Multiscale Dislocation Dynamics Plasticity Research Articles

Modeling the mechanical response and microstructure evolution of magnesium single crystals under c-axis compression

Atomistically informed multiscale dislocation dynamics plasticity (MDDP) framework is used to investigate the mechanical response and microstructure evolution in bulk magnesium single crystals subjected to c-axis compression. The MDDP framework was modified to account for the 〈c+a〉 dislocation slip on the pyramidal I and pyramidal II planes. Several aspects of the 〈c+a〉 dislocation reactions such as the transition of pyramidal I near edge and pyramidal II pure edge segments to basal plane, and the thermally activated cross slip are considered. Additionally, a generalized mobility law and anisotropic frictional stress models are implemented based on the findings of several molecular dynamics studies. MDDP predictions of the yielding and strain hardening behaviors, as well as the maximum stress prior to failure are in good agreement with the reported experimental values. Moreover, detailed study of the dislocation microstructure evolution and the dislocation density dependence on the applied stress are presented and compared with available experimental results.

On the homogeneous nucleation and propagation of dislocations under shock compression

The dynamic response of crystalline materials subjected to extreme shock compression is not well understood. The interaction between the propagating shock wave and the material’s defect occurs at the sub-nanosecond timescale which makes in situ experimental measurements very challenging. Therefore, computer simulation coupled with theoretical modelling and available experimental data is useful to determine the underlying physics behind shock-induced plasticity. In this work, multiscale dislocation dynamics plasticity (MDDP) calculations are carried out to simulate the mechanical response of copper reported at ultra-high strain rates shock loading. We compare the value of threshold stress for homogeneous nucleation obtained from elastodynamic solution and standard nucleation theory with MDDP predictions for copper single crystals oriented in the [0 0 1]. MDDP homogeneous nucleation simulations are then carried out to investigate several aspects of shock-induced deformation such as; stress profile characteristics, plastic relaxation, dislocation microstructure evolution and temperature rise behind the wave front. The computation results show that the stresses exhibit an elastic overshoot followed by rapid relaxation such that the 1D state of strain is transformed into a 3D state of strain due to plastic flow. We demonstrate that MDDP computations of the dislocation density, peak pressure, dynamics yielding and flow stress are in good agreement with recent experimental findings and compare well with the predictions of several dislocation-based continuum models. MDDP-based models for dislocation density evolution, saturation dislocation density, temperature rise due to plastic work and strain rate hardening are proposed. Additionally, we demonstrated using MDDP computations along with recent experimental reports the breakdown of the fourth power law of Swegle and Grady in the homogeneous nucleation regime.

On the ultra-high-strain rate shock deformation in copper single crystals: multiscale dislocation dynamics simulations

Multiscale dislocation dynamics plasticity (MDDP) calculations are carried out to simulate the mechanical response of copper single crystals that have undergone shock loading at high strain rates ranging from 1 × 106 to 1 × 1010 s−1. Plasticity mechanisms associated with both the activation of pre-existing dislocation sources and homogeneous nucleation of glide loops are considered. Our results show that there is a threshold strain rate of 108 s−1 at which the deformation mechanism changes from source activation to homogeneous nucleation. It is also illustrated that the pressure dependence on strain rate follows a one-fourth power law up to 108 s−1 beyond which the relationship assumes a one-half power law. The MDDP computations are in good agreement with recent experimental findings and compare well with the predictions of several dislocation-based continuum models.

Multiscale dislocation dynamics simulations of shock-induced plasticity in small volumes

Multiscale dislocation dynamics plasticity (MDDP) was used to investigate shock-induced deformation in monocrystalline copper. In order to enhance the numerical simulations, a periodic boundary condition was implemented in the continuum finite element (FE) scale so that the uniaxial compression of shocks could be attained. Additionally, lattice rotation was accounted for by modifying the dislocation dynamics (DD) code to update the dislocations’ slip systems. The dislocation microstructures were examined in detail and a mechanism of microband formation is proposed for single- and multiple-slip deformation. The simulation results show that lattice rotation enhances microband formation in single slip by locally reorienting the slip plane. It is also illustrated that both confined and periodic boundary conditions can be used to achieve uniaxial compression; however, a periodic boundary condition yields a disturbed wave profile due to edge effects. Moreover, the boundary conditions and the loading rise time show no significant effects on shock–dislocations interaction and the resulting microstructures. MDDP results of high strain rate calculations are also compared with the predictions of the Armstrong–Zerilli model of dislocation generation and movement. This work confirms that the effect of resident dislocations on the strain rate can be neglected when a homogeneous nucleation mechanism is included.

Modeling Shock Induced Plasticity in Copper Single Crystal: Numerical and Strain Localization Issues

Multiscale dislocation dynamics plasticity (MDDP) simulations are carried out to address the following issues in modeling shock-induced plasticity: 1- the effect of finite element (FE) boundary conditions on shock wave characteristics and wave-dislocation interaction, 2- the effect of the evolution of the dislocation microstructure on lattice rotation and strain localization. While uniaxial strain is achieved with high accuracy using confined boundary condition, periodic boundary condition yields a disturbed wave profile due the edge effect. Including lattice rotation in the analysis leads to higher dislocation density and more localized plastic strain.

