Статті в журналах: "Dislocation field mechanics"

1

Beyerlein, I. J., and 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, no. 2066 (April 28, 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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2

Fressengeas, Claude, and Vincent Taupin. "Revisiting the Application of Field Dislocation and Disclination Mechanics to Grain Boundaries." Metals 10, no. 11 (November 16, 2020): 1517. http://dx.doi.org/10.3390/met10111517.

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We review the mechanical theory of dislocation and disclination density fields and its application to grain boundary modeling. The theory accounts for the incompatibility of the elastic strain and curvature tensors due to the presence of dislocations and disclinations. The free energy density is assumed to be quadratic in elastic strain and curvature and has nonlocal character. The balance of loads in the body is described by higher-order equations using the work-conjugates of the strain and curvature tensors, i.e., the stress and couple-stress tensors. Conservation statements for the translational and rotational discontinuities provide a dynamic framework for dislocation and disclination motion in terms of transport relationships. Plasticity of the body is therefore viewed as being mediated by both dislocation and disclination motion. The driving forces for these motions are identified from the mechanical dissipation, which provides guidelines for the admissible constitutive relations. On this basis, the theory is expressed as a set of partial differential equations where the unknowns are the material displacement and the dislocation and disclination density fields. The theory is applied in cases where rotational defects matter in the structure and deformation of the body, such as grain boundaries in polycrystals and grain boundary-mediated plasticity. Characteristic examples are provided for the grain boundary structure in terms of periodic arrays of disclination dipoles and for grain boundary migration under applied shear.

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3

ROY, A. "Finite element approximation of field dislocation mechanics." Journal of the Mechanics and Physics of Solids 53, no. 1 (January 2005): 143–70. http://dx.doi.org/10.1016/j.jmps.2004.05.007.

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4

Mironova, M., V. Selvamanickam, D. F. Lee, and K. Salama. "TEM studies of dislocations in deformed melt-textured YBa2Cu3Ox superconductors." Journal of Materials Research 8, no. 11 (November 1993): 2767–73. http://dx.doi.org/10.1557/jmr.1993.2767.

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TEM studies have been conducted on melt-textured YBa2Cu3Ox samples that were uniaxially and isostatically deformed at high temperatures and compared with those of undeformed samples. Dislocation pile-ups along [100] and [010] are found to be the common feature between undeformed samples with the best Jc and the uniaxially deformed samples, and are suggested to be responsible for enhanced pinning when the magnetic field (H) is applied parallel to the a-b plane. Dislocation loops, tangles, and arrays are also observed, and are considered to contribute to pinning in field orientations other than H ‖ a-b. In addition to these dislocations, 〈301〉 type partial dislocations are found to be present in isostatically deformed samples. The strain field around these dislocations is considered to be an additional source of pinning in the intermediate field orientations.

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5

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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6

Puri, Saurabh, Amit Das, and Amit Acharya. "Mechanical response of multicrystalline thin films in mesoscale field dislocation mechanics." Journal of the Mechanics and Physics of Solids 59, no. 11 (November 2011): 2400–2417. http://dx.doi.org/10.1016/j.jmps.2011.06.009.

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7

Acharya, Amit. "Constitutive analysis of finite deformation field dislocation mechanics." Journal of the Mechanics and Physics of Solids 52, no. 2 (February 2004): 301–16. http://dx.doi.org/10.1016/s0022-5096(03)00093-0.

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8

Weertman, J. "Mode III Crack Tip Plastic Zone Solution for Work Hardening Solid Using Dislocation Motion." Journal of Applied Mechanics 56, no. 4 (December 1, 1989): 976–77. http://dx.doi.org/10.1115/1.3176200.

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The stress and strain field solutions for the stationary mode III crack in small-scale yielding is obtained from a direct physical picture in which the plastic strain is produced by the motion of infinitesimal dislocations. The analysis is based on a shifting center, cylindrical coordinate system. The nonredundant dislocation density is determined. The ratio of nonredundant to redundant dislocation density within the plastic zone may be a useful measure for placing cracks into a brittle class, a ductile class and semibrittle to semiductile classes.

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9

Luo, H. A., and Y. Chen. "An Edge Dislocation in a Three-Phase Composite Cylinder Model." Journal of Applied Mechanics 58, no. 1 (March 1, 1991): 75–86. http://dx.doi.org/10.1115/1.2897182.

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An exact solution is given for the stress field due to an edge dislocation embedded in a three-phase composite cylinder. The force on the dislocation is then derived, from which a set of simple approximate formulae is also suggested. It is shown that, in comparison with the two-phase model adopted by Dundurs and Mura (1964), the three-phase model allows the dislocation to have a stable equilibrium position under much less stringent combinations of the material constants. As a result, the so-called trapping mechanism of dislocations is more likely to take place in the three-phase model. Also, the analysis and calculation show that in the three-phase model the orientation of Burgers vector has only limited influence on the stability of dislocation. This behavior is pronouncedly different from that predicted by the two-phase model.

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10

Vivekanandan, Vignesh, Joseph Pierre Anderson, Yash Pachaury, Mamdouh S. Mohamed, and Anter El-Azab. "Statistics of internal stress fluctuations in dislocated crystals and relevance to density-based dislocation dynamics models." Modelling and Simulation in Materials Science and Engineering 30, no. 4 (April 11, 2022): 045007. http://dx.doi.org/10.1088/1361-651x/ac5dcf.

