Discrete element simulation of transverse cracking during the pyrolysis of carbon ﬁbre reinforced plastics to carbon/carbon composites Falk K. Wittel a, * , Jan Schulte-Fischedick b,1 , Ferenc Kun c , Bernd-H. Kr€ oplin a , Martin Frieß b a Institute for Statics and Dynamics of Aerospace Structures, University of Stuttgart, Pfaﬀenwaldring 27, 70569 Stuttgart, Germany b German Aerospace Center (DLR), Institute of Structures and Design, Pfaﬀenwaldring 38/40, D-70569 Stuttgart, Germany c Department of Theoretical Physics, University of Debrecen, P.O. Box 5, H-4010 Debrecen, Hungary Received 18 April 2002; accepted 11 July 2002 Abstract The fracture behavior of ﬁber-ceramics like carbon/carbon–silicon carbide strongly depends on the initial damage arising during the production process. We study the transverse cracking of the 90° ply in ½0=90 S crossply laminates due to the thermochemical degradation of the matrix material during the carbonization process by means of a discrete element method. The crack morphology strongly depends on the ﬁber–matrix interface properties, the transverse ply thickness as well as on the carbonization process itself. To model the 90° ply a two-dimensional triangular lattice of springs is constructed where nodes of the lattice represent ﬁbers. Springs with random breaking thresholds model the disordered matrix material and interfaces. The spring-lattice is coupled by interface springs to two rigid bars which capture the two 0° plies or adjacent sublaminates in the model. Molecular dynamics simulation is used to follow the time evolution of the model system. It was found that under gradual heating of the specimen, after some distributed cracking, segmentation cracks occur in the 90° ply which then develop into a saturated state where the ply cannot support additional load. The dependence of the microstructure of damage on the ply thickness and on the disorder in spring properties is also studied. Crack density and porosity of the system are monitored as a function of the tem- perature and compared to an analytic approach and experiments. Ó 2003 Elsevier Science B.V. All rights reserved. PACS: 02.60; 85.40; 83.20; 82.20.Wt; 81.60.Hv Keywords: Discrete element model; Numerical simulation; Composite material; Pyrolysis; Thermal degradation 1. Introduction In the recent years extensive investigations were focused on enhancing high-temperature per- formance and reliability for ﬁber reinforced ce- ramic matrix composites (CMC), especially their Computational Materials Science 28 (2003) 1–15 www.elsevier.com/locate/commatsci * Corresponding author. Tel.:+49-0711-685-7093/684-7093; fax.:+49-0711-685-3706/684-3706. E-mail address: wittel@isd.uni-stuttgart.de (F.K. Wittel). 1 Present address: DLR, Institute of Technical Thermody- namics. 0927-0256/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0927-0256(03)00035-1