35 15㼻

Specimen Punch

Die

3 mm/min

68

Fig. 4-4 Example of crack initiation in 3-point bending test: (a) w/t = 1.0, (b) w/t = 2.0, (c) w/t = 4.0

69 4.3 )(0 ゎᯒ᪉ἲ

4.3.1 ษḞ௜୸Წᘬᙇ㸦1%7㸧ヨ㦂ゎᯒ࡟ࡼࡿὶືᛂຊ᭤⥺ࡢ⿵ṇ᪉ἲ

NBT ヨ㦂ࡢ P- (a0-a)᭤⥺࠿ࡽ㸪ᛂຊ⿵ṇࢆ㐺⏝ࡋ࡚ὶືᛂຊ᭤⥺ࢆồࡵࡓ㸬 P- (a0-a)᭤⥺ࡢ FEM ゎᯒ࡜ᐇ㦂࡜ࡢㄗᕪࡢ᭱ᑠ໬ࢆ┠ⓗ࡜ࡋ㸪᭱㐺໬ᡭἲ࡟ࡣ SRSM (Successive Response Surface Method)ἲࢆ⏝࠸࡚㸪ከ┤⥺໬ࡉࢀࡓὶືᛂຊ

᭤⥺ࡢྛᛂຊ್ࡢ⿵ṇಀᩘࡢ᭱㐺್ࢆ᥈⣴ࡋࡓ^2-1)㸬ᮦᩱࡣᙎረᛶయ࡛von-Mises ࡢ㝆అ᮲௳࡟ᚑ࠺࡜௬ᐃࡋFig. 4-5࡟♧ࡍ㍈ᑐ⛠せ⣲ࢆ⏝࠸ࡓ㸬ࡃࡧࢀᗏ࡟࠾ࡅ

ࡿ௦⾲せ⣲ᑍἲࡣ 0.1 mm ࡜ࡋࡓ㸬ᘬᙇヨ㦂ᐇ ್ࡼࡾ㸪ࣖࣥࢢ⋡ࡣ 180GPa㸪

࣏࢔ࢯࣥẚࡣ 0.3 ࡛࠶ࡗࡓ㸬᭷㝈せ⣲ࢯࣝࣂ࡟ࡣ LS-DYNA971㸦Livermore Software Technology Corporation㸧 ࢆ 㸪 ᭱ 㐺 ໬ ࢯ ࣇ ࢺ ࢘ ࢚ ࢔ ࡟ ࡣ LS-OPT4.2 㸦Livermore Software Technology Corporation㸧ࢆ౑⏝ࡋࡓ㸬࡞࠾㸪ᮏㄽᩥ࡛ࡣ㸪ᚋ

㏙ࡢ3-PBヨ㦂ゎᯒ㸪UPSETヨ㦂ゎᯒ࡛ࡶLS-DYNA971ࢆ౑⏝ࡋࡓ㸬

4✀ࡢ NBTヨ㦂࡟ᑐࡍࡿᛂຊ⿵ṇ࡟ࡼࡾ᭱⤊ⓗ࡟ᚓࡽࢀࡓྛὶືᛂຊ᭤⥺ࢆ

Fig. 4-6 ࡟㸪ࡑࢀࡽࢆ⏝࠸࡚ゎᯒࡋࡓ⤖ᯝᚓࡽࢀࡓ P-(a0-a)᭤⥺ࢆ Fig. 4-7 ࡟♧

ࡍ㸬R0࡟ࡼࡽࡎྠ୍ࡢὶືᛂຊ᭤⥺ࡀྠᐃࡉࢀ࡚࠾ࡾ㸪ࡲࡓ㸪ᐇ㦂ࡢP-(a0-a)ࡢ 㛵ಀࢆⰋ࠸⢭ᗘ࡛෌⌧ࡋ࡚࠸ࡿࡇ࡜࠿ࡽ㸪ᛂຊ⿵ṇࡣṇࡋࡃ⾜ࢃࢀࡓ࡜ุ᩿࡛

ࡁࡿ㸬

Fig. 4-5 Boundary conditions and FE-mesh in notched round bar tensile test

20

200 mm/s

70

Fig. 4-6 Flow stress curves identified by proposed stress correction method

Fig. 4-7 Experimental and simulation results for notched round bar tensile tests

0

100 200 300 400 500 600 700 800 900 1000

0 0.05 0.1 0.15 0.2 0.25 0.3

Flowstress [MPa]

Equivalent plastic strain Tensile test result

with standard specimen

R₀ = 20 mm R₀ = 10 mm R₀ = 6 mm R₀ = 3 mm

Limit of uniform elongation

2 4 6 8 10 12 14 16 18 20 22 24

0 0.1 0.2 0.3 0.4

Tensile force [kN]

Change in radius a₀-a/mm

Experiment FEM

R₀ = 20 mm R₀ = 10 mm R₀ = 6 mm

R₀ = 3 mm

71 4.3.2 Ⅼ᭤ࡆ㸦3%㸧ヨ㦂ゎᯒ᪉ἲ

3-PB ヨ㦂ゎᯒ࡟౑⏝ࡋࡓ᭷㝈せ⣲ࣔࢹࣝࢆ Fig. 4-8 ࡟♧ࡍ㸬ヨ㦂∦ࡣᖜ᪉ྥ

࡜㛗ࡉ᪉ྥࡢᑐ⛠ᛶࢆ⪃៖ࡋ㸪඲యࡢ1/4㡿ᇦࢆࣔࢹࣝ໬ࡋࡓ㸬ࣃࣥࢳ࡜ࢲ࢖ࡣ

๛య࡜ࡋ㸪ヨ㦂∦࡟ࡣ 8 ⠇Ⅼ࢔࢖ࢯࣃ࣓ࣛࢺࣜࢵࢡせ⣲ࢆ㓄ࡋࡓ㸬ࣃࣥࢳ┤ୗ

ࡢ௦⾲せ⣲ᑍἲࡣ0.1 mm࡛࠶ࡿ㸬ὶືᛂຊ᭤⥺ࡣNBTヨ㦂㸦R0 = 20 mm㸧ࢆᑐ

㇟࡜ࡋࡓᛂຊ⿵ṇ࡟ࡼࡾྠᐃࡉࢀࡓࡶࡢࢆ㸪ḟᘧࡢࡼ࠺࡟ Swift ๎࡛㏆ఝࡋࡓ㸬

V _905.4(H_{p 2.2u10}¹³₎^0.038 _(MPa) (4-1)

