Issue 33

M. Sakane et alii, Frattura ed Integrità Strutturale, 33 (2015) 319-334; DOI: 10.3221/IGF-ESIS.33.36 324 Cell size has a close connection with the stress amplitude, so the stress ratio ( R  ) and the square root of average cell diameter ( R d ) is plotted in Fig. 7. The stress ratio is defined by the following equation to express the amount of the additional hardening of materials. The stress ratio represents the increase ratio caused by the additional hardening of each material. It is meaningless to take the stress increase by the additional hardening itself, because each material has different flow stress. So, this study employed the ratio shown in Eq. (2). Figure 7 : Stress ratio-mean cell size relationship. Figure 8 : Strain paths and loading sequence. mNP yP R mP yP ( ) ( )         (2) mNP  and mP  are the stress amplitude at the final cycle in the test in nonproportional and proportional loadings, respectively, and yP  is the yield stress in proportional loading. A linear relationship is found in the figure which indicates