THERMO-MECHANICAL MODELING OF DRAW-BEND FORMABILITY TESTS

Transcription

1 International Deep Drawing Research Group IDDRG 2009 International Conference -3 June 2009, Golden, CO, USA ABSTRACT THRMO-MCHANICAL MODLING OF DRAW-BND FORMABILITY TSTS Ji Hoon Kim I, Ji Hyun Sung 2, and R. H. Wagoner 3 I Department of Materials Science and ngineering kim.2502@osu.edu 2 Department of Mechanical ngineering sung.9@osu.edu 3 Department of Materials Science and ngineering wagoner.2@osu.edu The Ohio State University, 204 College Road, Columbus, OH 4320 USA Rolling-direction (RD) draw-bend fracture tests of dual-phase (DP) steels utilizing velocity control of both actuators revealed three patterns of failure depending on draw speed, draw speed ratio, and R/t ratio. In particular, shear failure occurs across the strip width just at the contact tangent point with the tooling. Shear failure occurs preferentially for smaller R/t and higher deformation rates. During draw bend tests, the temperature rises are significant, up 00 C before necking, with consequent loss of strength in affected regions. A coupled thermo-mechanical finite element (F) model of the draw-bend test was developed in Abaqus Standard 6.7. The model employs 5 layers of solid elements C3D8RT, which have both temperature and displacement degrees of freedom. The model is capable of representing softening and altered strain hardening of materials measured at elevated temperatures. Such capability was required because the mechanical properties of advanced high strength steels often change significantly with time and location during sheet forming processes because of significant deformation heating associated with the high plastic work involved. No account of damage mechanics or brittle fracture phenomena was taken. The simulated results were compared with companion draw-bend tests carried out over a range of process conditions. The F model predicted the observed failure types correctly except for the cases lying at the border between observed transitions between fracture types. The predicted normalized stress and displacement to failure showed good agreement with the measurements. It was concluded that coupled thermo-mechanical FM can accurately predict displacement to failure, temperatures, strain localization and formability of the two materials tested if an accurate constitutive equation is known. No accounting for internal damage is required. The results show that the unpredicted forming failures seen in die forming occur because of local temperature increases caused by the work of deformation. These temperature rises cannot currently be simulated by standard commercial sheet-forming simulation programs and do not occur in low-speed tests used to generate the fonning limit diagram (FLO), thus the predicted formability using such methods is unrealistically optimistic. Keywords: Thelmo-Mechanical Finite lement Model; Draw-Bend Fracture Test; Advanced High Strength Steel; Shear Failure; Thermally Assisted Strain Localization; Constitutive quation

2 J.II. Kim, J.II. Sung, and R. II. Wagoner. INTRODUCTION DP steels are a class of advanced high strength steel (AHSS) in wide and increasing use in the automotive industry. Depending on the application and the grade, failures in AHSS are not always able to be predicted by the usual forming simulation and application of forming limit diagrams (FLO). Such diagrams represent the forming limit based on localized deformation, or necking, which has proven successful in predicting failures for conventional sheet steels. The new type of failure, so-called "shear fracture", was observed at sharp radii where bending and unbending under tension during forming occurred [I]. The draw bend test mimics the mechanics of deformation of sheet metal as it is drawn, stretched, bent and straightened over a die radius entering a typical die cavity, Fig. I [2]. The test can produce both normal plastic localization/necking and shear fracture. For AHSS, the flow stress is affected significantly by deformation induced heating at even modest strain rates, so the constitutive equation must take into account these effects [3]. Deformation induced heating is usually expected to have a detrimental effect on ductility [4]. Original Position V2 i-:-:-: -:-:-.-.-:-~-:~ I '.~.'.'. I~~:.-:.~~~~~.~J ()Bend-/.. ~. Original U(2) Unbend Position Die Blank holder I i I ----t.-l.f ----,{- ; I I I tlx = 27 mol Final Position!. -j-:-:; ~.i. '...,... i... ' '... : : : : :' ~.... v~._+...j Figure. Schematic aldraw-bend test The objective of this research is to understand the draw-bend failures of AHSS and to improve FM predictability by taking into account thermal effect with a new 0 constitutive equation relating flow stress to strain, strain rate, and temperature

