Energetic approach for a sliding inclusion accounting for plastic dissipation at the interface, application to phase nucleation

Bluthé, Joffrey; Weisz-Patrault, Daniel; Ehrlacher, Alain

doi:10.1016/j.ijsolstr.2017.05.023

Cited by 3 publications

(3 citation statements)

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“…Sects 2-4 of this paper report on a simplified numerical method for a fast evaluation of the plastic slips in elastic-plastic 2D polycrystals. That method is based on incremental variational principles, which have proved to be a fruitful approach in many applications [9,10,2,16,26,22,25]. Starting from elastic-plastic constitutive equations detailed in Sect.…”

Section: Introductionmentioning

confidence: 99%

A Direct Method for Cyclic Crystal Plasticity with Application to High-Cycle Fatigue

Echerradi,

Weisz-Patrault,

Peigney

2023

Lecture Notes in Applied and Computational Mechanics

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The prediction of fatigue in materials and structures is usually based on experimental Wohler curves, relating the number of cycles to failure to the amplitude of the applied cyclic loading. Those curves show some scattering due notably to the variability of the microstructure. Predicting fatigue lifetime can thus be seen as a statistical problem that depends on microstructural descriptors. This paper paves the way to a probabilistic approach for quantitatively linking crystallographic and morphological texture data to fatigue lifetime prediction. In more detail, a simplified mesoscopic model is constructed for calculating the evolution of an elastic-plastic polycrystal with a prescribed texture. That model is limited to high cycle fatigue, corresponding to cyclic loadings of sufficiently low amplitude for plasticity to be mainly confined to few well-separated grains. The model obtained takes details of the texture into account, i.e. the distribution, shape and orientation of the individual grains. It relies on analytical formula and is mesh-free. A comparison with full-field finite element simulation shows that the proposed model leads to satisfactory results in regard to its complexity. In the case of cyclic loading, we show that the model presented leads to a direct method for calculating the asymptotic values of the plastic slips (and cumulated plastic slips) reached in each grain when the number of cycles grows to infinity. We show how that direct approach can be used for upscaling a local failure criterion to the mesoscopic scale and performing probabilistic analysis.

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Section: Introductionmentioning

confidence: 99%

A Direct Method for Cyclic Crystal Plasticity with Application to High-Cycle Fatigue

Echerradi,

Weisz-Patrault,

Peigney

2023

Lecture Notes in Applied and Computational Mechanics

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“…The total energy to be minimized is composed of the elastic bulk energy E γ p minus the work of external forces W γ p plus the plastic-like dissipated energy D γ p . A similar approach has been used for instance by Bluthé et al (2017) within a different context. The dissipation can be interpreted as a cost to reach a lower energy state as detailed by Fedelich andEhrlacher (1997) andMielke (2003).…”

Section: Introductionmentioning

confidence: 99%

Mixed analytic/energetic approach for a sliding orthotropic hollow cylinder. Application to coil sagging

Weisz-Patrault

Gantier

Ehrlacher

2019

International Journal of Solids and Structures

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This paper deals with the numerical simulation of coil sagging. This problem arises within the framework of the steel making industry where strips are wound on themselves for storage. Coil sagging is a major defect that can occur for recent grades undergoing phase transitions during the coiling process. The detailed mechanisms leading to coil sagging are still not well understood, making this phenomenon very difficult to prevent. The coil is a multilayer hollow cylinder where sliding takes place at each interface and significantly contributes to the overall deformation. However, a detailed numerical simulation addressing the contact problem, considering both pressure and sliding is difficult to perform under non-axisymmetric conditions. This paper presents a simplified approach considering an orthotropic hollow cylinder instead of a multilayer coil. The anisotropy is due to contact roughness that tends to decrease the radial stiffness. The hollow cylinder is subjected to gravity and an eigenstrain representing thermal expansion, phase transitions and transformation induced plasticity. Sliding at each interface is taken into account through a continuous plastic-like shear strain that is determined through an energetic principle. The proposed solution relies on analytical developments so that computation time is compatible with parametric studies. Results are addressed in order to give a better understanding of mechanisms and conditions under which coil sagging occur.

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“…It should be mentioned that the singularity problem arises only for the transformation induced plasticity and not for the classical plasticity due to temperature changes although both problems are very similar. That is why, in this paper this technical issue is solved by considering that nucleation of the product phase is discontinuous, that is to say that a minimal finite volume of product phase is created when a lower total energy state can be reached by rearranging the atomic lattice in this volume as suggested by Bluthé et al (2016) and in agreement with Delannay et al (2008). Therefore when there is no product phase (pure matrix of parent phase), one cannot consider an incremental variation of the product phase proportion, one should directly consider a finite size for the inclusion.…”

Section: Introductionmentioning

confidence: 99%

Multiphase model for transformation induced plasticity. Extended Leblond’s model

Weisz-Patrault

2017

Journal of the Mechanics and Physics of Solids

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To cite this version:Daniel Weisz-Patrault. Multiphase model for transformation induced plasticity. Extended Leblond's model. Journal of the Mechanics and Physics of Solids, Elsevier, 2017, 106, pp.152 -175 AbstractTransformation induced plasticity (TRIP) classically refers to plastic strains observed during phase transitions that occur under mechanical loads (that can be lower than the yield stress). A theoretical approach based on homogenization is proposed to deal with multiphase changes and to extend the validity of the well known and widely used model proposed by Leblond, J.-B., Devaux, J., and Devaux, J. (1989). Mathematical modelling of transformation plasticity in steels i: case of ideal-plastic phases. International journal of plasticity, 5(6):551-572. The approach is similar, but several product phases are considered instead of one and several assumptions have been released. Thus, besides the generalization for several phases, one can mention three main improvements in the calculation of the local equivalent plastic strain: the deviatoric part of the phase transformation is taken into account, both parent and product phases are elastic-plastic with linear isotropic hardening and the applied stress is considered. Results show that classical issues of singularities arising in the Leblond's model (corrected by ad hoc numerical functions or thresholding) are solved in this contribution excepted when the applied equivalent stress reaches the yield stress. Indeed, in this situation the parent phase is entirely plastic as soon as the phase transformation begins and the same singularity as in the Leblond's model arises. A physical explanation of the cutoff function is introduced in order to regularize the singularity. Furthermore, experiments extracted from the literature dealing with multiphase transitions and multiaxial loads are compared with the original Leblond's model and the proposed extended version. For the extended version, very good agreement is observed without any fitting procedures (i.e., material parameters are extracted from other dedicated experiments) and for the original version results are more qualitative.

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Energetic approach for a sliding inclusion accounting for plastic dissipation at the interface, application to phase nucleation

Cited by 3 publications

References 20 publications

A Direct Method for Cyclic Crystal Plasticity with Application to High-Cycle Fatigue

A Direct Method for Cyclic Crystal Plasticity with Application to High-Cycle Fatigue

Mixed analytic/energetic approach for a sliding orthotropic hollow cylinder. Application to coil sagging

Multiphase model for transformation induced plasticity. Extended Leblond’s model

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