Articles de revues : « Dislocation Dynamics Simulations »

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Mani Krishna, Karri V., et Prita Pant. « Dislocation Dynamics Simulations ». Materials Science Forum 736 (décembre 2012) : 13–20. http://dx.doi.org/10.4028/www.scientific.net/msf.736.13.

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Dislocation Dynamics (DD) simulations are used to study the evolution of a pre-specified dislocation structure under applied stresses and imposed boundary conditions. These simulations can handle realistic dislocation densities ranging from 1010 to 1014 m-2, and hence can be used to model plastic deformation and strain hardening in metals. In this paper we introduce the basic concepts of DD simulations and then present results from simulations in thin copper films and in bulk zirconium. In both cases, the effect of orientation on deformation behaviour is investigated. For the thin film simulations, rigid boundary conditions are used at film-substrate and film-passivation interfaces leading to dislocation accumulation, while periodic boundaries are used for bulk grains of Zr. We show that there is a clear correlation between strain hardening rate and the rate of increase of dislocation density.

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Demir, I., et A. N. Gulluoglu. « Dislocation Dynamics Simulations in the Presence of Interacting Cracks ». Journal of Engineering Materials and Technology 121, n^o 2 (1 avril 1999) : 151–55. http://dx.doi.org/10.1115/1.2812360.

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For an understanding failure behavior of crystalline solids, considerable interest is given to investigating interaction effects between the main crack and microcracks in the presence of mobile dislocations. Accurate analysis of these types of interaction problems may lead to accurate models for failure prevention and the history of plastic zone development. High stress concentration areas such as crack tips are the places where dislocations are subjected to higher forces. Therefore, a computer simulation technique based on dislocation dynamics has been developed to investigate the movement of dislocations in the presence of multiple cracks. Dislocation structures, dislocation distribution and strain rate results are presented as functions of applied stresses for different microcrack positions and orientations. Simulation results give a reasonable description of dislocation pattern development during deformation around the cracks and explain the shape and development of the plastic zone.

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YANG, XIYUAN. « THE MOBILITY OF THE EDGE DISLOCATION IN METAL : A MOLECULAR DYNAMICS SIMULATION ». International Journal of Modern Physics B 25, n^o 25 (10 octobre 2011) : 3315–24. http://dx.doi.org/10.1142/s021797921110103x.

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In this paper, we use molecular dynamics (MD) simulations and a modified analytic embedded-atom method to investigate the edge dislocation movement without imposed strain at 0 K. The obtained results indicate that the straight lines of the partial dislocations always preserve their original shapes and are parallel to each other during the simulation process. According to the energy of each atom, the positions of both partial dislocation cores are determined. Then the velocities in the period of the relaxation process are investigated in detail. The MD simulations reveal that the MD relaxation time dependence of the edge dislocation mobility is divided into two parts. First, during the initial period ranging from 0 to 6 ps, the relative velocity of the dislocation movement lineally increases with the incremental relaxation time. Second, in the latter period from 6 ps to the end of the simulated process the velocity decreases exponentially as the MD simulation time evolves.

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Derlet, P. M., P. Gumbsch, R. Hoagland, J. Li, D. L. McDowell, H. Van Swygenhoven et J. Wang. « Atomistic Simulations of Dislocations in Confined Volumes ». MRS Bulletin 34, n^o 3 (mars 2009) : 184–89. http://dx.doi.org/10.1557/mrs2009.50.

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AbstractInternal microstructural length scales play a fundamental role in the strength and ductility of a material. Grain boundaries in nanocrystalline structures and heterointerfaces in nanolaminates can restrict dislocation propagation and also act as a source for new dislocations, thereby affecting the detailed dynamics of dislocation-mediated plasticity. Atomistic simulation has played an important and complementary role to experiment in elucidating the nature of the dislocation/interface interaction, demonstrating a diversity of atomic-scale processes covering dislocation nucleation, propagation, absorption, and transmission at interfaces. This article reviews some atomistic simulation work that has made progress in this field and discusses possible strategies in overcoming the inherent time scale challenge of finite temperature molecular dynamics.

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Deng, Jie, et Anter El-Azab. « Dislocation pair correlations from dislocation dynamics simulations ». Journal of Computer-Aided Materials Design 14, S1 (décembre 2007) : 295–307. http://dx.doi.org/10.1007/s10820-008-9090-4.

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Roy, Shyamal, Sönke Wille, Dan Mordehai et Cynthia A. Volkert. « Investigating Nanoscale Contact Using AFM-Based Indentation and Molecular Dynamics Simulations ». Metals 12, n^o 3 (14 mars 2022) : 489. http://dx.doi.org/10.3390/met12030489.

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In this work we study nanocontact plasticity in Au thin films using an atomic force microscope based indentation method with the goal of relating the changes in surface morphology to the dislocations created by deformation. This provides a rigorous test of our understanding of deformation and dislocation mechanisms in small volumes. A series of indentation experiments with increasing maximum load was performed. Distinct elastic and plastic regimes were identified in the force-displacement curves, and the corresponding residual imprints were measured. Transmission electron microscope based measured dislocation densities appear to be smaller than the densities expected from the measured residual indents. With the help of molecular dynamics simulations we show that dislocation nucleation and glide alone fail to explain the low dislocation density. Increasing the temperature of the simulations accelerates the rate of thermally activated processes and promotes motion and annihilation of dislocations under the indent while transferring material to the upper surface; dislocation density decreases in the plastic zone and material piles up around the indent. Finally, we discuss why a significant number of cross-slip events is expected beneath the indent under experimental conditions and the implications of this for work hardening during wear.

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J. Chavez, Jose, Xiao W. Zhou, Sergio F. Almeida, Rodolfo Aguirre et David Zubia. « Molecular Dynamics Simulations of CdTe / CdS Heteroepitaxy - Effect of Substrate Orientation ». Journal of Materials Science Research 5, n^o 3 (7 avril 2016) : 1. http://dx.doi.org/10.5539/jmsr.v5n3p1.

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<p class="1Body">Molecular dynamics simulations were used to catalogue atomic scale structures of CdTe films grown on eight wurtzite (wz) and zinc-blende (zb) CdS surfaces. Polytypism, grain boundaries, dislocations and other film defects were detected. Dislocation lines were distributed in three distinct ways. For the growths on the wz {0001} and zb {111} surfaces, dislocations were found throughout the epilayers and formed a network at the interface. The dislocations within the films grown on the wz {1100}, wz {1120}, zb {110}, zb {010}, and zb {1/10 1 1/10} surfaces formed an interface network and also threaded from the interface towards the film’s surface. In contrast, the growth on the zb {112} surface only had dislocations localized to the interface. This film exhibited a different orientation from the substrate to reduce the lattice mismatch strain energies, and therefore, its misfit dislocation density. Our study indicates that the substrate orientation could be utilized to modify the morphology of dislocation networks in lattice mismatched multi-layered systems.</p>

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Godiksen, Rasmus B., Zachary T. Trautt, Moneesh Upmanyu, Søren Schmidt et Dorte Juul Jensen. « Simulation of Recrystallization Using Molecular Dynamics ; Effects of the Interatomic Potential ». Materials Science Forum 558-559 (octobre 2007) : 1081–86. http://dx.doi.org/10.4028/www.scientific.net/msf.558-559.1081.

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Recrystallization is governed by the migration of high angle grain boundaries traveling through a deformed material driven by the excess energy located primarily in dislocation structures. A method for investigating the interaction between a migrating grain boundary and dislocation boundaries using molecular dynamics (MD) was recently developed. During simulations migrating high angle grain boundaries interact with dislocation boundaries, and individual dislocations from the dislocation boundaries are absorbed into the grain boundaries. Results obtained previously, using a simple Lennard-Jones (LJ) potential, showed surprisingly irregular grain boundary migration compared to simulations of grain boundary migration applying other types of driving forces. Inhomogeneous boundary-dislocation interactions were also observed in which the grain boundaries locally acquired significant cusps during dislocation absorption events. The study presented here makes comparisons between simulations performed using a LJ- and an embedded atom method (EAM) aluminum potential. The results show similarities which indicate that it is the crystallographic features rather than the atomic interactions that determine the details of the migration process.

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Liu, Jianbin, et Shinji Muraishi. « Dislocation Dynamics Simulations of Dislocation-Particle Bypass Mechanisms ». Materials Science Forum 985 (avril 2020) : 35–41. http://dx.doi.org/10.4028/www.scientific.net/msf.985.35.

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Effect of precipitation strengthening on metal is generally attributed to the dislocation interaction with the precipitate which acts as the barrier to the dislocation motion on the slip plane. In order to achieve better understanding of critical events of dislocation motion and evolution of dislocation microstructure, we have developed numerical simulation method of dislocation-dislocation and dislocation-particle interactions by means of discrete dislocation dynamics at mesoscopic scale. In this work, Green’s function method is utilized for the computation of the stress fields of dislocation and misfitting particle, and the interaction forces acting on the dislocation. We also proposed the efficient algorithm of the connectivity vector for the dislocation line elements, linked-list data structure, to deal with the flexible interaction of dislocation line elements. The geometrical effect of dislocation slip planes on the dislocation bypassing behaviors is tested by changing the relative height of dislocation slip plane against the center plane of spherical particle, where cross slip event is also taken into account for the dislocation motion. Simulation results show a wide variety of topological changes of dislocation during motion on the slip planes around the particle, which results from the stress field of the particle varied with the relative height between the dislocation slip plane and center plane of particle. The full analysis of the mechanisms of dislocation line bypassing misfitting particle has been explained in this study.

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Jones, Reese E., Jonathan A. Zimmerman et 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, n^o 4 (1 septembre 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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Burbery, N. B., G. Po, R. Das, N. Ghoniem et W. G. Ferguson. « Dislocation dynamics in polycrystals with atomistic-informed mechanisms of dislocation - grain boundary interactions ». Journal of Micromechanics and Molecular Physics 02, n^o 01 (mars 2017) : 1750003. http://dx.doi.org/10.1142/s2424913017500035.

