1172 D. Koch et aL Composites Science and Technology 68(2008)1165-1172 Ligament 3 mm in a satisfying manner. The model takes into consideration 排 inelastic deformation and stifness degradation and can be applied to individual WMC materials with a marginal number of basic mechanical tests. It has been shown that the fe based model can also be applied for complex load- gament 12 mm a300 ing conditions as, e.g., DEN samples. The mechanical response of complex shaped CMC components can then be predicted. Acknowledgements Calculation The authors like to thank the german Science Founda- .304 0.5 tion DFG for financial support and the SGL Carbon group Laser Strain( Lo=25mm)[ %] for providing the material References -45°+45° Ligament 3 []He MY, Hutchinson Jw. Kinking of a crack out of an interface. J 豪 Appl Mech 1989: 56: 270-8 2] Camus G. Modelling of the mechanical behavior and damage of fibrous ceramic matrix composites: Application to a 2- iC. Int J Solids Struct 2000: 37: 919-42 方 Ligament 12 JC,Zok FW, Genin GM, Evans AG. Notch-sensitivity of nforced ceramic-matrix composites: Effects of inelastic 吧 straining and volume-dependent strength. J Am Ceram Soc 1999;5:1217-28. 4] Koch D, Tushtev K, Horvath J, Knoche R, Grathwohl G. Evaluation of mechanical properties and comprehens 50 Experiments =· FE-Calculation tiff and weak matrices. Ady sci Technol 2006: 45: 1435-43 5 Mamiya T, Kakisawa H, Liu WH, Zhu SJ, Kagawa Y. Tensile .2 damage evolution and notch sensitivity of Al2O3 fiber-ZrO2 matrix minicomposite-reinforced Al2O3 matrix composites. Mater Sci Eng A Laser Strain( Lo=25mm) [%] 2002;325(1-2:405-13. [6 Neumeister J, Jansson S, Leckie F. The effect of fiber architecture on Fig. ll. Stress-strain curves of DEn tests and respective modeling the mechanical properties of carbon/carbon fiber composites. Acta dependent on ligament width and fiber orientation(a)0°/90°;(b)+45° [7 Carelli EAV, Fujita H, Yang JY, Zok FW. Effects of thermal aging on the mechanical properties of a porous-matrix ceramic composite J The tests of DEN specimens have shown that the estab- Am Ceram Soc2002;8503):595-602. lished model is able to calculate the behavior of complex [8] Goto K, Hatta H, Takahashi H, Kawada H. Effect of shear damage shaped parts under multiaxial loading conditions. The the fracture behavior of carbon-carbon composites. J Am Ceram design of CMC components and the prediction of their fail- Soc2001;84(6:1327-33 ure behavior are then possible by this Fe tool Eng mater20046(8):664 8. Summary and conclusions [10] Heathcote JA, Gong X-Y, Yang JY, Ramamurty U, Zok FW. In- plane mechanical properties of an all-oxide ceramic composite. J Am The concept of weak interface composites WIC and Ceram Soc l'99982(10):2721-30 weak matrix composites WMC has been demonstrated as [ll] Tushtev K, Koch D, Horvath J, Grathwohl G. Mechanismen und Modellierung der verformung und Schadigung keramische Fas- boundary cases in order to evaluate the properties of erverbundwerkstoffe. Int J Mater Res 2006: 97(10): 1460-9 CMCS. If the matrix is stiff and strong the interfacial prop- [12] Hatta H, Denk L, Watanabe T, Shiota I, Aly-Hassan MS.Fracture erties become dominant and have to be adjusted in order to behavior of carbon-carbon composites with cross-ply lamination. J allow matrix cracks to deviate around the fibers Non brit- Compos Mater2004:3817):147994. tle behavior with high fracture toughness can then be [3]Koch D, Tushtev k. Kuntz M, Knoche R, Horvath J, Grathwohl G Modelling of deformation and damage evolution of CMC with achieved and explained by micromechanically based mod strongly anisotropic properties. In: Lara-Curzio E, editor. Proc of int els. If the matrix is weak and porous the material properties conf advanced ceramics and composites, vol. 26(2). Cocoa Beach do not follow these micromechanical approaches anymore Proceed;2005.p.107-14. Therefore a new model has been established which calcu [14Koch D, Kuntz M, Tushtev K, Knoche R, Horvath J, Grathwohl G lates the properties from macromechanical tests. With Keramische Faserverbundwerkstoffe mit schwacher Matrix- Eigens. chaften und Modellierung: Verbundwerkstoffe und Werkstoffverb. input data from three basic tests (tensile, shear and com- unde: Schlimmer M [ Hrsg. I Werkstoff-Informationsgesellschaft pressive) the complex behavior of WMC can be predicted Frankfurt; 2005. P. 133-8The tests of DEN specimens have shown that the estab￾lished model is able to calculate the behavior of complex shaped parts under multiaxial loading conditions. The design of CMC components and the