Evaluation of Hole Flangeability of Steel Sheet with respect to the Hole Processing Condition
Jong-Sup Lee
1,a, Yoon-Ki Ko
1,b, Hoon Huh
1,c, Hong-Ki Kim
2,dand Sung-Ho Park
2,e1Departmenet of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 373-1, Science Town, Daejeon, 305-701, Korea
2POSCO Technical Research Laboratories, 699, Cumho-dong, Gwangyang, Jeonnarm, 545-090, Korea
a[email protected], b[email protected], c[email protected], d[email protected],
Keywords: Hole Flangeability, Hole Expanding Ratio (HER), Ductile Fracture Criterion, Finite Element Method
Abstract. This paper is concerned with hole flangeability of steel sheet, which is evaluated by experiment and finite element analysis with respect to the hole processing condition. The hole flangeability of a material as a forming limit needs to be verified to predict and prevent the undesirable fracture during a flanging process. Hole expanding tests are carried out to identify the effect of hole processing conditions on the hole expanding ratio (HER), which is an indicator of the hole flangeability. Specimens with two different hole conditions are prepared: one is produced with punching process; and the other is reamed after punching to get smoother hole surface. Experimental results show that the facture mechanism and the HER are quite different with respect to the hole conditions. Thorough investigation of those effects is carried out with tensile tests of a specimen with notches. From the experiments, the fracture strain is obtained with different hole conditions and is used to determine the material constants of a new proposed ductile fracture criterion which is applied to finite element analyses of the hole flanging process for prediction of the HER. The experimental results are confirmed and reevaluated by the finite element analysis with the ductile fracture criterion.
Introduction
A hole flanging process is one of the sheet metal forming process, in which the hole is stretched and bended to make a flange. The flanges are used to strengthen the edges of sheet metal parts and to provide hidden joints for assembling parts by spot welding and many other joining processes. The hole flanging process involves very high tensile stress around the edge of the hole. Therefore, the major phenomenon is the tensile tearing of the flanges.
The hole flangeability, however, can not be exactly predicted by the fracture strain from a simple tensile test without an additional material test such as a hole expanding test. Some researchers have investigated the hole flanging and related processes using analytic methods or finite element methods to predict the forming limit of the hole flanging process. Yamada and Koide studied the effects of the initial yield stress and strain hardening on bore-expanding using the incremental theory of plasticity with a flat-headed cylindrical punch to determine the stress and strain distribution[1]. Wang and Wenner found that the state of stress in the flanged neck is dominantly uniaxial according to the total strain membrane theory of rigid-plasticity for analyzing the stretch flanging of a clamped sheet of an anisotropic material using a spherical punch[2]. Leu developed an elasto-plastic finite element program based on the updated Lagrangian formulation to simulate the hole flanging process of steel sheet and a relationship for estimating the maximum hole flanging ratio was derived by using the instability of the hole periphery in the hole flanging process. According to the results, the large value of the normal anisotropy R and strain-hardening exponent n increases the maximum hole-flanging
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ratio[3]. In theses studies, however, some ideal conditions were usually assumed or the conventional approaches based on the instability were not always sufficient to predict the hole flangeability.
Failure in the hole flanging process occurs due to large deformation followed by necking. The large deformation induces initiation and growth of voids and micro-cracks in metals and then the fracture occurs after coalescence of voids and necking. This phenomenon is termed as ductile fracture. Ductile damage models are developed to describe the evolution of damage during the plastic deformation and to predict the final fracture in ductile materials[4~7]. These models can be classified into two types:
coupled damage model; and uncoupled damage model. The coupled models incorporate with constitutive relations and lead to a redistribution of the stress and strain fields when damage develops[4,5]. The uncoupled models are analyzed from the stress and strain fields, but do not modify these fileds[6,7]. Takuda et al. applied the uncoupled damage model combined with the finite element analysis to the prediction of the forming limit of the hole flanging process[8,9].
In the hole expanding test, the hole expanding ratio (HER) obtained from the test is an indicator of the hole flangeability. It is noted that the HER is effected by the hole processing conditions and a higher HER may be obtained if the hole is reamed after punching to remove burrs, fractured edge and micro-cracks which is not done usually in the real process. However, the finite element analysis using the proposed ductile fracture criteria can predict only the HER of the hole with the reamed surface and can not consider the effect of burrs, micro-cracks and fractured edge of the hole. Thus, an extensive study about the effect of the hole processing condition is necessary to assess the hole flangeability accurately depending on the hole surface condition.
In this paper, hole expanding tests are carried out in order to identify the effect of the hole processing condition on the HER. Specimens with two different hole conditions are prepared: one is produced with punching process; and the other is reamed after punching to get smoother hole surface.
