Issue 49

M. Abbadeni et alii, Frattura ed Integrità Strutturale, 49 (2019) 282-290; DOI: 10.3221/IGF-ESIS.49.28 285 Figure 2 : Schematic representation of: (a) conventional deep drawing process and (b) hydromechanical deep drawing process principle. where  and  are the equivalent stress and the equivalent plastic strain, respectively,  0 =143.2 MPa is the yield stress, K = 296.9 MPa is the hardening coefficient and n = 0.40 is the strain hardening exponent. These material parameters are obtained from a bi-axial tensile test [16]. During the deep drawing, the blank is subjected to high plastic deformations. Sometimes these deformations become excessive, so that necking begins to appear in critical regions of the part. This represents the limit of the formability and the beginning of the fracture. The term formability is generally used to describe the ability of a material to be plastically deformed without necking or fracture. To characterize a material formability, forming limit diagrams (FLD) are widely used [20]. FLD is a plot of the combination of the minor and major strains at the beginning of localized necking. It becomes an essential tool in metal forming industry and also during finite element analysis or forming simulation. In this work, in order to evaluate the severity and the feasibility of the forming operation for the two processes, the FLD of the AA5086 aluminum alloy is used. This FLD is obtained by a biaxial tensile test [16]. R ESULTS AND DISCUSSION ig. 3 shows the equivalent plastic strain distribution, for the two processes, after 15 mm of punch displacement. In CDD process, maximum plastic strain value of approximately 38% is observed. This value decreases to 25% in the HDD process. For the two processes, the blank undergoes maximum deformation on punch and die corners. In the HDD process, a strain concentration occurred at the die corner as a result of bending. For the same reason and because of excessive stretching, high strain concentration is present at the punch corner in the CDD process. This can be clearly observed in Fig. 4 where the evolution of the plastic strain in the radial direction for a punch displacement of 15 mm is shown. We can see that the use of the fluid in the HDD process has a significant influence on the strain distribution. Maximum strain values are observed at the punch and the die corner where the blank is exposed to bending. Comparing the obtained results for the strain distribution, a large difference can be seen at the punch corner, at the die corner and at the blank-punch contact region. By contrast, a small difference is observed at the blank-blank holder contact zone (radial position is upper than 40 mm). The force exerted by the blank holder on the blank at this region supplies a restraining force which controls the metal flow and influences the strain distribution. In the HDD process, in addition to the blank holder force, there is high fluid pressure under the blank. The force generated by this pressure, which is opposite to the blank holder force, has also an influence on the strain distribution. This can explain the observed reverse behavior of the strain at this zone. According to the numerical results in Fig. 3 and Fig. 4, the resulting plastic strain distribution is more uniform and the maximum strain values are lower in the HDD process compared to CDD process. In CDD process, by the displacement of the punch, a radial traction force on the blank is produced. The absence of a fluid lubricating in the zone of contact blank-die causes a strong friction force in particular on the die corner. This implies a reduction in the slip of the blank under the blank holder. In this case, the force applied by the punch draws the blank and a plastic deformation dependent on this force is produced. Consequently, a radial effort is created on the blank, thus a higher traction force is necessary for the deformation. Drawing becomes significant producing an excessive thinning of the blank on the punch corner. As the traction force that the bank can resist is limited by the tensile strength of the used F (a) (b)