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In polycrystalline materials, dislocations can interact with grain boundaries (GBS) through a number of mechanisms including dislocation absorption, pile-up formation, dissociation reactions within the GB plane and (possibly) dislocation nucleation from the interface itself. The effects of dislocation pile-ups contribute significantly to the mechanical behavior of polycrystalline materials by creating back-stresses that inactivate the primary slip systems in the vicinity of the interface, corresponding with the celebrated Hall–Petch relationship between size and strength. However, dislocation pile-ups cannot be contained within the small grain sizes that can be accommodated by molecular dynamics simulations, which to-date remain the primary computational method used to study the discrete structure of GBs. Dislocation dynamics (DD) simulations are a promising framework for computational modeling that are used to provide insights about phenomena that can only be explained from the intermediate scale between atomistic and macro scales. However, a robust framework for modeling dislocation interactions with internal microstructure such as grain boundaries (GBs) has yet to be achieved for 3D models of DD. Furthermore, this is the first implementation which explicitly includes the dislocation content of the interface. The framework described in this paper is effective for studying GB-dislocation interactions (including inter-granular effects) and the approach for partitioning the DD simulation domain. To achieve a robust method to differentiate between crystal regions, the present framework utilizes a mesh-based partitioning system. Within each grain, slip systems are determined by the grain orientation. The versatile construction described, allows modeling of an arbitrary crystallography, size and grain geometry. Extrinsic dislocations that intersect the interface are constrained to glide on the line of intersection between the glide plane and GB plane. Atomistically informed criteria for slip transmission are implemented, based on the geometrically optimal outgoing glide plane which shares a common line of intersection on the GB plane. Slip transmission is only initiated when the resolved shear stress in one of the compatible outgoing slip directions exceeds an approximate threshold resolved shear stress, which is based on observations made with molecular dynamics studies. The primary aim of the present study was to establish a sufficiently ‘generic’ framework to enable the modelling of various GB structures, polycrystal geometries and crystallographic orientations. The framework described in the present work provides a means to study multi-grain deformation processes governed by dislocations pile-ups at GBs, in detail beyond feasible limits of experiments or atomistic simulation approaches.

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Mordehai, Dan, Emmanuel Clouet, Marc Fivel et Marc Verdier. « Annealing of dislocation loops in dislocation dynamics simulations ». IOP Conference Series : Materials Science and Engineering 3 (1 juillet 2009) : 012001. http://dx.doi.org/10.1088/1757-899x/3/1/012001.

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Swaminarayan, S., R. LeSar, P. Lomdahl et D. Beazley. « Short-range dislocation interactions using molecular dynamics : Annihilation of screw dislocations ». Journal of Materials Research 13, n^o 12 (décembre 1998) : 3478–84. http://dx.doi.org/10.1557/jmr.1998.0475.

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We present results of a large-scale atomistic study of the annihilation of oppositely signed screw dislocations in an fcc metal using molecular dynamics (MD) and an Embedded-Atom-Method (EAM) potential for Cu. The mechanisms of the annihilation process are studied in detail. From the simulation results, we determined the interaction energy between the dislocations as a function of separation. These results are compared with predictions from linear elasticity to examine the onset of non-linear-elastic interactions. The applicability of heuristic models for annihilation of dislocations in large-scale dislocation dynamics simulations is discussed in the light of these results.

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Sarikov, Andrey, Anna Marzegalli, Luca Barbisan, Francesco Montalenti et Leo Miglio. « Structure and Stability of Partial Dislocation Complexes in 3C-SiC by Molecular Dynamics Simulations ». Materials 12, n^o 18 (18 septembre 2019) : 3027. http://dx.doi.org/10.3390/ma12183027.

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In this work, the structure and stability of partial dislocation (PD) complexes terminating double and triple stacking faults in 3C-SiC are studied by molecular dynamics simulations. The stability of PD complexes is demonstrated to depend primarily on the mutual orientations of the Burgers vectors of constituent partial dislocations. The existence of stable complexes consisting of two and three partial dislocations is established. In particular, two types of stable double (or extrinsic) dislocation complexes are revealed formed by two 30° partial dislocations with different orientations of Burgers vectors, or 30° and 90° partial dislocations. Stable triple PD complexes consist of two 30° partial dislocations with different orientations of their Burgers vectors and one 90° partial dislocation, and have a total Burgers vector that is equal to zero. Results of the simulations agree with experimental observations of the stable PD complexes forming incoherent boundaries of twin regions and polytype inclusions in 3C-SiC films.

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

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liu, F. X., A. C. F. Cocks et 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, n^o 2250 (juin 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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Tanaka, Masaki, Kenji Higashida et Tomotsugu Shimokawa. « The Effect of Severe Plastic Deformation on the Brittle-Ductile Transition in Low Carbon Steel ». Materials Science Forum 633-634 (novembre 2009) : 471–80. http://dx.doi.org/10.4028/www.scientific.net/msf.633-634.471.

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Brittle-ductile transition (BDT) behaviour was investigated in low carbon steel deformed by an accumulative roll-bonding (ARB) process. The temperature dependence of its fracture toughness was measured by conducting four-point bending tests at various temperatures and strain rates. The fracture toughness increased while the BDT temperature decreased in the specimens deformed by the ARB process. Arrhenius plots between the BDT temperatures and the strain rates indicated that the activation energy for the controlling process of the BDT was not changed by the deformation with the ARB process. It was deduced that the decrease in the BDT temperature by grain refining was not due to the increase in the dislocation mobility controlled by short-range barriers. Quasi-three-dimensional simulations of dislocation dynamics, taking into account of crack tip shielding due to dislocations, were performed to investigate the effect of a dislocation source spacing along a crack front on the BDT. The simulation indicated that the BDT temperature is decreased with decreasing in the dislocation source spacing. Molecular dynamics simulations revealed that moving dislocations were impinged against grain boundaries and were reemitted from there with increasing strain. It indicates that grain boundaries can be new sources in ultra-fine grained materials, which increases toughness at low temperatures.

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Shimokawa, Tomotsugu, Toshiyasu Kinari et Sukenori Shintaku. « Atomic Simulations on the Grain Subdivision of a Crystalline Metal ». Materials Science Forum 561-565 (octobre 2007) : 1983–86. http://dx.doi.org/10.4028/www.scientific.net/msf.561-565.1983.