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Abstract A statistical analysis of internal stress fluctuations, defined as the difference between the local mean stress and stress on dislocations, is presented for deforming crystals with 3D discrete dislocation systems. Dislocation realizations are generated using dislocation dynamics simulations and the associated stress field is computed as a superposition of a regularized stress field of dislocation lines within the domain of the solution and a complementary stress field computed via a finite-element boundary value problem. The internal stress fluctuations of interest are defined by an ensemble of the difference between the stress on dislocation lines and the local mean field stress in the crystal. The latter is established in a piecewise fashion over small voxels in the crystal thus allowing the difference between the local average stress and stress on segments to be easily estimated. The results show that the Schmid stress (resolved shear stress) and Escaig stress fluctuations on various slip systems sampled over a random set of points follow a Cauchy (Lorentz) distribution at all strain levels, with the amplitude and width of the distribution being dependent on the strain. The implications of the Schmid and Escaig internal stress fluctuations are discussed from the points of view of dislocation cross-slip and the dislocation motion in continuum dislocation dynamics.

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11

Huang, Haiying, and George A. Kardomateas. "Single-Edge and Double-Edge Cracks in a Fully Anisotropic Strip." Journal of Engineering Materials and Technology 121, no. 4 (October 1, 1999): 422–29. http://dx.doi.org/10.1115/1.2812397.

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The mode I and II stress intensity factors in a fully anisotropic infinite strip with a single-edge or double-edge crack configuration are obtained from an approach based on the continuous dislocation technique. The elastic solution of a single dislocation in an anisotropic half plane is used in conjunction with an array of dislocations along the boundary of the infinite strip, which is supposed to be traction-free, to provide the solution of a single dislocation in an anisotropic infinite strip. The dislocation densities of the dislocation array are determined in such a way that the traction forces generated by the dislocation array cancel the residual tractions along the boundary due to the single dislocation in the half plane. The stress field of a single dislocation in the infinite strip is thus a superposition of that of the single dislocation and the dislocation array in the half plane. This solution is then applied to calculate the mixed mode I and II stress intensity factors for a single-edge and a double-edge crack in the anisotropic strip, by replacing the cracks with a series of dislocations and satisfying the crack surface traction-free conditions. To illustrate the results, typical material data for graphite/epoxy were used in a unidirectional construction with the fiber orientation, θ, measured from the load direction (perpendicular to the crack direction), varying between 0 and 90 degrees. It is found that the effect of anisotropy on the mode I stress intensity factor is significant between 30 and 60 degrees and depends strongly on the relative crack length, being larger for cracks of relative larger length. The mode mixity, defined such that it is zero for pure mode I and 90 degrees for pure mode II, is significant between 40 and 70 degrees, and is in general between zero and 20 degrees.

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12

Pustovoit, Viktor N., and Yuri V. Dolgachev. "Interaction of Ferromagnetically Ordered Clusters with Dislocations in Austenite and Twinning." Materials Science Forum 1052 (February 3, 2022): 134–39. http://dx.doi.org/10.4028/p-a8jty9.

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The relationship between the interaction of ferromagnetically ordered clusters in austenite with dislocations, twinning and nucleation of the martensite phase is considered. It is shown that the regions with short-range order existing in austenite affect the dislocation structure. In turn, dislocations are involved in the formation of twins and martensite nuclei. The imposition of an external magnetic field enhances the magnetic inhomogeneity of austenite and the effects of magnetoelastic interaction between clusters and dislocations.

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13

Zhang, H., A. H. King, and R. Thomson. "The interaction between dislocations and intergranular cracks." Journal of Materials Research 6, no. 2 (February 1991): 314–23. http://dx.doi.org/10.1557/jmr.1991.0314.

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The elastic interactions of dislocations and intergranular cracks in isotropic materials have been studied. In the first part of the paper, a model based on the Rice–Thomson theory is established under which the conditions for dislocation emission and crack propagation can be described in terms of an emission surface, cleavage surface, and loading line in the local k-space associated with a mixed mode intergranular crack. For a given crack, the local k-field changes with the emission of dislocations from the crack tip, which alters the balance of cleavage and emission. In the second part, we present experimental results of in situ TEM observations of intergranular cracks in molybdenum. Alternating brittle crack propagation and dislocation emission is observed. The number of emitted dislocations corresponding to each crack propagation is in good agreement with the calculated values.

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14

Shastry, Vijay, and Tomas Diaz de la Rubia. "The Interaction Between Point Defects and Edge Dislocation in BCC Iron." Journal of Engineering Materials and Technology 121, no. 2 (April 1, 1999): 126–28. http://dx.doi.org/10.1115/1.2812356.

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We present results of atomistic simulations of the interaction between self interstitial atoms and vacancies with edge dislocations in BCC iron. The calculations are carried out using molecular dynamics with an energy minimization scheme based on the quasi-Newton approach and use the Finnis-Sinclair interatomic potential for BCC iron developed by Ackland et al. Large anisotropy in the strain field of self interstitials is observed and it causes strong interaction with edge dislocations even when the defect is located on the dislocation glide plane. For vacancies, the relaxation volume is smaller and much more isotropic, which results in a far weaker interaction with the dislocation. A temperature dependent capture radius for vacancies and self interstitials is extracted from the simulations. The difference between the capture radii of vacancies and self interstitials is used to define the sink strength of the dislocation. Large deviations are observed from the predictions of elasticity based on treating point defects as isotropic dilatational centers. Further, the capture radius of edge dislocations in BCC iron is observed to be small and is of the order of 1–3 nm for self interstitials.

