I tried different methods and they all were very very complicated.
Is there an easy way to create this effect where the grunge is more visible on the inside?
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Use a technique similar to this first for the texture part:
You'll probably need to have the grunge texture in white intead of black as on the tutorial above.
Then put the grunge textures into a layer group and add a layer mask to this group.
Then use the brush tool and change the hardness on your bush to be smooth (eg. low hardness like 0%). Choose a brush size that is about 1/3 of the thickness of the letters. You can also play with the opacity of the brush and use something like 30%-70% opacity depending on how quick you want to delete the edges. A lower opacity will give you more control because you adjust more precisely the contrast, and a higher opacity will go faster because you won't need to trace the edges more than once.
Then simply mask some of the edges of your text on that group layer mask with the brush manually... for each letter. You might need to make a few tests to find the right size of brush and opacity, but that's one way to do it even if it's a very manual way.
If you want to add even more grainy effect, you can also use a brush that's different from the standard one. Like the ones with noise. Or your can play with the adjustment/threshold on that layer mask when you're done.
I unfortunately don't know any filter that does this effect automatically but they probably exist.