Experimental characterisation of rate-dependent compression behaviour of fibre reinforced composites

Fibre reinforced polymers (FRP) materials are being increasingly used for aerospace and automotive structural applications. One of the critical loading conditions for such applications is impact, consequently, understanding of the composite behavior under such loads becomes critical for structural design. The analysis and design process for achieving impact-resistant composite structures requires rate-dependent constitutive models, which, in turn, requires material properties of the composite over a range of strain rates. It is, therefore, the objective of the research to investigate the strain rate-dependent behavior of fiber reinforced composites under compressive loads for a wide range of fiber orientations. Quasi-static (≈ 1e-3 s-1) and high loading (≈ 200 s-1) rates are considered for the experimental study. Accordingly, two different test setups are utilized, a screw-driven universal testing machine for quasi-static tests and a Split Hopkinson Pressure Bar (SHPB) system for dynamic tests. The stress-strain response of the composite is reported for the different fiber orientations and the strain rates, revealing the rate-dependent characteristics of the carbon fiber reinforced composite. From the test results, it is observed that, the dependency of the fracture strength on the loading rate is significant. The results are summarised in terms of the failure envelope in the transverse compression-in-plane shear σ22-σ12 plane for the two strain rates

A Wedge-DCB Test Methodology to Characterise High Rate Mode-I Interlaminar Fracture Properties of Fibre Composites

A combined numerical-experimental methodology is presented to measure dynamic Mode-I fracture properties of fiber reinforced composites. A modified wedge-DCB test using a Split-Hopkinson Bar technique along with cohesive zone modelling is utilised for this purpose. Three different comparison metrics, namely, strain-displacement response, crack propagation history and crack opening history are employed in order to extract unique values for the cohesive fracture properties of the delaminating interface. More importantly, the complexity of dealing with the frictional effects between the wedge and the DCB specimen is effectively circumvented by utilising right acquisition techniques combined with an inverse numerical modelling procedure. The proposed methodology is applied to extract the high rate interlaminar fracture properties of carbon fiber reinforced epoxy composites and it is further shown that a high level of confidence in the calibrated data can be established by adopting the proposed methodology

On the Rate-dependent Plasticity Modelling of Unidirectional Fibre-reinforced Polymeric Matrix Composites

Three different approaches to plasticity are investigated to model the experimentally-observed non-linear behaviour of unidirectional fibre-reinforced polymeric matrix materials. The first and simplest approach consists on assuming independent one-dimensional rate-dependent plasticity on in-plane (12) and through-thickness longitudinal (13) shear components of the Cauchy stress tensor. The second, employs a 3D extension of the plane stress Hill'48 anisotropic plastic surface. The third and the last is formulated as a quadratic yield function inspired by Puck's fracture initiation criterion. It searches for a plastic localisation plane in which a certain combination of normal and shear stresses is maximum. Numerical simulations are conducted to analyse the off-axis compression behaviour of carbon fibre reinforced epoxy composite under varying loading rates. The afore-mentioned three different approaches are explored with an aim to predict the experimentally-observed non-linear response of such composites. The model parameters are determined using a deterministic inverse modelling strategy employing an iterative domain reduction optimisation technique. As far as the experiments are concerned, the quasi-static and medium rate tests were carried out in universal testing machines, while the experiments at high rate were conducted in a Split Hopkinson Pressure Bar system. The effectiveness in terms of accuracy and robustness of the three approaches are discussed

Characterisation of damage mechanisms in oxide ceramics indented at dynamic and quasi-static strain rates

Ceramic materials are known to display rate dependent behaviour under impact. Tests to establish the strain-rate dependent variations in damage mechanisms have been carried out on debased alumina, an alumina-zirconia composite, and 3Y-TZP. Materials were indented dynamically and quasi-statically using identical sharp hardened steel projectiles while recording the load profile. Characteristics typical of both sharp and blunt indentation types were observed using scanning electron microscopy and piezospectroscopic mapping. At dynamic strain rates both the depth of the indentation and the residual stress in the material were lower than for quasi-static tests. This was attributed to temperature-induced softening of the projectile. Unusual behaviour was observed in the 3Y-TZP samples due to the reversible transformation from tetragonal to monoclinic crystal structures during mechanical loading. These effects and the observed superior mechanical strength against impact suggest that zirconia or zirconia-composite materials may have advantages over debased alumina for application as ceramic armour materials

