Post microbuckling mechanics of fibre-reinforced shape-memory polymers undergoing flexure deformation

Abstract

The buckling mechanics of fibre-reinforced shape-memory polymer composites (SMPCs) under finite flexure deformation is investigated. The analytical expressions of the key parameters during the buckling deformation of the materials were determined, and the local post-buckling mechanics of the unidirectional fibre-reinforced SMPC were further discussed. The cross section of SMPC under flexural deformation can be divided into three areas: the non-buckling stretching area, non-buckling compression area and buckling compression area. These areas were described by three variables: the critical buckling position, the neutral plane position and the fibre buckling half-wavelength. A strain energy expression of the SMPC thermodynamic system is developed. According to the principle of minimum energy, the analytical expressions of key parameters in the flexural deformation process is determined, including the critical buckling curvature, critical buckling position, position of the neutral plane, wavelength of the buckling fibre, amplitude of the buckling fibre and macroscopic structural strain of the composite material. The results showed that fibre buckling occurred in the material when the curvature increasing from infinitesimal to the critical value. If the curvature is greater than the critical curvature, the neutral plane of the material will move towards the outboard tensile area, and the critical buckling position will move towards the neutral plane. Consequently, the half-wavelength of the buckling fibre was relatively stabilised, with the amplitude increasing dramatically. Along with the increasing of the shear modulus, the critical curvature and buckling amplitude increase, while the critical half-wavelength of the fibre buckling decrease and the critical strain of the composite material increase. Finally, we conducted experiments to verify the correction of the key parameters describing SMPC materials under flexural deformation. The values determined by the experiments proved that the theoretical prediction is correct. Additionally, the buckling deformation of the carbon fibre generated a large macroscopic structural strain of the composite material and obtained a resulting large flexural curvature of the structure with minimal material strain of the carbon fibre.