In this study, the mechanical properties and physical–chemical characteristics of curaua composites were evaluated using tensile and short beam testing and dynamic mechanical analysis. Curaua/polyester composites with different pretreatment (washing and drying), fiber length (10–50 mm) and fiber volume fraction (%Vf) (11, 22, and 38 vol%) were studied. The results show that the composites produced using 50 mm long washed/dried fibers and %Vf of 38 vol% achieved better mechanical properties, such as tensile strength and modulus and short beam strength. Fragility index “m” of the composites increased upon curaua incorporation, which may be attributed to a reduction in polyester chemical interactions (due to fiber dwelling of the polyester network). The energy required in initiating the cooperative motion at the “ideal” glass transition temperature and the cooperative rearrangement regions (CRR) also increased upon curaua incorporation, since CRR is considered the subsystem of the sample and for higher fiber content the greater the molecular heterogeneity. Finally, the Angell fragility concept was successfully applied to polymer composite systems.