Issue 47

P. Foti et alii, Frattura ed Integrità Strutturale, 47 (2019) 104-125; DOI: 10.3221/IGF-ESIS.47.09 109 Table 1 : Parameters 1 I for pointed V-notches under plane stress and plane strain conditions. The elastic deformation energy in the control volume around the notch tip is given as follows:   ( ) 1 2 12 0 ( , ) ( , ) ( , ) R R A E W dA W r W r W r rdrd                  (15) The integration field is symmetric with respect to the notch bisector; this condition sets to zero the contribution of 12 W . Therefore:               1 2 1 2 2 2 2 2 1 2 1 2 1 2 1 1 4 4 R R R I I E E E K R K R E E                 (16) Where   1 I  and   2 I  are:       2 2 2 2 (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) 1 2 2(1 ) rr zz rr zz zz rr r I d                                          (17)       2 2 2 2 (2) (2) (2) (2) (2) (2) (2) (2) (2) (2) 2 2 2(1 ) rr zz rr zz zz rr r I d                                          (18) Their values, assessed for different geometries and stresses field, are reported in Tab. 1 as a function of Poisson’s ratio. The value of the area on which the integration is carried out is given by:   0 2 0 0 R R A rdrd R           (19)  being expressed in radians. The averaged elastic deformation energy on the area results to be:         1 2 2 2 2( 1) 2( 1) 1 1 0 2 2 0 1 1 R R E W e K R e K R A E E              (20) Being:     1 1 2 1 4 I e      (21) 1 I Pl. Strain 1 I Pl. Stress 2  [°]   [rad] 1  0.10   0.15   0.20   0.25   0.30   0.35   0.40   0.30   0 1 0.5000 1.1550 1.0925 1.0200 0.9375 0.8450 0.7425 0.6300 1.0250 15 23/24 0.5002 1.1497 1.0880 1.0162 0.9346 0.8431 0.7416 0.6303 1.0216 30 11/12 0.5014 1.1335 1.0738 1.0044 0.9254 0.8366 0.7382 0.6301 1.0108 45 7/8 0.5050 1.1063 1.0499 0.9841 0.9090 0.8247 0.7311 0.6282 0.9918 60 5/6 0.5122 1.0678 1.0156 0.9547 0.8850 0.8066 0.7194 0.6235 0.9642 90 3/4 0.5445 0.9582 0.9173 0.8690 0.8134 0.7504 0.6801 0.6024 0.8826 120 2/3 0.6157 0.8137 0.7859 0.7524 0.7134 0.6687 0.6184 0.5624 0.7701 135 5/8 0.6736 0.7343 0.7129 0.6867 0.6558 0.6201 0.5796 0.5344 0.7058 150 7/12 0.7520 0.6536 0.6380 0.6186 0.5952 0.5678 0.5366 0.5013 0.6386