Journal of Materials Processing Technology 210 (2010) 415–422

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Journal of Materials Processing Technology

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Development of forging process design to close internal voids

Hideki Kakimotoa,!, Takefumi Arikawaa, Yoichi Takahashib, Tatsuya Tanakac, Yutaka Imaidac

a Mechanical Working Research Section, Materials Research Laboratory, KOBE STEEL,LTD., 1-5-5 Takatsukadai, Nishi-Ku, Kobe, Hyogo 651-2271, Japanb Development Section Technology Department, Steel Casting & Forging Division, Iron and Steel Department,KOBE STEEL,LTD., 2-3-1 Shinhama, Araicho, Takasago, Hyogo 676-8670, Japanc Applied Materials Engineering Laboratory, Faculty of Engineering and Science, Doshisha University, 1-3 Tataramiyakodani, Kyotanabe, Kyoto 610-0394, Japan

a r t i c l e i n f o

Article history:Received 5 May 2009Received in revised form23 September 2009Accepted 23 September 2009

Keywords:Open-die forgingNumerical simulationProcess designVoid behavior

a b s t r a c t

In this study, the closing behavior of internal voids was examined by a deformation analysis involving the2-D finite element method (FEM), which simulates voids in steel ingots in the compression process (upsetprocess). In the compression process, a model experiment that uses internal voids was carried out toconfirm the accuracy of the deformation analysis. By comparing the model experiment with the analyticalresults, it was confirmed to simulate the internal void behavior by this analysis. The relationship betweenthe reduction ratio and the void shape/void position was investigated by the analysis. In the forgingprocess, the closing evaluation value of internal voids (Q value) was calculated by a model experimentand 3-D FEM. Using the analysis results, a limit value of the closing behavior of voids was quantified, andit is now understood that the voids close at more than Q = 0.21. In addition, the forging process of fillingthe above-mentioned value was designed by the Taguchi method. The predicted Q value in the case ofusing the Taguchi method almost corresponds to the value calculated by the deformation analysis. It wasclarified that the process is capable of being designed simply.

Crown Copyright © 2009 Published by Elsevier B.V. All rights reserved.

1. Introduction

Recent years have seen an upward tendency in the diametersof steel ingots in response to the upsizing of products in order toachieve a desired forging ratio. However, as steel ingots increasein diameter, such problems as internal voids called cavity defects,segregation, and large crystal grains become more serious. A studyconducted by Ono et al. (1995) revealed that it was difficult tohomogenize the inside of steel ingots with a press in free forging.Upset (compression) and extend forging must be performed a fewtimes to make the inside of steel ingots sound and finally manufac-ture products from them. Watanabe (2002) investigated the effectof stress and strain caused by the extend forging process on theinternal quality.

Kopp and Schultes (1982) conducted a theoretical analysisof the compression process to determine whether the qualityof large-size free-forged products was improved. Bondnar andBramfitt (1987) examined a physical model of pressure weldingusing cylindrical plasticine, Park and Yang (1997) investigatedthe effect of the surface cooling temperature of steel ingots, and

! Corresponding author.E-mail addresses: kakimoto.hideki@kobelco.com (H. Kakimoto),

arikawa.takefumi@kobelco.com (T. Arikawa), takahashi.yoichi1@kobelco.com(Y. Takahashi), tatanaka@mail.doshisha.ac.jp (T. Tanaka),yimaida@mail.doshisha.ac.jp (Y. Imaida).

Ono et al. (1994) studied the effect of the cooling of steel ingotsurfaces on the closing of internal voids through an analyticalapproach. Wang and Ren (1993) also performed an investigationinto the relationship between the strain and the closing of voids.In connection with the extend forging process, Araki et al. (1985)scrutinized the effect of various extend forging methods due toa change in the density of powder sintered compacts, Rodic etal. (1987) calculated proper operation conditions for the closingof internal voids in rolling or forging, and Sun and Guo (1987)introduced void closing parameters using the finite element anal-ysis. In addition to the above-mentioned studies, Cho et al. (1998)investigated the effect of different forging methods for extendforging on the hydrostatic stress or axial stress, and Banaszeket al. (2004) studied die shapes and the distribution characteris-tic of the reduction ratio. A report was made by Nakasaki et al.(2006) on the application of hydrostatic integral parameters torolling.

