creep deformation and fracture
TRANSCRIPT
Engineering Materials
2189101
Chedtha PuncreobutrDepartment of Metallurgical Engineering
Chulalongkorn University
Creep Deformation and Fracture
http://pioneer.netserv.chula.ac.th/~pchedtha/
From last time… deformation behaviour
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From last time…yield strength and necking
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Leaf spring
Aircraft Fuselage
MetalRolling
Necking
Room temperature VS Higher temperature
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At room temperature
𝜀 = 𝑓 𝜎
At room temperature
𝜀 = 𝑓(𝜎, 𝑡, 𝑇)
As the temperature is raised, loads that give no permanent deformation at room temperature cause materials to creep
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Why creep is important?
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A tungsten lamp filament which has sagged under its own weight owing to creep reason that lamps burn out
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Turbine blades in aircraft
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Turbine Bladecracked due to creep
Gas turbine
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Can creep happens at room temperature?
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Lead pipes often creep noticeably over the years
Source: M.F. Ashby
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Creep VS Temperature
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The temperature at which materials start to creep depend on their melting point
As a general rule, creep start when
𝑇 > 0.3 𝑡𝑜 0.4 𝑇𝑀 for metals
𝑇 > 0.4 𝑡𝑜 0.5 𝑇𝑀 for ceramics
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Designing against creep
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The material must carry the design loads, without failure, for the design life at design temperature
• Displacement-limited applications• Precise dimensions or small clearance
must be maintained • Disc and blades of gas turbines
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• Rupture-limited applications• Dimensional tolerance is relatively
unimportant, but fracture must be avoided such as pressure piping
Designing against creep
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The material must carry the design loads, without failure, for the design life at design temperature
• Stress relaxation-limited applications• Pre-tensioning of Bolts get loosen
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• Buckling-limited applications• Structural steelwork exposed to fire
Creep testing and Creep curve
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• In steady-state creep, strain increases steadily with time.
• In designing, steady-state creep concerns us most
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Creep test usually applied intension at constant load andat constant temperature
3 Stages of Creep
ሶ𝜀𝑠𝑠
𝑡𝑓
𝜀𝑓
Variation of creep rate with stress
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ሶ𝜖𝑠𝑠 = 𝐵𝜎𝑛
n is creep exponent
Two regime of creep
1. Power-law creep
2. Diffusional creep
Variation of creep rate with temperature
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ሶ𝜖𝑠𝑠 = 𝐶𝑒−(𝑄𝑅𝑇
)
Q is Activation Energy (J/mol) R is Universal gas constant
(8.31 J/mol/K)
ሶ𝜖𝑠𝑠 = 𝐴𝜎𝑛𝑒−(𝑄𝑅𝑇)
A, Q and n characterise the creep of a material
Rate of steady-state creep
Creep damage and creep fracture
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During creep, damage accumulates in the form of internal cavities
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Creep rupture diagram
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Creep rates follow Arrhenius law
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ሶ𝜖𝑠𝑠 = 𝐴𝜎𝑛𝑒−(𝑄𝑅𝑇)
Rate of steady-state creep
Arrhenius law
• Creep rate increases exponentially with temperature
• The time for a given amount of creep decreases exponentially with temperature
Diffusion
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Elapsed time ≈ 0 minutes. Ring radius = 2.6 mm.
Dropped Potassium Permanganate into water
@ T = 18°C
Diffusion
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Elapsed time = 57 minutes. Ring radius = 30.3 mm.
The movement of Potassium permanganate ions by random exchanges with water molecules
Diffusion
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The ions/atoms move from concentrated regions to less concentrated regions, i.e.The ions/atoms move down the concentration gradient.
𝐽 = −𝐷𝑑𝑐
𝑑𝑥
Fick’s first law of diffusion
number of atoms diffusing down the concentration gradient per second per unit area, called flux of atoms
Concentration gradient
Diffusion coefficient (m2/s)
Diffusion of atoms
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𝑙2
𝑙1
Number of atoms actually jump from A to B per second
𝑣
6𝑛𝐴𝑒
−𝑄/𝑅𝑇
Diffusion requires atoms to cross the energy barrier
Number of atoms actually jump from B to A per second
𝑣
6𝑛𝐵𝑒
−𝑄/𝑅𝑇
Net number of atoms climbing over barrier per second
𝑣
6(𝑛𝐴−𝑛𝐵)𝑒
−𝑄/𝑅𝑇
Diffusion of atoms
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𝑙2
𝑙1
Net flux of atoms
𝐽 =𝑣
6𝑙1𝑙2(𝑛𝐴−𝑛𝐵)𝑒
−𝑄/𝑅𝑇
Concentrations
𝑐𝐴 =𝑛𝐴
𝑙1𝑙2𝑟0, 𝑐𝐵 =
𝑛𝐵𝑙1𝑙2𝑟0
atom size
Net flux of atoms
𝐽 = −𝐷0𝑒−𝑄/𝑅𝑇
𝑑𝑐
𝑑𝑥
where𝑑𝑐
𝑑𝑥=𝑐𝐵 − 𝑐𝐴
𝑟0
𝐷0 =𝑣𝑟0
2
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Diffusion of atoms
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Net flux of atoms
𝐽 = −𝐷0𝑒−𝑄/𝑅𝑇
𝑑𝑐
𝑑𝑥
𝐽 = −𝐷𝑑𝑐
𝑑𝑥
Fick’s first law of diffusion 𝐷 = 𝐷0𝑒−𝑄/𝑅𝑇
Diffusion coefficient(Diffusivity)
The diffusion coefficient isexponentially dependenceon temperature
ሶ𝜖𝑠𝑠 = 𝐴𝜎𝑛𝑒−(𝑄𝑅𝑇)Compared with so diffusion may be related to creep
Diffusion Mechanisms
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Bulk diffusion
Diffusion in the bulk of a crystal can occur by two mechanisms
Interstitial Diffusion Vacancy Diffusion
Small atoms diffuse interstitially to spaces between atoms
When atoms are comparable in size, atom has to wait and diffuse to the missing atom (vacancy) next to it.
