Page 289 - Biaxial Multiaxial Fatigue and Fracture

An Analysis of Elasto-Plastic Strains and Stresses in Notched Bodies Subjected to Cyclic ... 273

Equations (10)-(11) form a set of twelve simultaneous equations from which all deviatoric
strain and stress increments can be determined, based on the hypothetical linear elastic notch tip
stress path data, i.e. increments Aoi; (obtained from the linear-elastic analysis) and the
constitutive stress-strain curve (3).

For each increment of the external load, represented by increments of pseudo-elastic (fictitious)
deviatoric stresses, A&:, the deviatoric elastic-plastic notch tip strain and stress increments, Aei;
and ASi:, are computed from the equation set (12). With the help of equation (9) the calculated
deviatoric stress increments, AS,;, can subsequently be converted into the actual stress
increments, Boya.
1
AS; = AO; - -( AC; + aai2 + AC;~)
3
1
ASi2 = Ao;* - -( + Agi2 + A6i3)
3