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Journal articles on the topic 'Discrete dislocation'

Author: Grafiati

Published: 25 May 2024

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1

Diop, Mouhamadou, Hai Hao, Han Wei Dong, and Xing Guo Zhang. "Simulation of Discrete Dislocation Statics and Dynamics of Magnesium Foam." Materials Science Forum 675-677 (February 2011): 929–32. http://dx.doi.org/10.4028/www.scientific.net/msf.675-677.929.

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The simulation of magnesium plasticity at the microscopic and mesoscopic scale using space and time-discretized statics and dynamics dislocation was carried out. The complexity of discrete dislocation models dues to the fact that the mechanical interaction of ensembles of such defects is with an elastic nature, and therefore involves long-range interactions. The motion of dislocations or dislocation segments in their respective glide planes are usually described by assuming simple phenomenological viscous flows laws. The formulation of the dislocation dynamics is obtained by the Newton’s Second Law of motion for each dislocation or dislocation segment. The evolution of the dislocation position is obtained by simple difference algorithms.

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2

Záležák, Tomáš, and Antonín Dlouhý. "3D Discrete Dislocation Modelling of High Temperature Plasticity." Key Engineering Materials 465 (January 2011): 115–18. http://dx.doi.org/10.4028/www.scientific.net/kem.465.115.

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A 3D model is presented that addresses an evolution of flexible dislocation lines at high temperatures. The model is based on the linear theory of elasticity. A smooth dislocation line is approximated by a piecewise curve composed of short straight dislocation segments. Each dislocation segment is acted upon by a Peach-Koehler force due to a local stress field. All segment-segment interactions as well as an externally applied stress are considered. A segment mobility is proportional to the Peach-Koehler force, temperature-dependent factors control climb and glide motion of the segments. The potential of the model is demonstrated in simulations of simple high temperature processes including interactions of dislocations with secondary particles.

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3

Li, Luo, and Tariq Khraishi. "An Investigation of Spiral Dislocation Sources Using Discrete Dislocation Dynamics (DDD) Simulations." Metals 13, no. 8 (August 6, 2023): 1408. http://dx.doi.org/10.3390/met13081408.

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Discrete Dislocation Dynamics (DDD) simulations are a powerful simulation methodology that can predict a crystalline material’s constitutive behavior based on its loading conditions and micro-constituent population/distribution. In this paper, a 3D DDD model with spiral dislocation sources is developed to study size-dependent plasticity in a pure metal material (taken here as Aluminum). It also shows, for the first time, multipole simulations of spirals and how they interact with one another. In addition, this paper also discusses how the free surface of a crystalline material affects the plasticity generation of the spiral dislocation. The surface effect is implemented using the Distributed Dislocation Method. One of the main results from this work, shown here for the first time, is that spiral dislocations can result in traditional Frank–Read sources (edge or screw character) in a crystal. Another important result from this paper is that with more dislocation sources, the plastic flow inside the material is more continuous, which results in a lowering of the flow stress. Lastly, the multipole interaction of the spiral dislocations resulted in a steady-state fan-shaped action for these dislocation sources.

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4

Huang, C. C., C. C. Yu, and Sanboh Lee. "The behavior of screw dislocations dynamically emitted from the tip of a surface crack during loading and unloading." Journal of Materials Research 10, no. 1 (January 1995): 183–89. http://dx.doi.org/10.1557/jmr.1995.0183.

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The behavior of screw dislocations dynamically emitted from the tip of a surface crack during loading and unloading has been investigated using a discrete dislocation model. The critical stress intensity factor at the crack tip for dislocation emission is a function of friction stress, core radius of dislocation, and dislocations near the crack tip. During motion, the velocity of dislocation is assumed to be proportional to the effective shear stress to the third power. The effect of crack length and friction stress on dislocation distributions, plastic zone, and dislocation-free zone during loading and unloading was examined.

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5

Mastorakos, Ioannis N., Firas E. Akasheh, and Hussein M. Zbib. "Treating internal surfaces and interfaces in discrete dislocation dynamics." Journal of the Mechanical Behaviour of Materials 20, no. 1-3 (December 1, 2011): 13–20. http://dx.doi.org/10.1515/jmbm.2011.002.

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AbstractThe treatment of coherent interfaces and cracks is discussed in the framework of dislocation dynamics (DD). In the case of interfaces, we use DD to study dislocation interactions in nanoscale bimetallic laminates, and to predict their structure after relaxation and during loading. In agreement with experimental observations, our discrete dynamics simulations show that dislocation structure develops only at the interface between coherent layers leaving layers’ interior dislocation-free. The main dislocation mechanism at this length scale is Oworan bowing of threading dislocations confined to their respective layers by the sign-alternating coherency stress field in the layers. Slip transmission across the interfaces marks the end of the confined slip regime, hence, the breakdown of the interfaces and macroscopic yielding of these structures. In the case of crack, its long-range and singular stress field is determined by modeling the crack as continuous distribution of dislocation loops. The traction boundary condition to be satisfied at the crack surface, results into a singular integral equation of the first kind that is solved numerically. The model is integrated with the DD technique to investigate the behavior of a specimen containing cracks of different shapes under fatigue. The results are compared with the behavior of an uncracked specimen and conclusions are extracted. Extension of this crack treatment methodology to account for their presence at interfaces, all within the frame dislocations dynamics, opens the door for a more realistic approach to a wide range of interfaces-related problems.

