METALS AND MATERIALS International, Vol 12, No (2006), pp 121~129 Prediction of Forming Limit in Hydro-Mechanical Deep Drawing of Steel Sheets Using Ductile Fracture Criterion 2 2,* S.-T Oh , H.-J Chang , K H Oh and H N Han POSCO Technical Research Laboratories, 699, Geumho-dong, Gwangyang-si, Jeonnam, 545-090, Korea School of Materials Science and Engineering, Seoul National University, San 56-1 Sillim-dong, Gwanak-gu, Seoul 151-742, Korea It has been observed that the forming limit curve at fracture (FLCF) of steel sheets with a relatively higher ductility limit have linear shapes, similar to those of a bulk forming process In contrast, the FLCF of sheets with a relatively lower ductility limit have rather complex shapes approaching the forming limit curve at neck (FLCN) towards the equi-biaxial strain paths In this study, the FLCFs of steel sheets were measured and compared with the fracture strains predicted from specific ductile fracture criteria, including a criterion suggested by the authors, which can accurately describe FLCFs with both linear and complex shapes To predict the forming limit for hydro-mechanical deep drawing of steel sheets, the ductile fracture criteria were integrated into a finite element simulation The simulation results based on the criterion suggested by authors accurately predicted the experimental fracture limits of steel sheets for the hydro-mechanical deep drawing process Keywords: forming limit, ductile fracture criterion, hydro-mechanical deep drawing INTRODUCTION Prediction of the fracture limit during sheet metal forming is very important for identifying the critical conditions that lead to ductile fracture In particular, the forming limit curve at neck (FLCN) has become a well-established tool in the development of sheet metal forming operations It displays, in principal strain space, the combinations of strains at the onset of local necking It is known that ductile fracture due to void formation is induced just before the onset of the localized necking [1] In contrast, a forming limit curve at fracture (FLCF) is produced by the combined principal strains up to fracture Figure shows schematic diagrams that illustrate a forming limit curve at neck (FLCN) and at fracture (FLCF) In the Figure, α (= dσ2/dσ1) is a stress ratio, and ρ (= dε2/dε1) is a strain ratio For a given initial strain path, after the onset of strain localization, the material forms a neck, which continues to deform by an almost plane strain path up to failure To describe the forming limit diagram at sheet metal fracture, various ductile fracture criteria [2-7] have been used for bulk forming processes Recently, ductile fracture criteria were adopted to predict the fracture limit of various sheet *Corresponding author: hnhan@snu.ac.kr metal forming processes, such as deep drawing [8,9], boreexpanding [10], and stretch forming [11] These ductile fracture criteria have been based on the macroscopic variables associated with a specific process The empirical hypothesis of the ductile fracture criteria is that a ductile fracture occurs when the maximum damage value of the workpiece exceeds a critical damage value (CDV) These criteria generally have an integral form, representing the effect of the deformation history of process parameters εf ∫0 F( process parameters ) dε = CDV (1) where εf is the effective plastic strain at fracture, and F is a function related to the process parameters Equation indicates that the ductile fracture depends on the plastic deformation of the material Some ductile fracture criteria, which the present work addresses, are summarized in the Appendix (A.2-A.5) Takuda et al [11] experimentally obtained the FLCFs of A1100-O and A5182-O aluminum alloy sheets The FLCFs of these materials were found to be approximately linear and similar to those of bulk material In their study, they accurately describe FLCFs with an almost linear shape by using one of the ductile criteria with the form of Eq 1, as reported in the literature [2-5] In contrast, Jain et al [12] measured 122 S.