Issue 28

M.Malnati, Frattura ed Integrità Strutturale, 28 (2014) 12-18; DOI: 10.3221/IGF-ESIS.28.02 15 n = d d :d s s s for  y = 0 (13) Once the rules for the creation of the stress cycles are defined, a “deviatoric fatigue equivalent stress”  y is calculated for the yield surfaces bymeans of the following equations: d  EQ = f P (d X C ) + d  y for the active surface (14.a) d  EQ = 0 for all the other surfaces (14.b) The Eqs. (14.a) and (14.b) affirm that an increment of d  EQ is applied to the active surface only and not to the other surfaces: for both transported and resting surfaces the value of  EQ does not change at a given instant. At each instant of the stress history the result is thus the presence of a certain number of yield surfaces, eachonewith a related value of  EQ . The following figures show the concept illustrated above. They are intended only as a geometric plane representation of the stress cycles creation process, with pure explanation scope. The function f P used here is the Cartesian distance in the plane, so that the yield surfaces are circles. During the stress advancement, the size and the center of the surfaces are determined by the same differential hardening laws defined above: Eqs. (5.a), (5.b) for the active surface and Eqs. (12.a), (12.b) for transported and resting surfaces. A closed stress sequence is given, defined by the points numerated from 1 to 10 and represented by thick continuous line. At four different instants, the stress cycles already created by the moving stress point are sketchedwith thin continuous lines. A dashed line represents the smallest circle enclosing all the points of the sequence, which is used in theDangVan criterion for unlimited endurance [9]. Figure 1 : The stress point is moving between states ‘1’ and ‘2’. Only one stress cycle has been created. Figure 2 : Created stress cycles when the stress point is moving between states ‘5’ and ‘6’. Figure 3 : Created stress cycles when the stress point is moving between states ‘7’ and ‘8’. Figure 4 : Stress cycles at final instant of the sequence: the stress point has reached the instant ‘10’.