nuclear fuels and materials - 151-2017-00l · nuclear fuels and materials - 151-2017-00l ⌸lecture...
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WIR SCHAFFEN WISSEN – HEUTE FÜR MORGEN
Nuclear Fuels and Materials - 151-2017-00L
Manuel A. Pouchon :: Head of LNM :: Paul Scherrer Institut
Master of Nuclear Engineering ‐ Spring Semester 2016
Lecture 5: Adv. Systems, New Damage Mech. (Creep, ..) New Materials
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o Components, Materials, Requirements: • LWRs• Advanced systems• new damage mechanism
o Creep / Stress rupture• Basics / Stages• Diffusion creep / Dislocation creep / Grain Boundary Sliding• Rupture• Norton‘s Creep Law / Monkman-Grant plot• Increase creep properties
o New Materials• Ferritic-Martensitic / Intermetallics / ODS / Ceramics• Example “Irradiation Creep”
o Additions / Repetition• Water chemistry / Galvanic Corrosion• Strengthening of metallic materials• Plastic Deformation• Stress Behavior• Dislocations / Burgers Vector
TOC
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• Temperature 320 (400)• Thermal neutrons• Loads (static, dynamic)• Water as coolant
Materials related boundary conditions for LWRs
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http://dx.doi.org/10.1016/j.actamat.2012.11.004
Materials in PWR
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prio 1 prio 2
• Google the materials of the different components
•Which kind of steels where?
•Why?
•Make a list
Homework
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Component Material Mass (MT)
Materials Issues
Fuel • UO2
• (U,Pu)O2
100 Fission gas release; fission product swelling; thermal conductivity decrease with burnup
Cladding,spacer grids
• Zircaloy:1.5 Sn; 0.5 (Fe, Ni, Cr); 0.1 O; bal Zr
25 Waterside corrosion and hydriding; embrittlement, growth; pellet-claddinginteraction; creep; fretting
Neutron absorbers • Ag-Cd-In (PWR), • B4C (BWR); • Gd2O3 (both)
~1 Embrittlement, thermal-mechanical fatigue
Reactor Pressure Vessel • Low-alloy steel:2 Cr ; 1 Mo; bal Fe
400 - 500 Radiation embrittlement
Steam Generator(PWR only)
• Low-alloy steel • Inconel: 60 Ni; 25 Cr; 15 Fe
Tube plugging, cracking, denting; leakage fromthe primary coolant to the secondary loop water
Reactor Internals • Stainless Steel:18 Cr; 8 Ni; bal Fe;
• Inconel
Swelling/creep, Stress-Corrosion Cracking, Fatigue
Ex-core components, primary piping
• Stainless steel - Stress-corrosion cracking (esp. BWR)
Valves, pumps • Stainless steel;• stellite: high Co conc.
- Cobalt dissolution => activation in core=> deposition in primary circuit
Components, Materials, Mass, Materials Issues
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• Proliferation• Sustainability• Closure of fuel cycle• Safety
Demands for advanced reactors
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(10-12y) R&D (~1B€) before 1st prototype of techno demo (source CEA, F. Carré)
Gen IV systems
Sodium Fast Reactor
Molten Salt Reactor
Gas Fast Reactor
Supercritical Water-cooled ReactorVery High Temperature Reactor
Lead FastReactor
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SFR GFR LFR VHTR SCWR MSR Fusion
CoolantT(oC)
Liquid Na,few bars
He, 70 bars, 480-850
Lead alloys, 550-800
He, 70 bars, 600-1000
Water, 24 MPa, 280-550
Molten salt,500-720
He, 80 bar,300-480 / Pb-17, 480-700
Core Structures
Wrapper F/M steelsCladdingAFMA F/M ODS
Fuel & core structuresSiCf/SiC composite
Target, Wondow, CladdingF/M steels ODS
Core GraphiteControl rodsC/C SiC/SiC
Cladding & core structuresNi based Alloys & F/M steels
Core structureGraphite Hastelloy
First wall BlanketF/M steels ODS SiCf/SiC
Temp. (oC) 390 – 700 600 – 1200 350 – 480 600 – 1600 350 – 620 700 – 800 500 - 625
DoseCladding200 dpa
60/90 dpaCladding~100 dpa
7/25 dpa
~100 dpa+ 10 ppm He & 45 ppm H per dpa
Other components
IHX or turbineNi alloys
IHX or turbineNi alloys
Source CEA
Structural Materials in Advanced Systems
