Issue 48

M. Laredj et alii, Frattura ed Integrità Strutturale, 48 (2019) 193-207; DOI: 10.3221/IGF-ESIS.48.21 198 Figure 5 : Typical distribution of tangential residual stress around an-expanded hole Factors Outputs results 1 CRSEH CompressiveResidual Stress at the Edge of the Hole 2 MCRS Maximum Compressive Residual Stresses 3 DMCRS The Depth of the Maximum Compressive Residual Stress 4 CRSZ The Compressive Residual Stress Zone 5 MT The Maximum Tension 6 PDZ The Plastic Deformation Zone Table 2 : Output simulations results E XPERIMENTAL DESIGN APPROACH he experimental design is necessary to identify relevant information to establish a relationship between the input variables thickness (t), cold expansion (Ce) and yield strength (Ys)) and the output variables (CRSEH, MCRS, DMCRS, CRSZ, MT and PDZ). In order to predict the amount of residual stresses each parameter was tested at three different levels: the thickness (3,5,7 mm), cold expansion (2,4, 6  ) and yield strength (270, 349.25 ,428.5 MPa). The responses were calculated using the finite element method. The experimental design matrix of the experiments is given by MODDE 5.0 (Modeling and Design) software [25-26]. We have adopted a complete experimental design [27] of three factors at two levels. The mode of the experimenter is quadratic and has the following form: 3 3 2 0 1 1 3 1 i i ij i j ii i i i j i y a a x a x x a x e =    = = + + + +    (2) Where i, j vary from 1 to the number of process variables (3), y is the response of the process. The coefficient is the average of all the responses for the whole experiment; The coefficients represent the effect of the variable and are the regression coefficients that represent the effects of the interactions of the variables and e is the experimental error. The polynomial model proposed by MODDE 5.0 describes the variations of the response function to the factors (Ys), (Ce) and (t) is of the following form: 2 2 2 0 1 2 3 12 13 23 11 22 33 response . . . a a t a Ys a Ce a t Ys a t Ce a Ys Ce a t a Ys a Ce = + + + + + + + + + (3) T