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Effective elastic properties and residual stresses in directionally solidified eutectic Al2O3/YAG/ZrO2 ceramics estimated by finite element analysis

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Abstract

Effective elastic properties and residual stresses were assessed in directionally solidified ternary eutectic ceramic, Al2O3/YAG/ZrO2, by finite element analyses. A 3D finite element model was generated from a CT scan, representative of the microstructure and with a similar volume fraction. Effective elastic properties were calculated by numerical homogenisation. They highlight a quasi-isotropic behaviour of the ternary eutectic ceramics. Despite the difficulties to measure the strain, the dispersion observed in the results and the limited reliability of the materials properties, the results constitute a step towards a better understanding of the material behaviour. Thermal residual stresses induced by the manufacturing were also evaluated. Tensile residual stresses in yttria-stabilised zirconia and compressive residual stresses in YAG and alumina were highlighted. This evaluation also shed light on the influence of the phase morphology in the microstructure. Indeed, the computed spatial distribution of the residual stresses showed that they are different from one position to another due to the variation in phase morphology and also to material properties variability. Therefore, it is important when numerically assessing the thermomechanical properties to take into account the microstructure morphology as well as the variability of material properties.

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References

  1. Orera VM, Llorca J (2005) Directionally solidified eutectic oxide ceramics in the encyclopedia of materials: science and technology. Elsevier, Amsterdam

    Google Scholar 

  2. Waku Y, Nakagawa N, Wakamoto T et al (1997) A ductile ceramic eutectic composite with high strength at 1,873 K. Nature 389:49–52

    Article  Google Scholar 

  3. Waku Y, Nakagawa N, Wakamoto T et al (1998) High-temperature strength and thermal stability of a unidirectionally solidified Al2O3/YAG eutectic composite. J Mater Sci 33:1217–1225. doi:10.1023/A:1004377626345

    Article  Google Scholar 

  4. Waku Y, Nakagawa N, Wakamoto T et al (1998) The creep and thermal stability characteristics of a unidirectionally solidified Al2O3/YAG eutectic composite. J Mater Sci 33:4943–4951. doi:10.1023/A:1004486303958

    Article  Google Scholar 

  5. Nakagawa N, Ohtsubo H, Mitani A et al (2005) High temperature strength and thermal stability for melt growth composite. J Eur Ceram Soc 25:1251–1257

    Article  Google Scholar 

  6. Yasuda H, Ohnaka I, Mizutani Y et al (2005) Three-dimensional observation of the entangled eutectic structure in the Al 2 O 3–YAG system. J Eur Ceram Soc 25:1397–1403

    Article  Google Scholar 

  7. Waku Y, Sakata S-I, Mitani A, Shimizu K (2001) A novel oxide composite reinforced with a ductile phase for very high temperature structural materials. Mater Res Innov 5:94–100

    Article  Google Scholar 

  8. Llorca J, Orera VM (2006) Directionally solidified eutectic ceramic oxides. Prog Mater Sci 51:711–809. doi:10.1016/j.pmatsci.2005.10.002

    Article  Google Scholar 

  9. Mazerolles L, Perriere L, Lartigue-Korinek S, Parlier M (2011) Creep behavior and related structural defects in Al 2 O 3–Ln 2 O 3 (ZrO 2) directionally solidified eutectics (Ln= Gd, Er, Y). J Eur Ceram Soc 31:1219–1225

    Article  Google Scholar 

  10. Waku Y, Sakuma T (2000) Dislocation mechanism of deformation and strength of Al 2 O 3–YAG single crystal composites at high temperatures above 1500 C. J Eur Ceram Soc 20:1453–1458

    Article  Google Scholar 

  11. Palmero P, Pulci G, Marra F et al (2015) Al2O3/ZrO2/Y3Al5O12 composites: a high-temperature mechanical characterization. Materials 8:611–624

    Article  Google Scholar 

  12. Sha JJ, Ochiai S, Okuda H et al (2008) Residual stresses in YAG phase in directionally solidified eutectic Al 2 O 3/YAG ceramic composite estimated by X-ray diffraction. J Eur Ceram Soc 28:2319–2324

