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

Title 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( 本文(Fulltext) )} Author(s) 村田, 真伸 Report No.(Doctoral Degree) 博士(工学) 工博甲第532号 Issue Date 2018-03-25 Type 博士論文 Version ETD URL http://hdl.handle.net/20.500.12099/75259 ※この資料の著作権は、各資料の著者・学協会・出版社等に帰属します。

i

᭷㝈せ⣲ἲ㏫ゎᯒࢆ⏝࠸ࡓษḞ௜୸Წᘬᙇヨ㦂࡟࠾ࡅࡿ

኱ࡦࡎࡳᇦࡢὶືᛂຊྠᐃ

Flow stress identification in large strain range using FEM inverse analysis

on notched round bar tensile test

㸰㸮㸯㸶ᖺ㸱᭶

ᮧ⏣ ┿ఙ

ii



i

┠ ḟ

➨㸯❶ ᗎㄽ 1 1.1 ⥴ゝ 1 1.2 ᪤Ꮡࡢὶືᛂຊྠᐃ᪉ἲ 7 1.2.1 ᘬᙇヨ㦂 7 1.2.2 ◳໬๎ 9 1.2.3 Bridgman ἲࢆ⏝࠸ࡓᛂຊ⿵ṇ᪉ἲ 10 1.2.4 ㏫ゎᯒࢆ⏝࠸ࡓ᪉ἲ 13 1.3 ᘏᛶ◚ቯண ࣔࢹࣝ࠾ࡼࡧࡑࡢࣃ࣓࣮ࣛࢱྠᐃ᪉ἲ 15 1.3.1 ᘏᛶ◚ቯࡢ࣓࢝ࢽࢬ࣒ 15 1.3.2 ྛ✀ࡢᘏᛶ◚ቯண ࣔࢹࣝ 17 1.3.3 ᘏᛶ◚ቯࣃ࣓࣮ࣛࢱࡢྠᐃ᪉ἲ 20 1.4 ᮏㄽᩥࡢ┠ⓗ࡜ᵓᡂ 22  ཧ⪃ᩥ⊩ 25 ➨㸰❶ ษḞ௜୸Წᘬᙇヨ㦂ࢆ⏝࠸ࡓὶືᛂຊྠᐃᡭἲࡢ㛤Ⓨ 28 2.1 ⥴ゝ 28 2.2 ᐇ㦂᪉ἲ 29 2.2.1 ౪ヨᮦ࠾ࡼࡧヨ㦂∦ᙧ≧ 29 2.2.2 ᘬᙇヨ㦂᪉ἲ 31 2.3 ᩘ್ᐇ㦂᪉ἲ 32 2.4 ᛂຊ⿵ṇ᪉ἲ 33 2.4.1 Bridgman ἲ࡟ࡼࡿᛂຊ⿵ṇ㸦ᚑ᮶ἲ㸧 33 2.4.2 ㏫ゎᯒ࡟ࡼࡿᛂຊ⿵ṇ㸦ᥦ᱌ἲ㸧 34 2.5 ⤖ᯝ࡜⪃ᐹ 37 2.5.1 ᩘ್ᐇ㦂ࢆᑐ㇟࡜ࡋࡓᛂຊ⿵ṇ࡜ࡑࡢ⪃ᐹ 37 2.5.2 SS400 ᘬᙇヨ㦂ࢆᑐ㇟࡜ࡋࡓᛂຊ⿵ṇ࡜ࡑࡢ⪃ᐹ 42 2.6 ⤖ゝ 46  ཧ⪃ᩥ⊩ 47 ➨㸱❶ ษḞ௜୸Წᘬᙇヨ㦂ࢆ⏝࠸ࡓᘏᛶ◚ቯࣃ࣓࣮ࣛࢱྠᐃ 48 3.1 ⥴ゝ 48 3.2 ᐇ㦂᪉ἲ 49 3.2.1 ౪ヨᮦ࠾ࡼࡧヨ㦂∦ᙧ≧ 49

