A phase-field approach to viscoelastic fracture in rubbery polymers

IWPDF 2019 1st International Workshop on Plasticity, Damage and Fracture of Engineering Materials, Ankara, Türkiye, 22 - 23 Ağustos 2019, ss.1

Rubbery polymers are widely used in, e.g., the automotive, the aeronautical and

space industry. Rubbery polymers consist of network of long polymer chains responsible for

the elastic response and a secondary free chains superimposed to the elastic network in terms

of entanglements leading to the rate-dependent viscoelastic response. The fracture toughness

of rubbery polymers is a rate-dependent phenomenon which manifests itself in the sense of

monotonically increasing fracture toughness with rising crack velocity under tearing tests [1].

In order to communicate the above-mentioned phenomena, the ground state elasticity, in the

current study, is accounted by the eight-chain model of Arruda & Boyce [2], whereas the

superimposed viscous effects are incorporated into the model in terms of a number of

Maxwell elements [3]. For the evolution of the viscous deformations, a new relaxation

kinetics is introduced without the multiplicative split of the deformation gradient, thereby

capturing the shear and volumetric creep deformations. As a novel aspect, local phase field

approach similar to damage mechanics formulation governs the failure of the superimposed

chains, while the degradation of the elastic network is governed by a rate-dependent phasefield

approach [4,5]. The model parameters are fitted to extant experimental data from the

literature. We, afterwards, demonstrate qualitative results of the proposed model by means of

representative numerical examples.

References:

1. H. Dal and M. Kaliske (2009). A micro-continuum-mechanical material model for failure of

rubber-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 stretch

behavior 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 rubber

viscoelasticity: 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 to

failure 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 rubbery

polymers, Const. Models for Rubber VIII, Taylor & Francis Group, London, pp. 335–341