Deformation mechanisms maps & creep-resistant ...
Lecture 32 - Deformation mechanisms maps & creep-resistant materials DEFORMATION MECHANISM MAPS •
For steady-state creep (ignores microstructural changes, cavitation and elasticity)
•
Different mechanisms can operate simultaneously
•
Fastest mechanism will dominate ⇒ Depends on temperature, stress and grain size
•
Deformation-mechanism map ⇒ Dominant mechanisms for stress & temperature Includes lines of constant strain rate
Note on this map: “High-temperature” power-law creep is “lattice-diffusion” power-law creep “Low-temperature” power-law creep is “core-diffusion” power-law creep •
Boundary-diffusion creep ∝ d-3; lattice-diffusion creep ∝ d-2
ME382 - 11/iv/14
1
Lecture 32 - Deformation mechanisms maps & creep-resistant materials •
With small grain sizes, boundary diffusion may dominate for all temperatures
•
Lattice diffusion may dominate at higher temperatures with large grains (because Ql > Qb)
•
Increase in grain size reduces diffusional creep rate, but not power-law creep ∴
Regime of power-law creep dominance increases
Example: Cylindrical pressure vessel of pure nickel with grain size of 0.01 mm. Average radius of cylinder = 200 mm; wall thickness = 1 mm; internal pressure of 0.1 MPa. What is life time at 860 ºC if failure occurs at an effective strain of 0.01
σ˜ H = 3PR/2t = 17.3 MPa
σ θθ = PR/t; σ zz = PR/2t; σ rr = 0
⇒
But, from Mohr’s circle of stress:
σ˜ H = 3τ ;
∴
∴
τ = 17.3/ 3 = 10 MPa
At 860 ºC
γ˙ = 10 −5 s −1
But, from Mohr’s circle of strain:
ε˙˜H = γ˙ / 3
ε˙˜H = 5.7 × 10−6
s−1
∴
At 860 ºC
∴
Life time = 0.01/(5.7 x 10-6) = 1700 secs = 28.9 minutes
ME382 - 11/iv/14
2
Lecture 32 - Deformation mechanisms maps & creep-resistant materials •
Transient creep maps can be plotted by including elastic contribution ∴ Give total strain at fixed time ∴ Should, in principle, include effects of microstructure change, but ....
•
Relative contribution of creep to total strain increases with time
Case study
•
Turbine blade ω = 1000 rad/s, radius = 0. 3 m; design calls for γ˙ < 10 −8 s−1 ; T = 450 °C → 700 °C
σ = rω 2 ρl where l is distance from tip of blade; ρ (for Ni) = 8900 kg/m3 ∴
At root, the normal stress = 120 MPa (shear stress is about 60 MPa)
•
Start off with considering pure Ni
•
Pure nickel: power-law creep with large strain rates
•
Increasing grain size won’t help
•
Alloying helps suppress power-law creep
ME382 - 11/iv/14
3
Lecture 32 - Deformation mechanisms maps & creep-resistant materials
MARM200 wt %
Al
Ti
W
Cr
Nb
Co
C
B
Zr
Ni
5.0
2.0
12.5
9.0
1.0
10.0
0.15
0.15
0.05
Bal
•
MAR-M200 strengthened by solid solution of W, Co & pttes of Ni3(TiAL)
•
Contains Cr for corrosion resistance
•
Alloying cuts power-law creep
•
Leaves diffusional flow ⇒ increase grain size to 1 cm (e.g. directional solidification) DESIGN FOR HIGH-TEMPERATURE APPLICATIONS
•
Reduce temperature Ø
Cooling vents:
Allow cool fluid to pass over component
Ø
Thermal barrier coatings Often use ceramics which have a high Tm and low conductivity ME382 - 11/iv/14
4
Lecture 32 - Deformation mechanisms maps & creep-resistant materials Need to avoid damage to the coating Stresses induced by thermal expansion mismatch
⇒
delamination
•
Chose materials with good oxidation resistance
•
Fundamental creep resistance generally scales with melting temperature Ø
Chose materials with high melting temperatures
Ø
Ceramics would be appealing - but too brittle
Ø
Research being done on ceramic composites, but these still have problems
Ø
Probable role of ceramics is in coatings
•
Creep resistance can be tailored by changing microstructure
•
Must control both diffusional creep and dislocation creep in a concerted fashion ∴ If diffusional creep dominates, no point in reducing power-law creep ∴ If power-law creep dominates, no point in reducing diffusional creep
Control of diffusional creep •
Solid solutions may influence lattice diffusion coefficients
•
Precipitates at grain boundaries may interfere with boundary-diffusion
•
Precipitates in grains have little influence on lattice creep
•
Increase in grain size ⇒ reduces diffusional creep rate E.g.,
Directionally-solidified alloys (slow withdrawal from furnace) Better yet are single-crystal alloys
Control of power-law creep •
Solid solution influences diffusion ⇒ influences climb rates
•
Dispersion of strong particles ⇒ blocks glide & climb
•
Need to use stable precipitates that do not coarsen during service
•
Can develop alloys that form additional precipitates during creep
Note: Resistance against power law creep ⇒ same techniques for strengthening These are hard materials and cannot be machined to final shape - cast in intricate shape
