Presentation on theme: "Multiphysics simulations of surface under electric field"— Presentation transcript:
1 Multiphysics simulations of surface under electric field University of Tartu:V. ZadinA. AablooUniversity of Helsinki:A. PohjonenS. ParviainenF. DjurabekovaCERN:W. WuenchM. Aicheler2013
2 Electrical breakdowns Electrical breakdowns at CLIC accelerating structure materialsAccelerating gradients MV/mAccelerating structure damage due to electrical breakdownsLocal field enhancement up to factor 100Field enhancement caused by „invisible needles“M. Aicheler, MeVArc 2011Electrical breakdown rate must be decreased under 310-7 1/pulse/mVoids in the material as possible factors affecting surface defects
3 Void hypothesisA void as a possible mechanism for generating a field emitterVoid in material is a stress concentratorVoids are spherical due to surface energy minimizationIn hypothesis we consider a single void in metalWe aim to understand a protrusion growth mechanism in the case of spherical void in DC electric fieldSeveral mechanisms acting at once to produce a tip?May be, but for now we focus on oneField emitters as initiators of a breakdownThermal-electrical behavior of field emittersMechanical behavior of field emitters
4 Computer simulations in Chemistry and Physics DFTMolecular dynamicsMesoscale modelingFinite Element AnalysisDistance1Å1nm1μm10nm1mmfemtosecpicosecnanosecmicrosecsecondsyearsTime
5 Simulated systemFully coupled electric field – elastoplastic interactionElectric field deforms sampleDeformed sample causes local field enhancementDc El. field ramped from 0 … MV/mComsol Multiphysics 4.3bNonlinear Structural Materials ModuleAC/DC module3D-simulations, 2D-snapshotsSimulated materials:Soft copperSingle crystal copperStainless steel
6 Material modelElastoplastic deformation of material, simulation of large strainsValidation of material model and parameters by conducting tensile stress simulationsAccurate duplication of the experimental results (tensile and nanoindentation test)Parameters from tensile test are macroscopic, single crystal parameters are needed due to large grains in soft copperStructural SteelSoft Copper (CERN)Single crystal copper Often used copper parametersYoung’s modulus200 GPa3.05 GPa57 GPa110 GPaInitial yield stress290 MPa68 MPa98 MPa70 MPa Y. Liu, B. Wang, M. Yoshino, S. Roy, H. Lu, R. Komanduri,J. Mech. Phys. Solids, 53 (2005) 2718
7 MD vs FEM MD – exaggerated el. fields are needed MD simulations are accurate, but time consumingFEM is computationally fast, but limited at atomistic scaleVery similar protrusion shapeMaterial deformation starts in same region
8 Void at max. deformation – different materials Similar protrusion shape for all materialsHigher el. fields are needed to deform stronger materialsSlightly different maximum stress regionsPlastic deformation distribution highly dependent from material
9 Protrusion formation at different depths Close to surface void needs smallest el. field for deformationMax. stress for near surface voids is concentrate between void and sample surfaceMax. stress distribution moves to the sides of void by increasing depthDeeper voids cause whole material to deform plasticallySoft Cu
10 Cycling the voltage Cycling of the material under electric field Soft copper, spherical void, with h/r=0.5Electric field ramped up to 2500 MV/m -> 0 MV/mField is ramped until ultimate tensile strength is reachedProtrusion almost completely retracted after unloadingVery high residual stress after unloadingInitial yield stress ~70 MPaStress at void surface considerably higher than at material surfaceComplex evolution of stress distribution during unloading
11 Field enhancement factor Soft CuField enhancement factor to characterize protrusions shapeSoft copperElastic deformation affects field enhancementField enhancement increasing over whole el. field rangeField enhancement is continuous and smoothStainless steel, single crystal CuField enhancement almost constant until critical field valueVery fast increase of the field enhancement factorMaximum field enhancement is 2 timesField enhancement corresponds to protrusion growthSteel
