Determination of Temperature-Dependent Elastic Constants of Steel AISI 4140 by Use of In Situ X-ray Dilatometry Experiments
Abstract
:1. Introduction
2. Materials and Methods
2.1. Experimental Procedure
2.2. Data Evaluation
3. Results and Discussion
3.1. hkl Specific Elastic Constants
3.2. Macroscopic Elastic Constants
4. Conclusions
- In situ X-ray diffraction load dilatometry experiments provide a suitable tool to determine lattice plane specific elastic constants and hence .
- The experiments are much faster in comparison to conventional laboratory X-ray diffraction experiments for determination of ; annealing effects for steel samples can be safely neglected.
- Macroscopic and Poisson ratios can reliably be derived from averaging multiple specific elastic constants and can further be used as input data to improve FE heat treatment simulations, for example, laser hardening process simulation.
- Only for high-indexed planes with , for example, , in the first instance, it can be assumed that the temperature-dependent micro-mechanical behavior can accurately be approximated through the temperature dependency of the macroscopic elastic constants.
- For lower indexed planes like especially above large errors occur through the approximation based on macroscopic elastic constants.
- In summary, for temperatures higher than deviations occur from the thus far observed linear trend of the lattice plane specific and against temperature. These deviations have to be taken into account for precise stress calculations, especially at in situ diffraction studies on ferritic steels at elevated temperatures.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
DESY | Deutsches Elektronen Synchrotron |
DEC(s) | Diffraction Elastic Constant(s) |
HZG | Helmholtz-Zentrum Geesthacht |
DCM | Double Crystal Monochromator |
Appendix A
Experiment | Phase | Temperature | |||||
---|---|---|---|---|---|---|---|
No. | MPa | - | |||||
1 | 30 | ||||||
2 | 150 | ||||||
3 | 200 | ||||||
4 | 300 | ||||||
5 | 400 | ||||||
6 | 450 | ||||||
7 | 600 | ||||||
1 | 30 | ||||||
2 | 150 | ||||||
3 | 200 | ||||||
4 | 300 | ||||||
5 | 400 | ||||||
6 | 450 | ||||||
7 | 600 | ||||||
1 | 30 | ||||||
2 | 150 | ||||||
3 | 200 | ||||||
4 | 300 | ||||||
5 | 400 | ||||||
6 | 450 | ||||||
7 | 600 | ||||||
1 | 30 | ||||||
2 | 150 | ||||||
3 | 200 | ||||||
4 | 300 | ||||||
5 | 400 | ||||||
6 | 450 | ||||||
7 | 600 |
References
- Scholtes, B. Eigenspannungen in Mechanisch Randschichtverformten Werkstoffzuständen: Ursachen, Ermittlung und Bewertung; DGM Informationsgesellschaft: Oberursel, Germany, 1991. [Google Scholar]
- Schijve, J. Fatigue of Structures and Materials; Springer: Dordrecht, The Netherlands, 2008. [Google Scholar]
- Hauk, V. 2.13—X-ray elastic constants (XEC). In Structural and Residual Stress Analysis by Nondestructive Methods; Hauk, V., Ed.; Elsevier Science B.V.: Amsterdam, The Netherlands, 1997; pp. 279–336. [Google Scholar]
- Hauk, V.; Wolfstieg, U. Röntgenographische Elastizitätskonstanten, REK. HTM Haerterei-Techn. Mitt. 1976, 31, 38–47. [Google Scholar]
- Eshelby, J.D. The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 1957, 241, 376–396. [Google Scholar]
- Kröner, E. Berechnung der elastischen Konstanten des Vielkristalls aus den Konstanten des Einkristalls. Z. Phys. 1958, 151, 504–518. [Google Scholar] [CrossRef]
- Every, A.G.; McCurdy, A.K. Landolt-Börnstein—Group III Condensed Matter—Low Frqeuency Properties of Dielectric Crystals-Second and Higher Oder Elastic Constants; Springer: Berlin, Germany, 1992; Volume 29a. [Google Scholar]
- Wachtman, J.B.; Tefft, W.E.; Lam, D.G.; Apstein, C.S. Exponential Temperature Dependence of Young’s Modulus for Several Oxides. Phys. Rev. 1961, 122, 1754–1759. [Google Scholar] [CrossRef]
- Li, W.; Wang, R.; Li, D.; Fang, D. A Model of Temperature-Dependent Young’s Modulus for Ultrahigh Temperature Ceramics. Phys. Res. Int. 2011. [Google Scholar] [CrossRef]
