## Mesoscopic framework for modeling physical processes in multiphase materials with defects | ||

Source of funding: Marie-Curie International Reintegration grant (FP7-PEOPLE-RG-2009)Number: 207745 ("MesoPhysDef")Duration of funding: 4 years (12/2009-11/2013) |

Mesoscopic description of physical processes in structural materials is one of the most challenging aspects of understanding their behavior as it is the regime where atomic length scales merge with those of the continuum. It is the least understood regime compared to the atomic and continuum scales because the simplifications and advantages of theory in handling small/large length scales and fast/slow time scales no longer apply. One of the most challenging problems that has not been solved to date is how correlated defect domains affect the microstructure on the mesoscale and thus also the physical properties of materials. This problem will be solved by combining the classical Landau theory of phase transitions with the seminal 1958 work of Kröner in which dislocations are viewed as sources of incompatibility of elastic strains. The coupling of the microstructure with the incompatibility of strains will give rise to a new framework for the study of such mesoscale phenomena. In this formalism point defects will reduce to a simpler case as their fields are irrotational and thus do not contribute to the incompatibility of strains. The mesoscopic framework that will be developed in this project will contribute significantly to bridging of the so-called micron gap in the description of physical processes in crystalline materials. The role of defects, interfaces and microstructure is at the heart of understanding materials from nanometers to microns and the unique approach proposed here will address this issue. Implementing this theory will yield a mesoscopic computational tool for solving the inverse problem - designing novel materials with prescribed properties, such as resistance to fatigue and radiation damage.

## Calculation of the Peierls barrier of screw dislocations in bcc metals and its dependence on stress | |

Source of funding: Czech Science FoundationNumber: P204/10/0255Duration of funding: 3 years (01/2010-12/2012) |

Plastic deformation of bcc metals is governed by motion of 1/2<111> screw dislocations that possess a high lattice fiction (Peierls) stress. At finite temperatures and strain rates, the dislocation moves by overcoming the Peierls barrier that is a crucial ingredient of thermodynamic description of the dislocation glide. However, atomistic simulations provide only the maximum slope of the Peierls barrier and, therefore, its shape is generally unknown. In this project, we will develop a novel computational method that utilizes the Nudged Elastic Band method to calculate the entire shape of the Peierls barrier and its variation under stress. The interactions between atoms are described by the state-of-the-art Bond Order Potentials that capture the mixed metallic and covalent character of bonds in bcc transition metals. The main advantage of our model, that distinguishes it from other methods, is that we calculate directly the position of the dislocation in the perpendicular {111} plane. This allows for both a self-consistent use of boundary conditions along the transition path of the dislocation and an unambiguous identification of the positions of the dislocation. This work forms a basis for the development of physically justified macroscopic flow criteria for bcc metals.

## Thermodynamics and phase transformations in plutonium and its alloys

*funded by the Seaborg Institute (Los Alamos National Laboratory)*

At ambient pressures, plutonium (Pu) forms six stable allotropes whose structures range from the highly symmetric, high-temperature fcc (δ) phase to one of the low-symmetric monoclinic (α) structures that is stable below about 400 K. The underlying physics responsible for the phase transformations between individual phases is largely controversial. The main goal of this project is to utilize the chain of states calculations within the Nudged Elastic Band (NEB) method coupled with the semiempirical Modified Embedded Atom Method (MEAM) potential for Pu to elucidate the mechanism of structural phase transformations in elemental Pu and its dilute alloys. The current calculations aim to determine the energy barriers for α→β, β→γ, γ→δ and δ→ε phase transformations that are required for reliable formulation of the activation enthalpies and the free energy functional of Pu. The calculations of the energy barriers for α→β with the β structure containing both 32 and 34 atoms and the subsequent comparison of the calculated photoemission spectra with experimental measurements will shed new light on the still controversial structure of the β phase. Moreover, Lookman et al. have recently proposed a phonon mechanism for α(α')→δ phase transformation in Pu that is based purely on symmetry relations (group-subgroup) and which predicts existence of an intermediate trigonal (#166, R-3m) and simple hexagonal (#191, P6mm) phases. The emergence of these intermediate structures and thus the validity of this model can be checked by examining the calculated transformation pathway between the α' and δ phases. The same method will be utilized to investigate the influence of alloying on the transformation pathway and shape of the energy barrier between the α(α') and δ phases.