As described above, a wide range of studies has been conductedwith regard to the compression and extend forging processes alone.However, it is necessary to elucidate the deformation behavior ofinternal voids, which occur in the upper area of steel ingots whenthey are cast, and optimize each process because these voids areforwarded to the extend forging process through the compressionprocess. On the other hand, forging conditions, such as the shapeof cross-sections, the shape of dies, the reduction ratio and thetemperature distribution, differ among steel ingots, and this is anobstacle to simplifying these processes.

0924-0136/$ – see front matter. Crown Copyright © 2009 Published by Elsevier B.V. All rights reserved.doi:10.1016/j.jmatprotec.2009.09.022

416 H. Kakimoto et al. / Journal of Materials Processing Technology 210 (2010) 415–422

Fig. 1. Analytical model.

Fig. 2. Relationship between reduction ratio and void shape (d/d0 and h/h0) in thecase of analytical result and experimental result.

In this study, 2-D deformation analysis simulating internal voidsin steel ingots was carried out and the closing behavior of inter-nal voids in the compression process was examined. Regardingthe extend forging process, the closing evaluation value of inter-nal voids (Q value) was calculated and the limit value of the closingof internal voids was quantified based on the results of a modelexperiment and 3-D deformation analysis. A forging process designapproach was also developed, which easily determines the forgingconditions using quality engineering, and the effect of the forgingconditions on the closing of internal voids was studied.

2. Closing behavior of internal voids in the compressionprocess

2.1. Comparison between analytical model and modelexperiment results

The compression process requires the relationship between thepositions and sizes of voids and the reduction ratio to be clarifiedin connection with the behavior of cavity defects formed duringthe casting of steel ingots. So, the closing behavior of voids wasexamined by performing an analysis with a void whose position andsize were changed using general-purpose software (Forge2D) basedon the finite element method. Provided with material-to-materialcontact judgment and re-mesh functions, this software is capableof investigating the closing behavior of internal voids. A schematicof the analytical model is shown in Fig. 1. A 1/2 axisymmetric modelwith a simplified steel ingot shape as shown in the figure was usedfor this study.

The model experiment was first conducted to check the behav-ior of the internal void in deformation analysis. In this step, thedimensions of the void in an experimental material with a changedreduction ratio were measured with the aid of X-ray CT withoutcross-sectioning the material. Then, the material was cut, and theshape of the void in the cross-section was compared with the resultsof the analysis. The experimental specimen consists of three pieces.One is the thick-walled cylinder. And the other parts are drillingsimulated a void.

The specimen is made by combining the parts of simulated avoid and the thick-walled cylinder. Pure aluminum 1070 annealedat 450 "C for 3 h in advance was used for the dimensional mea-surement by X-ray CT. The H0/D0 of the material for the modelexperiment was defined as 2.0 for the purpose of observation from

Fig. 3. Internal void shape comparison with experimental result (left) and analytical result (right) (equivalent strain distribution).

H. Kakimoto et al. / Journal of Materials Processing Technology 210 (2010) 415–422 417

Table 1Analytical model (ingot shape H0/D0 = 1.5).

h0/d0 T/H0 d0/D0

1 1/2 0.012 1/4 0.055 0.1

0.2

the state with no strain given to the center of the material to thestate with strain given. The shape h0/d0, diameter d0/D0, and posi-tion T/H0 of the void were set at 5, 0.08, and 1/2, respectively.With regard to the friction coefficient for the deformation anal-ysis, on the other hand, the Coulomb friction ! was determined,! = 0.15 in this study, so that the maximum diameter obtained inthe model experiment would be matched. Flow stress data wasadditionally collected as material data for the analysis from a com-pression test using a test material. Eq. (1) is a flow stress equation.It was separately confirmed that the compression load measuredin the experiment and the analysis result matched to within 3%.

" = 91.1#0.287 (1)

The relationship between the reduction ratio and the diameterand height of the void in the model experiment and the deforma-tion analysis is shown in Fig. 2. In Fig. 3, the shapes of the internalvoid obtained at different reduction ratios in the model experimentand the deformation analysis are compared. From these figures, thevoid shape of the analytical result and that obtained from the exper-imental result at each reduction ratio are in close agreement witheach other, and the reduction percentage of the void height andthe increase percentage of the void diameter also match accurately.These facts indicate that the closing behavior of internal voids canbe clarified by making use of the deformation analysis.

