Dislocation mechanisms leading to protrusion growth under electric field induced stress on metal surfaces

The work presented in this thesis is related to the design of the future electron-positron collider, called the Compact Linear Collider (CLIC), which is currently under development at CERN. The designed operation of the collider requires accelerating electric field strengths of ∼ 100 MV/m range to reach the target energy range of 0.5 to 5 TeV for the collisions in a realistic and cost efficient way. An important limiting factor of the application of the very high electric fields is the electrical breakdown rate, which has drastic dependence on the accelerating electric field strength E (approximately proportional to E^30 ). In order to achieve material properties capable of tolerating higher electric fields, research on the materials related physical origin of the fundamental cause of electrical breakdown onset needs to be undertaken. The onset stage of the electrical breakdown on a broad area metal surfaces under electric field is still unknown, although many theories have been proposed earlier. In many of the theories, it has been common to postulate the existence of a geometric protrusion on the surface that is capable of causing high field enhancement and pre-breakdown electric currents in the vacuum over metal surfaces under electric field. However, such protrusions have never been seen on the metal surface prior to the breakdown. It has been recently experimentally observed that the average field that the material can tolerate without breakdown is correlated with the crystal structure of the material. This observation hints that some dislocation mechanism could be possibly related to the onset stage of the breakdown event. In this thesis, the following mechanism that can be responsible for the breakdown onset is analyzed. Application of the electric field exerts stress on a metal surface, which can cause the nucleation and mobility of the dislocations, i.e. plasticity. The localized plastic deformation can eventually lead to protrusion growth on the metal surface. Once a protrusion is formed on the surface, the electric field is enhanced on the protrusion site, further enhancing the protrusion growth. A defect such as a void can act as a stress concentrator which changes the otherwise uniform stress field and acts as an initiation site for plastic deformation caused by dislocations. In this thesis, we have examined the effect of an external stress on a near surface void in conditions which are relevant for the research and design of the accelerating structures of the CLIC collider. A void present at a near surface region of the accelerating structure causes local concentration of the stress induced by the external electric field on the conducting metal surface. The presence of such near surface void was experimentally observed in a metal sample prepared for experimental spark setup. By means of molecular dynamics simulation method we have shown that the stress can cause nucleation and/or movement of dislocations near the void. The mobility of dislocations then leads to formation of a protrusion on the material surface. We analyzed the nucleation of the dislocations in detail and constructed a simplified analytical model that describes the relevant physical factors affecting the nucleation event. Since the shear stress on the slip plane causes the mobility and nucleation of the dislocations, we analyzed the stress distribution on the slip plane between the void and surface by using finite element method and by calculating the atomic level stress with molecular dynamics method. The results were compared also to an analytic solution for a void located deep in the bulk under similar stress. It was found that the nearby surface had significant effect on the stress distribution only when the void depth was less than its diameter. Below this the maximum stress is equal to that for a void located deep in the bulk under similar external stress. The comparison of the finite element results to the atomic level stress revealed that the pre-existing surface stress near the void surface had significant effect on the stress distribution. In addition to the tensile stress caused by the electric field on the charged metal surface, pulsed surface heating also induces stress in the material surface region under alternating electric field. This cyclic thermal stress is known to cause fatigue and severe deformation of the metal surface. We investigated the condition relevant for yield by calculating atomic level von Mises strain which has been earlier related to dislocation nucleation. The strain concentration caused by the void was 1.9 times the bulk value. In order to see activated slip planes, we exaggerated the compressive stress to the extent that dislocation nucleation could be observed within the timespan allowed by the molecular dynamics simulation method. Dislocations were observed to nucleate at the sites of maximum von Mises strain. Taken together, the results presented in thesis contribute to the understanding of the stress distributions and possible dislocation related mechanisms under different stressing conditions assuming existence of a stress concentrator, such as a near surface void.Tässä väitöskirjassa esitetyt tulokset liittyvät CERNissä suunniteltuun Compact Linear Collider (CLIC) kiihdyttimen kehitystyöhön. Kiihdyttimessä käytetään elektronien ja positronien kiihdyttämiseen sähkökenttiä, joiden voimakkuuden suuruusluokka on ~100 MV/m. Näin voimakkailla sähkökentillä tyhjiökipinäpurkausten esiintymistiheys kasvaa huomattavasti sähkökentän kasvaessa, ja asettaa rajoituksia käytettävän sähkökentän suuruudelle. Jotta voitaisiin kehittää materiaaleja, joilla kipinäpurkausten esiintymistiheys olisi pienempi, on tutkittava niitä mekanismeja jotka johtavat kipinäpurkaukseen. Tyhjiökipinäpurkausten ensimmäisiä syntymekanismeja makroskooppisten metallipintojen välillä ei vielä täysin tunneta, vaikka useita terioita on esitetty ilmiötä kuvaamaan. Useissa teorioissa oletetaan, että jossakin metallipinnalla esiintyy hyvin pieni mutta korkea geometrinen kohouma, joka aiheuttaa suuren paikallisen sähkökentän voimistumisen. Tällaisia korkeita kohoumia ei kuitenkaan ole kokeellisesti suoraan havaittu, vaikka kentän paikallinen voimistuminen havaitaankin. Viimeaikaiset kokeelliset havainnot osoittavat, että materiaalien kyky vastustaa tyhjiökipinäpurkausta on yhteydessä niiden kiderakenteeseen. Tämä havainto viittaa siihen, että eräät kidevirheet, ns. dislokaatiot, saattaisivat liittyä tyhjiökipinäpurkausten syntymekanismiin, sillä niiden liike riippuu materiaalin kiderakenteesta. Dislokaatiot liikkuvat materiaalissa sen ollessa mekaanisessa jännityksessä. Koska sähkökenttä kohdistaa johdinmateriaalin pinnalle jännityksen ja muuttuvan sähkökentän alla materiaalin kuumeneminen aiheuttaa lämpölaajenemista, on tässä työssä muodostettu seuraavanlainen hypoteesi. Sähkökentän vaikutuksesta materiaalin pinnalle kohdistuu jännitys. Jos pinnan alla on esimerkiksi tyhjä suljettu onkalo tai muu täydellisestä kiteestä poikkeava rakenne, se aiheuttaa ulkoisen jännityksen keskittymisen. Jännitys synnyttää ja liikuttaa dislokaatioita, joiden vaikutuksesta pinnalle muodostuu kohouma. Kohouman muodostuminen aiheuttaa sähkökentän voimistumisen paikallisesti, johtaen lopulta kipinäpurkaukseen. Tätä hypoteesia ja mahdollisia dislokaatiomekanismeja on tutkittu molekyylidynamiikkasimulaatioiden ja äärellisten elementtien menetelmän avulla. Saadut tulokset ovat tuottaneet tietoa jännityksen jakautumisesta pinnan lähellä olevan onkalon ympäristössä, sekä mahdollisista dislokaatiomekanismeista, jotka voivat johtaa kohoumien muodostumiseen sekä materiaalin muodon muokkaantumiseen erilaisten ulkoisten jännitysten alla

