Foldable substrates and methods of making

A foldable substrate comprising:

• a substrate thickness in a range from about 60 micrometers to about 2 millimeters defined between a first major surface and a second major surface opposite the first major surface;
• a first portion comprising the substrate thickness, a first compressive stress region extending from a first surface area of the first major surface, and a second compressive stress region extending from a second surface area of the second major surface;
• a second portion comprising the substrate thickness, a third compressive stress region extending from a third surface area of the first major surface, and a fourth compressive stress region extending from a fourth surface area of the second major surface;
• and
• a central portion positioned between the first portion and the second portion, the central portion comprising:
• a central thickness less than the substrate thickness and in a range from about 25 micrometers to about 80 micrometers defined between a first central surface area and a second central surface area opposite the first central surface area, a first central compressive stress region extending from the first central surface area, a second central compressive stress region extending from the second central surface area, and a central total thickness variation (TTV) of the central portion over the first central surface area is less than or equal to 10 micrometers;
• a first transition region comprising a first transition surface area extending between the first surface area and the first central surface area, a second transition surface area extending between the second surface area and the second central surface area, a first transition compressive stress region extending from the first transition surface area, and a second transition compressive stress region extending from the second transition surface area;
• and
• a second transition region comprising a third transition surface area extending between the third surface area and the first central surface area, a fourth transition surface area extending between the fourth surface area and the second central surface area, a third transition compressive stress region extending from the third transition surface area, and a fourth transition compressive stress region extending from the fourth transition surface area,
• wherein the first central surface area is recessed from the first major surface by a first distance, a thickness of the first transition region smoothly and monotonically decreases between the substrate thickness of the first portion and the central thickness of the central portion, a thickness of the second transition region smoothly and monotonically decreases between the substrate thickness of the second portion and the central thickness of the central portion, and a first transition width of the first transition region is less than or equal to 2.2 millimeters minus a product of the central TTV in micrometers and 0.2 millimeters per micrometer.