2.2. Effect of the shapes, positions, and sizes of voids

In this study, the shape of steel ingots was kept constant,H0/D0 = 1.5, and the shape of the void (diameter: d0, height: h0)and the void central position (T) shown in Fig. 1 were changed. Theanalysis conditions are given in Table 1. A total of 24 cases (3 # 2 # 4)were calculated as shown in the table to derive the reduction ratioat which the closing behavior and area of the internal void reducedto zero at each reduction ratio (hereinafter called the limit critical

Fig. 4. Relationship between reduction ratio and void area ratio in case of changingvoid shape and position.

Fig. 5. Relationship between void shape (d0/D0) and critical upset ratio (H0/D0 = 1.5).

upset ratio).Shown in Fig. 4 is the relationship between the reduction ratio

and the area ratio of the internal void (S/S0) with different voidshapes and positions. The result implies that as the aspect ratioof the void shape (h0/d0) and the distance from the center to theposition of the void increase, the void is less likely to close.

In Fig. 5, the relationship between the void diameter/steel ingotdiameter (d0/D0) and the critical upset ratio at which the internalvoid closed under the condition of the steel ingot shape H0/D0 = 1.5and different void shapes (h0/d0) and positions (T/H0) is shown.The figure indicates that the critical upset ratio does not show asignificant change even if the void diameter (d0/D0) changes. On theother hand, as the void shape (h0/d0) increases, the critical upsetratio rises because the void becomes longer in the same directionas the compression direction. Judging from the figure, a reductionratio of at least 75% is required to close voids when the void shapeis h0/d0 = 5 or below, and the possibility that voids will completelyclose in the compression process is small.

3. Closing behavior of internal voids in the extend forgingprocess

3.1. Model experiment of internal void closing

If an internal void is large in size in the compression processas described earlier, it may remain with 35–45% of its initial areaand must, therefore, be completely closed in the following extendforging process. As the first step of this experiment, a model exper-iment was performed to make clear the closing behavior of internalvoids in the extend forging process. The shapes of the material usedfor the experiment are shown in Fig. 6. Lead was selected as thematerial because it shows a similar behavior to the deformation of

Fig. 6. Experimental material shape.

418 H. Kakimoto et al. / Journal of Materials Processing Technology 210 (2010) 415–422

Fig. 7. Appearance of forging method.

hot-rolled steel. This study considered a situation in which mate-rials underwent the extend forging process just after compression,and a situation with the shape of the cross-section changed by pre-forming. For these different situations, two models, a cylindricalmodel of an initial size of Ø 40 # L36 (Model 1) and a 35 # 35 # L36prismatic model (Model 2), were prepared. This study also assumeda void that was a through hole of 0.05 in d0/D0 and Ø 2. A schemeof the die shapes used for the experiment is shown in Fig. 7, andthe experimental conditions for each of Models 1 and 2 are statedin Table 2.

The used dies were a flat top die and a bottom die that waswider than the experimental materials. Both ends (1 and 2) werefirst pressed, followed by the central area (3), and finally either end(same position as 4:1), resulting in areas with the same reductionratio and different times of press (2 and 4) and areas with the samenumber of times of press and different reduction ratios (3 and 4).After the experiment, the materials were cross-sectioned, and thearea of the internal void was measured by measuring the longer andshorter diameters of the through hole. The relationship betweenthe reduction ratio and the internal void area ratio before and afterdeformation is shown in Fig. 8.

This result indicates that the void area ratio of both Models1 and 2 is almost the same irrespective of the number of timesof press if the total reduction ratio is the same. So, strain is con-sidered the predominating factor over the closing of voids. Givenbelow is the quadratic approximate equation with which the rela-tionship between the reduction ratio and the internal void arearatio was obtained from the minimum square method in the exper-iment using Model 2 shown in Fig. 8(B). The correlation coefficientis 0.986.

Y = 0.0027X2 $ 0.1044X + 1 (2)

where X is the reduction ratio, Y is the internal void area ratio, andX is equal to or smaller than 0.21. For the result of the experimentusing Model 1, the equation derived by translating the equationshown above in the incremental direction of the reduction ratio

Table 2Experimental conditions.