Towards industrial applicability of (medium C) nanostructured bainitic steels (TIANOBAIN)

The project aimed at exploring the industrial feasibility of new super-high strength steels (SHSS) made using innovative processing methods and based on medium carbon nanostructured bainitic microstructures. It was envisaged that the steels could be applied in engineering applications in the transport industry and wear-resistant applications for example in the mining industry. The microstructural concept that was exploited, with the purpose of attaining UTS > 1600MPa, is the ausformed bainite in medium carbon steels (0.4-0.5 wt.%). In this process, austenite is deformed and during subsequent cooling and holding at lower temperatures (than that in regular practice) the unrecrystallized austenite transform to refined bainite with enhanced strength and toughness properties. The industrialization of this new steel design concept, involving innovative process development and novel design of relatively inexpensive compositions, is accompanied by new manufacturing risks and uncertainties in terms of achieving advanced mechanical and in-use properties (tensile, impact and fracture toughness, wear, bendability, etc.). Therefore, this project intended to gather information in terms of chemical composition design, alternative TMCP routes, microstructural evolution, mechanical properties and in-use performance to assess the potential of novel bainitic steel grades in order to develop recommendations for viable industrial processes.European Commission RFCS/RPJ/2015-709607.Peer reviewe

Numerical experiments on the solution of advection equation for moving phase interface:encountered problems and their solutions

Abstract As a part of the effort of constructing fundamentally physics based numerical model for growth of a phase in solid-to-solid phase transformations, a suitable mathematical description for advancing phase front and its numerical solution are required. The advection equation can be used for simulating the propagating phase front. However, it is well known that simple explicit finite difference solution in this case is unstable. Averaging of the spatial derivative provides useful stabilization for the numerical scheme, but exacerbates numerical dissipation and broadening of the continuous function describing the diffuse phase front. Numerical experiments were made, where these problems were observed. Simple solution procedures were introduced that effectively solved the problems for time scales that were required for the numerical solver to operate in the designed context

Full field model describing phase front propagation, transformation strains, chemical partitioning, and diffusion in solid–solid phase transformations

