Ž . Materials and Design 22 2001 5359 Molecular dynamics  simulations of the fracture toughness of sapphire Wilfried Wunderlich  , Hideo Awaji Department of Material Science, Nagoya Institute of Technology, Gokiso, Showa-ku, 466-8555 Nagoya, Japan Abstract A new method for the estimation of the fracture toughness K by using the Molecular Dynamics method is presented. The IC Al O single crystals were deformed under constant displacement conditions with an initial crack of length 1 nm. The strain was 2 3 applied in the a axis, which was set perpendicular to the crack plane, so that the mode I crack deformation was achieved. The total energy, which is a result of MD simulations, was analyzed in the elastic, plastic and surface energy part. From the structural plots the crack propagation was measured and the analysis using the Griffith criterion was applied. From the critical condition the Ž fracture toughness was estimated. The experimental values for the fracture toughness in the four crack orientations plane and .Ž .  Ž .  Ž .  Ž .  12 direction 11.0 001 , 11.-2 12-1 , 00.1 100 , and 11.0 010 were 2.84, 2.71, 5.62, 2.67 MPa m , respectively, and the calculations are in good agreement. Also, a heterogeneous alumina  zirconia nanocomposite material was analyzed by this method. Although the particle had only a diameter of 1 nm, the toughness increased because the interface was found to be quite strong.  2000 Published by Elsevier Science Ltd. Keywords: Alumina; Molecular dynamics; Composite materials; Fracture toughness; Crack propagation; Gibbs free energy; Surface energy 1. Introduction Molecular Dynamics is a well established materials development process. At an atomic scale all processes, which have been observed by experiment, can be stud- ied more accurately and modeled in detail. Successful applications have been the calculation of atomic struc- tures of grain boundaries and interfaces and properties     1  4 . The computer program ‘ MOLDY’ 5,6 also con- siders the long-range Coulomb interaction and is espe- cially suitable for ceramic materials; especially for ZrO 2    2,7,8 and Al O 9 , good two-body pair potentials are 2 3 available. The crack propagation on an atomic scale is an unknown phenomena, which can not be studied by experiment, but which has been already studied by  Corresponding author. Tel.: 81-90-4119-1290; fax: 81-90- 7436-0253. Ž . E-mail address: wi-wunder@rocketmail.com W. Wunderlich . Ž a combined MD-FEM-Method Finite Element .   Method 10,11 . Computers are now capable of han- dling an increased number of atoms in a supercell. The output of the molecular dynamics calculations can be analyzed in different ways and it is the aim of this paper to evaluate the method of calculating the frac- ture toughness of ceramics from the output of the MD calculations. The Griffith criterion is based on the analysis of the energy release rate during the crack propagating as a function of the crack length. The improvement of fracture toughness is one of the important challenges for developing new structural cer- amic materials. Recently, functional gradient materials Ž . FGM have been introduced, which give the perspec- tive of making a smooth bonding between metal and ceramic materials. New composite materials consisting of an ultrafine distribution of alumina and zirconia   particles 12 promise better thermal-shock properties and higher fracture toughness than monolithic alumina   13 . The experimental search for suitable material 0261-306901$ - see front matter  2000 Published by Elsevier Science Ltd. Ž . PII: S 0 2 6 1 - 3 0 6 9 00 00044-3