Multi-phase-field modeling of anisotropic crack propagation for polycrystalline materials

Nguyen, Thanh Tung; Réthoré, Julien; Yvonnet, Julien; Baietto, Marie-Christine

doi:10.1007/s00466-017-1409-0

Cited by 157 publications

(89 citation statements)

References 52 publications

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“…The purpose of this study is to enhance phase field model to fracture in layered heterogeneous structures with a particular focus on the influences of interfacial properties. The effects of both perfect bonded and cohesive interfaces in terms of phase field model, which have previously been developed by the authors ( [50,51,47]), will be considered. To capture the mismatch between different materials at interface region, we thus introduce an regularized interfacial transition zone in the framework of variational approaches.…”

Section: Approach and Objectivementioning

confidence: 99%

“…In order to account the behavior of the cohesively bonded interface into phase field model, a new energy term is added to describe the cohesively bonded interface ψ I ([[u]] , κ), which depends on the displacement jump [[u]] across the interface Γ I , and κ is a history parameter to distinguish between loading and unloading. Once the cohesive fracture ψ I is determined, the cohesive tractions are derived through its differentiation, for more detail, see e.g., [47].…”

Section: Phase Field Model With the Cohesively Bonded Interfacementioning

confidence: 99%

“…Further, the displacement jump [[u]] created by interfacial decohesion is approximated as a smooth transition v(x). The two approaches have already been proposed and reported in our previous work [47], one based on a Taylor expansion at first order of the assumed smoothed regularized displacement field, and the other used an addition field coupled in the boundary value problems. The advantages and drawbacks of each method have been discussed in [47].…”

Section: Phase Field Model With the Cohesively Bonded Interfacementioning

confidence: 99%

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Role of interfacial transition zone in phase field modeling of fracture in layered heterogeneous structures

Nguyen

Waldmann

Bui

2019

Journal of Computational Physics

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A B S T R A C TMechanical behavior of layered materials and structures greatly depends on the mechanical behavior of interfaces. In the past decades, the failure in such layered media has been studied by many researchers due to their critical role in the mechanics and physics of solids. This study aims at investigating crackinterface interaction in two-dimensional (2-D) and three-dimensional (3-D) layered media by a phase field model. Our objectives are fourfold: (a) to better understand fracture behavior in layered heterogeneous systems under quasi-static load; (b) to introduce a new methodology for better describing interfaces by a regularized interfacial transition zone in the context of variational phase field approach, exploring its important role; (c) to show the accuracy, performance and applicability of the present model in modeling material failure at the interfaces in both 2-D and 3-D bodies; and (d) to quantitatively validate computed crack path with respect to experimental data. Phase field models with both perfectly and cohesive bonded interfaces are thus derived. A regularized interfacial transition zone is introduced to capture characteristics of material mismatch at the interfaces. Numerical examples for 2-D and 3-D layered systems with experimental validation provide fundamentals of fracture behavior in layered structures. The obtained results shed light on the behavior of crack paths, which are drastically affected by the elastic modulus mismatch between two layers and interface types, and reveal the important role of the proposed interfacial transition zone in phase field modeling of crack-interface interactions.

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Section: Approach and Objectivementioning

confidence: 99%

Section: Phase Field Model With the Cohesively Bonded Interfacementioning

confidence: 99%

Section: Phase Field Model With the Cohesively Bonded Interfacementioning

confidence: 99%

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Role of interfacial transition zone in phase field modeling of fracture in layered heterogeneous structures

Nguyen

Waldmann

Bui

2019

Journal of Computational Physics

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“…The PFM was applied to a range of materials, such as polymers, asphalt, concrete, and polycrystalline materials, including brittle and quasi‐brittle fracture, ductile fracture, hydraulic fracture, interfacial fracture, and anisotropic fracture . More details and comparisons of the phase field method with traditional damage mechanics could be found in Marigo et al and de Borst and Verhoosel …”

Section: Introductionmentioning

confidence: 99%

A novel phase field method for modeling the fracture of long bones

Shen

Waisman

Yosibash

et al. 2019

Numer Methods Biomed Eng

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A proximal humerus fracture is an injury to the shoulder joint that necessitates medical attention. While it is one of the most common fracture injuries impacting the elder community and those who suffer from traumatic falls or forceful collisions, there are almost no validated computational methods that can accurately model these fractures. This could be due to the complex, inhomogeneous bone microstructure, complex geometries, and the limitations of current fracture mechanics methods. In this paper, we develop a novel phase field method to investigate the proximal humerus fracture. To model the fracture in the inhomogeneous domain, we propose a power‐law relationship between bone mineral density and critical energy release rate. The method is validated by an in vitro experiment, in which a human humerus is constrained on both ends while subjected to compressive loads on its head, in the longitudinal direction, that lead to fracture at the anatomical neck. CT scans are employed to acquire the bone geometry and material parameters, from which detailed finite element meshes with inhomogeneous Young modulus distributions are generated. The numerical method, implemented in a high performance computing environment, is used to quantitatively predict the complex 3D brittle fracture of the bone and is shown to be in good agreement with experimental observations. Furthermore, our findings show that the damage is initiated in the trabecular bone‐head and propagates outward towards the bone cortex. We conclude that the proposed phase field method is a promising approach to model bone fracture.

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“…[21][22][23] Additionally, when a special enrichment function is utilized, the numerical integration should be performed with great caution. 6,24 Recently, a phase-field model was also utilized for cohesive zone modeling, whereas fracture properties, such as fracture energy and cohesive strength, should be calibrated in conjunction with internal length-scale parameters, 25,26 and some form of numerical regularization was needed to prevent a loss of ellipticity. 27,28 Among various computational methods, the present study employs the cohesive surface element approach while removing mesh bias.…”

Section: Introductionmentioning

confidence: 99%

Removing mesh bias in mixed‐mode cohesive fracture simulation with stress recovery and domain integral

Choi

Park

2019

Numerical Meth Engineering

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Summary To remove mesh bias and provide an accurate crack path representation in mixed‐mode investigation, a novel stress recovery technique is proposed in conjunction with a domain integral and element splits. Based on a domain integral and stress recovery technique, a maximum strain energy release rate is estimated to determine a crack path direction. Then, for a given crack path direction, continuum elements are split, and a cohesive surface element is adaptively inserted. One notes that the proposed stress recovery technique provides a more accurate stress field than a standard stress evaluation procedure. The proposed computational framework is verified and validated by solving mode‐I and mixed‐mode examples. Computational results demonstrate that the domain integral with the stress recovery accurately evaluates a crack path, even with a lower‐quality mesh and under a biaxial stress state. Furthermore, the cohesive surface element approach, with the element split in conjunction with the stress recovery and the domain integral, predicts mixed‐mode fracture behaviors while removing mesh bias in the crack path representation. Additionally, the condition numbers of stiffness matrices are within the same order of magnitude during cohesive fracture simulation.

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Multi-phase-field modeling of anisotropic crack propagation for polycrystalline materials

Cited by 157 publications

References 52 publications

Role of interfacial transition zone in phase field modeling of fracture in layered heterogeneous structures

Role of interfacial transition zone in phase field modeling of fracture in layered heterogeneous structures

A novel phase field method for modeling the fracture of long bones

Removing mesh bias in mixed‐mode cohesive fracture simulation with stress recovery and domain integral

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