# An Overview of Self-Heating Phenomena and Theory Related to Damping and Fatigue of Metals
## 2 Infrared-Thermography Cyclic Test and Self-Heating Phenomena  
A typical setup of the infrared (IR)-cyclic thermography test is schematically illustrated in Figure 1. The system employs an infrared camera to record the surface temperature on the fatigue coupon being tested. It sends the signals to a computer, which also receives the temperature measurement signals from a dummy coupon at the ambient temperature but not subjected to loading. All the signals are processed by the computer, where the temperature increments relative to the ambient temperature are calculated and shown on the screen. The fatigue testing is a typical mechanical testing setup (details of load cell and strain measurements are omitted), except that care must be exercised when clamping the specimen at its two ends to minimize heat loss by conduction to the grips.  
The typical temperature increment curves are schematically shown in Figure 2. The calorimetric behavior generally consists of three phases. Phase I exhibits a rather steep temperature increase. In phase II, the temperature is often stabilized at a constant level, \(\Delta T_{AS}\), or in some cases, it may also increase at nearly a constant rate. Phase III represents an unstable phase of temperature increase up to fracture. The Risitano method determines the fatigue endurance limit by plotting curves of the stabilized temperature increment \(\Delta T_{AS}\) or the initial rate of temperature increase \(\partial T/\partial N\) against the applied stress amplitude \(\sigma\). The intersection point with a slope change is determined to be the value of the fatigue limit \(\sigma_{\text{fl}}\), as shown in Figure 3. Below this \"intersection\" point, the self-heating mechanism is effectively \"non-damaging\", which means that Phase II could last forever; above it, fatigue damage would accumulate and eventually lead to Phase III (fracture). The Risitano method was established on the premise that the temperature increment had a well-defined stabilization stage with a constant \(\Delta T_{AS}\) at a constant stress amplitude in testing (the gray colored line). Thus, the sudden change in the \(\Delta T_{AS}\) vs. \(\sigma\) behavior could reflect additional heat generation mechanisms associated with damage nucleation and propagation; as a result, the point is inferred as the fatigue endurance limit [2]. In the case where the sample surface temperature increases continuously in phase II (the orange colored line) rather than reaching a stabilization temperature, the initial rate of temperature change has been used to correlate with the fatigue life (N\({}_{t}\)) [25]. IR-thermography fatigue tests are often carried out at a frequency in the range of 1 to 170 Hz [9; 12], depending on the material and specimen configuration, to generate measurable heat.  
Figure 1: A schematic of the thermographic fatigue test setup.  
Figure 2: Typical temperature evolution curve during fatigue test.  
The questions regarding the observed phenomena are:  
1. What controls the temperature variation in each phase of self-heating?
2. What is the functional dependence of self-heating temperature \(\Delta T_{AS}\) on the applied stress amplitude (bilinear as implied by the Risitano method [2], or curved as observed by [PERSON] et al. [22])?
3. What is the relationship between the dissipation energy (or \(\Delta T_{AS}\)) and fatigue damage (life)?  
The answers to Q1 are often sought from the laws of thermodynamics, as will be discussed later in Sections 3, 3.1 and 3.2. The answers to Q2 and Q3 are still phenomenologically-based. Once the stress-dependence functions of self-heating are derived from the underlying physical mechanisms, the fatigue endurance limit can be deduced from the \"damaging\" self-heating mechanism(s).