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• Combined cycle plants (electricity and heat)• VHTR gas cooled, thermal neutrons, up to 1000 C gas temperature,
direct/indirect cycle)• Closing the fuel cycle • Fast spectrum (SFR, GFR)• Other projects: LMR, ADS, Traveling Wave, MSR, SCWR• Small medium Sized Reactors (SMR)
Advanced nuclear plants –current priorities
Nuclear Fuels and Materials - 151-2017-00L ⌸ Lecture 5 - Page 11/83March 2011
Delivering Nuclear Solutions for America’s Energy Challenges
Industrial Application
District Heating
Seawater Desalination
Petroleum Refining
Oil Shale and Oil Sand
Processing
Cogeneration of Electricity and Steam
Steam Reforming of Natural Gas
Hydrogen Production
800-
1000
°C
100
300
200
1000
400
600
500
700
900
800
LWRs
80-2
00°C
250-
550°
C
300-
600°
C
500-
900°
C
350-
800°
C
VHTR
NGNP
Potential Contribution of Fission Reactors to Process Heat Industries
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March 2011Delivering Nuclear Solutions for America’s Energy Challenges
Existing Plants – Assuming 25% penetration of process heat & power market - - - 2.7 quads*
Coal‐to‐Liquids (24 – 100,000 bpd new plants )
Petrochemical
(170 plants in U.S.)
Fertilizers/Ammonia
(23 plants in U.S.–NH3 production)
Petroleum Refining
(137 plants in U.S.)
Oil Sands/Shale
* Quad = 1x1015 Btu (293 x 106 MWth) annual energy consumptionHydrogen Production
Growing and New Markets – Potential for 9.3 quads of HTGR Process Heat & Power
Oil Sands/Shale
Potential U.S. Market for HTGRs
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VHTR – Potential applications
Oil companies • Refinery• De-supfurization of heavy oils• Production of gas• Coal gasification • Extraction from oil shales and tar-
sands
Metallurgy• Steel making
Chemical industry• Hydrogen production• Ethylen production• Styren production• …
Others• Sea water desalination• District heating
Other industries• Production of other metals
(aluminum, …)• Glass making
Electricity• Electricity production
Cement industries• Production of cements• Production of lime
Paper mill• Production of paste• Drying
Process heat for industry
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March 2011 Delivering Nuclear Solutions for America’s Energy Challenges
Nuclear IslandPresent or future generationProcess heat and/or electricity
Nuclear IslandPresent or future generationProcess heat and/or electricity
Renewable‐Electric IntegrationElectrolysis or co‐electrolysis driverAdditional electricity to grid
Renewable‐Electric IntegrationElectrolysis or co‐electrolysis driverAdditional electricity to grid
Hydrogen Generation PlantUpgrade of fossil and bio feedstocksCatalytic feedstock for coal to liquids
Hydrogen Generation PlantUpgrade of fossil and bio feedstocksCatalytic feedstock for coal to liquids
Liquid Fuels & Chemicals PlantCoal and biomass to liquidsProcess chemicals
Liquid Fuels & Chemicals PlantCoal and biomass to liquidsProcess chemicals
Carbon FeedstockCoalBiomass
Carbon FeedstockCoalBiomass
Re-thinking Energy — Hybrid Energy Systems
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• Dow needs high temperatures in its unit operations. As high as 1000 oC to crack ethane to ethylene
Requires > 3,700 MW & > 22 Million Lbs/h (9979 t/h) of steam to operate
• ~40% of Dow’s energy use is for conversion of petrochemical feedstocks (natural gas components ethane/butane and liquids such as naphtha) to ethylene
At $8/MMBTU natural gas equivalent fuel cost, DOW steam and power bill alone is ~$5 Billion per year
This alone equates to 14 MM tons per year of CO2 alone
• It is not just about EnergyPetrochemical Industry’s raw materials are energy, natural gas liquids, naphtha Dow’s world-wide feedstock & energy demand is almost ~1 MM BBL/day,
estimated cost of ~$32 billion in 2008 (~ 45% total annual operating costs and expenses)
Production shifting overseas.