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6

Ayas, Can, and Vikram Deshpande. "Climb Enabled Discrete Dislocation Plasticity of Superalloys." Key Engineering Materials 651-653 (July 2015): 981–86. http://dx.doi.org/10.4028/www.scientific.net/kem.651-653.981.

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Ni-based superalloys comprising of elastic particles embedded in a single crystal elastic-plastic matrix are usually subject to loading at elevated service temperatures. In order to enhance the understanding of high temperature deformation mechanisms a two dimensional discrete dislocation plasticity framework wherein the dislocations movement that incorporates both glide and climb is formulated. The climbing dislocations are modelled as point sources/sinks of vacancies and the vacancy diffusion boundary value problem is solved by superposition of the vacancy concentration fields of the point sources/sinks in an infinite medium and a complementary non-singular solution that enforces the relevant boundary conditions. The vacancy concentration field along with the Peach-Kohler force provides the climb rate of the dislocations.

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7

Needleman, Alan, and E. Van der Giessen. "Discrete Dislocation Plasticity." Key Engineering Materials 233-236 (January 2003): 13–24. http://dx.doi.org/10.4028/www.scientific.net/kem.233-236.13.

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8

Stricker, Markus, Michael Ziemann, Mario Walter, Sabine M. Weygand, Patric Gruber, and Daniel Weygand. "Dislocation structure analysis in the strain gradient of torsion loading: a comparison between modelling and experiment." Modelling and Simulation in Materials Science and Engineering 30, no. 3 (February 8, 2022): 035007. http://dx.doi.org/10.1088/1361-651x/ac4d77.

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Abstract Complex stress states due to torsion lead to dislocation structures characteristic for the chosen torsion axis. The formation mechanism of these structures and the link to the overall plastic deformation are unclear. Experiments allow the analysis of cross sections only ex situ or are limited in spacial resolution which prohibits the identification of the substructures which form within the volume. Discrete dislocation dynamics simulations give full access to the dislocation structure and their evolution in time. By combining both approaches and comparing similar measures the dislocation structure formation in torsion loading of micro wires is explained. For the ⟨100⟩ torsion axis, slip traces spanning the entire sample in both simulation and experiment are observed. They are caused by collective motion of dislocations on adjacent slip planes. Thus these slip traces are not atomically sharp. Torsion loading around a ⟨111⟩ axis favors plasticity on the primary slip planes perpendicular to the torsion axis and dislocation storage through cross-slip and subsequent collinear junction formation. Resulting hexagonal dislocation networks patches are small angle grain boundaries. Both, experiments and discrete dislocation simulations show that dislocations cross the neutral fiber. This feature is discussed in light of the limits of continuum descriptions of plasticity.

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9

Zbib, Hussein M., Tomas Diaz de la Rubia, and Vasily Bulatov. "A Multiscale Model of Plasticity Based on Discrete Dislocation Dynamics." Journal of Engineering Materials and Technology 124, no. 1 (May 28, 2001): 78–87. http://dx.doi.org/10.1115/1.1421351.

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We present a framework coupling continuum elasto-viscoplasticity with three-dimensional discrete dislocation dynamics. In this approach, the elastic response is governed by the classical Hooke’s law and the viscoplastic behavior is determined by the motion of curved dislocations in a three-dimensional space. The resulting hybrid continuum-discrete framework is formulated into a standard finite element model where the dislocation-induced stress is homogenized over each element with a similar treatment for the dislocation-induced plastic strain. The model can be used to investigate a wide range of small scale plasticity phenomena, including microshear bands, adiabatic shear bands, stability and formation of dislocation cells, thin films and multiplayer structures. Here we present results pertaining to the formation of deformation bands and surface distortions under dynamic loading conditions and show the capability of the model in analyzing complicated deformation-induced patterns.

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10

Holec, David, and Antonín Dlouhý. "Stability and Motion of Low Angle Dislocation Boundaries in Precipitation Hardened Crystals." Materials Science Forum 482 (April 2005): 159–62. http://dx.doi.org/10.4028/www.scientific.net/msf.482.159.

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The present study investigates stability and motion of low angle dislocation boundaries in an array of precipitates. The model considers discrete dislocations and precipitates that are treated as impenetrable particles. Peach-Koehler forces, which originate due to the combined effect of dislocation-dislocation interactions and the applied stress, act the individual dislocations on. Both, the dislocation glide and the dislocation climb at elevated temperatures are taken into account. Results of the numerical study suggest that a critical applied shear stress (CASS) always exists which separates stable and unstable low angle boundary configurations. Varying particle size, interparticle spacing and density of dislocations in the boundary cause changes of the CASS that are systematically investigated. It is shown that the CASSs can considerably differ from the standard Orowan stress controlling the equilibrium of an isolated dislocation in a given microstructure. This result underlines the importance of long-range dislocation interactions that influence the high temperature strength of the precipitation-hardened alloys.

