A numerical analysis of the fracture toughness in phase‐field modelling of adhesive fracture

Hansen-Dörr, Arne Claus; Hennig, Paul; Kästner, Markus; Weinberg, Kerstin

doi:10.1002/pamm.201710094

Cited by 13 publications

(17 citation statements)

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“…Hence, a compensated interface fracture toughnessĜ i c is specified in a way, that a crack propagates along the interface midline at the true interface fracture toughness G i c , i.e.Ĝ i c < G i c . For more details on the compensation procedure, the reader is referred to [25,52,53]. The ratio of the elastic moduli with E 1 = 210 GPa varies, while the P ratio ν = 0.3 is kept constant, i.e.…”

Section: Crack Branching At Interfacesmentioning

confidence: 99%

Phase-field modeling of fracture in heterogeneous materials: jump conditions, convergence and crack propagation

2020

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In this contribution, a variational diffuse modeling framework for cracks in heterogeneous media is presented. A static order parameter smoothly bridges the discontinuity at material interfaces, while an evolving phase-field captures the regularized crack. The key novelty is the combination of a strain energy split with a partial rank-I relaxation in the vicinity of the diffuse interface. The former is necessary to account for physically meaningful crack kinematics like crack closure, the latter ensures the mechanical jump conditions throughout the diffuse region. The model is verified by a convergence study, where a circular bi-material disc with and without a crack is subjected to radial loads. For the uncracked case, analytical solutions are taken as reference. In a second step, the model is applied to crack propagation, where a meaningful influence on crack branching is observed, that underlines the necessity of a reasonable homogenization scheme. The presented model is particularly relevant for the combination of any variational strain energy split in the fracture phase-field model with a diffuse modeling approach for material heterogeneities.

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Section: Crack Branching At Interfacesmentioning

confidence: 99%

Phase-field modeling of fracture in heterogeneous materials: jump conditions, convergence and crack propagation

2020

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“…The length scale interaction of i and c is compensated by applyingĜ i c instead of G i c along the interface, cf. [8][9][10][11]. A sharp, conforming elastic jump beween the upper and lower half serves as reference.…”

Section: Numerical Resultsmentioning

confidence: 99%

Jump conditions in phase‐field modeling of interface fracture

Hansen-Dörr

Brummund

Kästner

2021

Proc Appl Math and Mech

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In this contribution, a variational framework for diffuse modeling of cracks in heterogeneous media is analyzed. A static order parameter smoothly bridges the discontinuity at material interfaces, while an evolving phase-field captures the regularized crack. The key novelty is the combination of a strain energy split with a partial rank-I relaxation in the vicinity of the diffuse interface. The former is necessary to account for physically meaningful crack kinematics like crack closure, the latter ensures the mechanical jump conditions throughout the diffuse region. The model is applied to crack propagation, where a significant influence on crack branching is observed, that underlines the necessity of a reasonable homogenization scheme for the diffuse interface region.

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“…In the plots of the top row of Fig with bulk stiffnesses C (2) = 2C (1) where the crack grows from soft into hard material. An initial crack of 1/4 times the edge length of the sample is located in material 1.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…In [1] interfaces are modeled as zones of finite width with appropriately adjusted fracture parameters. Furthermore, these models allow for a straightforward numerical implementation with standard finite elements, since displacement jumps and stress singularities are avoided in these models.…”

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Phase field modeling of interface effects on cracks in heterogeneous materials

Kuhn

Müller

2019

Proc Appl Math and Mech

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One of the reasons why the phase field approach has become very popular for modeling fracture processes is that therein the entire evolution of fracture follows from energetic principles without the need for different criteria for crack initiation, nucleation, kinking or branching. Furthermore, these models allow for a straightforward numerical implementation with standard finite elements, since displacement jumps and stress singularities are avoided in these models. Consequently, phase field fracture models are now also used to model and simulate fracture of heterogeneous materials such as composites, where cracks may be arrested, deflected or bifurcated at interfaces between the different components of the composite material, resulting in complicated crack patterns. The crack propagation is not only controlled by the elastic and fracture properties of the bulk phases of the material but also by the properties of the interfaces in between. Thus, it is crucial to take these interface properties into account. Therefore in this work, interfaces are equipped with a fracture energy corresponding to the phase field fracture energy of the bulk phases in order to model the interface fracture properties. In the finite element implementation, the interfaces are modeled by means of surface elements without introducing additional degrees of freedom. Phase field modeling of interfacial fractureThe overall fracture properties of heterogeneous materials not only depend on the elastic and fracture mechanical properties of the individual constituents α, i.e. the elastic stiffness tensor C (α) and the fracture resistance G (α) c , but also on the properties of the interfaces in between the different materials. While different properties of individual bulk phases can easily be dealt with in phase field fracture models, there are several approaches on how to integrate on how to incorporate the effect of interfaces. In [1] interfaces are modeled as zones of finite width with appropriately adjusted fracture parameters. Contrary, a combination with a cohesive type of modeling interface fracture is proposed in [2]. Another approach, which makes use of a new energetic formulation mixing bulk and cohesive surface energies, is proposed in [3].In this work, the bulk phase field energy accounting for elastic and fracture energy contributions of the different phases is supplemented by an additional interface term accounting for the effect of the interfaces, such that the total energy of a volume V = V (α) with interfaces Γ = Γ (αβ) readsTherein ε and s denote the infinitesimal strain tensor and the fracture field, respectively. The size of the transition zone between sound (s = 1) and broken (s = 0) material is controlled by the regularization parameter . The small stiffness margin η ensures well posedness when s = 0. By means of the interface parameter G (αβ) Γ , the fracture resistance at an interface between phases α and β can be adjusted to the effective valueNote that neglecting the interface contribution G (αβ) Γ yields the average of ...

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A numerical analysis of the fracture toughness in phase‐field modelling of adhesive fracture

Cited by 13 publications

References 3 publications

Phase-field modeling of fracture in heterogeneous materials: jump conditions, convergence and crack propagation

Phase-field modeling of fracture in heterogeneous materials: jump conditions, convergence and crack propagation

Jump conditions in phase‐field modeling of interface fracture

Phase field modeling of interface effects on cracks in heterogeneous materials

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