LAOS: The strain softening/strain hardening paradox

Abstract

Numerous materials, from biopolymers to filled rubbers, exhibit strain softening at high strain amplitudes during a strain sweep in oscillatory rheology: The modulus decreases with increasing deformation. On the other hand, if the nonlinear elastic response is analyzed within a single oscillation cycle (described by a Lissajous curve), these systems are often reported to exhibit strain hardening. We compare strain sweeps and single cycle LAOS (large amplitude oscillatory shear) analyses of stress vs strain on three very different materials. We conclude that the reported strain hardening is due to the use of a tangent modulus in the LAOS analysis, and that the overall rheology remains strain softening. To show that this conclusion is robust, we demonstrate a rescaling of the modulus that collapses the data from all the oscillatory measurements onto a single master curve that clearly exhibits the correct strain softening behavior.

Dependence of nonlinear elasticity on filler size in composite polymer systems

“…More information about the compounding and processing of the filled rubbers can be found (Baeza et al 2012). Several examples of the importance of the storage modulus over the loss modulus can be found in (Mermet-Guyennet et al 2015), with a ratio G″/G′ about 0.1. The modulus of the matrix and fillers can be found in Table 1.…”

“…Finite amplitude oscillatory measurements were performed using an Anton Paar Physica MCR 300 rheometer mounted with a plate/plate geometry at a frequency of 1 Hz, which is within the range where the linear viscoelastic properties of the rubber and gel are insensitive to frequency (Mermet-Guyennet et al 2015). For filled rubbers the diameter of the plates was 5 mm and the samples were disks with a thickness about 2.5 mm, attached to the plates with a Loctite glue to avoid wall slip (Montes et al 2003).…”

“…A more complete description of the rich microstructure of the aggregates in filled rubbers and the way to interpret the SAXS spectra from t h i s s y s t e m c a n b e f o u n d i n ( B a e z a , G e n i x , Degrandcourt, Petitjean, Gummel, Couty and Oberdisse 2012). -Guyennet et al 2015. Two of the filled rubbers are considered in this article, while the three filled rubbers with different particle radii (Rp) are nitrile-butadiene rubber with silica particles.…”

“…Adding particulate fillers to a polymer matrix dramatically changes the mechanical behavior (Fröhlich, et al 2005, Mermet-Guyennet, et al 2015, Payne 1962, Rattanasom, et al 2007. The physical properties of synthetic rubbers that are important for tire performance, for example, depend on the addition of fillers, typically silica or carbon black.…”

Shear localisation in interfacial particle layers and its influence on Lissajous-plots

“…For bulk rheology, LAOS measurements are far better exploited than for interfacial rheology. For example, Lee et al (2015), Mermet-Guyennet et al (2015), Dimitriou et al (2013), Ewoldt et al (2010) and Hyun et al (2011) have extensively reported on nonlinear bulk rheology and proposed models to quantify and predict LAOS measurements. Within interfacial 2D rheology, LAOS experiments were only recently performed (Sagis and Fischer 2014;Rühs et al 2013).…”