Free-Surface Effects in 3D Dislocation Dynamics: Formulation and Modeling

2002 ◽  
Vol 124 (3) ◽  
pp. 342-351 ◽  
Author(s):  
Tariq A. Khraishi ◽  
Hussein M. Zbib
Keyword(s):  
Free Surface ◽  
Stress Component ◽  
Dislocation Dynamics ◽  
Dislocation Segment ◽  
Shear Stresses ◽  
Dislocation Loops ◽  
Dislocation Interaction ◽  
Collocation Points ◽  
Image Segment ◽  
Selection Of

Recent advances in 3-D dislocation dynamics include the proper treatment of free surfaces in the simulations. Dislocation interaction and slip is treated as a boundary-value problem for which a zero-traction condition is enforced at the external surfaces of the simulation box. Here, a new rigorous method is presented to handle such a treatment. The method is semi-analytical/numerical in nature in which we enforce a zero traction condition at select collocation points on a surface. The accuracy can be improved by increasing the number of collocation points. In this method, the image stress-field of a subsurface dislocation segment near a free surface is obtained by an image segment and by a distribution of prismatic rectangular dislocation loops padding the surface. The loop centers are chosen to be the collocation points of the problem. The image segment, with proper selection of its Burgers vector components, annuls the undesired shear stresses on the surface. The distributed loops annul the undesired normal stress component at the collocation points, and in the process create no undesirable shear stresses. The method derives from crack theory and falls under “generalized image stress analysis” whereby a distribution of dislocation geometries or entities (in this case closed rectangular loops), and not just simple mirror images, are used to satisfy the problem’s boundary conditions (BCs). Such BCs can, in a very general treatment, concern either stress traction or displacements.

A New Dislocation-Dynamics Model and Its Application in Thin Film-Substrate Systems

2005 ◽  
Vol 875 ◽  
Author(s):  
E.H. Tan ◽  
L.Z. Sun
Keyword(s):  
Thin Films ◽  
Mechanical Performance ◽  
Dislocation Motion ◽  
Dislocation Dynamics ◽  
Dislocation Segment ◽  
Dislocation Loops ◽  
Dynamics Model ◽  
Proposed Model ◽  
Simulation Results ◽  
Film Substrate

AbstractBased on the physical background, a new dislocation dynamics model fully incorporating the interaction among differential dislocation segments is developed to simulate 3D dislocation motion in crystals. As the numerical simulation results demonstrate, this new model completely solves the long-standing problem that simulation results are heavily dependent on dislocation-segment lengths in the classical dislocation dynamics theory. The proposed model is applied to simulate the effect of dislocations on the mechanical performance of thin films. The interactions among the dislocation loops, free surface and interfaces are rigorously computed by a decomposition method. This framework can be used to simulate how a surface loop evolves into two threading dislocations and to determine the critical thickness of thin films. Furthermore, the relationship between the film thickness and yield strength is established and compared with the conventional Hall-Petch relation.

scholarly journals Defect mastering - one of the topic challenges for crystal growth

2014 ◽  
Vol 70 (a1) ◽  
pp. C32-C32
Author(s):  
Peter Rudolph
Keyword(s):  
Crystal Growth ◽  
Grain Boundaries ◽  
Point Defect ◽  
Dislocation Dynamics ◽  
Cell Diameter ◽  
Second Phase ◽  
Dislocation Loops ◽  
Misfit Stress ◽  
Dislocation Interaction

The quality of single crystals, epitaxial layers and devices made there from are very sensitively influenced by structural and atomistic deficiencies generated during the crystal growth. Crystalline imperfections comprise point defects, dislocations, grain boundaries, second-phase particles. Over more than a half-century of the development of crystal growth, most of the important defect-forming mechanisms have become well understood [1-2]. As a result, the present state of technology makes it possible to produce crystals of remarkably high quality. However, that is not to say that all problems are already solved. For instance, in comparison with silicon the point defect dynamics in semiconductor and oxide compounds is not nearly as well understood. The density of equivalent defect types and antisites in each sub-lattice is determined by deviation from stoichiometry. Their charge state depends on the Fermi level position leading via interaction with dopants to certain compensation level and complex formation. One measure proves to be the in situ control of stoichiometry. Due to high-temperature dislocation dynamics heterogeneous dislocation substructures are formed. Both, acting thermo-mechanical stress and given point defect situation force the dislocation to glide and climb. In the course of enthalpy minimization the long-range character of dislocation interaction produces agglomerates and patterns with polygonized cell walls, i.e. small angle grain boundaries [3]. Thanks to the rules of correspondence of Taylor and Kuhlmann-Wilsdorf one is able to estimate the interaction between shear stress, dislocation density and cell diameter (Fig.). In epitaxy the Nye tensor, describing dislocation distribution inhomogeneity, affects the layer stress considerably. The growth under minimum stress, solution hardening and in situ stoichiometry control are effective counteracting methods. One of the most serious consequences during cooling down of as-grown crystals is the point defect condensation in precipitates and micro-voids decorating dislocation patterns or inducing high mechanical misfit stress that generates dislocation loops. It proves to be favourable to anneal the crystal a few degrees below the melting point in order to dissolve the particles and re-diffuse their into the crystal matrix.

