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Scientific Events

Scientific Events

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MPIE Colloquium

11436 1509365877

Insights into the Role of Mechanics on Diffusion-Controlled Phase Transformations using Phase Field Models

The role played by the microstructures ensuing from phase transformations on the mechanical properties is now very well documented and thoroughly studied, in particular in metallic alloys. Although there is also a large number of works devoted to the reverse, i.e. the influence of mechanics on the microstructure formation and evolution, a general picture is still lacking, in particular when the phase transformations are diffusion-controlled. Indeed, drawing such a general picture requires to address at the same time the issues related to both mechanical behavior and phase transformations, as well as to address new issues arising from the tight coupling between evolving interfaces and evolving strain/stress fields.Besides the well-known modification of two-phase thermodynamic equilibrium by elasticity, as explored by Larché and Cahn (e.g. [10]) and Voorhees and Johnson (e.g. [9]), the trends are less obvious concerning the morphological evolutions when the chemical and mechanical driving forces are competing to reduce the overall free energy of the materials.In this contribution, an attempt will be made to draw some trends by examining several situations in different types of alloys where the different contributions that mechanics encompasses are decoupled. For that purpose, we will resort to extensive calculations with phase field models that have been specifically developed [1,7].First we will discuss the role of elasticity on the shape selection of precipitates, beyond the classical results of hard precipitates in a soft matrix against soft precipitates in a hard matrix, that are relevant only for isotropic elasticity.Indeed, we will show how the anisotropy of the elastic energy arising from either the moduli or the eigenstrain is crucial for the shape selection, even for diffusion-controlled transformation at high temperatures where it is usually believed that elasticity is totally relaxed by plasticity. The examples supporting our analysis will concern cuboidal ordered precipitates in Ni-base superalloys [6] and acicular structures in alloys exhibiting allotropic transformation such as Ti alloys, steels or brass [3].In a second part, we will show that in many cases, plasticity does not relax totally the elastic strain associated with the phase transformations [4]. As a direct consequence, plasticity may not change qualitatively the shape evolutions driven by elasticity, as it will be illustrated on the rafting of the ordered precipitates in Ni-base superalloys [5] and on the acicular structures [4], although it can change the kinetics of the processes. However, we will show that in some cases, plasticity may induce shape bifurcations [5,8] that are difficult to infer with simplified qualitative arguments, as usually done in the literature on diffusion-controlled phase transformations.We will conclude with a few open questions that we have been able to identify thanks to our phase field calculations, such as the inheritance of plastic strain by the growing phases [2].[1] K. Ammar, B. Appolaire, G. Cailletaud, and S. Forest. Combining phase field approach and homogenization methods for modelling phase transformation in elastoplastic media. European Journal of Computational Mechanics, 18(5-6):485–523, 2009.[2] K. Ammar, B. Appolaire, S. Forest, M. Cottura, Y. Le Bouar, and A. Finel. Modelling inheritance of plastic deformation during migration of phase boundaries using a phase field method. Meccanica, 49:2699–2717, 2014.[3] M. Cottura, B. Appolaire, A. Finel, and Y. Le Bouar. Phase field study of acicular growth: Role of elasticity in Widmanstätten structure. Acta Materialia, 72:200–210, 2014.[4] M. Cottura, B. Appolaire, A. Finel, and Y. Le Bouar. Plastic relaxation during diffusion-controlled growth of Widmanstätten plates. Scripta Materialia, 108:117–121, 2015.[5] M. Cottura, B. Appolaire, A. Finel, and Y. Le Bouar. Coupling the phase field method for diffusive transformations with dislocation density-based crystal plasticity: Application to Ni-based superalloys. Journal of the Mechanics and Physics of Solids, 94:473–489, 2016.[6] M. Cottura, Y. Le Bouar, B. Appolaire, and A. Finel. Rôle of elastic inhomogeneity in the development of cuboidal microstructures in Ni-based superalloys. Acta Materialia, 94:15–25, 2015.[7] M. Cottura, Y. Le Bouar, A. Finel, B. Appolaire, K. Ammar, and S. Forest. A phase field model incorporating strain gradient viscoplasticity: Application to rafting in Ni-base superalloys. Journal of the Mechanics and Physics of Solids, 60:1243–1256, 2012.[8] V. de Rancourt, K. Ammar, B. Appolaire, and S. Forest. Homogenization of viscoplastic constitutive laws within a phase field approach. Journal of the Mechanics and Physics of Solids, 88:291–319, 2016.[9] W.C. Johnson and P.W. Voorhees. Interfacial stress, interfacial energy, and phase equilibria in binary alloys. Journal of Statistical Physics, 95(5-6):1281– 1309, 1999.[10] F. Larché and J.W. Cahn. Thermochemical equilibrium of multiphase solids under stress. Acta Metallurgica, 26(10):1579–1589, 1978. [more]