Experimental results show that the facture mechanism and the hole expanding ratio are quite different with respect to the hole condition. The HER of a punched specimen is much smaller than that of a reamed one due to the difference of surface roughness and initial defects. For the thorough investigation of those effects, tensile tests of a specimen with notches are performed. The fracture strain is obtained with different hole conditions and finite element analyses is carried out.
Experimental results are confirmed and reevaluated by finite element analysis of the hole flanging process with the ductile fracture criterion proposed.
Experiment
Hole expanding test. In order to investigate the effect of the hole processing condition on the hole flangeability, specimens with two different hole conditions are tested for their hole flangeability. One is produced with the punching process and the other is reamed after drilling to get smoother hole surface. In the case of punching, 8 % and 16 % of the punching clearance are used to make the hole in the specimens. Fig. 1 illustrates a schematic diagram of the tool set and the dimension of a specimen used in the hole expanding test.
Fig. 1 Schematic diagram of the tool set and the dimension of a specimen
Table 1 Experiment conditions of the hole expanding test Material Hole Processing
Condition
Punching Clearance [%]
Number of Specimen
8 8
Punching
16 8
FB590
Reaming 8 8
8 8
Punching
16 8
CT440
Reaming 8 8
The thickness of the specimens is 3.2 mm and the initial diameter of a hole is 10 mm. The punch is a conical shape of 60° vertical angle and chrome plating is treated on the surface of the punch with the intention of reducing the friction between the punch and the specimen. Table 1 denotes the experimental conditions. Testing materials are FB590 and CT440 which are hot-rolled steel sheet and have the higher hole flangeability than conventional steels. The punch speed to expand the hole of a specimen is 10mm/min. In hole expanding tests, the hole expanding ratio (HER) is an indicator of the hole flangeability of a material. The HER is calculated by Eq. 1.
(%) 100
0 0 ×
= − D
D
HER Df (1)
where D0is the initial diameter of the hole in a specimen and Df is the diameter of the hole at the fracture.
Fig. 2 shows comparison of the HER of CT440 and FB590 with respect to the hole processing condition. The HER with the reaming condition is much higher than that with the punching condition and the HER in the condition slightly increases as the punching clearance increases. The fractured shapes of FB590 shown in Fig. 3 represent that the failure mechanisms with two hole conditions are quietly different from each other. In the reaming condition, fracture occurs following necking around the hole while from the punching condition, many micro-cracks around the hole are initiated and the propagation of the cracks leads to the final fracture. Results from a simple tensile test of these materials can not explain the difference of the fracture modes between the punching and the reaming condition as well as the HER. The finite element analysis using ductile fracture criteria in only the simple tensile test cannot correctly predict the HER of two hole processing conditions. Thus, another experiment which can quantitatively estimate the effect of the hole processing condition is required to assess more accurately the hole flangeability.
0 25 50 75 150 175 200 225 250 275
FB590 CT440
Hole Expanding Ratio (%)
Material Reaming
Punching, Clearance 8%
Punching, Clearance 16%
Fig. 2 HER of CT440 and FB590 with respect to the hole processing condition
(a) (b)
Fig. 3 Fractured shapes of FB590: a) Punching (8% clearance); b) Reaming
0 1 2 3 4 5 6
0 5 10 15 20 25
SAPH440
Load (kN)
Displacement (mm) Hole Processing Condition
Reaming
Punching, Clearance 8 % Punching, Clearance 16 %
0 1 2 3 4 5 6
0 5 10 15 20 25
CT440
Load (kN)
Displacement (mm) Hole Processing Condition
Reaming
Punching, Clearance 8 % Punching, Clearance 16 %
0 1 2 3 4 5 6
0 5 10 15 20 25 30
FB590
Load (kN)
Displacement (mm) Hole Processing Condition
Reaming
Punching, Clearance 8 % Punching, Clearance 16 %
(a) (b) (c) Fig. 6 Load and displacement curves of tensile test: a) SAPH440; b)CT440; c)FB590
(a) (b) (c) (d) (e) (f)
Fig. 7 Fracture shape with respect to the hole processing condition: a) FB590, reaming; b) FB590, punching 8%; c) FB590, punching 16%; d) SAPH440, reaming; e) SAPH440, punching 8%; f) SAPH440, punching 16%
Tension test of specimens with notches. Tension tests of specimens with notches are carried out to investigate the effect of the hole processing condition on the HER. Fig. 4 shows the drawing of the specimen used in the experiment. The specimen has two notches at the center of gage section. The notches are manufactured by punching and reaming after drilling. The punching clearances of 8% and 16% are used. Testing materials are SAPH440, CT440 and FB590. SAPH440 is a hot-rolled steel sheet for the structure of an auto-body. Tensile Tests were carried out with the crosshead speed of 1mm/min and repeated six times for each experimental condition.
