A methodology has been proposed to describe CMC and functionally graded materials (FGM) thermomechanical response subjected to sudden changes of the temperature field. Appropriate gradation of the composite properties can significantly improve thermal shock response of the material itself or a structural element. The governing equations for the temperature field under transient thermal loading are formulated, and solution of the analytical and two numerical methods FEA and FD were discussed. The role of the thermal residual stress is significant in the analysis of thermal shock problems. In a non-symmetrical gradation profile they create initial curvature of the FGM structural element. The basic fracture mechanics idea is presented and is applied to CMC and FGM which were subjected to a transient temperature field. In particular the crack-bridging mechanism plays an important role in the assessment of the composites response. Numerical examples dealing with 1-D and 2-D non-symmetric thermal shock problem illustrate the effectiveness of the theoretical methods to the solution of practical problems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. Aboudi, Mechanics of Composite Materials, Elsevier, Amsterdam, 1991
K.E. Aifantis, J.R. Willis, Mech. Mater., 2006, 38, 702–716
K.E. Aifantis, J.R. Willis, J. Mech. Phys. Solids, 2005, 53, 1047–70
A. Atkinson, A. Selçuk, Acta Mater., 1999, 47, 867–74
T.L. Becker, R.M. Cannon, R.O. Ritchie, Mech. Mater., 2000, 32, 85–97
Y. Benveniste, Mech. Mater., 1987, 6, 147–157
T.J. Chung, A. Neubrand, J. Rödel, T. Fett, Ceram. Trans., 2001, 114, 789–96
M. Dao, P. Gu, A. Maewal, J. Asaro, Acta Mater., 1997, 45, 3265–76
M. Dong, S. Schmauder, Acta Mater., 1996, 44, 2465–78
F. Erdogan, Com. Eng., 1995, 5, 753–70
F. Erdogan, B.H. Wu J. Therm. Stress, 1996, 19, 237–65
J.D. Eshelby, Proc. Roy. Soc.,1957, A 349, 376–96
A. Evans, J. Am. Cer. Soc., 1990, 73, 187–206
Z. Fan, A.P. Miodownik, P. Tsakiropoulos, Mat. Sci. Technol., 1992, 8, 922–29
Z. Fan, A.P. Miodownik, P. Tsakiropoulos, Mat. Sci. Technol., 1993, 9, 1094–100
F. Felten, S. Schneider, T. Sadowski, Int. J. Ref. Mat. Hard Mat., 2008, 26, 55–60
N.A. Fleck, J.R. Willis, J. Mech. Phys. Solids, 2004, 52, 1855–88
L.B. Freund, J. Cryst. Growth, 1993, 132, 341–44
L.B. Freund, J. Mech. Phys. Solids, 1996, 44, 723–36
L.B. Freund, J. Mech. Phys. Solids, 2000, 48, 1159–74
T. Fujimoto, N. Noda, J. Am. Cer. Soc., 2001, 84, 1480–86
A.E. Gianakopoulos, S. Suresh, M. Finot, M. Olsson, Acta Matall. Mater., 1995, 43, 1335–54
D. Gross, T. Seelig, Fracture Mechanics with an Introduction to Micromechanics, Springer,2006
Z. Hashin, S. Shtrikman, J. Mech. Phys. Solids, 1963, 11, 127–40
R. Hill, J. Mech. Phys. Solids, 1965, 13, 213–22
C.H. Hsueh, Thin Sol. Films, 2002a, 418, 182–88
C.H. Hsueh, J. Appl. Phys., 2002b, 91, 9652–56
C.H. Hsueh, A.G. Evans, J. Am. Cer. Soc., 1985, 68, 241–48
C.H. Hsueh, S. Lee, T.J. Chuang, J. Appl. Mech., 2003a, 70, 151–54
C.H. Hsueh, S. Lee, Composites B, 2003b, 34, 747–52
M. Jiang, I. Jasiuk, M. Ostoja-Starzewski, Comput. Mat. Sci., 2000, 25, 329–38
Z.-H. Jin, R.C. Batra, J. Mech. Phys. Solids, 1996a, 44, 1221–35
Z.-H. Jin, R.C. Batra, J. Therm. Stress, 1996b, 19, 317–39
Z.-H. Jin, R.C. Batra, J. Therm. Stress, 1998, 21, 151–76
Z.-H. Jin, G.H. Paulino, R.H. Dodds Jr., Eng. Fract. Mech., 2003, 70, 1885–912
D. Jeulin, M. Ostoja-Starzewski (Eds), (2001) .Mechanics of Random and Multiscale Microstruc-tures, CISM Courses and Lectures no. 430, Wien, Springer, New York