• Energy Plan America: http://energy.doe.com/perspectives/plan.htm
1 btu = 1055 joulesMM = million metricbbl = barrel
DOW Chemical – Real Example
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Delivering Nuclear Solutions for America’s Energy Challenges
U.S. Europe Africa Asia
Past • Peach Bottom (P)• St. Vrain (P)
• AVR (.de, PB)• THTR‐300 (.de, PB)
Cancelled • PBMR (.za, PB)
Operating • HTTR (.jp, P)
• HTR‐10 (.cn, PB)
UnderConstruction
• HTR‐PM (.cn, PB)
Planned NGNP • Allegro (GFR, fast)
(V)HTR current situation
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Influence of advanced fuel cycle on life‐time and radio‐toxicity of high level waste (ALI : annual limit on intake)
Concepts for advanced fuel recycling. Option 1 consists of two aqueous separation steps where U, Pu, and Np are extracted in one stage and the minor actinides are extracted in another stage. The GANEX process releases U, Pu, and the minor actinides in one process step. For both options, only the fission products (FP) have to be disposed
Advanced Fuel Cycles
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U.S. Europe Russia Asia
Past • Clementine (mercury)
• EBR I/II• SEFOR• FFTF
• Dounreay (DFR, PFR)• Rhapsodie• Superphénix1250 MWe (‐1997)
• Phénix (‐2009)
• BN‐350
Cancelled • Clinch River• IFR
• SNR‐300 (De)
Operating • BN‐600 • Joyo (Jp)• FBTR (In)• Monju (Jp)• CEFR (Cn)
UnderConstruction
• BN‐800 (testing) • PBFR (In)
Planned • ASTRID• ALFRED (lead)
• Allegro (helium)
• BN‐1200 (constr. 2016)
• BN‐1800 (constr. 2020)
• Toshiba S4 (Jp)• JSFR (Jp)• Kalimer (Kr)
SFR-projects
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Temperature/Dose exposures
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Requirements for materials in future nuclear systems
Technical challenges& Leading physical phenomena
60-year lifetime Fast neutron damage (fuel and core materials)
• Effect of irradiation on microstructure, phase instability, precipitation• Swelling growth, hardening, embrittlement• Effect on tensile properties (yield strength, UTS, elongation…)• Irradiation creep and creep rupture properties• Hydrogen and helium embrittlement
High temperature resistance (SFR > 550°C, V/HTR > 850-950°C)• Effect on tensile properties (yield strength, UTS, elongation…)• High temperature embrittlement• Effect on creep rupture properties• Creep fatigue interaction• Fracture toughness
Corrosion resistance (primary coolant, power conversion, H2 production)• Corrosion and stress-corrosion cracking
(IGSCC, IASCC, hydrogen cracking & chemical compatibility…) F. Carré, CEAF. Carré, CEA
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• Thermal creep• Swelling• Irradiation creep • HT-Helium embrittlement• Low Cycle Fatigue• HT corrosion• Crack Growth• Interactions
Most important new damage mechanisms
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o Components, Materials, Requirements: • LWRs• Advanced systems• new damage mechanism
o Creep / Stress rupture• Basics / Stages• Diffusion creep / Dislocation creep / Grain Boundary Sliding• Rupture• Norton‘s Creep Law / Monkman-Grant plot• Increase creep properties
o New Materials• Ferritic-Martensitic / Intermetallics / ODS / Ceramics• Example “Irradiation Creep”
o Additions / Repetition• Water chemistry / Galvanic Corrosion• Strengthening of metallic materials• Plastic Deformation• Stress Behavior• Dislocations / Burgers Vector
TOC
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• What is creep and stress rupture• Creep laws: Norton law, Monkman Grant rule• Creep of metals and alloys: ferritic, martensitic, austenitic,
nickel-base (solid solution, nickelbase (gamma prime), ODS, intermetallics, refractory alloys
• Creep damage• Extrapolation of creep data• Creep crack growth
Creep and stress rupture
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1. Collapse at the ideal strength -(flow when the ideal shear strength is exceeded).