From these experiment results, comparisons of total elongation and the load-displacement curve are made with respect to the hole processing condition in Fig.5 and Fig. 6 respectively. Fig. 7 illustrates fracture shapes of the specimen with respect to the hole processing condition. The hole expanding test shows that the punching case has smaller total elongation and larger deviation of the total elongation than the reaming case. Same tendency of fracture mechanism with the hole expanding test is also found in Fig. 7. To utilize finite element analysis for prediction of the HER, the strain at the final fracture is measured using the grid etched on the specimen.
0 1 2 3 4 5 6
SAPH440 CT440
FB590
Total Elongation (mm)
Material
Hole Processing Condition reaming
punching, clerance 8 % punching, clerance 16 %
Fig. 5 Total elongation with repect to the hole processing condition Fig. 4 Drawing of the specimen
Finite Element Analysis using a New Ductile Fracture Criterion
The HERs with the reaming and the punching condition are reevaluated by finite element analyses of the hole expanding test using a new ductile fracture criterion. The tool of finite element analysis is ABAQUS/Standard. A finite element model of the specimen is constructed using axi-symmetry of the hole expanding test. Fig. 8 depicts flow stress and strain curves of FB590 and SAPH440 used in the finite element analysis. For the efficiency of the analysis, the blank and die of the test is not considered and the periphery of specimen is fixed. The friction coefficient between the punch and the specimen is assigned as 0.1.
For the prediction of the HER, the uncoupled damage model is applied to the finite element analysis. The uncoupled damage model suggested by Oyane[6] and Brokken[7] is modified to consider the uniaxial stress state around the hole[2] and the triaxiality ratio of the stress. The new ductile fracture criterion is represented by Eq. 2
0 0 0
3 1 1
0 max
>
=
≤
=
+
=
∫
x for x x
x for x
C d
Inew εf mean ε
σ σ σ
σ
(2)
where εf denotes the equivalent strain at which fracture occurs, ε the equivalent strain, σ the equivalent stress, σmean the mean stress, σmax the maximum principal stress and Cdenotes a material constant determined using the fracture strain from material tests.
When Inewof an element exceeds one, it is assumed that the ductile fracture occurs at the element. To determine the material constant C in Eq. 2, the fracture strain measured in the tensile test of a specimen with notches is utilized and the results is expressed in Table 2. Fig. 9 shows the deformed shape and distribution of Inewfor FB590 in the punching condition with 8% clearance.
Table 2. Fracture strains and material constants of SAPH440 and FB590
Material SAPH440 FB590
Punching Punching
Hole
condition Reaming
(8% clearance) (16%clearance) Reaming
(8%clearance) (16 %clearance)
εf 0.4925 0.3084 0.4251 0.9867 0.6010 0.6432
C 1.2086 0.6186 0.6958 2.0366 1.2020 1.2210
Fig. 9 Deformed shape and distribution of Inewfor FB590 punching (clearance 8%) at the final fracture
0.0 0.1 0.2 0.3 0.4
0 100 200 300 400 500 600 700 800
FB590 SAPH440
Flow Stress (MPa)
Plastic Strain
Fig. 8 Flow stress and plastic strain curves of FB590 and SAPH440
0 25 50 75 100 125 150 175
16 % Punching 8 % Punching
Reaming
Hole Expanding Ratio (%)
SAPH440
By Experiments By Analysis
0 25 50 75 100 125 150 175 200 225
16 % Punching 8 % Punching
Reaming
Hole Expanding Ratio (%)
FB590
By Experiments By Analysis
(a) (b)
Fig. 10 Comparison of the HER between by the experiment and by the finite element analysis: a) SAPH440; b)FB590
The evaluations of the HER by the experiment and by the finite element analysis are compared each other in Fig. 10. The comparison shows that the finite element analysis can predict the HER with respect to the hole processing condition accurately.
Conclusion
In this paper, the hole flangeability of steel sheet is evaluated by the experiment and the finite element analysis with respect to the hole processing conditions. The hole expanding ratio (HER) is measured as an indicator of the hole flangeability by the hole expanding test. Experiment results show that the failure modes of two hole processing conditions are quietly different from each other and the HER in the reaming condition has much higher value than that in the punching condition. The HER is re-estimated by finite element analyses using a new ductile fracture criterion. The fracture strain calculated from the tensile test of a specimen with notches is employed to determine the material constant of the new ductile fracture criterion. Results demonstrate that the finite element analysis can accurately predict the HER with respect to the hole processing condition.
References
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[8] H. Takuda, K. Mori, H. Fujimoto and N. Hatta: J. Mater. Process. Tech. Vol. 92-93 (1999), p. 433 [9] H. Takuda, K. Mori and N. Hatta: J. Mater. Process. Tech. Vol. 95 (1999), p.116
