Issue 48

M. Laredj et alii, Frattura ed Integrità Strutturale, 48 (2019) 193-207; DOI: 10.3221/IGF-ESIS.48.21 199 The experimental plans used in this study are a complete quadratic plan which a mathematical model of the second degree. By removing the non-significant effects we obtain the following mathematical models: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 114.75 5.56 38.64 15.46 9.86 . 13.59 . 7.7 9.08 20.38( ) CRSEH t Ce Ys t Ys Ce Ys t Ce Ys = − − + − + + + + + + (4) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 238.07 21.49 8.11 26.34 7.43 . 12.82 5.9 16.15( ) MCRS t Ce Ys t Ce t Ys = − + + − + + + + + (5) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 1.44 0.08 0.49 0.2 0.08 . 0.03 . 0.02 4 0.04( ) DMCRS t Ce Ys t Ce Ce Ys t Ce Ys = + + − + − + − + (6) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 3.38 0.16 0.43 0.29 0.14 . 0.11 0.17 0.1( ) CRSZ t Ce Ys t Ce t Ce Ys = + + − + − − − (7) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 47 7.5 14.23 8.05 2.15 . 4.17 . 2.13 0.32 0.3( ) MT t Ce Ys t Ce t Ys t Ce Ys = − + + − + + + − (8) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 3.88 0.09 0.5 0.21 0.13 . 0.08 . 0.03 . 0.019648 0.13 0.05( ) PDZ t Ce Ys t Ce t Ys Ce Ys t Ce Ys = + + − + − + + − − − (9) A NALYSIS OF THE RESULTS rom the graphical analysis we can determine the influence of each factor on the response by plotting the response variation according to these factors. The evolution of surface residual stresses at the edge of the hole after expansion as a function of the thickness (t), the degree of expansion and the yield strength are presented respectively in the figures (6-a), (6-b) and (6-c). The analysis of Figure (6-a) shows that an increase in the thickness causes an increase of the residual stresses (absolute value) at the edge of the hole after expansion CRSEH. Figure 6 : The compressive residual stress at the edge of the hole after expansion From the results one can deduct the existence of the critical thickness (t = 4.92mm) of the material and beyond this value the CRSEH is almost independent of this geometrical parameter. The result show a good agreement with V. NIGRELLI et al work [28] which illustrated through FE analysis carried out on plate thicknesses of 3, 5 and 10 mm considering a F