    Article  Google Scholar 

  13. Ramírez-Rico J, Martínez-Fernández J, Peña JI et al (2012) Residual stresses in Al 2 O 3–ZrO 2 (3 mol.% Y 2 O 3) directionally solidified eutectic ceramics as a function of temperature. Mater Sci Eng, A 541:61–66

    Article  Google Scholar 

  14. Gouadec G, Colomban P, Piquet N et al (2005) Raman/Cr 3 + fluorescence mapping of a melt-grown Al 2 O 3/GdAlO 3 eutectic. J Eur Ceram Soc 25:1447–1453

    Article  Google Scholar 

  15. Gouadec G, Makaoui K, Perrière L et al (2012) Ruby micro-piezospectroscopy in GdAlO 3/Al 2 O 3 (/ZrO 2), Er 3 Al 5 O 12/Al 2 O 3 (/ZrO 2) and Y 3 Al 5 O 12/Al 2 O 3 (/ZrO 2) binary and ternary directionally solidified eutectics. J Eur Ceram Soc 32:2145–2151

    Article  Google Scholar 

  16. Orera VM, Cemborain R, Merino RI et al (2002) Piezo-spectroscopy at low temperatures: residual stresses in Al 2 O 3–ZrO 2 (Y 2 O 3) eutectics measured from 77 to 350 K. Acta Mater 50:4677–4686

    Article  Google Scholar 

  17. Perrière L, Valle R, Carrère N et al (2011) Crack propagation and stress distribution in binary and ternary directionally solidified eutectic ceramics. J Eur Ceram Soc 31:1199–1210

    Article  Google Scholar 

  18. Valle R, Carroz L, Ritti M-H et al (2017) Mechanical testing of directionally solidified eutectic ceramics (DSECs): specific problems and limitations. J Mater Sci 52:10047–10061. doi:10.1007/s10853-017-1203-6

    Article  Google Scholar 

  19. Ochiai S, Ikeda S, Iwamoto S et al (2008) Residual stresses in YAG phase of melt growth Al 2 O 3/YAG eutectic composite estimated by indentation fracture test and finite element analysis. J Eur Ceram Soc 28:2309–2317

    Article  Google Scholar 

  20. Lakiza SM, Lopato LM (1997) Stable and metastable phase relations in the system alumina–zirconia–yttria. J Am Ceram Soc 80:893–902

    Article  Google Scholar 

  21. Carroz L, Duffar T (2015) Working point of the EFG process. Cryst Res Technol 50:473–481

    Article  Google Scholar 

  22. Londaitzbéhère L (2016) Etude de nouveaux composites eutectiques à base d’oxydes réfractaires préparés à partir de l’état fondu. Propriétés mécaniques et mécanismes de déformation à haute température. Stabilité de la microstructure en présence de vapeur d’eau. Ph.D. thesis, ICMPE

  23. Cherif M (2016) Croissance de la céramique eutectique Al2O3-YAG-ZrO2:Y et étude de la microstructure Chinese Script. Ph.D. thesis, SIMaP-EPM, Grenoble

  24. Avizo 9.0 (2015) 3D Analysis Software for Scientific and Industrial Data, FEI, France

  25. Hazanov S, Huet C (1994) Order relationships for boundary conditions effect in heterogeneous bodies smaller than the representative volume. J Mech Phys Solids 42:1995–2011

    Article  Google Scholar 

  26. Pahr DH, Zysset PK (2008) Influence of boundary conditions on computed apparent elastic properties of cancellous bone. Biomech Model Mechanobiol 7:463–476

    Article  Google Scholar 

  27. Hovis DB, Reddy A, Heuer AH (2006) X-ray elastic constants for α-Al 2 O 3. Appl Phys Lett 88:131910

    Article  Google Scholar 

  28. Z-set 8.6.5 (2016) Zébulon, Non-linear finite element solver, Transvalor - Centre des Matériaux, France

  29. Bovet C, Parret-Fréaud A, Spillane N, Gosselet P (2017) Adaptive multipreconditioned FETI: scalability results and robustness assessment. Submitt Comput, Struct

