Fracture initiation in multi-phase materials: a systematic three-dimensional approach using a FFT-based solver

This paper studies a two-phase material with a microstructure composed of a hard brittle reinforcement phase embedded in a soft ductile matrix. It addresses the full three-dimensional nature of the microstructure and macroscopic deformation. A large ensemble of periodic microstructures is used, whereby the individual grains of the two phases are modeled using equi-sized cubes. A particular solution strategy relying on the Fast Fourier Transform is adopted, which has a high computational efficiency both in terms of speed and memory footprint, thus enabling a statistically meaningful analysis. This solution method naturally accompanies the regular microstructural model, as the Fast Fourier Transform relies on a regular grid. Using the many considered microstructures as an ensemble, the average arrangement of phases around fracture initiation sites is objectively identified by the correlation between microstructure and fracture initiation -- in three dimensions. The results show that fracture initiates where regions of the hard phase are interrupted by bands of the soft phase that are aligned with the direction of maximum shear. In such regions, the hard phase is arranged such that the area of the phase boundary perpendicular to the principal strain direction is maximum, leading to high hydrostatic tensile stresses, while not interrupting the shear bands that form in the soft phase. The local incompatibility that is present around the shear bands is responsible for a high plastic strain. By comparing the response to a two-dimensional microstructure it is observed that the response is qualitatively similar (both macroscopically and microscopically). One important difference is that the local strain partitioning between the two phases is over-predicted by the two-dimensional microstructure, leading to an overestimation of damage

Homogénéisation des lois de comportement élastoviscoplastique pour le calcul en champs de phase

International audienceLes lois de comportement des interfaces diffuses employées dans la méthode des champs de phase font souvent appel à des règles de mélanges heuristiques dont le choix n'est pas sans conséquence sur les résultats des simulations d'évolution de microstructure. Dans le travail récent [1] et des contributions antérieures consacrés au couplage entre champs de phase et mécanique, des règles issues des méthodes d'homogénéisation en mécanique des milieux hétérogènes sont proposées [2, 3, 4]. Elles sont motivées par des considérations de thermodynamique des processus irréversibles mettant en jeu les phénomènes de diffusion, de changements de phase diffusives et la viscoplasticité. On verra que le choix de potentiels thermodynamiques privilégiés conduit à sélectionner un schéma d'homogénéisation plutôt qu'un autre (par exemple, Voigt ou Reuss). Les exemples concerneront la croissance de précipités dans une matrice viscoplastique. L'influence du schéma d'homogénéisation dans l'interface sur la cinétique de croissance et la morphologie des précipités dans le cas anisotrope (viscoplasticité cristalline) fera l'objet d'une discussion. Mots clefs : Plasticité cristalline, tenseur densité de dislocations, théorie du second gradient Références [1] V. de Rancourt, B. Appolaire, S. Forest, and K. Ammar. Homogenization of viscoplastic constitutive laws within a phase field approach.Références[1] V. de Rancourt, B. Appolaire, S. Forest, and K. Ammar. Homogenization of viscoplastic constitutivelaws within a phase field approach.Journal of the Mechanics and Physics of Solids, 88 :35–48, 2016.[2] K. Ammar, B. Appolaire, S. Forest, M. Cottura, Y. Le Bouar, and A. Finel. Modelling inheritance ofplastic deformation during migration of phase boundaries using a phase field method.Meccanica,49 :2699–2717, 2014.[3] K. Ammar, B. Appolaire, G. Cailletaud, and S. Forest. Phase field modeling of elasto-plastic defor-mation induced by diffusion controlled growth of a misfitting spherical precipitate.PhilosophicalMagazine Letters, 91 :164–172, 2011.[4] K. Ammar, B. Appolaire, G. Cailletaud, and S. Forest. Combining phase field approach and homo-genization methods for modelling phase transformation in elastoplastic media.European Journalof Computational Mechanics, 18 :485–523, 2009

Modeling of the Isothermal δ → α’ Martensitic Transformation in Pu-1 at.% Ga Alloys

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In-situ characterization of growth of isothermal ω phase in metastable β-Ti alloy TIMETAL LCB

Metastable β-Ti alloys exhibit various solid-solid phase transitions. Our study is focused on the characterization of the diffusion controlled β→ωiso phase transition. The particles of ω phase play an important part in thermomechanical treatment since they serve as heterogeneous nucleation sites for precipitation of finely dispersed particles of hexagonal α phase. The in-situ observation of the growth of particles of ω phase could be difficult by conventional techniques. However, it was shown recently that the ω phase significantly influences the elastic constants of the material, and the different forms of ω phase have different effects on the elastic anisotropy, as well as on the internal friction coefficients. Therefore, the β→ω phase transformation could be in-situ observed by the precise measurement of the tensor of elastic constants. In this contribution, we present the study of the kinetics of the β→ωiso phase transformation by resonant ultrasound spectroscopy. The polycrystalline samples of TIMETAL LCB alloy were in-situ examined by this technique during isothermal and non-isothermal ageing at temperatures up to 300 °C

Prediction of the kinetics of the phase transformations and the associated microstructure during continuous coolingin the Ti17

The aim of this paper is to present recent experimental results and related simulation about the $\beta$ → $\alpha$$_GB$ + $\alpha$$_WGB$ and → $\alpha$$_WI$ transformations which occur in the Ti17 alloy during the thermal treatments following the heating in the $\beta$ phase field. These phase transformations were experimentally studied under isothermal conditions in samples with negligible thermal gradients. The IT diagram was obtained, on the basis of electrical resistivity measurements and microstructural SEM observations. The kinetics of the phase transformation was further numerically simulated for continuous cooling on the basis of a formerly developed model giving the amount of each morphology ($\alpha$$_WGB$, $\alpha$$_WI$). Experimental and calculated results are compared