Issue 42

M. Peron et alii, Frattura ed Integrità Strutturale, 42 (2017) 223-230; DOI: 10.3221/IGF-ESIS.42.24 228 This means that, at the critical load, the material is characterized by a value of strain energy density, averaged in a control volume having size variable with the loading-rate, which is independent of the ratio between the applied load and magnetic field. A good fit of R c versus loading-rate to a linear model has been found, then, adopting a simple linear regression model, the following relationship is proposed: 0.0195 0.05 c dP R dt   (11) P c [N] dP/dt B = 0 T B = 0.03 T 0.05 Ns -1 58.3 59.2 65.8 61.9 74.7 64.6 66.3 (5.81) 61.9 (1.91) 0.5 Ns -1 66.6 60.7 68.5 61.6 67.5 (0.78) 61.1 (0.37) 3.0 Ns -1 71.0 74.2 79.2 59.3 - 60.0 75.1 (3.35) 64.5 (5.95) Table 3 : Measured fracture loads as a function of the loading-rate and the magnetic field Figure 2 : Mean fracture loads as a function of the loading-rate and the magnetic field The approximated critical radius of 0.07 mm, obtained from (9) and suggested by Colussi et al. [16] without taking into account the loading-rate, falls amid of the range of variation here proposed. Fig. 3 shows a summary of the experimental data in terms of the square root of the ratio between the averaged strain energy density, W , and the critical value of strain energy, W c . This parameter has been chosen because of its proportionality to the fracture load. The averaged strain energy density, W , has been computed in control volumes having radius given by (11), whereas a critical strain energy equal to 0.02 MJ.m -3 is assumed. This critical value is obtained from Eq. (8), assuming Young's modulus equal to 30 GPa, Poisson's ratio equal to 0.25 and tensile strength equal to 34 MPa, which are the medium characteristics provided by the material supplier. Here, Young's modulus is assumed independent from the applied magnetic field. This assumption is reasonable in the range of variation of the applied magnetic field. In Fig. 3 experimental data from Narita et al. [25] have also been summarized. Data referred to fracture loads measured under three point bending, with and without magnetic a 0.03 T magnetic field, at the following loading- rate: 0.2 Ns -1 and 3.0 Ns -1 . Specimens were 3 mm thick, 5 mm wide and 15 mm long. Crack depth was 0.5 mm. Due to the different geometry (ratio between width and thickness equal to 5/3 instead of 3/5) plane strain condition instead of plane stress condition resulted more appropriate for their modeling. It has been found that about all experimental data fit in a narrow scatter band, which limits are drown here with an engineering judgment from 0.80 to 1.20 (4 data over 35 0 10 20 30 40 50 60 70 80 90 100 0.05 0.5 3 Pc [N] dP/dt [N/s] 0 T 0.03 T