Dynamic hysteresis modelling of entangled cross-linked fibres in shear

Abstract

The objective of this paper is to characterize and model the vibration behaviour of entangled carbon fibres cross-linked with epoxy resin. The material is tested in shear, in a double lap configuration. Experimental testing is carried out for frequencies varying from 1 Hz to 80 Hz and for shear strain amplitudes ranging from 5 10 4 to 1 10 2 . Measured shear stress – strain hysteresis loops show a nonlinear behaviour with a low frequency dependency. The hysteresis loops are decomposed in a linear part and three nonlinear parts: a dry friction hysteresis, a stiffening term and a stiction-like overshoot term. The Generalized Dahl Model is used in conjunction with other hysteresis models to develop an appropriate description of the measured hysteresis loops, based on the three nonlinear parts. In particular, a new one-state formulation of the Bliman – Sorine model is developed. A new identification procedure is also introduced for the Dahl model, based on the so-called backbone curve. The model is shown to capture well the complex shapes of the measured hysteresis loops at all amplitudes.