I quickly modelled a cymbal (upper half of sphere scaled along the Z axis, with an additional translation for the dome), and applied a bronze material from BlenderKit:
I then replaced the Roughness map the material shipped with, with the image you provided:
Is this the kind of thing you're after?
Not sure if you know this already, but for completeness' sake: the Roughness texture is responsible for the amount of reflectivity of your material. Scratches and other surface imperfections (like corrosion) will roughen up a surface, and diffuse the light it reflects.
The image you posted is of course not really suitable for this function, as it contains a watermark, has specular reflections (seen in the image above as the brightest and darkest spots), lumps all types of roughness into the same image (for more realism you might want to treat different kinds of imperfection differently), is a picture of a 3-dimensional object, resulting in a warped projection, &c.
For better roughness maps you can search online for "scratch maps" or "surface imperfections maps". To start with, here is a free pack, and you can find a few free ones here and here.
Additionally, since you mention your computer struggling with this model, you could bake the (what I assume are sculpted) curves into a normal map, which can in turn be applied to a simpler mesh with fewer polygons.
This process involves quite a few steps, and goes beyond your main question here, so please see this excellent Blender Guru tutorial to learn how to do that.