Phase-field modelling and analysis of rate-dependent fracture phenomena at finite deformation

TL;DR

This paper introduces a phase-field model for rate-dependent fracture at finite deformation, incorporating viscoelasticity and rate-dependent toughness, validated against experimental data for elastomers and used to study crack patterns and failure mechanisms.

Contribution

It presents a novel energetic phase-field model that accounts for rate-dependent fracture behavior at finite deformation, including viscoelasticity and toughness variations, validated with experimental data.

Findings

Rate-dependent toughness influences crack propagation.

Dissipative fracture driving force is not necessary for rubbery polymers.

Model captures crack patterns and failure modes in viscoelastic materials.

Abstract

Fracture of materials with rate-dependent mechanical behaviour, e.g. polymers, is a highly complex process. For an adequate modelling, the coupling between rate-dependent stiffness, dissipative mechanisms present in the bulk material and crack driving force has to be accounted for in an appropriate manner. In addition, the fracture toughness, i.e. the resistance against crack propagation, can depend on rate of deformation. In this contribution, an energetic phase-field model of rate-dependent fracture at finite deformation is presented. For the deformation of the bulk material, a formulation of finite viscoelasticity is adopted with strain energy densities of Ogden type assumed. The unified formulation allows to study different expressions for the fracture driving force. Furthermore, a possibly rate-dependent toughness is incorporated. The model is calibrated using experimental results from the literature for an elastomer and predictions are qualitatively and quantitatively validated against experimental data. Predictive capabilities of the model are studied for monotonic loads as well as creep fracture. Symmetrical and asymmetrical crack patterns are discussed and the influence of a dissipative fracture driving force contribution is analysed. It is shown that, different from ductile fracture of metals, such a driving force is not required for an adequate simulation of experimentally observable crack paths and is not favourable for the description of failure in viscoelastic rubbery polymers. Furthermore, the influence of a rate-dependent toughness is discussed by means of a numerical study. From a phenomenological point of view, it is demonstrated that rate-dependency of resistance against crack propagation can be an essential ingredient for the model when specific effects such as rate-dependent brittle-to-ductile transitions shall be described.