Predicting the high strain rate response of plasticised poly(vinyl chloride) using a fractional derivative model

Department of Engineering Science, University of Oxford, Parks Road, OX1 3PJ, UK

^* e-mail : akash.trivedi@eng.ox.ac.uk

Published online: 7 September 2018

Abstract

Polymers are frequently used in fields as diverse as aerospace, biomedicine, automotive and in-dustrial vibration damping, where they are often subjected to high strain rate or impact loading. Poly(vinyl chloride) (PVC), and its plasticised variants (PPVC), are just two examples of this broad category of materi-als. Since many polymers exhibit strong rate and temperature dependence, including a low temperature brittle transition, it is extremely important to understand their mechanical responses over a wide range of loading con-ditions.PVC with 60 wt% plasticiser is used in this study, as its highly rubbery nature lends itself well to being used in various load mitigation and energy absorption applications. It is challenging to obtain high strain rate data on rubbery materials using conventional techniques such as the split-Hopkinson (Kolsky) bar. Therefore, alternative approaches are required. Based on previous work developing a framework to predict high rate re-sponseusing a fractional derivative model, Dynamic Mechanical Analysis (DMA) experiments are conducted on the PPVC to construct a master curve of storage modulus. These data are used to part-calibrate a modified Mulliken-Boyce model which also takes into account specimen heating to derive stress-strain relationships at strain rates varying from 0.001 s_¹ to 13 500 s_¹. This model is further calibrated against experiments conducted in a previous study and shown to provide an excellent description of the behaviour at these rates.