The main purpose of this study is to exhibit failure prediction capability of polynomial-based yield functions with a basic damage model. For this purpose, a constitutive model considering anisotropic plasticity and ductile fracture was developed. In this model, anisotropic plastic behavior of dual phase steels, namely DP600 and DP800, was described by quadratic Hill48 and non-quadratic anisotropic homogeneous the fourth-order polynomial (HomPol4) stress potentials and the generalized plastic work criterion from ductile damage models was used for the prediction of fracture initiation. The model has been implemented into an implicit finite element (FE) code. The parameters of the constitutive model were calibrated with uniaxial tensile tests performed in different directions with respect to the rolling direction of the materials and anisotropic stress potentials were evaluated by comparison of the predicted in-plane variations of the plastic properties (yield stress ratios and Lankford coefficients), and yield locus contours with experimental data. The calibrated model was firstly applied to uniaxial tensile test and then to a hole expansion test to predict fracture. The stroke values at fracture, hole expansion ratios (HER) and fracture locations were investigated. Any significant difference between the anisotropic stress potentials was not observed in terms of HER predictions, however plastic work criterion in conjunction with HomPol4 function predicted the crack initiation locations accurately on the fractured samples. Afterward, the Lode parameter and stress triaxiality effects were investigated in fracture stroke prediction. Since the HomPol4 predictions of fracture initiation locations are accurate, the predicted HomPol4 results from the generalized plastic work criterion were compared with the modified Mohr-Coulomb ductile fracture model results. A significant improvement was observed in the fracture displacement predictions. However, it is seen that the failure location predictions of both models were the same. From these results, it can be concluded that the HomPol4 yield criterion has an effective potential to predict the failure locations even though with a basic damage model. In the current study, the out-of-plane anisotropy effect was assessed as well. To this end, Hill48’s parameter correlated with the out-of-plane shear components were adjusted. It was found that the out-of-plane anisotropy has a negligible effect on the predictions of HER and fracture initiation location.