Phase field modeling of Hertzian indentation fracture

Strobl, Michael; Seelig, Th.

doi:10.1016/j.jmps.2020.104026

Cited by 29 publications

(23 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There could be other factors influencing the precision of the phase field fracture model in predicting the initiation of crack growth. One aspect that has been discussed in the literature [50,51] is the influence of the damage irreversibility condition (§3a). In particular, it has been argued that the irreversibility condition (3.3) prevents the phase field from attaining its optimal crack profile, providing a source of inaccuracy.…”

Section: Resultsmentioning

confidence: 99%

“…It must be emphasized that our findings are related to solids containing cracks; phase field fracture models can also predict the nucleation of cracks from pristine samples and non-sharp defects such as notches, where the conclusions reported here might not apply. In particular, the conclusions drawn in regard to the irreversibility condition might change [50,51] and it has been reported that prescribing ϕ = 1 at the defect surface is not the most accurate way of capturing crack nucleation from blunted notches [10].…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

An assessment of phase field fracture: crack initiation and growth

Kristensen

Niordson

Martínez‐Pañeda

2021

Phil. Trans. R. Soc. A.

View full text Add to dashboard Cite

The phase field paradigm, in combination with a suitable variational structure, has opened a path for using Griffith’s energy balance to predict the fracture of solids. These so-called phase field fracture methods have gained significant popularity over the past decade, and are now part of commercial finite element packages and engineering fitness- for-service assessments. Crack paths can be predicted, in arbitrary geometries and dimensions, based on a global energy minimization—without the need for ad hoc criteria. In this work, we review the fundamentals of phase field fracture methods and examine their capabilities in delivering predictions in agreement with the classical fracture mechanics theory pioneered by Griffith. The two most widely used phase field fracture models are implemented in the context of the finite element method, and several paradigmatic boundary value problems are addressed to gain insight into their predictive abilities across all cracking stages; both the initiation of growth and stable crack propagation are investigated. In addition, we examine the effectiveness of phase field models with an internal material length scale in capturing size effects and the transition flaw size concept. Our results show that phase field fracture methods satisfactorily approximate classical fracture mechanics predictions and can also reconcile stress and toughness criteria for fracture. The accuracy of the approximation is however dependent on modelling and constitutive choices; we provide a rationale for these differences and identify suitable approaches for delivering phase field fracture predictions that are in good agreement with well-established fracture mechanics paradigms. This article is part of a discussion meeting issue ‘A cracking approach to inventing new tough materials: fracture stranger than friction’.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

An assessment of phase field fracture: crack initiation and growth

Kristensen

Niordson

Martínez‐Pañeda

2021

Phil. Trans. R. Soc. A.

View full text Add to dashboard Cite

show abstract

“…In case of the shear example (presented in Section 3.2) the nodes were doubled to physically represent the initial fracture. This was reported (Strobl and Seelig, 2020) to be essential because of the energy decomposition applied (see eq. 2).…”

Section: Materials Constant Young's Modulus (E)mentioning

confidence: 99%

Toughness or strength? Regularization in phase-field fracture explained by the coupled criterion

Molnár

Doitrand

Estevez

et al. 2020

Theoretical and Applied Fracture Mechanics

View full text Add to dashboard Cite

In recent years the phase-field method and the coupled energy and stress-based criterion have attracted much attention due to their adaptability in modeling fractures. Both approaches have been successfully used to determine crack initiation and have compared well with real-life experiments. The phase-field method diffuses the crack surface into the volume of the solid, thus making the solution viable through variational techniques. The diffusion is controlled by an internal length scale, which is primarily considered to be a numerical aid without any real physical meaning. In this paper, we question the consideration that the internal length is only a numerical parameter, and assess its mechanical significance with the help of the coupled criterion. Through elaborate benchmark examples, the correlation between the two methods is demonstrated based on the critical loading, the crack topology, and the crack arrest length. We reveal that independently of the chosen aspect, the phase-field approach and the coupled criterion present excellent correspondence. We show that the correlation between tensile strength and length scale is unique for the standard phase-field formulation. Interestingly, we find that both stress and energy criteria are satisfied in the phase-field fracture, and this is explained by demonstrating the alteration in global energy release rate due to the regularization introduced by the smeared model.

show abstract

“…Before proceeding with the comparisons per se, it is pertinent to mention that since the pioneering experiments of Hertz (1882) a multitude of investigators have studied how fracture nucleates and propagates in many nominally brittle ceramics, metals, and polymers when indented; see, e.g., the reviews by Lawn (1998), Guin and Gueguen (2019), and references therein. Yet, it was just very recently that the variational phase-field approach was used for the first time to study this kind of experimentally pervasive problems (Strobl and Seelig, 2020). In a nutshell, Strobl and Seelig (2020) first demonstrated that the variational phase-field model in its classical form fails to generate results that are consistent with experimental observations.…”

Section: Application To the Indentation Of Glass Plates With Flat-end...mentioning

confidence: 99%

The revisited phase-field approach to brittle fracture: Application to indentation and notch problems

Kumar,

Ravi-Chandar,

Lopez-Pamies

2022

Preprint

View full text Add to dashboard Cite

In a recent contribution, Kumar, Bourdin, Francfort, and Lopez-Pamies (J. Mech. Phys. Solids 142:104027, 2020) have introduced a comprehensive macroscopic phase-field theory for the nucleation and propagation of fracture in linear elastic brittle materials under arbitrary quasistatic loading conditions. The theory can be viewed as a natural generalization of the phase-field approximation of the variational theory of brittle fracture of Francfort and Marigo (J. Mech. Phys. Solids 46:1319-1342, 1998) to account for the material strength at large. This is accomplished by the addition of an external driving force -which physically represents the macroscopic manifestation of the presence of inherent microscopic defects in the material -in the equation governing the evolution of the phase field. The main purpose of this paper is to continue providing validation results for the theory by confronting its predictions with direct measurements from three representative types of experimentally

show abstract

Phase field modeling of Hertzian indentation fracture

Cited by 29 publications

References 37 publications

An assessment of phase field fracture: crack initiation and growth

An assessment of phase field fracture: crack initiation and growth

Toughness or strength? Regularization in phase-field fracture explained by the coupled criterion

The revisited phase-field approach to brittle fracture: Application to indentation and notch problems

Contact Info

Product

Resources

About