13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- Figure 1. Slow crack growth in ceramics (Zirconia) velocity V versus the stress intensity factor KI. The regime I shows a marked dependence with the relative humidity and temperature (data from [2]). The mechanism underlying failure is described with a cohesive model that represents the reaction rupture process for SCG. Thus, a thermally activated formulation is adopted for the cohesive model (see Romero de la Oso et al. [2]). The formulation is shown in Romero de la Osa et al. [2-4] able to capture the regime I, the load threshold being related to the presence of initial stress (Romero de la Osa et al. [4]). We also investigate the influence of residual thermal stresses originating from the sintering process on the kinetics of SCG and on K0. The influence of the water concentration on the kinetics of SCG and on the minimum threshold K0 is also investigated. 2. Cohesive zone model for the reaction-rupture mechanism in ceramic In this section, we present a cohesive zone model for the reaction-rupture mechanism underlying SCG in single and polycrystals ceramics. Michalske and Freiman [5] proposed an atomistic description accepted in the ceramic communities as a responsible for the process of SCG. They considered a bond of scilica in tension in presence of molecule of water that assists the breakdown of the bond to create two molecules of silanol. This model is reconsidered recently by Zhu et al. [6] by performing atomistic calculations. They observed that the reaction rupture is energetically favorable once a stress threshold is reached locally, with an activation energy that decrease with the applied stress. These observations are formulated with a cohesive zone methodology as Romero de la Osa et al. [3-4]. A thermally activated cohesive model is proposed where the damage opening rate for the description of the damage kinetics as 0 c n exp k T U B n 0 , (1) where c n is the opening rate between two surfaces in which damage occurs, U0 is an activation energy, has the dimension of a volume and n is the traction normal to the cohesive surface. The pre-exponential term 0 has the dimension of a velocity; kB is the Boltzmann gas constant and T the absolute temperature. Damage is triggered when n n 0, n 0 being a local load threshold. When the cumulated opening reaches a critical thickness n cr, a crack is nucleated locally. The critical thickness n cr is a material parameter, which is assumed to be about 1nm in crystalline material. According to Zhu et al. [6], the threshold stress n 0 for the process to be energetically favorable ranging from 0 to 25% of the
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