Dr. Ricardo A. Lebensohn






1) Second-order homogenization of viscoplastic polycrystals: The computation of large-strain mechanical behavior and texture evolution of viscoplastic (VP) polycrystals using self-consistent (SC) models is nowadays a standard approach in the materials science community. For this, several classical SC approximations for non-linear materials are available (e.g. the "secant", "tangent" and "affine" formulations), all of them based on linearization schemes at the local level that use information on mechanical field averages only, disregarding higher-order statistical information (i.e. average field fluctuations) in the grains. However, the above assumption may be questionable for single-phase aggregates of highly anisotropic grains or for two-phase polycrystals, where a strong directionality and large variations in local properties are to be expected. The non-dependence with higher-order statistical moments is particularly critical for the treatment of those highly-contrasted materials, since such information is essential to capture (in an average sense) the effect of the strong deformation gradients that are likely to develop inside grains which are highly anisotropic, or adjacent to another phase. Therefore, in order to overcome the above limitations we have implemented inside the code VPSC [1] a rigorous non-linear homogenization scheme [2] that takes into account information on the average field fluctuations at grain level [3].


2) Homogenization of the dilatational viscoplastic behavior of anisotropic porous polycrystals: The originally incompressible VPSC formulation [4] has been recently extended to deal with porous polycrystals taking into account: a) the dilatational deformation associated with void growth [5], and b) second-order statistical information in terms of average field fluctuations inside the constituent grains. Such extended model allows us to account for porosity evolution in voided polycrystals, while preserving the anisotropy and rate sensitivity capabilities of the VPSC formulation. This extended VPSC model has been applied to address the problem of coupling between texture, plastic anisotropy, void shape, triaxiality, rate sensitivity and porosity evolution [6,7].


3) Simulation of forming of anisotropic materials by direct coupling between SC polycrystal models and Finite Element (FE) codes: Simulating the forming of anisotropic materials, such as zirconium, requires a description of the anisotropy of the aggregate and the single crystal, and also of its evolution with deformation (due to texture development and hardening by slip and twinning). As a consequence, using polycrystal constitutive laws inside FE codes represents a considerable improvement over using empirical constitutive laws, since the former provides a physically-based description of anisotropy and its evolution. We have developed a polycrystal constitutive description for pure clock-rolled Zr deforming under quasi-static conditions at room and liquid nitrogen temperatures, using tensile and compressive experimental data to adjust the constitutive parameters of a SC polycrystal model [8]. This model was in turn implemented in an explicit FE code, assuming a full polycrystal at the position of each integration point. This methodology was successfully applied to simulate the inhomogeneous three-dimensional deformation of zirconium bars deforming under four-point bend conditions.


4) Macroscopic anisotropic yield functions and FE analysis to account for the effect of twinning on anisotropy and work-hardening: We have recently combined physically-based and experimentally-adjusted models for description of the twinning process and the interaction between twinning and slip systems in zirconium [8] and a macroscopic yield criterion that accounts for the effect of twinning on yielding [9] under quasiestatic (elastoplastic) [10] and dynamic (elasto-viscoplastic) [11] loading conditions, using a multiscale methodology based on: texture measurements, uniaxial mechanical tests, SC polycrystal models, interpolation techniques at macroscopic level, and FE analysis. We are also in the process of applying the above methodology to titanium [12].


5) Full-field formulation based on Fast Fourier Transforms for the calculation of the micromechanical behavior of plastically deformed 3-D polycrystals: This formulation (originally developed as a fast algorithm to compute the linear and nonlinear response of composites using as input a digital image of their microstructures [13]) has been adapted by us to treat  3-D polycrystals deforming by dislocation glide [14]. The FFT-based model provides an exact solution of the governing equations, has better performance than a Finite Element calculation for the same purpose and resolution, and can use voxelized microstructure data as direct input. Among the applications of this formulation we can mention: a) validation of predictions of statistical models on effective properties, field fluctuations, global and local texture evolution and hardening in plastically deformed cubic and hexagonal materials (e.g. [15,16]); b) direct comparison with intragranular orientation maps and micromechanical fields measured by imaging techniques (OIM, DIC, etc) in plastically deformed Cu polycrystals [17]; c) study of the effect of microstructure on strain localization [18]; d) prediction of subgrain structure formation, GND densities and implementation of length-scale-sensitive hardening laws [19].


