Probabilistic Modeling of Slip System-Based Shear Stresses and Fatigue Behavior of Coarse-Grained Ni-Base Superalloy Considering Local Grain Anisotropy and Grain Orientation
Round 1
Reviewer 1 Report
This paper is a very interesting probabilistic model for crack intitation life prediction in Ni-based superalloys using polycrystalline microstructure, elastoplastic anisotropy, crystal plasticity and grain interaction. Some minor comments need to be addressed and are suggested below:
1/ Please modify the denomination of "fine grain" in the manuscript since millimeter grains are not "fine grains" for fatigue purpose of Ni-based superalloys. In addition, it makes it confusing with the title since only "coarse grain" appears in the title.
2/ Please verify figure cross-references in the manuscript. It is written "Error! Reference source not found." everywhere in the PDF version of the manuscript.
3/ Page 3-line 138-140: "The mechanical properties of the specimens are simulated with 138
FEA models mimicking the polycrystalline microstructure and the anisotropic stiffness of the grains." ==> EBSD data and/or XRD measurement would have been useful to clearly identify the texture both the materials, i.e. "coarse grains" and "fine grains".
4/ Page 4 Line 152: Please add "and IN 738 LC" in the table caption.
5/ Page 5: Please describe the mesh size for both the microstructures.
6/ Line 301: Please add the full name of "SEM".
7/ Please detail the heat treatments undergone by the LCF specimens prior fatigue testing.
8/ Line 313-315: An error is noticed in the text : "during the solidifi...."
9/ Line 376: The Wöhler curve is missing.
10/ Figure 7: Th locations of the arrows are quite strange. Please verify and modify if needed.
11/ Figure 13 and lines 527-531: Please better explain how it is possible to obtain Schmid factor (SF) higher than 0.5 for {111}<011>slip systems. An analytical demonstration to support SF values higher than 0.5 would have been useful. Cfc single crystal are elastically anisotrope and have SF lower of equal to 0.5.
12/ Page 23, Figure 17?, Please discuss the fact that random grain orientation lead to higher variability in apparent Young's moduli compared to the textured fine grain microstructure.
Interestingly, the texture for the fine grain microstructure lead to a much more narrow variability in apparent Young's moduli, and thus to less strain/stress concentration due to the elastic anosotropic response. However, the textured microstructure depict several grains aligned with the highest SF orientation. Please discuss this point, while the global apparent of the fine grain structure is lower.
13/ Please provide regresion coefficients to show how good are the calibration and prediction for the modelling of the Wöhler curve with the three different models.
Author Response
1/ Please modify the denomination of "fine grain" in the manuscript since millimeter grains are not "fine grains" for fatigue purpose of Ni-based superalloys. In addition, it makes it confusing with the title since only "coarse grain" appears in the title.
Done. We clarified, that the fine-grained material with regard to the material science is still a really coarse material. But we decided to use the terminus “fine” to differentiate it from the three times coarser grained material.
2/ Please verify figure cross-references in the manuscript. It is written "Error! Reference source not found." everywhere in the PDF version of the manuscript.
Done. Please note that our submission did neither show these errors nor the misplaced vectors in the diagram. These errors must have occurred during pdf-compilation by the editorial team.
3/ Page 3-line 138-140: "The mechanical properties of the specimens are simulated with 138
FEA models mimicking the polycrystalline microstructure and the anisotropic stiffness of the grains." ==> EBSD data and/or XRD measurement would have been useful to clearly identify the texture both the materials, i.e. "coarse grains" and "fine grains".
We already mentioned, that using EBSD was not suitable because of the grain size. We tried a lot of different ways to determine orientation distribution, but the statistics were still insufficient. For the fine grained material about 15 grains were measurable during one scan with maximum in working distance. Scanning at least 500-1000 grains would have been necessary to achieve a sound statistic on the orientation distribution.
4/ Page 4 Line 152: Please add "and IN 738 LC" in the table caption.
Done.
5/ Page 5: Please describe the mesh size for both the microstructures.
Done. Details about the mesh generation and the properties were added to line 179-182.
6/ Line 301: Please add the full name of "SEM".
Done.
7/ Please detail the heat treatments undergone by the LCF specimens prior fatigue testing.
Done. We know that a typical two step heat treatment, as mentioned in the text, was applied to the material. Unfortunately, further details are kept confidential by the material vendor and hence we are not aware of explicit temperatures and times.
8/ Line 313-315: An error is noticed in the text : "during the solidifi...."
Done. See 2.
9/ Line 376: The Wöhler curve is missing.
Done. A misunderstanding must have occurred due to the missing reference.
10/ Figure 7: The locations of the arrows are quite strange. Please verify and modify if needed.
Done. See 2.
11/ Figure 13 and lines 527-531: Please better explain how it is possible to obtain Schmid factor (SF) higher than 0.5 for {111}<011>slip systems. An analytical demonstration to support SF values higher than 0.5 would have been useful. Fcc single crystals are elastically anisotrope and have SF lower or equal to 0.5.
The elastic anisotropy translates uniaxial stress loads to multiaxial stress states in the material. Due to the definition of the Schmid factor as maximum resolved shear stress at the slips systems normalized with the von Mises stress, they can reach values > 0.5. An example was added to subsection 4.2
12/ Page 23, Figure 17? Please discuss the fact that random grain orientation lead to higher variability in apparent Young's moduli compared to the textured fine grain microstructure.
