PSI - Issue 83

Davide D’Andrea et al. / Procedia Structural Integrity 83 (2026) 256–264

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(a)

(b)

Figure 2. Surface temperature’s trend of specimens subjected to a) constant amplitude and b) stepwise fatigue tests.

Crack area, A c , is correlated with temperature and number of cycles through Equation 1, where C 1 and n are material properties and Δ T st is the stabilization temperature characterizing the second phase. It is possible to assume that after the crack initiation the crack area follows the same law as temperature. In the limiting case, n can be assumed equal to 1, corresponding to a linear relationship. A c =C 1 Δ T st ሺ Δ N ሻ n (1) RTM is based on the dependence of stabilization temperature to applied stress. It is possible to express this metric as a variable dependent on the difference between the squares of applied stress and fatigue limit. The coefficient m in Equation 2 is the slope of the regression line describing the relation between stabilization temperatures and stress above fatigue limit and it can be experimentally determined. Δ T st =m ൫ σ 2 - σ 0 2 ൯ (2) Replacing Equation 2 into Equation 1 the relation describing crack area’s growth with respect to stress is given (equation 3) A c =C 1 m ൫ σ 2 - σ 0 2 ൯ Δ N (3) Crack area at failure, A c,r , could be experimentally measured but, in the present work, it has been chosen to estimate it through equation 4, which is the assumption that crack area at failure is the difference between the nominal area A and the area resulting from the ratio between the applied maximum cyclic load, σ r , and the ultimate strength of the material , σ U . A c,r =A ൬ 1 σ r σ u ൰ (4) By doing so, every term of Equation 3 is known, since Δ N c , which represents the number of cycles leading to failure in the third phase of the last applied stress step can be experimentally measured and A c,r is estimated by 5. A c,r =C 1 m ൫ σ r 2 - σ 0 2 ൯ Δ N c (5) Consequently, it is possible to determine the coefficient C 1 , which is a material property, by Equation 6 and, finally, the number of cycles which would have led to fatigue failure the specimen if subjected to the same stress level in a constant amplitude fatigue test (Equation 7).