2. Low-temperature plasticity by dislocation glide -(a) limited by a lattice resistance (or Peierls' stress); (b) limited by discrete obstacles; (c) limited by phonon or other drags; and (d) influenced by adiabatic heating.
3. Low-temperature plasticity by twinning.4. Power-law creep by dislocation glide, or glide-plus-climb -
(a) limited by glide processes; (b) limited by lattice-diffusion controlled climb (“high-temperature creep”); (c) limited by core diffusion controlled climb (“low-temperature creep”); (d) power-law breakdown, (the transition from climb-plus-glide to glide alone); (e) Harper-Dorn creep; (f) creep accompanied by dynamic recrystallization.
5. Diffusional Flow -(a) limited by lattice diffusion (“Nabarro-Herring creep”); (b) limited by grain boundary diffusion (“Coble creep”); and (c) interface-reaction controlled diffusional flow.
http
://en
gine
erin
g.da
rtm
outh
.edu
/def
mec
h/ch
apte
r_1.
htm
The mechanisms may superimpose in complicated ways.
5 types of deformation mechanisms
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Thermal creep testing
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• Creep occurs under load at high temperature.• Boilers, gas turbine engines, and ovens are some of the systems
that have components that experience creep.• An understanding of high temperature materials behavior is
beneficial in evaluating failures in these types of systems. • Failures involving creep are usually easy to identify due to the
deformation that occurs.• Failures may appear ductile or brittle. Cracking may be either transgranular or intergranular.
• While creep testing is done at constant temperature and constant load actual components may experience damage at various temperatures and loading conditions.
http://www.materialsengineer.com/CA-Creep-Stress-Rupture.htm
Creep and Stress-rupture (1)
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• High temperature progressive deformation of a material at constant stress is called creep.
• High temperature is a relative term that is dependent on the materials being evaluated.
• A typical creep curve is shown below: In a creep test a constant load is applied to a tensile specimen maintained at a constant temperature. Strain is then measured over a period of time. The slope of the curve, identified in the figure, is the strain rate of the test during stage II or the creep rate of the material.
• Primary creep, Stage I, is a period of decreasing creep rate. Primary creep is a period of primarily transient creep. During this period deformation takes place and the resistance to creep increases until stage II.
• Secondary creep, Stage II, is a periodof roughly constant creep rate.Stage II is referred to as steady state creep.
• Tertiary creep, Stage III, occurs when there is a reduction in cross sectionalarea due to necking or effective reduction in area due to internal void formation.
http://www.materialsengineer.com/CA-Creep-Stress-Rupture.htm
Creep and Stress-rupture (2)
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Temperaturen Dependance
Dynamic recrystallization replaces deformed by undeformed material, permitting a new wave of primary creep, thus accelerating the creep rate.
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Stress Dependence
Power-law creep involving cell-formation by climb. Power-law creep limited by glide processes alone is also possible.
Power-law breakdown: glide contributes increasingly to the overall strain-rate.
Diffusional flow by diffusional transport through and round the grains. The strain-rate may be limited by the rate of diffusion or by that of an interface reaction.
