Open source or free methods
Several methods are available to acquire and analyze iOS devices for free. Most of these tools have been built by practitioners in mobile forensics who recognize the need for affordable solutions that work to obtain the same amount of data as commercial kits. Jon Zdziarski has developed several scripts, tools, and methods to acquire data from iOS devices. Some of his methods such as physical acquisition scripts are restricted to law enforcement. Zdziarksi released his instructions to acquire data from iOS devices and this can be read at http://www.zdziarski.com/blog/wp-content/uploads/2013/05/iOS-Forensic-Investigative-Methods.pdf.
There are other tools that exist so you can logically acquire and analyze iOS device images and backup files. Some of these tools include iFunBox, iExplorer, iBackupBot, and more. Make sure that you test these tools before relying on them for a forensic investigation. Again, they are either free or request a donation for use. They are...