ii 3.2.2 ᘬᙇヨ㦂᪉ἲ 51 3.3 ᥦ᱌ᡭἲ࡟ࡼࡿᛂຊ⿵ṇ᪉ἲ 52 3.4 ᥦ᱌ᡭἲ࡟ࡼࡿὶືᛂຊ᭤⥺࠾ࡼࡧᘏᛶ◚ቯࣃ࣓࣮ࣛࢱࡢྠᐃ⤖ᯝ 53 3.4.1 ὶືᛂຊ᭤⥺ࡢྠᐃ⤖ᯝ 53 3.4.2 㝈⏺ࢲ࣓࣮ࢪ್ࡢྠᐃ⤖ᯝ 55 3.5 ᛂຊホ౯ࡢ᪉ἲࡀ㝈⏺ࢲ࣓࣮ࢪ್ࡢྠᐃ⤖ᯝ࡟ཬࡰࡍᙳ㡪 57 3.5.1 Bridgman ἲ࡟ࡼࡿ㝈⏺ࢲ࣓࣮ࢪ್ࡢྠᐃ⤖ᯝ 57 3.5.2 ⪃ᐹ 59 3.6 ⤖ゝ 61  ཧ⪃ᩥ⊩ 62 ➨㸲❶ ᭤ࡆヨ㦂࡜ษḞ௜୸Წᘬᙇヨ㦂ࢆ⏝࠸ࡓ෭㛫ᤣ㎸ࡳຍᕤࡢ⾲㠃๭ࢀண   63  4.1 ⥴ゝ 63  4.2 ᐇ㦂᪉ἲ 65   4.2.1 ౪ヨᮦ࠾ࡼࡧヨ㦂∦ᙧ≧ 65   4.2.2 ษḞ௜୸Წᘬᙇ㸦NBT㸧ヨ㦂᪉ἲ 65   4.2.3 3 Ⅼ᭤ࡆ㸦3-PB㸧ヨ㦂᪉ἲ 67  4.3 FEM ゎᯒ᪉ἲ 69   4.3.1 ษḞ௜୸Წᘬᙇ㸦NBT㸧ヨ㦂ゎᯒ࡟ࡼࡿὶືᛂຊ᭤⥺ࡢ⿵ṇ᪉ἲ 69   4.3.2 3 Ⅼ᭤ࡆ㸦3-PB㸧ヨ㦂ゎᯒ᪉ἲ 71  4.4 ᐇ㦂࠾ࡼࡧ FEM ゎᯒ⤖ᯝ 73  4.5 ➃㠃ᣊ᮰ᅽ⦰ヨ㦂࡟ࡼࡿ᳨ドᐇ㦂 76   4.5.1 ➃㠃ᣊ᮰ᅽ⦰㸦UPSET㸧ヨ㦂᪉ἲ 76   4.5.2 ➃㠃ᣊ᮰ᅽ⦰㸦UPSET㸧ヨ㦂ࡢ FEM ゎᯒ᪉ἲ 77   4.5.3 FEM ゎᯒ⤖ᯝ 78   4.5.4 ࢹ࢕ࣥࣉࣝᑍἲ ᐃ⤖ᯝ࠾ࡼࡧ⪃ᐹ 81  4.6 ⤖ゝ 85  ཧ⪃ᩥ⊩ 86 ➨㸳❶ ⥲ᣓ 87 㛵㐃ㄽᩥ┠㘓 90 ㅰ㎡ 92

iii グྕ A ኚᙧ୰ࡢ᩿㠃✚ A ᣦᩘ㛵ᩘᆺᘏᛶ◚ቯࣔࢹࣝࡢࣃ࣓࣮ࣛࢱ a ࡃࡧࢀᗏ࡟࠾ࡅࡿ᭱ᑠ᩿㠃༙ᚄ af ◚᩿᫬ࡢࡃࡧࢀᗏ᩿㠃༙ᚄ av Voce ๎ࡢࣃ࣓࣮ࣛࢱ A0 ึᮇ᩿㠃✚ a0 ࡃࡧࢀᗏ࡟࠾ࡅࡿึᮇ᭱ᑠ᩿㠃༙ᚄ B ᣦᩘ㛵ᩘᆺᘏᛶ◚ቯࣔࢹࣝࡢࣃ࣓࣮ࣛࢱ bv Voce ๎ࡢࣃ࣓࣮ࣛࢱ C Ludwik ๎ࡢࣃ࣓࣮ࣛࢱ CA Ayada ࣔࢹࣝ࡟࠾ࡅࡿ㝈⏺ࢲ࣓࣮ࢪ್