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The relationship between grain subdivision mechanisms of a crystalline metal and the strain gradient under severe plastic deformation is studied by using molecular dynamics simulations in quasi two dimensions. Two problems are simulated for single crystal models: (a) uniaxial tensile and compressive deformation and (b) localized shear deformation. In the case of uniaxial deformation, a large number of dislocation pairs with opposite Burgers vectors are generated under deformation, but most dislocations are vanished due to pair annihilation under relaxation. Therefore, no dislocation boundary can be formed. On the other hand, in case of localized shear deformation with large strain gradient, dislocation boundaries are formed between undeformed and deformed regions. These dislocations can be regarded as geometrically necessary dislocations. Consequently, the importance of the strain gradient to make grain boundaries under plastic deformation can be confirmed by atomic simulations.

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Stricker, Markus, Michael Ziemann, Mario Walter, Sabine M. Weygand, Patric Gruber et 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, n^o 3 (8 février 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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Gagel, J., D. Weygand et P. Gumbsch. « Discrete Dislocation Dynamics simulations of dislocation transport during sliding ». Acta Materialia 156 (septembre 2018) : 215–27. http://dx.doi.org/10.1016/j.actamat.2018.06.002.

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Siu, K. W., et A. H. W. Ngan. « Understanding acoustoplasticity through dislocation dynamics simulations ». Philosophical Magazine 91, n^o 34 (décembre 2011) : 4367–87. http://dx.doi.org/10.1080/14786435.2011.606237.

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Cai, Wei, et Vasily V. Bulatov. « Mobility laws in dislocation dynamics simulations ». Materials Science and Engineering : A 387-389 (décembre 2004) : 277–81. http://dx.doi.org/10.1016/j.msea.2003.12.085.

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Weinberger, Christopher R., Sylvie Aubry, Seok-Woo Lee et Wei Cai. « Dislocation dynamics simulations in a cylinder ». IOP Conference Series : Materials Science and Engineering 3 (1 juillet 2009) : 012007. http://dx.doi.org/10.1088/1757-899x/3/1/012007.

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Ebrahimi, Alireza, et Thomas Hochrainer. « Three-Dimensional Continuum Dislocation Dynamics Simulations of Dislocation Structure Evolution in Bending of a Micro-Beam ». MRS Advances 1, n^o 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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Zheng, Yong-Gang, Yi-Fei Fu, Hong-Wu Zhang et Hong-Fei Ye. « Atomistic investigations of tensile and shear mechanical properties of nanotwinned copper with embedded defects ». International Journal of Computational Materials Science and Engineering 03, n^o 02 (juin 2014) : 1450012. http://dx.doi.org/10.1142/s2047684114500122.

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The tensile and shear mechanical properties of nanotwinned copper with embedded defects have been investigated by using molecular dynamics simulations. Simulation results show that the stress concentration at the tips of crack-like defects dominates the first partial dislocation nucleation at the onset of plastic deformation, the joint action of twin boundaries and dislocations controls the yield stress at the earlier plastic deformation stage and the dislocation/twin boundary–dislocation interactions determine the plastic flow stage. Furthermore, it is found that the yield stress decreases nonlinearly with the increase of the crack length, while it decreases almost linearly with the increase of the temperature.

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Wang, Haoxiang, Shang Gao, Renke Kang, Xiaoguang Guo et Honggang Li. « Mechanical Load-Induced Atomic-Scale Deformation Evolution and Mechanism of SiC Polytypes Using Molecular Dynamics Simulation ». Nanomaterials 12, n^o 14 (20 juillet 2022) : 2489. http://dx.doi.org/10.3390/nano12142489.

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Silicon carbide (SiC) is a promising semiconductor material for making high-performance power electronics with higher withstand voltage and lower loss. The development of cost-effective machining technology for fabricating SiC wafers requires a complete understanding of the deformation and removal mechanism. In this study, molecular dynamics (MD) simulations were carried out to investigate the origins of the differences in elastic–plastic deformation characteristics of the SiC polytypes, including 3C-SiC, 4H-SiC and 6H-SiC, during nanoindentation. The atomic structures, pair correlation function and dislocation distribution during nanoindentation were extracted and analyzed. The main factors that cause elastic–plastic deformation have been revealed. The simulation results show that the deformation mechanisms of SiC polytypes are all dominated by amorphous phase transformation and dislocation behaviors. Most of the amorphous atoms recovered after completed unload. Dislocation analysis shows that the dislocations of 3C-SiC are mainly perfect dislocations during loading, while the perfect dislocations in 4H-SiC and 6H-SiC are relatively few. In addition, 4H-SiC also formed two types of stacking faults.

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Yang, Yang, Xiangdong Ding, Jun Sun et Ekhard K. H. Salje. « Twisting of a Pristine α-Fe Nanowire : From Wild Dislocation Avalanches to Mild Local Amorphization ». Nanomaterials 11, n^o 6 (18 juin 2021) : 1602. http://dx.doi.org/10.3390/nano11061602.

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The torsion of pristine α-Fe nanowires was studied by molecular dynamics simulations. Torsion-induced plastic deformation in pristine nanowires is divided into two regimes. Under weak torsion, plastic deformation leads to dislocation nucleation and propagation. Twisting-induced dislocations are mainly 12<111> screw dislocations in a <112>-oriented nanowire. The nucleation and propagation of these dislocations were found to form avalanches which generate the emission of energy jerks. Their probability distribution function (PDF) showed power laws with mixing between different energy exponents. The mixing stemmed from simultaneous axial and radial dislocation movements. The power-law distribution indicated strongly correlated ‘wild’ dislocation dynamics. At the end of this regime, the dislocation pattern was frozen, and further twisting of the nanowire did not change the dislocation pattern. Instead, it induced local amorphization at the grip points at the ends of the sample. This “melting” generated highly dampened, mild avalanches. We compared the deformation mechanisms of twinned and pristine α-Fe nanowires under torsion.

