2018 Volume 58 Issue 6 Pages 1102-1107
Since voids in a billet or an ingot are detrimental under tensile stress, they are closed by forging or rolling through a combination of collapse and contraction. In plane-strain forging or rolling, a cylindrical void or through-hole was found experimentally as well as analytically to be closed as the effective strain at the center of the void reached a certain value. In the present investigation, this finding was further examined for transverse forging, axial rolling and axial forging, in which the void was elongated or shortened in length. Since strain as well as stress components in length were irrelevant to a description of cross sectional changes, a concept of the planar effective strain and the planar hydrostatic stress was introduced. As a result, void closure on cross section was able to be predicted by the planar effective strain and the normalized planar hydrostatic stress at the center of the cross section, which were obtained from an analysis of non-void model. However, there were two exceptions; one was the case in which the planar hydrostatic stress was positive in sign and the other was the axial forging in which the void never collapsed on cross section.
Voids are often found in a billet or an ingot that evolved due to decreased gas solubility and volume contraction during cooling and solidification in manufacturing. Since they are detrimental to tensile or fatigue strength, they are usually required to be closed by subsequent processes such as forging or rolling.
Many studies have been performed to understand void closure during these processes. Depending upon the point of view, the studies can be grouped into three categories: general processes where void closure is progressed by a combination of contraction and collapse, collapse-dominant processes and contraction-dominant processes. In this context, contraction means a decrease in size that develops by hydrostatic stress while collapse means a change in shape that develops by deviatoric stress around a void. In the first category of studies, large reductions in height were suggested since the rate of void closure increased with the reduction in height. Also wide dies and rolls were recommended to develop high hydrostatic stress in magnitude.1,2,3,4) In addition, a sufficient time under high hydrostatic stress was found important for effective welding of closed voids.5) Asymmetric anvils in the initial stage and flat anvils in the final stage were recommended to enhance void closure in forging.6) Process parameters of reduction ratio, aspect ratio of cross section and cooling time were found important for void closure in forging of an ingot.7) Void closure at the middle layer of a heavy slab was difficult to be obtained in rolling where the effective strain and hydrostatic stress were smallest in magnitude.8) The rate of void closure was found to be related to the effective strain and the time integration of hydrostatic stress in forging of an ingot.9) Void closure was predicted as a parameter reached a certain limit in forging of an ingot.10) The progress in void closure for spherical and cylindrical voids was predicted by paths of strain and hydrostatic stress in plane-strain forging and rolling.11,12,13)
In the second category, the aspect ratios in a range of 1–1.5 on the cross section of a bloom and process conditions to develop large spread were recommended in rolling.14,15,16) The rate of void closure was related to the effective strain in forging of an ingot.17) Differential-speed rolling was found to be effective for thin strips to achieve void closure in the middle layer.18) In the third category, V-shaped dies were found to be beneficial for void closure at the center in forging of an ingot.19) Void closure at the center of an ingot was predicted by hydrostatic stress or volumetric strain.20,21) For reference, void closure was found to be very difficult by hydrostatic stress only in compaction of porous metals.22,23,24,25)
As an extension of the previous study,12) closure of a cylindrical through-hole was further investigated in the present study for other types of deformation, such as transverse forging, axial rolling and axial forging. A commercial FEM code DEFORM based on the rigid-plastic finite-element method was utilized for the purpose. As a result, a criterion for void closure was obtained that was represented by the planar effective strain and the normalized planar hydrostatic stress.
Closure of a cylindrical void in general is progressed through a combination of contraction and collapse on cross section. Collapse was found to be more effective for void closure in a practical point of view.12,18) As a void is smaller in size, its existence becomes less influential to the global stress distribution. Thus, the progress in void closure can be predicted by the stress and strain paths at the location of a void during deformation which can be obtained from an analysis of a non-void model. In fact, void closure in plane-strain forging was predicted by the effective strain under a certain range of hydrostatic stress.6,11,12,13,17) Also the effective strain for void closure was found to be dependent upon the aspect ratio of a cross section of a void, but not the size of the cross section. It is reminded that the effective strain is a scalar form of the integration of incremental plastic strains along the stress path during deformation.
In plane-strain forging of the rectangular block in Fig. 1(a), where relations of εy = −εz and εx = 0 are maintained, the void becomes elliptic in cross section and gradually closes on the y-z cross section. Since shear strain on the cross section helps to collapse, it should be considered in the prediction of void closure. On the other hand, in transverse forging of the block, where relations of εz = −(εx + εy) with εx>0 and εy>0 are maintained, εz is shared by εx and εy in magnitude. Compared to the plane-strain forging, the cross section becomes less elliptic due to the positive strain of εx, and thus collapses less. As a result, the effective strain for void closure increases. Since strain and stress components in x-axis are irrelevant to a description of the progress in void closure on cross section, a concept of the incremental planar effective strain and the planar hydrostatic stress was introduced in the present investigation. They are defined by Eqs. (1) and (2), respectively, for transverse forging of the rectangular block.
Cylindrical voids in blocks: (a) rectangular block and (b) cylindrical block.
