Issue 37

J. Albinmousa, Frattura ed Integrità Strutturale, 37 (2016) 94-100; DOI: 10.3221/IGF-ESIS.37.13 96 A NALYSIS AND MODELLING ormal and shear cyclic responses in Fig. 1 were transformed using plane stress-strain transformation relations over the range 0 ൑ ߮ ൑ 2 ߨ with an increment of ߮ ௜ ൌ 1.0° . Maximum stresses and strains at each angular increment were recorded and then plotted on polar diagrams. After that, each polar curve was fitted using proper parametric equation, Eqs. 1 to 8, as shown in Fig. 2 a to h, respectively. (1) (2) (3) (4) (5) (6) (7) (8) It should be noted here that the plus and minus signs in Eqs. 1 and 2 represents two different equations for the top and bottom parts of the curves in Figs. 2a and b, respectively. Similar to the stress and strain responses, fatigue damage parameter can also be represented in a parametric form. Figure 3 shows the parametric representation of the Fatemi-Socie [5] fatigue damage parameter for the proportional, Nr20, and nonproportional, Nr26, loading cases. Hence, the Fatemi-Socie damage parameter was expressed in a parametric form as in Eq. 9. (9) N