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Creep mechanisms (schematically)
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Different creep regimes
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Deformation mechanisms involved in creep include:
• viscous creep: for amorphous solids
• vacancies or atoms : diffusion
• dislocations : slip
• grain boundaries : grain rotation, grain boundary sliding
Basics
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Viscous creep for amorphous solids such as many types of plastics is a diffusion dependent processthat is enhanced by increasing the temperature, i.e., thermally activated process, and follows the Arrhenius equation.
Q/RT.
Ae
Where Q is the activation energy for creep in cal/mol, R is the gas constant, and T is the absolute temperature in K.
As seen before, during creep A depends on the applied stress.
Viscous Creep
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for amorphous solids
Viscous Creep Illustration
https://upload.wikimedia.org/wikipedia/commons/thumb/9/93/Laminar_shear.svg/800px-Laminar_shear.svg.pnghttps://upload.wikimedia.org/wikipedia/commons/thumb/9/93/Laminar_shear.svg/800px-Laminar_shear.svg.png
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In crystalline materials, creep occurs either by• diffusional-
or • dislocation-
creep
Diffusional creep involves the motion of vacancies and this may occur primarily through the grains or along the grain boundaries.
Vacancy motion through the grains is called the Nabarro-Herring mechanism.
Vacancy motion along the grain boundaries is called the Coble mechanism.
Diffusional Creep
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Note that the vacancies and atoms move in opposite directions.
Diffusional Creep: Illustration
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These strain rates are given by
Nabarro-Herring/RT)(Q
22
.
eTd
Av
Coble/RT)(Q
32
.
eTd
Ab
Where • d is the diameter of the grain,• Qv is the activation energy of self or volume diffusion, and• Qb is the activation energy for grain boundary diffusion, which is usually
half that of self or volume diffusion.• A2 is a material constant.
Diffusional Creep: Equations
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In crystalline materials, dislocation creep involves the motion of dislocations where dislocation climb is an important factor.
Dislocation climb means that the edge of the extra plane of atoms move to another plane parallel to the previous plane that it was before.
This dislocation motion also involves the diffusion of vacancies and thus the strain rate is thermally activated having the form,
Dislocation creep
Where m varies from one material to another and is typically on the order of 5.
Thus creep can become quite complex.
More sophisticated methods are often applied to creep by using the Sherby-Dorn parameter and Larson-Miller parameter.
(Q/RT).
eT
A m
Dislocation Creep
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Dislocation Creep: Illustration
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http://www.tf.uni‐kiel.de/matwis/amat/def_en/http://www.tf.uni‐kiel.de/matwis/amat/def_en/kap_5/backbone/r5_3_3.html
Dislocation Climb
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Only • solid solution hardening and • precipitation hardening
remain effective at elevated temperatures to help prevent creep.
Grain boundary sliding during creep causes
a) the creation of voids at an inclusion trapped at the grain boundary and
b) the creation of a void at a triple point where 3 grains are in contact.
Creep
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c
time
tertiary
creep
Creep damage starts
Tertiary Creep
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• Stress rupture testing is similar to creep testing except that thestresses used are higher than in a creep test.
• Stress rupture testing is always done until failure of the material.• In creep testing the main goal is to determine the minimum creep rate in stage II.
Once a designer knows the materials will creep and has accounted for this deformation a primary goal is to avoid failure of the component.
• Stress rupture tests are used to determine the time to cause failure. Data is plotted log-log as in the charts below. A straight line is usually obtained at each temperature. This information can then be used to extrapolate time to failure for longer times.
• Changes in slope of the stress rupture line are due to structural changes in the material. It is significant to be aware of these changes in material behavior, because they could result in large errors when extrapolating the data.
