称号及び氏名

博士（工学）Sung Wook Chung

学位授与の日付

平成 17 年 1 月 31 日

論文名「Study on Analyses of Plastic Deformation of Al- and Mg- Alloys
by Using Finite Controlled Volume Method Simulation」（有限差分法シミュレーションによるアルミニウムおよびマグネシウム合金の塑性変形解析に関する研究）

論文審査委員

主査

東健司

副査

今野豊彦

副査

高杉隆幸

Summary
Most of the industry (specially the steels, automobiles, aircrafts, railways) deals
the structural materials not only as tools but also as its bodies or frames. Recently,
the materials designers are subjected to relieve energy consumption as possible forthe energy efficiency and environmental friendliness. Light metals such as Al or Mg
are expected as next generation structural materials with its lightness and highspecific strength. The low density with sufficient stiffening can decrease the energy
to move the structure. Up to date, plenty of works have been carried out tounderstand the plastic deformation on these metals.
Plastic deformation depends on its deformation mechanisms in metal flow whichhave been reported as followed; diffusional creep, grain boundary sliding, slip at
high or elevated temperatures, and slip, twin at low temperatures. Eachdeformation mechanism has its constitutive equation which explains the metal’splastic deformation in the relationship among the stress, strain rate, temperatureand grain size. These constitutive equations can be applied to predict any material’s
flow behavior at high temperatures or superplastic behavior with limited number ofsome essential experiments.
The finite element method simulation, which was modeled with constitutive
equation, has been used to understand the plastic deformation of metals. By
accompanying appropriate simulation analysis to experiments, one can achieve theunderstandings on the plastic deformation behavior of interesting materials faster,easily and cost-effectively because of extensively simplified experimental steps.

However, this computer-aided analysis has shown lack of applicability because of
exponentially increasing calculation performance to perform large plastic
deformation. Therefore, a study to analyze high-strain plastic deformation withmore enhanced method than finite element method is required.
In this work, the author chose the finite controlled volume method code
(MSC.SuperForgeTM) for simulation analyses in order to understand the plastic
deformation behavior of light metals like Al or Mg alloys, and successfully
performed various high-strain metalworking simulations. For example, the equal
channel angular extrusion, the double shear extrusion and the superplastic forging,which have been recently issued in academic or industrial needs, were analyzed inthis work. With direct or indirect, confirming experiments for the simulation, more
realistic modelings were attempted and analyzed.
This thesis includes 7 chapters.
In chapter 1, the backgrounds of choosing light metals (Al, Mg alloys) werepresented as the next generation for strategic structural material. And therelationship between the plastic deformation and deformation mechanism wasrepresented with the constitutive equations and the deformation mechanism map.
Brief introduction to finite element method and finite controlled volume method
simulations were presented. These will be the bases of modeling of plasticdeformation.
In chapter 2, the full 3-dimensional finite controlled volume method simulation
successfully analyzed the high-strain plastic deformation of equal channel angular
extrusion, while the conventional finite element method simulation for the3-dimensional high-strain plastic deformation has been recognized as very difficult
work. The instantaneous strain, stress, strain rate and temperature distributions
during the equal channel angular extrusion processing were visualized. The
inhomogeneous strain distributions (0.4 ~ 0.8) at the cross-sectional plane toextrusion direction after 1 pass were detected. The ram speed affects on the stressor temperature distributions; faster ram speed (20 mm/s) caused low heatdissipation during deformation, so the material’s flow stress decreased slightly withincreased temperature, on the contrary, slow ram speed (1 mm/s) caused sufficientheat dissipation and subsequently increased flow stress with decreasing
temperature.

