My iPhone turns itself off when it has lots of battery charge left, sometimes 70% then I cant turn it on at all unless I plug it in to a charger....then the apple logo appears and it turns on as normal with lots of charge?
It appears your battery is faulty.
If you have an iPhone 5, check the iPhone 5 Battery Replacement Program to get a free replacement.
If your phone is under warranty or AppleCare extended warranty, go to the Apple Support webpage, "Start a service request" and fill in your problem details so Apple can help you.
If you have a Mac, you can find information about your battery by plugging into your computer and installing the free CoconutBattery app to check its health.