In axial forging of the cylindrical block in Fig. 1(b), where relations of εz = −(εr + εθ) with εr = εθ>0 are maintained, a cross section of the void may increase or decrease in radius depending upon the friction condition. However, the void would not be closed even under a high reduction in height since no collapse is expected to take place on cross section.
In general, metal forming processes to close voids in steel billets are carried out in a range of 900–1200°C. A higher temperature is recommended for effective welding at closed voids although more oxidation takes place on the surface. In the present study, numerical analyses were performed for transverse forging and axial rolling of the rectangular block in Fig. 1(a), and axial forging of the cylindrical block in Fig. 2(b) at 1100°C. The material was assumed AISI-1015 of which the flow stress at the temperature was represented by (MPa). The block was deformed in a short period of time and an isothermal condition was assumed in the numerical analysis neglecting heat transfer. As most of bulk-metal forming analyses, the shear friction was assumed in the present investigation. In general, the friction factors of 0.4 and 0.7 are used for good and poor lubrications, respectively, in hot forming.
Comparison of experiment with numerical analysis on the progress in void closure.12)
As shown in Fig. 2, numerical analysis of void closure was in good agreement with experiment in plane-strain forging.12) Plasticine specimens were compressed in a die set of transparent acrylic under plane strain conditions and the progress in void closure was analyzed with the friction factor of 0.7 at the interface. The curves of two different voids in diameter from experiment are almost identical, revealing that void closure is independent of the size of a void. The major axis increased and then decreased while the minor axis decreased consistently during the progress in void closure. Thus, the rate of closure increased as the reduction in height increased, revealing that collapse became dominant in the final stage of void closure.
Three dimensional analyses were performed for transverse forging of the rectangular block under different friction factors. The block of 50 mm in length, 20 mm in width and 20 mm in height was forged between two flat dies. The top die moved at a speed of 20 mm/s while the bottom die was stationary. The deformed shape at 40% reduction in height is shown in Fig. 3, where the void is through the block in x direction at the center of the Y-Z cross section. Voids in a billet in general are in a range from tens to hundreds of micrometers in size. The initial cross section of the void was assumed as a circle of 0.5 mm in diameter for convenience of mesh generation. The same analyses were also performed for a non-void model to obtain values of stress and strain at the location of a void.
Deformed shape at 40% reduction in height (m=0.4).
The progress in void closure was predicted for different friction factors, as shown in Fig. 4. The cross sections of the void at the middle, quarter and end planes became more elliptic as the reduction in height increased. All of them closed except the one on the end plane with the friction factor of 0.7.
Progresses in void closure under different friction factors: (a) m = 0.4 and (b) m = 0.7.
Variations of the major and minor axes are shown in Fig. 5 while those of the planar effective strain and εx are shown in Fig. 6. When the friction factor was 0.4, the cross sections closed at 18.5%, 22.5% and 36% reduction in height at the mid, the quarter and the end planes, respectively. Corresponding values of the planar effective strains were 0.31, 0.32 and 0.33, respectively and those of the normalized planar hydrostatic stresses were 1.0, 0.8 and 0.2, respectively. The normalized planar hydrostatic stress is the planar hydrostatic stress divided by the flow stress at the location. On the other hand, when the friction factor was 0.7, they closed at 13.5% and 17% reduction in height at the mid and quarter planes, respectively. Corresponding values of the planar effective strains were 0.3 for both and those of the normalized planar hydrostatic stresses were 1.1 and 1.0, respectively.
Variations in major and minor axes of a cross section: (a) m = 0.4 and (b) m = 0.7.
Variations in the effective strain and εx: (a) m = 0.4 and (b) m = 0.7.
However, void closure was incomplete on the end plane at 40% reduction in height although the planar effective strain increased to 0.33. It was due to the fact that hydrostatic stress became positive in sign from 25% reduction in height as shown in Fig. 7. The positive hydrostatic stress also caused a decrease in the εx variation with the reduction in height in Fig. 6(b).
Variations of hydrostatic stress, εy and εz at the center on the end plane (m= 0.7).
As shown in Fig. 8, an axial rolling of a block was analyzed in three dimensions under different friction conditions. The block contained a cylindrical void of 0.5 mm in diameter through the block in x direction at the center of the Y-Z cross section. The block was rolled by two identical rolls of 500 mm in diameter rotating at a speed of 0.3 rad/s. The same analyses were also performed for a non-void model to obtain values of stress and strain at the location of a void.
A block with FEM meshes in axial rolling.
