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 3: Toughness, Fatigue, Irradiation Effects, Corrosion, …. Nuclear Fuels and Materials - 151-2017-00L ⌸ Lecture 3 - Page 2/88 • Toughness o Impact test – Charpy o Fracture Toughness (KIC) o J-Integral (JIC) • Fatigue o Wohler S-N diagram • RPV & irradiation dose o Parts o Construction o Welding o Low carbon steel o Radiation dose • Irradiation Damage / Effect o Defect formation and annealing o Hardening / Embrittlement o Creep / Swelling • Corrosion / Segregation / IASCC TOC
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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
When dropping a ceramic piece to ground it breaks – metals usually not. The quantity relating the
• resistance of a material to sudden (impact) loads
• is called toughness.
Construction materials must have high toughness. For many metallic materials (including RPV-steels) the toughness is temperature dependent with a sudden change at a so-called transition temperature. This transition temperature can change during service (ageing) which means an increase of failure risk.
Toughness is measured with impact testing machines or with fracture mechanics samples as shown in the next viewgraphs.
Pile-up of dislocations at a barrier which might be a grain boundary or an included particle may result in a micro-crack. Within crystal lattice micro-cracks are created when three unit dislocations combine into a single dislocation.
It is possible that micro-cracks may exist in the metal due to the previous history of solidification or working. However, even an initially sound material may develop cracks on an atomic scale.
Crack tips produce a 1/√r singularity. The stress fields near a crack tip of an isotropic linear elastic material can be expressed as a product of 1/√r and a function of θ with a scaling factor K:
where the superscripts and subscripts I, II, and III denote the three different modes that different loadings may be applied to a crack. The detailed breakdown of stresses and displacements for each mode are summarized in [2].
“Goofy duck” analog for three modes of crack loading. (a) Crack/beak closed. (b) Opening mode. (c) Sliding mode. (d) Tearing mode. (Courtesy of M. H. Meyers.)
Fracture Toughness or different MaterialsGraphite/ Ceramics/ Semicond
Metals/ Alloys
Composites/ fibers
Polymers
5
KIc
(MP
a ·
m0.
5)
1
Mg alloys
Al alloys
Ti alloys
Steels
Si crystalGlass -soda
Concrete
Si carbide
PC
Glass 6
0.5
0.7
2
4
3
10
20
30
<100>
<111>
Diamond
PVC
PP
Polyester
PS
PET
C-C(|| fibers) 1
0.6
67
40506070
100
Al oxideSi nitride
C/C( fibers) 1
Al/Al oxide(sf) 2
Al oxid/SiC(w) 3
Al oxid/ZrO 2(p)4Si nitr/SiC(w) 5
Glass/SiC(w) 6
Y2O3/ZrO 2(p)4
K1c – plane strain stress concentration factor – with edge crack; A Material Property we use for design, developed using ASTM Std: ASTM E399 - 09 Standard Test Method for Linear-Elastic Plane-Strain Fracture Toughness K1c of Metallic Materials
Composite reinforcement geometry is: f = fibers; sf = short fibers; w = whiskers; p = particles. Addition data as noted (vol. fraction of reinforcement):1. (55vol%) ASM Handbook, Vol. 21, ASM Int.,
Materials Park, OH (2001) p. 606.2. (55 vol%) Courtesy J. Cornie, MMC, Inc.,
Waltham, MA.3. (30 vol%) P.F. Becher et al., Fracture
Mechanics of Ceramics, Vol. 7, Plenum Press (1986). pp. 61-73.
4. Courtesy CoorsTek, Golden, CO.5. (30 vol%) S.T. Buljan et al., "Development of
Ceramic Matrix Composites for Application in Technology for Advanced Engines Program", ORNL/Sub/85-22011/2, ORNL, 1992.
6. (20vol%) F.D. Gace et al., Ceram. Eng. Sci. Proc., Vol. 7 (1986) pp. 978-82.
