In this study, a new extension of a micromechanical approach proposed recently by the authors is developed to predict the damaged behavior of polycrystals under various multiaxial cyclic loading paths. The model is expressed in the time dependent plasticity for a small strain assumption. With the framework of the continuum damage mechanics (CDM), it is assumed that a scalar damage variable (d g) initiates and then evolves at the granular level where the phenomenon of the localized plastic deformation occurs. The driving force of this variable depends on the granular elastic and inelastic energies. This variable can globally describe the microcrack and/or microcavity. The developed aspects involve the development of a new mesodamage initiation criterion, which depends not only on the accumulated granular plastic strain but also on the applied loading path complexity; another new criterion related to macroscopic damage initiation is also developed through the probabilistic approach of Weibull. This gives finally a mixed approach (micromechanical-probabilistic). An experimental program is proposed with the purpose of studying the cyclic behavior of the aluminum alloy 2024. Hence, a series of cyclic uniaxial and biaxial tests is performed up to final fracture of the specimens. After the model parameters identification, the model is examined to demonstrate that it is powerful in reproducing the low-cycle fatigue behavior of the employed alloy. Moreover, an application of the model under various cyclic loading types is qualitatively conducted showing the model's ability in describing the principal phenomena observed, especially, in multiaxial plastic fatigue.