JOURNAL OF SCIENCE & TECHNOLOGV* No. 88 - 2HI2
NUMERICAL ANALYSIS T O DETERMINE DIE RADIUS AND BENDING ANGLE IN ROLL-BENDING PROCESS FOR SHEET M A T E R U L
PHAN TfCH S6 Dfi XAC D|NH B A N K I N H QUAY vA o6c U6N TRONG QuA TRINH U 6 N V6NG TAM K I M LOAI
Nguyen Due Toan, Banh Tien Long Hanoi University of Science and Technology Received February 8, 2012; accepted April 24, 2012
ABSTRACT
In order to obtain correctly curvature radii and 90 degree wall angles after spring-back In rot bending process when making door panel pmducts of automotive Industry, finite element method (FEM) was first used to predict spring-back occurrence by changing various die radius and bending angles. Based on the relationship between the curvature mdlusMall angle measurements afier spring- back (output data) and die radius/bending angle values (input data), a MATLAB tool is then used to express output data as functk>ns of Input data utilizing surtace Ming method. Depending on the desired shaped of products ive can easily calculate die radius and bending angle by solving system of nonlinear equattons. Finally, obtained die radii and bending angles for ratKiom cases were simulated, measumd and compared with desired ones. The simulation msults were in good egmement with the cak:ulations of die radius and bending angles.
T 6 M TAT
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1. INTRODUCTION which incorporates the shitting of a single-yield In recent years, finite elemem method surface. For this approach group, Prager [3) and (FEM) was shown as an effective method for J'^?'^'". [|1 P™P°^ ' ' " ^ '^"^^f,^
understanding and verified the cfTect of various ^ ^ ' T " ^ * ^"^ '*'^" Amstrong - Fredenck [5]
parameters on significant forming ^ ^ Chabochc [6] changed the linear model to characteristics such as ductile fracture. """''near forms by including transient behavior winkling, spring-back and so on [1].[2]. Among ^"'^. "^^ introducing an additional temi. TTie the various forming characteristics, spring-back -'dditional back stress temi. which decreases Ihe was recognized as a challenge in FEM ' ° ' ^ ' ^"^ ^^^^^ gradually with deformation, predictions. After Ihe pioneers work of FEM ^prcKluced nonlinear and smooth deformation the previous researchers shown that Ihe efTects **"""« '°^*^'"S ^"^ '^"^'^^ '^^'''"e- Nowadays ofconslitutive model on spring-back simulation ^^'^ ^PP™^^*^ ' ' ^'''^'^ " ' ^ '" commercial results are mainly significant based on the software to predict matenal behavior under correctly prediction of material behavior e.g. T ' ^ " ^ '''"^'"^ ^'^ especially spring-back stress-strain curve under reverse loading! One phenomena.
of approaches to describe the reverse loading In this study, roll-bending process (Fig.
phenomena in continuum phenomenologieal I) was proposed as a new method in order to plasticity is based on kinematic hardening, make the main dimensions of automobile door
JOURNAL OF SCIENCE & TECHNOLOGY + No. 88 - 2012 panel (Fig. 2). This process offers the
advantages of short lead times, high flexibility and lower cost for new applications. However, in roll-bending process, to achieve the desired comer radius value of products, a die radius and bending angle should be calculated carefully because of larger spring-back occurrence after bending process. But manual or experience calculations were shown as an unrealistic and low cost-effective method due to the effect of both material properties and forming process parameters on spring-back.
Fig. I Roll-bending process
Fig 2 Main dimensions of door panel.
To predict spring-back of roll-bending process, combined hardening model was applied and implemented to ABAQUS/Explicit finite element code. This model was first used to predict spring-back of successful product of roli-bending process to confirm the accuracy of prediction. Based on the agreement between simulation and experimental results, roll-
bending process is introduced to manufacture the main dimensions of door panel products with various curvature radiuses and 90 degree wall angle. Due to very big spring-back occurrence in roll-bending process, FEM spring-back predictions with several die radiuses and bending angles were simulated in order to verity the efTect of selected parameters on curvature radius and wall angle of Ihe products after spring-back. Output parameters (curvature radius and wall angle ofthe products after spring-back) were then expressed as functions of input parameters (die radius and bending angle) by utilizing least square fitting method of ihe MATLAB tool. Depending on the desired shaped of products we can easy select die radius and bending angle from relationship equations.
2. MATERIAL MODELLING
Table I Mechanical properties of tested material
Material Density (p, kg/mm') Young's modulus (E. kN/mm)
Possion's ratio Yield stress (oy.MPa)
PCM 7.8e-06 104700 0.3 165 Table 1 shows the mechanical properties of the pre-eoated material (PCM) sheet. Here, uni-axial tensile tests for a 0.5-mm-thick specimen were first conducted at capacity of 25 kN , nominal speed of 5 mm/min. The tensile specimens were cut from the sheet in parallel to the rolling direction. The parameters characterizing Ihe uniaxial-stress-plastic-strain response of the material can be experessed following Voce's hardening law Eq. (I).
CT = CT,.+^(l-exp(-Bff.^J)) (1) where A and B are the plastic coefficients. ^.EJf and CT, are the equivalent stress, equivalent strain, and tension yield stress, respectively.
