Characterisation of elastomers fracture behavior by energetic parameters A. Boulenouar, M. Mazari * Laboratory of Materials and Reactive Systems, Mechanical Engineering Department, University Djilali Liabes of Sidi-Bel-Abbes, BP. 89, Cité Larbi Ben Mhidi Sidi Bel Abbes 22000, Algeria article info Article history: Received 15 October 2007 Received in revised form 20 January 2008 Accepted 25 February 2008 Keywords: Elastomers Crack Hyper-elasticity Deformation energy density J integral Tearing energy abstract The knowledge of fracture behavior of elastomers necessitates the comprehension of crack initiation and propagation phenomena which pose difficulties related to the deformation of elastomers. The reliability of elastomer materials is linked to their resistance to rupture. This resistance can be evaluated using the global approach of fracture mechanics. The objective of this work is to numerically analyze by finite ele- ment method the characterization of rupture behavior of these materials on the basis of energetic param- eters. Consideration is given to the evolution of the deformation energy density to quantify the energy of tear of a real material identified by hyper-elastic material models. Ó 2008 Elsevier B.V. All rights reserved. 1. Introduction In general there exist two methods to study fracture of elasto- mers: the global approach and local approach. The first do not need the knowledge of stress and deformation distributions near singu- larities at the crack tip. It is based on the first principle of thermo- dynamics consisting of making an energetic analysis considering the complete structure. Rivlin and Thomas [1] consider the lost elastic energy in the specimen caused by the crack advance is the motor of propagation. They define the tearing energy by T T ¼ oW oA   l ð1Þ where W is the potential energy of global deformation; L is the suf- fix indicating that the derivation is made with constant displace- ment; T is the parameter equivalent to integral J introduced by Rice [2] given by J ¼ Z C W dy—T ou ox   ds ð2Þ with C is the contour of the crack tip; T is the stress vector defined by the normal vector n along T i = r ij n j , u is the displacement vector. In certain cases it is possible to calculate the tearing energy T and is expressed as T ¼ 2kWa ð3Þ k represents numerical factor. Many works have been done for analysis of the factor k. In the case of thin plate of elastomer material with a central crack of length 2a Sih and Liebowitz [3] had shown that k ¼ p ð4Þ In 1970, Lake [4] proposed analytical expression on the basis of lost energy necessary for the opening and closing of crack kðkÞ¼ p ffiffi k p ð5Þ where k is the principal elongation. Yeoh [5] established a relation between the central crack faces and the energy release rate T in an elastomer sheet by determining an analytical expression for k as k ¼ r y pb 4Wa ð6Þ where b is the crack opening. 2. Laws of hyper-elastic behavior The modelisation of the behavior of elastomers passes by the selection of a law which permits to quantitatively make the mechanical response of the material and its ability to support greater deformation reversible. For this two approaches based on the form of hyper-elastic energy density are proposed. The first approach concerns macromolecular material response static approach and the second gives mathematical forms capable to simulate tests. 0927-0256/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2008.02.029 * Corresponding author. E-mail address: mazari_m@yahoo.fr (M. Mazari). Computational Materials Science 43 (2008) 1042–1047 Contents lists available at ScienceDirect Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci