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A phase-field approach to viscoelastic fracture in rubbery polymers

Denli, Funda A.
Gültekin, Osman
Dal, Hüsnü
Rubbery polymers are widely used in, e.g., the automotive, the aeronautical andspace industry. Rubbery polymers consist of network of long polymer chains responsible forthe elastic response and a secondary free chains superimposed to the elastic network in termsof entanglements leading to the rate-dependent viscoelastic response. The fracture toughnessof rubbery polymers is a rate-dependent phenomenon which manifests itself in the sense ofmonotonically increasing fracture toughness with rising crack velocity under tearing tests [1].In order to communicate the above-mentioned phenomena, the ground state elasticity, in thecurrent study, is accounted by the eight-chain model of Arruda & Boyce [2], whereas thesuperimposed viscous effects are incorporated into the model in terms of a number ofMaxwell elements [3]. For the evolution of the viscous deformations, a new relaxationkinetics is introduced without the multiplicative split of the deformation gradient, therebycapturing the shear and volumetric creep deformations. As a novel aspect, local phase fieldapproach similar to damage mechanics formulation governs the failure of the superimposedchains, while the degradation of the elastic network is governed by a rate-dependent phasefieldapproach [4,5]. The model parameters are fitted to extant experimental data from theliterature. We, afterwards, demonstrate qualitative results of the proposed model by means ofrepresentative numerical examples.References:1. H. Dal and M. Kaliske (2009). A micro-continuum-mechanical material model for failure ofrubber-like materials: Application to aging induced fracturing, J. Mech. Phys. Solids, Vol. 57,pp. 1340–1356,2. E. M. Arruda. and M.C. Boyce (1993). A three-dimensional model for the large stretchbehavior of rubber elastic materials. J. Mech. Phys. Solids, 41(2), pp. 389–412.3. H. Dal and M. Kaliske (2009). Bergström-Boyce model for nonlinear finite rubberviscoelasticity: Theoretical aspects and algorithmic treatment for FE method. Comp. Mech.,44, 809–823.4. L. Schänzel, H. Dal and C. Miehe (2013) On the micromechanically-based approaches tofailure in polymers, Proc. Appl. Math. Mech., Vol. 13, pp. 557–560.5. L. Schänzel , H. Dal, and C. Miehe (2013). Phase-field modeling of fracture in rubberypolymers, Const. Models for Rubber VIII, Taylor & Francis Group, London, pp. 335–341