Cohesive zone model and slow crack growth in ceramic polycrystals

Abstract

Ceramics polycrystals are subjected to slow crack growth (SCG) and also environmentally assisted failure, similarly to what is observed for glasses. The kinetics of fracture are known to be dependent on the load level, the temperature and also on the Relative Humidity (RH). However, evidences are available on the influence of the microstructure on the SCG rate with a marked increase in the resistance to the crack advance when comparing the response of a single crystal to that of a polycrystal. The clarification of the origin of the latter observation motivates the development of a local approach of fracture. We propose a physically based cohesive zone description that mimics the reaction-rupture process underlying SCG. We present how the parameters involved in the cohesive zone formulation can be determined to capture SCG in a single crystal. We then present simulations of intergranular failure in a 2D plane strain polycrystal. The triple junctions are shown to be key in the resistance to crack growth. The presence of defects at these junctions and their influence on the crack propagation is then investigated. We also show that the description is able to capture the damage induced by the process cooling, thus providing insight of the appropriate temperature for the sintering, for instance. The present numerical tool is then thought valuable to perform virtual tests on ceramics fracture in order to estimate thermal as well as mechanical loads limits for a safe use as well as proper the process conditions.

New modelling approaches to predict wood properties from its cellular structure: image-based representation and meshless methods

“…The growth of cracks in heterogeneous materials is of crucial interest in many fundamental and industrial domains, and has been extensively studied using various numerical approaches, such as the finite element method (Zavattieri et al 2001;De la Osa et al 2009;Sancho et al 2007;Ruiz et al 2000;Itakura et al 2005), deformable lattice methods (Kitsunezaki 2013) and lattice element methods (Topin et al 2007;Affes et al 2012), to cite a few. Recently, the peridynamic approach emerged as an alternative method, based on integral equations, rather than partial differential equations (Silling 2000).…”

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

“…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…”

“…A quasi-static finite analysis is considered using a total Lagrangian description. For this problem, the incremental expression of virtual work is 4…”

“…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.…”