2.2 Hardening model
For combined hardening model, the von- Mises yield surface both translates and expands with plastic strain and is defined as Eq. (2)
.lUllRNAl. OF SCICNCF. & TECHNOLOGY * No. 88 - 2012
A")'^4,-4, -CT*„ (2) where CT„„(£^) is llie uni-axial equivalent yield stress, and 4 is tl^c stress dllTercnce measured from the center of the yield surface, as sitown in Eq. (3), where a is the bacit stress.
4 , ' S „ - - , . . , m The deviatoric part of ihe current stress is:
S„=a.,-aJ (4) where o, om are the current values ofthe
stress and mean stress, and / is the identity matrix. The kinematic hardening evolution is depicted by back stress increment as a function of equivalent plastic strain
da,. =^(a-,. -a,,)d€^-Ya„dE^,, (5) where C and y are the unknown material coefficients refer to kinematic behavior.
QDi a u iLOt lua DLI 0.1) a t i a.i» ai»
TnMStram
Fig 3 Stress-Strain curves of PCM material al various pre-slrains
To determine material parameters, flow stress curves of tension/compression test \\:LS firstly obtained at various pre-slrains for PCM sheet (Fig. 3). Back-stress a was then obtained by fitting as shown in Fig. 4. C and j* can be determined following Eq. (6) as 8843.6 MPa and 92.2, respectively, CT,^, fitting curve in 1 ig 4 are used to determine hardening parameters A and B as 73.6 MPa and 10.2, respectively.
o = - ( l - e " ' ^ ) (6) r
Fig. 5 shows stress strain curve prediction comparing with experimental data.
TriM strain
4 Determination of material parameters Fig
from experimental data.
0 9.1a not OM OM 0.1 0.11 a u OLU a i s True Strain
Fig. 5 The predictions jor stress-strain curves at various pre-straln.
3. ROLL BENDING SIMULATION 3.1 Spring-back predictions
In order to simulate spring-back, Ihe roll- bending process is first performed in two steps with Abaqus/Explicit. The blank holder force is applied in the first step of the analysis. The force is ramped on with a smooth step definition to minimize inertia effects. In the second step ofthe analysis the roller is rotated about center of die radius following decided bending angle. The spring-back analysis is then simulated with Abaqus/Standard. The results
JOURNAL OF SCIENCE & TECHNOLOGV * No. 88 - 2012 from the forming simulation in Abaqus/Explicit
are imported into Abaqus/Standard, and a static analysis calculates the spring-back. During this step an artificial stress state that equilibrates-the imported stress state is applied automatically by Abaqus/Standard and gradually removed during the step. The displacement obtained at Ihe end of the step is the spring-back, and the stresses give the residual stress state.
Fig. 6 Deformed shape In FE simulations for roll-bending process (a) and experiment product (b)
To validate the spring-back predictions, first we simulate roll-bending process and compare simulation result with the successful result of 90 degree wall and 34 mm comer radius from experiment test with 120.1 degree bending angle and 25.2 mm die radius. Figure 6 (a) shows Ihe simulation procedures lo predict spring-back then compares with experimental product (Fig. 6 (b)). The prediction of combined hardening law was in good agreement with experimental result.
Based on the good agreement between spring-back prediction of roll-bending simulation and experimental result, we introduce roll-bending process to make main dimensions of door panel whh larger curvature radius and 90 degree wall-angle. The purpose of this study is calculating die radius and bending angle of roll-bending in order to obtain desired shape of final door panel products. Figure 7
depicts the evolution of deformed shape before and after spring-back using combined hardening law and also define process parameters of roll-bending to make the main dimensions of door panel shape.
Fig. 7 Evolution of deformed shape and process parameters definition.
3.2 Bending parameters determination To verify the effect of die radius {Rj,J) and bending angle 2 {9h..„d-ng2) on curvature radius {Rpr«j,.c<) and wall angle (0 „..,(/) of final product, several values of input parameters (Rj,.:
and Ohcmiitt^i) was selected to simulate spring- back predictions (^p„,./„f, and 0.„,ii).
Table 2 lists the selected level for parameters defined in Fig. 7. As the FE simulation using the five-level factors of die radius (R.,,,) and bending angle 2 {dh,.„j,„g2) then the full factorial design is 25 experiments.
Table 3 and 4 show FEM simulation results of the curvature radius {Rpr„j,tu) and wall angle (9„„ii) of product after spring-back vs the level factors of die radius and bending angle 2.
respectively.