-T Oh al the FLCF of an AA6111-T4 sheet by using a hemispherical punch stretching method and via a stretch flanging experiment The FLCF of their study [12] was a non-linear shape approaching the FLCN towards the equi-biaxial strain path Note that, in the report of Jain et al [12], the maximum shear stress criterion, which had been originally proposed to predict local necking in sheet metal forming [13], provided a good agreement with the experimental FLCF over the whole range of strain ratios However, the maximum shear stress criterion could not describe the FLCF with the linear shape Very recently, Han and Kim [14] noticed that the ductile fracture criteria in the literature could not predict with precision those experimental FLCFs having both a linear shape and a complex shape approaching the FLCN towards the equi-biaxial strain paths Thus, they proposed a new ductile fracture model, in which a combination of the largest tensile stress criterion [2] and the maximum shear stress criterion [13] was utilized The criterion can be written as A 1- εf -σ dε + -1 τmax = I5 A2 ∫0 max A2 (2) where σmax is the largest tensile stress and τmax is the maximum shear stress In addition, A1 and A2 are material constants When the value of I5 becomes unity, a ductile fracture occurs In this study, the above ductile fracture criterion was applied to the hydro-mechanical deep drawing process of automotive steel sheets, and its reliability was verified by using the finite element calculation Hydro-mechanical deep drawing is an advanced process that combines the conventional deep drawing method with hydroforming technology Because of its advantages, such as the remarkable increase of limit drawing ratio, the low tooling cost, and the uniform thickness distribution of formed parts, the hydro-mechanical deep drawing process has been widely adopted for the forming of complex-shaped sheet metal parts [15] In this study, in order to predict the forming limit in the hydro-mechanical deep drawing of steel sheets, FLCFs of some automotive steel sheets were experimentally obtained and were compared with the fracture strains predicted from the ductile fracture criterion of Eq Then, the ductile fracture criterion was implanted into a finite element code to simulate the hydro-mechanical deep drawing process The calculation result was compared with the experimental fracture limits of the hydro-mechanical deep drawing process EXPERIMENTAL PROCEDURE The materials used in this study were three types of automotive steel sheets, all with a mm thickness The chemical compositions of the steel sheets are listed in Table Table shows the tensile properties of the materials obtained via a uniaxial tensile test The width and the gauge length of the tensile specimen were 12.5 and 50 mm, respectively Forming limit curves at fracture under various out-ofplane biaxial stretching conditions were determined by using a hemispherical punch-stretching test Rectangular blank with a side length of 200 mm was stretched by using a hemispherical punch with a diameter of 100 mm Various other specimen side lengths were used, ranging from 200 to 25 mm, so that different strain ratios could be applied and compared The imprinted surface grids on specimens were measured to determine a FLCF at the initiation of fracture The hydro-mechanical deep drawing experiments were carried out with an 800 kN-grade hydraulic press The experimental system is shown in Fig The process parameters in the hydro-mechanical deep drawing are listed in Table A blank holding force of 125 kN was used for the S1 and S2 sheets, while a 70 kN force was used for the S3 steel sheet The maximum liquid pressure of the hydro forming is normally required to increase with an increase of the drawing ratio; however, when the liquid pressure is too high, the blank may be ruptured at the die profile The liquid pressure pattern used in this study is shown in Fig In order to control the liquid pressure and the punch stroke, a servo-controlled computer system was used Table Chemical compositions of materials S1 S2 S3 C (wt.%) 0.002 0.050 0.081 Si (wt.%) 0.02 0.02 1.015 Mn (wt.%) 0.15 0.30 1.51 P (wt.%) 0.013 0.07 0.087 S (wt.%) 0.013 0.015 0.006 Ti (wt.%) 0.040 0.050 - Table Tensile properties of steel sheets S1 S2 S3 Tensile strength (MPa) 298 358 614 Uniform elongation (%) 30.5 19.7 21.6 Strength coefficient, K (MPa) 566 630.1 1090.2 Strain hardening exponent, n 0.298 0.2369 0.215 R0 R90 1.91 1.42 1.07 1.91 1.78 1.31 ... parts, the hydro- mechanical deep drawing process has been widely adopted for the forming of complex-shaped sheet metal parts [15] In this study, in order to predict the forming limit in the hydro- mechanical... combines the conventional deep drawing method with hydroforming technology Because of its advantages, such as the remarkable increase of limit drawing ratio, the low tooling cost, and the uniform thickness... implanted into a finite element code to simulate the hydro- mechanical deep drawing process The calculation result was compared with the experimental fracture limits of the hydro- mechanical deep drawing