PC Shuts Off When Gaming, I Think Its My PSU

[FlaminSkull000]

When I play video games my PC will randomly shut down right in the middle of what I am doing. I will be playing with my friends and randomly my screen will go black, all audio stops, and all my PC's LEDs turn off. I haven't tried to purposely recreate the issue, because the first time it started to happen 3-4 hours into the game and since then the time keeps going down. The last time it happened I wasn't 45 minutes into playing. I have only had it happen in one game, Tom Clancy's Rainbow Six Siege, and haven't had it happen in any other games I've played that are less intensive (HOI4 and Rimworld). After the issue happened 2-3 times I ordered 3 new fans and installed them all and it didn't help at all and it seems like it made it happen quicker. .

Specs:
Case: iBUYPOWER ARC 647
GPU: GeForce GTX 1070
CPU: AMD FX-8320 (Yes, I know it severly bottlenecking my GPU. I am getting a Intel i8700k as soon as I graduate.)
Motherboard: MSI 760GMA-P34
PSU: Allied AL-D500EXP
RAM: 8GB Kingston 99U5471-052.A00LF & 8GB A-Data Technology AB4400000
And a 1TB HDD

I think I have nailed it down to my PSU, but I need to make sure before i spend $75-100 on a new one. Any help is appreciated.

Edit: My PC doesn't reboot as I have it disabled in the BIOS.

 

[Martell1977]

The unit is overloaded, it's a horrible PSU and can't handle the parts.
http://www.jonnyguru.com/modules.php?name=NDReviews&op=Story4&reid=65
I'd say replace ASAP.

Here is a list for reference, the tiers are self explanatory. Your PSU is probably 5th tier.
http://www.tomshardware.com/forum/id-2547993/psu-tier-list.html

I'm partial to EVGA and Seasonic PSU's.

 

[dudio]

The symptoms you have are most likely due to high temperatures or the PSU.
Your Power Supply is questionable for sure ( REVIEW HERE ) and you should replace it regardless, but also rule out your temps. Grab HWInfo (it's free) and see what you're getting. Adding fans doesn't mean you've ruled that out.

 

[FlaminSkull000]

So, I picked up an EVGA Supernova 750 G2 and it seemed to help the first few days I had it, but today it happened again. I think the PSU had a hand in it because it is running way better, but I think another issue is that my case is not make with a GTX 1070 in kind and cannot keep up with the heat it outputs at high levels.

 

[Martell1977]

Seems like a standard Mid-tower case, do you have exhaust fans?