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11

NAKAYAMA, Munenori, and Yoji SHIBUTANI. "Dislocation Source Modeling and Interactions between Dislocations by three-dimensional Discrete Dislocation Model." Proceedings of Conference of Kansai Branch 2003.78 (2003): _7–9_—_7–10_. http://dx.doi.org/10.1299/jsmekansai.2003.78._7-9_.

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12

Bamney, Darshan, Aaron Tallman, Laurent Capolungo, and Douglas E. Spearot. "Virtual diffraction analysis of dislocations and dislocation networks in discrete dislocation dynamics simulations." Computational Materials Science 174 (March 2020): 109473. http://dx.doi.org/10.1016/j.commatsci.2019.109473.

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13

Gurrutxaga-Lerma, Beñat, Daniel S. Balint, Daniele Dini, Daniel E. Eakins, and Adrian P. Sutton. "A dynamic discrete dislocation plasticity method for the simulation of plastic relaxation under shock loading." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, no. 2156 (August 8, 2013): 20130141. http://dx.doi.org/10.1098/rspa.2013.0141.

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In this article, it is demonstrated that current methods of modelling plasticity as the collective motion of discrete dislocations, such as two-dimensional discrete dislocation plasticity (DDP), are unsuitable for the simulation of very high strain rate processes (10 6 s −1 or more) such as plastic relaxation during shock loading. Current DDP models treat dislocations quasi-statically, ignoring the time-dependent nature of the elastic fields of dislocations. It is shown that this assumption introduces unphysical artefacts into the system when simulating plasticity resulting from shock loading. This deficiency can be overcome only by formulating a fully time-dependent elastodynamic description of the elastic fields of discrete dislocations. Building on the work of Markenscoff & Clifton, the fundamental time-dependent solutions for the injection and non-uniform motion of straight edge dislocations are presented. The numerical implementation of these solutions for a single moving dislocation and for two annihilating dislocations in an infinite plane are presented. The application of these solutions in a two-dimensional model of time-dependent plasticity during shock loading is outlined here and will be presented in detail elsewhere.

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14

Mesarovic, Sinisa. "Plasticity of crystals and interfaces: From discrete dislocations to size-dependent continuum theory." Theoretical and Applied Mechanics 37, no. 4 (2010): 289–332. http://dx.doi.org/10.2298/tam1004289m.

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In this communication, we summarize the current advances in size-dependent continuum plasticity of crystals, specifically, the rate-independent (quasistatic) formulation, on the basis of dislocation mechanics. A particular emphasis is placed on relaxation of slip at interfaces. This unsolved problem is the current frontier of research in plasticity of crystalline materials. We outline a framework for further investigation, based on the developed theory for the bulk crystal. The bulk theory is based on the concept of geometrically necessary dislocations, specifically, on configurations where dislocations pile-up against interfaces. The average spacing of slip planes provides a characteristic length for the theory. The physical interpretation of the free energy includes the error in elastic interaction energies resulting from coarse representation of dislocation density fields. Continuum kinematics is determined by the fact that dislocation pile-ups have singular distribution, which allows us to represent the dense dislocation field at the boundary as a superdislocation, i.e., the jump in the slip filed. Associated with this jump is a slip-dependent interface energy, which in turn, makes this formulation suitable for analysis of interface relaxation mechanisms.

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15

Zhang, Ming Yi, Min Zhong, Shuai Yuan, Jing Song Bai, and Ping Li. "Influence of Initial Defects on the Mechanical Properties of Single Crystal Copper: Discrete Dislocation Dynamics Study." Materials Science Forum 913 (February 2018): 627–35. http://dx.doi.org/10.4028/www.scientific.net/msf.913.627.

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In this paper, three dimensional discrete dislocation dynamics method was used to quantitatively investigate the influence of initial defects on mechanical response of single crystal copper. Both the irradiation defects (interstitial loops) and random dislocation lines with different densities are considered. The simulation results demonstrate that the yield strength of single crystal copper is higher with higher initial dislocation density and higher interstitial loop density. Dislocation density increases quickly by nucleation and multiplication and microbands are formed during plastic deformation when only the random dislocation lines are initially considered. Characteristics of microbands show excellent agreement with experiment results. Dislocation multiplication is suppressed in the presence of interstitial loops, and junctions and locks between dislocations and interstitial loops are formed. Dislocation density evolution shows fluctuation accompanied with strain-stress curve fluctuation.

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16

Shao, Yu Fei, Xin Yang, Jiu Hui Li, and Xing Zhao. "Strain Fields around Dislocation Cores Studied by Analyzing Coordinates of Discrete Atoms." Materials Science Forum 817 (April 2015): 712–18. http://dx.doi.org/10.4028/www.scientific.net/msf.817.712.