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Tian, Xia, Kaipeng Ma, Guangyu Ji, Junzhi Cui, Yi Liao et Meizhen Xiang. « Anisotropic shock responses of nanoporous Al by molecular dynamics simulations ». PLOS ONE 16, n^o 3 (17 mars 2021) : e0247172. http://dx.doi.org/10.1371/journal.pone.0247172.

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Mechanical responses of nanoporous aluminum samples under shock in different crystallographic orientations (<100>, <111>, <110>, <112> and <130>) are investigated by molecular dynamics simulations. The shape evolution of void during collapse is found to have no relationship with the shock orientation. Void collapse rate and dislocation activities at the void surface are found to strongly dependent on the shock orientation. For a relatively weaker shock, void collapses fastest when shocked along the <100> orientation; while for a relatively stronger shock, void collapses fastest in the <110> orientation. The dislocation nucleation position is strongly depended on the impacting crystallographic orientation. A theory based on resolved shear stress is used to explain which slip planes the earliest-appearing dislocations prefer to nucleate on under different shock orientations.

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ROBLES, MIGUEL, VILLE MUSTONEN et KIMMO KASKI. « MOLECULAR DYNAMIC STUDY OF A SINGLE DISLOCATION IN A TWO-DIMENSIONAL LENNARD–JONES SYSTEM ». International Journal of Modern Physics C 14, n^o 04 (mai 2003) : 407–21. http://dx.doi.org/10.1142/s0129183103004620.

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In this work the motion of a single dislocation in a two-dimensional triangular lattice is studied by using classical Molecular Dynamics method with the Lennard–Jones inter-atomic potential. The dislocation motion is investigated with an interactive simulation program developed to track automatically the movement of lattice defects. Constant strain and constant strain-rate deformations were applied to the system. From constant strain simulations a curve of shear stress versus dislocation velocity is obtained, showing a nonlinear power law relation. An equation of motion for the dislocation is proposed and found to be applicable when the movement of dislocation follows a quasi-static process. Numerical simulations at different strain rates show an elastic-to-plastic transition that modifies the dynamics of the dislocation motion.

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Li, Xiaoyan, et Wei Yang. « Size Dependence of Dislocation-Mediated Plasticity in Ni Single Crystals : Molecular Dynamics Simulations ». Journal of Nanomaterials 2009 (2009) : 1–10. http://dx.doi.org/10.1155/2009/245941.

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We investigate the compressive yielding of Ni single crystals by performing atomistic simulations with the sample diameters in the range of 5 nm ∼ 40 nm. Remarkable effects of sample sizes on the yield strength are observed in the nanopillars with two different orientations. The deformation mechanisms are characterized by massive dislocation activities within a single slip system and a nanoscale deformation twining in an octal slip system. A dislocation dynamics-based model is proposed to interpret the size and temperature effects in single slip-oriented nanopillars by considering the nucleation of incipient dislocations.

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Shen, Yixi, et Douglas E. Spearot. « Mobility of dislocations in FeNiCrCoCu high entropy alloys ». Modelling and Simulation in Materials Science and Engineering 29, n^o 8 (15 novembre 2021) : 085017. http://dx.doi.org/10.1088/1361-651x/ac336a.

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Abstract Dislocations in high entropy alloys (HEAs) are wavy and have natural pinning points due to the variable chemical and energetic landscape surrounding the dislocation core. This can influence the critical shear stress necessary to initiate dislocation motion and the details associated with sustained dislocation glide. The objective of this work is to determine the relationship between Schmid shear stress and dislocation velocity in single phase FCC FeNiCrCoCu HEAs using molecular dynamics simulations, with comparisons made to dislocation motion in homogeneous Ni and Cu. Simulations are performed for four different dislocation character angles: 0° (screw), 30°, 60° and 90° (edge). Several key differences are reported, compared to what is previously known about dislocation motion in homogeneous FCC metals. For example, the drag coefficient B in the phonon damping regime for HEAs has a nonlinear dependence on temperature, whereas this dependence is linear in Ni. Mobility relationships between different types of dislocations common in homogeneous FCC metals, such as the velocity of screw and 60° dislocations being lower than edge and 30° dislocations at the same shear stress, do not necessarily hold in HEAs. Dislocation waviness is measured and is found to correlate with the ability of dislocations to glide under an applied shear stress, including the temperature dependence of the drag coefficient B. These results confirm that the influence of HEA chemical complexity on dislocation motion is important and this data can be used to guide development of analytical or empirical models for dislocation mobility in HEAs.

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Wirth, B. D., V. V. Bulatov et T. Diaz de la Rubia. « Dislocation-Stacking Fault Tetrahedron Interactions in Cu ». Journal of Engineering Materials and Technology 124, n^o 3 (10 juin 2002) : 329–34. http://dx.doi.org/10.1115/1.1479692.

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In copper and other face centered cubic metals, high-energy particle irradiation produces hardening and shear localization. Post-irradiation microstructural examination in Cu reveals that irradiation has produced a high number density of nanometer sized stacking fault tetrahedra. The resultant irradiation hardening and shear localization is commonly attributed to the interaction between stacking fault tetrahedra and mobile dislocations, although the mechanism of this interaction is unknown. In this work, we present results from a molecular dynamics simulation study to characterize the motion and velocity of edge dislocations at high strain rate and the interaction and fate of the moving edge dislocation with stacking fault tetrahedra in Cu using an EAM interatomic potential. The results show that a perfect SFT acts as a hard obstacle for dislocation motion and, although the SFT is sheared by the dislocation passage, it remains largely intact. However, our simulations show that an overlapping, truncated SFT is absorbed by the passage of an edge dislocation, resulting in dislocation climb and the formation of a pair of less mobile super-jogs on the dislocation.

