14. Conversion of Dynamical Stresses into Effective Static Values

The time-to-failure models which were developed in the previous chapters assume that the stress remains constant with time until the material fails. Even when we discussed fatigue (a failure mechanism caused by a cyclical stress), it was assumed that the stress range Δσ remained constant with time. However, seldom is the applied stress constant with time, as illustrated in Fig. 14.1. In integrated circuits, the currents and fields are continually changing during operation and generally depend on the frequency of operation. In mechanical devices, the mechanical stress usually varies with time (the mechanical stress in a metal light pole changes with wind direction and with wind speed while the mechanical stress in the shaft of a rotor changes with the number of rpm). Therefore, a question naturally arises: how does one convert dynamical stresses (time-dependent stresses) ξ(t) into an effective static form ξeffective so that all of the previously developed time-to-failure models can be used? This chapter presents a methodology for that conversion.