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15

Cui, Yinan, Kailun Li, Chan Wang, and Wei Liu. "Dislocation evolution during additive manufacturing of tungsten." Modelling and Simulation in Materials Science and Engineering 30, no. 2 (December 21, 2021): 024001. http://dx.doi.org/10.1088/1361-651x/ac40d3.

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Abstract Additive manufacturing (AM) frequently encounters part quality issues such as geometrical inaccuracy, cracking, warping, etc. This is associated with its unique thermal and mechanical cycling during AM, as well as the material properties. Although many efforts have been spent on this problem, the underlying dislocation evolution mechanism during AM is still largely unknown, despite its essential role in the deformation and cracking behavior during AM and the properties of as-fabricated parts. In this work, a coupling method of three-dimensional dislocation dynamics and finite element method is established to disclose the mechanisms and features of dislocations during AM. Tungsten (W) is chosen as the investigated material due to its wide application. The internal thermal activated nature of dislocation mobility in W is taken into account. The correlations between the combined thermal and mechanical cycles and dislocation evolutions are disclosed. The effect of adding alloying element Ta in W is discussed from the perspectives of tuning dislocation mobility and introducing nanoparticles, which helps to understand why higher dislocation density and fewer microcracks are observed when adding Ta. The current work sheds new light on the long-standing debating of dislocation origin and evolutions in the AM field.

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16

Xin, Y., K. Han, N. Mateeva, H. Garmestani, P. N. Kalu та K.-H. Dahmen. "Microstructures of La1−xAx(A = Ca or Sr)MnO3−δ thin films by liquid-delivery metalorganic chemical vapor deposition". Journal of Materials Research 16, № 11 (листопад 2001): 3073–83. http://dx.doi.org/10.1557/jmr.2001.0425.

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The microstructure of La1–xAx(A = Ca or Sr)MnO3–δ thin films grown by liquid-delivery metalorganic chemical vapor deposition on (001) MgO and (110)pseudo-cubic LaAlO3 were studied by transmission electron microscopy. The La1–xCaxMnO3–δ thin film on large lattice mismatched MgO exhibited very defective microstructures and consisted of two typical regions. The first region was close to the film–substrate interface and had an epitaxial relationship to the substrate with many differently oriented domains nucleated on the substrate surface. The second region consisted of columnar grains with some degree of texture. In contrast, the smaller lattice-mismatched La1–xSrxMnO3–δ/(110)pseudo-cubic LaAlO3 film had good crystalline quality with highly oriented columnar grains but exhibited complicated dislocation structures. Apart from the misfit dislocations formed at the film–substrate interface, two types of anomalous dislocations with limited contribution to relieving misfit stresses were also observed. One type of dislocation had extra planes in the film and some climbed into the substrate. These dislocations were considered to form from dislocation loops during nucleation of the film. The other type of dislocations had extra planes parallel to the film–substrate interface and glided into the substrate side resulting in a 2° tilt of the film with respect to the substrate. The complicated dislocation configurations present in the sample were related to the complex strain field in the film. The relative strains along the interface measured in the film were heterogeneous. The variations of the strains in the film were related to the local Curie temperature changes and second-order phase transitions of the film.

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17

Siddique, Abu Bakar, and Tariq Khraishi. "A holed-plate with material dislocations: Formulation and verification." Mathematics and Mechanics of Solids 27, no. 5 (November 5, 2021): 896–909. http://dx.doi.org/10.1177/10812865211053369.

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Standard text-book dislocation theory for the elastic fields of a dislocation is provided in an infinite medium. For problems involving free surfaces, or image stresses, the solution for such elastic fields is more complex. The current article extends the state of knowledge for problems with free surfaces to address the stress field of a screw dislocation in a plate (two planar free surfaces) containing a hole/void. Such surfaces interact and thus affect the stress field of a dislocation in deviation of the infinite medium solution. The numerical solutions provided herein, based on reflective image stresses and the collocation-point method, have been verified to the extent available and such solutions allow for further applied problems. One main finding of the paper is that the equilibrium location of a screw dislocation is always closer to the hole/void surface than the planar free surface.

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18

Horstemeyer, Mark F., and M. I. Baskes. "Atomistic Finite Deformation Simulations: A Discussion on Length Scale Effects in Relation to Mechanical Stresses." Journal of Engineering Materials and Technology 121, no. 2 (April 1, 1999): 114–19. http://dx.doi.org/10.1115/1.2812354.

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In this study, atomistic finite deformation calculations employing the Embedded Atom Method show three items of interest related to continuum field theory. First, a spatial size scale effect on the yield stress is found. In these calculations, mechanical yield point occurred from dislocation initiation at the edge of the numerical specimens. The spatial size scale continued to affect the plastic response up to strains of 30 percent in simple shear for nickel oriented at 〈011〉. The second point is related to the continuum mechanics observation about oscillating global shear stress under simple shear conditions is shown to dampen as the spatial size scale increases. As the spatial length scale increases, the continuum rotational effect coupled with the increase in dislocation population reduces the oscillatory behavior. This confirms the notion proposed by Bammann and Aifantis (1987) in that when more dislocations are initiated with different orientations of the Burger’s vectors then the oscillations decrease. Finally, a length scale bridging idea is proposed by relating a continuum single degree of freedom loss coefficient, which relates the plastic energy to the total strain energy, to varying sizes of blocks of atoms. This study illustrates the usefulness of employing the Embedded Atom Method to study mechanisms related to continuum mechanics quantities.