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Dislocation core structures in Au and Cu crystals are investigated by means of quasicontinuum simulations combined with the embedded atom method potentials. A dislocation pair in a graphene sheet, which is observed by Warner et al. experimentally, is also analyzed in the present work. The strain fields around these dislocations in Au, Cu, and graphene crystals are calculated by analyzing the coordinates of discrete atoms, which is a strain tensor calculation method proposed by Zimmerman et al., and compared with theoretical predictions based on Foreman dislocation model. It is shown that the strain fields given by Zimmerman theory are completely suitable for describing the dislocation core structures of Au, Cu and graphene crystals. However, compared with the results of Au and Cu, the Zimmerman strain field in the vicinity of graphene dislocation core is a little less accurate, possibly due to the effect of lattice symmetry of graphene, which needs to be clarified in the future study.

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17

Hiratani, Masato, and Hussein M. Zbib. "Stochastic Dislocation Dynamics for Dislocation-Defects Interaction: A Multiscale Modeling Approach." Journal of Engineering Materials and Technology 124, no. 3 (June 10, 2002): 335–41. http://dx.doi.org/10.1115/1.1479693.

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A stochastic dislocation dynamics (SDD) model is developed to investigate dislocation glide through dispersed obstacles. The model accounts for: 1) the dynamics of the flight process between successive meta-stable dislocations under various drag mechanism using discrete dislocation dynamics, and 2) thermal activation processes for meta-stable pinned dislocations using a stochastic force. The integration of the two processes allows one to examine the transient regime of dislocation motion between obstacle-controlled motion and drag-controlled motion. Result pertaining to the stress-strain rate behavior in copper are obtained. The stress and temperature dependence of the average dislocation velocity show obstacle-controlled region below the critical resolved shear stress (CRSS) and drag controlled region above the CRSS, which is in good qualitative agreement with experimental data. In the transient region right below the CRSS, negative temperature sensitivity is observed due to the competition between the drag effects in dislocation flight process and thermal activation process.

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18

Homma, Hiroomi, and Huu Nhan Tran. "Crack Tip Plasticity By Classic Dislocation Dynamics." Advanced Materials Research 33-37 (March 2008): 97–102. http://dx.doi.org/10.4028/www.scientific.net/amr.33-37.97.

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Under very short pulse loads in range from 25 to 100 μs, crack tip plasticity a head of the crack tip in the mode I condition was investigated by discrete dislocation dynamics. The obtained dislocation array parameters such as the number of dislocations, dislocation distribution density, crack tip opening displacement and plastic zone size increase with the magnitude of stress intensity factor, KI and pulse durations. The numerical results were well compared with the experimental ones.

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19

Záležák, Tomáš, and Antonín Dlouhý. "3D Discrete Dislocation Dynamics Applied to a Motion of Low-Angle Tilt Boundaries." Key Engineering Materials 592-593 (November 2013): 87–91. http://dx.doi.org/10.4028/www.scientific.net/kem.592-593.87.

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This paper presents a 3D discrete dislocation dynamics (DDD) model describing dislocation processes in crystals subjected to loadings at high temperatures. Smooth dislocations are approximated by short straight segments. Every segment is acted upon by a Peach-Koehler force obtained by summing up forces from all dislocation segments and a force due to the applied stress. The model addresses interactions between individual dislocations and rigid precipitates. The model is applied to a migration of low angle tilt boundaries (LATBs) characterized by different initial dislocation density and constrained by precipitates of different sizes. The calculations showed that, for applied shear stresses σxzlower than a certain threshold σcrit.(h), the LATB is inhibited by the precipitate field. For σxzabove σcrit.(h), the LATB passes through the precipitate field. Some combinations of σxz and h lead to a decomposition of the LATB. The LATBs thus may evolve in three distinct modes depending on the initial microstructure. The threshold stress behaviour is known from creep tests of dispersion-strengthened NiCr alloys [1]. Furthermore, the critical stresses obtained from our calculations are below Orowan stresses for corresponding particle distribution. This behaviour has been also reported in creep experiments [1].

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20

Déprés, Christophe, Christian F. Robertson, Marc Fivel, and Suzanne Degallaix. "A Three Dimensional Discrete Dislocation Dynamics Analysis of Cyclic Straining in 316L Stainless Steel." Materials Science Forum 482 (April 2005): 163–66. http://dx.doi.org/10.4028/www.scientific.net/msf.482.163.

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The early stages of the formation of dislocation microstructures in low strain fatigue are analysed,using three-dimensional discrete dislocation dynamics modelling (DDD). A detailed analysis of the simulated microstructures provide a detailed scheme for the persistent slip band formation, emphasizing the crucial role of cross-slip for both the initial strain spreading inside of the grain and for the subsequent strain localization in the form of slip bands. A new ad-hoc posttreatment tool evaluates the surface roughness as the cycles proceed. Slip markings and their evolutions are analysed, in relation to the dislocation microstructure. This dislocation-based study emphasizes the separate contribution of plastic slip in damage nucleation. A simple 1D dislocation based model for work-hardening in crystal plasticity is proposed. In this model, the forest dislocations are responsible for friction stress (isotropic work-hardening), while dislocation pile-ups and dislocation trapped in Persistent Slip Bands (PSB) produce the back stress (kinematic workhardening). The model is consistent with the stress-strain curves obtained in DDD. It is also consistent with the stress-strain curves experimentally obtained for larger imposed strain amplitudes.