12 Yield point Nonlinear dependence from the void depth For h/r<0.3, yielding starts at void tipFor h/r=0.3, yielding equal at tip and sidesFor h/r>0.3, stress is carried to the sides of the voidThree deformation mechanismsDeformation at metal surfaceDeformation at void surfaceDeformation due to decreased surface areaToo deep void starts to decrease the effective surface area of the sampleh/r=0.2SteelSingle crystal copperSoft copper
13 Deformation at realistic electric field strength Void formation starts at fields > 400 MV/mMaterial is plastic only in the vicinity of the defectThin slit may be formed by combination of voids or by a layer of fragile impuritiesField enhancement factor ~2.4Thin material layer over the void acts like a lever, decreasing the pressure needed for protrusion formation
14 Rising tip in el. fieldE=0.01 MV/mσMises, max<< 1PaσMises, max=68 MPaE=56 MV/mField emitting tip, raising from the surface is assumedSimulation starts, when the emitter is ~40o angleSimulation ends when fast increase of field enhancement factor startsE=75 MV/mσMises, max=165 MPaDynamic behavior of field enhancement factorElastic deformation up to ~56MV/mCorresponding field enhancement factor 35Raising tip can cause significant increase of the field enhancementElastic limit
15 Single tip deformation Plastic deformation in FEMDislocations in MDDislocations are carriers of plastic deformationPlastic deformationNeckingNanoscale tip under electric field induced stressSimulations with FEM and MDConstant temperatureNo emission currentsLinear ramping of el. fieldMD and FEM predict the same location for plastic deformationPiece of material is removed from the tipFEM overestimates plastically deformed area!
16 Interacting emitters Plastic regime: Elastic regime: Reversible deformation of the emittersPlastic regime:Highest stress is at inner side of the tipLimiting effect to the density of emitters?E=1V/mE=135 MV/mE=166 MV/mσMises, max << 1 PaTwo closely located emittersEmitter aspect ratio ~10Distance between the emitters – 0.3H (H – height of the emitter)Linear ramping of el. fieldσMises, max=60 MPaNearby emitters interactThe emitters repel due to the surface chargeσMises, max=130 MPa
17 Heating and emission currents Fowler-Nordheim eq. for emission currents – connection to the experimentFast, exponential temperature rise in the tipEmission currents concentrated to the top of the tipMelting temperature reached at ~204 MV/mEmission current localized to the „tip of the tip“
18 Selective heating of the tips Temperature of the tips, relative height 0.75Simulation of two field emittersEmitter 1 – height H fixedEmitter 2 – height changed from 0.1H to 1HRamping of the el. fieldOnly the highest tip emits currentsSignificant emission from smaller tip started, when its height was 85%-90% of the largest tip heightTemperature (oC)Tip behavior under the el. field:only the highest tips start to emit the current, when the field is turned onlongest tips heat, melt/vaporize, until they shorten to the height of the smaller tipsfinally, all the emitters should have equal height
19 Material heating during the breakdown Surface temp. of breakdown spot – melting temp. of copperRadius of breakdown spot – 100μmThermal expansion and corresponding stress are calculatedFast heating of the materialThermal expansion generates large stressesStress significantly larger than yield strength or ultimate tensile strength of copperFormation of large plastically deformed area around the breakdown spotTemperature 1 ns after the start of the dischargeTemperature (degC)von Mises stress (MPa)Can thermal expansion and resulting plastic deformation produce the conditions required for repeated breakdowns?
20 Conclusions FEM is a viable tool to simulate material defects MD is still needed to determine physics behind the effectsProtrusion shape is similar for all simulated materialsSignificant material deformation starts after exceeding yield strengthField enhancement corresponds to protrusion growthThree protrusion generation mechanismsDeformation mechanisms change at h/r~0.3 and h/r~ 1Near field emitters interact due to chargingSignificant field enhancement by rising emitterOnly the highest tips emit currentsEmitting tips are with equal height
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