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.