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21

Yashiro, K., M. Konishi, and Y. Tomita. "Discrete dislocation dynamics study on interaction between prismatic dislocation loop and interfacial network dislocations." Computational Materials Science 43, no. 3 (September 2008): 481–88. http://dx.doi.org/10.1016/j.commatsci.2007.12.015.

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22

liu, F. X., A. C. F. Cocks, and E. Tarleton. "Dislocation dynamics modelling of the creep behaviour of particle-strengthened materials." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477, no. 2250 (June 2021): 20210083. http://dx.doi.org/10.1098/rspa.2021.0083.

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Plastic deformation in crystalline materials occurs through dislocation slip and strengthening is achieved with obstacles that hinder the motion of dislocations. At relatively low temperatures, dislocations bypass the particles by Orowan looping, particle shearing, cross-slip or a combination of these mechanisms. At elevated temperatures, atomic diffusivity becomes appreciable, so that dislocations can bypass the particles by climb processes. Climb plays a crucial role in the long-term durability or creep resistance of many structural materials, particularly under extreme conditions of load, temperature and radiation. Here we systematically examine dislocation-particle interaction mechanisms. The analysis is based on three-dimensional discrete dislocation dynamics simulations incorporating impenetrable particles, elastic interactions, dislocation self-climb, cross-slip and glide. The core diffusion dominated dislocation self-climb process is modelled based on a variational principle for the evolution of microstructures, and is coupled with dislocation glide and cross-slip by an adaptive time-stepping scheme to bridge the time scale separation. The stress field caused by particles is implemented based on the particle–matrix mismatch. This model is helpful for understanding the fundamental particle bypass mechanisms and clarifying the effects of dislocation glide, climb and cross-slip on creep deformation.

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23

Hudson, Thomas, Patrick van Meurs, and Mark Peletier. "Atomistic origins of continuum dislocation dynamics." Mathematical Models and Methods in Applied Sciences 30, no. 13 (December 15, 2020): 2557–618. http://dx.doi.org/10.1142/s0218202520500505.

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This paper focuses on the connections between four stochastic and deterministic models for the motion of straight screw dislocations. Starting from a description of screw dislocation motion as interacting random walks on a lattice, we prove explicit estimates of the distance between solutions of this model, an SDE system for the dislocation positions, and two deterministic mean-field models describing the dislocation density. The proof of these estimates uses a collection of various techniques in analysis and probability theory, including a novel approach to establish propagation-of-chaos on a spatially discrete model. The estimates are non-asymptotic and explicit in terms of four parameters: the lattice spacing, the number of dislocations, the dislocation core size, and the temperature. This work is a first step in exploring this parameter space with the ultimate aim to connect and quantify the relationships between the many different dislocation models present in the literature.

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24

Jones, Reese E., Jonathan A. Zimmerman, and Giacomo Po. "Comparison of Dislocation Density Tensor Fields Derived from Discrete Dislocation Dynamics and Crystal Plasticity Simulations of Torsion." Journal of Materials Science Research 5, no. 4 (September 1, 2016): 44. http://dx.doi.org/10.5539/jmsr.v5n4p44.

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<p class="1Body">The importance of accurate simulation of the plastic deformation of ductile metals to the design of structures and components is well-known. Many techniques exist that address the length scales relevant to deformation processes, including dislocation dynamics (DD), which models the interaction and evolution of discrete dislocation line segments, and crystal plasticity (CP), which incorporates the crystalline nature and restricted motion of dislocations into a higher scale continuous field framework. While these two methods are conceptually related, there have been only nominal efforts focused on the system-level material response that use DD-generated information to enhance the fidelity of plasticity models. To ascertain to what degree the predictions of CP are consistent with those of DD, we compare their global and microstructural response in a number of deformation modes. After using nominally homogeneous compression and shear deformation dislocation dynamics simulations to calibrate crystal plasticity flow rule parameters, we compare not only the system-level stress-strain response of prismatic wires in torsion but also the resulting geometrically necessary dislocation density tensor fields. To establish a connection between explicit description of dislocations and the continuum assumed with crystal plasticity simulations, we ascertain the minimum length-scale at which meaningful dislocation density fields appear. Our results show that, for the case of torsion, the two material models can produce comparable spatial dislocation density distributions.</p>

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25

Davoudi, Kamyar M., Lucia Nicola, and Joost J. Vlassak. "Dislocation climb in two-dimensional discrete dislocation dynamics." Journal of Applied Physics 111, no. 10 (May 15, 2012): 103522. http://dx.doi.org/10.1063/1.4718432.

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26

Widjaja, Andreas, Erik Van der Giessen, Vikram S. Deshpande, and Alan Needleman. "Contact area and size effects in discrete dislocation modeling of wedge indentation." Journal of Materials Research 22, no. 3 (March 2007): 655–63. http://dx.doi.org/10.1557/jmr.2007.0090.