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Burbery, Nathaniel James, Raj Das, Giacomo Po et Nasr Ghoniem. « Understanding the Threshold Conditions for Dislocation Transmission from Tilt Grain Boundaries in FCC Metals under Uniaxial Loading ». Applied Mechanics and Materials 553 (mai 2014) : 28–34. http://dx.doi.org/10.4028/www.scientific.net/amm.553.28.

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Plastic deformation in face-centred cubic (or ‘FCC’) metals involves multi-scale phenomena which are initiated at atomic length and time scales (on order of 1.0e-15seconds). Understanding the fundamental thresholds for plasticity at atomic and nano/meso scales requires rigorous testing, which cannot be feasibly achieved with current experimental methods. Hence, computer simulation-based investigations are extremely valuable. However, meso-scale simulations cannot yet accommodate atomically-informed grain boundary (or ‘GB’) effects and dislocation interactions. This study will provide a stress - strain analysis based on molecular dynamics simulations of a series of metastable grain boundaries with identical crystal orientations but unique grain boundary characteristics. Relationships between dislocation slip systems, resolved shear stresses and additional thermo-mechanical conditions of the system will be considered in the analysis of dislocation-grain boundary interactions, including GB penetration. This study will form the basis of new phenomenological relationships in an effort to enable accommodation of grain boundaries into meso scale dislocation dynamic simulations.

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Li, Maosheng, Chan Gao et Jianing Xu. « Discrete dislocation dynamics simulations in a cylinder ». IOP Conference Series : Materials Science and Engineering 74 (17 février 2015) : 012009. http://dx.doi.org/10.1088/1757-899x/74/1/012009.

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Arsenlis, A., W. Cai, M. Tang, M. Rhee, T. Oppelstrup, G. Hommes, T. G. Pierce et V. V. Bulatov. « Enabling strain hardening simulations with dislocation dynamics ». Modelling and Simulation in Materials Science and Engineering 15, n^o 6 (25 juillet 2007) : 553–95. http://dx.doi.org/10.1088/0965-0393/15/6/001.

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CLAPP, P. C., M. V. GLAZOV et J. A. RIFKIN. « Dislocation dynamics and multiplication via atomistic simulations ». Le Journal de Physique IV 03, n^o C7 (novembre 1993) : C7–2005—C7–2014. http://dx.doi.org/10.1051/jp4:19937320.

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Mastorakos, Ioannis N., Firas E. Akasheh et Hussein M. Zbib. « Treating internal surfaces and interfaces in discrete dislocation dynamics ». Journal of the Mechanical Behaviour of Materials 20, n^o 1-3 (1 décembre 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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Guénolé, J., Julien Godet et Sandrine Brochard. « Investigation of Plasticity in Silicon Nanowires by Molecular Dynamics Simulations ». Key Engineering Materials 465 (janvier 2011) : 89–92. http://dx.doi.org/10.4028/www.scientific.net/kem.465.89.

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We have performed molecular dynamics simulations on silicon nanowires (Si-NW) with [001] axis and square section. The forces are modeled by well-tested semi-empirical potentials. First we investigated the edge reconstruction of Si nanowires. Then, we studied the behavior of the NW when submitted to compression stresses along its axis. At low temperature (300K), we observed the formation of dislocation loops with a Burgers vector 1/2 [10-1]. These dislocations slip in the unexpected {101} planes having the largest Schmid factor.

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Beyerlein, I. J., et A. Hunter. « Understanding dislocation mechanics at the mesoscale using phase field dislocation dynamics ». Philosophical Transactions of the Royal Society A : Mathematical, Physical and Engineering Sciences 374, n^o 2066 (28 avril 2016) : 20150166. http://dx.doi.org/10.1098/rsta.2015.0166.

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In this paper, we discuss the formulation, recent developments and findings obtained from a mesoscale mechanics technique called phase field dislocation dynamics (PFDD). We begin by presenting recent advancements made in modelling face-centred cubic materials, such as integration with atomic-scale simulations to account for partial dislocations. We discuss calculations that help in understanding grain size effects on transitions from full to partial dislocation-mediated slip behaviour and deformation twinning. Finally, we present recent extensions of the PFDD framework to alternative crystal structures, such as body-centred cubic metals, and two-phase materials, including free surfaces, voids and bi-metallic crystals. With several examples we demonstrate that the PFDD model is a powerful and versatile method that can bridge the length and time scales between atomistic and continuum-scale methods, providing a much needed understanding of deformation mechanisms in the mesoscale regime.

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Zotov, Nikolay, et Blazej Grabowski. « Molecular dynamics simulations of screw dislocation mobility in bcc Nb ». Modelling and Simulation in Materials Science and Engineering 29, n^o 8 (20 octobre 2021) : 085007. http://dx.doi.org/10.1088/1361-651x/ac2b02.

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Abstract The screw dislocation mobility in bcc Nb has been studied by molecular dynamics (MD) simulations at different strain rates and temperatures using an embedded-atom method (EAM) potential. Static properties of the screw dislocation, as determined with the EAM potential, are in agreement with previous density-functional-theory calculations. The elementary slip plane of the screw dislocation remains (110) for all studied strain rates (in the range 6.3 × 107–6.3 × 109 s−1) and temperatures (5 to 550 K). However, the consecutive cross-slip on different symmetry-equivalent (110) planes leads to an effective glide on (112) planes. It is demonstrated that the screw dislocation trajectories, velocities and waviness of the screw dislocation depend on the crystallographic indices, (110) or (112), of the maximum resolved shear stress plane. The waiting time for the start of the screw dislocation motion increases exponentially with decreasing strain rate, substantiating the necessity to apply in future accelerated MD techniques in order to compare with macroscopic stress-strain experiments.

