Minimizing the Formation of Thermal Residual Stresses of the Elasto-Plastic Zone in Functionally Graded Materials

Abstract

Functionally graded materials (FGM’s) are advanced composites consisting of two or more materials whose composition and structure changes gradually over the volume, leading to gradual change in its property. Typically one component is a ceramic, while the other is metal or metal alloy. In common embodiments, the composition can change gradually from all ceramic on one side to all metal on the other side, the ceramic contributing high resistance to temperature with the metal contributing high ductility. It’s a way to incorporate favorable properties of two materials into different locations of a single structure. In ideal cases the composition changes gradually but for manufacturing reasons, the changes occurs in homogeneous layers. The boundaries between the layers cause thermal residual stresses to arise, especially during material processing and in cases of cyclic loading. These thermal residual stresses are a result of differences in the thermal expansion coefficient of the varying compositions of materials. Thermal residual stresses may lead to cracking and ultimate failure of FGM’s. This study investigates the formation of thermal residual stresses for a Nickel-Alumina Ni-Al?O? FGM. The Ni-Al?O? system is chosen because it is one of the most common systems used in practice. This work explores the formation, impact and minimization of thermal residual stresses for a number of practical conditions that may arise during processing. All relevant properties are calculated using the rule of mixture equations. Abaqus, a non-linear FEA solver, is used for all the simulation work.

Introduction

I. INTRODUCTION

The use of functionally graded materials is a relatively new phenomenon in industry. The control of thermal residual stresses (TRSs) in functionally graded materials (FGMs) is critical. The change in material properties lead to the possibility of residual stresses due to the variation in material properties. In this research we use finite element analysis (ABAQUS) as a numerical technique to predict the formation of residual stresses. “Functionally graded materials are engineered materials that are made of two or more materials in such a way that properties of these composites vary along one dimension [1]. Possible applications of this type of materials are diesel internal combustion engines (top surface of a piston), outer skin of space reentry vehicles, inner linings of nuclear power plants and turbine blades in jet engines.  In the case of the latter, the two ends of the turbine blades are exposed to extreme temperatures and stresses, thus needing to have a wide variation in properties for optimal functionality. This wide variation in properties may be achieved by using thermal barrier coating system (TBC) and/or using functionally graded materials (FGM). In a traditional thermal barrier coating a ceramic layer is applied as a coating on a metal substrate where the properties change abruptly between the two layers. In a functionally graded material (FGM) the fraction of each material (and therefore, the properties) vary continuously or stepwise over the interface region between the two materials.

A fundamental understanding of these composites is needed both for designing them as well as for manufacturing. During manufacturing, residual stresses in these types of materials is a typical problem that could cause early failure during their use [2], [3]. The purpose of this research is to develop a fundamental understanding of how residual stresses are formed and developed in these types of materials during their thermo-mechanical processing and then to optimize process parameters and design parameters to minimize these stresses.

In this paper, the study of the formation, concentration and how to minimize the thermal residual stresses at the interface surface between layers of the two constituents, which is called the nickel-Alumina (Ni-Al?O?) system in 50 mm length and 10 mm thick plate is investigated and the parameter such as volume fraction is used to compute mechanical and physical properties such as Young’s module (E), Poisson ratio (ν), thermal expansion coefficients (α), thermal conductivity(k) and heat capacity (C) of each layer of stepwise of Functionally Graded Material(FGM).

This is accomplished through rule of mixture equations, number of layers such as two, three and ten layers. The Functionally graded Material (FGM) can consist of two; three and ten layers are subjected to transient of 300 ?K as initial temperature and cool dawn to 100?K as a sink temperature. Finally based on finite element as numerical analysis model and an Abaqus technique software is used as numerical model for simulation.” [14], [15].

Conclusion

The Finite Element modeling of the Functionally Graded Material FGM was analyzed in the elastoplastic zone to study the minimization of formation of thermal residual stresses in FGM. In this study, Alumina and Nickel FGM was considered in the analysis. The stress-strain curves for thermal residual stresses of Alumina Nickel were produced, it is evident in the outcome of the Finite Element modeling that as the percentage of ceramic increases (i.e. the percentage of Nickel decreases), the thermal residual stresses are increasing. It is concluded from this study that the thermal residual stresses in the Alumina Nickel FGM is behaving smoothly except at the partitions between ductile component (in this case Nickel) and brittle material (in this case the alumina). This conclusion is helpful in designing arrangements of layers of FGM to minimize fluctuation of residual thermal stresses in across material thickness emphasizing the conclusion of our previous work. Please see references [14], [15] and [16].

