Modelling tooth-shape errors using random variables

The development of the industry consecutively requires more exact and more efficient power transmission techniques. In order to create efficiently meshing gears it is mandatory to manufacture the gears with accurate geometrical shape. This is especially true for worm gears in hypoid or in spiroid drives. Former approaches were focusing on the properties of geometrically ideal worm gears. Taking manufacturing limitations into account the ideal shape is not the case of real gears. The authors´ indication is that these inaccuracies should not be neglected. Accordingly the goal of our study is to work out an adaptable mathematical approach for handling the shape errors of worm gears

Abnormal subgrain growth in a dislocation-based model of recovery

Simulation of subgrain growth during recovery is carried out using two-dimensional discrete dislocation dynamics on a hexagonal crystal lattice having three symmetric slip planes. To account for elevated temperature (i) dislocation climb was allowed and (ii) a Langevin type thermal noise was added to the force acting on the dislocations. During the simulation, a random ensemble of dislocations develop into subgrains and power-law type growth kinetics are observed. The growth exponent is found to be independent of the climb mobility, but dependent on the temperature introduced by the thermal noise. The in-depth statistical analysis of the subgrain structure shows that the coarsening is abnormal, i.e. larger cells grow faster than the small ones, while the average misorientation between the adjacent subgrains remains nearly constant. During the coarsening Holt's relation is found not to be fulfilled, such that the average subgrain size is not proportional to the average dislocation spacing. These findings are consistent with recent high precision experiments on recovery.Comment: 17 pages, 11 figure

The role of weakest links and system size scaling in multiscale modeling of stochastic plasticity

Plastic deformation of crystalline and amorphous matter often involves intermittent local strain burst events. To understand the physical background of the phenomenon a minimal stochastic mesoscopic model was introduced, where microstructural details are represented by a fluctuating local yielding threshold. In the present paper, we propose a method for determining this yield stress distribution by lower scale discrete dislocation dynamics simulations and using a weakest link argument. The success of scale-linking is demonstrated on the stress-strain curves obtained by the resulting mesoscopic and the discrete dislocation models. As shown by various scaling relations they are statistically equivalent and behave identically in the thermodynamic limit. The proposed technique is expected to be applicable for different microstructures and amorphous materials, too.Comment: 13 pages, 12 figure

Dislocation patterning in a two-dimensional continuum theory of dislocations

Understanding the spontaneous emergence of dislocation patterns during plastic deformation is a long standing challenge in dislocation theory. During the past decades several phenomenological continuum models of dislocation patterning were proposed, but few of them (if any) are derived from microscopic considerations through systematic and controlled averaging procedures. In this paper we present a two-dimensional continuum theory that is obtained by systematic averaging of the equations of motion of discrete dislocations. It is shown that in the evolution equations of the dislocation densities diffusionlike terms neglected in earlier considerations play a crucial role in the length scale selection of the dislocation density fluctuations. It is also shown that the formulated continuum theory can be derived from an averaged energy functional using the framework of phase field theories. However, in order to account for the flow stress one has in that case to introduce a nontrivial dislocation mobility function, which proves to be crucial for the instability leading to patterning

Submicron plasticity: yield stress, dislocation avalanches, and velocity distribution

The existence of a well defined yield stress, where a macroscopic piece of crystal begins to plastically flow, has been one of the basic observations of materials science. In contrast to macroscopic samples, in micro- and nanocrystals the strain accumulates in distinct, unpredictable bursts, which makes controlled plastic forming rather difficult. Here we study by simulation, in two and three dimensions, plastic deformation of submicron objects under increasing stress. We show that, while the stress-strain relation of individual samples exhibits jumps, its average and mean deviation still specify a well-defined critical stress, which we identify with the jamming-flowing transition. The statistical background of this phenomenon is analyzed through the velocity distribution of short dislocation segments, revealing a universal cubic decay and an appearance of a shoulder due to dislocation avalanches. Our results can help to understand the jamming-flowing transition exhibited by a series of various physical systems.Comment: 5 page

Diszlokáció rendszerek statisztikus tulajdonságainak vizsgálata = Investigation of the statistical properties of dislocation ensembles

A pályázat célkitűzéseinek megfelelően diszlokációk kollektív tulajdonságait vizsgáltuk mint elméletileg mind kísérletileg. Analitikus számításokkal és numerikus szimulációval vizsgáltuk a diszlokációk következtében kialakuló belső feszültségeloszlás tulajdonságait. Megállapítottuk, hogy az eloszlás központi része Lorentz eloszlású, míg a lecsengő tartományban a feszültség köbével fordítottan arányos. Továbbá kimutattuk, hogy a külső feszültség hatására egy a feszültség 4. hatványával leeső aszimmetrikus tag jelenik meg. Megmutattuk, hogy egy 2D diszlokációrendszer relaxációja során a különböző fizikai mennyiségek az idő hatványfüggvényeként csengenek le. Kimutattuk, hogy a diszlokáció climb bekapcsolása jól definiált cellaszerkezet kialakulásához vezet.. A korábban mikroszkopikus meggondolásokkal kidolgozott diszlokáció kontinuum elméletet sikerült egy variációs elvből származtatni. Ez lehetővé tette az elmélet általánosítását többszörös csúszásra ill. oldott atomok hatásának beépítését is. Az elmélet segítségével részletesen megvizsgáltuk egy extra hozzáadott diszlokáció terének árnyékolását a többi diszlokáció átrendeződése következtében (Debye screening) . A kísérleti munka során nanoindentációval Cu egykristályokon meghatároztuk a mikrokeménység relatív fluktuációját. Az irodalomban először megállapítottuk, hogy a diszlokációsűrűséghez hasonlóan ez is az alkalmazott feszültség függvényében egy éles maximumot mutat. | According to the proposal the collective properties of dislocations were investigated both by theoretical and experimental methods. The properties of the internal stress distribution generated by dislocations were investigated by analytical calculations and computer simulations. It was found that the central part of the distribution is Loretzian while its tail decays with the invers cube of the stress. If external stress is applied the distribution becomes asymmetric. The antisymmetric part decaying with the invers fourth power of the stress. Numerical studies show that during the relaxation of the dislocation ensemble the different macroscopic quantities decay with some power of the time. Beside this, it is obtained that the dislocation climb leads to the the formation of cell structure. The continuum theory of dislocations derived earlier from microscopic considerations was reformulated into a phase field theory. This allowed us to extend the theory to multiple slip and study the influence of solute atoms. With this framework the Debye screening of the stress field of an extra dislocation was analysed in details . The relative fluctuation of microhardness (RFM) was determined by nanoindentation performed on deformed Cu single crystals. It was found that like the fluctuation of the dislocation density the RFM alo exhibits a sharp maximum as a function of applied stress