Physically the J-integral is related to the area under the curve of a load versus load-point displacement
J. R. Rice, Appl. Mech. 35(2), 379-386 (1968) doi:10.1115/1.3601206
J-Integral and Fracture Toughness
The J-integral can be described as follows
where• F is the force applied at the crack tip • A is the area of the crack tip • is the change in energy per unit length • σ is the stress • is the change in the strain caused by the stress
Fracture toughness is then calculated from the following equation
where • K1c is the fracture toughness in mode one loading • v is the Poisson's ratio • E is the Young's Modulus of the material
• E: Young's modulus of the material• γ: surface energy density
• a: flaw length• σf: and the stress at fracture
The growth of a crack requires the creation of two new surfaces and hence an increase in the surface energy. Griffith found an expression for the constant C in terms of the surface energy of the crack by solving the elasticity problem of a finite crack in an elastic plate. Briefly, the approach was:
• Compute the potential energy stored in a perfect specimen under a uniaxial tensile load.
• Fix the boundary so that the applied load does no work and then introduce a crack into the specimen. The crack relaxes the stress and hence reduces the elastic energy near the crack faces. On the other hand, the crack increases the total surface energy of the specimen.
• Compute the change in the free energy (surface energy − elastic energy) as a function of the crack length. Failure occurs when the free energy attains a peak value at a critical crack length, beyond which the free energy decreases by increasing the crack length, i.e. by causing fracture
The growth of a crack requires the creation of two new surfaces and hence an increase in the surface energy. Griffith found an expression for the constant C in terms of the surface energy of the crack by solving the elasticity problem of a finite crack in an elastic plate. Briefly, the approach was:
• Compute the potential energy stored in a perfect specimen under a uniaxial tensile load.
• Fix the boundary so that the applied load does no work and then introduce a crack into the specimen. The crack relaxes the stress and hence reduces the elastic energy near the crack faces. On the other hand, the crack increases the total surface energy of the specimen.
• Compute the change in the free energy (surface energy − elastic energy) as a function of the crack length. Failure occurs when the free energy attains a peak value at a critical crack length, beyond which the free energy decreases by increasing the crack length, i.e. by causing fracture ht
Repeated loading for high cycle fatiguehttp://www.finiteelementanalysis.com.au/featured/what-is-fatigue/http://www.finiteelementanalysis.com.au/featured/what-is-fatigue/
Material (Curve ) A:endurance limit which represents a stress level below which the material does not fail and can be cycled infinitely. e.g. Steel & Ti
Material (Curve ) B:do not exhibit well-defined endurance limits. These materials instead display a continuously decreasing S-N response. Fatigue strength Sf for a given number of cycles must be specified.e.g. non-ferrous metals and alloys (Al, Cu, Mg, …)
Gas tungsten arc welding (GTAW) / tungsten inert gas (TIG) welding
Gas metal arc welding (GMAW)(1) Direction of travel(2) Contact tube(3) Electrode(4) Shielding gas(5) Molten weld metal(6) Solidified weld metal(7) Workpiece
• Type I damage is oriented either longitudinal or transverse, located in the weld metal and remains within the weld metal.
• Type II damage is similar to Type I, but grows out of the weld metal into the adjacent HAZ and base material.
• Type III damage is located in the coarse-grained region of the HAZ.
• Type IV damage is located in the fine-grained/partially transformed region of the HAZ
Chan W, McQueen R, Prince J, Sidey D (1991) Metallurgical experiences with high temperature piping in ontario hydro ASME PVP 22. Service experience in operating plants, New York
• Transition zones between two alloys (dissimilar welds)
doi: 10.1115/1.4031129For DMW joints preparation, two root passes have been employed using TIG process and Inconel 82/52 TIG rods for the respective weld joints. The close chamber purging was provided during root passes of the both joints. The subsequent fill passes applied with shielded metal arc welding process using Inconel 182 and Inconel 152 electrodes at reverse polarity.
A ladle containing 150 tons of liquid steel is lowered into the tank degasser at Pennsylvania Steel Technologies to remove hydrogen from steel for harder railheads.
