# An Overview of Self-Heating Phenomena and Theory Related to Damping and Fatigue of Metals
## 1 Introduction  
Traditionally, for structural design, the fatigue properties of a material need to be determined through a large amount of fatigue testing at many stress levels until down to a stress level with fatigue life exceeding \(10^{7}\) cycles. The fatigue data generated this way in stress control are often presented in the form of an S-N curve, first investigated by [PERSON] [1]. The stress amplitude at which the material has endured \(10^{7}\) fatigue cycles is called the fatigue endurance limit. Such fatigue characterization practices are extremely time-consuming and expensive for industrial design.  
In recent years, the phenomena of self-heating in metals and composites during cyclic (or fatigue) loading have attracted a great deal of interest, as it provides an alternative, often rapid method for determination of fatigue endurance limit, as compared to conventional fatigue testing. A method called the Risitano method using infrared thermography techniques was developed to track the temperature increase on the coupon surface with loading cycles (or time), where a transition point in the relationship of sample surface temperature change vs. stress corresponded to the fatigue endurance limit [2]. Following [PERSON]'s work, a significant amount of studies have been carried out on metals [3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30] andcomposites as well [31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43]. Physically, the self-heating phenomena are related to energy dissipation and entropy change in damping, thermoelastic, viscoelastic, viscoplastic, and (rate-independent) plastic deformation. Therefore, it is important to understand the different aspects of the self-heating process, to achieve a holistic view of material deformation, energy dissipation, and damage accumulation. Due to the limited space, the current review only focuses on metals, outlined below.  
The experimental technique of IR thermographic fatigue is briefly introduced, and the key phenomena of self-heating are summarized in Section 2, representing the points of discussion. The general thermodynamic laws governing heat generation are reviewed in Section 3 with various terms as the heat sources [7; 43; 44]. In particular, heat sources are classified by their controlling mechanisms, such as thermoelastic deformation (Section 3.1), internal friction (Section 3.2), and intrinsic dissipation (Section 3.3). The laws of thermodynamics govern the heat generation, heat transfer, internal energy, and entropy changes associated with every physical mechanism with the self-heating temperature change as an overall result. Wherever applicable, mathematical equations for the observed calorimetric responses are given, which have been used by researchers to analyze the heat generation mechanisms and responses. Damping is discussed in association with thermographic fatigue in Section 3.4. The concept of fatigue fracture entropy is introduced in Section 3.5[16]. The dislocation-based Tanaka-Mura-Wu model for fatigue crack nucleation is introduced in Section 3.6[45; 46], which can provide class A prediction of fatigue life, independent of conventional and thermographic fatigue testing. Dislocation dipole pile-ups are formed by alternating slips under cyclic loading, which has been well-recognized as the very mechanism of mechanical fatigue in metallic materials. Thus, the energy release for fatigue crack nucleation is naturally a part of the thermodynamic energy dissipation process. To include the crack formation energy into the thermodynamic framework, energy arguments are discussed in Section 3.7. Critical questions are also raised in discussions to identify the gaps in the current state-of-the-art. It is hoped that a unified thermodynamic framework will be established for deformation, damping, and fatigue, including heat generation, by amending those gaps.