Dislocation core field. I. Modeling in anisotropic linear elasticity theory

Aside from the Volterra field, dislocations create a core field, which can be modeled in linear anisotropic elasticity theory with force and dislocation dipoles. We derive an expression of the elastic energy of a dislocation taking full account of its core field and show that no cross term exists between the Volterra and the core fields. We also obtain the contribution of the core field to the dislocation interaction energy with an external stress, thus showing that dislocation can interact with a pressure. The additional force that derives from this core field contribution is proportional to the gradient of the applied stress. Such a supplementary force on dislocations may be important in high stress gradient regions, such as close to a crack tip or in a dislocation pile-up

Sliding Crack Model for Nonlinearity and Hysteresis in the Triaxial Stress‐Strain Curve of Rock, and Application to Antigorite Deformation

Under triaxial deviatoric loading at stresses below failure, rocks generally exhibit nonlinearity and hysteresis in the stress‐strain curve. In 1965, Walsh first explained this behavior in terms of frictional sliding along the faces of closed microcracks. The hypothesis is that crack sliding is the dominant mode of rock inelasticity at moderate compressive stresses for certain rock types. Here we extend the model of David et al. (2012, https://doi.org/10.1016/j.ijrmms.2012.02.001) to include (i) the effect of the confining stress; (ii) multiple load‐unload cycles; (iii) calculation of the dissipated strain energy upon unload‐reload; (iv) either frictional or cohesive behavior; and (v) either aligned or randomly oriented cracks. Closed‐form expressions are obtained for the effective Young's modulus during loading, unloading, and reloading, as functions of the mineral's Young's modulus, the crack density, the crack friction coefficient and cohesion for the frictional and cohesive sliding models, respectively, and the crack orientation in the case of aligned cracks. The dissipated energy per cycle is quadratic and linear in stress for the frictional and cohesive models, respectively. Both models provide a good fit to a cyclic loading data set on polycrystalline antigorite, based on a compilation of literature and newly acquired data, at various pressures and temperatures. At high pressure, with increasing temperature, the model results reveal a decrease in friction coefficient and a transition from a frictionally to a cohesively controlled behavior. New measurements of fracture toughness and tensile strength provide quantitative support that inelastic behavior in antigorite is predominantly caused by shear crack sliding and propagation without dilatancy

Mesoscopic Analysis of Structure and Strength of Dislocation Junctions in FCC Metals

We develop a finite element based dislocation dynamics model to simulate the structure and strength of dislocation junctions in FCC crystals. The model is based on anisotropic elasticity theory supplemented by the explicit inclusion of the separation of perfect dislocations into partial dislocations bounding a stacking fault. We demonstrate that the model reproduces in precise detail the structure of the Lomer-Cottrell lock already obtained from atomistic simulations. In light of this success, we also examine the strength of junctions culminating in a stress-strength diagram which is the locus of points in stress space corresponding to dissolution of the junction.Comment: 9 Pages + 4 Figure

Generalized Stacking Fault Energy Surfaces and Dislocation Properties of Silicon: A First-Principles Theoretical Study

The generalized stacking fault (GSF) energy surfaces have received considerable attention due to their close relation to the mechanical properties of solids. We present a detailed study of the GSF energy surfaces of silicon within the framework of density functional theory. We have calculated the GSF energy surfaces for the shuffle and glide set of the (111) plane, and that of the (100) plane of silicon, paying particular attention to the effects of the relaxation of atomic coordinates. Based on the calculated GSF energy surfaces and the Peierls-Nabarro model, we obtain estimates for the dislocation profiles, core energies, Peierls energies, and the corresponding stresses for various planar dislocations of silicon.Comment: 9 figures (not included; send requests to [email protected]

Theoretical study of dislocation nucleation from simple surface defects in semiconductors

Large-scale atomistic calculations, using empirical potentials for modeling semiconductors, have been performed on a stressed system with linear surface defects like steps. Although the elastic limits of systems with surface defects remain close to the theoretical strength, the results show that these defects weaken the atomic structure, initializing plastic deformations, in particular dislocations. The character of the dislocation nucleated can be predicted considering both the resolved shear stress related to the applied stress orientation and the Peierls stress. At low temperature, only glide events in the shuffle set planes are observed. Then they progressively disappear and are replaced by amorphization/melting zones at a temperature higher than 900 K

1/f1/f noise and avalanche scaling in plastic deformation

We study the intermittency and noise of dislocation systems undergoing shear deformation. Simulations of a simple two-dimensional discrete dislocation dynamics model indicate that the deformation rate exhibits a power spectrum scaling of the type $1/f^{\alpha}$. The noise exponent is far away from a Lorentzian, with $\alpha \approx 1.5$. This result is directly related to the way the durations of avalanches of plastic deformation activity scale with their size.Comment: 6 pages, 5 figures, submitted to Phys. Rev.