Typical isochronous annealing curve for pure Cu after irradiation at 4.2 K with fast neutrons to typical doses of 10-5 dpa. The annealing temperature T is normalized to the melting temperature of Cu. 10 minutes at successively higher temperatures
FD: Frenkel Defects
Tipping PG (ed) Understanding and mitigating ageing in nuclear power plants, WoodhaedPublishing Ltd, Cambridge
Stages - I: initiation self-interstitial atom migration (correlated & uncorrelated)II: long-range migration of SIA clusters and SIA-impurity complexesIII: associated with vacancy migration IV: mitigation of vacancy clusters and vacancy-solute complexesV: thermal dissociation of (displacement cascade produced) vacancy clusters
Influence of irradiation temperature on the formation of different obstacles taking an austenitic steel as an example
At lower temperatures the irradiation induced defects are predominant, whereas with increasing temperature the point defect concentration of thermal equilibrium governs microstructural development and irradiation damage starts to disappear. This can also be seen from an analysis of the diffusion coefficients shown in the next slide.
Wiedersich H (1986) In: Physics of radiation effects in crystals Elsevier 237
Dth: Thermal diffusion
Drad: radiation induced diffusion
Dm: ion mixing
• At high temperatures thermal diffusion is predominant.
• Radiation induced diffusion depends on the density of sinks. Sinks reduce the amount of excess point defects which decreases the respective diffusion coefficient as shown here with „no sinks“, p=10-4 and p=10-3.
• Ion mixing which happens at low temperatures independent of the temperature will not further be discussed here.
Uniform Corrosion Uniform corrosion, as the name suggests, occurs over the majority of the surface of a metal at a steady and often predictable rate
homogeneous
Galvanic Corrosion Can occur when tow different metals are placed in contact with each other
localized
Pitting Corrosion Pitting corrosion occurs in materials that have a protective film such as a corrosion product or when a coating breaks down
localized
Crevice Corrosion If two areas of a component in close proximity differ in the amount of reactive constituent available the reaction in one of the areas is speeded up
Intergranular Corrosion
Preferential attack of the grain boundaries of the crystals that form the metal
• Corrosion can cause local attack such as pitting or grain boundary degradation which can be considered as crack-like defects from which fatigue cracks can propagate.
• The formation of intrusions and extrusions can destroy a protective layer and expose fresh material to the corrosive atmosphere leading eventually to severe degradation of the newly created fresh surface and consequently to local damage.
• Protective layers (e.g. oxides) can spall off removing material and creating a new surface which can be attacked again.
• Reaction between the atmosphere and the material (nitriding, oxydation etc.) can lead to microstructural changes like carbide-or nitride formation or the dissolution of aluminum-containing phases when aluminum oxide is formed which can result in a change of the mechanical properties. ISBN 978-1-4471-2915-8
• porous layer at the right side. The porous layer can easily spall off and it also allows penetration of corrosive species. https://192.107.58.30/D19/Heikinheimo.pdf
A Pourbaix diagram for iron. Similar to phase diagrams which are based on thermodynamic equilibrium a potential/phdiagram mapping out equilibrium phases of an aqueous electrochemical systemcan be derived form the Nernst equation.
Aqueous corrosion can be studied by measuring the potential of the corrosion system against a standard electrode.
In the polarization curve the potential is plotted as a function of the current density.
• The actual corrosion potential i.e. the potential difference between standard electrode and corrosion system becomes zero and no current flows.
• Increasing the potential leads at first to an increase in the current (active part) and
• turns back to a passive part where the current remains constant. In this area passivation (self-protection) of the surface happens.
• Further increase of the potential leads to increase of current which means that the passivation is no longer fully maintained. Radiolysis taking place mainly in the reactor core region changes the composition of the water which has an influence on the electrochemical behavior. ISBN 978-1-4471-2915-8
Hypothetical polarization diagram for a passivable system with active, passive and transpassive regions.
Only a few systems exhibit this behavior in an appreciable and usable way. The corrosion rate of an active-passive metal can be significantly reduced by shifting the potential of the metal so that it is at a value in the passive range.
The current required to shift the potentialin the anodic direction from the corrosion potential Ecorr can be several orders of magnitude greater than the current necessary to maintain the potential at a passive value.
The current will peak at the passivation potential value shown as Epp.
• AB represents cathodic behavior, • BG is the active zone. The metal is not passivated at its free
corrosion potential, B. • AC and DC are Tafel-type straight lines drawn for the reduction and
oxidation reactions of the normal metal dissolution (M=M++e). • At potentials more positive than B, corrosion rate increases, and
reaches a maximum at the passivation potential, G, which is often given the symbol, Epp.
