Issue 35

K. Slámečka et alii, Frattura ed Integrità Strutturale, 35 (2016) 322-329; DOI: 10.3221/IGF-ESIS.35.37 325 tetrahedrons) to simulate complex sample geometries, with computational efficiency. In order to model quasi-brittle fracture in materials with a complex microstructure, we insert variations in its discretization and the relationship between the CA and FE layers through the introduction of a Meshfree framework as further layer between them. The versatility of the Meshfree framework allows us to connect variable domains with different geometries and numbers of nodes. Each layer defines a different size scale and is solved with a different method. For the large size scale macromechanical layer a standard, relatively coarse, finite element model is used. In the small size scale layer we use a cellular automata method, where the different cells represent the properties of the quasi-brittle material. A Microstructural Adaptive Meshfree (MAM) framework has been developed to solve the displacements of the microstructural features in the intermediate layer. The Meshfree model uses the microstructural features as its discretization, dividing the microstructure into Particle Domains (PD) that represent each particle with a single domain, and Inter Particle Domains (IPD) that link the particles and represent the matrix, Fig. 3. From the large scale downwards to the small scale the information is shared between layers by the displacements, which provide the boundary conditions. From the small scale upwards to the larger scale the information is shared by the energy homogenization of the damage in the material to link the effects of the eroded (i.e. damaged) cells of the CA with the FE behavior [13]. Figure 3 : Detail of the different layers of the FEMME model (i.e.: FE mesh, IPD, pores and eroded cells), and the local initiation of the damage. The aim is to evaluate the influence of the fully developed TGO layer geometry on the development of damage in the TBC system deposited on a tube with an internal radius of 3.5 mm, outer radius of 5.53 mm and length of 5 mm. The modeled system consists of a nickel base superalloy single crystal CMSX-4 substrate, MCrAlY bond coat and YSZ top coat with temperature dependent material properties obtained from reference [14]. The effect of a quasi-static increase in the external temperature, with constant internal temperature (20°C), was simulated. The thicknesses are 1.5 mm for the metallic substrate, 150  m for the BC, 8  m for the TGO and 300  m for the top coat. The TGO interface geometry is defined using a three-dimensional sine wave with amplitude ( A ) and wavelength (  ) with A /  of 0.32: i.e.  = 314  m and A = 100  m. These parameters permit a good quality FE mesh with reasonable computational cost, although due to this current limitation, the model represents, as in the FE calculations, only the waviness surface component. The ratio A /  , rather than the amplitude A itself, is expected to be the dominant factor affecting the magnitude of stresses developed due to anisotropic volume changes related to the TGO growth at high temperatures and also the stresses developed due to different coefficients of thermal expansion upon cooling; in both cases the stresses have been reported to increase with increasing interfacial roughness. R ESULTS AND DISCUSSION Evolution of stresses in TBC due to irregular YSZ/BC interface he YSZ/BC interface represents the critical location where damage ultimately always occurs because of the presence of growing TGO layer. As evidenced by internal cracks within the TGO that follow the traces of earlier interfacial separations, the ceramic/metallic interface between the TGO and the bond coat is more susceptible to cracking [15]. The magnitudes of normal stresses at this interface increases with increasing thickness of the TGO layer, T