Modeling fracture in polymeric material using phase field method based on critical stretch criterion

In this work, the phase field method (PFM) is applied for modeling fracture in the polymeric type of materials. Considering the large extensibility of polymer chains before fracture, a crack initiation criteria based on a critical stretch value is proposed. The tensile stretches in the material contribute to the active strain energy, which is responsible for driving fracture. Additive decomposition of strain energy into active and passive parts is adopted based on the critical stretch value of polymer chains in a phase-field setting. This critical value is determined by assuming an equivalent uniaxial tensile state of stress in front of the crack tip at the onset of fracture. The stretch of individual polymeric chains is determined by using a polymer network model. The critical fracture toughness of the polymer is kept constant up to the onset of fracture and a gradually reducing value of it is adopted in front of the crack tip beyond the critical stretch. A hybrid phase-field formulation with a staggered solver is used owing to its numerical efficiency and robustness. The effectiveness and applicability of the present model are demonstrated through various numerical examples.