Abstract A novel mathematical formulation is presented for describing growth of phase in solid-to-solid phase transformations and it is applied for describing austenite to ferrite transformation. The formulation includes the effects of transformation eigenstrains, the local strains, as well as partitioning and diffusion. In the current approach the phase front is modeled as diffuse field, and its propagation is shown to be described by the advection equation, which reduces to the level-set equation when the transformation proceeds only to the interface normal direction. The propagation is considered as thermally activated process in the same way as in chemical reaction kinetics. In addition, connection to the Allen–Cahn equation is made. Numerical tests are conducted to check the mathematical model validity and to compare the current approach to sharp interface partitioning and diffusion model. The model operation is tested in isotropic 2D plane strain condition for austenite to ferrite transformation, where the transformation produces isotropic expansion, and also for austenite to bainite transformation, where the transformation causes invariant plane strain condition. Growth into surrounding isotropic austenite, as well as growth of the phase which has nucleated on a grain boundary are tested for both ferrite and bainite formation

Numerical simulations of gradient cooling technique for controlled production of differential microstructure in steel strip or plate

Abstract Numerical studies were conducted to investigate the applicability of cooling strategies for controlledly producing a microstructure in the steel strip or plate, which changes as function of the plate length. In the numerical simulations, the water spray cooling was varied as function of the plate length and as a result, the different parts of the plate were cooled at different rates. We applied the previously developed numerical code where the transformation latent heat is coupled with the heat conduction and transfer model, which has also been calibrated to correspond to experimental laboratory cooling line. The applicability of the method was investigated for controlledly creating alternating bainite and polygonal ferrite regions in plates of two different thicknesses (0.8 cm and 1.2 cm thick plates) by cooling different parts of the plate to different temperatures before switching off the water cooling so that polygonal ferrite forms in the part which has been cooled to higher temperature and bainite forms in the low temperature part. The simulation results indicate that the controlled production of such alternating regions is possible, but the resulting regions in the studied scenario cannot be very thin. The transition regions between the ferrite and bainite regions in the simulated cases are in the range of 5–15 cm. Controlled production of zones consiting of softer phase in the otherwise bainitic steel could offer a possibility for creating designed tracks in a steel bainitic strip or plate, where the mechanical working or cutting of the material is easier

Solving partial differential equations in deformed grids by estimating local average gradients with planes

Abstract For constructing physical science based models in irregular numerical grids, an easy-to-implement method for solving partial differential equations has been developed and its accuracy has been evaluated by comparison to analytical solutions that are available for simple initial and boundary conditions. The method is based on approximating the local average gradients of a field by fitting equation of plane to the field quantities at neighbouring grid positions and then calculating an estimate for the local average gradient from the plane equations. The results, comparison to analytical solutions, and accuracy are presented for 2-dimensional cases

Atomistic modeling of metal surfaces under electric fields: direct coupling of electric fields to a molecular dynamics algorithm

The effect of electric fields on metal surfaces is fairly well studied, resulting in numerous analytical models developed to understand the mechanisms of ionization of surface atoms observed at very high electric fields, as well as the general behavior of a metal surface in this condition. However, the derivation of analytical models does not include explicitly the structural properties of metals, missing the link between the instantaneous effects owing to the applied field and the consequent response observed in the metal surface as a result of an extended application of an electric field. In the present work, we have developed a concurrent electrodynamic–molecular dynamic model for the dynamical simulation of an electric-field effect and subsequent modification of a metal surface in the framework of an atomistic molecular dynamics (MD) approach. The partial charge induced on the surface atoms by the electric field is assessed by applying the classical Gauss law. The electric forces acting on the partially charged surface atoms (Lorentz and Coulomb) are then introduced in the MD algorithm to correct the atomic motion in response to the applied field. The enhancement factor at sharp features on the surface for the electric field and the assessment of atomic charges are discussed. The results obtained by the present model compare well with the experimental and density-functional theory results

Effects of chemical composition and austenite deformation on the onset of ferrite formation for arbitrary cooling paths

Abstract We present a computational method for calculating the phase transformation start for arbitrary cooling paths and for different steel compositions after thermomechanical treatments. We apply the method to quantitatively estimate how much austenite deformation and how many different alloying elements affect the transformation start at different temperatures. The calculations are done for recrystallized steel as well as strain hardened steel, and the results are compared. The method is parameterized using continuous cooling transformation (CCT) data as an input, and it can be easily adapted for different thermomechanical treatments when corresponding CCT data is available. The analysis can also be used to obtain estimates for the range of values for parameters in more detailed microstructure models

Modelling of austenite transformation along arbitrary cooling paths

Abstract A computational model based on the Johnson-Mehl-Avrami-Kolmogorov equation for simulating the onset and kinetics of austenite to bainite and martensite transformation has been fitted to experimental continuous cooling data for two different steels. We investigated how deformation below recrystallization temperature affected the transformation onset and kinetics in comparison to the same steel in the undeformed state. The fitted model can be used to simulate phase transformations occurring when the steel is cooled along any cooling path. The model can be fully coupled to heat transfer and conduction simulations in order to optimize cooling practice, for example in industrial thermomechanical processing of steel. The fitted model can also be used to predict the hardness of the steel after cooling