system state - TU Graz
Transcript of system state - TU Graz
Physical Modeling of Dislocation Creep in High Temperature SteelsF. Riedlsperger1, B. Krenmayr1, B. Fercher1, B. Sonderegger1
1. Graz University of Technology, Institute of Materials Science, Joining and Forming, Kopernikusgasse 24/I, 8010 Graz, Austria
Institute of Materials Science, Joining and Forming (IMAT)
Graz University of Technology, Austria
To raise the efficiency of thermal power plants, operating temperatures have to be increased. However, metal components exposed to high temperatures and
mechanical stress show the phenomenon of creep, which can be described as slow and irreversible plastic deformation. As a result, there are limits concerning
the lifetime of components to guarantee safety during operation. The main purpose of creep modelling therefore lies in predicting remaining lifetime and
reproduce creep deformation rates for specific materials.
The current IMAT creep model (coded in MATLAB) features the following microstructural elements: mobile dislocations, boundary dislocations, dipoles and
precipitates. All these constituents interact with each other and have an evolution over time, depending on temperature and stress level. This leads to a complex
system of differential equations that can be solved numerically.
Recent innovations of our creep model in MATLAB include the possibility to step-wise import particle data from precipitation kinetic software MatCalc as well as
a function to calculate a time-to-rupture diagram. Theories of glide and climb velocities have also been improved.
INTRODUCTION
EXPERIMENTAL AND SIMULATION RESULTS
CONCLUSIONS
21.09.2018
MatCalc precipitation kinetic simulation:
Input parameters:
• chemical composition & heat treatment
• microstructural data
o PAGS, subgrain size, dislocation density
o → Nucleation sites for precipitates
Output:
• Precipitation evolution over time for one
temperature, for instance 10 years at 625°C
• → Diameter, phase fraction, number density
• Export to MATLAB creep simulation
MATLAB MatCalc
Our MATLAB creep model (based on [1], [2])
includes boundary dislocations 𝜌b, mobiles 𝜌m,
dipoles 𝜌dip, subgrains Rsgb and precipitates rppt
as microstructural constituents. Various reactions
or interactions are considered:
EBSD data from a martensitic Cr-steel [3]
highlighting the fine substructure. Subgrain size
& boundary dislocation density were evaluated.
→ Start values creep simulation
[1] N. Ghoniem, J. Matthews, R. Amodeo, “A dislocation model for creep in engineering materials”, Res. Mech. 29 (1990) pp. 197-219
[2] S. D. Yadav, B. Sonderegger, M. Stracey, C. Poletti, “Modelling the creep behaviour of tempered martensitic steel based on a hybrid approach“, Mat.Sc.Eng. A,vol 662 (2016) pp. 330-341
[3] F. Riedlsperger, “Thermodynamic Precipitation Kinetic Simulation of Martensitic Cr- Steels”- Master Thesis @ IMAT Institute, TU Graz (2016)
[4] J. Schmid, “Modellierung der Mikrostuktur eines kriechfesten Stahls”- Master Thesis @ IMAT Institute, TU Graz (2018)
[5] B. Fercher, “Modelling the microstructure of creep resistant steel P91” - Master Thesis (Work in Progress) @ IMAT Institute, TU Graz (2018)
Creep curve (strain vs. time) of a 9 % Cr-steel
for applied stress of 80 MPa and 650°C [4].
Stress was then varied between 50 - 100 MPa
and all points in time at 6 % strain were taken to
create the final time-to-rupture diagram. For
comparison see NIMS, ECCC and ASME data.
Although there are still a number of open questions with respect to the underlying differential equation system and the interactions therein, the current model is
a huge leap towards physically justified creep modelling of complex steels.
