Question

Spokes usually need to be tightened to a stress of about 350 MPa on a bicycle wheel. If 304stainless steel is to be used it needs to be sufficiently strong so that during tensioning and under moderate overloads it will always deform elastically. In fact the stress-strain behavior of an as-manufactured stainless steel spoke, as opposed to the starting softer material, is shown in Fig.2 (see link at the end of question). The spoke owes its strength to the amount of strain it has undergone in the cold work processes used to form it: either wire drawing or a process known as swageing,by which rod is reduced in diameter by the hammering action applied to a split die through which it is fed. Paradoxically, even just straining the initial softer material (Fig.1(a)) toits tensile strength then unloading, increases the tensile strength of the material. This arises from the way in which tensile strength is defined - as an engineering stress. The true stress the specimen carries at its tensile strength is greater than the conventionally defined engineering tensile strength, because of the very much reduced cross-sectional area of the deformed specimen. If the strained material is retested it is this true stress value which must be reached before the material deforms plastically (vields) - and the "new" deforms plastically (yields) - and the "new"tensile strength will be close to this stress. Using the data in Fig.2, what are the tensile strength, the apparent yield stress(limit of proportionality), % elongation to failure, and Young's modulus of the as-manufactured spoke?

Fig: 1

Fig: 2