Image Contrast of Dislocation Loops Near a Free Surface

1977 ◽  
Vol 35 ◽  
pp. 52-53
Author(s):  
S. M. Ohr
Keyword(s):  
Free Surface ◽  
Dislocation Loop ◽  
Image Contrast ◽  
Stress System ◽  
Shear Stresses ◽  
Dislocation Loops ◽  
Axially Symmetric ◽  
Displacement Fields ◽  
Elastic Fields ◽  
Analytical Expressions

The image contrast of dislocation loops computed in the past has made use of the displacement fields which do not take into account the presence of stress- free foil surfaces. The free surface modifies the elastic fields around a dislocation loop and hence can influence the image contrast observed in the electron microscope. The effect can be significant particularly when the loops lie close to one of the foil surfaces. In general, the elasticity problem of dislocation loops that takes the free surface into account is difficult to handle mathematically. In the present paper, the method of Bastecka1 was extended to obtain explicitly the analytical expressions for the displacement fields around a pure edge circular dislocation loop lying parallel to the foil surface. In this method, the stress fields of an image dislocation loop and another axially symmetric stress system were added in order to eliminate the normal as well as shear stresses at the surface.

Sedimentation in Storage Tank Structures

1994 ◽  
Vol 29 (1-2) ◽  
pp. 363-372 ◽  
Author(s):  
Virginia R. Stovin ◽  
Adrian J. Saul
Keyword(s):  
Numerical Models ◽  
Effective Means ◽  
Design Guidelines ◽  
Laboratory Model ◽  
Shear Stresses ◽  
Model Situation ◽  
Combined Sewer ◽  
Urban Watercourse ◽  
Storage Structures ◽  
Selection Of

Although storage tanks provide an effective means of reducing the magnitude and frequency of combined sewer overflow discharges, and thereby of alleviating urban watercourse pollution, poorly designed storage structures frequently suffer from maintenance problems arising from sedimentation. The development of design guidelines that optimise the self-cleansing operation of storage structures is clearly a priority for urban drainage research. This paper describes a system that has been developed to study sediment deposition in laboratory model-scale storage structures. The patterns of deposition resulting from a selection of flow regimes are described, and the need for time-varying and time series storm tests is highlighted. Sedimentation patterns are shown to predominantly depend on the flow field, and the critical bed shear stresses for deposition and erosion in the model situation are identified. Hence, the potential application of numerical models to the design problem is discussed.

Annealing of dislocation loops in dislocation dynamics simulations

2009 ◽  
Vol 3 ◽  
pp. 012001 ◽  
Author(s):  
Dan Mordehai ◽  
Emmanuel Clouet ◽  
Marc Fivel ◽  
Marc Verdier
Keyword(s):  
Dislocation Dynamics ◽  
Dislocation Loops ◽  
Dynamics Simulations

Utilizing Modeling in a Reliability Study of ACA Joints in Humidity Tests

2013 ◽  
Vol 10 (1) ◽  
pp. 30-39 ◽  
Author(s):  
Kirsi Saarinen ◽  
Laura Frisk
Keyword(s):  
Radio Frequency Identification ◽  
Cost Savings ◽  
Experimental Tests ◽  
Shear Stresses ◽  
Cycling Test ◽  
Humidity Level ◽  
Anisotropic Conductive Adhesive ◽  
Frequency Identification ◽  
Identification Tags ◽  
Selection Of

