Dislocation Dynamics Simulations Research Articles

Dislocation evolution and properties enhancement of GH2036 by laser shock processing: Dislocation dynamics simulation and experiment

This paper systematically investigated the effect of laser shock processing (LSP) on dislocation evolution and microstructure configuration of GH2036 alloy. Surface topography and roughness were tested by Axio CSM 700 microscope. The dislocation configurations were characterized by transmission electron microscope (TEM) and simulated by multi-scale discrete dislocation dynamics (DD) method. The results have confirmed that LSP had a beneficial effect on micro-hardness, which could be increased by 16%, and the surface topography exhibited excellent stability even after thermal cycle. The dislocation density and stress–strain response have strong dependence on laser power intensity. Reasonable agreement between DD simulation and experiments is achieved. The results showed that complex random microstructures can be observed in the shocked surface. The grain refinement mechanism of LSP GH2036 involves dislocation segmentation and twin intersections.

Equivalent plastic strain gradient plasticity with grain boundary hardening and comparison to discrete dislocation dynamics

The gradient crystal plasticity framework of Wulfinghoff et al. (Wulfinghoff et al. 2013 Int. J. Plasticity 51, 33–46. ( doi:10.1016/j.ijplas.2013.07.001 )), incorporating an equivalent plastic strain γ eq and grain boundary (GB) yielding, is extended with GB hardening. By comparison to averaged results from many discrete dislocation dynamics (DDD) simulations of an aluminium-type tricrystal under tensile loading, the new hardening parameter of the continuum model is calibrated. Although the GBs in the discrete simulations are impenetrable, an infinite GB yield strength, corresponding to microhard GB conditions, is not applicable in the continuum model. A combination of a finite GB yield strength with an isotropic bulk Voce hardening relation alone also fails to model the plastic strain profiles obtained by DDD. Instead, a finite GB yield strength in combination with GB hardening depending on the equivalent plastic strain at the GBs is shown to give a better agreement to DDD results. The differences in the plastic strain profiles obtained in DDD simulations by using different orientations of the central grain could not be captured. This indicates that the misorientation-dependent elastic interaction of dislocations reaching over the GBs should also be included in the continuum model.

O69] Energetic investigation of metastable Al60Sm11-ω, Al5Sm-π, Al4Sm-γ,Al11Sm3-α and Al4Sm-β phase formation

This work examines binary dislocation interactions, junction formation and junction strengths in hexagonal close-packed (hcp) crystals. Through a line-tension model and dislocation dynamics (DD) simulations, the interaction and dissociation of different sets of binary junctions are investigated involving one dislocation on the (011¯0) prismatic plane and a second dislocation on one of the following planes: (0001) basal, (11¯00) prismatic, (11¯01) primary pyramidal, or (2¯112) secondary pyramidal. Varying pairs of Burgers vectors are chosen from among the common types: the basal type <a>:13<112¯0>, prismatic type <c>:<0001>, and pyramidal type <a+c>:13<112¯3¯>. For binary interaction due to dislocation intersection, both the analytical results and DD-simulations indicate a relationship between symmetry of interaction maps and the relative magnitude of the Burgers vectors that constitute the junction. Using analytical formulae, a simple regressive model is also developed to represent the junction yield surface. The equation is treated as a degenerated super elliptical equation to quantify the aspect ratio and tilting angle. The results provide analytical insights on binary dislocation interactions that may occur in general hcp metals.

Prismatic and helical dislocation loop generation from defects

Plastic deformation induced by stress concentrations near crystal defects occurs through the generation of prismatic dislocation loops (PDL). The production of PDLs leads to void growth and particle decoherence. In this work we use dislocation dynamics simulations to characterize two mechanisms for PDL formation. The first mechanism corresponds to a classical model of PDL generation from dislocation nucleation. The second mechanism considers PDL generation through cross-slip of a screw dislocation intersecting the particle. We systematically study the effect of the crystal lattice and defect type on PDL generation for both mechanisms as a function of pressure. The simulations show image stresses produced by the dislocation's interaction with the free surface of a void suppresses PDL generation. The highest PDL generation rates are found for a dislocation nucleated from a void in a body-centered cubic lattice. Our simulations also show helical coiling of screw dislocations produces a continuous emission of PDLs without the need for dislocation nucleation at pressures as low as 1.0 GPa.

