Bigger is better, right? So here you have some large carbon fiber.
Source Factorio.us Collective
A slightly more textured pattern, medium gray. A bit like a potato sack?
Source Bilal Ketab
Alternative colour scheme. Not a pattern for fabrics, but one produced from a jpg of a stack of fabric items that was posted on Pixabay. The tile that this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Made by distorting a simple pattern using the 'sin waves' plugin for Paint.net and vectorising in Vector Magic
Source Firkin
Colour version that is close to the original drawing uploaded to Pixabay by pencilparker.
Source Firkin
Design drawn in Paint.net, vectorised using Vector Magic and finished in Inkscape.
Source Firkin
One more sharp little tile for you. Subtle circles this time.
Source Blunia
That’s what it is, a dark dot. Or sort of carbon looking.
Source Tsvetelin Nikolov
Just like your old suit, all striped and smooth.
Source Alex Berkowitz
Remixed from a drawing in 'The March of Loyalty', Letitia MacClintock, 1884.
Source Firkin
A seamless light gray paper texture with horizontal double lines.
Source V. Hartikainen
From a drawing in 'Les Chroniqueurs de l'Histoire de France depuis les origines jusqu'au XVIe siècle', Henriette Witt, 1884.
Source Firkin
Seamless , tileable CC-0 texture. Created by my own, feel free to use wherever you want!
Source Linolafett
Nicely executed tiling for an interesting pattern.
Source Ignasi Àvila Padró
A lovely light gray pattern with stripes and a dash of noise.
Source V. Hartikainen