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Plane strain indentation of a single crystal by a rigid wedge is analyzed using discrete dislocation plasticity. We consider two wedge geometries having different sharpness, as specified by the half-angle of the indenter: α = 70° and 85°. The dislocations are all of edge character and modeled as line singularities in a linear elastic material. The crystal has initial sources and obstacles randomly distributed over three slip systems. The lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles, and dislocation annihilation are incorporated through a set of constitutive rules. Several definitions of the contact area (contact length in plane strain) are used to illustrate the sensitivity of the hardness value in the submicron indentation regime to the definition of contact area. The size dependence of the indentation hardness is found to be sensitive to the definition of contact area used and to depend on the wedge half-angle. For a relatively sharp indenter, with a half-angle of 70°, an indentation size effect is not obtained when the contact area is small and when the hardness is based on the actual contact length, while there does appear to be a size effect for some hardness values based on other measures of contact length.

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27

Fan, J. M., W. Y. Wang, Y. Y. Zhu, Q. Liu, S. Q. Chen, A. Godfrey, H. Q. Che, and X. X. Huang. "TEM observations of variation of dislocation cell structures along the building direction in SLM-316L stainless steel." Journal of Physics: Conference Series 2635, no. 1 (November 1, 2023): 012037. http://dx.doi.org/10.1088/1742-6596/2635/1/012037.

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Abstract Ultra-fast cooling and cyclic thermal heating associated with the additive manufacturing by selective laser melting (SLM) often lead to the formation of multi-scale microstructures in manufactured metallic materials. It has been frequently reported that a dislocation cell structure develops within the grains in SLM-316L stainless steels (ss), which has important effects on their mechanical properties and thermal stability. However, the formation mechanism of the dislocation cell structure is still under debate. In this study, we used transmission electron microscopy (TEM) techniques to characterize the variation of dislocation structures along the building direction in a SLM-316L ss sample. It exhibits various dislocation structures in the very surface melt pools. The distribution of dislocations at shallower locations is relatively discrete. While the dislocation cell structures are completely formed at deeper locations, which are similar to the bulk interior of the sample. The thermal cycle is not the main contribution to the formation of dislocation cell structures, but plays the role in enhancing the annihilation of dislocations inside the cells and sharpening the cell boundaries.

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28

Takahashi, Akiyuki, Akihiko Namiki, and Taiki Kogure. "CM-JP-6 A Discrete Dislocation Model for Polycrystal Plasticity." Proceedings of Mechanical Engineering Congress, Japan 2012 (2012): _CM—JP—6–1—_CM—JP—6–7. http://dx.doi.org/10.1299/jsmemecj.2012._cm-jp-6-1.

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29

O’Day, M. P., and W. A. Curtin. "A Superposition Framework for Discrete Dislocation Plasticity." Journal of Applied Mechanics 71, no. 6 (November 1, 2004): 805–15. http://dx.doi.org/10.1115/1.1794167.

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A superposition technique is introduced that allows for the application of discrete dislocation (DD) plasticity to a wide range of thermomechanical problems with reduced computational effort. Problems involving regions of differing elastic and/or plastic behavior are solved by superposing the solutions to i) DD models only for those regions of the structure where dislocation phenomena are permitted subject to either zero traction or displacement at every point on the boundary and ii) an elastic (EL) (or elastic/cohesive-zone) model of the entire structure subject to all desired loading and boundary conditions. The DD subproblem is solved with standard DD machinery for an elastically homogeneous material. The EL subproblem requires only a standard elastic or elastic/cohesive-zone finite element (FE) calculation. The subproblems are coupled: the negative of the tractions developed at the boundaries of the DD subproblem are applied as body forces in the EL subproblem, while the stress field of the EL subproblem contributes a driving force to the dislocations in the DD subproblem structure. This decomposition and the generic boundary conditions of the DD subproblem permit the DD machinery to be easily applied as a “black-box” constitutive material description in an otherwise elastic FE formulation and to be used in a broader scope of applications due to the overall enhanced computational efficiency. The method is validated against prior results for crack growth along a plastic/rigid bimaterial interface. Preliminary results for crack growth along a metal/ceramic bimaterial interface are presented.

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30

Deshpande, V. S., A. Needleman, and E. Van der Giessen. "Finite strain discrete dislocation plasticity." Journal of the Mechanics and Physics of Solids 51, no. 11-12 (November 2003): 2057–83. http://dx.doi.org/10.1016/j.jmps.2003.09.012.

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31

Ayas, C., J. A. W. van Dommelen, and V. S. Deshpande. "Climb-enabled discrete dislocation plasticity." Journal of the Mechanics and Physics of Solids 62 (January 2014): 113–36. http://dx.doi.org/10.1016/j.jmps.2013.09.019.

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32

Keralavarma, S. M., and A. A. Benzerga. "High-temperature discrete dislocation plasticity." Journal of the Mechanics and Physics of Solids 82 (September 2015): 1–22. http://dx.doi.org/10.1016/j.jmps.2015.05.003.

