Nonlinear deflection analysis of helical spring in elastic–perfect plastic material: Application to the plastic extension of piano wire spring

Abstract A mechanics-of-materials theory of the nonlinear deflection of helical spring within and beyond the elasticity limit was developed. The theory examined the nonlinearity due to the combined stresses of the torsion and bending of spring element by assuming the elastic–perfect plastic material obeying Tresca yield criterion. Free rotation of spring around the spring axis was taken into account. It was shown in experiment that the stress–strain curve of a piano wire was close to elastic–perfect plastic one. The outcome of the theory was compared with the experimental result of nonlinear load–deflection curves in plastically extended helical spring made of the piano wire.