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19

Cleja-Ţigoiu, Sanda. "Disclinations and GND tensor effects on the multislip flow rule in crystal plasticity." Mathematics and Mechanics of Solids 25, no. 8 (February 3, 2020): 1643–76. http://dx.doi.org/10.1177/1081286519896394.

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This paper deals with new elastoplastic models for crystalline materials with microstructural defects, such as dislocations and disclinations, which are consistent with the multislip plastic flow rule, and compatible with the free energy imbalance principle. The defect free energy function is a function of the disclination tensor and its gradient, and of the geometrically necessary dislocation (GND) tensor, via the Cartan torsion. By applying the free energy imbalance, the appropriate viscoplastic (diffusion-like) evolution equations are derived for shear plastic rates (in slip systems) and for the disclination tensor. The two sets of differential (or partial differential, i.e., non-local) equations describe the rate form of the adopted disclination–dislocation model. The first set is typical for finite deformation formalism, while the second set refers to the evolution equations with respect to the reference configuration. The dislocation appears to be a source for producing disclination defects. A pure dislocation elastoplastic model is also proposed. Multislip models with disclination within the small deformation approach are derived from the finite deformation models. The initial and boundary value problems are formulated and the incremental (rate) equilibrium equation leads to a variational equality for the velocity field, at any time, which is coupled with the rate type models for the set of variables. First, the elastic problem is solved for a certain time interval by assuming that the existing defects inside the body remain inactive. Subsequently, the variational equality is solved for the velocity field, at any time, if the slip systems are activated. Consequently, the state of the body with defects is defined by the solution of the differential-type equations, when the velocity field is known for a certain time interval. Appropriate initial conditions are necessary, including those associated with defects which became active. Finally, an update algorithm must be provided in order to compute the fields at the current moment.

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20

Wu, Wenwang, Cunjing Lv, Shucai Xu, and Jinhuan Zhang. "Elastic field due to dislocation loops in isotropic bimaterial with dislocation-like and force-like interface models." Mathematics and Mechanics of Solids 22, no. 5 (January 27, 2016): 1190–204. http://dx.doi.org/10.1177/1081286515622808.

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Based on the two-dimensional discrete Fast Fourier Transformation (FFT) method, a semi-analytical solution is developed for calculating the elastic fields of dislocation loops within isotropic bimaterials, where the imperfect interface can be described as two types of models: (a) dislocation-like and (b) force-like. Calculation examples of dislocation loops within Al–Cu bimaterials are performed to verify the reliability of the semi-analytical approach. Effects of constant matrix for the dislocation-like and force-like models on the interface elastic fields are studied, and it is shown that the interface elastic field is remarkably influenced by the interface conditions. Comparisons between perfect-bonding, dislocation-like and force-like imperfect interface models are performed to study the effects of interface conditions on the in-plane and out-of-plane elastic fields across the bimaterial interface plane.

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21

Roy, A., S. Puri, and A. Acharya. "Phenomenological mesoscopic field dislocation mechanics, lower-order gradient plasticity, and transport of mean excess dislocation density." Modelling and Simulation in Materials Science and Engineering 15, no. 1 (December 7, 2006): S167—S180. http://dx.doi.org/10.1088/0965-0393/15/1/s14.

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22

Takaki, Seiya, Tomokazu Yamamoto, Masanori Kutsuwada, Kazuhiro Yasuda, and Syo Matsumura. "Atomistic observation of electron irradiation-induced defects in CeO2." MRS Proceedings 1514 (2013): 93–98. http://dx.doi.org/10.1557/opl.2013.199.

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ABSTRACTWe have investigated the atomistic structure of radiation-induced defects in CeO2 formed under 200 keV electron irradiation. Dislocation loops on {111} habit planes are observed, and they grow accompanying strong strain-field. Atomic resolution scanning transmission electron microscopy (STEM) observations with high angle annular dark-field (HAADF) and annular bright-field (ABF) imaging techniques showed that no additional Ce layers are inserted at the position of the dislocation loop, and that strong distortion and expansion is induced around the dislocation loops. These results are discussed that dislocation loops formed under electron irradiation are non-stoichiometric defects consist of oxygen interstitials.

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23

Taupin, V., S. Berbenni, C. Fressengeas, and O. Bouaziz. "On particle size effects: An internal length mean field approach using field dislocation mechanics." Acta Materialia 58, no. 16 (September 2010): 5532–44. http://dx.doi.org/10.1016/j.actamat.2010.06.034.

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24

Acharya, A., R. J. Knops, and J. Sivaloganathan. "On the structure of linear dislocation field theory." Journal of the Mechanics and Physics of Solids 130 (September 2019): 216–44. http://dx.doi.org/10.1016/j.jmps.2019.06.002.

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25

Acharya, Amit. "Stress of a Spatially Uniform Dislocation Density Field." Journal of Elasticity 137, no. 2 (January 7, 2019): 151–55. http://dx.doi.org/10.1007/s10659-018-09717-5.