Anisotropic Size-Dependent Plasticity in Face-Centered Cubic Micropillars Under Torsion

Three-dimensional dislocation dynamics (DD) simulations are performed to investigate the size-dependent plasticity in submicron face-centered cubic (FCC) micropillars under torsion. By using a previously implemented surface nucleation algorithm within DD, we show that the plastic behavior of FCC micropillars under torsion is strongly affected by the crystallographic orientation: In 〈110〉 oriented submicron pillars, coaxial dislocations nucleate and pile up near the axis, leading to homogeneous deformation along the pillars. In contrast, in 〈100〉 and 〈111〉 oriented pillars, heterogeneous plasticity has been observed due to the formation of localized dislocation arrays. As a result of the existence of a coaxial slip plane in 〈110〉 oriented pillars, stronger size-dependent plasticity is observed in this case compared with those in other orientations.

INVITED] A review: Warm laser shock peening and related laser processing technique

This paper reviews the recent progress in warm laser shock peening (WLSP) and related laser processing technique. The process design, enhanced mechanical performance, and microstructure evolution of WLSP are discussed in details. The fundamental process mechanism is reviewed by building the processing-microstructure-property relationship. In particular, the precipitation kinetics during WLSP is discussed to study the effect of process parameters on the nucleation of nano-precipitates, and multiscale discrete dislocation dynamics (MDDD) simulation results are summarized to investigate the dislocation multiplication and propagation behaviors as well as the dislocation pinning effect. In addition, the research progress of thermal engineered laser shock peening (TE-LSP) technique is reviewed with a focus on the coarsening of precipitates, the extended fatigue life, and more importantly, the fundamental process mechanism.

Grain size effects on dislocation and twinning mediated plasticity in magnesium

Grain size effects on the competition between dislocation slip and 101¯2-twinning in magnesium are investigated using discrete dislocation dynamics simulations. These simulations account for dislocation–twin boundary interactions and twin boundary migration through the glide of twinning dislocations. It is shown that twinning deformation exhibits a strong grain size effect; while dislocation mediated slip in untwinned polycrystals displays a weak one. This leads to a critical grain size at 2.7μm, above which twinning dominates, and below which dislocation slip dominates.

Capturing the effects of free surfaces on void strengthening with dislocation dynamics

Void strengthening in crystalline materials refers to the increase in yield stress due to the impediment of dislocation motion by voids. Dislocation dynamics (DD) is a modeling method well suited to capture the physics, length scales, and time scales associated with void strengthening. However, previous DD simulation of dislocation–void interactions have been unable to accurately account for the strong image forces acting on the dislocation due to the void’s free surface. In this article, we employ a finite-element-based DD method to determine the obstacle strength of voids, defined as the critical resolved shear stress for a dislocation to glide past an array of voids. Our results demonstrate that the attractive image forces between the dislocation and free surface significantly reduce the obstacle strength of voids. Effects of surface mobility and stress concentrations around the void are also explored and are shown to have minimal effect on the critical stress. Finally, a new model relating void size and spacing to obstacle strength is proposed.

Screw dislocation cross slip at cross-slip plane jogs and screw dipole annihilation in FCC Cu and Ni investigated via atomistic simulations

Using atomistic simulations, the effect of jogs on the cross-slip of screw character dislocations and screw-dipole annihilation was examined for both FCC Cu and Ni. The stress-free activation energy for cross-slip at jogs is close to 0.4eV in Cu, determined using a nudged elastic band method. This value is a factor of 4-to-5 lower than the activation energy for cross-slip of screw dislocations in the absence of a jog. Similar results were obtained for Ni. Molecular dynamics simulations were used to study the annihilation of a jog-containing screw dipole. The critical Escaig stress on the glide plane for dipole annihilation drops quickly from the 0K value of ∼400MPa and, dipole annihilation is nearly athermal at room temperature. At 5K, Escaig stresses on the cross-slip plane are a factor of 1.5 less effective than Escaig stresses on the glide plane and, glide stresses on the cross-slip plane are a factor of 3 less effective for dipole annihilation by cross-slip. The activation volume for cross-slip of screw dislocations at jogs with respect to these three stress components range from 6 to 20b3. These results have been found to be useful in physics-based modeling of bulk cross-slip in higher length scale 3D dislocation dynamics simulations investigating dislocation pattern formation and fatigue structures in FCC crystals.

Primary combination of phase-field and discrete dislocation dynamics methods for investigating athermal plastic deformation in various realistic Ni-base single crystal superalloy microstructures

Three-dimensional discrete dislocation dynamics (DDD) simulations in combination with the phase-field method are performed to investigate the influence of different realistic Ni-base single crystal superalloy microstructures with the same volume fraction of precipitates on plastic deformation at room temperature. The phase-field method is used to generate realistic microstructures as the boundary conditions for DDD simulations in which a constant high uniaxial tensile load is applied along different crystallographic directions. In addition, the lattice mismatch between the γ and phases is taken into account as a source of internal stresses. Due to the high antiphase boundary energy and the rare formation of superdislocations, precipitate cutting is not observed in the present simulations. Therefore, the plastic deformation is mainly caused by dislocation motion in γ matrix channels. From a comparison of the macroscopic mechanical response and the dislocation evolution for different microstructures in each loading direction, we found that, for a given phase volume fraction, the optimal microstructure should possess narrow and homogeneous γ matrix channels.