ME382 - 11/iv/14
5
For steady-state creep (ignores microstructural changes, cavitation and elasticity)
•
Different mechanisms can operate simultaneously
•
Fastest mechanism will dominate ⇒ Depends on temperature, stress and grain size
•
Deformation-mechanism map ⇒ Dominant mechanisms for stress & temperature Includes lines of constant strain rate
Note on this map: “High-temperature” power-law creep is “lattice-diffusion” power-law creep “Low-temperature” power-law creep is “core-diffusion” power-law creep •
Boundary-diffusion creep ∝ d-3; lattice-diffusion creep ∝ d-2
ME382 - 11/iv/14
1
Lecture 32 - Deformation mechanisms maps & creep-resistant materials •
With small grain sizes, boundary diffusion may dominate for all temperatures
•
Lattice diffusion may dominate at higher temperatures with large grains (because Ql > Qb)
•
Increase in grain size reduces diffusional creep rate, but not power-law creep ∴
Regime of power-law creep dominance increases
Example: Cylindrical pressure vessel of pure nickel with grain size of 0.01 mm. Average radius of cylinder = 200 mm; wall thickness = 1 mm; internal pressure of 0.1 MPa. What is life time at 860 ºC if failure occurs at an effective strain of 0.01
σ˜ H = 3PR/2t = 17.3 MPa
σ θθ = PR/t; σ zz = PR/2t; σ rr = 0
⇒
But, from Mohr’s circle of stress:
σ˜ H = 3τ ;
∴
∴
τ = 17.3/ 3 = 10 MPa
At 860 ºC
γ˙ = 10 −5 s −1
But, from Mohr’s circle of strain:
ε˙˜H = γ˙ / 3
ε˙˜H = 5.7 × 10−6
s−1
∴
At 860 ºC
∴
Life time = 0.01/(5.7 x 10-6) = 1700 secs = 28.9 minutes
ME382 - 11/iv/14
2
Lecture 32 - Deformation mechanisms maps & creep-resistant materials •
Transient creep maps can be plotted by including elastic contribution ∴ Give total strain at fixed time ∴ Should, in principle, include effects of microstructure change, but ....
•
Relative contribution of creep to total strain increases with time
Case study
•
Turbine blade ω = 1000 rad/s, radius = 0. 3 m; design calls for γ˙ < 10 −8 s−1 ; T = 450 °C → 700 °C
σ = rω 2 ρl where l is distance from tip of blade; ρ (for Ni) = 8900 kg/m3 ∴
At root, the normal stress = 120 MPa (shear stress is about 60 MPa)
•
Start off with considering pure Ni
•
Pure nickel: power-law creep with large strain rates
•
Increasing grain size won’t help
•
Alloying helps suppress power-law creep
ME382 - 11/iv/14
3
Lecture 32 - Deformation mechanisms maps & creep-resistant materials
MARM200 wt %
Al
Ti
W
Cr
Nb
Co
C
B
Zr
Ni
5.0
2.0
12.5
9.0
1.0
10.0
0.15
0.15
0.05
Bal
•
MAR-M200 strengthened by solid solution of W, Co & pttes of Ni3(TiAL)
•
Contains Cr for corrosion resistance
•
Alloying cuts power-law creep
•
Leaves diffusional flow ⇒ increase grain size to 1 cm (e.g. directional solidification) DESIGN FOR HIGH-TEMPERATURE APPLICATIONS
•
Reduce temperature Ø
Cooling vents:
Allow cool fluid to pass over component
Ø
Thermal barrier coatings Often use ceramics which have a high Tm and low conductivity ME382 - 11/iv/14
4
Lecture 32 - Deformation mechanisms maps & creep-resistant materials Need to avoid damage to the coating Stresses induced by thermal expansion mismatch
⇒
delamination
•
Chose materials with good oxidation resistance
•
Fundamental creep resistance generally scales with melting temperature Ø
Chose materials with high melting temperatures
Ø
Ceramics would be appealing - but too brittle
Ø
Research being done on ceramic composites, but these still have problems
Ø
Probable role of ceramics is in coatings
•
Creep resistance can be tailored by changing microstructure
•
Must control both diffusional creep and dislocation creep in a concerted fashion ∴ If diffusional creep dominates, no point in reducing power-law creep ∴ If power-law creep dominates, no point in reducing diffusional creep
Control of diffusional creep •
Solid solutions may influence lattice diffusion coefficients
•
Precipitates at grain boundaries may interfere with boundary-diffusion
•
Precipitates in grains have little influence on lattice creep
•
Increase in grain size ⇒ reduces diffusional creep rate E.g.,
Directionally-solidified alloys (slow withdrawal from furnace) Better yet are single-crystal alloys
Control of power-law creep •
Solid solution influences diffusion ⇒ influences climb rates
•
Dispersion of strong particles ⇒ blocks glide & climb
•
Need to use stable precipitates that do not coarsen during service
•
Can develop alloys that form additional precipitates during creep
Note: Resistance against power law creep ⇒ same techniques for strengthening These are hard materials and cannot be machined to final shape - cast in intricate shape
ME382 - 11/iv/14
5