A.C. Kaya, F. Erdogan, Quart. Appl. Math., 1987, 45, 105–22
A. Kawasaki, R. Watanabe, Ceram. Trans., 1993, 34, 157–64
A. Kawasaki, R. Watanabe, Compos. Part B, 1997, 28, 29–35
A. Kawasaki, R. Watanabe, Eng. Fract. Mech., 2002, 69, 1713–28
K.-S. Kim, N. Noda” Arch. Appl. Mech., 2002, 72, 127–37
M. Kouzeli, D.C. Dunand, Acta Mater., 2003, 51, 6105–21
W. Kreher, W. Pomope, Internal Stress in Heterogeneous Materials, Akademie Verlag, Berlin,1989
V.D. Krstic, Phil. Mag. A, 1983, 48, 695–708
G. Li, P. Ponte Castañeda, Appl. Mech. Rev., 1994, 47, S77–94
Z. Li, S. Schmauder, M. Dong, Comput. Mater. Sci., 1999, 15, 11–21
M.N. Miller, J. Math. Phys., 1969, 10, 1988–2004
R.J. Moon, M. Tilbrook, M. Hoffman, A. Neubrand, J. Am. Cer. Soc., 2005, 88, 666–74
T. Mori, K. Tanaka, Acta Metall., 1973, 21, 571–74
K.W. Morton, D.F. Mayers, Numerical Solutions of Partial Differential Equations, An Introduction, Cambridge Univ. Press, Cambridge, 2005
H. Moulinec, P. Sequet, Eur. J. Mech. A/Solids, 2003, 22, 751–70
R.J. Munro, J. Am. Cer. Soc., 2001, 84, 1190–92
D. Munz, T. Fett, Ceramics: Mechanical Properties, Failure Behaviour, Materials Selection,Springer, Berlin, 1999
K. Nakonieczny and T. Sadowski, Comput. Mater. Sci., 2008, (doi: 10.1016/j.commatsci.2008.08.0.19)
S. Nemat-Nasser, M. Hori, Micromechanics: Overall Properties of Heterogeneous Materials,Nordh-Holland, Amsterdam, 1993
A. Neubrand, J. Rödel, Z. Metallkd., 1997, 88, 358–71
A. Neubrand, T.J. Chung, J. Rödel, E.D. Steffler, T. Fett, J. Mat. Res., 2002, 17, 2912–20
N. Noda, J. Thermal Stress, 1999, 22, 477–512
N. Noda, R.B. Hetnarski, Y. Tanigawa, Thermal stress, Lastran Corporation, USA, 2000
M. Ostoja-Starzewski, Appl. Mech. Rev., 1994, 47, S221–S230
M. Ostoja-Starzewski,Microstructural Randomness and Scaling in Mechanics of Materials,Chapman&Hall/CRC, 2007
M. Ostoja-Starzewski, J. Schulte, Phys. Rev. B, 1996, 54, 278–85
M. Ostoja-Starzewski, P.Y. Sheng, I. Jasiuk, ASME J. of Engng. Mat. Tech., 1994, 116, 384–91
G.A. Papadopoulos, Fracture Mechanics. The Experimental Method of Caustics and the Det.-Criterion of Fracture, Springer, 1993
M.J. Pindera, J. Aboudi, S.M. Arnold, J. Am. Cer. Soc., 1998, 81, 1525–36
M.J. Pindera, J. Aboudi, S.M. Arnold, Eng. Fract. Mech., 2002, 69, 1587–606
S. Pitakthapanaphong, E.P. Busso, J. Mech. Phys. Solids, 2002, 50, 695–716
P. Ponte Castañeda, J. Mech. Phys. Solids, 1991, 39, 45–71
P. Ponte Castañeda, P. Sequet, Adv, in Appl. Mech., 1998, 34, 171–302
E. Postek” T. Sadowski, S.J. Hardy, 2005. The mechanical response of a ceramic polycrys-talline material with inter-granular layers. In: Proc. VIII International Conference on Computational Plasticity, COMPLAS VIII, E. Oñate, D.R.J. Owen eds., CIMNE, Barcelona, pp.1075–78
R. Pyrz, Comp. Sci. Techn., 1994, 50, 539–46
R. Pyrz and B. Bochenek, Sci. Engng. Comp. Mat., 1994, 3, 95–109
R. Pyrz and B. Bochenek, Int. J. Solids Struct., 1998, 35, 2413–27
K.S. Ravichandran, J. Am. Cer. Soc., 1994, 77, 1178–84
K.S. Ravichandran, Mat. Sci. Eng., 1995, A201, 269–76
T. Reiter, G.J. Dvorak, V. Tvergaard, J. Mech. Phys. Solids, 1997, 45, 1281–302
T. Sadowski, Mech. Mater., 1994, 18, 1–16
T. Sadowski (Ed.), (2005a) Multiscale Modelling of Damage and Fracture Processes in Composite Materials, CISM Courses and Lectures no. 474, Wien, Springer, New York
T. Sadowski, Modelling of Damage and Fracture Processes of Ceramic Matrix Composites. In CISM Courses and Lectures No. 474, ed. T. Sadowski, Springer, Wien, New York, 2005b,pp. 271–309
