# HIPERCOAT Résumé de rapport

Project ID:
G5RD-CT-2001-00573

Financé au titre de:
FP5-GROWTH

Pays:
United Kingdom

## Models for TGO peg formation

In systems comprising a two-phase NiCrAlY bond coat, the TGO develops thickness heterogeneities often referred to as pegs, which contain oxides other than alumina, such as fluorite. Delamination occurs primarily along the interface between the TGO and the bond coat. The study addresses whether the pegs adversely affect failure by acting as local stress intensification sites at the interface. The stress state in the vicinity of a peg is obtained for two types of loading: thermal expansion mismatch and TGO growth. The stress evolution with increasing number of thermal cycles is obtained and the sensitivity of these stresses to the geometry of the peg is ascertained. A fracture mechanics analysis is performed to determine the conditions under which a crack might initiate and grow.

Constituent properties

A suitable behaviour for the peg must be incorporated. Since its growth involves the internal formation of fluorite, it is considered to expand volumetrically. This effect is captured in the model by imposing a relatively large volumetric strain. Observations of delaminations at the TGO/Bond coat interface in NiCoCrAlY systems indicate that they form at low temperature, usually during cooling. Consequently, the cracks develop within a residual stress field induced by prior thermal cycling. Moreover, the system is essentially elastic during cracking, subject to a relatively low crack opening displacement, with no attendant plasticity. Again, by using elastic concepts of fracture, the worst-case scenario is envisaged: since the presence of plasticity local to the crack would reduce the energy release rate.

Finite Element Model

The peg is regarded as an isolated, semi-ellipsoidal domain consisting of TGO. The underlying super-alloy substrate is taken to be sufficiently thick (1000 times the TGO thickness) to behave as a half-space. Since the bond coat shares the same elastic properties as the substrate and the plastic zone within the bond coat does not reach the bond coat/substrate interface, the precise value of bond coat thickness is unimportant.

The finite element analysis was performed using ABAQUS Standard. A cylindrical co-ordinate system is adopted for the axisymmetric model. In the first part of this study, the evolution of stress state is determined in the vicinity of the peg, absent cracking. The possibility of cracking is also addressed. The stresses are largest, and the interfacial toughness between bond coat and TGO is least at ambient temperature. Simplified finite element calculations are performed to assess the likelihood of cracking: it is envisaged that a putative penny-shaped crack is loaded by the residual stress state, and the energy release rate is calculated.

The thermal loading history is taken to be spatially uniform. Initially, the TBC system is taken to be stress-free at the peak temperature (1000C). The TGO is allowed to grow at this temperature by imposing stress-free strains in accordance with a user material subroutine. As remarked above, the peg is considered to expand volumetrically by imposing a relatively large growth strain of 0.025/cycle. Due to computational limitations, a maximum of 30 thermal steps is considered.

Crack formation

Cracks can form within the residual stress field, and extend along the interface outside the peg as well as through the TGO internal to the peg. In order to explore the likelihood of such cracking, it is imagined that a circular penny shaped crack, radius c, develops along the adjacent interface, with its centre coincident with the axis of the peg. The energy release rate J and mode-mix have been determined.

The crack is modelled by gap elements, with negligible initial opening. Since the system is elastic at ambient temperature, when the cracks form, the J-integral can be calculated by the nodal release method within the finite element code, ABAQUS. Typical results indicate that J has a characteristic variation with crack length, starting at zero, increasing to a peak, and then decreasingly rapidly with further increase in crack length, attributed to the change in the sign of the shear stress. Because of the normal compression, the crack is mode II throughout. The peak value of J increases linearly with increase in peg size, with magnitude strongly dependent on the level of friction. However, even for the largest pegs and the lowest friction, the J-values are less than the typical value of interfacial toughness, 20Jm-2. Consequently, the likelihood of cracks forming at pegs is minimal, unless the interface has been severely embrittled (for example, by the segregation of S).

It is concluded that the magnitude of energy release rate is too small to form a crack unless the peg is unrealistically large (requiring a radius greater than 30 microns). Thus, pegs may serve more of a protective role in fastening the TGO layer to the underlying bond coat rather than promoting interfacial separation.

Constituent properties

A suitable behaviour for the peg must be incorporated. Since its growth involves the internal formation of fluorite, it is considered to expand volumetrically. This effect is captured in the model by imposing a relatively large volumetric strain. Observations of delaminations at the TGO/Bond coat interface in NiCoCrAlY systems indicate that they form at low temperature, usually during cooling. Consequently, the cracks develop within a residual stress field induced by prior thermal cycling. Moreover, the system is essentially elastic during cracking, subject to a relatively low crack opening displacement, with no attendant plasticity. Again, by using elastic concepts of fracture, the worst-case scenario is envisaged: since the presence of plasticity local to the crack would reduce the energy release rate.

Finite Element Model

The peg is regarded as an isolated, semi-ellipsoidal domain consisting of TGO. The underlying super-alloy substrate is taken to be sufficiently thick (1000 times the TGO thickness) to behave as a half-space. Since the bond coat shares the same elastic properties as the substrate and the plastic zone within the bond coat does not reach the bond coat/substrate interface, the precise value of bond coat thickness is unimportant.

The finite element analysis was performed using ABAQUS Standard. A cylindrical co-ordinate system is adopted for the axisymmetric model. In the first part of this study, the evolution of stress state is determined in the vicinity of the peg, absent cracking. The possibility of cracking is also addressed. The stresses are largest, and the interfacial toughness between bond coat and TGO is least at ambient temperature. Simplified finite element calculations are performed to assess the likelihood of cracking: it is envisaged that a putative penny-shaped crack is loaded by the residual stress state, and the energy release rate is calculated.

The thermal loading history is taken to be spatially uniform. Initially, the TBC system is taken to be stress-free at the peak temperature (1000C). The TGO is allowed to grow at this temperature by imposing stress-free strains in accordance with a user material subroutine. As remarked above, the peg is considered to expand volumetrically by imposing a relatively large growth strain of 0.025/cycle. Due to computational limitations, a maximum of 30 thermal steps is considered.

Crack formation

Cracks can form within the residual stress field, and extend along the interface outside the peg as well as through the TGO internal to the peg. In order to explore the likelihood of such cracking, it is imagined that a circular penny shaped crack, radius c, develops along the adjacent interface, with its centre coincident with the axis of the peg. The energy release rate J and mode-mix have been determined.

The crack is modelled by gap elements, with negligible initial opening. Since the system is elastic at ambient temperature, when the cracks form, the J-integral can be calculated by the nodal release method within the finite element code, ABAQUS. Typical results indicate that J has a characteristic variation with crack length, starting at zero, increasing to a peak, and then decreasingly rapidly with further increase in crack length, attributed to the change in the sign of the shear stress. Because of the normal compression, the crack is mode II throughout. The peak value of J increases linearly with increase in peg size, with magnitude strongly dependent on the level of friction. However, even for the largest pegs and the lowest friction, the J-values are less than the typical value of interfacial toughness, 20Jm-2. Consequently, the likelihood of cracks forming at pegs is minimal, unless the interface has been severely embrittled (for example, by the segregation of S).

It is concluded that the magnitude of energy release rate is too small to form a crack unless the peg is unrealistically large (requiring a radius greater than 30 microns). Thus, pegs may serve more of a protective role in fastening the TGO layer to the underlying bond coat rather than promoting interfacial separation.