Example MP10: Yield strength prediction in Ni-base superalloy with shearable γ' and γ'' precipitates

Compatibility

MatCalc version: 5.53.0027
Database: mc_ni.tdb, mc_sample_ni.ddb
Author: M.R. Ahmadi
Created: 2013-12-06
Revisions:

Objectives

A sample heat treatment of the Inconel-718 alloy is shown. The material yield strength is evaluated. The contributions of various material properties to the yield strength are also discussed.

Complementary files

Click here to view the script for this tutorial.

Main document

Setup thermodynamics

Set up the thermodynamics by loading the mc_ni database

Select the following phases, elements and enter the chemical composition in wt-%:

Elements Chemical composition [wt.%] Phases
Al 1.5 FCC_A1
C 0.03 DELTA
Co 9.1 GAMMA_PRIME
Cr 17.4 GAMMA_DP
Fe 9.7
Mo 2.7
Nb 5.5
Ti 0.7
W 1.0

Set Ni to reference element. Continue in the thermodynamic setup by loading the diffusion database for Ni (mc_sample_ni.ddb). To ensure correct thermodynamic values and no driving force errors (DFM-errors), set automatic start values and calculate an equilibrium at 1000°C.

Precipitation domain and precipitates

Create a precipitation domain with the name 'nickel_matrix' with FCC_A1 matrix phase. Change the value of Taylor factor to 2.6. Leave all other domain settings on default value.

 Activate dislocation density evolution model

Follow by setting up the precipitates. Create one precipitate phase for gamma_prime phase and one for the delta phase. Choose the settings of the precipitate phases, as given in the table below

Precipitate Tab Option Value
cementite_p0 Precipitate #size classes 25 (Initialize!)
cementite_p0 Attached to pd ferrite
cementite_p0 Kinetic alias name Cementite
cementite_p0 Nucl. sites Nucleation sites dislocations
Precipitate Tab Option Value
fcc_a1#01_p0 Precipitate #size classes 25 (Initialize!)
fcc_a1#01_p0 Kinetic alias name NbC(aust,d)
fcc_a1#01_p0 Nucleation Restrict nucleation to prec domain ✔, select austenite
fcc_a1#01_p0 Nucl. sites Nucleation sites dislocations
Precipitate Tab Option Value
fcc_a1#01_p1 Precipitate #size classes 25 (Initialize!)
fcc_a1#01_p1 Kinetic alias name NbC(aust,gb)
fcc_a1#01_p1 Nucleation Restrict nucleation to prec domain ✔, select ferrite
fcc_a1#01_p1 Nucl. sites Nucleation sites grain boundary
Precipitate Tab Option Value
AlN_p0 Precipitate #size classes 25 (Initialize!)
AlN_p0 Kinetic alias name AlN(aust,d)
AlN_p0 Nucleation Restrict nucleation to prec domain ✔, select austenite
AlN_p0 Account for coherent misfit stress
AlN_p0 Nucl. sites Nucleation sites dislocations
AlN_p0 Structure Vol. misfit 0.27, remove ✔ from 'auto'
Precipitate Tab Option Value
AlN_p1 Precipitate #size classes 25 (Initialize!)
AlN_p1 Kinetic alias name AlN(aust,gb)
AlN_p1 Nucleation Restrict nucleation to prec domain ✔, select austenite
AlN_p1 Nucl. sites Nucleation sites grain boundary
Precipitate Tab Option Value
AlN_p2 Precipitate #size classes 25 (Initialize!)
AlN_p2 Kinetic alias name AlN(ferr,d)
AlN_p2 Nucleation Restrict nucleation to prec domain ✔, select ferrite
AlN_p2 Account for coherent misfit stress
AlN_p2 Nucl. sites Nucleation sites dislocations
AlN_p2 Structure Vol. misfit 0.27, remove ✔ from 'auto'
Precipitate Tab Option Value
AlN_p3 Precipitate #size classes 25 (Initialize!)
AlN_p3 Kinetic alias name AlN(ferr,gb)
AlN_p3 Nucleation Restrict nucleation to prec domain ✔, select ferrite
AlN_p3 Nucl. sites Nucleation sites grain boundary

Heat treatment

Define the heat treatment with the following segments:

  1. Start at temperature of 1500 C. Cool down to 1200 C with 1 C/s cooling rate. Select austenite as precipitation domain.
  2. Hold at 1200 C for 30 minutes.
  3. Cool down to 1000 C with 1 C/s cooling rate.
  4. In the field 'Ramp control', choose 'Accumulated strain' option. Deform material with the strain rate ('eps-dot') of 0.15 till the accumulated strain reaches the 0.7 value. Hold the material at 1000 C (cooling rate is 0 C/s).