ࡇࡇ࡛㸪εpࡣ┦ᙜረᛶࡦࡎࡳ࡛࠶ࡿ㸬ࣖࣥࢢ⋡࠾ࡼࡧ࣏࢔ࢯࣥẚࡣNBTヨ㦂ゎ ᯒ࡜ྠ୍࡜ࡋࡓ㸬ヨ㦂∦࡜ᕤල㛫ࡢᦶ᧿ࡣ㠀ᖖ࡟ᑠࡉ࠸࡜௬ᐃࡋ㸪ࢡ࣮ࣟࣥᦶ᧿

ಀᩘࡣ0.03࡜ࡋࡓ㸬Fig. 4-9࡟ᐇ㦂࡜ゎᯒ࡟࠾ࡅࡿ᭤ࡆⲴ㔜࡜ࣃࣥࢳࢫࢺ࣮ࣟࢡ

ࡢ㛵ಀࢆ♧ࡍࡀ㸪୧⪅ࡣ࠾࠾ࡴࡡ୍⮴ࡋ࡚࠸ࡿ㸬

Fig. 4-8 Example of FE-mesh in 3-point bending test simulation

72

Fig. 4-9 Experimental and simulation results for 3-point bending force 0

1 2 3 4 5 6 7 8 9

0 2 4 6 8 10 12 14

Force [kN]

Stroke [mm]

w/t = 4.0

w/t = 2.0

w/t = 1.0

Experiment (n=3) FEM

Bending force [kN]

73 4.4 ᐇ㦂࠾ࡼࡧ )(0 ゎᯒ⤖ᯝ

FEMゎᯒ࡟ࡼࡗ࡚ィ⟬ࡋࡓ NBTヨ㦂࠾ࡼࡧ 3-PBヨ㦂ࡢ◚ቯ㉳Ⅼ࡟࠾ࡅࡿ η

࡜┦ᙜࡦࡎࡳε^㹝ࡢᒚṔࢆFig. 4-10࡟♧ࡍ㸬NBTヨ㦂࡟࠾࠸࡚ࡣ㸪R0࡟㛵ࢃࡽࡎ㸪

᭱ࡶηࡀ㧗࠿ࡗࡓࡃࡧࢀᗏ᩿㠃୰ᚰࢆ◚ቯ㉳Ⅼ࡜ࡳ࡞ࡋࡓ㸬3-PBヨ㦂ゎᯒ࡛ࡣ㸪 3 ᅇࡢ⧞ࡾ㏉ࡋᐇ㦂࡟࠾ࡅࡿᖹᆒ◚ቯࣃࣥࢳࢫࢺ࣮ࣟࢡࡲ࡛ࡢ⤖ᯝࢆ♧ࡋ࡚࠸

ࡿ㸬Fig. 4-11࡟ࡣ㸪3-PBヨ㦂ゎᯒ࡟࠾ࡅࡿη࡜ε^㹝ࡢホ౯఩⨨ࢆ㸪◚ቯุᐃ᫬Ⅼࡢ ኚᙧᅗ࡜ඹ࡟♧ࡍ㸬

ηfࢆ◚ቯุᐃ᫬ࡢᛂຊ୕㍈ᗘ㸪ε^㹝f ࡣ◚ቯุᐃ᫬ࡢ┦ᙜረᛶࡦࡎࡳ࡜ࡍࡿ㸬Fig.

4-10ࡼࡾ㸪NBTヨ㦂࡛ࡣR0ࡀᑠࡉࡃ࡞ࡿ࡯࡝ηfࡣ኱ࡁࡃ㸪ε^㹝fࡣᑠࡉࡃ࡞ࡿഴྥ

ࡀ☜ㄆ࡛ࡁࡓ㸬ࡲࡓ㸪3-PBヨ㦂࡟࠾࠸࡚ࡶ㸪w/tࡀ኱ࡁࡃ࡞ࡿ࡯࡝ηfࡣ኱ࡁࡃ㸪 ε㹝

fࡣᑠࡉࡃ࡞ࡿഴྥࡀ☜ㄆ࡛ࡁࡿ㸬ࡇࢀࡣ㸪w/t ࡀ኱ࡁࡃ࡞ࡿ࡟ࡘࢀ࡚㸪ヨ㦂∦

୰ኸ㒊㸦BⅬ㸪CⅬ㸪DⅬ㸧ࡣᖹ㠃ࡦࡎࡳ≧ែ࡟㏆࡙ࡁ㸪ᖜ᪉ྥ࡟ࡶᘬᙇᛂຊࡀ స⏝ࡋࡓࡓࡵ࡜⪃࠼ࡽࢀࡿ㸬ࡲࡓ㸪3-PB ヨ㦂࡛≉ᚩⓗ࡞ࡢࡣ㸪࠸ࡎࢀࡢヨ㦂∦

࡟࠾࠸࡚ࡶኚᙧึᮇ࠿ࡽ◚ቯⓎ⏕࡟⮳ࡿࡲ࡛㸪ηࡀ࡯ࡰ୍ᐃ࡛᥎⛣ࡋ࡚࠸ࡿⅬ࡛

࠶ࡿ㸬࡞࠾㸪w/t = 1.0ヨ㦂∦ࡢ࢚ࢵࢪ㒊㸦AⅬ㸧࡟࠾࠸࡚ࡣ༢㍈ᛂຊ≧ែ㸦η = 0.33㸧࡜࡞ࡗ࡚࠸ࡓࡀ㸪ηࡢᒚṔࡸ㸪ηf࡜ε^㹝fࡢ㛵ಀࡣ㸪୰ኸ㒊㸦BⅬ㸧࡜ࡉ࡯࡝㐪