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26

Brenner, R., A. J. Beaudoin, P. Suquet, and A. Acharya. "Numerical implementation of static Field Dislocation Mechanics theory for periodic media." Philosophical Magazine 94, no. 16 (March 26, 2014): 1764–87. http://dx.doi.org/10.1080/14786435.2014.896081.

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27

Acharya, Amit, Karsten Matthies, and Johannes Zimmer. "Travelling wave solutions for a quasilinear model of field dislocation mechanics." Journal of the Mechanics and Physics of Solids 58, no. 12 (December 2010): 2043–53. http://dx.doi.org/10.1016/j.jmps.2010.09.008.

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28

Djaka, Komlan Sénam, Aurélien Villani, Vincent Taupin, Laurent Capolungo, and Stéphane Berbenni. "Field Dislocation Mechanics for heterogeneous elastic materials: A numerical spectral approach." Computer Methods in Applied Mechanics and Engineering 315 (March 2017): 921–42. http://dx.doi.org/10.1016/j.cma.2016.11.036.

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29

Breeden, Ja’Nya, Dow Drake, Jay Gopalakrishnan, and Saurabh Puri. "A one-dimensional field dislocation mechanics model using discontinuous Galerkin method." Computational Materials Science 216 (January 2023): 111870. http://dx.doi.org/10.1016/j.commatsci.2022.111870.

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30

Albrecht, Claire, Irene J. Beyerlein, and Morgan R. Jones. "Temperature dependent phase field dislocation dynamics model." European Journal of Mechanics - A/Solids 100 (July 2023): 104987. http://dx.doi.org/10.1016/j.euromechsol.2023.104987.

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31

Zhang, Tong-Yi, and J. E. Hack. "Interaction of a screw dislocation with a crack in an anisotropic body." Journal of Materials Research 6, no. 12 (December 1991): 2578–84. http://dx.doi.org/10.1557/jmr.1991.2578.

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The stress field, image force, and shielding effect of a screw dislocation in the vicinity of a Mode III crack were formulated for both semi-infinite and finite length cracks. The results show that there is an abnormal stress component, ŝ31, on the crack plane. This leads to a nonzero image force along the axis perpendicular to the crack plane when the dislocation is located on the crack plane. However, the abnormal stress component and image force disappear for orthotropic and isotropic media. The image force along a slip plane has the same expression as in isotropic media with an effective shear modulus. Generally the shielding effects are the same as in isotropic media. The anisotropy changes only the magnitude of the shielding effects. The case of multiple dislocations is also discussed.

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32

Katz, Y., W. Mook, R. Mukherjee, A. Gidwani, J. Deneen, and William W. Gerberich. "Mechanical Response of Semi-Brittle Nano Particles under an Imposed Cyclic Field." Materials Science Forum 482 (April 2005): 51–54. http://dx.doi.org/10.4028/www.scientific.net/msf.482.51.

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In elastic plastic solids, approaching the sub micron scale, critical experiments indicated significant differences in the mechanical response. Thus, mainly in small volume behavior a length scale issue is introduced with implications on the basic understanding of deformation and fracture processes. The current study is centered on the mechanical response of silicon particles in the range of 20-50 nm on sapphire substrate. Monotonic and cyclic mechanical tests have been performed by contact mechanics methodology at ambient temperature. Mechanical information and visualization assisted by scanning probe microscope-based nano indentation alluded to a model founded on dislocation dynamic effects. This facilitated developments regarding the length scale subject in the light of fatigue concepts and structural integrity aspects.

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33

Vasilevich, Yu V., and O. M. Ostrikov. "The Equilibrium Condition of a Non-Thin Screw Wedge-Shaped Twin Located in the Distance from the Surface of an Undeformed Crystal." Science & Technique 17, no. 6 (December 13, 2018): 515–20. http://dx.doi.org/10.21122/2227-1031-2018-17-6-515-520.

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The equilibrium condition for a non-thin helical wedge-shaped twin located far from the surface of the crystal is obtained. The case of an undeformed solid is considered. It is established that under such conditions a helical twin can not twin can not exist under such conditions. The result is in full conformity with generally known results for dislocation walls from helical dislocations. An approximation for continuous distribution of twinning dislocations at twin boundaries has been used in methodology for deriving an equilibrium condition. The shape of the twin boundaries has been described by functions that depend on density of the twinning dislocations at the twin boundaries. It has been assumed that the forces acting on the twin boundaries from the side of the twin dislocations are equal to zero. One degree of freedom along a twinning direction has been presupposed for twinning dislocations. Dislocation creeping effects have been excluded in the model. A calculation of stress fields for a twin has been carried out within the framework of an elasticity theory. In this case a superposition of stresses from each twin boundary has been considered. The solution of equations has been sought in the form of a polynomial. A linear approximation of such solution is considered in detail. The ем resulting equilibrium condition is satisfied for two values equal to zero that is a twin length and its width at the mouth. The result is important in the field of mechanics for twinning materials, shape memory materials, and in the development of techniques for predicting destruction and functioning of twinning materials.

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34

Chiang, C. R. "The dislocation field around a mode-II crack tip." Engineering Fracture Mechanics 29, no. 3 (January 1988): 349–54. http://dx.doi.org/10.1016/0013-7944(88)90022-7.

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35

Morin, Léo, Renald Brenner, and Pierre Suquet. "Numerical simulation of model problems in plasticity based on field dislocation mechanics." Modelling and Simulation in Materials Science and Engineering 27, no. 8 (October 1, 2019): 085012. http://dx.doi.org/10.1088/1361-651x/ab49a0.