CCL Cockcroft and Latham ࣔࢹࣝ࡟࠾ࡅࡿ㝈⏺ࢲ࣓࣮ࢪ್

CM McClintock ࣔࢹࣝ࡟࠾ࡅࡿ㝈⏺ࢲ࣓࣮ࢪ್

CRT Rice and Tracy ࣔࢹࣝ࡟࠾ࡅࡿ㝈⏺ࢲ࣓࣮ࢪ್

cv Voce ๎ࡢࣃ࣓࣮ࣛࢱ d ࢹ࢕ࣥࣉࣝࡢ㏆ఝ෇┤ᚄ dave ࢹ࢕ࣥࣉࣝࡢ㏆ఝ෇┤ᚄࡢᖹᆒ dε ┦ᙜረᛶࡦࡎࡳቑศ D0 ෇ᰕヨ㦂∦ࡢึᮇ┤ᚄ E ࣖࣥࢢ⋡ e Pi࡜Fi(x)ࡢ㛫ࡢᖹᆒ஧஌ㄗᕪ F ረᛶಀᩘ㸦F ್㸧 Fi(x) ㏫ゎᯒࡢⲴ㔜ࡢィ⟬Ⅼ H ⥺ᙧ◳໬๎ࡢࣃ࣓࣮ࣛࢱ Lf ◚ቯุᐃ᫬ࡢヨ㦂∦㧗ࡉ L0 ኚᙧ๓ࡢཎᶆⅬ㊥㞳 L0 ෇ᰕヨ㦂∦ࡢึᮇ㧗ࡉ L ኚᙧᚋࡢᶆⅬ㊥㞳 N ὶືᛂຊ᭤⥺ࡢศ๭ᩘ n P̺(a0-a)᭤⥺ࡢศ๭ᩘ n ຍᕤ◳໬ᣦᩘ㸦n ್㸧 P ᘬᙇⲴ㔜 Pi ᘬᙇⲴ㔜ࡢᐇ㦂Ⅼ R ࡃࡧࢀᗏ࡟࠾ࡅࡿ᭤⋡༙ᚄ r ࡃࡧࢀᗏ᩿㠃୰ᚰ࠿ࡽࡢ༙ᚄ᪉ྥࡢ㊥㞳

iv R0 ࡃࡧࢀᗏ࡟࠾ࡅࡿึᮇ᭤⋡༙ᚄ t 3 Ⅼ᭤ࡆヨ㦂∦ཌࡳ w 3 Ⅼ᭤ࡆヨ㦂∦ᖜ x = xI ᛂຊ⿵ṇಀᩘ㸦᭱㐺໬ィ⟬ࡢタィኚᩘ㸧 Y ึᮇ㝆అᛂຊ Y0 ࡃࡧࢀィ ᫬ࡢ༙ᚄ᪉ྥࡢᇶ‽㊥㞳 εE ᙎᛶࡦࡎࡳ εeq ┦ᙜࡦࡎࡳ εf ◚᩿┦ᙜረᛶࡦࡎࡳ εN බ⛠ࡦࡎࡳ ε0 Swift ๎ࡢࣃ࣓࣮ࣛࢱ εp ┦ᙜረᛶࡦࡎࡳ εT ┿ࡦࡎࡳ㸦ᑐᩘࡦࡎࡳ㸧 εu ୍ᵝఙࡧ㝈⏺ࡢ┦ᙜࡦࡎࡳ ε 㹝 ┦ᙜࡦࡎࡳ ε 㹝 f ◚᩿┦ᙜረᛶࡦࡎࡳ ε 㹝_* η ࡀṇࡢሙྜࡢࡳ⣼✚ࡋࡓ┦ᙜረᛶࡦࡎࡳ ε 㹝 f* η ࡀṇࡢሙྜࡢࡳ⣼✚ࡋࡓ◚᩿┦ᙜረᛶࡦࡎࡳ η ᛂຊ୕㍈ᗘ ηf ◚ቯุᐃ᫬ࡢᛂຊ୕㍈ᗘ T ᖹᆒLode ゅ σ ┦ᙜᛂຊ σflow ὶືᛂຊ σflowI ὶືᛂຊ σr ༙ᚄ᪉ྥᛂຊ σref ᩘ್ᐇ㦂࡟౑⏝ࡍࡿཧ↷ὶືᛂຊ᭤⥺ σ(swift) ref ᩘ್ᐇ㦂࡟౑⏝ࡍࡿཧ↷ὶືᛂຊ᭤⥺㸦Swift ᆺ㸧 σ(voce) ref ᩘ್ᐇ㦂࡟౑⏝ࡍࡿཧ↷ὶືᛂຊ᭤⥺㸦Voce ᆺ㸧 σm ᖹᆒᛂຊ σmax ᭱኱୺ᛂຊ σN බ⛠ᛂຊ σz ᘬᙇ᪉ྥᛂຊ σzave ᖹᆒᘬᙇᛂຊ㸦┿ᛂຊ㸧 σzaveI ᖹᆒᘬᙇᛂຊ σθ ࿘᪉ྥᛂຊ