࠸ࡣ࡞࠿ࡗࡓ㸬

௨ୖࡢNBTヨ㦂࠾ࡼࡧ3-PBヨ㦂ࡢᐇ㦂࡜ゎᯒ࡟ࡼࡾ㸪0.33<ηf <1.2ࡢ⠊ᅖ࡛

ࡢ㸪ε^㹝fࢆྠᐃࡍࡿࡇ࡜ࡀ࡛ࡁࡓ㸬ḟ࡟㸪ᚓࡽࢀࡓηf࡜ε^㹝fࡢ㛵ಀ࠿ࡽ㸪ᘏᛶ◚ቯࣔ

ࢹࣝࡢࣃ࣓࣮ࣛࢱࢆỴᐃࡍࡿ㸬

Hancock࡜Mackenzie ^4-2)ࡣ㸪ᚤᑠ✵Ꮝࡢᡂ㛗࡟㛵ࡍࡿ⪃ᐹ࠾ࡼࡧึᮇษḞ༙ᚄ

ࢆኚ໬ࡉࡏࡓ୸Წᘬᙇヨ㦂ࡢ⤖ᯝ࠿ࡽ㸪ε^㹝fࡣηࡢᣦᩘ㛵ᩘ࡜ࡋ࡚⾲⌧࡛ࡁࡿࡇ࡜

ࢆ♧ࡋࡓ㸬ࡲࡓ㸪ྜྷ⏣ࡽ^4-8)ࡣ㸪ࡏࢇ᩿ຍᕤゎᯒ࡟࠾࠸࡚ᚤᑠ✵Ꮝࡢ⏕ᡂ࡟ᚲせ

࡞ረᛶࡦࡎࡳࢆηࡢᣦᩘ㛵ᩘ࡜௬ᐃࡋ࡚࠸ࡿ㸬ࡑࡇ࡛㸪ᮏㄽᩥ࡛ࡣ㸪ε^㹝fࡀୗグࡢ ᘧ࡛⾲ࡉࢀࡿ࡜௬ᐃࡋࡓ㸬

ε^㹝f = A exp(B ηf) (4-2) ࡇࡇ࡛㸪A࡜Bࡣᮦᩱࣃ࣓࣮ࣛࢱ࡛࠶ࡿ㸬Fig. 4-12 ࡣNBTヨ㦂࠾ࡼࡧ3-PBヨ 㦂࡟࠾ࡅࡿηf࡜ε^㹝fࢆ♧ࡋࡓࡶࡢ࡛࠶ࡿ㸬ࡇࢀࡽࡢࢹ࣮ࢱ࠿ࡽ᭱ᑠ஧஌ἲ࡟ࡼࡾᘧ (4-2) ࡟࠾ࡅࡿA࡜BࢆỴᐃࡋࡓ࡜ࡇࢁ㸪A = 1.01㸪B = -1.87࡜ࡍࡿࡇ࡜࡛㸪࠾

࠾ࡴࡡ1ᮏࡢ᭤⥺࡛ᩚ⌮ࡍࡿ࡛ࡁࡿࡇ࡜ࡀࢃ࠿ࡗࡓ㸬

74

Fig. 4-10 Loading path of stress triaxiality at the fracture points in notched round bar tensile (NBT) tests and 3-point bending (3-PB) tests

Fig. 4-11 Simulation results of 3-point bending test: (a) w/t = 1.0, (b) w/t = 2.0, (c) w/t

= 4.0 (A–D: Evaluation points for loading path of stress triaxiality)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0 0.3 0.6 0.9 1.2 1.5

Equi valent pl astic strain ε

Stress triaxiality η R

₀

= 20 mm

R

₀

= 10 mm R

₀

= 6 mm

R

₀

= 3 mm w/t = 1.0

w/t = 2.0 w/t =4.0 Edge

Center NBT test

3-PB test

75

Fig. 4-12 Relationship between stress triaxiality at fracture (ηf) and equivalent plastic strain at fracture (ε^㹝f)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0 0.3 0.6 0.9 1.2 1.5

Equivalent plastic strain at fracture

Stress triaxiality at fracture

η_f

NBT test 3-PB test

R₀

= 20 mm

R₀

= 10 mm

R₀

= 6 mm

R₀

= 3 mm

w/t = 1.0

(Edge)

fH

w/t=2.0

w/t=4.0

w/t = 1.0 (Center)

) 87 . 1 exp(

01 .

1

_f

f

K

H

76 4.5 ➃㠃ᣊ᮰ᅽ⦰ヨ㦂࡟ࡼࡿ᳨ドᐇ㦂 4.5.1 ➃㠃ᣊ᮰ᅽ⦰㸦836(7㸧ヨ㦂᪉ἲ

Ỵᐃࡉࢀࡓᘧ(4-2)ࡢᘏᛶ◚ቯࣔࢹࣝࡢ᭷ຠᛶࢆ᳨ドࡍࡿࡓࡵ࡟㸪෇ᰕヨ㦂∦

ࡢ➃㠃ᣊ᮰ᅽ⦰ヨ㦂㸦UPSET ヨ㦂㸧ࢆᐇ᪋ࡋࡓ㸬ヨ㦂∦ࡢึᮇ┤ᚄ D0 ࡣȭ12 mm㸪ึᮇ㧗ࡉL0ࡣ12㸪18㸪24࠾ࡼࡧ30 mmࡢ4✀㢮㸦L0/D0 = 1.0㸪1.5㸪2.0࠾

