C. Paul Buckley

Computational modelling of large deformations in layered-silicate/PET nanocomposites near the glass transition

Layered-silicate nanoparticles offer a cost-effective reinforcement for thermoplastics. Computational modelling has been employed to study large deformations in layered-silicate/poly(ethylene terephthalate) (PET) nanocomposites near the glass transition, as would be experienced during industrial forming processes such as thermoforming or injection stretch blow moulding. Non-linear numerical modelling was applied, to predict the macroscopic large deformation behaviour, with morphology evolution and deformation occurring at the microscopic level, using the representative volume element (RVE) approach. A physically based elasto-viscoplastic constitutive model, describing the behaviour of the PET matrix within the RVE, was numerically implemented into a finite element solver (ABAQUS) using an UMAT subroutine. The implementation was designed to be robust, for accommodating large rotations and stretches of the matrix local to, and between, the nanoparticles. The nanocomposite morphology was reconstructed at the RVE level using a Monte-Carlo-based algorithm that placed straight, high-aspect ratio particles according to the specified orientation and volume fraction, with the assumption of periodicity. Computational experiments using this methodology enabled prediction of the strain-stiffening behaviour of the nanocomposite, observed experimentally, as functions of strain, strain rate, temperature and particle volume fraction. These results revealed the probable origins of the enhanced strain stiffening observed: (a) evolution of the morphology (through particle re-orientation) and (b) early onset of stress-induced pre-crystallization (and hence lock-up of viscous flow), triggered by the presence of particles. The computational model enabled prediction of the effects of process parameters (strain rate, temperature) on evolution of the morphology, and hence on the end-use properties.

HIGH‐RATE COMPRESSION OF POLYPROPYLENE

Three grades of polypropylene were tested in compression at room temperature, across an unusually wide range of strain rate: 10−4 to 104 s−1. The quasi‐static testing was done in a Hounsfield machine fitted with a digital image acquisition kit, while tests at the highest strain rates were carried out using a compression split Hopkinson pressure bar. The strain rate dependence of compressive yield stress was compared with the Eyring prediction, and found to be a nonlinear function of log10(strain‐rate). The nonlinearity is attributed to the presence of two relaxation processes in polypropylene, with differing activation volumes: the α‐ and β‐processes. According to the Bauwens two‐process model this would lead naturally to curved Eyring plots, where the apparent activation volume decreases with increasing strain‐rate. Another prominent feature in the experimental results was the increase in magnitude of post‐yield strain‐softening with increase in strain‐rate. This indicates that the dominant structural re...

Viscoelasticity of tendons under transverse compression

Tendons are highly anisotropic and also viscoelastic. For understanding and modeling their 3D deformation, information is needed on their viscoelastic response under off-axis loading. A study was made, therefore, of creep and recovery of bovine digital extensor tendons when subjected to transverse compressive stress of up to ca. 100 kPa. Preconditioned tendons were compression tested between glass plates at increasing creep loads. The creep response was anomalous: the relative rate of creep reduced with the increasing stress. Over each ca. 100 s creep period, the transverse creep deformation of each tendon obeyed a power law dependence on time, with the power law exponent falling from ca. 0.18 to an asymptote of ca. 0.058 with the increasing stress. A possible explanation is stress-driven dehydration, as suggested previously for the similar anomalous behavior of ligaments. Recovery after removal of each creep load was also anomalous. Relative residual strain reduced with the increasing creep stress, but this is explicable in terms of the reducing relative rate of creep. When allowance was made for some adhesion occurring naturally between tendon and the glass plates, the results for a given load were consistent with creep and recovery being related through the Boltzmann superposition principle (BSP). The tendon tissue acted as a pressure-sensitive adhesive (PSA) in contact with the glass plates: explicable in terms of the low transverse shear modulus of the tendons.

Transverse Compression of Tendons

A study was made of the deformation of tendons when compressed transverse to the fiber-aligned axis. Bovine digital extensor tendons were compression tested between flat rigid plates. The methods included: in situ image-based measurement of tendon cross-sectional shapes, after preconditioning but immediately prior to testing; multiple constant-load creep/recovery tests applied to each tendon at increasing loads; and measurements of the resulting tendon displacements in both transverse directions. In these tests, friction resisted axial stretch of the tendon during compression, giving approximately plane-strain conditions. This, together with the assumption of a form of anisotropic hyperelastic constitutive model proposed previously for tendon, justified modeling the isochronal response of tendon as that of an isotropic, slightly compressible, neo-Hookean solid. Inverse analysis, using finite-element (FE) simulations of the experiments and 10 s isochronal creep displacement data, gave values for Youngs modulus and Poissons ratio of this solid of 0.31 MPa and 0.49, respectively, for an idealized tendon shape and averaged data for all the tendons and E = 0.14 and 0.10 MPa for two specific tendons using their actual measured geometry. The compression load versus displacement curves, as measured and as simulated, showed varying degrees of stiffening with increasing load. This can be attributed mostly to geometrical changes in tendon cross section under load, varying according to the initial 3D shape of the tendon.

Multiscale modelling of layered-silicate/PET nanocomposites during solid-state processing

This work aims to develop a continuum, multi-scale, physically-based model of the forming process for layered-silicate nanocomposites based on poly(ethylene terephthalate) (PET) matrices, as might be used for packaging. This challenge is tackled using: (1) a physically-based model of PET implemented into the FEM-based code ABAQUS, (2) RVEs with prescribed morphologies reflecting TEM images, and (3) nonlinear computational homogenisation. As a result, 2-D two-scale FEM-based simulations under biaxial deformations (constant width) enabled the extraction of macroscopic stress-strain curves at different silicate contents and processing temperatures. In particular, interesting features in terms of morphology changes and its impact on the macroscopic stress response were captured: (a) morphology change by particle re-orientation and pronounced bending, (b) macroscopic strain hardening due to platelet re-orientation and local strain stiffening, (c) facilitated platelet alignment, and platelet delamination in tactoids through sheardominated deformations and increasing temperature.

Solid‐State Constitutive Modelling of Glassy Polymers: Coupling the Rolie‐Poly Equations for Melts with Anisotropic Viscoplastic Flow

This paper investigates the behaviour of a well‐characterised monodisperse grade of entangled atactic polystyrene across a very wide temperature and strain rate range through linear and non‐linear melt rheology and solid‐state deformation. In an effort to construct a constitutive model for large deformations able to describe rheological response right across this wide timescale, two well‐established rheological models are combined: the well known RoliePoly (RP) conformational melt model and the Oxford glass‐rubber constitutive model for glassy polymers. Comparisons between experimental data and simulations from a numerical implementation of the model illustrate that the model can cope well with the range of deformations in which orientation is limited to length‐scales longer than an entanglement length. One approach in which the model can be expanded to incorporate the effects of orientation on shorter length scales using anisotropic viscoplastic flow is briefly discussed.