Non-kinking self-wrapping woven sleeve and method of construction thereof

1. A method of constructing a wrappable textile sleeve, comprising:

weaving an elongate wall from at least one lengthwise extending warp yarn extending along a longitudinal axis of the sleeve between opposite ends and a plurality of circumferentially extending weft yarns extending circumferentially between opposite overlapping edges; and

forming a plurality of discrete circumferentially extending annular bands extending between the opposite edges with the weft yarns during the weaving process with each of the bands being formed including a plurality of the weft yarns, with adjacent bands being formed with weft yarns having different diameters from one another, wherein the adjacent bands are formed including weft yarns having a diameter ratio of about 1:3.

2. The method of claim 1 further including forming the bands with the smaller diameter weft yarns having an increased axially extending width relative to the bands with the larger diameter weft yarns.

3. The method of claim 1 further including forming alternating bands spaced axially from one another by intervening bands, and forming the alternating bands having weft yarns with substantially the same diameter as one another and forming the intervening bands having weft yarns of a different diameter from the alternating bands.

4. The method of claim 3 further including forming the alternating bands entirely from weft yarns having a larger diameter relative to the weft yarns forming the intervening bands.

5. The method of claim 1 further including weaving the wall having a plain weave.

6. The method of claim 1 further including bonding an outer layer to an outer surface of the wall.

7. The method of claim 1 further including heat-setting at least some of the weft yarns to bias the opposite edges into overlapping relation with one another.

8. The method of claim 6 further including providing the outer layer as a layer of foil.