Issue 41

P. Gallo et alii, Frattura ed Integrità Strutturale, 41 (2017) 456-463; DOI: 10.3221/IGF-ESIS.41.57 458 where σ max can be expressed as a function of stress concentration factor K t (evaluated through linear elastic finite element analysis) and the applied load σ nom , max t nom K    (2) Employing the more general conformal mapping of Neuber [19] that permit a unified analysis of sharp and blunt notches, the notch radius, ρ , and the origin of the coordinate system, r 0 , are related by the following equation on the basis of trigonometric considerations: 0 1 q r q     (3) where 2 2 q      . The main steps to extend the method to blunt V-Notches can be summarised as follows:  Assumption of Lazzarin-Tovo equations to describe the stress distribution ahead the notch tip instead of Creager-Paris equations;  Calculation of the origin of the coordinate system, r 0 , as a function of the opening angle and notch radius, as described by Eq. (3);  Re-definition of the plastic zone correction factor C p that is a function of plastic zone size r p and plastic zone increment Δ r p ; The definition of the parameters C p , r p , Δ r p is very similar to that clearly reported by Glinka [20], except for the assumption of different elastic stress distribution equations. Definition of these variables is briefly reported hereafter. Referring to Fig. 2, considering the Von Mises [21] yield criterion in polar coordinate: 2 2 ys r r           (4) and introducing Eqs. (1) into Eq. (4), a first approximation of r p that can be solved numerically is obtained. Once r p is known, the force F 1 can be evaluated as follows:                  0 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 0 0 0 1 1 1 1 0 1 1 1 0 0 0 1 1 1 1 3 4 1 1 1 (3 ) p r p p r p p p t nom p p p p p F dr r r r r r r K r r r r r r r r r r r r r                                                                                                                     1 1                   (5) The stress σ y ( r p ) is considered to be constant inside the plastic zone, which means elastic-perfectly plastic behavior is assumed. The lower integration limit is r 0 , which depends on the opening angle and notch tip radius. Due to the plastic yielding at the notch tip, the force F 1 cannot be carried through by the material in the plastic zone r p . But in order to satisfy the equilibrium conditions of the notched body, the force F 1 has to be carried through by the material beyond the plastic zone r p . As a result, stress redistribution occurs, increasing the plastic zone r p by an increment ∆ r p . If the plastic zone is small in comparison to the surrounding elastic stress field, the redistribution is not significant, and it can be interpreted as a shift of the elastic field over the distance ∆ r p away from the notch tip. Therefore the force F 1 is mainly carried through the material over the distance ∆ r p , and therefore the force F 2 (represented by the area depicted in the Fig.