Adding texture in Adobe Photoshop is easy, because there we are dealing with pixels. When working with vectors we need to think about anchor points. So all the that grungy looking textures also have to be in vector format. And while there are so many different ways to do the same I will share one technique which you can apply any time and without any stock images or other assets. All you need is Adobe Illustrator.
1. So first thing you need to do is creating a shape you want to apply your grunge texture on. Important part is to expand all elements into closed paths (shapes). If you used a path without a fill but only stroke to create a shape. Select that part of your artwork and go to Object -> Path -> Outline Stroke or if you go Object -> Expand it will do the same.
2. Convert it into a single shape. Go Object -> Compound Path -> Make
3. Creating shapes for texturing. And for this we can use Paintbrush. To reveal more brushes click on a Brush Library icon at the bottom left corner in a Brush panel.
The one I decided to go with were Artistic -> Artistic_ChalkCharcoalPencil library.
Another panel will pop up.
4. Change the stroke colour so it is different from the shape you want to put this texture on. I’ve picked yellow.
5. Add as many brush stroke as you want for the texturing. Notice, that changing the size of the stroke will impact the texture.
So finally I’ve got the result I wanted. But it is not done yet.
To cut the holes based on the shape of these brush stroke we need to convert them into shapes.
6. Select all the brush strokes and go Object -> Path -> Outline Stroke
This is how it should look after expanding.
7. Maybe t his step is not required, but just for making it simple go and combine the selected objects into one by going Object -> Compound Path -> Make
8. Now when we are dealing with only two shape. Make sure that the texture is the top object. Then select both objects and open Pathfinder panel by going to Window -> Pathfinder.
9. In a Pathfinder panel choose Minus Front.
10. And finally. Here we are. The object now is with the texture.
This is a destructive effect. I means that if you would like to remove it later it would be impossible.
If you want to do this effect non-destructively consider applying transparency mask.