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36

Peng, Xianghua, Min Yu, and Yuxuan Yang. "Interaction between a generalized screw dislocation in the matrix and an inhomogeneity containing an elliptic hole in piezoelectric–piezomagnetic composite materials." Mathematics and Mechanics of Solids 24, no. 10 (March 5, 2019): 3080–91. http://dx.doi.org/10.1177/1081286519832064.

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The paper deals with the interaction of a generalized screw dislocation and an elliptic inhomogeneity containing a confocal elliptic hole in a magneto-electro-elastic composite material. Exact solutions are derived for the case where the generalized screw dislocation is located in the matrix under a remote anti-plane shear stress field, an in-plane electric field, and a magnetic field. Based on the complex variable method, the complex potentials of both the matrix and the inhomogeneity are obtained in series, and analytic expressions for the generalized stress and strain field, the image force, the generalized stress intensity factor of the blunt crack tip, and the energy release rate are derived explicitly. The presented solutions include some previous solutions, such as pure elastic, piezoelectric, piezomagnetic, and circular inclusions. Typical numerical examples are presented and the influences of the dislocation position, the volume of inhomogeneity, and the elliptic hole on these physical quantities are discussed. The results show that the magneto-electro-elastic coupling effect has a great influence on the image force and the equilibrium position of dislocation, especially when the dislocation approaches the interface; the coupling effect makes the image force on the screw dislocation follow different variation laws in piezoelectric–piezomagnetic composite materials compared with elastic materials.

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37

Henager, Charles H., and Richard G. Hoagland. "Forces between Dislocations due to Dislocation Core Fields." MRS Proceedings 652 (2000). http://dx.doi.org/10.1557/proc-652-y7.7.

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ABSTRACTAtomistic dislocation models were used to determine the properties of dislocation core fields in Al using an EAM potential. Equilibrium atom configurations were compared with initial configurations displaced according to the Volterra field to determine core displacement fields for edge, screw, and mixed (60° and 30°) geometries. The core field was approximated by a line force defect field lying parallel to the dislocation line direction. Best-fit parameters for the core fields were obtained in terms of the anisotropic elastic solution for a line force defect, from which the line force strengths and the origin of the line forces were determined. The line force stress fields were then used to compute the forces between dislocations for several dislocation configurations. The Volterra field dominates beyond 50b but core field forces modify the equilibrium angle of edge dislocation dipoles and determine the force between otherwise noninteracting edge and screw dislocations at distances out to 50b compared to the Volterra-only forces.

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38

Kobayashi, Shunsuke, and Ryuichi Tarumi. "Geometrical frustration in nonlinear mechanics of screw dislocation." Royal Society Open Science 11, no. 12 (December 2024). https://doi.org/10.1098/rsos.240711.

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The existence of stress singularities and reliance on linear approximations pose significant challenges in comprehending the stress field generation mechanism around dislocations. This study employs differential geometry and calculus of variations to mathematically model and numerically analyse screw dislocations. The kinematics of the dislocation are expressed by the diffeomorphism of the Riemann–Cartan manifold, which includes both the Riemannian metric and affine connection. The modelling begins with a continuous distribution of dislocation density, which is transformed into torsion τ through the Hodge duality. The plasticity functional is constructed by applying the Helmholtz decomposition to bundle isomorphism, which is equivalent to the Cartan first structure equation for the intermediate configuration B . The current configuration is derived by the elastic embedding of B into the standard Euclidean space ℝ 3 . The numerical analysis reveals that the elastic stress fields effectively eliminate the singularity along the dislocation line and exhibit excellent conformity with Volterra’s theory beyond the dislocation core. Geometrical frustration is the direct source of dislocation stress fields, as demonstrated through the multiplicative decomposition of deformation gradients. By leveraging the mathematical properties of the Riemann–Cartan manifold, we demonstrate that the Ricci curvature determines the symmetry of stress fields. These results substantiate a long-standing mathematical hypothesis: the duality between stress and curvature.

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39

Weidner, Timmo, Vincent Taupin, Sylvie Demouchy, Karine Gouriet, Antoine Guitton, Patrick Cordier, and Alexandre MUSSI. "From Electron Tomography of Dislocations to Field Dislocation Mechanics: Application to Olivine." Modelling and Simulation in Materials Science and Engineering, November 7, 2023. http://dx.doi.org/10.1088/1361-651x/ad0a42.

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Abstract We propose a new procedure to extract information from electron tomography and use them as an input in a field dislocation mechanics. Dislocation electron tomography is an experimental technique that provides three-dimensional information on dislocation lines and Burgers vectors within a thin foil. The characterized 3D dislocation lines are used to construct the spatial distribution of the equivalent Nye dislocation density tensor. The model dislocation lattice incompatibility equation and stress balance equation are solved with a spectral code based on fast Fourier transform algorithms. As an output of the model, one obtains the three-dimensional distribution of mechanical fields, such as strains, rotations, stresses, resolved shear stresses and energy, inside the material. To assess the potential of the method, we consider two regions from a previously compressed olivine sample. Our results reveal significant local variations in local stress fields and resolved shear stresses in various slip systems, which can impact the strong plastic anisotropy of olivine and the activation of different dislocation slip systems. It also evidences the built-up of kinematic hardening down to the nanometre scale.