## Landau-Ginzburg theory of structural phase transformations incorporating plasticity

*with T.Lookman and A.Saxena (Los Alamos National Laboratory)*

In recent years, Landau-Ginzburg theory of square (austenite) to rectangle (martensite) martensitic phase transformation has been shown to successfully reproduce the evolution of elastic texture in shape memory alloys such as FePd and NiTi. Currently, this theory only applies to defect-free crystals and, therefore, is not directly extendable to real materials in which the martensitic phase transformations are often accompanied by large plastic deformations caused by motion of defects, particularly dislocations. This is especially important in shape memory materials such as U6Nb that display significant strain hardening in the martensitic phase. In order to incorporate plasticity into the Landau-Ginzburg theory of structural phase transformations, I revisited the Saint Venant derivation of the elastic compatibility constraint. In the presence of defects, this changes to an incompatibility constraint, where the degree of incompatibility between the three components of the strain tensor is shown to be proportional to the gradients of a scalar dislocation density field that is expressed using the Nye tensor. I have shown that the presence of defects induces large internal stresses in certain regions of the material and these act as nucleation sites for plastic deformation. When the external loading is applied, dislocations moving from these sites cause strain hardening that is detectable in experimental uniaxial measurements. A simple rate-independent incremental theory of plasticity as formulated by Prandtl and Reuss is utilized to calculate the increments of the plastic strain as a function of the applied load. This simple model serves as a starting point for the development of fully three-dimensional, strain-rate dependent Landau-Ginzburg theory of plasticity for martensitic phase transformations. This framework will be used not only to explain the stress-driven (pseudoelastic) phase transformations in the already known shape memory alloys but also to stimulate an experiment-free search for new shape memory materials.

## Multiscale modeling of plastic flow of bcc metals based on single-dislocation atomistic studies

*with V.Vitek and J.Bassani (University of Pennsylvania)*

Plastic flow of all bcc metals is controlled by the glide of 1/2<111> screw dislocations since they possess non-planar cores and thus experience high Peierls stress. Atomistic studies at 0 K determine the Peierls stress and reveal that it is strongly dependent on non-glide stresses, i.e. components of the stress tensor other than the shear stress in the slip plane parallel to the Burgers vector. At finite temperatures the corresponding Peierls barrier is surmounted via the formation of pairs of kinks. Theoretical description of this thermally activated process requires knowledge of not only the height and shape of the barrier but also its intrinsic dependence on the applied stress tensor. This information is not obtainable from any experimental data and the atomistic studies at 0 K determine the Peierls stress but not the shape of the Peierls barrier. In this project we study how the shape of the Peierls barrier and its dependence on the applied loading can be extracted from the data obtained in atomistic studies at 0 K. We consider the Peierls barrier as a two-dimensional periodic function of the position of the intersection of the dislocation line with the perpendicular {111} plane, with adjustable terms dependent on the shear stresses parallel and perpendicular to the slip direction. The functional forms of these terms are based on the effective yield criterion recently developed on the basis of atomistic modeling of the glide of screw dislocations at 0 K. The minimum energy path between two potential minima, and thus the corresponding activation barrier, is obtained using the Nudged Elastic Band method. The constructed Peierls barrier reproduces correctly both the well-known twinning-antitwinning asymmetry observed for pure shear parallel to the slip direction and the effect of shear stresses perpendicular to the slip direction. This advancement introduces for the first time the effect of both shear stresses parallel and perpendicular to the slip direction into the model of thermally activated dislocation motion. Based on this model we formulate a general yield criterion that includes not only the full stress tensor but also effects of temperature and strain rate. This approach forms a basis for multislip yield criteria and flow relations for continuum analyses in both single and polycrystals the results of which can be compared with experimental observations.