Radio frequency identification tags (RFID) with anisotropic conductive adhesive (ACA) joints are used in various applications where the environmental conditions may impair their reliability. Thus the effects of different environmental stresses on reliability need to be investigated. The purpose of this work was to study whether a relatively simple shear stress model can be utilized in reliability prediction of anisotropically conductive paste (ACP) joints in an accelerated humidity test on the basis of the information obtained from another humidity test. If modeling gives accurate results when studying reliability, the need for actual testing would decrease and thereby time and cost savings could be achieved. In this study, finite element models were made to calculate shear stresses in ACP joints induced by two different humidity tests. Additionally, experimental tests were performed and the results were compared with those of modeling. The test samples were RFID tags whose microchips were attached with ACP. A constant humidity test was used to study the effects of high humidity level and a humidity cycling test was used to examine the effects of constantly varying humidity. In the modeling it was observed that the selection of the stress-free temperature has a significant effect on the results. With three different stress-free temperatures, three different sets of results were obtained. Although the tags saturated in the extreme conditions of the humidity cycling test, according to modeling, the change in relative humidity level in the humidity cycling test did not increase the harshness of the test. However, the temperature change in the humidity cycling test increased the harshness.

A Continuous Desingularized Source Distribution Method Describing Wave–Body Interactions of a Large Amplitude Oscillatory Body

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Aichun Feng ◽  
Zhi-Min Chen ◽  
W. G. Price
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Water Surface ◽  
Numerical Solutions ◽  
Free Water ◽  
Source Distribution ◽  
Surface Boundary ◽  
Distribution Method ◽  
Collocation Points ◽  
Calm Water

A Rankine source method with a continuous desingularized free surface source panel distribution is developed to solve numerically a wave–body interaction problem with nonlinear boundary conditions. A body undergoes forced oscillatory motion in a free water surface and the variation of wetted body surface is captured by a regridding process. Free surface sources are placed in continuous panels, rather than points in isolation, over the calm water surface, with free surface collocation points placed on the calm water surface. Nonlinear kinematic and dynamic free surface boundary conditions along the collocation points on the calm water surface are solved in a time domain simulation based on a Lagrange time dependent formulation. Compared with isolated desingularized source points distribution methods, a significantly reduced number of free surface collocation points with sparse distribution are utilized in the present numerical computation. The numerical scheme of study is shown to be computationally efficient and the accuracy of numerical solutions is compared with traditional numerical methods as well as measurements.

scholarly journals Assessment of Susceptibility to Liquefaction of Saturated Road Embankment Subjected to Dynamic Loads

2014 ◽  
Vol 36 (1) ◽  
pp. 15-22 ◽  
Author(s):  
Anna Borowiec ◽  
Krzysztof Maciejewski
Keyword(s):  
Factor Of Safety ◽  
Stress Component ◽  
Critical Time ◽  
Water Reservoir ◽  
Constitutive Relationship ◽  
Plastic Behavior ◽  
Shear Stresses ◽  
Time Step ◽  
The Road ◽  
Liquefaction Susceptibility

Abstract Liquefaction has always been intensely studied in parts of the world where earthquakes occur. However, the seismic activity is not the only possible cause of this phenomenon. It may in fact be triggered by some human activities, such as constructing and mining or by rail and road transport. In the paper a road embankment built across a shallow water reservoir is analyzed in terms of susceptibility to liquefaction. Two types of dynamic loadings are considered: first corresponding to an operation of a vibratory roller and second to an earthquake. In order to evaluate a susceptibility of soil to liquefaction, a factor of safety against triggering of liquefaction is used (FSTriggering). It is defined as a ratio of vertical effective stresses to the shear stresses both varying with time. For the structure considered both stresses are obtained using finite element method program, here Plaxis 2D. The plastic behavior of the cohesionless soils is modeled by means of Hardening Soil (HS) constitutive relationship, implemented in Plaxis software. As the stress tensor varies with time during dynamic excitation, the FSTriggering has to be calculated for some particular moment of time when liquefaction is most likely to occur. For the purposes of this paper it is named a critical time and established for reference point at which the pore pressures were traced in time. As a result a factor of safety distribution throughout embankment is generated. For the modeled structure, cyclic point loads (i.e., vibrating roller) present higher risk than earthquake of magnitude 5.4. Explanation why considered structure is less susceptible to earthquake than typical dam could lay in stabilizing and damping influence of water, acting here on both sides of the slope. Analogical procedure is applied to assess liquefaction susceptibility of the road embankment considered but under earthquake excitation. Only the higher water table is considered as it is the most unfavorable. Additionally the modified factor of safety is introduced, where the dynamic shear stress component is obtained at a time step when its magnitude is the highest - not necessarily at the same time step when the pore pressure reaches its peak (i.e., critical time). This procedure provides a greater margin of safety as the computed factors of safety are smaller. Method introduced in the paper presents a clear and easy way to locate liquefied zones and estimate liquefaction susceptibility of the subsoil - not only in the road embankment.

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