• The transition from active dissolution occurs as a solid species becomes more thermodynamically stable than the metal ion. A protective film begins to form and causes a sudden drop in corrosion current density in the region G to J.
• From J to P, the passive zone, the current density is maintained at a steady, low level, until,
• at P, breakdown of the protective film begins. It is here that the likelihood of pitting is greatest, and consequently
• the potential Ec, often called the critical pitting or breakdownpotential. It is a useful parameter in assessing pitting properties of materials. It should be noted that it is not an absolute parameter, and varies according to both metallurgical and environmental conditions.
• At potentials more positive than P, the current density begins to rise as more and more pits propagatehttp://www.corrosionclinic.com/
Stage 1: below a threshold value of K1, called K1SCC, growth of a crack by SCC is not expected, but above this value the initial SCC growth rate increases with increasing K1, called stage 1 cracking
Stage 2: the crack growth rate is independent of K1 and depends instead on the corrosive environment and temperature. During stage 2 growth, K1 continues to increase and this leads to the rapid acceleration of the crack in …
Stage 3: …and final fast fracture when K1 reaches K1C which is the Fracture Toughness of the material.
Predicted radiation temperature and flux effects on radiation induced segregation behaviour of austenitic steels. The left bar refers to typical reactor conditions
Was GS, Busby J, Andresen PL (2006) Effect of irradiation on stress-corrosion cracking and corrosion in light water reactors. ASM Handbook 13C corrosion environments and industries ASM international, pp 386–414
Segregation: thermally driven movement of atoms to grain boundaries.
Temper embrittlement of steels is a very well known example for segregation related deterioration of toughness. Elements like phosphorus, sulphur or manganese diffuse to grain boundaries. The cohesion along the grain boundaries is weakened which leads to a reduction of toughness (reduction of fracture toughness or increase of ductile-to-brittle fracture transition temperature). Such grain boundaries can also act as preferential corrosion sites leading to stress corrosion cracking as discussed later.
Radiation induced segregation is the radiation-induced redistribution of alloy constituents at point defect sinks such as grain boundaries. Radiation induced segregation can be described in terms of the so called « Inverse Kirkendall Effect ». This inverse Kirkendall effect refers to cases where an existing flux of point defects affects the interdiffusion of A and B. In case of irradiation segregation in a homogeneous AB alloy occurs because the irradiation has produced excess point defects and a flux of point defects.
The above left figure explains the mechanism for a binary alloy more in detail. The ordinates represent the concentrations of vacancies and interstitials, respectively, in arbitrary units. The x-axis gives the distance from the grain boundary. The differences in the diffusion coefficients of A and B lead to a dilution of the concentration of atoms A and to an increase of the concentration of atoms of type B towards the grain boundaries.
The figure on the right shows the proton irradiated austenitic steel (304 SS) as an example. The chromium concentration diminishes at the grain boundary, whereas nickel increases
• Irradiation damage leads to hardening of the matrix making basically the grain boundaries more attractive as path for growing cracks. This is what often happens as a result of hardening also without irradiation.
• Irradiation is also responsible for changes in grain boundary compositions by radiation induced segregation (primarily chromium depletion) which can further weaken the coherence of them.
• The surface of the cracks (particularly at the crack tip) is exposed to the radiolysis products which lead to chemical corrosion attack.
• Additionally, the crack can act as crevice supporting crevice corrosion.
In March 2002, plant staff discovered that the borated water that serves as the reactor coolant had leaked from cracked control rod drive mechanisms directly above the reactor and eaten through more than six inches (150 mm) of the carbon steel reactor pressure vessel head over an area roughly the size of a football.
A breach most likely would have resulted in a loss-of-coolant accident.http://en.wikipedia.org/wiki/Davis-Besse_Nuclear_Power_Station
An incomplete mixing area of high and low temperature fluids in nuclear components, fluid temperature fluctuates with random frequencies. It induces random variations of local temperatures gradients in structural walls, which lead to cyclic thermal stress. When thermal stress and cycle number are large, there are possibilities of crack initiations and propagations. This couple thermal hydraulic and thermal mechanical phenomenon is called thermal striping, which should be prevented.