    Google Scholar 

  30. Baste S, Hosten B (1990) Evaluation de la matrice d’élasticité des composites orthotropes par propagation ultrasonore en dehors des plans principaux de symétrie. Rev Phys Appliquée 25:161–168

    Article  Google Scholar 

  31. Gourdin S, Marcin L, Podgorski M, et al (2017) Mechanical properties of ternary eutectic ceramic from room to very high temperature. In: 41st internationl conference on expo on advanced ceramic and composites

  32. Perrière L (2008) Élaboration par solidification dirigée et comportement mécanique de céramiques eutectiques à base d’oxydes réfractaires: rôle de la microstructure sur la fissuration et la déformation plastique à haute température. PhD thesis, Paris Est

  33. Alton WJ, Barlow AJ (1967) Temperature dependence of the elastic constants of yttrium aluminum garnet. J Appl Phys 38:3023–3024

    Article  Google Scholar 

  34. Peña JI, Larsson M, Merino RI et al (2006) Processing, microstructure and mechanical properties of directionally-solidified Al 2 O 3–Y 3 Al 5 O 12–ZrO 2 ternary eutectics. J Eur Ceram Soc 26:3113–3121

    Article  Google Scholar 

  35. Hillman C, Suo Z, Lange F (1996) Cracking of laminates subjected to biaxial tensile stresses. J Am Ceram Soc 79:2127–2133

    Article  Google Scholar 

  36. Londaitzbéhère L, Lartigue-Korinek S, Mazerolles L (2017) Microstructure, interfaces and creep behaviour of Al2O3–Sm2O3 (ZrO2) eutectic ceramic composites. J Mater Sci 52:1–14. doi:10.1007/s10853-016-0726-6

    Article  Google Scholar 

  37. Perrière L, Valle R, Mazerolles L, Parlier M (2008) Crack propagation in directionally solidified eutectic ceramics. In: Paper presentation second international workshop directiolal solidified eutectic ceram solidified eutectic ceram workshop II 28:2337–2343. doi:10.1016/j.jeurceramsoc.2008.01.005

  38. Niederreiter H (1992) Random number generation and quasi-Monte Carlo methods. Society for Industrial and Applied Mathematics

  39. McKay MD, Beckman RJ, Conover WJ (1979) Comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21:239–245

    Google Scholar 

  40. Sobol IM (1993) Sensitivity estimates for nonlinear mathematical models. Math Model Comput Exp 1:407–414

    Google Scholar 

  41. Piquet N (2006) Microstructures interconnectées dans des eutectiques à base d’oxydes réfractaires élaborés par solidification dirigée. Ph.D. thesis, Paris-Est

Download references

Acknowledgements

The authors are grateful to the competitiveness cluster ‘MATERALIA’ and to the French MAT&PRO Program ‘CiNATRA’ ref: ANR-12-RMNP-0008 for financial support. The authors also thank P. Lhuissier from SIMaP-GPM2 for the CT scan.

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Authors and Affiliations

  1. Safran Tech – Safran Group, rue des Jeunes Bois, 78772, Magny-les-Hameaux, France

    S. Gourdin, L. Marcin & M. Podgorski

  2. SIMaP-EPM, UMR 5266 CNRS, 38402, Saint Martin d’Hères, France

    M. Cherif

  3. RSA Le Rubis SA, 38560, Jarrie, France

    L. Carroz

  4. Safran Aircraft Engines – Safran Group, Etablissement de Villaroche, 77550, Moissy Cramayel, France

    M. Cherif & L. Carroz

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  1. S. Gourdin
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  2. L. Marcin
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  3. M. Podgorski
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  4. M. Cherif
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  5. L. Carroz
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Correspondence to S. Gourdin.

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Gourdin, S., Marcin, L., Podgorski, M. et al. Effective elastic properties and residual stresses in directionally solidified eutectic Al2O3/YAG/ZrO2 ceramics estimated by finite element analysis. J Mater Sci 52, 13736–13747 (2017). https://doi.org/10.1007/s10853-017-1479-6

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