Number Press place

1 2 3 4

Redution ratio/%Model 1R-1 5 5 10 5 UpperR-2 10 10 20 10 UpperR-3 7.5 7.5 15 7.5 UpperR-4 15 15 15 – Upper and lower

Model 2S-1 5.7 5.7 11.4 5.7 UpperS-2 11.4 11.4 22.9 11.4 Upper

Fig. 8. Relationship between reduction ratio and void area ratio.

is shown in Fig. 8(A). As the result of Model 1 shows, an initialreduction ratio of about 10% does not affect the central area, but theinternal void increases in size probably because the central area issubjected to tensile stress due to the small reduction. The behaviorof the internal void area ratio after the central area was excludedis similar to that in Model 2 as a result of, in our view, an increasein the contact length between the dies and the material with anincrease in the reduction ratio.

3.2. Calculation of an internal void closing evaluation index bydeformation analysis

The quantification of the closing behavior of internal voids isan essential factor for process design for the closing of internalvoids. An internal void closing evaluation index Q utilizing Oyane’sequation has been proposed by Ono et al. (1993), and the clos-ing behavior of internal voids was quantified by the equation inthis study. The internal void closing evaluation index (hereinafterreferred to as the Q value) is defined by the equation shown below.

Q =! #f

0($"m/"eq)d#eq =

n"

i=1

($"m/"eq)i$#ieq (3)

where "m is hydrostatic stress, "eq is equivalent stress, #eq is equiv-alent strain, #f is final equivalent strain, and n is number of step.

H. Kakimoto et al. / Journal of Materials Processing Technology 210 (2010) 415–422 419

Fig. 9. Analytical model.

Fig. 10. Cross-section shape comparison with experimental result (right) and analytical result (left).

The analysis conducted in this study used the same conditions ofthe model experiment to calculate the Q value. An analytical modelis shown in Fig. 9. Using a 1/2 axisymmetric model as the analyticalmodel, void shapes were compared with a through hole present.Stress and strain components were integrated with regard to eachstep and each element using Eq. (3) shown above with no throughhole. The friction coefficient and flow stress used for the analysisare shown in Table 3. For these values, the ones calculated by Tauraet al. (1981) were used.

Representative examples of the shapes of the cross-sectionsobtained in the experiment and analysis of Models 1 and 2 areshown in Fig. 10, and the internal void area ratios obtained from theexperiment and analysis results are compared in Fig. 11. The resultshown in Fig. 11 proves good matching between the void shapeand the area ratio. The relationship between the Q value derivedfrom the analysis and the internal void area ratio obtained fromthe experiment is shown in Fig. 12. It was confirmed from the resultthat the Q value at which internal voids close in the extend forg-ing process was 0.21 or over irrespective of the initial shape of thecross-section.

3.3. Process design approach in the extend forging process

In the extend forging process, the initial state of materials cannotbe taken into account because press operators perform operationsaccording to operation instructions. In fact, however, the initialstate of materials, particularly their temperature distribution, is

Table 3Analytical conditions.

Friction coefficient ! 0.30Flow stress " (MPa) " = 46.2 # #0.194 # #̇0.026

quite different depending on the time from the end of heating tothe start of forging. Taking this fact into account, the setting of forg-ing conditions according to the state of each material is consideredan efficient approach to the closing of internal voids. However, itis difficult to analyze deformation by changing the temperaturecondition based on each material. So, this study used the qualityengineering proposed by Taguchi (1999) as a means of obtainingforging conditions in an efficient manner.

As described earlier, internal voids seem to close when the Qvalue is 0.21 or over. On the other hand, this internal void closing

Fig. 11. Void area ratio comparison with analytical result and experimental result.

420 H. Kakimoto et al. / Journal of Materials Processing Technology 210 (2010) 415–422

Fig. 12. Relationship between Q value and void area ratio of experimental result.

evaluation index is a function of equivalent strain, equivalent stress,and hydrostatic stress and greatly affected by the shape and tem-perature distribution of the material, the shapes of the dies, and thereduction ratio. It is, therefore, necessary to quantify the relation-ship between these forging conditions and the internal void closingevaluation index. In this study, a quality engineering approach wasapplied in order to quantitatively identify the effect of each factoron the internal void closing evaluation index, and a process designmethod was established using that approach.

As the first step, four factors affecting the closing of internalvoids and three levels were selected, and a deformation analysiswas conducted based on an orthogonal table (L9). Following thedeformation analysis, the sensitivity was calculated, and the degreeof its effect was examined. The four factors and their levels areshown in Table 4.