1

➨㸯❶ ᗎ ㄽ

 1.1 ⥴ゝ 㗰ࡢ㘫㐀㒊ရࡢ⏕⏘㔞ࡣ 1960 ᖺ௦࠿ࡽᛴ⃭࡟ቑຍࡋ 2007 ᖺ࡟ࡣ 2,500 ༓ࢺ ࣥࢆ㉸࠼ࡓ 1-1) _{㸬Fig. 1-1 ࡟♧ࡍࡼ࠺࡟㸪ࡑࡢ⣙ 7 ๭ࢆ⮬ື㌴⏝㏵ࡀ༨ࡵ࡚࠸ࡿ㸬} Fig. 1-2 ࡟ࡣ㸪᪥⣔࣓࣮࣮࢝ࡢ⮬ື㌴⏕⏘ྎᩘࡢ㛗ᮇ᥎⛣ࢆ♧ࡍࡀ㸪㘫㐀㒊ရࡢ ⏕⏘㔞ࡢቑຍ࡟࿧ᛂࡍࡿࡼ࠺࡟㸪ࢃࡀᅜ࡟࠾ࡅࡿ⮬ື㌴ࡢ⏕⏘ྎᩘࡣ㸪1960 ᖺ ௦࠿ࡽᛴ⃭࡟ቑຍࡋ㸪1980 ᖺ௦࡟ࡣᅜෆ⏕⏘ࡀᖺ㛫 1000 ୓ྎࢆ㉸࠼࡚࠸ࡿ 1-2)_㸬 ᅜෆ⏕⏘ࡣ1990 ᖺ㡭ࢆቃ࡟ᶓࡤ࠸࡜࡞ࡿࡀ㸪1985 ᖺ㡭࠿ࡽࡣ㸪ᾏእ⏕⏘ࡀᮏ᱁ ໬ࡍࡿࡇ࡜࡛㸪᪥⣔࣓࣮࣮࢝ࡢ⮬ື㌴⏕⏘ྎᩘ࡜ࡋ࡚ࡣ㸪2004 ᖺ࡟ 2000 ୓ྎࢆ ㉸࠼࡚࠸ࡿ㸬㘫㐀㒊ရࡢ〇㐀ࡣ㸪1960 ᖺ௦࠿ࡽጞࡲࡗࡓ⮬ື㌴ࡢ኱㔞⏕⏘ࢆᨭ ࠼ࡿ㔜せ࡞ᇶ┙ᢏ⾡࡛࠶ࡿࡇ࡜ࡣ␲࠸ࡼ࠺ࡀ࡞࠸㸬  㘫㐀ࡣ⣲ᮦࡢ෌⤖ᬗ ᗘ௨ୖ࡛ᡂᙧࡍࡿ⇕㛫㘫㐀࡜㸪୺࡟ᐊ ࡛ᡂᙧࡍࡿ෭ 㛫㘫㐀࡟኱ูࡉࢀࡿ㸬⇕㛫㘫㐀ࡣᮦᩱࢆຍ⇕ࡍࡿࡓࡵᮦᩱࡢኚᙧ᢬ᢠࡀᑠࡉࡃ ຍᕤᛶ࡟ඃࢀࡿࡀ㸪⾲㠃ᛶ≧ࡸᑍἲ⢭ᗘࡣຎࡿ㸬୍᪉㸪෭㛫㘫㐀ࡣᡂᙧᚋࡢ⾲㠃 ᛶ≧ࡸᑍἲ⢭ᗘ࡟ඃࢀ㸪㒊ရ࡟ࡼࡗ࡚ࡣษ๐➼ࡢ௙ୖࡆᕤ⛬ࢆᚲせ࡜ࡋ࡞࠸ࢿ ࢵࢺࢩ࢙࢖ࣉᡂᙧ㸪࡞࠸ࡋࡣ௙ୖࡆᕤ⛬ࢆ࡯࡜ࢇ࡝ᚲせ࡜ࡋ࡞࠸ࢽ࢔ࢿࢵࢺᡂ ᙧࡀྍ⬟࡜࡞ࡿ1-3)_{㸬ษ๐ࡀ୙せ࡛࠶ࢀࡤ↓㥏࡞౑⏝ᮦᩱࢆ๐ῶ࡛ࡁ㸪ࡲࡓ࣓ࢱ} ࣝࣇ࣮ࣟࢆษ᩿ࡋ࡞࠸ࡇ࡜࡛㸪㧗ᙉᗘ໬ࡀᮇᚅ࡛ࡁࡿ࡞࡝࣓ࣜࢵࢺࡀ኱ࡁ࠸㸬 Fig. 1-3 ࡣࢺࣚࢱ⮬ື㌴࡟࠾࠸࡚஌⏝㌴࡟ᦚ㍕ࡉࢀࡿ෭㛫㘫㐀ရࡢኚ㑄ࢆ♧ࡋ ࡓࡶࡢ࡛࠶ࡿࡀ㸪1965 ᖺ௨㝆෭㛫㘫㐀ࡢ㐺⏝⠊ᅖࡀᛴ㏿࡟ᣑ኱ࡋ࡚࠸ࡿࡇ࡜ࡀ ࢃ࠿ࡿ 1-4)_㸬  ࡑࡢ཯㠃㸪෭㛫㘫㐀࡛ࡣ㸪ձຍᕤ࡟ᚲせ࡞Ⲵ㔜ࡀ┦ᙜ࡟኱ࡁ࠸㸪ղᮦᩱࡢᘏᛶ ୙㊊࡟క࠺๭ࢀ㸦ᘏᛶ◚ቯ㸧ࡀⓎ⏕ࡍࡿ㸪࡞࡝ࡢၥ㢟Ⅼࡶ࠶ࡿ㸬  ձ࡟㛵ࡋ࡚㸪㏻ᖖࡣ┦ᛂ࡟⬟ຊࡢ㧗࠸ࣉࣞࢫᶵࢆ⏝࠸ࡿࡀ㸪ຍᕤⲴ㔜ࡢぢ✚ࡾ ࢆぢㄗࢀࡤ㸪ᕤ⛬タィࡢ኱ᖜ࡞ぢ┤ࡋࢆ㏕ࡽࢀ㸪᭱ᝏࣉࣞࢫᶵᲔࡢ⬟ຊ୙㊊࡟ࡼ ࡾᡂᙧ࡛ࡁ࡞࠸࡞࡝ࡢၥ㢟ࢆ⏕ࡌࡿ㸬ࡲࡓ㸪࣮࣡ࢡࡀ᥋ࡍࡿ㔠ᆺ㸦ࢲ࢖࢖ࣥࢧ࣮ ࢺ㸧࡟ࡣ㠀ᖖ࡟㧗࠸㈇Ⲵࡀຍࢃࡿࡓࡵ㸪୍⯡࡟ࡣࢩ࣓௦ࢆタࡅࡓ⿵ᙉࣜࣥࢢ࡟ᅽ ධࡶࡋࡃࡣ↝ࣂ࣓ࡍࡿ࡞࡝ࡋ㸪ணᅽ⦰ᛂຊࢆ࠿ࡅ࡚㔠ᆺ◚ᦆࢆ㜵ࡄ࡞࡝ࡢᕤኵ ࡀ᪋ࡉࢀࡿ 1-5)_{㸬ࡋ࠿ࡋ࡞ࡀࡽ㸪ᡂᙧ࡟ࡼࡾ㔠ᆺ࡟Ⓨ⏕ࡍࡿᘬᙇᛂຊࡀணᅽ⦰ᛂ} ຊࢆ㉸࠼࡚㝆అᛂຊ௨ୖ࡟㐩ࡍࡿ࡜㔠ᆺ◚ᦆࢆ⏕ࡌࡿ㸬 ղ࡟㛵ࡋ࡚㸪෭㛫㘫㐀ࡢึᮇᕤ⛬࡛࠶ࡿᤣ㎸ࡳ࡛ࡣ㸪Fig. 1-4 ࡟♧ࡍࡼ࠺࡞⾲ 㠃๭ࢀࡀ⏕ࡌࡿ 1-6)_{㸬ࡲࡓ㸪࢔ࢫࢡࣝࢩࣕࣇࢺࡢࡼ࠺࡞ẁ௜ࢩࣕࣇࢺࡢ๓᪉ᢲฟ} ࡋ࡛ࡣ㸪Fig. 1-5 ࡟♧ࡍࡼ࠺࡞ࢩ࢙ࣈࣟࣥࢡࣛࢵࢡࡀ⏕ࡌࡿ1-7)_{㸬ࡶࡋ㸪ヨసࡢẁ}

