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Cracks are described as sharp and diffusive surfaces in failure mechanical models. In this paper, a finite element model is developed by using a diffusive description of crack discontinuities. The main objective of this study is to prove the accuracy of the phase-field model in which the alternate minimization iteration and the spectral decomposition formulation are considered. We conduct a set of benchmark numerical tests on notched specimens using the phase-field model, which allows the prediction of the quasi-brittle failure. The fracture surface is approximated by a diffusive field, which interpolates between undamaged and fully damaged states. A mechanical loading was applied on quenched C90 steel and different obtained crack patterns are discussed. Microstructural analyses are performed to prove the accuracy of the proposed numerical approach. Through the determination of microstructural properties of untreated and quenched C90 steel, it is concluded that the presence of the micro-cracks may have a great influence on the crack path evolution. [ABSTRACT FROM AUTHOR]