Hi, Julian.
There are a few reasons why a graphics card may crash and black screen when trying to play a set game title, and where it does not when playing another title.
Each game when it is run will use a set percentage of the Gpu in % utilization.
Some use more of the Gpu`s processing power than others.
The more the processing power of the gpu is used the more power the card will draw from the power supply unit in your system.
The GTX 970 cards have a good power consumption of a max of 180w drawn from the power supply unit.
It would help if you named the power supply unit by it`s brand name.
Half of the problem is finding out how good the power supply unit in the system is, as a lot of not well known or branded power supply's often do not really out put the wattage ratings that they state, or have a low amp value or rating for the 12v power rails found on the power supply.
Power supply's come in what we call tier rating, based on there ability to produce the stated wattage output on the unit, and the amount of amp rating they provide for the 12v power rails, the protection circuits built into them, and also how efficient they are at supplying the wattage and amp outputs.
It is one of the first things to suspect when running a graphics card fitted to a system, and to test by using another power supply if the current unit is also of some age as power supply units degrade over there up time or powered on state, and often loose the ability to output the correct voltages or amps of the unit.
The second thing that can cause some games to black screen, can be as simple as the current video driver used with the video card. The easy way to test this is if the driver is the latest version try an older version to see if it makes a difference. preventing black screen problems when running a game or your system freezing.
Make sure that your version of direct X is up to date also.
Visually check the graphics card for any dust build up, if it has been in the system for a few months, and clean it also.
Check the temperatures of the card, Gpu when the system is Idle and when running a game to see if it is running hot.
Air flow is essential, so if you have room for case fans in the system tower then fit some to help with air flow around the graphics card as it will keep it slightly cooler.
You can also try if you wish, to alter the clock settings of the gpu on the card.
Simply down clock the Gpu, and the memory of the graphics card by about 100Mhz each and see if it helps to stop the card from crashing or the system freezing when you run a game.
By lowering the Gpu and the memory frequency by 100Mhz you will only loose about 1 to 2 fps in games.
But it helps keep the card cooler slightly.
Plus in relation to the Gpu and the memory a reduction in the speed it works at reduces the amount of power required.
If you can borrow a power supply from a friend, for at least a hour or so to test with your system to see if it stabilizes
It and the graphics card it is a good idea before you go out and blindly by another power supply yourself to confirm if the problem is the power supply unit you currently use, and not something else in the system causing the problem.
Anyway there is just a few things to check other than the power supply.
And if your feeling brave it never hurts to take the cooling solution off the card and re apply some fresh thermal paste between the gpu chip, and the cooling of the card.
But only if the warranty is out on the card, would I do this as an option.