Issue 41

P. Gallo et alii, Frattura ed Integrità Strutturale, 41 (2017) 456-463; DOI: 10.3221/IGF-ESIS.41.57 459 1-b) must be equal to F 1 . For this reasons, F 1 = F 2 = σ θ ( r p )Δ r p , and the plastic zone increment can be expressed as the ratio between F 1 and σ θ evaluated (through Lazzarin-Tovo equations [16]) at a distance equal to the previously calculated r p :   1 p p F r r     (6) Substituting in Eq. (6) the formula given by Eq. (5) for F 1 and the explicit form of σ θ , the expression for the evaluation of Δ r p is obtained:                 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 1 1 1 1 1 0 1 1 1 0 0 0 1 1 1 1 3 1 1 1 3 p p p p p p p p p p r r r r r r r r r r r r r r r r r r r                                                                                                                                        1 1 1 1 1 1 1 1 1 0 0 / 1 1 1 3 p p r r r r                                                          (7) The last step consists in the definition of the plastic zone correction factor C p , which is according to Glinka [20] but introducing the Lazzarin-Tovo equations:                 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 1 1 1 1 1 0 1 1 1 0 0 0 1 Δ 1 1 1 1 1 3 1 1 1 3 p p p p p p p p p p p p r r r r r C r r r r r r r r r r r r r r r                                                                                                                                 1 1 1 1 1 1 1 1 1 0 0 / 1 1 1 3 p p p r r r r r                                                                             (8) At this point, the general stepwise procedure to be followed to generate a solution is identical to that proposed by Nuñez and Glinka [13]: 1. Determine the notch tip stress, 22 e  , and strain, 22 e  , using the linear-elastic analysis. 2. Determine the elastic-plastic stress, 0 22  , and strain, 0 22  , using the Neuber [14] rule (or other methods e.g. ESED by Molski and Glinka [22], finite element analysis). 3. Begin the creep analysis by calculating the increment of creep strain, 22 Δ n c  , for a given time increment Δ t n . The selected creep hardening rule has to be followed.   22 22 Δ Δ ; n c c n t t      (9) 4. Determine the decrement of stress, 22 Δ n t  , from Eq. (10), due to the previously determined increment of creep strain, 22 Δ n c  :