The selected factors are: (A) cross-section shape (width/height),(B) die shape, (C) reduction ratio, and (D) temperature distribu-tion. As shown in the table, two flat dies were used. Flat Die 2was 1.6 times longer than Flat Die 1 in the axial direction of thematerial. In pressing, the material was forged in the axial directionby applying pressure to the top and bottom faces and then turnedupside down and forged in the same manner. Two temperature dis-tributions inside the cross-section of the material were set: 1200 "Cuniformly over the entire cross-section, and 1200 "C at the centerand 1000 "C and 900 "C at the surface center. The minimum Q valuewas calculated in the axial direction at the center of the materialobtained from the deformation analysis. The temperature distribu-tions inside the cross-section of the material are shown in Fig. 13.The analytical model was 1/2 symmetrical as shown in the figure.

The following equation using the strain rate sensitivity index mwas adopted for the flow stress " for the deformation analysis.

" = K#m (4)

Table 4Factors and levels for Taguchi method.

Control factor Level 1 Level 2 Level 3

(A) Cross-section shape 1.00 1.25 1.50

(B) Dies shapeUpper Flat 1 Flat 1 Flat 2Lower Flat 1 Wide Flat 2

(C) Reduction (%) 10% # 2 15% # 2 20% # 2(D) Temperature distribution ("C) 1200 constant 1200–1000 1200–900

Fig. 13. Cross-sectional temperature distribution of material (cross-sectionshape = 1.00).

Table 5Example of K and m in case of 1300 "C.

Strain rate K m

0.02 15.02 0.1430.2 31.99 0.2062 40.44 0.208

where K is the constant relating to temperature and material and# is the strain rate. K and m were determined based on the resultsof compression tests that were conducted at six different temper-atures from 800 "C to 1300 "C at 100 "C intervals and three strainrates of 0.02, 0.2, and 2.

In the deformation analysis, an approximate equation was inter-polated and extrapolated. Examples of the K and m values obtainedin the compression tests are shown in Table 5. For the frictioncoefficient, the Coulomb friction coefficient ! = 0.15 obtained byKakimoto et al. (2008) in an extend forging experiment was used.

Now, the Q value is no dimension, and the flow stress ratiois important. So the units are not relevant for the general resultsachieved. A factorial effect diagram of the sensitivity in connectionwith the Q value obtained in the analysis is shown in Fig. 14, anda table of variance analysis relating to the sensitivity is given inTable 6. The results shown in the table indicate the marked effects

Fig. 14. Sensitivity for Q value.

H. Kakimoto et al. / Journal of Materials Processing Technology 210 (2010) 415–422 421

Table 6Analysis of variance table.

Factor F S V S% % (%)

A 2 22.330 11.165 22.330 4.74B 2 234.876 117.438 234.876 49.85C 2 157.474 78.737 157.474 33.42D 2 56.510 28.255 56.510 11.99e 0 0 0 0 0Total 8 471.189 – 471.189 100

of (B) die shape, (C) reduction ratio, and (D) temperature distri-bution. In quality engineering, the sensitivity is calculated on theassumption that there is no interaction. It can be said that there is nointeraction if the sensitivity matches with the predicted tendency.Contrary to this, if there is interaction, the sensitivity is significantlydeviated from the predicted result.

Judging from Fig. 14, the effect on the Q value increases in orderof the upper–lower asymmetrical die, Flat Die 2, and Flat Die 1 in(B) die shape, as the reduction ratio increases in (C) reduction ratio,and when a difference in the temperature distribution is assignedin (D) temperature distribution. On the other hand, the effect of thedifference in (A) cross-section shape on the Q value is small, whichis in agreement with the predicted result and indicates that thereis no interaction among the factors selected in this study.