2 㝵࡛๭ࢀࡀ⏕ࡌࡓሙྜ࡟ࡣ㸪ᕤ⛬ࡸ㔠ᆺࡢ኱ᖜ࡞ぢ┤ࡋࢆᙉ࠸ࡽࢀ㸪኱ᖜ࡞ᕤᮇ ࡢ㐜ᘏࡸࢥࢫࢺቑࢆᣍࡃ㸬ࡍ࡞ࢃࡕ㸪෭㛫㘫㐀ࡢศ㔝࡟࠾࠸࡚ࡣ㸪࠸ࡎࢀࡢၥ㢟 ࡟ᑐࡋ࡚ࡶ㸪ᕤᮇ▷⦰ࡸࢥࢫࢺ๐ῶࢆᐇ⌧ࡍࡿࡓࡵ࡟ࡣ㸪ᕤ⛬タィ᫬࡟㸪ᡂᙧⲴ 㔜㸪࣮࣡ࢡࡢᮦᩱὶື㸪࣮࣡ࢡࡢ๭ࢀ㸪㔠ᆺࡢᛂຊ࡞࡝㸪ண ࡋ࠺ࡿ୙ලྜ࡟㛵 ࡋ࡚㸪஦๓࡟ண ࡍࡿࡇ࡜ࡀ㠀ᖖ࡟㔜せ࡛࠶ࡿ࡜࠸࠼ࡿ㸬