3 .I.R Kim,..-. Sung. and R. -.Wagoner 2. MATRIALS A dual-phase (DP) steel Dr 980 was used for this study. In order to capture the essential behavior, a novel constitutive equation ("H/V") relating flow stress to strain, strain rate, and temperature was developed as follows: ( Co J CJ(c,i, T) = [a(t)fho"o + (- a(t)). f"oce]';-. [- D(T - Tin)] ill (I) where a(t)=a,-a 2 (T-T R l')'.i~ollo is Hollomon equation (0"= Ks"),.I;'oce is Voce equation (0" = A(I- Be-ell»), T and T RT are current and room temperature, respectively, m is a rate sensitivity parameter varying with strain rate (m =a[logi]+b), and D, ai' and a, are material constants. The material parameters used in this study are listed in Table I. Table. Material Parameters/or DP 980. K (MPa) n A (MPa) B C a,, a 2 a b D i o (S.l) XPRIMNTAL PROCDUR 3. Draw-bend fracture test Novel draw-bend fracture (DBF) testing is based on a modification of draw-bend tests that have been used for friction and springback testing, as shown in Fig. I. For typical springback or friction applications, a strip of sheet metal is constrained and bent 90 degree around a roller by two grips. While one (back) grip applies constant back force to the sample, the other (front) grip pulls the sample away from the roller at a constant speed, V;, so that material moves over the roller under controlled conditions. This test has been applied for draw-bend fracture testing under constant back force [5,6]. In DBF test developed here, the speed of the back grip, 7 2, is controlled instead of the force as shown in Fig. I. This guarantees the forward movement of sample, thus fracture always occurs toward the front leg of the specimen (which is not guaranteed otherwise, leading to difficult-to-interpret results). Sheet samples having width of 25mm are used with fixed rollers and lubricants to mimic typical fonning processes. The test proceeds until the sample fails, either by tensile plastic localization/necking or by shear failure, depending on the material properties and testing conditions (die radius, draw speeds, sheet thickness ). 3.2 Thermo-mechanical finite clement analysis A thermo-mechanical finite element model of draw-bend tests was developed to investigate the failure mechanisms of AHSS deformation, as shown in Fig. 3. The model accounts for deformation heating and heat transfer and is capable of representing softening and altered strain hardening of materials measured at elevated temperatures. Such capability was required because... 50S...

4 J.I-I. Kim, J.I-I. Sung, and R. H. Wagoner temperatures rise much beyond room temperature during draw-bend tests by deformation heating. A symmetric 3D solid model (C3D8RT) was used with 5 layers through thickness in Abaqus 6.7 Standard. Isotropic yield and isotropic hardening were assumed for simplicity. Thermal coefficients were measured from independent experiments or obtained from the literatures. The friction coefficient was based on a comparison of forces of front grip and back grip between F simulation and DBF test using Coulomb friction law. / hmetal,air = 20W/m 2 K Abaqus Standard (V6.7) 3D solid elements (C3D8RT), 5 layers Von Mises, isotropic hardening Symmetric model hmetal,metal = 5kW/m 2 K 4. RSULTS Figure 2. The coupled thermo-mechanicaljinite element modelfor the draw-bend test DBF tests of the DP steel revealed three patterns of failure based on process conditions as shown in Fig. 3: Type I is a standard tensile failure far removed from small radius bending regions. It occurs in material that has not been bent and unbent over the die radius. Type III is what is often called "shear failure" that occurs at the exit tangent point with little deformation in the width direction, in a direction perpendicular to the strip axis. Type II has a mixed appearance that appears to initiate like Type III but propagates at an angle in material that has been drawn over the tooling. Type II and Type III failures, here associated with what are typically called shear failures, occur preferentially for smaller Rlt and higher deformation rates, Figs. 2 and 3. In order to understand the origin of the phenomena involved, temperatures were measured during draw bend deformation using thermocouples and an infrared camera. The temperature rises were significant, up 00 C at locations near from the localization depending on failure type and forming rate. Therefore, thenno-mechanical analysis using temperature-sensitive constitutive relations is essential to understanding the behavior _...

5 J.I-I. Kim, HI. Sung, and R. -.Wagoner Figure 3. Three/ai/lire types Fig. 4 shows the normalized stress-front displacement curve for the case with V; = 5lmm / S, V 2 / V; = 0, and R/t=2.2. The normalized stress is defined as the front force divided by the product of the initial cross-section area and the ultimate tensile strength (=997 MPa). The stress increases as the sheet rolls over the roller and the sheet fails at the roller (Type TIl)

6 J.II. Kim, J.H. Sung, and R. H. Wagoner II) II) Q) s.. ṯj) Thermo-Mechanical (Type III) '0 Q).~ 0.6 Measured ca (Type III) s z DP980(D)-GA-.45mm V =5mmls, V 2 N =0 0.2 Rt= _~L. _._,---. _._._._L. _._._._ ~l-_ I J I_J_ Front Displacement (mm) Figure 4. Normalized stress vs..ii'ont displacement. Fig. 5a shows the variation of maximum normalized stress for ~ / ~ = O. For the small R/t ratios (R/t < 6), the Type III failure was observed and the maximum normalized stress increases as R/t increases. For larger R/t ratios (R/t > 6), the Type I failure was observed and the maximum normalized stress remained constant, close to the ultimate tensile strength. Fig. 5b shows the variation of displacement to failure for V 2 / ~ = 0. A similar pattern was observed: for the small R/t ratios (R/t < 6), the displacement to failure increases as R/t increases, while for larger R/t ratios (R/t > 6), the displacement to failure showed no dependence on R/t. Fig. 6a shows the variation of maximum normalized stress for V 2 / ~ = 0.3. The stress kept increasing with a decreasing slope as R/t increases and the failure type changes from III to II at R/t of 6. The displacement to failure for ~ / ~ = 0.3 increases as R/t increases, as shown in Fig. 6b