The width of the sensitivity becomes narrow in order of (B) dieshape, (C) reduction ratio, (D) temperature distribution, and (A)cross-section shape, demonstrating that the degree of the effect onthe Q value decreases. With regard to the die shape, the effect of theupper–lower asymmetrical dies on the Q value is strong as alreadymentioned, and the longer one of the upper–lower asymmetricaldies exerts a greater effect on the Q value. In general, the internalequivalent strain of the material and the hydrostatic strain increasebecause the material comes closer to the plane strain state with alonger die. Additionally, when asymmetrical dies are used, asym-metrical deformation occurs and the equivalent strain increasesdue to the difference in the contact area between the dies and thematerial. The sensitivity levels of the die shapes used for this studyare as shown in Fig. 14, but are expected to considerably changeif the length of the dies is changed. The sensitivity levels tend toincrease almost linearly with an increase in the reduction ratio.More specifically, only the area close to the surface deforms andstrain does not reach the inside of the material at a low reduc-tion ratio, but the equivalent strain increases as the reduction ratiorises. Regarding the temperature distribution, it is confirmed thatthe Q value shows an upward tendency with a drop of the sur-face temperature because a difference of the flow stress arises asa result of a surface temperature drop, the widthwise deformationis restrained, and the hydrostatic stress into the material increases.Finally, the Q value tends to increase as the width and height of thematerial increase. This is probably because if the material is wide,the restraint force produced by the friction between the dies andthe material makes the material less likely to spread the width andthe hydrostatic stress into the material increases.

These facts mean that both the equivalent strain and the hydro-static stress must be increased to close internal voids. As for theforging conditions, it is desirable that the cross-section of the mate-rial be a rectangular shape that is wide in the widthwise direction,the dies be as long as possible so that the plane strain state can beachieved wherever possible, and the reduction ratio be increasedwith a temperature distribution assigned. On the other hand, it isdifficult to fulfill all equipment requirements, such as press capa-bility. For this reason, the optimum forging conditions capable ofmeeting the limit value of the Q value obtained as described earliermust be set.

In quality engineering, Qe and m can be calculated from theequation shown below assuming that the estimated Q value is Qe,

Fig. 15. Q value distribution at the material center.

the sensitivity is m, and the total average value of the sensitivityis ma, Ai, Bi, Ci, and Di are the sensitivity values of the respectivefactors at each level.

Qe = 10m/20 (5)

m = Ai + Bi + Ci + Di $ 3ma (6)

where i = 1, 2, and 3 represent the levels. The forging process designis considered feasible by selecting the level of each factor in theequation shown above with the estimated value Qe as a targetvalue. So, the level of each of the die shape, the cross-section shape,and the temperature distribution was selected from Table 4, and areduction ratio fulfilling the set target value was calculated.

In this study, Q = 0.21 obtained in the model experiment of theextend forging process was set as a target value Qe = 0.21, the actualforging process was taken into account in the selection of each fac-tor, and Level 1 (A1) showing a general cross-section shape andLevel 3 (B3) representing upper–lower flat dies were selected forthe cross-section shape and for the die shape, respectively. Addi-tionally, Level 2 (D2), or a normal operation state, was selectedfor the temperature distribution. The sensitivity of the reductionratio calculated by substituting these values into Eqs. (4) and (5)was $15.45, and a reduction ratio of 16.0% was obtained twice. Indetermining the reduction ratio from the sensitivity value, it wascalculated from the proportional distribution between levels. Thepredicted value of the above-mentioned internal void closing eval-uation index was verified by conducting a deformation analysisunder the conditions stated earlier.

The Q value distribution obtained from the deformation analysisis shown in Fig. 15. The horizontal axis in the figure shows thearea from 0.1 to 0.9 of the entire length except both ends in theaxial direction. Judging from the result, the minimum value of theQ value obtained in the deformation analysis is in close agreementwith the calculated value using the sensitivity and the Q value canbe estimated from the sensitivity value.

As a result, the process design capable of fulfilling Q = 0.21 isconsidered easily feasible by making use of the result in Fig. 14.

4. Conclusions

The closing behavior of internal voids was discussed using adeformation analysis approach. The results obtained in this studyare summarized below.

(1) As the result of an investigation into the relationship betweenthe shapes, sizes, and positions of voids and the reduction ratiothrough the deformation analysis, the reduction ratio of 75% orover is required to close voids in the compression process.

(2) The internal void closing evaluation index was quantifiedthrough the model experiment and 3-D deformation analysis,

422 H. Kakimoto et al. / Journal of Materials Processing Technology 210 (2010) 415–422

and it was confirmed that voids close in the extend forging pro-cess when the internal void closing evaluation index Q is 0.21or over.

(3) Through an examination of a forging process design approachusing quality engineering, the degree of the effect of each of thecross-section shape, the die shape, the reduction ratio, and thetemperature distribution on the closing of voids was identifiedquantitatively, making the forging process design capable offulfilling the target value feasible.

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