Analysis of heterogeneous deformation and dislocation dynamics in single crystal micropillars under compression

The size dependent deformation of Cu single crystal micropillars with thickness ranging from 0.2 to 2.5 μm subjected to uniaxial compression is investigated using a Multi-scale Dislocation Dynamics Plasticity (MDDP) approach. MDDP is a hybrid elasto-viscoplastic simulation model which couples discrete dislocation dynamics at the micro-scale (software micro3d) with the macroscopic plastic deformation. Our results show that the deformation field in these micropillars is heterogeneous from the onset of plastic flow and is confined to few deformation bands, leading to the formation of ledges and stress concentrations at the surface of the specimen. Furthermore, the simulation yields a serrated stress–strain behavior consisting of discrete strain bursts that correlates well with experimental observations. The intermittent operation and stagnation of discrete dislocation arms is identified as the prominent mechanism that causes heterogeneous deformation and results in the observed macroscopic strain bursts. We show that the critical stress to bow an average maximum dislocation arm, whose length changes during deformation due to pinning events, is responsible for the observed size dependent response of the single crystals. We also reveal that hardening rates, similar to that shown experimentally, occur under relatively constant dislocation densities and are linked to dislocation stagnation due to the formation of entangled dislocation configuration and pinning sites.

Multiscale dislocation dynamics analyses of laser shock peening in silicon single crystals

Although laser shock peening (LSP) has been applied in metals for property enhancement for a long time, its application on brittle materials has not been investigated so far. The present work is the first computational attempt to show that strong dislocation activity can be generated in silicon crystal by a modified LSP process. Multiscale dislocation dynamics plasticity (MDDP) simulations are conducted to predict the dislocation structure and stress/strain distribution in silicon crystal during LSP. In the modified LSP process, dislocation mobility of silicon and shock pressure is sufficiently high to generate and transport dislocation. The relationships between dislocation activities, the laser processing conditions and ablative coating material are systematically investigated. It is found that dislocation density, dislocation multiplication rate, and dislocation microstructure strongly depend on LSP processing conditions. This LSP process can also be applied in other brittle materials.

Dislocation behavior in silicon crystal induced by laser shock peening: A multiscale simulation approach

Abstract This paper presents a modified laser shock peening (LSP) technique to generate plastic deformation in silicon crystal. The induced dislocation activity in silicon crystal is studied by integrated shock dynamics and multiscale dislocation dynamics plasticity simulations. This LSP process can also be applied to other brittle materials to generate plastic deformation.

Multiscale dislocation dynamics simulations of shock compression in copper single crystal

Ultra short pulse shock wave propagation, plastic deformation and evolution of dislocations in copper single crystals with (0 0 1), (0 1 1) and (1 1 1) orientations are investigated using multiscale dislocation dynamics plasticity analyses. The effects of peak pressure, pulse duration, crystal anisotropy and the nonlinear elastic properties on the interaction between shock wave and dislocations are investigated. The results of our calculations show that the dislocation density has a power law dependence on pressure with a power of 1.70 and that the dislocation density is proportional to pulse duration and sensitive to crystal orientation. These results are in very good agreement with the analytical predications of Meyers et al. [Meyers, M.A., Gregori, F., Kad, B.K., Schneider, M.S., Kalantar, D.H., Remington, B.A., Ravichandran G., Boehly, T., Wark, J., 2003. Laser-induced shock compression of monocrystalline copper: characterization and analysis. Acta Materialia 51, 1211–1228] and the experimental results of Murr [Murr, L.E., 1981. Residual microstructure-mechanical property relationships in shock loaded metals and alloys. In: Meyers, M.A., Murr, L.E. (Eds.), Shock Waves and High Strain Rate Phenomena in Metals. Plenum, New York, pp. 607–673]. It is shown also that incorporating the effect of crystal anisotropy in the elastic properties results in orientation dependent wave speed and peak pressure. The relaxed configurations of dislocation microstructures show the formation of microbands coincident with the slip planes.

Multiscale Dislocation Dynamics Plasticity

A recently developed discrete dislocation dynamics (DD) model for crystalline materials coupled with finite elements (FE) analysis is reviewed. The three-dimensional continuum-based FE formulation for elastoviscoplasticity incorporates the DD simulation, replacing the usual plasticity constitutive relationships, leading to what is called multiscale dislocation dynamics plasticity (MDDP). The coupling involves a nontrivial homogenization to obtain local plastic strains from the contributions of discrete plastic events captured in DD. The superposition principle is used in order to find the effects of the boundaries (free, rigid, or interfaces) on the dislocation movement. The developed computer code can efficiently handle size-dependent small-scale plasticity phenomena and related material instabilities at various length scales ranging from the nano-microscale to the mesoscale. The DD modeling is based on the fundamental physical laws governing dislocation motions and their interactions with various defects, interfaces, and external loadings. The multiscale frame of consideration merges the two scales of nano-microscale, where plasticity is determined, and the continuum scale, where the energy transport is based. In order to illustrate the usefulness of this approach in investigating a wide range of plasticity phenomena, results for a set of case studies are presented. This includes the deformation and dislocation structure during nano-indentation in bcc and fcc single crystals, analyses pertaining to the formation of dislocation boundaries during heavy deformation, dislocations interaction with shock-waves during impact loading conditions, and dislocation–defect interaction.