In chapter 3, another high-strain plastic deformation (the double shear extrusion)
was analyzed with the finite controlled volume method simulation by using
conventional constitutive modeling. 2-dimensional axi-symmetric finite controlled
volume method simulations were carried out in order to visualize the proper die
geometries at various parametric conditions for the double shear extrusion. The
instantaneous strain distributions along the thickness of the pipe and high effective
strains (about 2 ~ 4) were detected from the parametric simulations. A round outertaper resulted in a more homogeneous distribution than with a linear outer taper.
Applying smaller taper rather than raising temperature could decrease theinhomogeneity of the strain distribution. Moreover, dead zone’s possibility wasexpected in the die with no taper from the distributions of metal flow vector andstrain rate at the area where deformed firstly. When there was no outer taper, metal
flow was retarded at the corner, which increased the possibility of a dead-zone
forming. This indicates the need for a small taper to allow smooth metal flow during
double shear extrusion. Optimum die geometry could be predicted for the double
shear extrusion from the results of the instantaneous strain distribution. When wechanged width of the space, the best die geometry was that has narrow space after
upsetting, then wide space between inner and outer walls, smaller outer taper andlarge inner taper. Because the strain distribution was higher and homogeneous, andthere were no gaps in the inner wall of the pipe and die.
In chapter 4, an analysis linking the results by experiments and those by
simulation was conducted. Full 3-dimensional finite controlled volume method
simulation for equal channel angular extrusion process was carried out. It
represented the non-uniform deformation by detecting regional gradients from theinner arc to the outer arc area. A prolonged strain contour may come from backward
dragging force caused by friction on the material/die interface. Particle tracking
analyses showed similar to the contoured results but presented more detailed
histories of effective strain and stress for any local position. Load-stroke and grid
distortions could be visualized from 3-dimensional symmetric simulation, whichshowed slight flow-localization. The Vickers hardness results supported the non-uniform deformation during 1 pass of equal channel angular extrusion correlatingwith simulation results of effective strain and effective stress distribution. The local
instantaneous strain distribution along the line from top and bottom of the rod
obtained by finite controlled volume method simulation was in line with thehardness results for the actual equal channel angular extrusion in Al-Mg alloy.
Moreover, higher hardness values in the backward region could be explained byhydrostatic stress state before the deforming zone. In this work, the reliability
between simulation and experiment has been confirmed.
In chapter 5, another analysis linking experiment and simulation was carried out
for superplastic forging. The changes in mechanical properties such as effective
strain or stress distributions were discovered by 3-dimensional finite controlled
volume simulation of virtual forging for Zn-22Al (wt%) eutectoid alloys. Forging
simulations on Zn-22Al eutectoid alloys, which have different microstructurestransformed by different thermo-mechanical controlling processes, were carried out.
Two models, which were based on constitutive equations of creep or grain boundary
sliding, resulted local instability in the high strain rate region (the corner) in thefinite controlled volume method simulation on the seismic damper of Zn-22Al alloy.
Higher and concentrated strain distribution, lower level of stress distribution, andhigher strain rate were detected at the corner. The followed cold forging of seismic
dampers confirmed the prediction of simulation. The actual forging experiments
confirmed that microstructure played a great role in superplastic forging. The
corner where most severe deformation is expected showed low temperature
superplasticity in the extruded Zn-22Al, on the contrary, the corner in the rolled one
showed not sufficient formability. A proper thermo-mechanical controlling
processed one with fine grain size and non-lamella structure showed low-leveledand uniform deformation in effective stress. However, another sample, which had
relatively large grain size and ~ 15 vol% lamella structure, required more higher
load to be deformed.
In chapter 6, a modeling considering dynamic recrystallization was attempted in
finite controlled volume method simulation. The actual double shear extrusion
experiment was carried out at 573 K, and serial microstructures were measured at
the interesting regions where were predicted to be severely deformed. The double
shear extrusion processed product had uniform and refined grain size. In the
microscopic measurements, dynamic recrystallization in some range of strain(up to ~ 0.7) has occurred during double shear extrusion. During dynamic
recrystallization, there existed not only coarse- but also fine- grains, and combined
grain size for mixed grains (coarse-grain group and fine-grain group) wasrepresented. By finite controlled volume method simulation based on typicalconstitutive model, the strain distribution was detected during double shearextrusion. The combination of the grain size distributions by actual double shearextrusion experiment and the instantaneous strain distribution by simulation
enabled to determine the relationship of dynamically recrystallized grain size andinstantaneous strain distribution. Then, new model with flow stress, which wascalculated by the constitutive equations determined by the parameters such astemperature, strain, strain rate, dynamically recrystallized grain size, has beenconstructed. Comparison of instantaneous distributions of effective strain, stressand strain rate for two models revealed that the model considering dynamic
recrystallization predicted more clearly the local stress concentration on high strain
rate regions.
In chapter 7, the concluding remarks summarized this thesis. In short,
High-strain plastic deformations such as equal channel angular extrusion, double
shear extrusion could be analyzed successfully by finite controlled volume method
simulation. The hardness results in equal channel angular extrusion of Al-Mg alloy
indicated the local inhomogeneous strain distribution as predicted in simulation.
This experimental result indicated that the results from simulation were reliable toreal experiment. Forging simulation in Zn-22Al alloy, which showed thatsuperplastic deformation had good formability, supported above statement. The
instantaneous strain distribution achieved by finite controlled volume method
simulation predicted the optimum die geometry in double shear extrusion. By
combining strain (by simulation) and d (by experiment), new constitutive model wasconstructed with considering dynamic recrystallization. This work will be helpful to
who may want to predict the metalworking with least actual test, or may want toconfirm his metalworking results with simulation.