Toughening and asymmetry in peeling of heterogeneous adhesives

The effective adhesive properties of heterogeneous thin films are characterized through a combined experimental and theoretical investigation. By bridging scales, we show how variations of elastic or adhesive properties at the microscale can significantly affect the effective peeling behavior of the adhesive at the macroscale. Our study reveals three elementary mechanisms in heterogeneous systems involving front propagation: (i) patterning the elastic bending stiffness of the film produces fluctuations of the driving force resulting in dramatically enhanced resistance to peeling; (ii) optimized arrangements of pinning sites with large adhesion energy are shown to control the effective system resistance, allowing the design of highly anisotropic and asymmetric adhesives; (iii) heterogeneities of both types result in front motion instabilities producing sudden energy releases that increase the overall adhesion energy. These findings open potentially new avenues for the design of thin films with improved adhesion properties, and motivate new investigation of other phenomena involving front propagation.Comment: Physical Review Letters (2012)

The importance of temporal stress variation and dynamic disequilibrium for the initiation of plate tectonics

We use 1-D thermal history models and 3-D numerical experiments to study the impact of dynamic thermal disequilibrium and large temporal variations of normal and shear stresses on the initiation of plate tectonics. Previous models that explored plate tectonics initiation from a steady state, single plate mode of convection concluded that normal stresses govern the initiation of plate tectonics, which based on our 1-D model leads to plate yielding being more likely with increasing interior heat and planet mass for a depth-dependent Byerlee yield stress. Using 3-D spherical shell mantle convection models in an episodic regime allows us to explore larger temporal stress variations than can be addressed by considering plate failure from a steady state stagnant lid configuration. The episodic models show that an increase in convective mantle shear stress at the lithospheric base initiates plate failure, which leads with our 1-D model to plate yielding being less likely with increasing interior heat and planet mass. In this out-of-equilibrium and strongly time-dependent stress scenario, the onset of lithospheric overturn events cannot be explained by boundary layer thickening and normal stresses alone. Our results indicate that in order to understand the initiation of plate tectonics, one should consider the temporal variation of stresses and dynamic disequilibrium

Hematite (U-Th)/He Thermochronometry Detects Asperity Flash Heating During Laboratory Earthquakes

Evidence for coseismic temperature rise that induces dynamic weakening is challenging to directly observe and quantify in natural and experimental fault rocks. Hematite (U-Th)/He (hematite He) thermochronometry may serve as a fault-slip thermometer, sensitive to transient high temperatures associated with earthquakes. We test this hypothesis with hematite deformation experiments at seismic slip rates, using a rotary-shear geometry with an annular ring of silicon carbide (SiC) sliding against a specular hematite slab. Hematite is characterized before and after sliding via textural and hematite He analyses to quantify He loss over variable experimental conditions. Experiments yield slip surfaces localized in an ∼5–30-µm-thick layer of hematite gouge with71% ± 1% (1σ) and 18% ± 3% He loss, respectively. Documented He loss requires short-duration, high temperatures during slip. The spatial heterogeneity and enhanced He loss from FM zones are consistent with asperity flash heating (AFH). Asperities \u3e200–300 µm in diameter, producing temperatures \u3e900 °C for ∼1 ms, can explain observed He loss. Results provide new empirical evidence describing AFH and the role of coseismic temperature rise in FM formation. Hematite He thermochronometry can detect AFH and thus seismicity on natural FMs and other thin slip surfaces in the upper seismogenic zone of Earth’s crust

Undissociated screw dislocations in silicon: calculations of core structure and energy

The stability of the perfect screw dislocation in silicon has been investigated using both classical potentials and first-principles calculations. Although a recent study by Koizumi et al . stated that the stable screw dislocation was located in both the 'shuffle' and the 'glide' sets of {111} planes, it is shown that this result depends on the classical potential used, and that the most stable configuration belongs to the 'shuffle' set only, in the centre of one hexagon. We also investigated the stability of an sp 2 hybridization in the core of the dislocation, obtained for one metastable configuration in the 'glide' set. The core structures are characterized in several ways, with a description of the three-dimensional structure, differential displacement maps and derivatives of the disregistry