- Kostov, V. Untersuchungen zur zeitaufgelösten Spannungsentwicklung und Eigenspannungsentstehung beim Laserstrahlstandhärten am Beispiel des Stahls 42CrMo4. Ph.D. Thesis, Karlsruhe Institute of Technology, Karlsruhe, Germany, 2014. [Google Scholar]
- Kiefer, D.; Gibmeier, J.; Beckmann, F.; Wilde, F. Fast Temporal and Spatial Resolved Stress Analysis at Laser Surface Line Hardening of Steel AISI 4140. In Proceedings of the International Conference on Mechanical Stress Evaluation by Neutron and Synchrotron Radiation, Skukuza, South Africa, 19–21 September 2017; Marais, D., Holden, T.M., Venter, A.M., Eds.; Materials Reserach Forum LLC: Millersville, PA, USA, 2017; Volume 4, pp. 91–96. [Google Scholar]
- ASTM E1426-14:2014. Standard Test Method for Determining the X-Ray Elastic Constants for Use in the Measurement of Residual Stress Using X-Ray Diffraction Techniques; ASTM International: West Conshohocken, PA, USA, 2014. [Google Scholar]
- Macherauch, E.; Müller, P. Das sin2ψ-Verfahren der röntgenographischen Spannungsmessung. Z. Angew. Phys. 1961, 13, 305–312. [Google Scholar]
- Kiefer, D.; Schüssler, P.; Mühl, F.; Gibmeier, J. Experimental and Simulative Studies on Residual Stress Formation for Laser-Beam Surface Hardening. HTM J. Heat Treat. Mater. 2019, 74, 23–35. [Google Scholar] [CrossRef] [Green Version]
- Hammersley, A.P. FIT2D: An Introduction and Overview; ESRF Internal Report, ESRF97HA02T; ESRF: Grenoble, France, 1997. [Google Scholar]
- Daymond, M.R. The determination of a continuum mechanics equivalent elastic strain from the analysis of multiple diffraction peaks. J. Appl. Phys. 2004, 96, 4263–4272. [Google Scholar] [CrossRef]
- Kocks, F.; Tomé, C.; Wenk, H.R. Texture and Anisotropy. Preferred Orientations in Polycrystals and Their Effect on Material Properties; Cambridge University Press: Cambridge, UK, 2000. [Google Scholar]
- Manns, T.; Scholtes, B. DECcalc—A Program for the Calculation of Diffraction Elastic Constants from Single Crystal Coefficients. Mater. Sci. Forum 2011, 681, 417–419. [Google Scholar] [CrossRef]
- Roberts, C.S. Effect of Carbon on the Volume Fractions and Lattice Parameters Of Retained Austenite and Martensite. JOM 1953, 5, 203–204. [Google Scholar] [CrossRef]
- Dutta, R.; Huizenga, R.; Amirthalingam, M.; King, A.; Gao, H.; Hermans, M.; Richardson, I. In situ synchrotron diffraction studies on the temperature-dependent plane-specific elastic constants in a high-strength quenched and tempered structural steel. Scr. Mater. 2013, 69, 187–190. [Google Scholar] [CrossRef]
- Miokovic, T. Analyse des Umwandlungsverhaltens bei ein- und mehrfacher Kurzzeithärtung bzw. Laserstrahlhärtung des Stahls 42CrMo4. Ph.D. Thesis, TU Karlsruhe, Karlsruhe, Germany, 2005. [Google Scholar]
C | Si | Mn | Cr | Mo | S | P | Fe |
---|---|---|---|---|---|---|---|
Experiment No. | Temperature | Max. Stress | Phase |
---|---|---|---|
1 | 30 | 795 | |
2 | 150 | 795 | |
3 | 200 | 636 | |
4 | 300 | 795 | |
5 | 400 | 556 | |
6 | 450 | 795 | |
7 | 600 | 318 |
Experiment | Temperature | ||
---|---|---|---|
No. | C | MPa | - |
1 | 30 | ||
2 | 150 | ||
3 | 200 | ||
4 | 300 | ||
5 | 400 | ||
6 | 450 | ||
7 | 600 |
© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Kiefer, D.; Gibmeier, J.; Stark, A. Determination of Temperature-Dependent Elastic Constants of Steel AISI 4140 by Use of In Situ X-ray Dilatometry Experiments. Materials 2020, 13, 2378. https://doi.org/10.3390/ma13102378
Kiefer D, Gibmeier J, Stark A. Determination of Temperature-Dependent Elastic Constants of Steel AISI 4140 by Use of In Situ X-ray Dilatometry Experiments. Materials. 2020; 13(10):2378. https://doi.org/10.3390/ma13102378
Chicago/Turabian StyleKiefer, Dominik, Jens Gibmeier, and Andreas Stark. 2020. "Determination of Temperature-Dependent Elastic Constants of Steel AISI 4140 by Use of In Situ X-ray Dilatometry Experiments" Materials 13, no. 10: 2378. https://doi.org/10.3390/ma13102378