Homogenized model of environmental barrier coatings for evaluation of energy release rate

For efficient calculation of energy release rate (ERR) for interface cracks in environmental barrier coatings (EBCs) with a columnar layer, we propose a simple and versatile homogenization method of the columnar layer. The columnar layer consisting of a number of fine columns is modeled as an anisotropic homogenized layer whose elastic properties are isotropic in the plane perpendicular to the layer thickness direction. The homogenization was achieved by a finite element method (FEM) analysis for a single columnar model to obtain elastic parameters that characterize the homogenized layer. For validation of the homogenization method, we conduct an FEM analysis for a typical EBC structure and obtain the ERRs of an interface crack with various crack length and columnar size. We demonstrate that the homogenization method provides estimation of ERR with a good accuracy on the safer side, which is advantageous for EBC structure design. In addition, the method can reduce the calculation time by more than 50%. From these results, we conclude that the proposed homogenization method can be applied generally for estimation of ERR in EBCs with a columnar layer.