The progresses in void closure for different rolling conditions were predicted, as shown in Fig. 9. The void gradually closed on cross section from the entrance to the exit. From the top to the bottom among the cases in Fig. 9(a), where the block was 50 mm in width and 3 mm in thickness, the planar effective strains at the exit were 0.17, 0.17, 0.23 and 0.23, respectively and corresponding values of the normalized planar hydrostatic stress were 1.7, 2.3, 1.9 and 2.8, respectively. Void closure was achieved only in the case at the bottom where hydrostatic stress was large in magnitude. On the other hand, from the top to the bottom among the cases in Fig. 9(b), where the block was 200 mm in width and 30 mm in thickness, the planar effective strains at the exit were 0.28, 0.28, 0.28 and 0.37, respectively and corresponding values of the normalized planar hydrostatic stresses were 1.2, 0.8, 1.0 and 1.2, respectively. Void closure was achieved only in the case at the bottom; the void closed as the planar effective strain reached 0.32 in the middle of the deformation zone during the third pass. Comparing the first two cases in Fig. 9(b), single-pass is more effective than multi-pass for void closure under the same reduction in thickness.
Progress in void closure: (a) wo = 50 mm, to = 3 mm and (b) wo = 200 mm, to = 30 mm.
Variations of the aspect ratios of the cross section for the cases in Fig. 9(a) are presented in Fig. 10. In the first three cases, the aspect ratios increased to 3, 4.7 and 7.7, respectively, while that of the last increased abruptly in the middle of the deformation zone. Large reductions in thickness or high friction conditions are noted to promote void closure.
Variations of the aspect ratio of a cross section from the entrance to exit.
Axial forging of a cylindrical block containing a spherical void at the center was analyzed in the present study for comparison with experimental data available in literature.10) The block was made of aluminum 1070 annealed at 450°C for 3 hours and dimensional measurement was carried out by X-ray CT. The block was 50 mm in diameter and 100 mm in height, while the void was 4 mm in diameter. The progress in void closure was predicted with the friction factor of 0.7 at the interface. As shown in Fig. 11, results of the analysis were in good agreement with those of experiment. Here, d and h stand for the horizontal and vertical lengths of the void, respectively.
Comparison of analytical results with experimental data.
Other analytical study was also investigated in which the voids were different in aspect ratio as well as location.10) The results are summarized in Table 1. The reduction in height for void closure increased as the aspect ratio increased or the location was distant from the center. However, the effective strain for void closure was noted to be almost constant for the voids with the same aspect ratio regardless their locations. This fact agrees with those found in the past works.12)
Axial forging of a cylindrical block in Fig. 1(b) was analyzed. The block was 20 mm in diameter and 50 mm in height, and the cylindrical void was 0.5 mm in diameter. Since the aspect ratio of the void was as great as 100, the effective strain required for void closure was expected to be very large according to the data in Table 1, if the void were ever closed. The same analyses were also performed for a non-void model to obtain values of stress and strain at the location of a void.
As shown in Fig. 12(a), six locations were selected on the void surface and their variations in radial coordinate were predicted. In this process, the radial and circumferential strains were positive and thus the void was expected to increase in radius. Vertical cross sections of the cylinder at 80% reduction in height under different friction conditions are shown in Figs. 12(b) and 12(c). As expected, the void never closed at all since it did not collapse on horizontal cross section. However, the void was a little narrower under high friction condition. In practice, an ingot undergoes an extensive axial forging for homogenization of grains and microstructure and then a series of side-pressing for void closure.
Axial compression of a cylinder containing a cylindrical void: (a) initial stage, (b) 80% reduction in height with m = 0.4 and (c) 80% reduction in height with m = 0.7.
Variations of the six locations in radial coordinate are presented in Fig. 13. The one on the surface decreased consistently but others increased up to 60–70% reduction in height, where the diameter-to-height ratio was about 1.6–2.4, and then decreased.
Variations in radial coordinate during axial forging: (a) m = 0.4 and (b) m = 0.7.
Values of the planar effective strain required for void closure obtained in the present study are plotted with those of the previous studies in Fig. 14. The planar effective strain decreases as the normalized planar hydrostatic stress increases in magnitude. The normalized planar hydrostatic stress for void closure without the planar effective strain was found to be 5 or more, which was in good agreement with the studies of porous metals.22,23,24,25) Void closure is dominated by collapse under low hydrostatic stress while it is dominated by contraction under high hydrostatic stress in magnitude.
A criterion for void closure.
A cylindrical through-hole in a billet or an ingot was found to close by transverse forging or axial rolling, but not by axial forging. The void gradually closed on cross section by a combination of collapse and contraction while being elongated in length. Since strain and stress components in length direction were irrelevant to a description of cross sectional changes, a concept of the planar effective strain and the planar hydrostatic stress was introduced. The planar effective strain for void closure was found to be about 0.27–0.33 under low magnitudes of the planar hydrostatic stress. It decreased as the planar hydrostatic stress increased in magnitude. Without the planar effective strain, the normalized planar hydrostatic stress for void closure was found out to be 5 or more.
There was an abnormal situation on the end plane in transverse forging under high friction condition where hydrostatic stress became positive in sign during deformation. In result, void closure was incomplete although the planar effective strain increased to 0.33. Also, in axial compression, the void never closed since it never collapsed on cross section. It confirmed the fact that a void hardly closes by contraction only.
This research was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (NRF-2015R1D1A1A09058893). This work was also supported by 2017 Hongik University Research Fund. The author appreciates H. Shin and W. Jung for their assistance in preparing the manuscript.