Coupon scale Z-pinned IM7/8552 delamination tests under dynamic loading

Dynamic impact onto laminated composite structures can lead to large-scale delamination. This can be mitigated by the introduction of through-thickness reinforcement, such as z-pins. Here, mode I & II and mixed-mode delamination tests have been designed and conducted at high loading rate, for both unpinned and Z-pinned coupons to study the effect of rate of loading. It was found that the Z-pins were not effective in delaying the dynamic crack initiation or resisting the dynamic propagation of delaminations shorter than 5 mm. However, the further growth of cracks was substantially delayed by Z-pinning, especially for the pure mode I and mode I dominated failure modes. On the other hand, the effectiveness of Z-pins in shear tests was relatively modest. The mode I dominated delamination resistance of Z-pinned laminates was found to be sensitive to the loading rate

Predictions of the mechanical properties of unidirectional fibre composites by supervised machine learning

We present an application of data analytics and supervised machine learning to allow accurate predictions of the macroscopic stiffness and yield strength of a unidirectional composite loaded in the transverse plane. Predictions are obtained from the analysis of an image of the material microstructure, as well as knowledge of the constitutive models for fibres and matrix, without performing physically-based calculations. The computational framework is based on evaluating the 2-point correlation function of the images of 1800 microstructures, followed by dimensionality reduction via principal component analysis. Finite element (FE) simulations are performed on 1800 corresponding statistical volume elements (SVEs) representing cylindrical fibres in a continuous matrix, loaded in the transverse plane. A supervised machine learning (ML) exercise is performed, employing a gradient-boosted tree regression model with 10-fold cross-validation strategy. The model obtained is able to accurately predict the homogenized properties of arbitrary microstructures

An integrated inverse numerical–experimental approach to determine the dynamic Mode-I interlaminar fracture toughness of fibre composites

A combined numerical–experimental methodology is presented to determine the dynamic Mode-I fracture properties of Fibre-Reinforced Polymer (FRP) composites. The experimental aspect consists of a modified Wedge-Double cantilever Beam (WDCB) test using a Split Hopkinson Pressure Bar (SHPB) set-up followed by a numerical inverse modelling strategy using cohesive-zone approach. The proposed method is inherently robust due to the use of three independent comparison metrics namely, the strain–displacement response, the crack length history and the crack opening history to uniquely determine the delamination properties. More importantly, the complexity of dealing with the frictional effects between the wedge and the DCB specimen is effectively circumvented by utilising appropriate acquisition techniques. The proposed methodology is applied to extract the high-rate interlaminar fracture properties of a carbon fibre reinforced composite, IM7/8552 and it is further shown that a high level of confidence in the calibrated data can be established by adopting the proposed methodology

Effect of damage evolution on the auxetic behavior of 2D and 3D re-entrant type geometries

In this work, a mathematical formulation based on variational asymptotic method (VAM) has been proposed to determine the effect of damage on the auxetic properties of two-dimensional (2D) and three-dimensional (3D) re-entrant geometries. The influence of damage progression on the auxetic behavior was captured using a geometrically exact one-dimensional beam theory and an isotropic damage law, implemented in a nonlinear finite element framework. The effect of material degradation on the macroscale effective elastic properties such as the elastic modulus and Poisson’s ratio for the two-dimensional and three-dimensional re-entrant auxetic geometries was quantified. The mechanical behavior as predicted by the in-house Python-based implementation of the proposed VAM-based formulation is verified with the results from the commercial finite element solver Abaqus, wherein the user material subroutine was used to capture damage evolution. The numerical examples presented in this paper reveal that the macroscale auxetic behavior of the geometries was affected significantly by damage progression. The results of this research will provide insights into the design and analysis of auxetic materials for applications that warrant consideration of damage evolution

Exploiting nonlinearities through geometric engineering to enhance the auxetic behaviour in re-entrant honeycomb metamaterials

Classical approaches to enhance auxeticity quite often involve exploring or designing newer architectures. In this work, simple geometrical features at the member level are engineered to exploit non-classical nonlinearities and improve the auxetic behaviour. The structural elements of the auxetic unit cell are here represented by thin strip-like beams, or thin-walled tubular beams. The resulting nonlinear stiffness enhances the auxeticity of the lattices, especially under large deformations. To quantify the influence of the proposed structural features on the resulting Poisson's ratio, we use here variational asymptotic method (VAM) and geometrically exact beam theory. The numerical examples reveal that 2D re-entrant type micro-structures made of thin strips exhibit an improvement in terms of auxetic behaviour under compression. For the auxetic unit cell with thin circular tubes as members, Brazier's effect associated with cross-sectional ovalisation improves the auxetic behaviour under tension; the enhancement is even more significant for the 3D re-entrant geometry. Thin strip-based auxetic unit cells were additively manufactured and tested under compression to verify the numerical observations. The experimentally measured values of the negative Poisson's ratio are in close agreement with the numerical results, revealing a 66% increase due to the nonlinearity. Simulation results showcase these alternative approaches to improve the auxetic behaviour through simple geometric engineering of the lattice ribs