6) Other projects:

a) Simulation of texture development and grain refinement during equal channel angular extrusion (ECAE) of fcc materials [20].

b) Prediction of intracrystalline fields in deformed ice and its implications in the deformation-recrystallization behavior of polar ice sheets [21].

c) Second-order micromechanical modeling of rocks of the Earth's interior and implementation of a multiscale simulation of the regional upper mantle flow beneath a mid-ocean ridge [22].

d) In the context of an European project [23], we'll soon begin the interface of the FFT-based approach and the Elle platform [24]. Elle is a code for the simulation of micro-process coupling in geological materials via an iterative modification of the microstructure by a whole range of processes (grain boundary migration, diffusion, sub-grain evolution). The Elle and FFT-based approaches share a similar numerical structure and the incorporation of the latter in Elle will provide a fully anisotropic crystal plasticity capability, an essential feature to model plastic deformation and its interaction with other micro-process of low-symmetry geological materials.

e) SC modeling of semi-crystalline polymers for the study their constitutive behavior, texture and morphology evolution during large plastic deformation [25].

f) Micromechanical study the role played by dislocation glide and grain boundary accommodation in the determination of the plastic behavior of nanostructured materials [26].

g) Based on a recent mesoscale description of martensitic materials [27] using a relaxation technique by coarse-graining over a martensitic microstructure and Fast Fourier Transforms, we have proposed a theoretical, numerical and experimental study to understand the interplay between the slip and transformation-induced deformation in Ni-Ti shape-memory alloys [28].

h) In the context of the Generation IV Reactor Materials Working Group of the Advanced Fuel Cycle Initiative (AFCI) Program, we are involved in the development of improved models for the creep response of irradiated structural materials by incorporating irradiation hardening in polycrystal models of austenitic and ferritic-martensitic steels [29].



[1] The code VPSC (developed and maintained by R.A. Lebensohn and C.N Tome) is a multipurpose polycrystal plasticity research code, based on the knowledge of the mechanisms of slip and twinning that are active in single crystals of arbitrary symmetry. VPSC can be used to predict the effective stress-strain response, texture evolution, anisotropy, etc., and it is presently used as a predictive tool for metallic and geological material systems, for parameter identification, interpretation of experimental results and multiscale calculations, in academic and industrial applications, etc., by numerous research groups worldwide (at present, the VPSC code distribution list has more than registered 80 users).

[2] P. Ponte Castaneda: "Second-order homogenization estimates for nonlinear composites incorporating field fluctuations. I. Theory". J. Mech. Phys. Solids 50, 737, 2002.

[3] R.A. Lebensohn, C.N. Tome and P. Ponte Castaneda: "Improving the self-consistent predictions of texture development of polycyrystals incorporating intragranular field fluctuations". Materials Science Forum, 495-497, 955, 2005.

[4] R.A. Lebensohn and C.N. Tome: "A selfconsistent approach for the simulation of plastic deformation and texture development of polycrystals: application to zirconium alloys" Acta Mater 41, 2611, 1993.

[5] R.A. Lebensohn, C.N Tome and P.J. Maudlin: "A selfconsistent formulation for the prediction of the anisotropic behavior of viscoplastic polycrystals with voids". J Mech. Phys. Solids 52, 249, 2004.

[6] R.A. Lebensohn: "Anisotropic modelling of the plastic deformation of damaged polycrystalline materials". TCG-I Meeting, Dahlgren, USA, March 2006.

[7] R.A. Lebensohn, C.N. Tome and P. Ponte Castaneda, in preparation.

[8] C.N. Tome, P.J. Maudlin, R.A. Lebensohn and G.C. Kaschner: "Mechanical response of zirconium. Part I: Derivation of a polycrystal constitutive law and finite element analysis". Acta Mater. 49, 3085, 2001.

[9] O. Cazacu, B. Plunkett, F. Barlat: "Orthotropic yield criterion for hexagonal closed packed metals". Int. J. Plasticity 22, 1171, 2006.

[10] B. Plunkett, R.A. Lebensohn, O. Cazacu and F. Barlat: "Evolving yield function of hexagonal materials taking into account texture development and anisotropic hardening". Acta Mater 54, 4159, 2006.