References

[1] Miyamoto, Y., W.A. Kaysser, B.H. Rabin, A. Kawasaki, and R.G. Ford, eds. Functionally Graded Materials: Design, Processing and Applications. Kluwer Academic Publishers, 1999. [2] Teng, Lidong, and Wenchao Li. “Residual Stress Analysis of Ti-ZrO2 Thermal Barrier Graded Materials.” Materials and Design 23 (2002): 627–32. [3] Product Handbook of High- Performance Nickel Alloys, n.d. http://www.specialmetals.com/files/PCC-8064-SM-AlloyHandbook_v04.pdf. [4] Cho, J.R., and D.Y. Ha. “Volume Fraction Optimization for Minimizing Thermal Stress in Ni–Al2O3 Functionally Graded Materials.” Materials Science and Engineering: A 334, no. 1–2 (September 2002): 147–55. doi:10.1016/S0921-5093(01)01791-9. [5] Cho, J.R., and D.Y. Ha. “Averaging and Finite-Element Discretization Approaches in the Numerical Analysis of Functionally Graded Materials.” Materials Science and Engineering: A 302, no. 2 (April 2001): 187–96. doi:10.1016/S0921-5093(00)01835-9. [6] Cho, J.R., and J. Tinsley Oden. “Functionally Graded Material: A Parametric Study on Thermal-Stress Characteristics Using the Crank-Nicolson-Galerkin Scheme.” Computer Methods in Applied Mechanics and Engineering 188 (2000): 17–38. [7] Birman, Victor, and Larry W. Byrd. “Modeling and Analysis of Functionally Graded Materials and Structures.” Applied Mechanics Reviews 60, no. 5 (2007): 195. doi:10.1115/1.2777164. [8] Nemat-Alla, Mahmoud, Khaled I.E. Ahmed, and Ibraheem Hassab-Allah. “Elastic–plastic Analysis of Two-Dimensional Functionally Graded Materials under Thermal Loading.” International Journal of Solids and Structures 46, no. 14–15 (July 2009): 2774–86. doi:10.1016/j.ijsolstr.2009.03.008. [9] Noda, Naotake. “Thermal Stresses in Functionally Graded Materials.” Journal of Thermal Stresses 22, no. 4–5 (June 1999): 477–512. doi:10.1080/014957399280841 [10] Delandar, Arash Hosseinzadeh. Finite Element Analysis of Thermally Induced Residual Stresses in Functionally Graded Materials, 2012. [11] Giannakopoulos, A. E., S. Suresh, M. Finot, and M. Olsson. “Elastoplastic Analysis of Thermal Cycling?: Layered Materials with Compositional Gradients.” Acta Metallurgica et Materialia 43, no. 4: 1335–54. Accessed October 26, 2014. http://cat.inist.fr/?aModele=afficheN&cpsidt=3440794. [12] Joshi, Shailendra, Abhijit Mukherjee, and Siegfried Schmauder. “Numerical Characterization of Functionally Graded Active Materials under Electrical and Thermal Fields.” Smart Materials and Structures 12, no. 4 (August 01, 2003): 571–79. doi:10.1088/0964-1726/12/4/309. [13] Lee, Caroline, Sung-hoon Ahn, Lutgard DeJonghe, and Gareth Thomas. “Effect of Functionally Graded Material (FGM) Layers on the Residual Stress of Polytypoidally Joined Si3N4-Al2O3.” Materials Science and Engineering: A 434 (2006): 160–65. [14] Farag Khouja and Nassif Rayess, Finite Element Modeling of the Plastic Zone Thermal Residual Stresses in Functionally Graded Materials, International Journal for Research in Applied Science & Engineering Technology (IJRASET), ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.538, Volume 12 Issue IIFeb 2024- Available at www.ijraset.com [15] Farag Khouja and Nassif Rayess, Towards Understanding of the Plastic Zone Thermal Residual Stresses in Functionally Graded Materials, International Journal for Research in Applied Science & Engineering Technology (IJRASET), ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.538, Volume 12 Issue IIFeb 2024- Available at www.ijraset.com [16] Farag Khouja, Minimizing the Formation of Thermal Residual Stresses of the Elastic Zone in Functionally Graded Materials, Submitted to the International Journal for Research in Applied Science & Engineering Technology (IJRASET), Feb 2024- www.ijraset.com

Copyright

Copyright © 2024 Farag A. Khouja. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.