prediction of their fail￾ure behavior are then possible by this FE tool. 8. Summary and conclusions The concept of weak interface composites WIC and weak matrix composites WMC has been demonstrated as boundary cases in order to evaluate the properties of CMCs. If the matrix is stiff and strong the interfacial prop￾erties become dominant and have to be adjusted in order to allow matrix cracks to deviate around the fibers. Non brit￾tle behavior with high fracture toughness can then be achieved and explained by micromechanically based mod￾els. If the matrix is weak and porous the material properties do not follow these micromechanical approaches anymore. Therefore a new model has been established which calcu￾lates the properties from macromechanical tests. With input data from three basic tests (tensile, shear and com￾pressive) the complex behavior of WMC can be predicted in a satisfying manner. The model takes into consideration inelastic deformation and stiffness degradation and can be applied to individual WMC materials with a marginal number of basic mechanical tests. It has been shown that the FE based model can also be applied for complex load￾ing conditions as, e.g., DEN samples. The mechanical response of complex shaped CMC components can then be predicted. Acknowledgements The authors like to thank the German Science Founda￾tion DFG for financial support and the SGL Carbon group for providing the material. References [1] He MY, Hutchinson JW. Kinking of a crack out of an interface. J Appl Mech 1989;56:270–8. [2] Camus G. Modelling of the mechanical behavior and damage processes of fibrous ceramic matrix composites: Application to a 2- D SiC/SiC. Int J Solids Struct 2000;37:919–42. [3] McNulty JC, Zok FW, Genin GM, Evans AG. Notch-sensitivity of fiber-reinforced ceramic–matrix composites: Effects of inelastic straining and volume-dependent strength. J Am Ceram Soc 1999;5:1217–28. [4] Koch D, Tushtev K, Horvath J, Knoche R, Grathwohl G. Evaluation of mechanical properties and comprehensive modeling of CMC with stiff and weak matrices. Adv Sci Technol 2006;45:1435–43. [5] Mamiya T, Kakisawa H, Liu WH, Zhu SJ, Kagawa Y. Tensile damage evolution and notch sensitivity of Al2O3 fiber-ZrO2 matrix minicomposite-reinforced Al2O3 matrix composites. Mater Sci Eng A 2002;325(1–2):405–13. [6] Neumeister J, Jansson S, Leckie F. The effect of fiber architecture on the mechanical properties of carbon/carbon fiber composites. Acta Mater 1996;44(2):573–85. [7] Carelli EAV, Fujita H, Yang JY, Zok FW. Effects of thermal aging on the mechanical properties of a porous-matrix ceramic composite. J Am Ceram Soc 2002;85(3):595–602. [8] Goto K, Hatta H, Takahashi H, Kawada H. Effect of shear damage on the fracture behavior of carbon–carbon composites. J Am Ceram Soc 2001;84(6):1327–33. [9] Tushtev K, Horvath J, Koch D, Grathwohl G. Deformation and failure modeling of fiber reinforced ceramics with porous matrix. Adv Eng Mater 2004;6(8):664–9. [10] Heathcote JA, Gong X-Y, Yang JY, Ramamurty U, Zok FW. In￾plane mechanical properties of an all-oxide ceramic composite. J Am Ceram Soc 1999;82(10):2721–30. [11] Tushtev K, Koch D, Horvath J, Grathwohl G. Mechanismen und Modellierung der Verformung und Scha¨digung keramischer Fas￾erverbundwerkstoffe. Int J Mater Res 2006;97(10):1460–9. [12] Hatta H, Denk L, Watanabe T, Shiota I, Aly-Hassan MS. Fracture behavior of carbon–carbon composites with cross-ply lamination. J Compos Mater 2004;38(17):1479–94. [13] Koch D, Tushtev K, Kuntz M, Knoche R, Horvath J, Grathwohl G. Modelling of deformation and damage evolution of CMC with strongly anisotropic properties. In: Lara-Curzio E, editor. Proc of int conf advanced ceramics and composites, vol. 26(2). Cocoa Beach Proceed; 2005. p. 107–14. [14] Koch D, Kuntz M, Tushtev K, Knoche R, Horvath J, Grathwohl G. Keramische Faserverbundwerkstoffe mit schwacher Matrix – Eigens￾chaften und Modellierung: Verbundwerkstoffe und Werkstoffverb￾unde; Schlimmer M [Hrsg.], Werkstoff-Informationsgesellschaft, Frankfurt; 2005. p. 133–8. 0.0 0.1 0.2 0.3 0.4 0.5 0 100 200 300 400 500 Ligament 12 mm Ligament 3 mm Experiments FE - Calculation Nominal Stress [MPa] Laser Strain (Lo=25mm) [%] 0°/90° 0.0 0.2 0.4 0.6 0.8 1.0 0 50 100 150 200 250 300 350 Ligament 3 mm Ligament 12 mm Experiments FE - Calculation Nominal Stress [MPa] Laser Strain (Lo=25mm) [%] -45°/+45° Fig. 11. Stress–strain curves of DEN tests and respective modeling dependent on ligament width and fiber orientation (a) 0/90; (b)+45/ 45. 1172 D. Koch et al. / Composites Science and Technology 68 (2008) 1165–1172