What is the effect of 'Work Hardening' during the coiling process on the final spring rate of a stainless steel wave spring?

During the cold-coiling of 302 or 316 stainless steel, the material undergoes work hardening, which increases its yield strength but can also slightly increase the effective Young's Modulus ($E$) due to the formation of strain-induced martensite. This can result in a spring rate that is 2-5% higher than calculated using the nominal $E$ values of annealed material. Engineers must use the 'as-coiled' or 'work-hardened' property values in their FEA models. Additionally, a low-temperature 'stress-relief' heat treatment (approx. $600-750^{\circ}F$) is usually performed after coiling to stabilize the dimensions and ensure the calculated rate is maintained throughout the spring's service life.