Phase-field modeling of fatigue coupled to cyclic plasticity in an energetic formulation

Ulloa, Jacinto; Wambacq, Jef; Alessi, Roberto; Degrande, Geert; François, Stijn

doi:10.1016/j.cma.2020.113473

Cited by 70 publications

(61 citation statements)

References 105 publications

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“…For instance, gradient-extended internal variables, which have been omitted so far for explanatory simplicity, can be easily incorporated, as will be shown in section 6. In such cases, Formulation 2 automatically provides boundary conditions for the gradients of internal variables [59,63]. Moreover, higher-order stability conditions can be considered in Formulation 2 by replacing the first-order condition (45) with the more general directional stability condition (41) [60,86].…”

Section: Evolution Problemmentioning

confidence: 99%

“…The point of departure is the model proposed by Houlsby et al [21] to describe the behavior of a monopile foundation as a one-dimensional mechanical system with a cyclic accumulation of plastic strains. However, when developed in a continuum setting, the model is applicable to a wide range of responses that exhibit ratcheting under cyclic loading [59].…”

Section: Ratcheting Plasticitymentioning

confidence: 99%

“…Interestingly, a similar idea was considered by Germain et al [7] for nonassociative viscoplasticity. Moreover, state-dependent dissipation potentials have been used in several studies involving non-associative plasticity [21,[51][52][53][54][55][56], as well as gradient-damage models [57] and fatigue [58,59].…”

Section: Introductionmentioning

confidence: 99%

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On the variational modeling of non-associative plasticity

Ulloa

Alessi

Wambacq

et al. 2021

International Journal of Solids and Structures

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In this work, the energetic formulation for rate-independent dissipative materials is extended to consider non-associative plasticity models. In associative models, the fulfilment of the principle of maximum dissipation naturally leads to a variational formulation of the evolution problem. This is no longer true for non-associative models, which are generally presented in the literature in a non-variational form. However, recent studies have unveiled the possibility to recover a variational structure in non-associative plasticity by relying on a suitable state-dependent dissipation potential. Here, this idea is further elaborated in the framework of the energetic formulation, providing a systematic variational approach to non-associative plasticity. A clear link between the classical governing equations of non-associative plasticity and the energetic formulation is established, for which a state-dependent dissipation potential is derived from a generalization of the principle of maximum dissipation. The proposed methodology is then applied to recast specific non-associative plasticity models in variational form, highlighting the flexibility of the formulation. The examples include a Drucker-Prager model with combined isotropic-kinematic hardening and a ratcheting plasticity model. Several thermomechanical insights are provided for both examples. Moreover, exploiting the flexibility of the energetic formulation, extensions to gradient plasticity are devised, leading to representative finite element simulations.

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Section: Evolution Problemmentioning

confidence: 99%

Section: Ratcheting Plasticitymentioning

confidence: 99%

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On the variational modeling of non-associative plasticity

Ulloa

Alessi

Wambacq

et al. 2021

International Journal of Solids and Structures

Self Cite

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show abstract

“…The models are developed under the assumption of elastic material behaviour, which corresponds to the so-called high-cyclic fatigue regime. Recently, a phase-field fatigue model with elastoplastic material behaviour for low-cyclic regime was proposed in [54].…”

Section: Introductionmentioning

confidence: 99%

A general phase-field model for fatigue failure in brittle and ductile solids

et al. 2021

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In this work, the phase-field approach to fracture is extended to model fatigue failure in high- and low-cycle regime. The fracture energy degradation due to the repeated externally applied loads is introduced as a function of a local energy accumulation variable, which takes the structural loading history into account. To this end, a novel definition of the energy accumulation variable is proposed, allowing the fracture analysis at monotonic loading without the interference of the fatigue extension, thus making the framework generalised. Moreover, this definition includes the mean load influence of implicitly. The elastoplastic material model with the combined nonlinear isotropic and nonlinear kinematic hardening is introduced to account for cyclic plasticity. The ability of the proposed phenomenological approach to naturally recover main features of fatigue, including Paris law and Wöhler curve under different load ratios is presented through numerical examples and compared with experimental data from the author’s previous work. Physical interpretation of additional fatigue material parameter is explored through the parametric study.

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“…While some models reduce the crack resistance of the material as a result of its cyclic degradation [6,23,36], others increase the crack driving force [11,34]. There are first approaches to cover plastic [40] and viscous [21] materials. To tackle the crucial problem of computational time when simulating repetitive loading, Loew et al [22] and Schreiber et al [34] use cycle jump techniques.…”

mentioning

confidence: 99%

Phase-field modelling for fatigue crack growth under laser shock peening-induced residual stresses

et al. 2021

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For the fatigue life of thin-walled components, not only fatigue crack initiation, but also crack growth is decisive. The phase-field method for fracture is a powerful tool to simulate arbitrary crack phenomena. Recently, it has been applied to fatigue fracture. Those models pose an alternative to classical fracture-mechanical approaches for fatigue life estimation. In the first part of this paper, the parameters of a phase-field fatigue model are calibrated and its predictions are compared to results of fatigue crack growth experiments of aluminium sheet material. In the second part, compressive residual stresses are introduced into the components with the help of laser shock peening. It is shown that those residual stresses influence the crack growth rate by retarding and accelerating the crack. In order to study these fatigue mechanisms numerically, a simple strategy to incorporate residual stresses in the phase-field fatigue model is presented and tested with experiments. The study shows that the approach can reproduce the effects of the residual stresses on the crack growth rate.

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Phase-field modeling of fatigue coupled to cyclic plasticity in an energetic formulation

Cited by 70 publications

References 105 publications

On the variational modeling of non-associative plasticity

On the variational modeling of non-associative plasticity

A general phase-field model for fatigue failure in brittle and ductile solids

Phase-field modelling for fatigue crack growth under laser shock peening-induced residual stresses

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