ࡼࡧ2.5㸧࡜ࡋ㸪 S45C୸Წࡢ㍈᪉ྥ࡜ヨ㦂∦ࡢ㧗ࡉ᪉ྥࡀᖹ⾜࡟࡞ࡿࡼ࠺࡟ษ

ࡾฟࡋࡓ㸬㔠ᆺ࡟ࡣ㸪෭㛫ᤣ㎸ࡳヨ㦂ἲ^4-7)࡛ᣦᐃࡉࢀ࡚࠸ࡿᑍἲࡢྠᚰ⁁௜෇

┙㔠ᆺࢆ⏝࠸㸪1000kNࡢἜᅽࣉࣞࢫ㸦ᓥὠ〇సᡤ㸪UH-1000kN㸧࡟࡚㸪3 mm/min ࡢ୍ᐃ㏿ᗘ࡛ヨ㦂ࢆᐇ᪋ࡋࡓ㸬ࡲࡓ㸪ヨ㦂୰㸪2ྎࡢCCD࣓࢝ࣛ࡜ 2ᯛࡢ࣑ࣛ

࣮ࢆ⏝࠸࡚㸪෇ᰕヨ㦂∦ࡢഃ㠃඲࿘ࡀ᧜ᙳど㔝࡟ධࡿࡼ࠺࡞≧ែ࡛ື⏬᧜ᙳࢆ

⾜࠸㸪࠾࠾ࡴࡡ1 mmࡢட⿣ࡀ☜ㄆ࡛ࡁࡓ᫬Ⅼ࡛◚ቯࡢุᐃࢆ⾜࠸㸪㝈⏺ᅽ⦰⋡

(L0-Lf)/L0ࢆ ᐃࡋࡓ㸬ࡇࡇ࡛㸪Lfࡣ◚ቯุᐃ᫬ࡢヨ㦂∦㧗ࡉ࡛࠶ࡿ㸬࡞࠾㸪ᐇ㦂 ࡣྛヨ㦂∦࡟ᑐࡋ 2 ᅇ⧞ࡾ㏉ࡋ㸪ࡍ࡭࡚ࡢヨ㦂∦࡛㸪ヨ㦂∦እ࿘⾲㠃࡟࠾ࡅࡿ

㧗ࡉ᪉ྥࡢ୰ኸ㒊࠿ࡽ⦪๭ࢀࢆ⏕ࡌࡓ㸬

77

4.5.2 ➃㠃ᣊ᮰ᅽ⦰㸦836(7㸧ヨ㦂ࡢ )(0 ゎᯒ᪉ἲ

UPSETヨ㦂ゎᯒࡣ㸪Fig. 4-13࡟♧ࡍFEMࣔࢹࣝࢆ⏝࠸࡚⾜ࡗࡓ㸬ୖ㔠ᆺࡣ๛

య࡜ࡋ㸪ヨ㦂∦ࡣ㧗ࡉ᪉ྥᑐ⛠ᛶ࠾ࡼࡧ㍈ᑐ⛠ᛶࢆ⪃៖ࡋ㸪㧗ࡉ᪉ྥ࡟1/2࠿ࡘ

࿘᪉ྥ90ᗘศࢆ8⠇Ⅼ࢔࢖ࢯࣃ࣓ࣛࢺࣜࢵࢡせ⣲࡛ࣔࢹࣝ໬ࡋࡓ㸬ヨ㦂∦እ࿘

⾲㠃ࡢ௦⾲せ⣲ᑍἲࡣNBTヨ㦂ゎᯒ࠾ࡼࡧ3-PBヨ㦂ゎᯒ࡜ྠ➼ࡢ0.1 mm࡜ࡋ ࡓ㸬ヨ㦂∦ୖ➃ࡢ⠇Ⅼࡣୖ㔠ᆺࡢせ⣲࡜ᅛ╔ࡍࡿቃ⏺᮲௳ࢆ୚࠼㸪ኚᙧࡀ㐍⾜ࡋ

࡚ヨ㦂∦ഃ㠃ࡢせ⣲ࡀୖ㔠ᆺࡢせ⣲࡜᥋ゐ㸦ࣇ࢛࣮ࣝࢹ࢕ࣥࢢ㸧ࡋࡓሙྜࡶ㸪ࡑ ࡢ᫬Ⅼ࡛ྠᵝࡢ᮲௳ࢆ୚࠼ࡓ㸬ὶືᛂຊ᭤⥺ࢆࡣࡌࡵ࡜ࡍࡿᮦᩱࣃ࣓࣮ࣛࢱࡣ 3-PBヨ㦂FEMゎᯒ࡜ඹ㏻࡜ࡋࡓ㸬

Fig. 4-13 Example of FE-mesh in upsetting test simulation

78 4.5.3 )(0 ゎᯒ⤖ᯝ

◚ቯ㉳Ⅼ࡛࠶ࡿヨ㦂∦ഃ㠃ࡢ୰ኸ㒊ࡢη࡜ε^㹝ࡢᒚṔࢆFig. 4-14࡟♧ࡍ㸬UPSET ヨ㦂ゎᯒ࡛ࡣ㸪2ᅇࡢ⧞ࡾ㏉ࡋᐇ㦂࡟࠾ࡅࡿᖹᆒ◚ቯᅽ⦰ࢫࢺ࣮ࣟࢡࡲ࡛ࡢ⤖ᯝ

ࢆ♧ࡋ࡚࠸ࡿ㸬࠸ࡎࢀࡢヨ㦂∦࡟࠾࠸࡚ࡶ㸪ኚᙧࡢึᮇ࡛ࡣᅽ⦰≧ែ࡛࠶ࡿࡓࡵ

ηࡣ㈇࡛࠶ࡿࡀ㸪ኚᙧࡢ㐍⾜࡟ᚑ࠸ヨ㦂∦⾲㠃ࡀࣂࣝࢪࣥࢢࡍࡿࡓࡵ㸪ᚎࠎ࡟ᘬ ᙇᛂຊ≧ែ࡟㑄⛣ࡋ㸪᭱⤊ⓗ࡟ࡣ࠸ࡎࢀࡢヨ㦂∦ࡶηࡀ0.5๓ᚋ࡛◚᩿࡟⮳ࡿ㸬 ࡑࡢ㝿ࡢε^㹝fࡣ㸪L0/D0࡟ẚ౛ࡋ࡚኱ࡁࡃ࡞ࡿ㸬ᅗ୰࡟ࡣ㸪Fig. 4-12 ࡢ⤖ᯝࡶྜࢃ