Creep and Stress-rupture
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Modified 9Cr-1Mo ferritic-martensitic steel
Creep rupture Data: Example T91 VHTR RPV steel
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Norton‘s Creep Lawσ = A. ε̇n . exp (U/kT)
Monkman Grant Rulet F . ε̇ = Const
ε̇…. secondary creep ratet F … time to fracture
Important creep laws
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Norton’s Law for TiAl as an example
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Monkman-Grant plot
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Temperature limits of RPV materials
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Effect Consequence in material Kind of degradation in component
Displacement damageFormation of point defect clusters and dislocation loops
Hardening, embrittlement
Irradiation-induced segregationDiffusion of detrimental elements to grain boundaries
Embrittlement, grain boundary cracking
Irradiation-induced phase transitions
Formation of phases not expected according to phase diagram, phase dissolution
Embrittlement, softening
SwellingVolume increase due to defect clusters and voids
Local deformation, eventually residual stresses
Irradiation creep Irreversible deformationDeformation, reduction of creep life
Helium formation and diffusionVoid formation (inter- and intra-crystalline)
Embrittlement, loss of stress rupture life and creep ductility
Radiation Damage
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USC: ultra supercritical coal
Boiler Materials for USC plants
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Change matrix tohigher creep resistance (austenitic / fcc)
Change matrix tohigher creep resistance (austenitic / fcc)
Change other austenitic system e.g. Ni‐base (solid solution, precipitation hardening)
Change other austenitic system e.g. Ni‐base (solid solution, precipitation hardening)
Change to higher melting points and deformation mechanisms (refractory alloys, intermetallics )
Change to higher melting points and deformation mechanisms (refractory alloys, intermetallics )
Change to ceramicsChange to ceramics
Introduce stable obstacles to dislocation movement (oxide dispersoids, nano‐clusters)
Introduce stable obstacles to dislocation movement (oxide dispersoids, nano‐clusters)
Possibilities to increase creep properties
Possibilities to increase creep properties
Increase Creep Properties
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o Components, Materials, Requirements: • LWRs• Advanced systems• new damage mechanism
o Creep / Stress rupture• Basics / Stages• Diffusion creep / Dislocation creep / Grain Boundary Sliding• Rupture• Norton‘s Creep Law / Monkman-Grant plot• Increase creep properties
o New Materials• Ferritic-Martensitic / Intermetallics / ODS / Ceramics• Example “Irradiation Creep”
o Additions / Repetition• Water chemistry / Galvanic Corrosion• Strengthening of metallic materials• Plastic Deformation• Stress Behavior• Dislocations / Burgers Vector
TOC
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• Graphite (as moderator and core material)• Ferritic-martensitic 9 -12%Cr steels• Austenitic superalloys• Oxide dispersion strengthened steels• Intermetallics• Refractory alloys• Ceramics (bulk, reinforced)
Materials for advanced fission and fusion plants
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http://www.threeplanes.net/tmartensite.html
Tempered Matensite
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Development of ferritic-martensitic steels
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Advanced Metallic Materials (ODS)
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Intermetallics (Titanium-aluminide)
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Graphite SiC/SiC
Ceramic materials
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Irradiation Creep Experiment
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kT
QneB
Thermal and irradiation creep
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kT
QneB
Irradiation creep
Biased flow of point defects (interstitials and vacancies) to sinks
Thermal Creep
Dislocation slip and climb
Diffusion flow
Grain boundary sliding
strongly temperature‐dependence
power law stress‐dependence
n=1 or 2 ?
m 1 or 1/2 ?
Principle of Creep
mnKB
SDBB 0
K: dpa / rate
Thermal Creep – Irradiation Creep
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Comparison of irradiation creep compliance B0 as a function of irradiation temperature T. • The large black and grey‐filled symbols indicate light‐ion irradiations before and after damage efficiency correction, respectively:
• He‐implanted ODS PM2000 (•, •) and 19Cr‐ODS (▲,▲)• p‐irradiated ODS Ni‐20Cr‐1ThO2 (■,■), p‐irradiated martensitic DIN1.4914 (◆,◆).
