Modeling of fatigue in amorphous solid polymers undergoing viscoelastic-viscoplastic deformations

International audienceManufacturers of polymer materials are interested in the assurance of components life-time, especially when the lifetime cannot be easily inspected. Due to the costly and time-consuming testing of long-term fatigue life, there is a need to develop approachesthat can simulate tests well. An approach suitable for modeling isothermal fatigue in amorphous polymers is proposed. The theory is written in a rate form within continuum mechanics framework, and it explicitly accounts for the dependence of the free energy on both the viscoelastic-viscoplastic deformation and fatigue damage in a thermodynamically consistent manner. In contrast to cumulative damage theories, which determine the damage growth per a well-defined cycle, the damage evolution is formulated by benefiting an endurance surface which shifts in an effective, damage-free stress space. The proposed approach avoids a complex relationship between the deformation and damage as well as challenges in numerical implementation due to a damage-inducedstress reduction. The idea is suitable for polymers in which the fatigue behavior is ductile, i.e. damage during the formation of micro-cracks, which typically takes majority (over 95%) of the total fatigue life, is low in relation to that which develops during thesubsequent cracking phase. The numerical treatment of the model is presented, and the capability of the approach under uni- and multi-axial loadings is addressed. The approach is also implemented in a finite element program, and simulations show thatthe fatigue damage development in a disordered molecular structure of PC strongly depends on both the rigidity of the involved inhomogeneities (second phase particles) and the loading conditions applied