Dogs can easily rip your arm apart. My dad hit and killed a puppy (by accident) with a truck when she bolted under it (they didn't want to train her early on and she liked hiding under vehicles), and when he rushed to help her, she bit him. It was a desperation thing as she was dying, and he had serious stitches.

Do not let a full grown dog bite your arm.

I don't know if this is right, but my instinct would be to pivot and knock the dog down onto its side, pinning its head and neck. If it does bit me, I now have control of the head and have a size and position advantage. I can attempt to work out of the dog's jaw grip. At the very least, it won't be able to wrench and tug at my arm.