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33

Akhondzadeh, Sh, R. B. Sills, S. Papanikolaou, E. Van der Giessen, and W. Cai. "Geometrically projected discrete dislocation dynamics." Modelling and Simulation in Materials Science and Engineering 26, no. 6 (July 20, 2018): 065011. http://dx.doi.org/10.1088/1361-651x/aacf31.

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34

Kreuzer, H. G. M., and R. Pippan. "Discrete dislocation simulation of nanoindentation." Computational Mechanics 33, no. 4 (March 1, 2004): 292–98. http://dx.doi.org/10.1007/s00466-003-0531-3.

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35

Fan, Hai Dong, Qing Yuan Wang, and Muhammad Kashif Khan. "Cyclic Bending Response of Single- and Polycrystalline Thin Films: Two Dimensional Discrete Dislocation Dynamics." Applied Mechanics and Materials 275-277 (January 2013): 132–37. http://dx.doi.org/10.4028/www.scientific.net/amm.275-277.132.

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The bending behavior of single- and polycrystalline thin films is modeled by two-dimensional discrete dislocation dynamics (DDD) to study the cyclic bending response. In the polycrystalline films, grain boundaries (GBs) are simulated with a penetrable dislocation-GB interaction model. Our results reveal that the single- and polycrystalline thin films under pure bending exhibit strong Bauschinger effect but no cyclic hardening or softening. Furthermore, the uploading response of each cycle can be divided into three stages, which are associated with the glide, annihilation and nucleation of dislocations, respectively.

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36

Irani, Nilgoon, Yaswanth Murugesan, Can Ayas, and Lucia Nicola. "Effect of dislocation core fields on discrete dislocation plasticity." Mechanics of Materials 165 (February 2022): 104137. http://dx.doi.org/10.1016/j.mechmat.2021.104137.

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37

Zheng, Zebang, Nikoletta G. Prastiti, Daniel S. Balint, and Fionn P. E. Dunne. "The dislocation configurational energy density in discrete dislocation plasticity." Journal of the Mechanics and Physics of Solids 129 (August 2019): 39–60. http://dx.doi.org/10.1016/j.jmps.2019.04.015.

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38

Gagel, J., D. Weygand, and P. Gumbsch. "Discrete Dislocation Dynamics simulations of dislocation transport during sliding." Acta Materialia 156 (September 2018): 215–27. http://dx.doi.org/10.1016/j.actamat.2018.06.002.

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39

Adlakha, Ilaksh, Kuntimaddi Sadananda, and Kiran N. Solanki. "Discrete dislocation modeling of stress corrosion cracking in an iron." Corrosion Reviews 33, no. 6 (November 1, 2015): 467–75. http://dx.doi.org/10.1515/corrrev-2015-0068.

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AbstractMaterial strengthening and embrittlement are controlled by interactions between dislocations and hydrogen that alter the observed deformation mechanisms. In this work, we used an energetics approach to differentiate two fundamental stress corrosion mechanisms in iron, namely, hydrogen-enhanced localized plasticity and hydrogen-enhanced decohesion. Considering the small-scale yielding condition, we use a discrete dislocation framework with line dislocations to simulate the crack-tip plastic behavior. The crack growth was modeled using the change in surface energies (cohesive zone laws) due to hydrogen segregation. The changes in the surface energies as a function of hydrogen concentration are computed using atomistic simulations. Results indicate that, when hydrogen concentrations are low, crack growth occurs by alternating mechanisms of cleavage and slip. However, as the hydrogen concentrations increased above some critical value, the crack grows predominately by the cleavage-based decohesion process.

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40

Shiari, Behrouz, Ronald E. Miller, and William A. Curtin. "Coupled Atomistic/Discrete Dislocation Simulations of Nanoindentation at Finite Temperature." Journal of Engineering Materials and Technology 127, no. 4 (January 25, 2005): 358–68. http://dx.doi.org/10.1115/1.1924561.

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Simulations of nanoindentation in single crystals are performed using a finite temperature coupled atomistic/continuum discrete dislocation (CADD) method. This computational method for multiscale modeling of plasticity has the ability of treating dislocations as either atomistic or continuum entities within a single computational framework. The finite-temperature approach here inserts a Nose-Hoover thermostat to control the instantaneous fluctuations of temperature inside the atomistic region during the indentation process. The method of thermostatting the atomistic region has a significant role on mitigating the reflected waves from the atomistic/continuum boundary and preventing the region beneath the indenter from overheating. The method captures, at the same time, the atomistic mechanisms and the long-range dislocation effects without the computational cost of full atomistic simulations. The effects of several process variables are investigated, including system temperature and rate of indentation. Results and the deformation mechanisms that occur during a series of indentation simulations are discussed.

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41

VAN MEURS, P., A. MUNTEAN, and M. A. PELETIER. "Upscaling of dislocation walls in finite domains." European Journal of Applied Mathematics 25, no. 6 (August 28, 2014): 749–81. http://dx.doi.org/10.1017/s0956792514000254.