SOURCES
Figure 7: Time-to-rupture diagram of P91 @650°C, comparison between simulation
and literature data [5]
Figure 6: Creep curve of P91 @650°C & 80 MPa, comparison of experimental and
simulated curve [4]
Figure 4: EBSD data from P91 welding-HAZ for evaluation of microstructural data;
(left) IPF-map, (right) boundary map (1°- 4°, 4°-15°, 15°-180°)
𝜌𝑚
𝜌b
𝜌dip
𝑟𝑝𝑝𝑡
Reactions/ Interactions [1]:
1. Multiplication of
mobiles
2. Dipole formation
3. Absorption in
boundary dislocation
4. Annihilation by climb
5. Annihilation by glide
6. Annihilation of
boundaries by creation
of new subgrains
7. Subgrain growth &
Zener backpressure
8. Subgrain nucleation
4,5
2
34,5
𝑅𝑠𝑔𝑏8
78
6
1
Figure 3: Sketch of reactions & interactions of dislocations with grain structure
Figure 2b: Schematic sequence of creep simulation with details of the influence factors
9 % Cr-Steel Service @ 625°C
M23C6
LavesVN & NbC
Z-phase
Figure 1: Evolution of precipitates simulated with MatCalc
Figure 5: EBSD data from P91 BM for
evaluation of microstructural data; (top) IPF-
map, (bottom) boundary map (18°- 50°)
1
𝑣𝑒𝑓𝑓=
1
𝑣𝑔+
𝑖
𝜋
2𝑁𝑉𝑖 ∙ 𝑟𝑖
3∙1
𝑣𝑐
ሶ𝜀 = 𝑏 ∙ 𝑀−1 ∙ 𝜌𝑚 ∙ 𝑣𝑒𝑓𝑓 I: Orowan’s Equ.
II: Eff. Velocity
Creep Strain
RateEvolution of Mobile
Dislocation Density
Effective Dislocation
Velocity
Glide
VelocityClimb over
Precipitates
Climb
Velocity
Number Density & Particle Radius
MatCalc precipitation kineticsrmean = rmean (kd, t, rinitial) (2.31)
Nv = Nv (Nv,initial, rinitial, rmean) (2.32)
constraints for Rsbg
γsb = γsb (μ, b, ρb, Rsbg) (2.15)Psb = Psb (μ, b, ρb) (2.16)
hb = hb (ρb, ρdip, Rsbg) (2.17)Msb = Msb (ηv, Ds, Ω, b, k, T, Dvp, hb
development of sub-grain boundariesρb = ρb (vc, ρdip, hb, ζ, Msb, Psb, rmean, Nv, γsb, ρb, Rsbg) (2.23)
Rsbg = Rsbg (Msb, Psb, rmean, Nv, γsb) (2.24)
precipitates damageDppt,i = Dppt,i (kp, l, t) (2.27)
Dppt = Dppt (Dppt,i) (2.28)
deformation with damageε= ε(b, ρm, veff, M, Dppt, Dcav)
deformation without damageε= ε(b, M, ρm, veff) (2.5)
cavities damageDcav = Dcav (A, ε, ε) (2.29)
ρ inside grainρm = ρm (vg, ρm, Rsbg, vc, danh, ρdip) (2.21)
ρdip = ρdip (vg, Rsbg, ρm, vc, hb, ρdip, danh) (2.22)
vg
vg = vg (a1, Q, k, T, σi, σapp, Ω, Ωmult)
σσapp = σapp (σapp0, ε, ν) (2.6)
σi = σi (α, M, μ, b, ρm, cdip, ρdip) (2.7)αeff = αeff (αapp, αi) (2.8)
vc
Lp = Lp (ag, W, k, T)vcp = vcp (b, Dvp, σapp, Ω, Lp, k, T)
Lα = Lα (ν, μ, b, Ω, k, T)vcl = vcl (ηv, Ds, σapp, Ω, Lα, ρt, b, k, T)
vc = vc (vcp, vcl) (2.14)
system stateρm, ρdip, ρb, ρt
Rsbg, ε, b, M,
...
veff
veff = veff (vg, vc, Nv, rmean)
Figure 2a: Schematic sequence of creep simulation
Determination of PAGS by EBSD → to MatCalc
ACKNOWLEDGEMENT
Support of the Austrian Science Fund (FWF) and of Voestalpine Böhler Welding GmbH is gratefully acknowledged.