Issue 33

J. Toribio et alii, Frattura ed Integrità Strutturale, 33 (2015) 434-443; DOI: 10.3221/IGF-ESIS.33.48 437 -3500 -3000 -2500 -2000 -1500 -1000 -500 0 500 3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6  =0º  =20º  =40º  =60º    (MPa) r (mm) (a) (b) Figure 3 : Distribution of hoop stress after the sixth loading cycle: (a) 3D view at the contact of one of the balls and (b) radial distribution for diverse hoop coordinates  . -3500 -3000 -2500 -2000 -1500 -1000 -500 0 500 3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6  =0º  =20º  =40º  =60º  z  (MPa) r (mm) (a) (b) Figure 4 : Distribution of axial stress after the sixth loading cycle: (a) 3D view at the contact of one of the balls and (b) radial distribution for diverse hoop coordinates  . Results shown in Figs. 2a-4a, reveal a heavy multiaxial stress concentration localized at the contacting zones of each ball with the rolling rod. This effect progressively vanishes as the distance from the contact zone increases. Outside of the local affected zone, the stress state is homogenously distributed with a stress concentration ring located at the vicinity of the rod surface. The radial distributions shown in Figs. 2b-4b reveal a huge compressive stress at the contact radius (  = 0º) in the radial direction caused by the pressure applied by the ball. This stress concentration is more intense for the radial stress than for the other components of the stress tensor. In addition, the extension of the local effect of contacting balls spreads through a deeper zone (around 1.5 mm) for the radial stress (Fig. 2) than those corresponding to the hoop and axial stress (around 200  m). The extension and the maximum value of the compressive state is notably reduced at planes placed outside the contacting planes (i.e. for  0º) with slight variations for hoop coordinates higher than 20º. The distributions of the hoop and axial stresses show the same high reduction of the magnitude of the stress state but, in these cases, without significant changes in the extension of the affected zone. The distribution for the other radius in contact with the other balls   = 120º and  = 240º) is equivalent to that shown in Figs. 2b-4b. Within the stress concentration zone, the values of the von Mises stress reach the material yield strength; it implies the appearance of plastic strains near the rod skin, as revealed in previous studies [2,3]. As a consequence of the values of the stress state at the rod surface vicinity, plastic strains are distributed through such a zone. Fig. 5a shows the 3D view of the field of equivalent (cumulative) plastic strain after the six cycles of the test was completed and the radial distribution of such a variable is plotted in Fig. 5b. In the same way, Fig. 6a shows the 3D view of the field of hydrostatic stress after the sixth cycle of the test was completed and Fig. 6b shows the radial distribution of such a variable for diverse values of  .