ࡏ࡚♧ࡋ࡚࠸ࡿࡀ㸪ࡇࡢ᫬Ⅼ࡛ࡣ㸪UPSETヨ㦂ࡢηf࡜ε^㹝fࡢ㛵ಀࡣ㸪NBTヨ㦂࡜

3-PBヨ㦂࠿ࡽỴᐃࡋࡓᘧ(4-2)࡟ࡣᩚྜࡋ࡞࠸㸬

ࡇࡇ࡛㸪Rice࡜Tracy^1-45)ࡢᚤᑠ࣎࢖ࢻࡢᡂ㛗⌮ㄽࢆᇶ࡟㸪ηࡀ㈇ࡢ㡿ᇦ࡛ࡣ࣎

࢖ࢻࡣᡂ㛗ࡋ࡞࠸࡜௬ᐃࡋ㸪ηࡀṇࡢሙྜࡢࡳ⣼✚ࡍࡿ┦ᙜረᛶࡦࡎࡳε^㹝*ࢆḟᘧ

࡛ᐃ⩏ࡍࡿ㸬

³

t^t d

0 H

H (4-3)

ࡇࡇ࡛㸪dε^㹝ࡣ┦ᙜረᛶࡦࡎࡳቑศ࡛࠶ࡿ㸬ᘧ(4-3)ࡢ✚ศࡣȞ<0ࡢ༊㛫࡛ࡣdε^㹝 = 0࡜ࡋ࡚ྲྀࡾᢅ࠺㸬ᘧ(4-3)࡟ࡼࡾ㸪UPSETヨ㦂ࡢε^㹝ࢆ㸪ε^㹝*࡛෌ᩚ⌮ࡋࡓ⤖ᯝࢆFig.

4-15࡟♧ࡍ㸬UPSETヨ㦂࡟࠾ࡅࡿη࡜ε^㹝*ࡢᒚṔࡣ㸪L0/D0ࡢᙳ㡪ࢆ࡯࡜ࢇ࡝ཷࡅ

ࡿࡇ࡜࡞ࡃ࡯ࡰ㔜࡞ࡗ࡚࠸ࡿ㸬ࡲࡓ㸪◚᩿┦ᙜረᛶࡦࡎࡳε^㹝f*ࡣ㸪L0/D0 = 1.0ࡢሙ

ྜ0.367࡛᭱ࡶ኱ࡁࡃ㸪ḟ࠸࡛L0/D0 = 2.0࡛0.315㸪L0/D0 = 1.5࡛0.312㸪L0/D0 = 2.5࡛0.297࡜࡞ࡾ㸪L0/D0 ࡀᑠࡉࡃ࡞ࡿ࡟ࡘࢀ࡚ⱝᖸపୗࡍࡿࡀ㸪࠸ࡎࢀࡶᘧ(4-2) ࠿ࡽࡑࢀ࡯࡝እࢀ࡚࠸࡞࠸㸬

Fig. 4-16ࡣ㸪η࡜ε^㹝*ࡢ㛵ಀࡀᘧ(4-2)࡟࠾ࡅࡿε^㹝f࡟㐩ࡋࡓ᫬Ⅼ࡛◚ቯࡀⓎ⏕ࡍࡿ

࡜௬ᐃࡋ࡚㸪ྛL0/D0ࡢ᮲௳࡛ࡢ㝈⏺ᅽ⦰⋡ࢆண ࡋࡓ⤖ᯝ࡛࠶ࡿ㸬L0/D0 = 1.0 ௨እ࡛ࡣ㸪ᐇ㦂⤖ᯝࢆⱝᖸ㧗ࡵ࡟ぢ✚ࡶࡗ࡚࠸ࡿࡶࡢࡢ㸪L0/D0ࡢᙳ㡪ࡣⰋࡃ෌

⌧ࡉࢀ࡚࠾ࡾ㸪ᘧ(4-2)ࡢᘏᛶ◚ቯண ࣔࢹࣝࡢ᭷ຠᛶࡣ༑ศ☜ㄆࡉࢀࡓ㸬

79

Fig. 4-14 Loading path of stress triaxiality at the fracture points in upsetting (UPSET) tests

Fig. 4-15 Modified loading path of stress triaxiality at the fracture points in upsetting (UPSET) tests

0 0.2 0.4 0.6 0.8 1 1.2

-0.6 -0.3 0.0 0.3 0.6 0.9 1.2 1.5

Equivalent plastic strain

Stress triaxiality

1.0

L₀

/D

₀

=2.5

L₀

/D

₀

=2.0

L₀

/D

₀

=1.5

L₀

/D

₀

=1.0

) 87 . 1 exp(

01 .

1 _f

f K

H

Kf

K,

Equivalent plastic strain ε, εf NBT test

3-PB test

Stress triaxiality

η, η_f

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0.0 0.3 0.6 0.9 1.2 1.5

Equivalent plastic strain

Stress triaxiality L₀/D₀= 1.0 L₀/D₀= 2.5

L₀/D₀= 2.0

L₀/D₀= 1.5

) 87 . 1 exp(

01 .

