Here is an explanation, but the cranks is still the strongest moving part of an engine. I would build up the rods/pistons/valvetrain before replacing a crank.
The surface of all metal parts contain some degree of micro-cracking, tiny cracks, discontinuties or even tool marks that can be a source of failure.
When a metal part is stressed and subjected to cyclic loading these micro-cracks enlarge and propogate through the part.
At some point in time the part will fail.
Normally, tensile stresses concentrates at the top or bottom of crack during loading.
However, the compressive skin created by peening tends to cancel out the tensile stresses and the cracks do not propogate.