One more updated pattern. Not really carbon fiber, but it’s the most popular pattern, so I’ll give you an extra choice.
Source Atle Mo
Prismatic Groovy Concentric Background 5 No Black
Source GDJ
An interesting dark spotted pattern at an angle.
Source Hendrik Lammers
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
Light gray paper pattern with small traces of fiber and some dust.
Source Atle Mo
From a drawing in 'In an Enchanted Island', William Mallock, 1892.
Source Firkin
Sharp pixel pattern looking like some sort of fabric.
Source Dmitry
Prismatic Curved Diamond Pattern 8 No Background
Source GDJ
A large (588x375px) sand-colored pattern for your ever-growing collection. Shrink at will.
Source Alex Tapein
No, not the band but the pattern. Simple squares in gray tones, of course.
Source Atle Mo
A huge one at 800x600px. Made from a photo I took going home after work.
Source Atle Mo
To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i
Source Firkin
A large pattern with funky shapes and form. An original. Sort of origami-ish.
Source Luuk van Baars
Same classic 45-degree pattern, dark version.
Source Luke McDonald
Remixed from a drawing in 'Chambéry à la fin du XIVe siècle', Timoleon Chapperon, 1863.
Source Firkin
The first pattern on here using opacity. Try it on a site with a colored background, or even using mixed colors.
Source Nathan Spady
Zero CC tileable wood texture, made by me procedurally in Neo Texture Edit.
Source Sojan Janso
Just what the name says, paper fibers. Always good to have.
Source Heliodor jalba