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40

Koslowski, M., M. Ortiz, and A. M. Cuitino. "Statistical Modeling of a Dislocation Phase-Field in Ductile Single Crystals." MRS Proceedings 701 (2001). http://dx.doi.org/10.1557/proc-701-t4.5.1.

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ABSTRACTA model for the description of strain hardening and hysteresis at different temperatures and strain rates in ductile single crystals is introduced. The theory accounts for: and arbitrary number and arrangement of dislocation lines over a slip plane; the long-range elastic interactions between dislocation lines; the core structure of the dislocations; the interaction between the dislocations and applied resolved shear stress field; and the dissipative in teractions with short-range obstacles and lattice friction, resulting in hardening, path dependency and hysteresis. We introduce a variational formulation for the statistical mechanics of dissipative systems. The influence of finite temperature as well as the mechanics are modeled with Metropolis Monte Carlo simulations and a mean field approximation. The theory predicts a range of behaviors which are in qualitative agreement with observation, including: hardening and dislocation multiplication under monotonic loading and hysteresis loops under under cyclic loading. The flow stress was found to be dependent on the temperature and on the strain rate only at finite temperature.

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41

Anderson, Joseph Pierre, Vignesh Vivekanandan, Peng Lin, Kyle Starkey, Yash Pachaury, and Anter El-Azab. "Situating the Vector Density Approach Among Contemporary Continuum Theories of Dislocation Dynamics." Journal of Engineering Materials and Technology 144, no. 1 (August 30, 2021). http://dx.doi.org/10.1115/1.4052066.

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Abstract For the past century, dislocations have been understood to be the carriers of plastic deformation in crystalline solids. However, their collective behavior is still poorly understood. Progress in understanding the collective behavior of dislocations has primarily come in one of two modes: the simulation of systems of interacting discrete dislocations and the treatment of density measures of varying complexity that are considered as continuum fields. A summary of contemporary models of continuum dislocation dynamics is presented. These include, in order of complexity, the two-dimensional statistical theory of dislocations, the field dislocation mechanics treating the total Kröner–Nye tensor, vector density approaches that treat geometrically necessary dislocations on each slip system of a crystal, and high-order theories that examine the effect of dislocation curvature and distribution over orientation. Each of theories contain common themes, including statistical closure of the kinetic dislocation transport equations and treatment of dislocation reactions such as junction formation. An emphasis is placed on how these common themes rely on closure relations obtained by analysis of discrete dislocation dynamics experiments. The outlook of these various continuum theories of dislocation motion is then discussed.

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42

Bakhtiyari, Ensiye, Mahdi Javanbakht, and Mohsen Asle Zaeem. "Evolution of edge dislocations under elastic and inelastic strains: A nanoscale phase-field study." Mathematics and Mechanics of Solids, January 12, 2023, 108128652211405. http://dx.doi.org/10.1177/10812865221140527.

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A phase-field approach is used to study the evolution of edge dislocations in single crystals at the nanoscale. The characteristics of an advanced phase-field approach for dislocation evolution are investigated, and some advancements are made to make it more accurate in predicting the dislocation evolution. To verify the model and numerical procedure, the height of a slip system, the Burgers vector, and the distance between the cores of dislocations are calculated, which show a very good agreement with those of the existing theoretical solutions. The analytical and numerical solutions for the equilibrium shear stress versus order parameter are obtained, and in contrast to the previous models, the current model represents a physical model for the dislocation growth. Different methods are investigated to prevent dislocation widening, revealing that the periodic step-wise function of crystalline energy coefficient performs better than the periodic step-wise function of the Burgers vector and can keep dislocations inside their physical height. Several functions for the coefficient of normal gradient energy are investigated to prevent dislocation localization inside the dislocation band. The sample size effect on the dislocation evolution is also studied which reveals a non-linear variation of the number of dislocations inside the slip system versus the sample size. The presented model and results are useful for understanding and predicting the dislocation evolution and its interaction with other phenomena such as phase transformation.

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43

Huang, Yuanjie. "Electric features of dislocations and electric force between dislocations." Mathematics and Mechanics of Solids, October 20, 2020, 108128652096564. http://dx.doi.org/10.1177/1081286520965640.

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Dislocations and dislocation dynamics are the cores of material plasticity. In this work, the electric features of dislocations were investigated theoretically. An intrinsic electric field around a single dislocation was revealed. In addition to the well-known Peach–Koehler force, it was established that an important intrinsic electric force exists between dislocations, which is uncovered here for the first time and has been neglected since the discovery of dislocations. The electric forces may be large and sometimes could exceed the Peach–Koehler force for metals and some dielectric materials with large dielectric constant. Therefore, the electric force is anticipated to play a vital role in dislocation dynamics and material plasticity. Moreover, an external electric field could exert an electric force on dislocations and a threshold electric field was subsequently discovered above which this force enables dislocations to glide. Interestingly, it was found that some dislocations move in one direction, but others move in reverse in an identical electric field, which is in agreement with experimental observations. Despite dislocation motion under an electric field, to one’s surprise, both edge and screw dislocations do not carry net charges by themselves, which may tackle the long-standing puzzle on the charges of dislocations. These findings may supply people with new fundamental knowledge on dislocations as well as dislocation dynamics, and may assist people in understanding related phenomena.

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44

Acharya, Amit, and Jorge Viñals. "Field dislocation mechanics and phase field crystal models." Physical Review B 102, no. 6 (August 31, 2020). http://dx.doi.org/10.1103/physrevb.102.064109.