Prediction of macroscopic damage behaviour of precipitation strengthened steels via multiscale simulations

AbstractA multiscale modelling approach is presented that sequentially connects in total five simulation methods via parameter transfers in order to capture the macroscopic damage behaviour due to an underlying nano structure of copper precipitates in bcc iron. In this multiscale approach, information on precipitation states is taken from kinetic Monte‐Carlo and Phasefield simulations as well as from experimental data. Based on a calibration of Dislocation Dynamics by Molecular Dynamics simulations as well as on testing conditions known from experiments, Dislocation Dynamics simulations with an infinite dislocation on a single glide plane provide strengthening levels which are related to a reference stress‐strain curve obtained from experiments. Subsequently, the macroscopic damage behaviour is simulated with the Finite‐Element‐Method including the Rousselier Damage Model for the reference state as well as for the virtually aged states. The results are validated by comparison with experimental results and predictions are made with respect to specific precipitation cases. (© 2015 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Internal stresses in a homogenized representation of dislocation microstructures

To develop a continuum theory based on the evolution of dislocation microstructures, two challenges have to be resolved: the correct representation of the kinematics of dislocation motion in terms of dislocation density and the formulation of a mobility law reflecting an effective description of the physical behavior of the discrete many-body problem.Kröner's classical continuum theory has inspired different approaches to model plasticity based on the motion of dislocations. Amongst them, the Continuum Dislocation Dynamics (CDD) theory was formulated as a generalization of the classical theory. The CDD theory allows for a continuous representation of the evolution of dislocation microstructures and is found to be kinematically complete.Here, a numerical formulation of the CDD theory is presented and constitutive laws for the incorporation of dislocation interactions are derived based on the representation of the dislocation microstructure in two dimensions. An error measure is introduced to analyze the constitutive law and the results are compared to discrete dislocation dynamics simulations. Important aspects for the implementation of a 3D theory are discussed.

Micropolar crystal plasticity simulation of particle strengthening

The yield and work hardening behavior of a small-scale initial-boundary value problem involving dislocation plasticity in an idealized particle strengthened system is investigated using micropolar single crystal plasticity and is compared with results for the same problem from dislocation dynamics simulations. A micropolar single crystal is a work-conjugate higher-order continuum that treats the lattice rotations as generalized displacements, and supports couple stresses that are work-conjugate to the lattice torsion-curvature, leading to a non-symmetric Cauchy stress. The resolved skew-symmetric component of the Cauchy stress tensor results in slip system level kinematic hardening during heterogeneous deformation that depends on gradients of lattice torsion-curvature. The scale-dependent mechanical response of the micropolar single crystal is dictated both by energetic (higher-order elastic constants) and dissipative (plastic torsion-curvature) intrinsic material length scales. We show that the micropolar model captures essential details of the average stress–strain behavior predicted by discrete dislocation dynamics and of the cumulative slip and dislocation density fields predicted by statistical dislocation dynamics.

A FFT-based formulation for efficient mechanical fields computation in isotropic and anisotropic periodic discrete dislocation dynamics

In this paper, we propose a novel full-field approach based on the fast Fourier transform (FFT) technique to compute mechanical fields in periodic discrete dislocation dynamics (DDD) simulations for anisotropic materials: the DDD-FFT approach. By coupling the FFT-based approach to the discrete continuous model, the present approach benefits from the high computational efficiency of the FFT algorithm, while allowing for a discrete representation of dislocation lines. It is demonstrated that the computational time associated with the new DDD-FFT approach is significantly lower than that of current DDD approaches when large number of dislocation segments are involved for isotropic and anisotropic elasticity, respectively. Furthermore, for fine Fourier grids, the treatment of anisotropic elasticity comes at a similar computational cost to that of isotropic simulation. Thus, the proposed approach paves the way towards achieving scale transition from DDD to mesoscale plasticity, especially due to the method’s ability to incorporate inhomogeneous elasticity.