[11] B. Plunkett, O. Cazacu, R.A. Lebensohn, and F. Barlat: "Strain-rate effects on the texture evolution of high-symmetry and low-symmetry metals: modeling and validation using the Taylor cylinder impact test". Int. J. Plasticity, accepted.

[12] R.A. Lebensohn (PI) et al.: "Characterization of hcp Materials". LANL's WFO Program, sponsored by Eglin Air Force Research Laboratory, 2005-2007.

[13] H. Moulinec and P. Suquet: "A fast numerical method for computing the linear and nonlinear properties of composites". C.R. Acad. Sci. Paris II 318, 1417, 1994.

[14] R.A. Lebensohn: "N-site modelling of a 3D viscoplastic polycrystal using Fast Fourier Transform". Acta Mater. 49, 2723, 2001.

[15] R.A. Lebensohn, Y. Liu and P. Ponte Castaneda: "On the accuracy of the self-consistent approximation for polycrystals: comparison with full-field numerical simulations". Acta Mater. 52, 5347, 2004.

[16] O. Castelnau, R. Brenner and R.A. Lebensohn: "The effect of strain heterogeneity on the work-hardening of polycrystals predicted by mean-field approaches". Acta Mater. 54, 2745, 2006.

[17] R.A. Lebensohn, O. Castelnau, R. Brenner: "Full-field modelling and experimental validation of subgrain texture and microstrucure evolution of polycrystalline copper". 9th Int. Conf. on Numerical Method in Industrial Forming Process (NUMIFORM 2007), Porto, Portugal, June 2007.

[18] A. Rollett, S. Lee, S. Sintay, R.A. Lebensohn: "Exploration of the effect of polycrystal microstructure on strain localization with a Fourier Transform viscoplastic model". 2007 TMS Annual Meeting & Exhibition, Orlando, USA, February 2007.

[19] R.A. Lebensohn: "A formulation based on Fast Fourier Transforms for the calculation of the micromechanical behavior of plastically deformed 3-D polycrystals". 3rd International Conference on Multiscale Materials Modeling, Freiburg, Germany, September 2006.

[20] I.J. Beyerlein, R.A. Lebensohn and C.N. Tome: "Modeling of texture and microstructural evolution in the equal channel angular process". Mat. Sci. Eng. A 345, 122, 2003.

[21] R.A. Lebensohn, M. Montagnat and P. Duval: "Modeling the viscoplastic behavior and calculation of intracrystalline fields in columnar ice polycrystals", in preparation.

[22] O. Castelnau, D. Blackman, R.A. Lebensohn: "Modelisation micromecanique des roches du manteau terrestre: Influence sur l'ecoulement regional sous une dorsale oceanique". Demande de mise a disposition, Olivier Castelnau, CNRS, 2006-2007.

[23] S. Piazolo (PI) et al.: "Subgrain structure development in rocks and metals". 2006-2008 Collaborative Research Project, EUROCORES Programme, European Science Foundation.

[24] M.W. Jessell, P.D Bons, L. Evans., T. Barr and K. Stuwe: "Elle: a micro-process approach to the simulation of microstructures". Computers and Geosciences 27, 17, 2001.

[25] S. Nikolov, R.A. Lebensohn and D. Raabe: "Self consistent modeling of large plastic deformation, texture and morphology evolution in semi-crystalline polymers". J. Mech. Phys. Solids 54, 1350, 2006.

[26] R.A. Lebensohn, E.M Bringa and A. Caro: "A viscoplastic micromechanical model for the yield strength of nanocrystalline materials", Acta Mater, in press.

[27] K. Bhattacharya and P. Suquet: "A model problem concerning recoverable strains of shape-memory polycrystals". Proc. Royal Soc. London A 461, 2797, 2005.

[28] K. Bhattacharya (PI), R. Lebensohn and G. Ravichandran: "Interplay between slip and transformation induced deformation in polycrystalline solids". US Department of Energy, Basic Energy Sciences (BES) proposal, 2006.

[29] C. Deo, C.N. Tome, R.A. Lebensohn and S. Maloy: "Modeling and simulation of irradiation hardening in structural ferritic steels for advanced nuclear reactors". Journal of Nuclear Materials, submitted.