A second source of low cycle vibration is perhaps repeated tuning and detuning of the instrument.
This is again difficult to quantify but it is not impossible that some tens of cycles of 10% of the axial tension are involved.
Many musicians initially initially apply higher axial tensions to stabilize the attachment of the string at the machine (tuning) head prior to reducing to the required value (relaxation tuning).
This may slightly increase the effective cyclic stress amplitude and reduce the maximum tensile stress at the bridge.
In any case, it is clear that the vibratory stresses are likely to be small in comparison with the steady mean stress.
Fig. 8 shows a schematic Goodman diagram for a typical fretted instrument string.
The allowable stresses are determined from the (R=0) fatigue tests on ASTM A228 wire reported in [6] and the Goodman law.
The applied stresses are those calculated for the main portion of the string and those at the bridge.
Finally, we investigate the critical flaw size for rapid fracture in order to investigate the transition from fatigue to final failure.
The stress intensity factor for a circular section containing a transverse crack has been given by James and Mills [7] for a straight-edged crack and by Shih and Chen [8] for an elliptical crack
Fig. 8 Schematic Goodman diagram for A228 music wire, showing typical operating conditions for treble guitar string.