1980 ᖺ௨㝆㸪ረᛶຍᕤࡢᕤ⛬タィ࡟᭷㝈せ⣲ἲ㸦FEM㸸Finite Element Method㸧 ࢆ࣮࣋ࢫ࡜ࡋࡓࢩ࣑࣮ࣗࣞࢩࣙࣥᢏ⾡㸦CAE㸸Computer Aided Engineering㸧ࡀᮏ ᱁ⓗ࡟ά⏝ࡉࢀࡿࡼ࠺࡟࡞ࡗ࡚ࡁࡓ㸬㧗ᶵ⬟࡞CAE ࢯࣇࢺ࢚࢘࢔ࡀ┦ḟ࠸࡛ᕷ ㈍ࡉࢀࡓࡇ࡜ࡶ௻ᴗ࡟࠾ࡅࡿCAE ࡢά⏝ࢆᚋᢲࡋࡋࡓ㸬ỗ⏝ࡢ㠀⥺ᙧᵓ㐀ゎᯒ ࢯࣇࢺ࢚࢘࢔࡟ࡣ LS-DYNA㸦⡿ Livermore Software Technology Corporation㸧㸪 ABAQUS㸦௖ Dassault Systems㸧㸪MARC㸦⡿ MSC Software Corporation㸧࡞࡝ࡀ ࠶ࡾ㸪ゎᯒᑐ㇟ࡣ㘫㐀࡟࡜࡝ࡲࡽ࡞࠸㸬ࡲࡓ㸪ࣉࣜ࠾ࡼࡧ࣏ࢫࢺࣉࣟࢭࢵࢧࢆ㘫 㐀ᕤ⛬࡟≉໬ࡉࡏࡓ㸪࠸ࢃࡺࡿ㘫㐀ᑓ⏝ࢯࣇࢺ࢚࢘࢔࡟ࡣ㸪DEFORM-2D/3D㸦⡿ Scientific Forming Technologies Corporation㸧㸪Simfact Forming㸦⡿ MSC Software Corporation㸧㸪FORGE㸦௖ Transvalor㸧࡞࡝ࡀ࠶ࡆࡽࢀࡿ㸬ࡇࢀࡽ CAE ࢯࣇࢺ࢘ ࢚࢔ࢆ⏝࠸ࡿࡇ࡜࡛㸪౛࠼ࡤ㸪㘫㐀⣲ᮦࡢὶࢀ࡜ᡂᙧⲴ㔜ࡢண 㸪㔠ᆺࡢ☻⪖ၥ 㢟ᑐ⟇㸪ᮦᩱ๭ࢀ㸪㔠ᆺࡢ๭ࢀၥ㢟ᑐ⟇࡞࡝ࢆࢩ࣑࣮ࣗࣞࢩ࣮ࣙࣥ࣋ࢫ᳨࡛ウ࡛ ࡁࡿࡼ࠺࡟࡞ࡗ࡚ࡁࡓ 1-8), 1-9)_㸬  CAE ࢯࣇࢺ࢚࢘࢔ࡢᬑཬึᮇ࡟࠾࠸࡚ࡣ㸪ࡑࡢᑟධࡣ኱௻ᴗࡀ୰ᚰ࡛࠶ࡗࡓ ࡀ㸪2000 ᖺ௨㝆࡟࡞ࡿ࡜࣮࣡ࢡࢫࢸ࣮ࢩࣙࣥࡢࡼ࠺࡞Ᏻ౯࡞ィ⟬ࢩࢫࢸ࣒࡛ࡶ ᐇ⏝ⓗ࡞ゎᯒࡀᐇ⾜ྍ⬟࡜࡞ࡗࡓࡇ࡜࡛㸪୰ᑠ௻ᴗ࡬ࡶCAE ࢯࣇࢺ࢚࢘࢔ࡀᬑ ཬࡋጞࡵࡿ㸬ࡇࢀࡣ㸪୰ᑠ௻ᴗ⮬㌟ࡀ⮬ࡽᢏ⾡ຊྥୖࢆ┠ⓗ࡟ᑟධࡋࡓࡔࡅ࡛࡞ ࡃ㸪ぶ௻ᴗ࠿ࡽࡢせㄳ࡟ࡼࡿ࡜ࡇࢁࡶᑡ࡞࠿ࡽࡎ࠶ࡿࡼ࠺࡛࠶ࡿ㸬ࡋ࠿ࡋ࡞ࡀࡽ ୰ᑠ௻ᴗࡀ CAE ࢯࣇࢺ࢚࢘࢔ࢆᑟධࡋ㸪ᕤ⛬タィ࡟༑ศά⏝࡛ࡁࡿࡲ࡛࡟ࡣ㸪 ࠸ࡃࡘ࠿ࡢࣁ࣮ࢻࣝࡀ࠶ࡿ࡜⪃࠼ࡽࢀࡿ㸬  ୰ᑠ௻ᴗࡀ┤㠃ࡍࡿึࡵࡢࣁ࣮ࢻࣝࡣ㸪CAE ࢯࣇࢺ࢚࢘࢔ࡢ㧗㢠࡞ᑟධ㈝⏝ ࠾ࡼࡧࡑࡢᚋࡢಖᏲ㈝⏝࡞࡝ࢆྵࡵࡓࢥࢫࢺ㠃࡛࠶ࡿ㸬ࡓࡔࡋ㸪ࡇࢀ࡟ࡘ࠸࡚ࡣ㸪 2006 ᖺ࡟ᡂ❧ࡋࡓ୰ᑠ௻ᴗࡢࡶࡢ࡙ࡃࡾᇶ┙ᢏ⾡ࡢ㧗ᗘ໬࡟㛵ࡍࡿἲᚊ 1-10)_ࢆ ᇶ࡟ࡋࡓ㸪ᨻᗓࡢᡓ␎ⓗᇶ┙ᢏ⾡㧗ᗘ໬ᨭ᥼஦ᴗ㸦࠸ࢃࡺࡿࢧ࣏࢖ࣥ஦ᴗ㸧1-11) ࢆά⏝ࡍࡿࡇ࡜࡛㸪ゎỴ࡛ࡁࡿሙྜࡀ࠶ࡿ㸬୍᪉࡛㸪⏘ᴗ➇தຊ᠓ㄯ఍㸦COCN㸧 ࡀ 2011 ᖺ࡟⾜ࡗࡓ௻ᴗ࢔ࣥࢣ࣮ࢺ࡟ࡼࡿ࡜㸪୰ᑠ௻ᴗࡀ CAE ࢯࣇࢺ࢚࢘࢔ࢆ ᑟධ࡛ࡁࡓ࡜ࡋ࡚ࡶ㸪࠺ࡲࡃά⏝࡛ࡁࡿ࠿࡝࠺࠿ࡣࡴࡋࢁᑟධࡋࡓᚋࡢ㐠⏝㠃 ࡀ㔜せ࡛࠶ࡿࡇ࡜ࡀᣦ᦬ࡉࢀ࡚࠸ࡿ 1-12)_{㸬ձၥ㢟ࡢᮏ㉁ࢆぢᢤࡁ㐺ษ࡞ࣔࢹࣝ} ໬ࡀ࡛ࡁࡿேᮦࢆ࡝ࡢࡼ࠺࡟⫱ᡂࡍࡿ࠿㸪ղᮦᩱࣃ࣓࣮ࣛࢱࢆጞࡵ࡜ࡍࡿ㐺ษ ࡞ゎᯒ᮲௳ࡢྲྀࡾᢅ࠸ࡀ࡛ࡁࡿࡼ࠺࡟ࡍࡿ࠿㸪࡞࡝ࡀࡑࢀ࡟࠶ࡓࡿ㸬 ձࡢேᮦ⫱ᡂ࡟㛵ࡋ࡚ࡣ㸪ᮏㄽᩥࡢ୺㢟࠿ࡽእࢀࡿࡓࡵࡇࡇ࡛ࡣᅜෆ࡟࠾ࡅ