1 _f

f K

H

Stress triaxialityη, η_f Equivalent plastic strain ε* , εf*

UPSET

w/t = 2.0 ^{NBT test}_{3-PB test}

80

Fig. 4-16 Prediction results of critical compression ratio (L0-Lf)/L0 using ductile fracture model of Eq. (2) (L0: Initial specimen height; Lf: Specimen height at fracture)

0 0.2 0.4 0.6 0.8 1

0.5 1.0 1.5 2.0 2.5 3.0

Critical compression ratio (L0-Lf)/L0

L₀

/D

₀

Experiment (n=2) Prediction from Eq. ( )

1.0

(4-2)

81 4.5.4 ࢹ࢕ࣥࣉࣝᑍἲ ᐃ⤖ᯝ࠾ࡼࡧ⪃ᐹ

ᚤᑠ࣎࢖ࢻࡢᡂ㛗࠾ࡼࡧྜయᣲື࡟ཬࡰࡍ η ࡢᒚṔࡢᙳ㡪ࡣ኱ࡁࡃ㸪◚᩿㠃 ࡢࢹ࢕ࣥࣉࣝࡢ኱ࡁࡉ࡜ η ࡜ࡢ㛫࡟┦㛵ࡀ࠶ࡿࡇ࡜ࡀ኱ሯࡽ࡟ࡼࡗ࡚☜ㄆࡉࢀ

࡚࠸ࡿ4-9), 4-10)㸬ࡑࡇ࡛㸪ᘧ(4-2)࡟ࡼࡗ࡚UPSETヨ㦂ࡢ㝈⏺ᅽ⦰⋡ࡀ࠾࠾ࡴࡡண

 ࡛ࡁࡓ⌮⏤ࢆ㸪◚᩿㠃ࡢࢹ࢕ࣥࣉࣝࡢ኱ࡁࡉ࡜ηfࡢ㛵ಀࡢほⅬ࠿ࡽ⪃ᐹࡍࡿ㸬 NBT㸪3-PB࠾ࡼࡧ UPSET ヨ㦂∦࡟࠾࠸࡚㸪SEM ࡟ࡼࡾ◚ቯ㉳Ⅼ࡟࠾ࡅࡿ◚

᩿㠃ࡢほᐹࢆ⾜ࡗࡓ㸬SEMࡢほᐹ⤖ᯝࢆFig. 4-17࡟♧ࡍࡀ㸪࠸ࡎࢀࡢヨ㦂∦ࡶ

ᚤᑠ࣎࢖ࢻྜయᆺᘏᛶ◚㠃ࡢ≉ᚩ࡛࠶ࡿࢹ࢕ࣥࣉࣝࣃࢱ࣮ࣥࡀほᐹࡉࢀࡿ㸬ྛ

SEM෗┿ࡢඹ㏻ど㔝ෆ㸦64 μm™48 μm㸧࡛☜ㄆࡉࢀࡿࢹ࢕ࣥࣉࣝࡢ࠺ࡕ㸪50ಶ

ࢆᢳฟࡋ࡚㸪ࡑࡢ㏆ఝ෇┤ᚄdࢆィ ࡋࡓ㸬

Fig. 4-18࡟㸪ィ ࡉࢀࡓdࡢࣄࢫࢺࢢ࣒ࣛࢆ♧ࡍ㸬ࡲࡓ㸪Fig. 4-19࡟㸪ྛヨ㦂

∦ࡢ◚ቯ㉳Ⅼ࡟࠾ࡅࡿ ηf࡜㸪d ࡢᖹᆒ್ dave࡜ࡢ㛵ಀࢆ♧ࡍ㸬NBT ヨ㦂࡟࠾࠸

࡚ࡣR0 = 3 mmЍ10 mmЍ20 mmࡢ㡰࡛㸪3-PBヨ㦂࡟࠾࠸࡚ࡣw/t = 4.0Ѝ2.0ࡢ 㡰࡛㸪η࡟ᛂࡌ࡚daveࡶᑠࡉࡃ࡞ࡿ┦㛵㛵ಀࡀ☜ㄆࡉࢀࡓ㸬ࡓࡔࡋ㸪ηfࡀ᭱ࡶᑠ ࡉ࠸w/t = 1.0࡛ࡣ㸪daveࡣ㏫࡟኱ࡁࡃ࡞ࡗࡓ㸬

ࡇࡇ࡛㸪Fig. 4-15୰ࡢⅬ⥺෇ෆ㸪ࡘࡲࡾUPSETヨ㦂ࡢྛヨ㦂∦࠾ࡼࡧࡑࢀࡽ

ࡢ ηf࡜ε^㹝f*ࡢ㛵ಀ࡟᭱ࡶ㏆࠿ࡗࡓ 3-PB ヨ㦂ࡢ w/t = 2.0 ヨ㦂∦࡟╔┠ࡋ࡚⪃ᐹࡍ

ࡿ㸬Fig. 4-18ࡼࡾ㸪UPSETヨ㦂࡛ࡣL0/D0ࡀ␗࡞ࡗ࡚ࡶ㸪dࡢศᕸ࡟࡯࡜ࢇ࡝㐪

࠸ࡣ☜ㄆࡉࢀࡎ㸪ࡉࡽ࡟Fig. 4-19ࡼࡾ㸪dave࡜ηfࡢ㛵ಀࡶL0/D0࡟ࡼࡿᕪ␗ࡀ࡯

࡜ࢇ࡝࡞࠸ࡇ࡜ࡀศ࠿ࡿ㸬ࡇࢀࡽࡣ㸪Fig. 4-15࡛♧ࡋࡓࡼ࠺࡟㸪L0/D0࡟㛵ࢃࡽ

ࡎ㸪ηࡀṇ࡟㑄⛣ࡋ࡚࠿ࡽࡢηࡢ㈇ⲴᒚṔ࡟࡯࡜ࢇ࡝㐪࠸ࡀ࡞࠿ࡗࡓࡇ࡜࡟ࡼࡿ

࡜᥎ᐹࡉࢀࡿ㸬

ࡲࡓ㸪Fig. 4-18࠿ࡽศ࠿ࡿࡼ࠺࡟㸪 UPSETヨ㦂ࡢྛヨ㦂∦ࡢd ࡢศᕸࡣ㸪3-PBヨ㦂࡟࠾ࡅࡿw/t = 2.0ࡢࡑࢀ࡜㢮ఝࡋ࡚࠾ࡾ㸪ࡉࡽ࡟Fig. 4-19ࡼࡾ㸪dave࡜ ηf ࡢ㛵ಀࡶ୧⪅࡛㏆࠸⤖ᯝ࡜࡞ࡗ࡚࠸ࡿ㸦Fig. 4-19 ୰ࡢⅬ⥺෇㸧㸬ࡍ࡞ࢃࡕ㸪 UPSET ヨ㦂࡜ 3-PB(w/t = 2.0)ヨ㦂ࡢ◚ቯ᫬ࡢᛂຊ୕㍈ᗘ࡜ࢹ࢕ࣥࣉࣝࡢ≧ែࡣ 㢮ఝࡋ࡚࠾ࡾ㸪◚ቯ᫬ࡢ┦ᙜረᛶࡦࡎࡳࡶ୧⪅࡛ྠ➼࡟࡞ࡗࡓ࡜⪃࠼ࡽࢀࡿ㸬 S45C࡜ྠᵝ࡟㸪ᚤᑠ࣎࢖ࢻྜయᆺࡢᘏᛶ◚ቯࢆ࿊ࡍࡿᮦᩱ࡟ᑐࡋ࡚㸪ᮏᡭἲࡀ