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We wish to understand the macroscopic plastic behaviour of metals by upscaling the micro-mechanics of dislocations. We consider a highly simplified dislocation network, which allows our discrete model to be a one dimensional particle system, in which the interactions between the particles (dislocation walls) are singular and non-local. As a first step towards treating realistic geometries, we focus on finite-size effects rather than considering an infinite domain as typically discussed in the literature. We derive effective equations for the dislocation density by means of Γ-convergence on the space of probability measures. Our analysis yields a classification of macroscopic models, in which the size of the domain plays a key role.

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42

Ebrahimi, Alireza, and Thomas Hochrainer. "Three-Dimensional Continuum Dislocation Dynamics Simulations of Dislocation Structure Evolution in Bending of a Micro-Beam." MRS Advances 1, no. 24 (2016): 1791–96. http://dx.doi.org/10.1557/adv.2016.75.

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ABSTRACTA persistent challenge in multi-scale modeling of materials is the prediction of plastic materials behavior based on the evolution of the dislocation state. An important step towards a dislocation based continuum description was recently achieved with the so called continuum dislocation dynamics (CDD). CDD captures the kinematics of moving curved dislocations in flux-type evolution equations for dislocation density variables, coupled to the stress field via average dislocation velocity-laws based on the Peach-Koehler force. The lowest order closure of CDD employs three internal variables per slip system, namely the total dislocation density, the classical dislocation density tensor and a so called curvature density.In the current work we present a three-dimensional implementation of the lowest order CDD theory as a materials sub-routine for Abaqus®in conjunction with the crystal plasticity framework DAMASK. We simulate bending of a micro-beam and qualitatively compare the plastic shear and the dislocation distribution on a given slip system to results from the literature. The CDD simulations reproduce a zone of reduced plastic shear close to the surfaces and dislocation pile-ups towards the center of the beam, which have been similarly observed in discrete dislocation simulations.

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43

Gao, Siwen, Zerong Yang, Maximilian Grabowski, Jutta Rogal, Ralf Drautz, and Alexander Hartmaier. "Influence of Excess Volumes Induced by Re and W on Dislocation Motion and Creep in Ni-Base Single Crystal Superalloys: A 3D Discrete Dislocation Dynamics Study." Metals 9, no. 6 (June 1, 2019): 637. http://dx.doi.org/10.3390/met9060637.

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A comprehensive 3D discrete dislocation dynamics model for Ni-base single crystal superalloys was used to investigate the influence of excess volumes induced by solute atoms Re and W on dislocation motion and creep under different tensile loads at 850 ° C. The solute atoms were distributed homogeneously only in γ matrix channels. Their excess volumes due to the size difference from the host Ni were calculated by density functional theory. The excess volume affected dislocation glide more strongly than dislocation climb. The relative positions of dislocations and solute atoms determined the magnitude of back stresses on the dislocation motion. Without diffusion of solute atoms, it was found that W with a larger excess volume had a stronger strengthening effect than Re. With increasing concentration of solute atoms, the creep resistance increased. However, a low external stress reduced the influence of different excess volumes and different concentrations on creep.

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44

Kreuzer, H. G. M., and R. Pippan. "Discrete dislocation simulation of nanoindentation: The effect of statistically distributed dislocations." Materials Science and Engineering: A 400-401 (July 2005): 460–62. http://dx.doi.org/10.1016/j.msea.2005.01.065.

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45

Katiyar, T., and E. Van der Giessen. "Effective mobility of BCC dislocations in two-dimensional discrete dislocation plasticity." Computational Materials Science 187 (February 2021): 110129. http://dx.doi.org/10.1016/j.commatsci.2020.110129.

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46

Mordehai, Dan, Emmanuel Clouet, Marc Fivel, and Marc Verdier. "Introducing dislocation climb by bulk diffusion in discrete dislocation dynamics." Philosophical Magazine 88, no. 6 (February 21, 2008): 899–925. http://dx.doi.org/10.1080/14786430801992850.

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47

Srivastava, K., R. Gröger, D. Weygand, and P. Gumbsch. "Dislocation motion in tungsten: Atomistic input to discrete dislocation simulations." International Journal of Plasticity 47 (August 2013): 126–42. http://dx.doi.org/10.1016/j.ijplas.2013.01.014.

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48

Mastorakos, I. N., and H. M. Zbib. "Dislocation-cracks interaction during fatigue: A discrete dislocation dynamics simulation." JOM 60, no. 4 (April 2008): 59–63. http://dx.doi.org/10.1007/s11837-008-0051-x.

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49

Graham, J. T., A. D. Rollett, and R. LeSar. "Fast Fourier transform discrete dislocation dynamics." Modelling and Simulation in Materials Science and Engineering 24, no. 8 (October 13, 2016): 085005. http://dx.doi.org/10.1088/0965-0393/24/8/085005.

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50

Widjaja, Andreas, Erik Van der Giessen, and Alan Needleman. "Discrete dislocation modelling of submicron indentation." Materials Science and Engineering: A 400-401 (July 2005): 456–59. http://dx.doi.org/10.1016/j.msea.2005.01.074.

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