Physics-based void nucleation model using discrete dislocation dynamics and cluster dynamics models

Focusing on cavity nucleation, continuum damage mechanics models rely on a posteriori calibration of initial site density and loading conditions. However, empirically calibrated parameters are unreliable due to accelerated testing conditions and cannot be transferred to novel materials. To provide a more accurate description of the relationship between temperature, stress, microstructure, and the kinetics of void nucleation, we develop a physically-based nucleation model by coupling discrete dislocation dynamics (DDD) and cluster dynamics (CD) models. First, a continuum statistical approach developed for this study is shown, demonstrating the ability to model vacancies cluster size evolution as a function of time. Second, the implementation of the DDD method in the study of local energetics within a microstructure is presented. DDD has the capability to accurately model complex dislocation networks permitting a high-fidelity account of the local energy landscape arising from defect-defect interactions. Lastly, multiple potential nucleation sites in bulk are examined for nucleation. Our results are consistent with experimental observations indicating that nucleation is highly improbable in bulk

Accelerated computational micromechanics

We present an approach to solving problems in micromechanics that is amenable to massively parallel calculations through the use of graphical processing units and other accelerators. The problems lead to nonlinear differential equations that are typically second order in space and first order in time. This combination of nonlinearity and nonlocality makes such problems difficult to solve in parallel. However, this combination is a result of collapsing nonlocal, but linear and universal physical laws (kinematic compatibility, balance laws), and nonlinear but local constitutive relations. We propose an operator-splitting scheme inspired by this structure. The governing equations are formulated as (incremental) variational problems, the differential constraints like compatibility are introduced using an augmented Lagrangian, and the resulting incremental variational principle is solved by the alternating direction method of multipliers. The resulting algorithm has a natural connection to physical principles, and also enables massively parallel implementation on structured grids. We present this method and use it to study two examples. The first concerns the long wavelength instability of finite elasticity, and allows us to verify the approach against previous numerical simulations. We also use this example to study convergence and parallel performance. The second example concerns microstructure evolution in liquid crystal elastomers and provides new insights into some counter-intuitive properties of these materials. We use this example to validate the model and the approach against experimental observations

A fast Fourier transform-based mesoscale field dislocation mechanics study of grain size effects and reversible plasticity in polycrystals

International audienceA numerical implementation of a non-local polycrystal plasticity theory based on a mesoscale version of the field dislocation mechanics theory (MFDM) of Acharya and Roy (2006) is presented using small-strain elasto-viscoplastic fast Fourier transform-based (EVPFFT) algorithm developed by Lebensohn et al. (2012). In addition to considering plastic flow and hardening only due to SSDs (statistically stored dis-locations) as in the classic EVPFFT framework, the proposed method accounts for the evolution of GND (geometrically necessary dislocations) densities solving a hyperbolic-type partial differential equation, and GND effects on both plastic flow and hardening. This allows consideration of an enhanced strain-hardening law that includes the effect of the GND density tensor. The numerical implementation of a reduced version of the MFDM is presented in the framework of the FFT-based augmented Lagrangian procedure of Michel et al. (2001). A Finite Differences scheme combined with discrete Fourier transforms is applied to solve both incompatibility and equilibrium equations. The numerical procedure named MFDM-EVPFFT is used to perform full field simulations of polycrystal plasticity considering different grain sizes and their mechanical responses during monotonic tensile and reversible tension-compression tests. Using Voronoi tessellation and periodic boundary conditions , voxelized representative volume elements (RVEs) with different grain sizes are generated. With MFDM-EVPFFT, a Hall-Petch type scaling law is obtained in contrast with the conventional crystal plasticity EVPFFT. In the case of reversible plasticity, a stronger Bauschinger effect is observed with the MFDM-EVPFFT approach in comparison with conventional EVPFFT. The origin of these differences is analyzed in terms of heterogeneity, GND density and stress evolutions during the compression stage

A FFT-based numerical implementation of mesoscale field dislocation mechanics: Application to two-phase laminates

International audienceIn this paper, we present an enhanced crystal plasticity elasto-viscoplastic fast Fourier transform (EVPFFT) formulation coupled with a phenomenological Mesoscale Field Dislocation Mechanics (MFDM) theory here named MFDM-EVPFFT formulation. In contrast with classic CP-EVPFFT, the model is able to tackle plastic flow and hardening due to polar dislocation density distributions or geometrically necessary dislocations (GNDs) in addition to statistically stored dislocations (SSDs). The model also considers GND mobility through a GND density evolution law numerically solved with a recently developed filtered spectral approach, which is here coupled with stress equilibrium. The discrete Fourier transform method combined with finite differences is applied to solve both lattice incompatibility and Lippmann-Schwinger equations in an augmented Lagrangian numerical scheme. Numerical results are presented for two-phase laminate composites with plastic channels and elastic second phase. It is shown that both GND densities and slip constraint at phase boundaries influence the overall and local hardening behavior. In contrast with the CP-EVPFFT formulation, a channel size effect is predicted on the shear flow stress with the present MFDM-EVPFFT formulation. The size effect originates from the progressive formation of continuous screw GND pileups from phase boundaries to the channel center. The effect of GND mean free path on local and global responses is also examined for the two-phase composite

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Department of Mechanical EngineeringMacroscopic plastic deformation is an irreversible consequence proceeded by the motion of dislocations under applied stress in micro- and nano-scales. Therefore, numerous efforts to understand the plastic deformation has finally led one to study the dynamics of individual dislocation. According to the continuum theory, the drag force leads to a linear relationship between the dislocation velocity and the stress. However, a discrete nature of the dislocation core induces nonlinear drag force on the moving dislocation in reality. Therefore, the continuum approach is limited in its ability to describe the dislocation motion under the general loading conditions although it has been widely used so far in mesoscale dislocation dynamics (DD) simulation. In the first part of the dissertation (Chapter 1~4), I focus on fundamentals of the drag force with considering the discrete nature of dislocation and propose a theoretical framework to describe the dislocation motion including the nonlinear drag effect. And the proposed model is supported by molecular dynamics (MD) simulations. In a discrete medium that consists of atoms, the dislocation glides with emitting elastic waves and they are scattered around the dislocation core by various sources. Therefore, the phonon scattering is the dominant drag source and determines the dynamic behaviors of a dislocation. And by extension, the theoretical model is applied to the low-angle grain boundary (LAGB) given that it characterized as an array of dislocations. As a result, the proposed model can describe the dynamics of both dislocation and LAGB in the discrete system and expect unusual behaviors that do not follow the continuum theory. In the second part of the dissertation (Chapter 5), a deeper analysis of the drag force is carried out in the frame of Eshelbian mechanics. Since the origin of drag force acting on the dislocation stems from interaction between the dislocation and phonons, the drag force is analytically derived by adopting the dislocation-phonon coordinate system. As a result, it is proved that the drag force breaks a path-independent behavior of J-integral and its magnitude is determined by structural properties of the dislocation. This reconfirms that the drag force is closely related to the discreteness nature of dislocation. In this regard, the proposed approach sheds light on the essence of drag effect and further provides an integrated viewpoint on describing various drag mechanisms. Hence, I expect that the present work elucidates the fundamentals of dislocation dynamics in nanoscale in which the discreteness of medium may be important, and contributes to more realistic prediction of material plasticity.clos