An Improved Fracture Mechanics-Informed Multiscale Thermomechanical Damage Model for Ceramic Matrix Composites

  • Travis SkinnerEmail author
  • Jacob Schichtel
  • Aditi Chattopadhyay
Conference paper
Part of the The Minerals, Metals & Materials Series book series (MMMS)


This paper extends recent work done by the authors in modeling length scale-dependent damage behavior of ceramic matrix composites (CMCs) to include effects of local anisotropy introduced by matrix cracking. This model captures scale-dependent damage initiation and propagation behavior of the brittle matrix by employing internal state variable (ISV) theory within a multiscale modeling framework to obtain damaged matrix stress/strain constitutive relationships at each length scale. The damage ISV captures the effects of matrix cracking and growth by using fracture mechanics and the self-consistent scheme to determine the reduced stiffness of the cracked matrix. Matrix cracks, which activate when stress intensity factors near manufacturing induced cavities exceed the fracture toughness of the material, are assumed to be transversely isotropic in the plane of the crack, and matrix anisotropy occurs when the damaged stiffness tensor is rotated from the crack plane to the global axes. The crack progression and temporal evolution of the damage ISV are governed by fracture mechanics and crack growth kinetics. The model effectively captures first matrix cracking, which is the first significant deviation from linear elasticity. The nonlinear predictive capabilities of the material model are demonstrated for monolithic silicon carbide (SiC) and a 2D woven five-harness satin (5HS) carbon fiber SiC matrix (C/SiC) CMC.


Ceramic matrix composite Multiscale Damage Fracture mechanics Internal state variable 



This research was sponsored by the Air Force Office of Scientific Research and was accomplished under grant number FA9550-18-1-00129. Dr. Jaimie Tiley is the program manager. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Air Force Office of Scientific Research or the US Government. The US Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.


  1. 1.
    Schmidt S, Beyer S, Knabe H, Immich H, Meistring R, Gessler A (2004) Advanced ceramic matrix composite materials for current and future propulsion technology applications. Acta Astronautica 55(3–9):409–420CrossRefGoogle Scholar
  2. 2.
    Krenkel W (ed) (2008) Ceramic matrix composites: fiber reinforced ceramics and their applications, John Wiley & SonsGoogle Scholar
  3. 3.
    Prewo KM, Brennan JJ, Layden GK (1986) Fiber reinforced glasses and glass-ceramics for high performance applications. Am Ceram Soc Bull 65:305–313Google Scholar
  4. 4.
    Lamouroux F, Bertrand S, Pailler R, Naslain R, Cataldi M (1999) Oxidation-resistant carbon-fiber reinforced ceramic matrix composites. Compos Sci Technol 59(7):1073–1085CrossRefGoogle Scholar
  5. 5.
    Sadowski T, Marsavina L (2011) Multiscale modelling of two-phase ceramic matrix composites. Comput Mater Sci 50(4):1336–1346CrossRefGoogle Scholar
  6. 6.
    Kanoute P, Boso DP, Chaboche JL, Schrefler BA (2009) Multiscale methods for composites. Arch Comput Methods Eng 16(1):31–75CrossRefGoogle Scholar
  7. 7.
    Sadowski T (ed) (2007) Multiscale modelling of damage and fracture processes in composite materials, Springer Science and Business MediaGoogle Scholar
  8. 8.
    Aboudi J, Arnold S, Bednarcyk B (2012) Micromechanics of composite materials: a generalized multiscale analysis approach, Butterworth-HeinemannGoogle Scholar
  9. 9.
    Liu KC, Chattopadhyay A, Bednarcyk B, Arnold SM (2011) Efficient multiscale modeling framework for triaxially braided composites using generalized method of cells. J Aerosp Eng 24(2):162–169CrossRefGoogle Scholar
  10. 10.
    Hild F, Burr A, Leckie F (1996) Matrix cracking and debonding of ceramic-matrix composites. Int J Solids Struct 33(8):1209–1220CrossRefGoogle Scholar
  11. 11.
    Camus G (2000) Modelling of the mechanical behavior and damage processes of fibrous ceramic matrix composites: application to a 2-D SiC/SiC. Int J Solids Struct 37(6):919–942CrossRefGoogle Scholar
  12. 12.
    Maire JF, Lesne PM (1997) A damage model for ceramic matrix composites. Aerosp Sci Technol 1(4):256–266Google Scholar
  13. 13.
    Caputo AJ, Lackey WJ (1984) Fabrication of fiber-reinforced ceramic composites by chemical vapor infiltrationGoogle Scholar
  14. 14.
    Liu KC, Chattopadhyay A, Arnold SM (2011) Impact of material and architecture model parameters on the failure of woven CMCs via the multiscale generalized method of cells. In: Developments in strategic materials and computational design II: ceramic engineering and science proceedings, pp 175–192Google Scholar
  15. 15.
    Skinner T, Rai A, Chattopadhyay A (2019) Fracture mechanics-informed multiscale thermomechanical damage model for ceramic matrix composites. In: 22nd International Conference on Composite Materials, Melbourne, AU, 2019Google Scholar
  16. 16.
    Budiansky B, O’Connell RJ (1976) Elastic moduli of a cracked solid. Int J Solids Struct 12(2):81–97CrossRefGoogle Scholar
  17. 17.
    Lemaitre JA (2012) A course on damage mechanics. Springer Science and Business MediaGoogle Scholar
  18. 18.
    Lemaitre J, Desmorat R (2005) Engineering damage mechanics. Springer, BerlinGoogle Scholar
  19. 19.
    Wachtman J, Cannon WR, Matthewson MJ (2009) Linear elastic fracture mechanics. In: Mechanical Properties of Ceramics, John Wiley & Sons, 63–87Google Scholar
  20. 20.
    Paliwal B, Ramesh KT (2008) An interacting micro-crack damage model for failure of brittle materials under compression. J Mech Phys Solids 56:896–923CrossRefGoogle Scholar
  21. 21.
    Wang H, Ramesh KT (2003) Dynamic strength and fragmentation of hot-pressed silicon carbide under uniaxial compression. Acta Mater 52:355–367CrossRefGoogle Scholar
  22. 22.
    Paliwal B, Ramesh KT, MaCauley JW (2006) Direct observation of the dynamic compressive failure of a transparent polycrystalline ceramic. J Am Ceram Soc 89:2128–2133Google Scholar

Copyright information

© The Minerals, Metals & Materials Society 2020

Authors and Affiliations

  • Travis Skinner
    • 1
    Email author
  • Jacob Schichtel
    • 1
  • Aditi Chattopadhyay
    • 2
  1. 1.School for Engineering of Matter, Transport and Energy, Arizona State UniversityTempeUSA
  2. 2.Regents’ Professor, School for Engineering of Matter, Transport and EnergyArizona State UniversityTempeUSA

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