11332 1508915187

Application of Scientific Principles to Aluminium Automotive Sheet

Abstract Aluminium has been used in the manufacture of automobiles for more than 100 years and current usage averages more than 150kg per vehicle. Recent demands for higher fuel economy, improved vehicle performance, and lower CO2 emissions are currently driving a dramatic increase in the usage of specially designed aluminium alloys in the automotive industry. Aluminium flat-rolled sheet products are currently seeing wide-spread application for many components previously produced from steel. The technical requirements for aluminium sheet include high levels of formability, high strength, corrosion resistance, surface appearance, and long term reliability of joints. While these requirements are often in direct conflict, improved understanding of microstructure and surface has enabled the economical production of sheet that can meet the necessary customer demands. Three key developments in metallurgy and surface science that have made aluminium automotive sheet possible are reviewed: control of precipitate morphology for high strength, surface microstructure for bond durability, and crystallographic texture for surface appearance after forming. [more]

11334 1508916120

Shear bands in metallic glasses: what are they, how to find them?

The plastic deformation in metallic glasses proceeds through the activation and sliding of shear bands (SBs). A better plasticity in metallic glasses can be achieved through the enhancement of SB stability and proliferation. Therefore, efforts have been made to understand the true nature of SBs in metallic glasses. However, direct measurements on SBs are limited due to the small width of a shear band (few tenths of nanometers) and the lack of resolution at the atomic scale. In this context, atom probe tomography could bring some missing information about SBs.In the first part of the talk, I present the current state of knowledge on shear bands in metallic glasses. I give information concerning the commonly accepted formation, nature and location of shear bands. In the second part of the talk, I present my own results with Pd- and Pt-based bulk metallic glasses (BMGs) samples deformed by High-Pressure Torsion. HR-TEM and DSC measurements indicate some changes in the short-range order of the samples. The importance of pre-existing SB spacing on the mechanical response during nanoindentation measurements is also presented. The influence of residual stresses on SB proliferation around indenter imprint is shown. Finally, we show the possibility of a phase separation in amorphous Au-based metallic glass thin films and Zr-based BMGs. Atom probe tomography could also be used to confirm the presence of multiple amorphous phases. [more]

Diffusion and segregation of solutes in grain boundaries: from pure metals to high-entropy alloys

MPIE Colloquium

11145 1506515863

Phase-field Modeling of Polycrystalline Structures: From Needle Crystals to Spherulites Phase-field Modeling of Polycrystalline Structures: From Needle Crystals to Spherulites

Results in modeling complex polycrystalline structures by phase-field models that monitor the local crystallographic by scalar or vector orientation fields will be reviewed. The applied models incorporate homogeneous and heterogeneous nucleation of growth centers, and several mechanisms to form new grains at the perimeter of growing crystals, a phenomenon termed growth front nucleation. Examples for PF modeling of such complex polycrystalline structures are shown as impinging symmetric dendrites, polycrystalline growth forms (ranging from disordered dendrites to spherulitic patterns), and various eutectic structures, including spiraling two-phase dendrites. Simulations exploring possible control of solidification patterns in thin films via external fields, confined geometry, particle additives, scratching/piercing the films, etc. are also displayed. Advantages, problems, and possible solutions associated with quantitative PF simulations are discussed briefly. [more]

11333 1508915638

Variational Methods in Material Modeling: Applications of Hamilton’s Principle

The aim of modern material modeling is the realistic prediction of the behavior of materials and construction parts by numerical simulation. Experimental investigations prove that the microstructure and thus the mechanical properties may vary under loads. It is thus essential to describe the load-dependent microstructure in these cases by material models to close the system of fundamental physical equations. One elegant way for the derivation of such material models is given by the Hamilton principle which belongs to the class of variational, energy-based modeling strategies. The talk starts with fundamental investigations for modeling the simple harmonic oscillator. Afterwards, the presented modeling concept is generalized to the Hamilton principle which is also applicable to deformable solids with evolving microstructure. As first example for such materials, phase transformations in solids are modeled. The numerical results are compared to experimental observations and an industrially relevant application is presented. In the last part of the talk, the universal character of the Hamilton principle is demonstrated by solving the inverse problem of topology optimization. To this end, a growth approach as observed in biological processes is presented which computes component structures with minimal weight at maximum stiffness. [more]

International conference “Intermetallics 2017”

17707 1551253876

International conference “Intermetallics 2017”

 
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