# An Overview of Self-Heating Phenomena and Theory Related to Damping and Fatigue of Metals
## 4 Conclusions  
This paper presents an overview of the self-heating phenomena and continuum thermodynamics framework that formulates energy dissipation and heat generation. It is also emphasized that a mechanistic understanding of the self-heating mechanism/heat source should be achieved to quantify the self-heating effect on fatigue behavior and better define the transition from \"non-damaging\" to \"damaging\" self-heating. The main conclusions from this review are as follows. Infrared thermographic techniques have been developed to interrogate the self-heating phenomena during fatigue testing, which generally undergoes three phases: Phase I with steeply increasing temperature to a stabilized or steady-state, i.e., Phase II, followed by an accelerating temperature increase to specimen rupture, Phase III. The initial slope \(\partial T/\partial N\) of Phase I, the stabilized temperature increment \(\Delta T_{AS}\) in Phase II, and the heat loss slope \(\partial T/\partial N\) when the test is stopped in the middle of Phase II are heat generation or heat loss characteristics. The fatigue endurance limit is often sought at the point of intersection of the \"non-damaging\" and \"damaging\" heat generation curves (e.g., \(\Delta T_{AS}\) vs. stress relations). As the thermographic method only depends on the data to establish the stabilized Phase II, not to failure), it may provide a rapid alternative means to determine the fatigue endurance limit. A continuum thermodynamics framework has been established from which the heat equation is derived as the balance between mechanical work input, heat generation and conduction (with convection as the boundary condition), and an increase in the internal energy. Heat sources are expressed as (i) hysteresis energy due to internal friction/intrinsic dissipation, (ii) thermoelastic energy, and (iii) energy arising from changes of internal state variables. The second law of thermodynamics or the Clausius-Duhem inequality permits a set of internal state variables as long as the product with their thermodynamic conjugate forces are greater than zero. However, within the continuum framework, which assumes the material is homogenous, the exact entropy production due to internal structural changes is unknown. In general, the heat generation processes include (i) thermoelasticity, internal frictions, and (iii) intrinsic dissipation. Internal friction involves dislocation bowing back and forth between weak pinning points, and returning to their original lattice position once the stress is removed, which is a form of anelastic dislocation motion. Intrinsic dissipation occurs by irreversible dislocation motion at either or both macro/microscopic scales, depending on the load level, which will eventually lead to fatigue crack nucleation. For irreversible processes, e.g., fatigue, the increase in internal energy is comprised of energy stored in structural changes (entropy increase) and energy dissipated into heat (self-heating), as well as energy to be released by cracking. The Tanaka-Mura-Wu model, based on the dislocation dipole pile-up and release of its energy to form new crack surfaces, is shown to provide class-A predictions for fatigue crack nucleation life in terms of the material's elastic modulus, the Burgers vector, the surface energy, and the cyclic stress or plastic strain range. Therefore, it can predict fatigue life, independent of conventional and thermographic fatigue testing. Regarding the energy argument, according to the first law of thermodynamics, the heat-dissipated energy, \(Q_{h}\), is contributed partly via the irreversible mechanical work, \(\Delta W\). In deformation processes with structural changes and crack formation, \(Q_{h}<\Delta W\). Only until each working term is rigorously derived from the underlying physical mechanisms can the heat energy dissipation be accurately described, and thus defining the fatigue endurance limit through calorimetric analysis could be physically proven and established. Conceptualization, L.L. and X.W. ; methodology, X.W.