7 J.l. Kim. J.I-I. Sung. and R. H. Wagoner til '------' ~ en "0 Q).~ 0.95 en Ẹ.. o z :J 0.9 'x en 0.85 ~ \,. Measured Type III ~ Type III,F Simulated Measured fitypel "...". Type I DP980(D)-GA-.45mm V = 5 mm/s V N = o R I t (a) , 50 Measured 40 Type III - ~ :J '--' Type I ~. \ F Simulated DP980(D)-GA-.45mm V = 5 mm/s V N = R I t (b) Figure 5. (a) Normalized maximum stress and (b) displacement to/ai/ure with V 2 / ~ =

8 J.B. Kim, J.B. Sung, and R. B. Wagoner C/) C/) <II..... en 'U <II.~ 0.95 l:l Ẹ.. 0 z 0.9 ::J 'x l:l 0.85 " :2: Type\\:. Measured 2 ~t Measured Type II. " F Simulated 4 " Type I DP980(D)-GA-.45mm V = 5 mm/s V IV = (aj R / t ,--, ----,- -,- -~ _., -, Type I F Simulated ,- -,- -_.,--," --,--,- 20- DP980(D)-GA-.45mm V = 5 mm/s V IV = o o (b) R / t Figure 6. (a) Normalized maximllm stress and (b) displacement to/ai/lire with V 2 / V, = 0.3. The stress-displacement curve predicted using the thermo-mechanical model compared well with the measurement, as shown in Fig. 4, while the isothermal model over-predicted the displacement to failure by 50%. The predicted variation of maximum stresses compared well with the measurements, as shown in Figs. 5a and 6a. When V 2 / V,= 0, the thenno-mechanical model correctly predicted the failure types and captured the transition from Type III to Type I as R/t increases, as shown in

9 .-.Kim,.-.Sung, and R. -.Wagoner Fig. Sa. When V 2 / ~ = 0.3, however, the thermo-mechanical model did not predicted the observed Type II failures, as shown in Fig. 6a. The predicted displacement to failure showed good agreements with the measurements in both cases, regardless of the failure type, as shown in Figs. 5b and 6b. 5. CONCLUSIONS In order to understand the fundamental mechanisms of the formability behavior of AHSS, novel bi-velocity controlled draw-bend tests were developed and three types of failure including the shear failure were reproduced. A coupled thermo-mechanical finite element model of the draw-bend test was constructed to predict the failures. From the experiments and simulations, the following conclusions were drawn: Three kinds of failure patterns were observed for the dual phase steel DP 980 depending on process parameters (radius-to-thickness ratio, drawing speed, and drawing ratio): Type I is a standard tensile failure, Type III is the shear failure that occurs in a bending region as material is drawn over a die radius, and Type II is a mixed failure that initiates because of acute bending but propagates more like a tensile failure. Type II or Type III failures occur for small R/t and or higher deformation rates. The measured temperature rises during draw-bend are significant, up to 00 ac. The developed thermo-mechanical model accurately predicted the failure type, maximum stress, and displacement to failure for DP 980, whereas the isothermal simulations over-predicted the displacement to failure by 00%. This result suggests that thennally assisted strain localization controls the type of failure and its time of occurrence. No damage mechanics is required to understand and predict the failure ofdp ACKNOWLDGMNTS This work was supported cooperatively by the Department of nergy (Contract D-FC26-020R229I 0), the Auto/Steel Partnership, the National Science Foundation (Grant CMMI ), and the Transportation Research ndowment Program at the Ohio State University. This work was supported in part by an allocation of computing time from the Ohio Supercomputer Center (PAS0080). We are grateful to Amitesh Madeshia for early developments of, and measurements using, the fixed-velocity, draw-bend formability test. 7. RFRNCS I. R.H. Wagoner: "Fundamental research issues", Proc. Of NSF Workshop, Arlington, VA, Oct , F.F. Damborg, R.H. Wagoner, J. Danckert, and O.K. Matlock: "Stretch bend formability", Ph.D. Dissertation, Aalborg University, Aalborg, Denmark, S.l. Kim, Y. Lee, and S.M. Byon: "Study on constitutive relation of AISI 440 steel subject to large strain at elevated temperatures", Journal of Material Processing Technology 40 (2003) Y. Gao and R.H. Wagoner: "A simplified model of heat generation during the uniaxial tensile test" Metallurgical. Transactions A 8A (987)

10 J.H. Kim, J.I-I. Sung, and R. H. Wagoner 5. F.F. Damborg, R.H. Wagoner, K.B. Nielsen, J. Danckert: "Application of ductile fracture criteria to bending under tension", IDDRG 98; Brussels; Belgium; June 7-9, 998, F.F. Damborg: "Prediction of fracture in bending-under-tension", Riso National Laboratory, Modelling of Structure and Mechanics of Materials from Microscale to Product (Denmark), Sept. 998,