A non-isothermal thermodynamically consistent phase field framework for structural damage and fatigue

Boldrini, José Luiz; Moraes, Eduardo A. Barros de; Chiarelli, Luis Renato; Fumes, F. G.; Bittencourt, Marco L.

doi:10.1016/j.cma.2016.08.030

Cited by 66 publications

(65 citation statements)

References 25 publications

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“…h = f (ψ elas ). The fatigue phase-field damage models of [3] and [5] use h = h(ψ bulk = P :Ḟdt, ), while [2] sets h = f ( ,˙ ). We see micro-crack formation as a dissipative mechanism and therefore propose a load history variable depending on the energy dissipated under cyclic loading in the bulk:…”

Section: Fatigue Damage Sourcementioning

confidence: 99%

“…To the best of the authors' knowledge, [3] was the first to consider fatigue damage in a phase-field model by introducing a fatigue history variable in the Ginzburg-Landau equation. [7] additionally introduced damage caused by aging, while [5] defined the internal fatigue history variable with a differential constitutive law to be found. [2] used a different approach and reduced the fracture toughness with cyclic loading.…”

Section: Introductionmentioning

confidence: 99%

“…The fatigue framework could alternatively be derived with a balance law for micro-forces as the basis, first introduced by[12] and later used for phase-field damage models by[5].…”

mentioning

confidence: 99%

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Fatigue phase-field damage modeling of rubber using viscous dissipation: Crack nucleation and propagation

Loew

Peters

Beex

2020

Mechanics of Materials

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Section: Fatigue Damage Sourcementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fatigue phase-field damage modeling of rubber using viscous dissipation: Crack nucleation and propagation

Loew

Peters

Beex

2020

Mechanics of Materials

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“…The model allows to describe fatigue crack initiation, propagation and residual fracture and can reproduce Paris behaviour. arXiv:1903.06465v3 [cond-mat.mtrl-sci] 23 Oct 2019 Recently, several propositions to extend the phase-field method to fatigue [16,17,18,19,20] have been published. Representatively for the range of different approaches, two models which are able to reproduce Paris behaviour shall be highlighted here: Carrara et al [19] introduce a phase-field model for fatigue fracture in brittle materials.…”

mentioning

confidence: 99%

An efficient phase-field model for fatigue fracture in ductile materials

Seiler

Linse

Hantschke

et al. 2020

Engineering Fracture Mechanics

105

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Fatigue fracture in ductile materials, e. g. metals, is caused by cyclic plasticity. Especially regarding the high numbers of load cycles, plastic material models resolving the full loading path are computationally very demanding. Herein, a model with particularly small computational effort is presented. It provides a macroscopic, phenomenological description of fatigue fracture by combining the phase-field method for brittle fracture with a classic durability concept. A local lifetime variable is obtained, which degrades the fracture resistance progressively. By deriving the stress-strain path from cyclic material characteristics, only one increment per load cycle is needed at maximum. The model allows to describe fatigue crack initiation, propagation and residual fracture and can reproduce Paris behaviour. arXiv:1903.06465v3 [cond-mat.mtrl-sci] 23 Oct 2019 Recently, several propositions to extend the phase-field method to fatigue [16,17,18,19,20] have been published. Representatively for the range of different approaches, two models which are able to reproduce Paris behaviour shall be highlighted here: Carrara et al. [19] introduce a phase-field model for fatigue fracture in brittle materials. The basic idea of their approach is that due to repetitive loading the crack resistance decreases, allowing cracks to evolve even far below the static crack resistance. The fracture toughness is modified depending on a measure of locally accumulated elastic strain energy density. Mesgarnejad et al. [20] follow a similar approach, but link the lowering of the fracture toughness also to the phase-field, localising the degradation to the vicinity of the crack tip.Although the authors use different approaches, they are not yet overcoming one key challenge inherent to fatigue crack initiation and propagation: The immense computational effort related to the high number of load cycles. This issue is addressed in the present paper. In particular, we introduce an efficient phase-field model of fatigue fracture in ductile materials, such as metals. Analogously to [19], it is based on the reduction of the critical fracture energy, but uses a different local fatigue measure. In contrast to brittle materials, fatigue crack propagation in ductile materials is caused by cyclic plastic deformations. The straightforward way to treat the problem with an elasto-plastic material model is numerically expensive. Therefore, a different approach is chosen. With the help of the LSA, a local lifetime variable is introduced, accounting for cumulative elasto-plastic deformations. Since the stress-strain path within a load cycle is derived from material curves from cyclic experiments, the explicit simulation of each load cycle would be redundant and can therefore be avoided, saving computational costs. In other words, instead of introducing a ductile phasefield model, an elastic, brittle phase-field formulation which considers the elasto-plastic origins of fatigue is presented. As cracks are described on a macroscopic scale, microscopic effects are...

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“…The hypothesis of small deformation was considered. This model is an extension of the approach developed by Boldrini et al (2016) by including the fracture anisotropy in a similar manner as described by Clayton & Knap (2015), Nguyen et al (2017). The ideas presented by these authors were chosen due to the easiness of implementation and ability to capture the crack path dependency on the material symmetry.…”

mentioning

confidence: 99%

A Thermodynamically Consistent Phase Field Framework for Anisotropic Structural Damage

Petrini¹,

Bittencourt²,

Boldrini³

2019

Proceedings of the 7th International Symposium on Solid Mechanics

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Phase-field damage models have gained large attention as an efficient way of modeling crack propagation, specially for avoiding the sharp interface between the material and the cracks (Dal et al. 2017). Phase field models based on a variational approach including anisotropic damage growth have been applied to different materials exhibiting complex cracking mechanisms such as unidirectional laminates and biological tissues(Li, some of these models the thermodynamic consistency is unclear, while others consider just isothermal case. Therefore, to overcome these deficiencies and to contribute to the development of damage models for anisotropic materials such as composite laminates we present in this work an thermodynamically consistent non-isothermal model for anisotropic structural damage. The hypothesis of small deformation was considered. This model is an extension of the approach developed by Boldrini et al. (2016) by including the fracture anisotropy in a similar manner as described by Clayton & Knap (2015), Nguyen et al. (2017). The ideas presented by these authors were chosen due to the easiness of implementation and ability to capture the crack path dependency on the material symmetry. The model was implemented in Matlab and simulations of tensile tests in I-shaped and notched specimens showed that the model is capable to recover the isotropic damage evolution and to reproduce the expected crack propagation pattern for a material with one or two preferential direction of fracture oriented at 45 o and −45 o . It is worth mentioning that in this approach the crack orientation is predefined based on observations of the morphology of the material and is not a consequence of the anisotropic material response to the boundary conditions and applied load. In an attempt to address this problem and make the model more general, we are working on the transformation of the degradation function into a symmetric tensor with its own evolution equation, as an internal variable, with dependence on the damage scalar variable.

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A non-isothermal thermodynamically consistent phase field framework for structural damage and fatigue

Cited by 66 publications

References 25 publications

Fatigue phase-field damage modeling of rubber using viscous dissipation: Crack nucleation and propagation

Fatigue phase-field damage modeling of rubber using viscous dissipation: Crack nucleation and propagation

An efficient phase-field model for fatigue fracture in ductile materials

A Thermodynamically Consistent Phase Field Framework for Anisotropic Structural Damage

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