PSI - Issue 42
R. Fernandes et al. / Procedia Structural Integrity 42 (2022) 992–999 Fernand s et al. / Structural Integrity Procedia 00 (2019) 00 – 000
996
5
400
400
300
300
(MPa)
200 (MPa)
200
100
100
0
0
-1.5
-0.5
0.5
1.5
-1.5 -0.75
0
0.75
1.5
400
(%)
(%)
-100
-100
300
-200
-200
(MPa)
200
-300
-300
(b)
(c)
100
-400
-400
0
400
400
-1.5 -0.75
0
0.75 1.5
(%)
-100
300
300
200 (MPa)
(MPa)
-200
200
-300
(a)
100
100
-400
0
0
-1.5 -0.75
0
0.75 1.5
-1.5 -0.75
0
0.75 1.5
(%)
(%)
-100
-100
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-200
Cyclic curve, Eq. (1)
-300
-300
(d)
(e)
-400
-400
Fig. 3. Stable hysteresis loops and cyclic stress-strain curves for the different tested conditions: (a) as-built; (b) T6; (c) 300ºC stress-relief; (d) 250ºC stress-relief; and (e) 250ºC stress-relief and HIP treatment.
From an engineering point of view, the fatigue resistance can be defined using stress-based, strain-based, and energy-based parameters. Under strain-controlled conditions, the two last approaches are generally more convenient. Regarding the strain-life relationships, the Coffin-Manson-Basquin (CMB) model, since it accounts for both the elastic and the plastic components, is often used. This model can be formulated as follows: ε a = ε a,e + ε a,p = σ f ' E (2N f ) b + ε f ' (2N f ) c (2) where a is the total strain amplitude, a,e is the elastic strain amplitude, a,p is the plastic strain amplitude f ’ is the fatigue strength coefficient, E is the Young’s modulus, b is the fatigue strength exponent, f ’ is the fatigue ductility coefficient, c is the fatigue ductility exponent, and 2 N f is the number of reversals to failure. Figure 4 plots the fitted functions, see Eq. (2), for the tested conditions. The dashed lines represent the as-built conditions (total strain and plastic strain components) which were added for the sake of comparability. At the first sight, it is clear that the CMB model can satisfactorily fit the datapoints regardless of the material state. For all cases studied, it was also found that the plastic strain ( a,p ) versus life relationship exhibits a bi-linear trend. Therefore, as can be seen in the figure, the total strain life ( a ) versus life relationship is better described by a two-part piecewise function. On the other hand, by comparing the fitted functions with those determined for the as-built condition, it can be concluded that the post-processing treatments significantly affect the fatigue response. Regarding the T6 condition, see Figure 4(a), although the plastic strain versus life relationship is relatively different
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