strongly affect the local fibre/matrix level stress development [3]. Among other trends, correlations between the yield and softening stresses and strains and the corresponding Tg and cross-linking densities are found for the tested resins. The re-hardening is mainly dictated by the cross-linking density, as expected