Modelling of PEEK crystallisation kinetics using fractional differential equations

Abstract

The crystallisation process of high-performance thermoplastic composites is complex, affecting properties such as strength and toughness. During thermoplastic composite manufacturing, such as over-moulding, the material undergoes a complex thermal history. Process optimisation requires a versatile description of material behaviour. Models to address this must predict crystallinity changes at arbitrary cooling cycles and the process's history dependence, with clear parameter identification. Differential Scanning Calorimetry (DSC) on polyether ether ketone (PEEK) showed discrepancies between dynamic and isothermal data in the crystallinity/crystallisation rate/temperature space, challenging conventional models. A fractional rate model, using the Caputo derivative, was developed to align both datasets. Two fractional kinetics model forms were proposed: one fitted data in the fractional space using Weibull distribution functions of crystallinity and temperature; the other used piecewise surface fit and interpolation. These models were tested against ramp dwell tests and predicted crystallinity with a 5 % error margin. This flexible approach is applicable to thermoplastics and their composites, in a manufacturing context for optimising processes such as over-moulding and additive manufacturing.

Research data is included in “Veyrat Cruz-Guzman, Maria; Ivanov, Dmitry (2025), “Modelling of PEEK Crystallisation Kinetics Using Fractional Differential Equations”, Mendeley Data, V1, doi: 10.17632/xxb7rpm8fj.1”