The discussion between lines 661-690 and the caption of figure 17 was slightly modified in order to accommodate this remark.
Interestingly, the texture for the fine grain microstructure leads to a much narrower variability in apparent Young's moduli, and thus to less strain/stress concentration due to the elastic anisotropic response. However, the textured microstructure depicts several grains aligned with the highest SF orientation. Please discuss this point, while the global Young’s modulus of the fine grain structure is apparently lower.
The previously shown distributions of Young’s moduli (single grain) were only dependent on the grain orientation. In the FEA, the mutual grain interaction has a big impact on the local stress state. Hence, local stress maxima can occur in the textured material which are of similar magnitude as in the coarse grain batch. The discussion subsection 4.1 was modified and respective remarks were made.
13/ Please provide regression coefficients to show how good are the calibration and prediction for the modelling of the Wöhler curve with the three different models.
Table 6 shows the negative Log-Likelihood values for all fit and prediction curves as a coefficient of determination. The typically used R^2 measure is inappropriate for non-linear regression models. Most of all the assumed residual distribution is not of normal type (which is the underlying assumption for the principles of least-squares). The physics-based modeling of the life distribution leads to distributions as shown in figures 13-16 and Table 5. A short explanation was added in the draft as well.
Reviewer 2 Report
The submitted manuscript entitled ‘Probabilistic modeling of slip system-based shear stresses and fatigue behavior of coarse-grained Ni base superalloy considering local grain anisotropy and grain orientation’ deals with the fatigue investigation and simulation of a Ni based superalloy. The manuscript is well-written, logic and comprehensive, therefore worths to publisch. During its review only a few questionas and remarks arose as listed below.
- Please provide heat treatment details for the materials.
- Please check the submission for unvalid references: ‘Error! Reference source not found.’
- How were the chemical compositions of table 1 determined?
- ‘Cycles to failure were determined by a load drop of 2.5 % from the stabilized measured stress amplitude.’ – wha tis the reason behind? Is this drop can be connected any visual damage of the sample?
- ‘As the authors are not aware of any values for the elastic constants of René80 at high temperature, elastic constants for IN 738 LC were taken from the literature [42]. Since both, composition and content of the γ’ phase are very similar in IN 738 LC and René80, it is assumed that the elastic behavior of both alloys are qualitatively comparable.’ –this is quite speculative in the opinion of this Reviewer. With the apparatus of the Authors, the properties of the material in question could be measured.
- Please identify the microstructures and / or phases in fig 3.
- Please add values to the vertical axis of fig 6 and also list the fitting parameters and R2 values.
- The markers in fig 7 are misplaced, please revise.
- Please add values to the horizontal axis of figs 14-16.
- Please revise the figure numberings, the first figure in the Discussion is fig 1 and should be fig 17.
Author Response
- Please provide heat treatment details for the materials.
Done. We know that a typical two step heat treatment, as mentioned in the text, was applied to the material. Unfortunately, further details are kept confidential by the material vendor and hence we are not aware of explicit temperatures and times.
- Please check the submission for invalid references: ‘Error! Reference source not found.’
Done. Please note that our submission didn’t show these errors as well the misplaced vectors in the diagram. During pdf-compilation by the editorial team these errors occurs.
- How were the chemical compositions of table 1 determined?
Done. The chemical composition of the Rene80 was provided by the material vendor measured by an unknown procedure. The values for the IN738LC were taken from literature.
- ‘Cycles to failure were determined by a load drop of 2.5 % from the stabilized measured stress amplitude.’ – what is the reason behind? Is this drop can be connected any visual damage of the sample?
An explanation was added to subsection 2.2. The main reason was comparability of the values to data obtained in previous experiments and projects.
- ‘As the authors are not aware of any values for the elastic constants of René80 at high temperature, elastic constants for IN 738 LC were taken from the literature [42]. Since both, composition and content of the γ’ phase are very similar in IN 738 LC and René80, it is assumed that the elastic behavior of both alloys are qualitatively comparable.’ –this is quite speculative in the opinion of this Reviewer. With the apparatus of the Authors, the properties of the material in question could be measured.
At the time when the experiments were conducted at TU Kaiserslautern, neither an appropriate test apparatus nor appropriate specimen material was available to the authors within the scope of the project.
- Please identify the microstructures and / or phases in fig 3.
Done.
- Please add values to the vertical axis of fig 6 and also list the fitting parameters and R2 values.
Due to confidentiality agreements with industrial partners, we are not legally not entitled to publish explicit values of the experimental results.
Table 6 shows the negative Log-Likelihood values for all fit and prediction curves as a coefficient of determination. The typically used R^2 measure is inappropriate for non-linear regression models. Most of all the assumed residual distribution is not of normal type (which is the underlying assumption for the principles of least-squares). The physics-based modeling of the life distribution leads to distributions as shown in figures 13-16 and Table 5. A short explanation was added in the draft as well.
- The markers in fig 7 are misplaced, please revise.
Done.
- Please add values to the horizontal axis of figs 14-16.
Due to confidentiality agreements with industrial partners, we are not legally not entitled to publish explicit values of the experimental results.
- Please revise the figure numberings, the first figure in the Discussion is fig 1 and should be fig 17.
Done. Please note that our submission did neither show these errors nor the misplaced vectors in the diagram. These errors must have occurred during pdf-compilation by the editorial team.
Round 2
Reviewer 1 Report
Very good revision of the paper.
