Bi material interface

Fig. 6.16. Crack paths al the bi-material interface (a) penetrating crack (b) singly deflected crack and (c) doubly deflected crack. After He and Hutchinson (1989).

Mathematically, the stress field surrounding a geometric comer, such as a crack tip, a re-entrant comer or the edge of a bi-material interface can be given as a series expansion of the form ... 

Zak, A. R. and Williams, M. L. (1963), Crack point singularities at a bi-material interface, Journal of Applied Mechanics 30, 142-143. 

We employ the finite element method and interface fracture mechanics concepts to parametrieally examine interfacial crack path selection in a unit brick-and-mortar structure. The analysis methodology, to be described below briefly, is based on the analyses of cracks kinking into and out of a bi-material interface as discussed by He and Hutchinson [5], He et al [6,7], and Suo and Hutchinson [8]. 

TBCs, which are typically comprised of yttiia stabilized zirconia (YSZ) and a bond coat, are deposited onto Ni-based superalloy substrates. The objective herein is to enable higher surface temperatures while protecting e superalloy substrate from the harsh thermo-physical environment. It has been reported previously by Evans et al [1] that thermal stress gradients within TBCs as a result of differential thermal expansion produce bending moments that foster interfacial delaminations, leading to the spallation of TBCs. While not being an exhaustive study, a preliminary effort is made herein to predict the crack driving force at the bi-material interface between the TBC and substrate. 

The fracture mechanics problem studied herein is motivated by the need to account for 3D stress states at the interfacial junction between TBCs and blades, for instance, in advanced gas turbine engine applications. For this purpose, the techniques developed in [2] and [3], which were essentially applied to 2D modeling spaces, are used here in a 3D Finite Element (FE) framework. As such, the objective is to use Finite Element Models (FEMs) to predict the interfacial crack driving force at the bi-material interface between the TBC and the substrate in model TBC systems. 

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