• The small symbols indicate neutron irradiations to doses below 25 dpa (filled symbols) and above 25 dpa (empty symbols):
• ODS MA957 (▼, ▼ ), HT9 ( ■ , ■), HT9 (•), F82H ( ▲), Fe‐16Cr (◆).
neutrons
ions
Irradiaton Creep Compliance (update)
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Graphite
HTR‐10 core
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Single grain:
without creep
with creepJ.F.B. Payne, NNL
Graphite: anisotropy
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CTE: Coefficient of Thermal Expansion
Graphite Irradiation behavior
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Graphite Irradiation behavior
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Pyrolytic carbon (PyC)
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o Components, Materials, Requirements: • LWRs• Advanced systems• new damage mechanism
o Creep / Stress rupture• Basics / Stages• Diffusion creep / Dislocation creep / Grain Boundary Sliding• Rupture• Norton‘s Creep Law / Monkman-Grant plot• Increase creep properties
o New Materials• Ferritic-Martensitic / Intermetallics / ODS / Ceramics• Example “Irradiation Creep”
o Additions / Repetition• Water chemistry / Galvanic Corrosion• Strengthening of metallic materials• Plastic Deformation• Stress Behavior• Dislocations / Burgers Vector
TOC
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Addition: Corrosion Groups
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Addition: Water Chemistry
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At anodic sites:
Zn Zn2+ + 2e
Al Al3+ + 3e ;
Fe Fe 2+ + 2e
At the Cathodic sites:
2H+ + 2e H2
O2+ 4H+ + 4e 2H2O
O2 + 2H2O + 4e 4OH-
Addition: Water Chemistry
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Cathodic Protections
• By controlling the electrode potential so that the metal becomes immune orpassive (cathodic or anodic protection)
• By reducing the rate of corrosion with the aid of corrosion inhibitors added to theenvironment
• By applying an organic or inorganic protective coating• By proper materials selection, designing components
Anodic ProtectionKeeping material in anodic/passive range
Corrosion Protection Methods
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Mechanism At Room Temperature At high Temperature
Grain hardening Fully operative Diffusion processes and grain boundary sliding become important, large grains show better properties
Dislocation hardening operative Annealing of dislocationSolid solution strengthening
operative operative
Particle strengthening Orowan bowing or cutting Mainly climbingOrder effects Moderate influence Dislocation movement
through ordered lattice difficult due to diffusion effects
Strengthening of metallic materials
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Low temperature
lattice resistance
discrete obstacles resistance
High temperaturePower-law creep involving cell-formation by climb
Power-law breakdown: glide contributes increasingly
Dynamic recrystallization replaces deformed by undeformed material
Diffusional flow by diffusional transport through and round the grains
Overview: Plastic Deformation
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Typical for many
Metals and alloysCarbon steels (RT)
Bulk ceramics
Fiber reinforced
ceramics
Single Crystal
Stress-strain behaviour
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(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.
The stress-strain curve for an aluminum alloy
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http://dolbow.cee.duke.edu/TENSILE/tutorial/node4.html
Stress-strain behaviour
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http://dolbow.cee.duke.edu/TENSILE/tutorial/node3.html
Stress Strain: Engineering – Real
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In many materials, the yield stress is not very well defined and for this reason a standard has been developed to determine its value.
The standard procedure is to project a line parallel to the initial elastic region starting at 0.002 strain. The 0.002 strain point is often referred to as the 0.2% offset strain point.
0.2% offset strain point
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Is a vector, that represents the magnitude and direction of the lattice distortion of dislocation in a crystal lattice
Burgers Vector
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The perfect crystal in a) is cut and sheared one atom spacing in b) and c). The line along which the shearing occurs is a screw dislocation. A Burgers vector b is required to close a loop of equal atom spacings around the screw dislocation.
Dislocation: Screw
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The perfect crystal in a) is cut and an extra plane of atoms is inserted in b). The bottom edge of the extra plane is an edge dislocation in c). A Burgers vector b is required to close a loop of equal atom spacings around the edge dislocation.
a) b) c)
Dislocation: Edge
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A mixed dislocation showing a screw dislocation at the front of the crystal gradually changing to an edge dislocation at the side of the crystal. Note that the line direction of the dislocation is parallel to the Burgers vector of the screw dislocation and perpendicular to the edge dislocation.
Dislocation: Mixed