Patterned reduction of surface area for abradability

1. A gas turbine component comprising:

a substrate;

a layer of ceramic material disposed over the substrate;

a repeating pattern of unconnected cross-shaped depressions formed in the layer of ceramic material defining a continuous labyrinth of walls of the ceramic material and defining a wear surface, the walls comprising a uniform thickness at the wear surface separating adjacent depressions;

wherein a representative measurement boundary defines a border of one half of the uniform wall thickness around one of the cross-shaped depressions;

wherein within the representative measurement boundary along the wear surface, a ratio of a total length of a perimeter of said one depression divided by an area of the measurement boundary is at least 0.9 per unit of measurement; and

wherein within the measurement boundary the area of said one depression at the wear surface divided by the area of the measurement boundary is between 0.4 and 0.6.

2. The gas turbine component of claim 1 , further comprising the ratio of the perimeter length of said one depression divided by the area of the measurement boundary being at least 1.0 per unit of measurement.

3. The gas turbine component of claim 1 , further comprising:

the ceramic material of the walls comprising a plurality of hollow ceramic spheres disposed in a ceramic matrix; and

the uniform wall thickness is between 0.5 and 1.5 times a diameter of a largest of the spheres.

4. The gas turbine component of claim 1 , wherein the representative measurement boundary is a boundary within which an area of the wear surface is representative of an amount of surface area removed from the wear surface by the cross-shaped depressions versus an amount of surface area remaining in the wear surface.

5. A gas turbine component comprising:

a ceramic material defining a surface;

a repeating pattern of nested cross-shaped depressions in the surface, the depressions arranged in rows and columns defining a continuous labyrinth of walls, the walls extending in two orthogonal directions between adjacent ones of the depressions, the walls comprising a uniform thickness at the surface separating adjacent depressions and making the depressions discontinuous from each other;

the ceramic material of the walls comprising hollow ceramic spheres in a ceramic matrix, the thickness of the walls comprising 0.5-1.5 times a diameter of a largest of the hollow ceramic spheres;

wherein the depressions each comprise a cross-shaped geometry with a gap width that is equal to the wall thickness;

wherein a representative measurement boundary defines a border of one half of the uniform wall thickness around one of the cross-shaped depressions;

wherein within the representative measurement boundary the area of said one depression at the surface divided by a total area within the measurement boundary is between 0.4 and 0.6; and

wherein P/A defined as a perimeter length of said one depression at the surface divided by the total area of the measurement boundary is greater than 0.9 per unit of measurement.

6. The gas turbine component of claim 5 wherein the P/A is at least 1.0 per unit of measurement.

7. The gas turbine component of claim 5 , wherein the repeating pattern of depressions comprises first and second cross-shaped depressions separated laterally by less than a width of the first cross-shaped depression and vertically by less than a height of the first cross-shaped depression.

8. The gas turbine component of claim 5 , wherein the repeating pattern of the cross-shaped depressions comprises a plurality of rows and columns of the cross-shaped depressions, each row of cross-shaped depressions offset laterally from each adjacent row by approximately 40% of a distance of separation between the cross-shaped depressions in a given row, each column of cross-shaped depressions offset vertically from each adjacent column by 40% of a distance of separation between the cross-shaped depressions in a given column.

9. The gas turbine component of claim 8 , wherein the distance of separation between the cross-shaped depressions in the given row is equal to the distance of separation between the cross-shaped depressions in the given column.

10. A gas turbine component comprising:

a ceramic material defining a surface;

a repeating pattern of unconnected nested cross-shaped depressions in the surface, the repeating pattern of cross-shaped depressions comprising a first row of unconnected cross-shaped depressions, a second row of unconnected cross-shaped depressions, the second row offset diagonally from the first row, and a third row of unconnected cross-shaped depressions, the third row offset diagonally from the first and second rows; and

a continuous labyrinth of walls separating and defining the cross-shaped depressions;

wherein a representative measurement boundary defines a border of one half of a wall thickness around one of the cross-shaped depressions; and

wherein P/A defined as a perimeter length of said one depression at the surface divided by a total area of the measurement boundary is greater than 0.9 per unit of measurement.

11. The gas turbine component of claim 10 , further comprising:

the ceramic material comprising a plurality of hollow ceramic spheres disposed in a ceramic matrix;

walls defined between adjacent depressions comprising the wall thickness of between 0.5 and 1.5 times a diameter of a largest of the spheres.

12. The gas turbine component of claim 10 , wherein the representative measurement boundary is a boundary within which an area of the surface is representative of an amount of surface area removed from the surface by the cross-shaped depressions versus an amount of surface area remaining in the surface.