Turbine blade track with ceramic matrix composite segments having attachment flange draft angles

A turbine shroud assembly for use with a gas turbine engine, the turbine shroud assembly comprising:

• a carrier segment arranged circumferentially at least partway around a central axis of the gas turbine engine,
• a blade track segment made of ceramic matrix composite materials and supported by the carrier segment, the blade track segment including a shroud wall that extends circumferentially partway around the central axis, a first attachment flange that extends radially outward away from the shroud wall into the carrier segment, and a second attachment flange spaced apart axially from the first attachment flange that extends radially outward away from the shroud wall into the carrier segment, and
• a retainer that extends axially into the carrier segment and through the first attachment flange and the second attachment flange of the blade track segment, and
• wherein the first attachment flange of the blade track segment includes a first axially aft-facing surface that faces the second attachment flange and extends radially outward and axially forward away from the shroud wall at a first angle relative to a first radial plane that is orthogonal to the central axis of the gas turbine engine, the second attachment flange of the blade track segment includes a first axially forward-facing surface that faces the first attachment flange and extends radially outward and axially aft away from the shroud wall at a second angle relative to a second radial plane parallel to the first radial plane, and
• wherein the second attachment flange of the blade track segment includes a second axially aft-facing surface opposite the first axially forward-facing surface that extends away from the shroud wall at a third angle relative to a third radial plane that is parallel to the first and second radial planes and the third angle is different from the first angle and the second angle.

A shroud segment made of ceramic matrix composite materials for use with a gas turbine engine, the shroud segment comprising:

• a shroud wall that extends circumferentially partway around a central axis of the gas turbine engine,
• a first attachment flange that extends radially outward away from the shroud wall, and
• a second attachment flange spaced apart axially from the first attachment flange that extends radially outward away from the shroud wall,
• wherein the first attachment flange of the blade track segment includes a first axially aft-facing surface that faces the second attachment flange and extends radially outward and axially forward away from the shroud wall at a first angle relative to a first radial plane that extends radially and circumferentially relative to the central axis of the gas turbine engine, the second attachment flange of the blade track segment includes a first axially forward-facing surface that faces the first attachment flange and extends radially outward and axially aft away from the shroud wall at a second angle relative to a second radial plane parallel to the first radial plane,
• wherein one of the first attachment flange and the second attachment flange of the blade track segment includes a second axially facing surface opposite one of the first axially aft-facing surface of the first attachment flange and the first axially forward-facing surface of the second attachment flange that extends radially outward and axially away from the shroud wall at a third angle relative to a third radial plane that is parallel to the first and second radial planes and the third angle is different from the first angle and the second angle.