All materials are able to change shape at least a little bit without breaking. Steel might be willing to get about 0.1% longer before it starts to permanently change shape. Closer to 1% before it actually breaks. Some materials, like runner, can have *far* higher numbers here.
Now, to bend a bar, one side of the bar must become longer than the other. For a thin bar, this difference is much smaller, so for a really thin sheet like a tape measure the stretching is pretty small and the metal does not reach 0.1% stretch.
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