French engineer and researcher Georges Cailletaud will be featured as part of the Innovation Lecture Series, sponsored by the Institute for Materials. Cailletaud’s presentation, “A multi-scale strategy for the modeling of directionally solidified ni-base superalloys,” will take place Oct. 19 at 11 a.m. at the Paper Tricentennial Building, Room 114.

**Abstract**

His present work is dedicated to the mechanical behavior of directionally solidified superalloys. This type of material is characterized by a columnar microstructure along a macroscopic axis, so that all the grains have a common <001> crystallographic direction, and a random secondary orientation. For the case of Ni-Base superalloys, each grain has a cubic symmetry, and the DS aggregate is orthotropic. The purpose of the lecture is to introduce a crystal plasticity approach, and to shed the light on two main topics: /1/ the development of a uniform field model, including the suitable scale transition rule; /2/ the investigation of the so called “oligogranular effect”: in real structures, such as aeronautical turbine blades, the grain size is not negligible if compared with component size, so that full field modeling may produce a large scatter that has to be characterized.

The uniform field model uses a classical phenomenological single crystal model that has been characterized in the past on several Ni-Base single crystalline superalloys [1]. It is valid for single crystal, but it is also valid to simulate the tensile response of a perfect DS material, in <001> crystallographic direction, the longitudinal direction of the columnar aggregate. For any other loading path, the stress and strain are no longer homogeneous in the grains, and a scale transition rule must be applied. The heterogeneity is modeled in the framework of “mean field” models, where a scale transition rule is used to estimate the local variables (stress and strain) as a function of the macroscopic stress and strain states and of the loading history. An extension of the classical “β rule” previously developed for isotropic materials is used [2]. It accounts for non-uniform elasticity and viscoplasticity in the grains. Each new crystallographic orientation g is attached a scale transition variable β^{g} in order to account for plastic accommodation. The parameters introduced to define the evolution of this variable are calibrated by means of Finite Element Crystal Plasticity (FECP) simulations of a Representative Volume Element (RVE) [3].

Oligo granular components open the question of the representativeness of a numerical model, which introduces a material homogenization. In fact, the estimation of the stress field obtained by a macroscopic model is framed by the estimates of the mean field model, which themselves are framed by the estimates of the full field (FECP) model. Numerical investigations are carried out in order to characterize the relations between the various values. The purpose of the final calibration is to be able to perform a “one shot” calculation to provide the engineer with the extreme values of the critical fields, to be used as input for the life prediction models.

**Bio-Sketch**

Georges Cailletaud was educated as a civil engineer in Ecole Centrale de Paris, a French ``Grande Ecole'', where he received a general background in engineering, and a specialty in civil engineering. He joined ONERA (the French Aerospace Lab) for his PhD, in Jean-Louis Chaboche's group, in connection with University of Paris 6 (Professor Jean Lemaitre). The topic of the thesis (1979) was the an isothermal behavior of a Nickel Base alloy. This work offered the opportunity to make a clear connection between metallurgical and mechanical approaches to characterize the mechanical response in presence of dissolution-precipitation phenomena. After his PhD, he worked as a research engineer at ONERA for five years, and he joined the Centre des Matériaux of MINES ParisTech in 1984 as an assistant professor. He got his tenure in 1987, after the defense of a thesis on micromechanical modeling of inelastic behavior of alloys (Professor Paul Germain, at Paris 6). He became full professor in mechanics of materials in 1993. He served as deputy director of Centre des Matériaux, in charge of the CNRS team (CNRS is the national scientific research center) between 2006 and 2012. He is now owner of the SAFRAN-MINES ParisTech chair «High Temperature Materials »

His main contributions deal with material modeling at macro-, meso- and microscale, the models being devoted to cyclic plasticity, non-isothermal loadings, precipitate hardening, phase transformation. A generic class of multipotential models has been developed for specific applications such as ratcheting modeling. Crystal plasticity models are used for single crystal modeling and for polycrystal applications. All these developments have been made possible thanks to the finite element code Z\'eBuLoN, an object oriented finite element code, developed at Centre des Matériaux and ONERA since 1984, with a material library that can be coupled with the main commercial codes.

Together with these research subjects, Georges Cailletaud has devoted a large part of his working time to teaching and to the development of numerical resources in the field of mechanics of materials (see for instance http://mms2.ensmp.fr/emms_paris/mms_Paris.php). He is the co-author of one handbook on Mechanics of Materials, in French, translated in English (Springer) and Russian.

**References **[1] L. Méric, G. Cailletaud, *Single crystal modeling for structural calculations*, JEMT **113**:162-182, 1991 [2]G. Cailletaud and P. Pilvin. *Utilisation de modèles polycristallins pour le calcul par éléments fi*