List of Publications

No.

Title of the Article

Author(s)1The effect of ram speed onmechanical and thermal
properties in ECAE processsimulation

S.W. Chung
W.J. Kim
M. Kohzu
K. Higashi

234

5

Journal’s Name, Vol.,

Corresponding

Pages (Year)Chapter

Mater. Trans.,
Vol. 44, No.5,pp. 973-980(2003)

Chapter 2

The effect of friction S.W. Chung
coefficient on mechanical W.J. Kim
properties during full 3-D K. Higashi
ECAE simulation

Proc. of 5th Int.
Conf. on Oxford
Kobe
Materials
Seminarfor
Automotive
materials, p.252(Kobe, Japan, 2002)

Chapter 2

The effect of die geometry on S.W. Chungthe double shear extrusion by W.J. Kim
parametric FVM simulation
K. Higashi

Scripta Mater.,Vol. 51, No. 11,
pp.1117-1122(2004)

Chapter 3

The non-uniform behavior S.W. Chungduring ECAE process by 3-D H. Somekawa
FVM simulation
T. Kinoshita
W.J. Kim
K. Higashi

Scripta Mater.,Vol. 50, No. 7,pp. 1079-1083(2004)

Optimizing Forming-Process
for Seismic Damper Device
using Superplastic Zn-Al
alloy

Proc. of 3rd
EuropeanConferenceonSuperplastic
Forming,Euro-SPF04,pp. 81-86(Albi, France, 2004)

S.W. Chung
T. Tanaka
L.F. Chaing
K. Makii
A. Kushibe
M. Kohzu
K. Higashi

Chapter 4

Chapter 5

678910

A finite volume controlled
method simulation on thedouble shear extrusion ofMg-3Al-1Zn alloy withmodel considering dynamic
recrystallization

S.W. Chung
H. Watanabe
T. Mukai
H. Somekawa
W.J. Kim
K. Higashi

Submitted in Acta
Materilia (2004)
Chapter 6

Superplastic gas pressure S.W. Chung
forming of fine-grained K. Higashi
AZ61 magnesium alloy sheet W.J. Kim

Mater. Sci. Eng. A,Vol. 372, No.1-2,pp. 15-20 (2004)

Creep
mechanisms

deformation S.W. Chungin H. Watanabecoarse-grained solid solution W.J. Kim
K. Higashi
Mg alloys

Mater. Trans.,
Vol. 45, No. 4,pp.1266-1271(2004)

Superplastic
deformation S.W. Chung
behavior in the commercial W.J. Kim
AZ61 Mg alloy during K. Higashi
biaxial gas-pressure forming

Mater. Sci. Forum.,Vol. 419-422,
pp. 539-543 (2003)

Superplastic formability of S.W. Chungfine-grained AZ61 and AZ31 W.J. Kim
magnesium alloy sheets anddeformation
mechanismmaps for magnesium alloys

Proc. of 2nd Int.
Conf. on Light
Materials
forTransportation
Systems ,
LiMAT
2001,
pp.417-422 (Pusan,Korea, 2001)

Chapter 6

Chapter 6

Chapter 6

Chapter 6

List of Publications Related to This Thesis

No.

