Issue 45

L.M. Viespoli et alii, Frattura ed Integrità Strutturale, 45 (2018) 121-134; DOI: 10.3221/IGF-ESIS.45.10 125       2 2 2 2 2 2( 1) 2 (2) (2) (2) (2) (2) (2) (2) (2) (2) (2) 2 2 1 ( , ) 2 2 1 2 rr zz rr zz rr zz r W r r K E                                       1 2 2 (1) (2) (1) (2) (1) (2) 12 1 2 1 ( , ) rr rr zz zz W r r K K E                            (1) (2) (1) (2) (1) (2) (1) (2) (1) (2) (1) (2) (1) (2) 2 1 rr zz rr rr zz zz zz rr r r                                             The integration of the strain energy density on a volume of radius R around the notch tip yields the elastic deformation energy:                            R A E R WdA W r W r W r rdrd 1 2 12 0 , , , being the integration field symmetric to the notch bisector, the term W 12 gives a null contribution, the resulting energy is:                     I I E R E R E R K R K R E E 1 2 2 2 2 2 1 2 1 2 1 2 1 2 1 1 4 4 where:                                                                rr zz rr zz rr zz r I d           2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 2 2 1                                                                rr zz rr zz rr zz r I d           2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 and the integration area is:             R A R rdrd R 2 0 The average of the strain energy density on the area A gives:                E R W e K R e K R A R E E 2 1 2 1 2 2 1 2 1 1 2 2 1 1 with:          I e 1 1 1 2 4          I e 2 2 2 2 4