Not claiming it's used (see NOTE1), but the result resembles how BW photos in the past came out from photographic printing. Here's described one old process for hobbyists http://www.alternativephotography.com/an-introduction-to-the-gum-bichromate-process/ One makes his own photosensitive paper which will take ink differently depending on how strongly it's exposed. The reproduction of the grayscale is highly non-linear and grainy. This is a snippet from the linked article:
Many xerographic copiers were possible to adjust to make same looking prints of photos, too. The grain works like a randomized halftone raster which makes the apparent greyscale reproduction better than it actually is.
We can simulate the the result in Photoshop by starting from a good contrast BW photo. I have my example in RGB mode because the inverted curves in Greyscale mode can look counter-intuitive.
So, I have a good contrast photo, but I make it flatter with a curves layer:
(The photo is a snippet from a web site which tells of actor Vivien Leigh)
The curve lightens black and darkens white.
The next step is to make a copy of the original to the top layer. It gets a slight gaussian blur to reduce finest details. Then it gets noise. Finally it's tresholded to BW:
The noise is Photoshop's Add noise. I guess a high contrast copy of scanned paper would be better, but I haven't one.
We can combine the tresholded version with blending mode hard light and reduced opacity. These give grainy gradients and partially restore the contrast:
This is nearly ready, but there's a fake beard which needs shaving. In addition you wanted somehow metallic effect. It can be achieved by going back to the curves layer or preferably by adding a new one which reduces midtone contrast or even causes a sight partial tone inversion. The grain prevents the image getting too flat.
The noise layer is erased near the mouth to shave off the fake beard.
The partial tone inversion was said also in the older answer. There it was called solarization.
NOTE1: In the era before computers and Photoshop another common way to get same looking graininess and distorted grayscale was an attempt to make image compositions by inserting on a photo carefully clipped snippets of other photos and shooting a new photo of the composition. There was available special duplicating films for the purpose. Using ordinary film for the final shot created hopelessly
too low contrast results.
Editing manually the composition to be ready for the final shot must have been extemely difficult. Making precise enough clips, matching lights and shadows and painting off all disturbing discontinuities is still a must with computer software, but in the past there wasn't available such things as undo, curves, clone brush etc...