176 MATERIA£Y CERAMICZNE /CERAMIC MATERIALS/, 68, 2, (2016), 176-182 www.ptcer.pl/mccm 1. Introduction Silicon carbide belongs to the group of materials with a dominant covalent bond. It causes that SiC has very high hardness, high temperature creep resistance and very good chemical stability. The wider application of SiC as a structural material is limited due to its relatively low fracture toughness (K IC = 2-5 MPa· m 0.5 [1-3]). The toughening effect in SiC can be reached by the modiｿcation of its composition. Incorpo- ration of inclusions into SiC matrix can put into motion some additional mechanisms that increase fracture energy. Particulate composites in the SiC-TiB 2 system are the materials showing improved fracture toughness. Final values of K IC depend on the volume fraction of TiB 2 and can reach even 6-8 MPa· m 0.5 [4-6]. The fracture energy increase in the composites compared to single phase SiC is connected with some additional processes such as: the crack deﾀection, crack bridging, creation of microcracks and inﾀuence of residual thermal stress on a crack propagating through the material [4, 7-13]. The level of inﾀuence of each individual mechanism is not recognized quantitatively. Depending on inclusion and matrix size and shape, some mechanisms could affect positively the fracture toughness and others affect them negatively. One of the main factors, decisive for the effectiveness of the toughness increase mechanisms is constituted by the presence of residual thermal stress in the material. Despite GRZEGORZ GRABOWSKI*, ZBIGNIEW PĉDZICH AGH University of Science and Technology, Faculty of Materials Science and Ceramics, Department of Ceramics and Refractory Materials, al. A. Mickiewicza 30, 30-059 Kraków, Poland *e-mail: grzegorz.grabowski@agh.edu.pl Modeling of thermal residual stresses in the SiC-TiB 2 composite system considering real microstructure and thermo-mechanical properties anisotropy Abstract The results are presented concerning simulations of the distribution of thermal residual stresses in a ceramic matrix particulate-rein- forced composite in the SiC-TiB 2 system. The stresses arise during cooling of the material after sintering due to differences in thermal expansion and elastic properties of the component phases, and belong to the most important factors for increasing fracture toughness of ceramic composites. A computational model was built on the basis of the real microstructure of the SiC-TiB 2 composite. The material properties of component phases used in calculations included their temperature dependences. A temperature difference caused shrinka- ge and residual stress was adopted by means of the analysis of the sintering curves. The simulations were performed by using the ｿnite element method. The results of simulations were compared with the calculated values of residual stresses, basing on analytical models and experimental data. The comparison shows good agreement. This allows an elaborated model to be used to solve more complex problems concerning fracture analysis of ceramic matrix composites. Keywords: SiC-TiB 2 , Ceramic matrix composites, Fracture toughness, Thermal residual stress, Finite element method MODELOWANIE CIEPLNYCH NAPRĉĩEē RESZTKOWYCH W KOMPOZYTACH Z UKàADU SiC-TiB 2 Z UWZGLĉDNIENIEM RZECZYWISTEJ MIKROSTRUKTURY I ANIZOTROPII WàAĝCIWOĝCI TERMO-MECHANICZNYCH Zaprezentowano wyniki dotyczące symulacji rozkáadu cieplnych naprĊĪeĔ resztkowych w kompozycie dyspersyjnych z osnową cera- miczną z ukáadu SiC-TiB 2 . NaprĊĪenia powstaáy podczas studzenia materiaáu po spieczeniu z powodu róĪnic w rozszerzalnoĞci cieplnej i wáaĞciwoĞciach sprĊĪystych skáadowych, a naleĪą one do najwaĪniejszych czynników odpowiedzialnych za zwiĊkszenie odpornoĞci na pĊkanie kompozytów ceramicznych. Model obliczeniowy zostaá zbudowany na bazie rzeczywistej mikrostruktury kompozytu SiC-TiB 2 . WáaĞciwoĞci materiaáowe skáadowych faz uĪyte w obliczeniach uwzglĊdniaáy ich zaleĪnoĞü od temperatury. RóĪnica temperatury powodu- jąca skurcz i naprĊĪenia resztkowe zostaáa uzyskana za pomocą analizy krzywych spiekania. Symulacje przeprowadzono z wykorzysta- niem metody elementów skoĔczonych. Otrzymane wyniki porównano z wynikami obliczeĔ naprĊĪeĔ resztkowych opartych na modelach analitycznych i danych eksperymentalnych, uzyskując dobrą zgodnoĞü, co pozwoliáo na opracowanie modelu uĪytecznego do rozwiązy- wania bardziej skomplikowanych problemów dotyczących analizy pĊkania kompozytów z osnową ceramiczną. Sáowa kluczowe: SiC-TiB 2 , kompozyty z osnową ceramiczną, odpornoĞü na pĊkanie, cieplne naprĊĪenia resztkowe, metoda elementów skoĔczonych