Diffusion Mechanisms
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Fast diffusion paths
Diffusion rate is much greater than in the bulk
Grain-boundary Diffusion Dislocation-core Diffusion
When grains are small or dislocations numerous, their contributions become important
Creep mechanisms
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Creep mechanisms in metals and ceramics
• Dislocation creep (power-law creep)
• Core diffusion
• Bulk diffusion
• Diffusion creep (linear-viscous creep)
• Grain-boundary diffusion
• Bulk diffusion
Creep mechanisms in polymers
• Viscous flow
Dislocation creep (power-law creep)
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How an edge dislocation moves (glide) through a crystal
The stress required to make a crystalline material to deform plastically is that needed to make the dislocations in it move.
Dislocation creep (power-law creep)
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The movement of dislocation is restricted by (a) intrinsic lattice resistance and (b) obstructing effect of obstacles (e.g. solute atoms and precipitates)
Dislocation creep (power-law creep)
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ሶ𝜖𝑠𝑠 = 𝐴𝜎𝑛𝑒−(𝑄𝑅𝑇)
Higher the higher the climb force so more dislocations become unlock
Diffusion creep (linear-viscous creep)
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• When the stress is reduced, the rate of power-law creep falls quickly. Creep does not stop!
• Instead creep takes place by diffusion (dislocations are not involved)
• At high T/TM : Bulk diffusion
• At low T/TM : Grain-boundary diffusion
Deformation Mechanism Diagram
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Creep in polymer
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• Example of creep in polymer : plastic clips slowly lose their grip
• Glass transition temperature (TG) is a criterion of creep resistance
• Glass transition temperature increases with degree of cross-
linking so cross-linked polymers are more creep-resistant at room
temperature than less cross-linked polymers
• Crystalline polymers are more creep-resistant than glassy
polymers
• Creep rate is reduced by filling them with glass or silica powder
Creep-limited design
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High Temperature Materials for Turbines
Efficiency VS Inlet temperature
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An increase in combustion temperature in a turbofan engine will generate an increase in engine efficiency
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Power VS Inlet temperature
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Power output of engine increases linearly with temperature
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Ni-based Superalloys
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• A superalloy is a metallic alloy which can be used at high temperatures, often up to 0.8 Tm
• Exceptional heat resistance, creep resistance, and corrosion resistance
Typical composition of creep-resistant blade (e.g. Nimonic)
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Ni-based Superalloys
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The effect of temperature on the tensile strength of several nickel-based alloys
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Ni-based Superalloys
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Simple reasons for complicated alloying addition
• to have as many atoms in solid solution as possible
(the cobalt, the tungsten, and the chromium)
• to form stable, hard precipitates of compounds such
as Ni3Al, Ni3Ti, MoC, TaC to obstruct the dislocations
• to form a protective surface oxide film of Cr2O3 to
protect the blade itself from attack by oxygen
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Ni-based Superalloys
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• Solid solution hardening
• Coherent precipitate
hardening
• Carbide phases on grain
boundaries
Three strengthening mechanisms are used in Ni Superalloys
Processing of turbine blade
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Investment casting of turbine blades. This produces a fine-grained material which may undergo a fair amount of diffusion creep, and which may fail rather soon by cavity formation.
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Microstructure of Superalloys in Turbine Blades
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Directional solidification (DS) of turbine blades.
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Single crystal (SX) of superalloy blade
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Deformation Mechanism Diagram
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Effect of grain size on diffusion creep
Improved manufacturing method
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The high-temperature capability of Superalloys has increased with improvements in manufacturing methods
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Active cooling
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A turbine blade designed for active cooling by a gas
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Temperature evolution and materials trends in turbine blades
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