We briefly discussed equilibrium versus non-equilibrium (NE) thermodynamics damage in Section 1.3.1. Here we will use an energy approach to physics of failure problems. In NE thermodynamic degradation, we are concerned about how the aging process takes place over time so that it can be modeled. In a sense we already have one approach to this. In Chapter 2, we devised a consistent measurement process *f* to help measure the damage that may have occurred between times *t*_{1} and *t*_{2}, finding the entropy damage was, as given by Equation (2.14):

(3.1)

where Δ*S*_{f} (*t*_{i}) is a quasistatic measurement. Here we can add as many intermediate quasistatic thermodynamics measurements as needed to trace out the aging path. Each measurement is taken when the system is either under very little stress or over a short enough time period, so that we are able to sample the system’s state variables over time. We then trace out how the damage is evolving over an extended time period. In this way we will be able to model the aging that is occurring by fitting the data. However, using this method we need to keep track and measure a number of states throughout the aging process. Often we are able to model the degradation (damage) so we do not have to make many measurements. In this chapter, ...

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