Issue 41

F. Berto et alii, Frattura ed Integrità Strutturale, 41 (2017) 79-89; DOI: 10.3221/IGF-ESIS.41.12 86 R 1 2  R 3 Figure 4 : Control volumes for V-shaped notches under tension and torsion loadings. On the basis of Eqs. (9a) and (9b), the control radii result to be R 1 = 0.051 mm and R 3 = 0.837 mm, respectively. Accordingly, the control radius R 1 has been adopted to compute the averaged strain energy contribution tied to tension loading, whereas the control radius R 3 has been employed to evaluate the averaged SED contribution due to torsion loading. It should be noted that the control radius R 3 is highly affected by the presence of larger plasticity under torsion loading as compared to tension loading, and by friction and rubbing between the crack surfaces, as previously discussed also for different materials [23,30]. Under these conditions, the averaged SED is called also ‘apparent linear elastic SED’ to highlight that the strain energy density calculation over two different control volumes (under tension and torsion, respectively, as determined from experimental data) allows us to overcome the problem tied to shielding mechanisms, keeping a linear elastic criterion. To summarise in the same scatter band experimental results obtained by adopting different nominal load ratios R, a coefficient c w , defined on the basis of simple algebraic considerations (reported in detail in Ref. [24, 31]), must be introduced. The coefficient c w results to be dependent on the nominal load ratio R according to the following expression:                         2 2 2 2 1 0 1 1 0 1 0 1 1 W R for R R c for R R for R R (10) The parameter c w equals 1.0 in the case R = 0, while it results equal to 0.5 for R = -1. By adopting the coefficient c w , the closed-form expressions to evaluate the averaged SED, related to smooth samples (Eqs. (1, 2)) and to components weakened by sharp notches (Eq. (8)), become as follow:                                              2 2 2 2 3 1 1 3 2 1 2 1 1 3 1 3 2 1 nom W nom W W c un notched specimens pure tension E SED c un notched specimens pure torsion E c K K e e V notched specimens multiaxial loading E R R (11)