Cohesive zone model for intergranular slow crack growth in ceramics: influence of the process and the microstructure

Abstract

Ceramic polycrystals are prone to slow crack growth (SCG) which is stress and environmentally assisted, similarly to observations reported for silica glasses. The kinetics of fracture are known to be dependent on the load level, the temperature and the relative humidity. In addition, evidence is available on the influence of the microstructure on the SCG rate with an increase in the crack velocity with decreasing the grain size. Crack propagation takes place beyond a load threshold, which is grain size dependent. We present a cohesive zone model for the intergranular failure process. The methodology accounts for an intrinsic opening that governs the length of the cohesive zone and allows the investigation of grain size effects. A rate and temperature-dependent cohesive model is proposed (Romero de la Osa M, Estevez R et al 2009 J. Mech. Adv. Mater. Struct. 16 623–31) to mimic the reaction–rupture mechanism. The formulation is inspired by Michalske and Freiman's picture (Michalske and Freiman 1983 J. Am. Ceram. Soc. 66 284–8) together with a recent study by Zhu et al (2005 J. Mech. Phys. Solids 53 1597–623) of the reaction–rupture mechanism. The present investigation extends a previous work (Romero de la Osa et al 2009 Int. J. Fracture 158 157–67) in which the problem is formulated. Here, we explore the influence of the microstructure in terms of grain size, their elastic properties and residual thermal stresses originating from the cooling from the sintering temperature down to ambient conditions. Their influence on SCG for static loadings is reported and the predictions compared with experimental trends. We show that the initial stress state is responsible for the grain size dependence reported experimentally for SCG. Furthermore, the account for the initial stresses enables the prediction of a load threshold below which no crack growth is observed: a crack arrest takes place when the crack path meets a region in compression.

Modeling and numerical investigation of slow crack growth and crack arrest in ceramic polycrystals

“…A thermally activated formulation is adopted for the cohesive model which is presented by Romero de la Osa et al. 4,5 It is shown that the formulation can capture the regime I and the load threshold that originates in the a) Corresponding author. lgV K I K I 0 I 0 T, r II III H O 2 Fig.…”

“…The mechanism underlying SCG is described with a cohesive model that represents the reaction-rupture mechanism. A thermally activated formulation is adopted for the cohesive model which is presented by Romero de la Osa et al 4,5 It is shown that the formulation can capture the regime I and the load threshold that originates in the presence of initial stress related to the processing. In this section, a cohesive zone model (CZM) for the reaction-rupture mechanism underlying SCG in single and polycrystal ceramics is presented based on the description of SCG by Michalske and Freiman.…”

“…These observations are formulated with a cohesive zone methodology. 4,5 A thermally activated cohesive model is proposed where the opening rate describing the damage kinetics is taken aṡ…”

“…8 The parameters β and∆ 0 remain to be identified: β controls the slope of V -K I curve and∆ 0 controls its position in the V -K I graph. 4,5 These parameters are adjusted to obtain the best fit to the experimental data. 3 Their values are reported in Table 1.…”

“…A calibration of the cohesive zone parameters is presented for zironica single crystal based on the cohesive zone description proposed by Romero de la Osa et al, 4,5 in the reaction-rupture mechanism for SCG in ceramics. It is shown that the cohesive model can capture realistically experimental data of SCG in a single crystal.…”