Moono Rhee

On plastic deformation and the dynamics of 3D dislocations

Abstract A three-dimensional (3D) mesoscopic model to simulate the collective dynamic behavior of a large number of curved dislocations of finite lengths has been developed for the purpose of analyzing deformation patterns and instabilities, including the formation of dislocation cell structures. Each curved dislocation is approximated by a piecewise continuous array of straight line segments. The interactions among the segments, including line-tension and self-interactions, are treated explicitly. For longer-range interactions, the space is divided into a regular cellular array and the elastic fields of the dislocations in a remote cell approximated by a multipolar expansion, leading to an order N algorithm for the description of a cell containing N dislocations. For large arrays, the simulation volume is divided into cubical cells. A discrete random starting array is selected for the master cell and its nearest neighbors, which constitute an order 2 cell. Reflection boundary conditions are imposed for near-neighbor order 2 cells and so forth, creating an NaCl-type lattice array. The boundaries between the cells are considered to be relaxed grain boundaries. That is, recovery within the boundaries and rotation across them are considered to occur so that the boundaries have no associated elastic fields. This cell hierarchy, coupled with the multipole expansion, is suitable for the use of massively parallel computation, with individual cells assigned to separate processors.

3D dislocation dynamics : Stress-strain behavior and hardening mechanisms in fcc and bcc metals

A dislocation dynamics (DD) model for plastic deformation, connecting the macroscopic mechanical properties to basic physical laws governing dislocation mobility and related interaction mechanisms, has been under development. In this model there is a set of critical reactions that determine the overall results of the simulations, such as the stress-strain curve. These reactions are, annihilation, formation of jogs, junctions, and dipoles, and cross-slip. In this paper we discuss these reactions and the manner in which they influence the simulated stress- strain behavior in fcc and bcc metals. In particular, we examine the formation (zipping) and strength of dipoles and junctions, and effect of jogs, using the dislocation dynamics model. We show that the strengths (unzipping) of these reactions for various configurations can be determined by direct evaluation of the elastic interactions. Next, we investigate the phenomenon of hardening in metals subjected to cascade damage dislocations. The microstructure investigated consists of small dislocation loops decorating the mobile dislocations. Preliminary results reveal that these loops act as hardening agents, trapping the dislocations and resulting in increased hardening.

A superdislocation model for the strengthening of metal matrix composites and the initiation and propagation of shear bands

Abstract Strengthening in metallic alloys resulting from dislocation-particle interaction is investigated in connection with the initiation and propagation of shear bands. A dislocation model is presented in this work to explain these phenomena. It consists of a discontinuous tilt wall initially containing N infinite straight dislocations. The wall interacts with rigid particles and bows out between them as these particles act as pinning points. At a critical stress, the bow-out becomes unstable and its front propagates to form a shear band. An analytical solution is formulated for the increase in the elastic strain energy as the tilt wall bows out between the two rigid particles. The bow-out configuration is approximated by a finite number of straight line segments. The critical state at the onset of instability is obtained by minimizing the free energy, leading to an estimate for the flow stress and its dependence on particle spacing. The model is in good agreement with experimental data found in the literature.

Dislocation stress fields for dynamic codes using anisotropic elasticity: methodology and analysis

Abstract A numerical methodology to incorporate anisotropic elasticity into three-dimensional dislocation dynamics codes has been developed, employing theorems derived by Lothe [J. Lothe, Philos. Mag. 15 (1967) 353], Brown [L.M. Brown, Philos. Mag. 15 (1967) 363], Indenbom and Orlov [V.L. Indenbom, S.S. Orlov, Sov. Phys. Crystallogr. 12 (6) (1968) 849], and Asaro and Bamett [R.J. Asaro, D.M. Barnett, in: R.J. Arsenault, J.R. Beeler Jr., J.A. Simmons (Eds.), Computer Simulation for Materials Applications, Part 2. Nuclear Metallurgy, Vol. 20, p. 313]. The formalism is based on the stress field solution for a straight dislocation segment of arbitrary orientation in three-dimensional space. The general solution is given in a complicated closed integral form. To reduce the computation complexity, look-up tables are used to avoid heavy computations for the evaluation of the angular stress factor ( Σ ij ) and its first derivative term ( Σ ij ′). The computation methodology and error analysis are discussed in comparison with known closed form solutions for isotropic elasticity. For the case of Mo single crystals, we show that the difference between anisotropic and isotropic elastic stress fields can be, for some components of the stress tensor, as high as 15% close to the dislocation line, and decrease significantly away from it. This suggests that short-range interactions should be evaluated based on anisotropic elasticity, while long-range interactions can be approximated using long-range elasticity.

Stability of dislocation short-range reactions in BCC crystals

The stability of short-range reactions two dislocations of parallel line vectors which guide on two parallel slip planes in BCC crystals is determined. The two dislocations are assumed to be infinitely long, and their interaction is treated as elastic. The interaction and self-energies are both computed for dynamically moving dislocations, where the dependence on dislocation velocity is taken into account. The stability of the reaction is determined as a function of the following phase space variables: relative angle, relative speed, dislocation mobility, Burgers vector, separation of slip planes, and external force. The results indicate that the dynamic formation of dislocation dipoles or tilt wall embryos occurs only over a small range of the investigated phase space. Inertial effects are shown to be important at close separation, because of the large force between the two dislocations comprising the dipole or tilt wall embryo. The authors find that destabilization of the dislocation dipoles or tilt wall embryos is enhanced by externally applied stresses or by stress fields of neighboring dislocations.

