PSI - Issue 79

Andrea Avanzini et al. / Procedia Structural Integrity 79 (2026) 88–96

90

reached, cyclic loading started, with a fast temperature increase (phase I), more noticeable for high-load levels. Then temperature stabilization eventually followed (Phase II) and, if the specimen did not fail prematurely, the cyclic load was stopped upon reaching the target value of cycles. After measuring the consequent temperature decrease, when the temperature was stabilized, the static mean load was finally removed, recording the temperature increase.

Fig. 1 Thermographic indexes for a single stepped test (a) dT/dt,  T steady and Q parameters (b) Area for dissipative energy ( Φ )

The primary categories of parameters used for fatigue limit estimation include temperature-based and energy-based approaches and the thermal indexes needed for their implementation can be determined by analyzing the ∆ T-N curve obtained with the test protocol described. The temperature-based approach leverages on the temperature evolution during the cyclic test described in Fig. 1a and two types of thermal indexes can be extracted. The first is the slope (dT/dt) of the initial (fast) temperature increase in phase I (Cura et al., 2005), the second is the stabilized temperature (  T steady) observed in phase II (Luong, 1998) (La Rosa, 2000). Considering energetic approaches, the specific heat loss (Q) refers to the energy dissipated per cycle within a unit volume of the specimen. A complete mathematical review of this approach can be found in (Ricotta et al., 2019), but the key step when using this method is to determine the temperature evolution after the test is stopped. In particular, the slope of the ∆ T-N curve immediately after stopping the cyclic load is first measured for each stress level (see Fig. 1a), then the corresponding Q can be computed and plotted versus the stress, similarly to temperature-based methods. Following the methods in literature, reviewed in (Liu et al., 2023), when the values of these measured quantities are plotted as a function of applied stress, they exhibit a transition around the stress level corresponding to the fatigue limit. Taking advantage of continuous temperature monitoring during the test, a further parameter accounting for dissipative energy ( Φ ) can be determined based on measurements of the areas under the curve ( ∆ T-N) (Santonocito et al., 2021). This parameter Φ is proportional to a limiting energy E c , the characteristic energy associated with failure, which can be determined by running a test up to failure. With this approach, it is possible to estimate, in principle, the whole life curve, because under the hypothesis that E c is material property, the number of cycles to failure can be determined for any given load.