The transport of deformable objects by a turbulent flow is common in environmental sciences which are interested, for instance, in the dynamics of plankton in the ocean, and in industry, such as the papermaking or textile industries. In this study, the deformations of flexible fibres in homogeneous isotropic turbulence are experimentally and numerically investigated, focusing on the local curvature κ . By comparing our results to the predictions for worm-like chain polymers in an ideal solvent, we are able to identify the role of the spatial and temporal correlations of the turbulent forcing. In particular, we show that these correlations are responsible for a straightening of long fibres which become statistically less distorted by turbulence as their length increases.