᭷ຠ࡟㐺⏝࡛ࡁࡿࡇ࡜ࡀᮇᚅࡉࢀࡿ㸬

82

Fig. 4-17 Examples of SEM image of fractured surface of (a) notched round bar tensile test R0 = 3.0 mm, (b) notched round bar tensile test R0 = 20 mm, (c) 3-point

bending test w/t = 2.0, and (d) upsetting test L0/D0 = 1.5

83

Fig. 4-18 Histogram of diameter of dimples (d) (NBT: notched round bar tensile; 3-PB: 3-point bending; UPSET: upsetting; dave: average diameter of 50 dimples)

0 10 20 30 40

0 10 20 30 40

0 10 20 30 40 0 10 20 30 400 10 20 30 400 10 20 30 400 10 20 30 40

0 10 20 30 40

0 10 20 30 40

0 10 20 30 0 10 20 30 0 10 20 30

0.00 0.75 1.00 1.50 3.00 6.00 0.00 0.75 1.00 1.50 3.00 6.00 0.00 0.75 1.00 1.50 3.00 6.00 12.0

Frequency

Diam eter of dim ples d / μ m

R₀

=3 mm

R₀

=20 mm

R₀

=10 mm

w/t=1.0 w/t=2.0 w/t=4.0

L₀

/D

₀

=2.0

L₀

/D

₀

=1.5

L₀

/D

₀

=1.0

NBT tes t 3-PB test UPSET test

Edge Center

d_ave

=2.05

d_ave

=1.50

d_ave

=1.27

d_ave

=1.21

d_ave

=1.07

d_ave

=1.23 (C)

d_ave

=1.39 (E)

d_ave

=0.90

d_ave

=0.92

d_ave

=1.00

84

Fig. 4-19 Relationship between stress triaxiality at fracture (ηf) and average diameter of dimples (dave)

0.0 0.5 1.0 1.5 2.0 2.5

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Average diameter of dimplesdave/μm

Stress triaxiality at fracture η

_f w/t = 1.0

(Edge) L₀/D₀= 2.0

Average diameter of dimples dave/μm

NBT specimens 3-PB specimens UPSET specimens R₀ = 10 mm

R₀ = 20 mm

R₀ = 3 mm w/t = 2.0 w/t = 4.0

w/t = 1.0 (Center)

L₀/D₀= 1.5

L₀/D₀= 1.0

85 4.6 ⤖ゝ

ᮏ◊✲࡛ࡣ㸪෭㛫㘫㐀࡟࠾ࡅࡿᤣ㎸ࡳ➼ࡢ⾲㠃๭ࢀண ࡟ࡶᑐᛂ࡛ࡁࡿᗈ࠸

ᛂຊ୕㍈ᗘ⠊ᅖ࡛ࡢᘏᛶ◚ቯ㝈⏺ࢆྠᐃࡍࡿᡭἲࡢ㛤Ⓨࢆ┠ⓗ࡜ࡋ㸪Ⅳ⣲㗰 S45Cࢆᑐ㇟࡟4✀ࡢษḞ௜୸Წᘬᙇ㸦NBT㸧ヨ㦂࡜3✀ࡢ3Ⅼ᭤ࡆ㸦3-PB㸧ヨ 㦂ࢆᐇ᪋ࡋࡓ㸬ࡲࡓ㸪୧ヨ㦂ࡢ⤖ᯝ࠿ࡽᣦᩘ㛵ᩘᆺࡢᘏᛶ◚ቯண ࣔࢹࣝࡢࣃࣛ

