A phase-field approach to viscoelastic fracture in rubbery polymers


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Denli F. A. , Gültekin O., Dal H.

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

  • Basıldığı Şehir: Ankara
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.1

Özet

 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