I saw an experiment where the scientists were measuring how strong the bones of children were during healing a fracture. They used a special device to measure the stiffness of the bone. How do they do this without re-breaking the bone?

Testing bone strength and stiffness outside of a laboratory can be a challenging task. Just as you are suggesting, to find out how much tension or force the bone can really handle requires applying enough pressure to actually break the bone. That breaking point is the maximum tensile strength of that bone.

When measuring bone stiffness, other factors come into the picture. The surrounding ligaments, muscles, and other soft tissues support the bone, too. The strength and interaction of these must be considered.

So it’s not really ethical to test a bone to and beyond the point of failure. But it is possible to test bone strength and progress in healing by calculating its stiffness. Enough force is applied to deform the bone within its elastic range.

A special device called Orthometer can be used. It is a commercially available goniometer-based system designed to measure the stiffness of healing fractures. A goniometer is a tool used to measure joint (and bone) angles.

This device is used under general anesthesia. It uses a three-point bending test and a microcomputer to calculate pressure applied to the bone. Bending angle and force can both be measured safely and accurately.