࣓࣮ࢱࢆྠᐃࡋࡓ㸬ࡉࡽ࡟㸪ྠᐃࡉࢀࡓᘏᛶ◚ቯࣔࢹࣝࡢ᭷ຠᛶࢆ᳨ドࡍࡿࡓࡵ㸪

➃㠃ᣊ᮰ᅽ⦰㸦UPSET㸧ヨ㦂࡟࠾ࡅࡿ㝈⏺ᅽ⦰⋡ࡢண ࢆヨࡳࡓ㸬௨ୗ࡟㸪ᚓࡽ

ࢀࡓ▱ぢࢆ♧ࡍ㸬

1) NBTヨ㦂࡟ᛂຊ⿵ṇἲࢆ㐺⏝ࡋࡓ⤖ᯝ㸪◚᩿ࡲ࡛ࡢὶືᛂຊ᭤⥺ࡀྠᐃࡉ

ࢀ㸪◚ቯ㉳Ⅼࡢᛂຊ୕㍈ᗘη࡜┦ᙜࡦࡎࡳε^㹝ࡢᒚṔࢆྠᐃࡍࡿࡇ࡜ࡀ࡛ࡁ ࡓ㸬

2) 3-PBヨ㦂࡛ࡣ㸪ヨ㦂∦ࡢᖜ࡜ཌࡳࡢẚ⋡㸦w/t㸧ࢆኚ໬ࡉࡏࡿࡇ࡜࡛㸪◚ቯ

ุᐃ᫬ࡢᛂຊ୕㍈ᗘηfࡀ0.33㹼0.56ࡢ⠊ᅖ࡛◚ቯヨ㦂ࢆᐇ᪋ࡍࡿࡇ࡜ࡀ࡛

ࡁࡓ㸬ࡲࡓ㸪◚ቯ㉳Ⅼ࡟࠾ࡅࡿᛂຊ୕㍈ᗘηࡣ㸪ኚᙧึᮇ࠿ࡽ◚ቯ࡟⮳ࡿ

ࡲ࡛࡯ࡰ୍ᐃ࡛࠶ࡿࡇ࡜ࡀศ࠿ࡗࡓ㸬

3) NBT࡜3-PBࡢ୧ヨ㦂⤖ᯝ࠿ࡽỴᐃࡋࡓᣦᩘ㛵ᩘᆺࡢᘏᛶ◚ቯࣔࢹࣝࢆ⏝

࠸࡚UPSETヨ㦂ࡢ㝈⏺ᅽ⦰⋡ࢆண ࡋࡓ࡜ࡇࢁ㸪ṇࡢᛂຊ୕㍈ᗘᒚṔ࡟╔

┠ࡍࡿࡇ࡜࡛㸪ᐇ㦂⤖ᯝ࡜࠾࠾ࡴࡡ୍⮴ࡋࡓ㸬

4) SEM࡟ࡼࡿ◚᩿㠃ほᐹࡢ⤖ᯝ㸪UPSETヨ㦂࡜3-PB(w/t = 2.0)ヨ㦂ࡢ◚ቯ᫬

ࡢᛂຊ୕㍈ᗘ࡜ࢹ࢕ࣥࣉࣝࡢ≧ែࡣ㢮ఝࡋ࡚࠾ࡾ㸪◚ቯ᫬ࡢ┦ᙜረᛶࡦࡎ

ࡳࡶ୧⪅࡛ྠ➼࡟࡞ࡗࡓ࡜⪃࠼ࡽࢀࡿ㸬

86 ཧ⪃ᩥ⊩

4-1) ᮧ⏣┿ఙ㸪ྜྷ⏣ె඾㸪す⬥Ṋᚿ : ᭤ࡆヨ㦂࡜ษḞ௜୸Წᘬᙇヨ㦂ࢆ⏝࠸

ࡓ෭㛫ᤣ㎸ࡳຍᕤࡢ⾲㠃๭ࢀண , ረᛶ࡜ຍᕤ, 59-686 (2018)㸦In print, ᥖ

㍕Ỵᐃ㸧

4-2) Hancock, J.W. & Mackenzie, A. C.㸸On the mechanisms of ductile failure in high-strength steels subjected to multi-axial stress-states, J. Mech. Phys. Solid, 24 (1976), 147-169.

4-3) ᕤ⸨ⱥ࣭᫂㟷஭୍႐㸸S45Cࡢᤣ࠼㎸ࡳ๭ࢀヨ㦂, ረᛶ࡜ຍᕤ, 8-72 (1967), 17-27.

4-4) ᪥ᮏ㔠ᒓᏛ఍㸸㔠ᒓຍᕤ-ㅮᗙ࣭⌧௦ࡢ㔠ᒓᏛ ᮦᩱ⦅, (1986), 128.

4-5) ▼㯮ኴᾈ࣭㜿㒊ⱥႹ࣭ୖ㔝⣫୍࣭‮ᕝఙᶞ࣭⸨ཎṇᑦ࣭ྜྷ⏣ᗈ࣭᫂▼ᕝᏕ

ྖ㸸୰Ⅳ⣲㗰ࡢᘏᛶ◚ቯ࡟ཬࡰࡍᛂຊ୕㍈ᗘ࡜⤌⧊␗᪉ᛶࡢᙳ㡪, ረᛶ࡜

ຍᕤ, 54-634 (2013), 993-997.

4-6) ᮧ⏣┿ఙ࣭ྜྷ⏣ె඾࣭す⬥Ṋᚿ㸸ᘏᛶ◚ቯࣃ࣓࣮ࣛࢱྠᐃ࡟ཬࡰࡍDIC   ᐃ⢭ᗘࡢ᳨ド ᘏᛶ◚ቯࣃ࣓࣮ࣛࢱྠᐃࡢ㧗⢭ᗘ໬ ➨2 ሗ, ᖹᡂ 29ᖺᗘ ረᛶຍᕤ᫓Ꮨㅮ₇఍ㄽᩥ㞟, (2017), 259-260.

4-7) ෭㛫㘫㐀ศ⛉఍ᮦᩱ◊✲⌜㸸෭㛫ᤣ㎸ࡳᛶヨ㦂᪉ἲ, ረᛶ࡜ຍᕤ, 22-241 (1981), 139-144.

4-8) ྜྷ⏣ె඾࣭ᮧ℩Ὀ❶࣭‮ᕝఙᶞ࣭▼ᕝᏕྖ㸸ࡏࢇ᩿ຍᕤࡢኚᙧゎᯒ࡟࠾ࡅ

ࡿ✵Ꮝ⏕ᡂ⮫⏺ࡦࡎࡳࣔࢹࣝࡢᑟධ, ረᛶ࡜ຍᕤ, 46-532 (2005), 392-396.

4-9) ኱ሯ᫛ኵ࣭ᐑ⏣㝯ྖ࣭すᮧㄔ஧࣭ᮌᮧ㞞ಖ࣭㤿ῡ᐀ே㸸పᙉᗘ㗰࡟࠾ࡅࡿ

ᘏᛶ◚ቯࡢⓎ⏕࡟ཬࡰࡍᛂຊ୕㍈ᗘࡢᙳ㡪, ᮦᩱ㸪29-322(1980)㸪717-723.

4-10) ኱ሯ᫛ኵ࣭ᐑ⏣㝯ྖ࣭ᱜ஭ຮ࣭㣤⏣ᾈ㸸ᘏᛶ◚ቯ࡟ཬࡰࡍᛂຊ୕㍈ᗘࡢᙳ

㡪, ᮦᩱ, 34-381 (1984), 622-626.

87

ドキュメント内 有限要素法逆解析を用いた切欠付丸棒引張試験における大ひずみ域の流動応力同定 (ページ 74-94)