Dislocation multiplication mechanisms – Glissile junctions and their role on the plastic deformation at the microscale

Dislocation junctions are considered to control the hardening behavior of crystalline materials during plastic deformation. Here the influence of the glissile junction on the plastic deformation of microscale samples is investigated, based on discrete dislocation dynamics simulation results. It is found that with increasing dislocation density ρ, sample size d, which can be collapsed into a single dimensionless parameter dρ, and an increasing number of activated slip systems due to different global crystallographic orientations, the glissile junction forms frequently and can bow out easily, acting as an effective source. The resulting new dislocations are mobile and contribute to the macroscopic plastic deformation on the order of 30–60%. In the size regime from 0.5 to 2μm and dislocation densities in the range of 1012–1014m-2, the glissile junction is therefore an important source for generating mobile dislocation density. Furthermore a significant correlation between stress drops and activity of dislocations originating from glissile junctions is found. A rate formulation is proposed to include these findings in crystal plasticity or continuum dislocation density frameworks.

Statistical analysis and stochastic dislocation-based modeling of microplasticity

AbstractPlastic deformation of micro- and nanoscale samples differs from macroscopic plasticity in two respects: (i) the flow stress of small samples depends on their size, and (ii) the scatter of plastic deformation behavior increases significantly. In this work, we focus on the scatter of plastic behavior. We statistically characterize the deformation process of micropillars using results from discrete dislocation dynamics (DDD) simulations. We then propose a stochastic microplasticity model that uses the extracted information to make statistical predictions regarding the micropillar stress-strain curves. This model aims to map the complex dynamics of interacting dislocations onto stochastic processes involving the continuum variables of stress and strain. Therefore, it combines a classical continuum description of the elastic-plastic problem with a stochastic description of plastic flow. We compare the model predictions with the underlying DDD simulations and outline potential future applications of the same modeling approach.

A continuum model for dislocation dynamics in three dimensions using the dislocation density potential functions and its application to micro-pillars

In this paper, we present a dislocation-density-based three-dimensional continuum model, where the dislocation substructures are represented by pairs of dislocation density potential functions (DDPFs), denoted by ϕ and ψ. The slip plane distribution is characterized by the contour surfaces of ψ, while the distribution of dislocation curves on each slip plane is identified by the contour curves of ϕ which represents the plastic slip on the slip plane. By using DDPFs, we can explicitly write down an evolution equation system, which is shown consistent with the underlying discrete dislocation dynamics. The system includes (i) a constitutive stress rule, which describes how the total stress field is determined in the presence of dislocation networks and applied loads; (ii) a plastic flow rule, which describes how dislocation ensembles evolve. The proposed continuum model is validated through comparisons with discrete dislocation dynamics simulation results and experimental data. As an application of the proposed model, the “smaller-being-stronger” size effect observed in single-crystal micro-pillars is studied. A scaling law for the pillar flow stress σflow against its (non-dimensionalized) size D is derived to be σflow∼log(D)/D.

Modeling the creep properties of olivine by 2.5-dimensional dislocation dynamics simulations

In this work we performed 2.5-dimensional (2.5D) dislocation dynamics simulations coupling climb with the glide dislocation motion to model the creep behavior of olivine, one of the main component of the Earth's upper mantle. In particular, we present an application of this method to determine the creep strain rate in a material with high lattice resistance, such as olivine. We show that by including the climb mechanism we reach steady state creep conditions. Moreover, we find that a creep power law with a stress exponent close to 3 can be extracted from our simulations and we provide a model based on Orowan's law to predict the creep strain rates in the high temperature and low stress regime. The model presented is relevant to describe the plastic flow of olivine in the Earth's mantle deformation conditions and can be useful to derive the high temperature creep behavior of other materials.

Young’s Modulus Determination: Influence of Microplasticity and Pseudo-Elasticity on Metal Forming

This paper shows that non-linearity of mechanical behaviour of metal in the elastic regime has an influence on the forming process. Discrete Dislocation Dynamics simulations show that pure elastic behaviour is altered when reversible dislocation displacements occur even in the very beginning of the elastic stage. The influence of such a non-linearity has an impact on the results of numerical simulations of industrial forming of very thin metal sheets of copper.

Multiscale Simulation of Plasticity in bcc Metals

Significant progress in our understanding of plasticity in body-centered cubic (bcc) metals during the last decade has enabled rigorous multiscale modeling based on quantitative physical principles. Significant advances have been made at the atomistic level in the understanding of dislocation core structures and energetics associated with dislocation glide by using high-fidelity models originating from quantum mechanical principles. These simulations revealed important details about the influence of non-Schmid (nonglide) stresses on the mobility of screw dislocations in bcc metals that could be implemented to mesoscopic discrete dislocation simulations with atomistically informed dislocation mobility laws. First applications of dislocation dynamics simulations to studies of plasticity in small-scale bcc single crystals have been performed. Dislocation dynamics simulations inspired the development of continuum models based on advanced 3D dislocation density measures with evolution equations that naturally track dislocation motion. These advances open new opportunities and perspectives for future quantitative and materials-specific multiscale simulation methods to describe plastic deformation in bcc metals and their alloys.