Title of the Article

Post-mechanical Properties
Superplastically-forged
Zn-22wt%Al AlloyAuthor(s)Journal’s Name, Vol., Pages(Year)

1of T. Tanaka
S.W. Chung
L.F. Chaing
K. Makii
A. Kushibe
M. Kohzu
K. Higashi

Mater. Trans.,
Vol. 45, No. 4,
pp.2542-2546 (2004)

2

Post-characteristics of Formed T. Tanaka
Zn-22 mass%Al Alloy to Seismic S.W. Chung
Damper for General Residence
L.F. Chaing
K. Makii
A. Kushibe
M. Kohzu
K. Higashi

3

Superplasticity in thin magnesium
alloy sheets and deformation
mechanism maps for magnesium
alloys at elevated temperatures

W.J. Kim
S.W. Chung
C.S. Chung
D. KumActa. Mater.,Vol. 49, No. 16,
pp. 3337-3345 (2001)

4

Superplasticity in a relatively W.J. Kimcoarse-grained AZ61 magnesium S.W. Chungalloy
C.W. An
K. Higashi

J. Mater. Sci. Lett.,Vol. 20, No. 17,
pp. 1635-1637 (2001)

Superplasticity in fine-grained W.J. Kim
AZ61 magnesium alloy
S.W. Chung

Met. Mater. KIM.,
Vol. 6, No. 3,
pp. 255-259 (2000)

5

Key Eng. Mater.,Vol. 274-276,
pp.283-288 (2004)

審査結果の要旨
有限要素法などのシミュレーションは金属の塑性変形挙動を理解するために用いられてきた手法である。最近 Equal Channel Angular Extrusion (ECAE)法、DoubleShear Extrusion (DSE)、室温超塑性鍛造といった新規加工技術が提案され、超微細組織を有する材料の大変形域（強ひずみ）までの変形挙動が注目されている。本論
文では、軽金属材料の大変形域までの変形挙動を理解するため、有限体積法を用いた塑性加工シミュレーションを行うシステムを構築した。ここでは、実験による材料パラメータを用いた構成式を確立するともに、このモデルにより解析を行い、さらに解析結果と実験結果の比較から、解析結果の信頼性を確保した現実的なモデルの構築を目指している。
本論文では、以下に述べるような具体的研究成果を得ている。
① ３次元有限差分法シミュレーションを用いて ECAE 加工における高ひずみ塑性変形の解析を行った。その結果、押出方向に沿った断面において不均一なひずみ分布の存在が確認された。また ECAE 加工におけるプレス速度が応力あるいはひずみの分布に影響を及ぼすことを確認した。
② 実験結果と比較した結果、シミュレーションによって解析された ECAE 加工された変形途中のひずみ分布は実際に ECAE 加工された Al-Mg 合金における硬さ試験結果と良い一致を示すことが分かった。
③ 異なる微細組織を有する合金の超塑性鍛造プロセスに関する有限差分法によるシミュレーションを行った。解析結果より、各合金とも高いひずみ速度で変形するコーナー部で局部的に不均一変形することが明らかにされた。
④ 実際の鍛造実験の結果、微細組織が超塑性成形においては重要な役割を果たすことが確認された。微細結晶粒有する Zn-22Al 合金押出材が低温超塑性を発現することを明らかにした。
⑤ 高ひずみ塑性変形において２次元軸対称有限差分法を行いた不均一ひずみ分布の解析結果より最適な金型形状を予測できることを明らかにした。また実験を行うことにより導出した動的再結晶を考慮したモデルは、従来のモデルと比べ、高ひずみ領域における局部的な応力集中をより正確に予測できることを明らかにした。
以上の研究成果は有限差分法シミュレーションを用いたアルミニウムおよびマグネシウム合金の塑性変形に関する解析の有用性を示すものである。この成果は学術的のみならず工業的にも大いに期待できる有益な手法であり、材料技術の一層の高度化に貢献するところ大である。また申請者が自立して研究を行うに十分な能力と学識を有することを証したものである。
３．最終試験結果の要旨
審査委員会は、平成 16 年 12 月 24 日、委員全員出席のもとに申請者に論文内容の説明を行わせ、関連する諸問題について試問を行った結果、合格と判定した。
４．公聴会の日時
平成 16 年 12 月 24 日、午前 11 時 00 分～12 時 30 分
５．審査委員会の所見
本委員会は、本論文の審査ならびに最終試験の結果から、博士（工学）の学位を授与することを適当と認める。