I live in the countryside and I keep my 3 dogs in a fairly large fenced area. I let them out to play regularly, but they've started chewing holes through the chainlink fence to get out. It's insulated with plastic but I'm afraid they might get hurt because the chewing cut through the metal and left it exposed. For now I closed the holes with some rope, and I'm letting them out more frequently, which seems to have solved the problem. But I'm afraid they might do it again and seriously injure themselves, plus having a functional enclosing would be nice. We don't really have time for training them not to chew the fence, so I'm thinking that a new fence might be the best solution. Do you have any recommendations, for a dog-proof fence (the cheapest the better, preferably still chained links) or any other idea?
A chainlink fence is one of the better styles of fencing for dogs. You hit the answer on the head when you said since you've been letting them out more often they've stopped it.
The dogs need stimulation. In this case it sounds like they're motivated by boredom and are destructive to try and find more interest in theirs lives, i.e. roam outside of the fenced area. Some breeds require more activity than others and this needs to be taken into consideration.
The other thing you can do is add some toys into the yard and bones - if they won't brawl over them.
As for the fencing, I wouldn't recommend timber. Determined dogs can claw and chew their way through timber, including wooden doors.
Perhaps consider the type of fencing that is used for pools, where there's metal posts spaced closely enough to prevent the dogs from escaping. Then there's always the issue of dogs digging to get under the fence. The only way this can be prevented is by using either concrete, rocks or digging tin down into the ground to prevent the digging. Concrete around the base of the fence is probably the most reliable and safest. digging tin down into the earth may cause injury.
However, the safest option is to keep them occupied and stimulated, this is the optimal way to avoid injury.