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The plastic constraint factor based on Hill´s theory of plasticity is widely used to check the stress state applying the essential-work-of-fracture (EWF) approach to polymers. However, the plastic constraint factor experimentally determined as the ratio of the net section stress in cracked specimens and the yield stress does not match the theoretical predictions of the theory of plasticity because assuming ideal-plastic behaviour for polymer materials does not consider material-specific viscoelastic?viscoplastic effects adequately. Therefore, a correction term for amorphous thermoplastic polymer materials is derived introducing the influence of the material on the plastic constraint factor. This correction term is based on the Williams-Landel-Ferry (WLF) equation for different thermodynamic quantities such as temperature and stress (negative pressure) and the introduction of a glass stress to be comparable to the glass temperature. Analytical calculation of this correction term, taking polycarbonate as an example, is used as a comparison to empirical values in literature for numerous amorphous and semi-crystalline thermoplastic as well as partial-plastically deformable elastomeric polymer materials. It can be concluded that this enhanced Hill´s theory is well suited to amorphous polymers.