Spatial variability and characteristic length-scales of strain fields in tow-based discontinuous composites: Characterisation and modelling

Abstract

Tow-Based Discontinuous Composites (TBDCs, composed by chopped carbon-fibre tows embedded in polymer) combine high performance with manufacturability; the random orientation and large dimensions of the tows generates significant variability of properties, which governs the response of TBDC structures. This paper proposes the concept of characteristic length-scale as the intrinsic property of a TBDC governing its spatial variability (i.e. how properties are distributed in space). A new methodology to experimentally measure a TBDC’s characteristic length-scale, based on the triangulation of peaks and troughs in elastic strain fields of unnotched specimens, is developed; this is complemented by another methodology based on the cross-correlation of strain fields. A meso-scale Finite Element (FE) methodology (based on an explicit representation of the tows) reveals that a TBDC’s characteristic length-scale can be approximated as the harmonic mean of the tow length and width. A new macro-scale FE methodology, based on generating stochastic equivalent laminates at discrete points (separated by the TBDC’s characteristic length-scale) and interpolating their orientation tensors into continuously smooth stochastic fields, is proposed and validated against experiments; this methodology is mesh-objective and does not require explicit representations of the tows, making it computationally-efficient and suitable to complex geometries.