On the bowed out tilt wall model of flow stress and size effects in metal matrix composites

A model of bowed-out tilt-wall array has been recently proposed by the authors to provide a correlation between the flow stress and particle size/spacing of metal matrix composites. Here, the authors elaborate on the tilt-wall model and show that the number of dislocations needed to predict the experimental result, for aluminum alloys reinforced with alumina or TiB[sub 2] particulates, is not affected by the dislocation spacing for realistic pile-ups with 2 < d/[bar d] < 7, where [bar d] is the spacing between two adjacent slip planes. The model is also used to explain new experimental results for an Al-Si alloy with Si particles of different sizes.

Calculation of the Slip System Activity in Deformed Zinc Single Crystals Using Digital 3-D Image Correlation Data

A 3-D image correlation system, which measures the full-field displacements in three dimensions, has been used to experimentally determine the full deformation gradient matrix for two zinc single crystals. Based on the image correlation data, slip system activity for the two crystals has been calculated. The results of the calculation show that, for one crystal, only the primary slip system is active, which is consistent with traditional theory. The other crystal, however, shows appreciable deformation on slip systems other than the primary. An analysis was conducted verifying the experimental observation that the net result from slip on the secondary slip systems is approximately one third the magnitude and directly orthogonal to the primary system.

Dislocation multiplication in bcc molybdenum: A dislocation dynamics simulation

Plastic deformation of Mo single crystals is examined by direct simulation of dislocation dynamics under stress. Initial dislocation populations are made to mimic real dislocation microstructures observed in transmission electron microscopy cross-sections of pure annealed Mo single crystals. No a priori sources for dislocation multiplication are introduced, and yet multiplication takes place through a sequence involving aggregation of grown-in superjogs, bowing of screw dislocation segments and fast lateral motion of edge segments, producing a large number of elongated loops and a characteristic cross-grid pattern of screw dislocations.

A 3D DISLOCATION SIMULATION MODEL FOR PLASTIC DEFORMATION AND INSTABILITIES IN SINGLE CRYSTALS

An account of recent progress in a 3D dislocation simulation model for plastic deformation and instabilities in single crystals is given. 1. Extended Summary Discrete dislocation dynamics models (see, for example, Kubin and coworkers, 1992, 1993; Hirth et al„ 1996; Zbib et al., 1996-7; Schwarz and Tersoff, 1996) have the potential of rigorously describing the complex relationship between the macroscopic mechanical properties of materials and the underlying dislocation structures. There is a rich body of literature that deals with this subject, providing numerous experimental results about various dislocation phenomena, such as slip bands, shear bands, and persistent slip bands, etc. As in many physical problems involving the interaction of a large number of particles, the main difficulty in explaining the formation of dislocation structures lies in understanding the collective dynamical behavior of a large group of dislocations. The dynamics of dislocations can be viewed as a nonlinear system that may exhibit dynamical instabilities leading to self-organization and the spontaneous formation of structures (see, e.g., the work of Walgreaf and Aifantis, 1985). In this paper we briefly outline the main features of a 3D dislocation dynamics model that has been developed recently by the authors for modeling deformation in bcc and fee materials. The fundamental kinetics of dislocation mobility by kink formation, and activation of cross slip using Monte Carlo simulation are incorporated into the model. The model is used to investigate various fundamental mechanisms, including, production of dislocations by Frank-Read sources, hardening effects by the formation of jogs and junction, strengthening in metal-matrix composites by dislocation pinning, and the stress-strain behavior under uniaxial loading conditions. We consider a random distribution of dislocation loops and curves of arbitrary shapes and lying on crystallographic planes. For bcc single crystals the {110}<111> and {112}<111> are the most closed packed slip systems and both are active at low temperatures. Each plane contains a number of dislocation curves whose configurations are approximated by a set of straight segments of mixed characters as shown in Figure 1.

3D dislocation dynamics: stress-strain behavior and hardening mechanisms in FCC and BCC metals

A dislocation dynamics (DD) model for plastic deformation, connecting the macroscopic mechanical properties to basic physical laws governing dislocation mobility and related interaction mechanisms, has been under development. In this model there is a set of critical reactions that determine the overall results of the simulations, such as the stress-strain curve. These reactions are, annihilation, formation of jogs, junctions, and dipoles, and cross-slip. In this paper we discuss these reactions and the manner in which they influence the simulated stress- strain behavior in fcc and bcc metals. In particular, we examine the formation (zipping) and strength of dipoles and junctions, and effect of jogs, using the dislocation dynamics model. We show that the strengths (unzipping) of these reactions for various configurations can be determined by direct evaluation of the elastic interactions. Next, we investigate the phenomenon of hardening in metals subjected to cascade damage dislocations. The microstructure investigated consists of small dislocation loops decorating the mobile dislocations. Preliminary results reveal that these loops act as hardening agents, trapping the dislocations and resulting in increased hardening.