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45

Pal, Dayeeta, Yifan Wang, Ramya Gurunathan, and Leora Dresselhaus-Marais. "Measuring the Burgers vector of dislocations with dark-field X-ray microscopy." Journal of Applied Crystallography 58, no. 1 (February 1, 2025). https://doi.org/10.1107/s1600576724011968.

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The subsurface dynamics of dislocations are essential to many properties of bulk crystalline materials. However, it is challenging to characterize a bulk crystal by conventional transmission electron microscopy (TEM) due to the limited penetration depth of electrons. A novel X-ray imaging technique – dark-field X-ray microscopy (DFXM) – was developed to image hierarchical dislocation structures in bulk crystals. While today's DFXM can effectively map the line structures of dislocations, it is still challenging to quantify the Burgers vectors, the key characterization governing the dislocation behaviors. We extend the `invisibility criterion' formalism from the TEM theory to the geometrical-optics model of DFXM and demonstrate the consistency between DFXM and dark-field TEM using multi-diffraction-peak imaging for a single edge dislocation. Due to the practical difficulty of multi-peak DFXM experiments, we further study how the Burgers vector effect is encoded for a single-peak DFXM experiment. Using the geometrical-optics DFXM simulation, we explore the asymmetry of rocking tilt scans at different rolling tilts and develop a new method to characterize the Burgers vector. The conclusions of this study advance our understanding of the use of DFXM in characterizing individual dislocations, enabling the connection from bulk DFXM imaging to dislocation mechanics.

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46

Loiko, Konstantin V., Giri Nallapati, Keith M. Jarreau, Shashank S. Ekbote, Roy A. Hensley, Dale Simpson, Thomas E. Harrington, William R. Frensley, and Igor V. Peidous. "The Impact of Point Defects on Stress-Induced Dislocation Generation in Silicon." MRS Proceedings 610 (2000). http://dx.doi.org/10.1557/proc-610-b6.13.

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AbstractFactors responsible for the onset of dislocation generation in the fields of localized high stresses have been studied in LOCOS-isolated test structures by means of preferential etching, junction leakage analysis, and computer simulation. A strong correlation between densities of stacking faults and dislocations was observed in the experiments. Defect distributions also correlated to leakage currents. 2D simulations of stresses, interstitial injection, and stacking fault growth during field oxidation showed that maximum resolved shear stress in the structures did not exceed the critical level for dislocation generation and that the agglomeration of silicon interstitial atoms did not play a notable role in dislocation nucleation. Dislocation and stacking fault formation was attributed to surface mechanical damage introduced during plasma processing.

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47

Sozio, Fabio, and Arash Yavari. "A Geometric Field Theory of Dislocation Mechanics." Journal of Nonlinear Science 33, no. 5 (July 19, 2023). http://dx.doi.org/10.1007/s00332-023-09919-9.

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48

Sun, Y. Q., P. M. Hazzledine, and D. M. Dimiduki. "Stress-Driven Collective Nucleation of Dislocation Loops." MRS Proceedings 481 (1997). http://dx.doi.org/10.1557/proc-481-261.

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ABSTRACTThis paper presents an analysis of the collective nucleation of glide dislocation loops under the bias of a high shear stress. It introduces the concept of an ‘induced’ stress field associated with the planar distribution of glide dislocation loops. It shows that, due to the ‘induced’ field, glide dislocations nucleate in a collective, self-catalytic fashion at critical stresses and temperatures.

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49

Eymery, J., F. Fournel, K. Rousseau, D. Buttard, F. Leroy, F. Rieutord, and J. L. Rouvière. "Dislocation Networks Strain Fields Induced By Si Wafer Bonding." MRS Proceedings 673 (2001). http://dx.doi.org/10.1557/proc-673-p6.9.

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ABSTRACTBuried dislocation superlattices are obtained by bonding ultra-thin single crystal Si (001) films on Si (001) wafers. The twist of two Si wafers induces a regular square grid of dissociated screw dislocations and the tilt a 1-D array of mixed dislocation. The Burgers vector is a/2 <110> for both types of dislocation. The atomic displacements and deformations of pure screw and edge dislocations are calculated with an isotropic elasticity approximation taking into account the free surface and the thickness of the upper crystal. It is shown by these calculations that the elastic strain field propagates up to the surface, and quantitative arguments are given to choose the network period / film thickness ratio.

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50

Zhang, D., and R. C. Picu. "On the Interaction Between Mg Solute Atoms and Dislocations in Al-Mg Binary Alloys." MRS Proceedings 779 (2003). http://dx.doi.org/10.1557/proc-779-w5.1.

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AbstractThe interaction between solute atoms and dislocations is known to lead to negative strain rate sensitivity and poor formability. The negative rate sensitivity causes inhomogeneous flow and the Portevin-LeChatelier (PLC) effect. These observations motivate the present study of the solute-dislocation interaction in binary Al-Mg alloys. We report here on three issues. First, we determine the size and shape of stable Mg clusters at stationary dislocations of edge, 60° and pure screw type. We then evaluate the accuracy with which clustering is predicted by the classical pressure field-solute interaction formula, i.e. within the assumption that solute do not interact and the pressure field of the dislocation is unperturbed by the solute. Second, we investigate to what extent the presence of the cluster perturbs the far field of the dislocation. Finally, the effect of the solute on the stacking fault energy is investigated.

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