Formulation and implementation of strain rate‐dependent fracture toughness in context of the phase‐field method

Abstract

Summary The phase‐field approach is a promising technique for the realistic simulation of brittle fracture processes, both in quasi‐static and transient analysis. Considering fast loading, experimental evidence indicates a strong relationship between the rate of strain and the material's resistance against fracture, which can be considered by a dynamic increase factor for the strength of the material. The paper at hand presents a novel approach within the framework of phase‐field models for brittle fracture. A rate‐dependent fracture toughness is formulated as a function of the rate of crack driving strain components, which results in higher strength for faster loading. Beside the increased amount of energy necessary to evolve a crack at a high strain rate loading situation, the model incorporates quasi‐viscous stress‐type quantities that are not directly related to the formation of the crack and exist only in the phase‐field transition zone between broken and sound material. The governing strong form equations for a transient simulation are derived and the relevant information for an implementation of the model into a finite element code is outlined in detail. The performance of the model is demonstrated for static and dynamic benchmark simulations and for a comparison to experimental findings.

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

“…Furthermore, it is noted that, different from e.g. [48], in the proposed model, rate-dependency of fracture toughness does not affect the density of free energy 𝛹 , since dissipation due to crack growth is not supposed to enter 𝛹 . Accordingly, no additional stress terms arise from rate-dependent toughness, see the evaluation of the entropy inequality below in Sect.…”

“…for shear-loaded metals. Yin et al [48] assumed the toughness of a linear elastic material to depend on rate of deformation. In their formulation, dissipation due to crack formation is incorporated into the free energy so that additional stress contributions are obtained from the rate-dependent fracture toughness.…”

“…In their formulation, dissipation due to crack formation is incorporated into the free energy so that additional stress contributions are obtained from the rate-dependent fracture toughness. In these two models [30,48], rate-independent models for the deformation of the bulk are considered. To the best of the authors' knowledge, so far, there are no phase-field models that consider both a rate-dependent toughness and a model of rate-dependent deformation.…”

Rate‐dependent fracture simulation of viscoelastic material by the phase‐field method

“…Representative applications are referred to the work of MIEHE et al [2] in quasi-static situations and the work of KUHN & MÜLLER [3] in transient situations. Moreover, motivated by experimental findings from BISCHOFF & PERRY [4] and FINEBERG et al [5], YIN et al [6] formulate a rate-dependent fracture toughness for the fracture evolution, obtaining good agreements with experimental data. Nevertheless, few formulations of the phasefield method to viscoelastic materials are studied.…”

An anisotropic phase‐field model at finite strains for composite fracture

“…In the sequel, brittle phase-field modeling is extended to several other fracture features, e.g. for rate-dependent fracture analysis [1,2], for ductile fracture simulation [3][4][5] , for fatigue failure prediction [6] and for anisotropic failure modeling [7]. This paper introduces a novel phase-field approach, which is motivated physically by fiber reinforcement, to obtain an anisotropic fracture evolution in composite materials.…”