     Introducing deformation characteristics

  5. Cool down to 950 C with 1 C/s cooling rate.
  6. Deform material with the strain rate of 0.15 till the accumulated strain reaches the 0.7 value. Hold the material at 950 C (cooling rate is 0 C/s).
  7. Cool down to 900 C with 1 C/s cooling rate.
  8. Deform material with the strain rate of 0.15 till the accumulated strain reaches the 0.7 value. Hold the material at 900 C (cooling rate is 0 C/s).
  9. Cool down to 750 C with 1 C/s cooling rate.
  10. Cool down to 650 C with 1 C/s cooling rate. Switch precipitation domain to ferrite.
  11. Cool down to 400 C within 10 hours.

 Heat treatment

Precipitation simulation

Before starting the simulation, create 4 diagrams which will describe the precipitation characteristics (temperature, phase fraction, number densities, mean radii) - this is conveniently done by clicking on 'View' → 'Create new window …' → 'user-defined' tab → '03_kinetics_4_frames_T_f_n_r_linX'. Start the simulation with the temperature controlled by the defined heat-treatment.

The first look on the calculation results suggests that the whole precipitation appears in the ferrite domain (after ~2560 seconds). By magnifying the time axis (default x-axis!) from 2200 to 2600 seconds, one can notice the precipitates occurring in the austenite domain already where the deformation stage was introduced.

 Precipitate phase fractions in austenite

This deformation process can be illustrated by the following plots:

- Strain rate ('EPS_DOT' variable found in the 'kinetics:general' group). The three peaks correspond to the deformation segments.

 Strain rate

- Strain accumulated in the sample ('ACC_EPS' variable found in the 'kinetics:general' group). Every deformation segment resulted in increasing the strain by 0.7.

 Accumulated strain

- Dislocation density in the austenite ('DDT$austenite' variable found in the 'kinetics:pd struct' group). Again, three peaks corresponding to the deformation stages can be recognized. The dislocation density rises by two orders of magnitude.

 Dislocation density in austenite

- Pipe diffusion correction factor ('PIPE_DCF$austenite$*' variable found in the 'kinetics:pd special' group). The dislocations allow for a faster diffusion of the atoms. This effect is known as “pipe diffusion” and is represented with a correction factor, by which the diffusion coefficients of elements are multiplied (the same factor is assumed for all elements). The magnitude of this factor depends on the amount of the excess dislocation density and temperature. Increasing the number of dislocations during the deformation results in the faster diffusion in the material.

 Pipe diffusion correction factor in austenite


The influence of the deformation on the precipitation kinetics can be discussed on the following two plots:

- Number density of the precipitates. The number of precipitates nucleating on dislocations in austenite is increasing significantly during the deformation segments. Three increments for NbC(aust,d) and two for AlN(aust,d) precipitates can be identified. This observation is explained by the increasing number of the dislocations and thus the increasing number of the available nucleation sites for those precipitates.

 Number density of precipitates

- Mean radii of the precipitates. The rapid descent of the mean radius for the NbC(aust,d) and AlN(aust,d) precipitates nucleating at dislocations is observed during the dislocation segments. This is an effect of the outburst of the new nuclei for these phases. These falls are immediately compensated by the significant radius growth which is a result of the enhanced diffusion due to the increased dislocation number (pipe-diffusion).

 Mean radii of precipitates

Comparison with no deformation case

In order to demonstrate the effects of the deformation on the precipitation process, the calculation will be repeated for the system without any deformation steps. Rename the current buffer to 'w_deform'. Create the new buffer and rename it to 'no_deform'. Duplicate and lock all series in the plots. Next, edit the segments which describe the deformation stages in the heat treatment and write zero to 'eps-dot'. In options window for the plots switch the displayed buffer to 'no_deform' and start the precipitation kinetics calculation.

Let's compare the results for the NbC(aust,d) and AlN(aust,d) from the both simulations

- Number densities. The number densities for these phases are a few order smaller than in the deformed material. The phase fractions show a similar behavior. Noteworthy, the precipitates for AlN are virtually non-existent in the samples without strain. As expected, the excess dislocations increase the nucleation rates in the deformed material resulting in the higher number of precipitates.

 Number density comparison

- Mean radii. The differences here are not very prominent. Nevertheless, the radii in the strained samples are larger, as the introduced dislocations enable the pipe-diffusion.

 Mean radius comparison

FIXME References, technical paper FIXME

examples/mprops/mp10.txt · Last modified: 2014/04/10 14:45 by pwarczok