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Nikonov, Anton Y., Andrey I. Dmitriev, Dmitry V. Lychagin, Lilia L. Lychagina, Artem A. Bibko et Olga S. Novitskaya. « Numerical Study and Experimental Validation of Deformation of <111> ; FCC CuAl Single Crystal Obtained by Additive Manufacturing ». Metals 11, n^o 4 (2 avril 2021) : 582. http://dx.doi.org/10.3390/met11040582.

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The importance of taking into account directional solidification of grains formed during 3D printing is determined by a substantial influence of their crystallographic orientation on the mechanical properties of a loaded material. This issue is studied in the present study using molecular dynamics simulations. The compression of an FCC single crystal of aluminum bronze was performed along the <111> axis. A Ni single crystal, which is characterized by higher stacking fault energy (SFE) than aluminum bronze, was also considered. It was found that the first dislocations started to move earlier in the material with lower SFE, in which the slip of two Shockley partials was observed. In the case of the material with higher SFE, the slip of a full dislocation occurred via successive splitting of its segments into partial dislocations. Regardless of the SFE value, the deformation was primarily occurred by means of the formation of dislocation complexes involved stair-rod dislocations and partial dislocations on adjacent slip planes. Hardening and softening segments of the calculated stress–strain curve were shown to correspond to the periods of hindering of dislocations at dislocation pileups and dislocation movement between them. The simulation results well agree with the experimental findings.

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Pachaury, Yash, Tomohisa Kumagai et Anter El-Azab. « Microplasticity in inhomogeneous alloys ». IOP Conference Series : Materials Science and Engineering 1249, n^o 1 (1 juillet 2022) : 012038. http://dx.doi.org/10.1088/1757-899x/1249/1/012038.

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Abstract We report on a preliminary modelling effort to understand the influence of compositional inhomogeneity on alloy microplasticity from a dislocation dynamics perspective. We tackle this problem by multiscale simulations in three steps: (1) analysis of the 3D composition morphology in alloys with tendency to undergo spinodal instability both thermally and under irradiation, with bcc FeCrAl alloys as a model system, (2) atomistic simulation of the dislocation mobility as a function of the local alloy composition, and (3) using dislocation dynamics simulations to understand the impact of composition inhomogeneity on microplasticity. The dislocation dynamics model takes into consideration the coherency stress associated with composition inhomogeneity when computing the forces driving the dislocation motion and on cross slip. Our preliminary investigation shows that the stress-strain response of the alloy and the dislocation density evolution depend on the wavelength of the composition fluctuations. Our investigation also shows that the alloy inhomogeneity may alter the cross-slip activity, which, in turn, influences the dislocation density evolution. The dependence of the dislocation mobility and coherency stress on local composition and its variation, as well as the altered cross slip rates, cause the dislocation microstructure to differ relative to that in the homogeneous alloy of the same average composition.

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Ma, Zhi-Chao, Xiao-Zhi Tang, Yong Mao et Ya-Fang Guo. « The Plastic Deformation Mechanisms of hcp Single Crystals with Different Orientations : Molecular Dynamics Simulations ». Materials 14, n^o 4 (4 février 2021) : 733. http://dx.doi.org/10.3390/ma14040733.

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The deformation mechanisms of Mg, Zr, and Ti single crystals with different orientations are systematically studied by using molecular dynamics simulations. The affecting factors for the plasticity of hexagonal close-packed (hcp) metals are investigated. The results show that the basal <a> dislocation, prismatic <a> dislocation, and pyramidal <c + a> dislocation are activated in Mg, Zr, and Ti single crystals. The prior slip system is determined by the combined effect of the Schmid factor and the critical resolved shear stresses (CRSS). Twinning plays a crucial role during plastic deformation since basal and prismatic slips are limited. The 101¯2 twinning is popularly observed in Mg, Zr, and Ti due to its low CRSS. The 101¯1 twin appears in Mg and Ti, but not in Zr because of the high CRSS. The stress-induced hcp-fcc phase transformation occurs in Ti, which is achieved by successive glide of Shockley partial dislocations on basal planes. More types of plastic deformation mechanisms (including the cross-slip, double twins, and hcp-fcc phase transformation) are activated in Ti than in Mg and Zr. Multiple deformation mechanisms coordinate with each other, resulting in the higher strength and good ductility of Ti. The simulation results agree well with the related experimental observation.

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Fertig, Ray S., et Shefford P. Baker. « Dislocation dynamics simulations of dislocation interactions and stresses in thin films ». Acta Materialia 58, n^o 15 (septembre 2010) : 5206–18. http://dx.doi.org/10.1016/j.actamat.2010.06.001.

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Křišt'an, Josef, et Jan Kratochvíl. « Estimate of Stress in the Channel of Persistent Slip Bands Based on Dislocation Dynamics ». Materials Science Forum 567-568 (décembre 2007) : 405–8. http://dx.doi.org/10.4028/www.scientific.net/msf.567-568.405.

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To estimate the fatigue endurance limit at the micro-scale two unlike dislocations gliding in a channel of a persistent slip bands are considered. The dislocations are modeled as moving planar flexible curves. The objective of the simulations is to determine the averaged stress in the channel needed for the dislocations to escape one another using statistics of encounters of such dislocation pairs. We employed an iso-strain approach, i.e. the assumption that the total strain everywhere in the channel is the same.