JOURNAL OF .SCIENCE & TECHNOLOGV * No. 88 - 2012 Table 2 Level of die radius and bending angle 2
in FE simulation Level Factora
^'Ff (f""^)
_%«taul!*!^
1 50 0:15
2 60 0.3
3 75 0.5
4 80 0.6 J
5 IOO 0.8 Table 3 Curvature radius R p„^,u (mm) after spring-hack based on die radius and hending- angle 2
/ I . , (mm) (Rad)
0.15 0.3 0.5 0.6 0.8
50 116.6 113,9 112:5 109.3 95.2
60 190.1 180.1 159.0 144.0 123.0
75 278:4 272.1 264:7 226.1 190.4
80 339.2 336.9 321.4 313:5 238.9
100 603.2 545.5 452.5
•111.5 402.4 Table 4 Wall aiiftlf 19 ..M) (deg) after spritif'- back based <m tile i adius and benditig.atigle 2
K
(Rad) 0.15 0.3 0.5 0.6 0 8
50 90.95 95 81 105.9 115.9 134.4
60 72.2 84.1 100.2 109.3 128.7
jtr(mm) 75 54.1 60.9 75.9 85.3 104 4
80 48.9 55.1 69.1 77.7 96.5
100 19.8 28.9 45.4 53.3 70 9 In order to select die radius and bending angle 2 for desired shape, we first utilized the relationship between Ihe output results (curvature radiuses and wall angles after spring- back prediction) and the input data (die radii
and bending angles 2) as shown in table 3 and 4, then employed surface fitting method of MATLAB tool to express the output results as functions ofthe changed die radii and bending angles. The fltting melhod called ;7o/()7/n, which suggests that it is just an extension of polyfii to problems with several independent variables.
Polyfltn will allow estimating any simple polynomial model which needs to build. Of course, polyfltn will not help to decide what order polynomial mode to use. That is a problem that usually requires knowledge ofthe system, in terms of how much noise is preseni in the data. It also requires some appreciation of Ihe goals in Ihe process, and what we will do with the model. Here, we represent the curvature radii {Rp,„j^,) and wall angles (ftoff) after spring-back prediction as polyiwmial functions of die radiuses and bending angle as shown in Eq. (7 and 8). High order polynomial models are not in general something. Linear or quadratic models often are useful. They provide information about the parameters, about the relative importance of Ihe variables in a model.
R,^^, = " l + " l ( ^ ) + « j ( ^ i W . , 2 )
*o,{R,^tB^^,)*a,(R^)Ua,{e,^^,f ^^
+ft.(/WK^*™*^.) + ^(/<*,)' ^h(0^ (8) where a, and b, are fitted constants delermined hy surface fining melhod.
Fig. 8 Filling surfaces for a) curvature radius and b) wall angle.
The values of filled constants obtained Now we can calculate die radius and from surface filling were listed in lable 5 and bending angle 2 based on desired shaped of the fitting surfaces were depicted in 1 ig 8. products (e.g. various Rp„.j,^, and 0,..,,r^O
JOliRNAL OF SCIENCE & TECHNOLOGV * No. 88 - 2012 degree) using fsolve command of MATLAB
tool. The calculation results of validated cases were compared with FEM simulation measurement as shown in table 6. The simulation results were in good agreement with the calculations of die radius and bending angles by solving system of nonlinear equations Eq. (7 and 8).
Table 5 Fitting constants obtained by surface fitting method
"'"">"
^TOff a, -75.07
b, 14S3
Ol 0.43
* J - 1 3 0
a.
311 33 ftT 28 42
04 -5 35
ftv 0 10
as 0 065
ft,
-5 3E-4 On
•72 4
h
43 35
Table 6 Comparisons between calculation and simulation results
4. CONCLUSION
In this study, to predict spring-back in roll-bending process, ABAQUS version 6.10.1 was adopted and compared with successful experimetal result. This process are then applied to simulate of manufacturing door panel shape. Several values of die radiuse and bending angle were selleeted to predict curvature radius and wall angle after spring- back. Based on the relationship beween output and input data (radius and angle), surface fitting method was ultilized m formulate curvature radius and wall angle after spring-back as functions of die radius and bending angle.
Those equations can be solved by subtituting desired curvature radius and wall angle of final product to obtain die radius and bending angle.
The analysis results show that the combinations of die radius (fij„.) and bending angle i0ba<a,ns) were identified as the important selections for improving the accuracy of roll-bending process.
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Prager, W.; A new melhod of analyzing stresses and strains in work harden ing. Plastic Solids; J.
Appl. Meeh. ASME Vol. 23, pp. 493. (1956).
Ziegler, H.; A modification of Prager's hardening rule," Quart. Appl. Math Quart. Appl. Math.
Vol. 17,pp. 55, (1959).
Amstrong, P.J.; A Mathematical Representation of the Multiaxial Bauschinger Effect; CO.
Frederick, G.E.G.B. Report RD/B/N 731. 1966.
Chaboche, J.L.; Time independent constitutive theories for cyclic plasticity; Int. J. Plast. Vol. 2.
pp. 149-188,(1986).
(mm) 150 170 220 250 300
0.M (deg) 90 90 90 90 90
(mm) 56.50 60.64 72.29 79.76 92.13
(Rad) 0.341 0.421 0.612 0.717 0.869
(mm) 149.26 168.11 216.64 242.95 294 89
(dw) 91.42 93.32 93.01 91.28 89.88
Author's address: Nguyen Due Toan - Tel: (+84) 988693047 - Email: toannd-mcii^
School of Mechanical Engineering Hanoi University of Science and Technology No.l Dai Co Viel Str.. Ha Noi. Viet Nam
)mail.hut.edu.vn