T. Sadowski, S. Samborski, Comput. Mater. Sci., 2003a, 28, 512–17
T. Sadowski, S. Samborski, J. Am. Ceram. Soc., 2003b, 86, 2218–21
T. Sadowski, A. Neubrand, Int. J. Frac. 2004, 127, L135–L140
T. Sadowski T., A. Nowicki, Comput. Mater. Sci., 2008, 43, 235–41
T. Sadowski, K. Nakonieczny, Comput. Mater. Sci., 2008, 43, 171–78
T. Sadowski, S. J. Hardy, E. Postek, Comput. Mater. Sci., 2005a, 34, 46–63
T. Sadowski, S. Samborski, Z. Librant, Key Eng. Mat., 2005b, 290, 86–93
T. Sadowski, M. Boniecki, Z. Librant, Adv. Sci. Tech., 2006a, 45, 1640–45
T. Sadowski, S. J. Hardy, E. Postek, Mater. Sci. Eng. A, 2006b,424, 230–38
T. Sadowski, M. Boniecki, Z. Librant, Proc. ECERS'07, Berlin 17–21 June 2007b. (CD-ROM)
T. Sadowski, E. Postek, Ch. Denis, Comput. Mat. Sci., 2007c, 39, 230–36
T. Sadowski, S. Ataya, A. Nakonieczny, Comput. Mater. Sci. In: 2008a. (doi:10.1016/j.commatsci.2008.07.011)
T. Sadowski, M. Boniecki, Z. Librant, A. Nakonieczny, Int. J. Heat Mass Transfer, 2007a, 50,4461–67
T. Sadowski, T. Niezgoda, K. Kosiuczenko, M. Boniecki, Z. Librant, 2008b, (in preparation)
S. Schmauder, U. Weber, I. Hofinger, A. Neubrand, Te c h. M e c h., 1999, 19, 313–20
S. Schmauder, U. Weber, E. Soppa, Comput. Mater. Sci., 2003, 26, 142–53
P. Suquet, (1997) Continuum Micromechanics, CISM Courses and Lectures no. 377, Wien,Springer, New York
R. Stevens, Introduction to Zirconia, Magnesium Elektron Ltd., 1986
S. Suresh, A. Mortensen, Fundamentals of Functionally Graded Materials, Institute of Materials, London, 1998
D.R.S. Talbot, J.R. Willis, IMA J. Appl.Math., 1985, 35, 39–54
D.R.S. Talbot, J.R. Willis, Int. J Solids Struct., 1992, 29, 1981–87
D.R.S. Talbot, J.R. Willis, Proc. Roy. Soc., 1994, A447, 365–84
D.R.S. Talbot, J.R. Willis, Proc. Roy. Soc., 2004, A460, 2705–23
I. Tamura, Y. Tomota, H. Ozawa, In: Proc. Third Int. Con. Strength Metal land Alloys, Vol. 1.,Cambridge: Institute of Metals, 1973, 611–15
Y. Tanigawa, M. Matsumoto, T. Akai, JSME Int. Journal, Series A, 1997, 40, 84–93
S. Torquato, Int. J. Sol. Struct., 1998, 35, 2385–2406
S. Torquato, Random Heterogeneous Materials, Springer, New York, 2002
F. Trancert, F. Osterstock, Scr. Mat., 1997, 37, 443–447
L.I. Tuschinskii, Poroshk. Metall., 1983, 7, 85 (translated in .Powder Metallurgy and Metall Ceramics, 1983
B.-L. Wang, Y.-W. Mai, Int. J. Mech. Sci., 2005, 47, 303–17
B.-L. Wang, Y.-W. Mai, X.-H. Zhang, Acta Mater., 2004, 52, 4961–72
L.D. Wegner, L.J. Gibson, Int. J. Mech. Sci., 2000, 42, 925–42
E. Werner, T. Siegmund, H. Weinhandl, F.D. Fisher, Appl. Mech. Rev., 1994, 47, S231–S240
D.S. Wilkinson, W. Pompe, M. Oeshner, Prog. Mat. Sci., 2001, 46, 379–405
B-L. Wang, Y.-W. Mai, Int. J.Mech. Sci., 2005, 47, 303–317
B-L. Wang, Y.-W. Mai, X-H. Zhang, Acta Mater., 2004, 52, 4961–72
J.R. Willis, J. Mech. Phys. Solids, 1977, 25, 185–202
J.R. Willis, Eur. J. Mech. A/Solids, 2000, 19, S165–S184
O.C. Zienkiewicz, R.L. Taylor, The Finie Element Method, McGraw-Hill, New York, 1987
J.R. Zuiker, Com. Eng., 1995, 7, 807–19
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Sadowski, T. (2009). Non-Symmetric Thermal Shock In Ceramic Matrix Composite (Cmc) Materials. In: de Borst, R., Sadowski, T. (eds) Lecture Notes on Composite Materials. Solid Mechanics And Its Applications, vol 154. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8772-1_4
Download citation
DOI: https://doi.org/10.1007/978-1-4020-8772-1_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-8771-4
Online ISBN: 978-1-4020-8772-1
eBook Packages: EngineeringEngineering (R0)