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Prakash, Aditya, Tawqeer Nasir Tak, Namit N. Pai, S. V. S. Narayana Murty, P. J. Guruprasad, R. D. Doherty et Indradev Samajdar. « Slip band formation in low and high solute aluminum : a combined experimental and modeling study ». Modelling and Simulation in Materials Science and Engineering 29, n^o 8 (11 novembre 2021) : 085016. http://dx.doi.org/10.1088/1361-651x/ac3369.

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Abstract Direct ex situ observations related slip band formation with deformed microstructures in commercial AA1050 and AA2219. The samples from both grades had similar grain sizes (∼250 μm) and nearly random crystallographic textures. However, AA2219 contained significantly more solute. Slip bands, on the internal long transverse (LT) plane in split channel die specimens, were characterized by primary spacings (λ) of 2–9 μm, heights (Z) of 160–360 nm and secondary shear strains ( γ LT S ). Higher deformation temperatures for both grades increased λ, decreased, Z and r e d u c e d γ LT S . At all deformation temperatures, AA1050 had smaller λ and higher Z, while AA2219 showed higher γ LT S . In-grain misorientations, but not residual strains, were larger in grains with finer λ in AA1050, but less so in AA2219. Discrete dislocation dynamics (DDD) simulations reported realistic slip bands with slip localizations. The simulations, initiated with static obstacles and sources, led to dislocation interactions and junction formation. The probability of junction stabilization (p) determined the ratio of dynamic sources to obstacles. Slip band formation appeared to be an outcome of the release of piled up dislocations leading to dislocation avalanches. Slip localization increased weakly with finer active slip plane spacing (λ *), giving higher dynamic obstacle strengths and densities, but strongly with smaller p. In particular, the DDD simulations captured experimental patterns of higher slip localizations and dislocation densities in low solute aluminum with finer λ *.

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Monnet, G. « Investigation of precipitation hardening by dislocation dynamics simulations ». Philosophical Magazine 86, n^o 36 (24 novembre 2006) : 5927–41. http://dx.doi.org/10.1080/14786430600860985.

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Chang, Hyung Jun, Heung Nam Han et Marc Fivel. « Multiscale Modelling of Nanoindentation ». Key Engineering Materials 345-346 (août 2007) : 925–30. http://dx.doi.org/10.4028/www.scientific.net/kem.345-346.925.

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Nanoindentation is an interesting technique used to probe the local mechanical properties of a material. Although this test has been widely used and developed over the world during the past few years, it remains a lot of uncertainties regarding the interpretation of nanoindentation data. In this study, we propose to simulate the nanoindentation test of FCC single crystals like Cu or Ni using three numerical models. At the lowest scale, molecular dynamics simulations give details of the nucleation of the first dislocations induced by the indentation. At an intermediate scale, discrete dislocation dynamics simulations are performed to study the evolution of the dislocation microstructure during the loading. Finally, at the upper scale, 3D finite element modelling using crystal plasticity constitutive equations give a continuum description of the indentation induced plasticity. It is shown how the different models are interconnected together.

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Tanaka, Masaki, Naoki Fujimoto, Tatsuo Yokote et Kenji Higashida. « Fracture Toughness Enhanced by Severe Plastic Deformation in Low Carbon Steel ». Materials Science Forum 584-586 (juin 2008) : 637–42. http://dx.doi.org/10.4028/www.scientific.net/msf.584-586.637.

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The enhancement of toughness at low temperatures in fine-grained low carbon steel was studied, basing on the theory of crack-tip shielding due to dislocations. Low carbon steel was subjected to an accumulative roll bonding (ARB) process for grain refining. The grain size perpendicular to the normal direction was decreased to approximately 200nm after the ARB process. The fracture toughness of low carbon steel with the ARB process was measured at 77K by four-point bending, comparing with the fracture toughness of those without the ARB. It was found that the value of fracture toughness at 77K was increased by grain refining due to the ARB process, indicating that the ARB process enhances toughness at low temperatures and that the brittle-to-ductile transition (BDT) temperature shifted to a lower temperature. Quasi-two-dimensional simulations of dislocation dynamics, taking into account crack tip shielding due to dislocations, were performed to investigate the effect of a dislocation source spacing along a crack front on the BDT. The simulation indicates that the BDT temperature is decreased by decreasing the dislocation source spacing.

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Jia, Li Xia, Xin Fu He, Shi Wu, Dong Jie Wang, Han Cao, Yan Kun Dou et Wen Yang. « Study of Helium Bubble Induced Hardening in BCC-Fe by Molecular Dynamics Simulation ». Materials Science Forum 944 (janvier 2019) : 378–86. http://dx.doi.org/10.4028/www.scientific.net/msf.944.378.

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The interaction between an moving edge dislocation and helium bubble was studied in BCC-Fe using Molecular dynamics（MD）simulation. Edge dislocation passed the bubble via cut mechanism. A step with a length of b is left on both sides of the bubble after dislocation left away. The influence of simulation temperature, defect size and He/V ratio in bubble on critical resolved shear stress (CRSS) for dislocation to shear bubble were investigated. The CRSS increases with increasing defect sizes, and decreases with increasing temperature. When He/V ratio is at the range of 0-1, CRSS depends weakly on the He/V ratio. The estimated obstacle strength of helium bubble based on MD simulations is acceptable and reasonable agreement with one deduced from the dispersion barrier-hardening model applied to experimental results.

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