3

ࡿྛ✀ᅋయࡢྲྀࡾ⤌ࡳࡢ୍➃ࢆ⤂௓ࡍࡿ࡟࡜࡝ࡵࡿ㸬౛࠼ࡤ㸪 NPO ἲே CAE ᠓ヰ఍࡛ࡣ㸪㛵す㸪୰㒊㸪㛵ᮾ㸪໭㝣㸪ᗈᓥ࡞࡝ࡢྛᆅ࡛ゎᯒሿࢆ㛤ദࡋ࡚࠸ࡿ

1-13)_{㸬NPO ἲே㠀⥺ᙧ CAE ༠఍࡛ࡣ㸪ᖺ 2 ᅇ㠀⥺ᙧ CAE ຮᙉ఍ࢆ㛤ദࡋ࡚࠸ࡿ}

1-14)_{㸬NPO ἲே CAE ᨭ᥼ࢿࢵࢺ࡛ࡣ㸪୺࡟㔠ᆺࢆ〇㐀ࡍࡿ୰ᑠ௻ᴗ࡟ᑐࡋ࡚㸪} ࢯࣇࢺ࢚࢘࢔ࡢ᧯సカ⦎ࡸረᛶຍᕤ࡟㛵ࡍࡿᇶ♏▱㆑ࢆㅮ⩦ࡍࡿࡓࡵࡢຮᙉ఍ ➼ࢆᐇ᪋ࡋ࡚࠸ࡿ 1-15)_{㸬ࡑࡢ௚࡟ࡶ㸪ᆅ᪉⮬἞యࡢබタ◊✲ᶵ㛵ࡸCAE ࡢࢯࣇ} ࢺ࢚࢘࢔࣋ࣥࢲ࣮ࡀ୺ദࡍࡿㅮ⩦఍࡞࡝ከᩘ࠶ࡿ㸬  ղ࡟㛵ࡋ࡚㸪๓㏙ࡢࡼ࠺࡞෭㛫㘫㐀≉᭷ࡢၥ㢟ࢆCAE ࡛⢭ᗘࡼࡃ෌⌧ࡍࡿࡓ ࡵ࡟ࡣ㸪ᮦᩱࡢኚᙧ᢬ᢠࢆ⾲⌧ࡍࡿὶືᛂຊ᭤⥺ࡸ㸪ᮦᩱࡢᘏᛶ㝈⏺ࢆண ࡍࡿ ࡓࡵࡢྛ✀ࡢᘏᛶ◚ቯண ࣔࢹࣝࡢࣃ࣓࣮ࣛࢱ㸦ᘏᛶ◚ቯࣃ࣓࣮ࣛࢱ㸧࡞࡝ࡀ㠀 ᖖ࡟㔜せ࡞ᙺ๭ࢆᯝࡓࡍ㸬୍᪉㸪ࡑࢀࡽࡢࢹ࣮ࢱ࣮࣋ࢫ࡟㛵ࡋ࡚CAE ࢯࣇࢺ࢘ ࢚࢔ࡢᑐᛂࡣ༑ศ࡜ࡣゝ࠼࡞࠸㸬ỗ⏝ࡢ㠀⥺ᙧCAE ࢯࣇࢺ࢚࢘࢔࡟ࡣ࡯࡜ࢇ࡝ ࡢሙྜ࡛㸪ࡑࡶࡑࡶᮦᩱࡢࢹ࣮ࢱ࣮࣋ࢫࡀഛࢃࡗ࡚࠸࡞࠸㸬౛࠼ࡤ㸪ࣉࣞࢫᡂᙧ ゎᯒᑓ⏝ࢯࣇࢺࡢ JSTAMP ࡸ㘫㐀ࡢᑓ⏝ࢯࣇࢺ࢚࢘࢔ࡢ DEFORM ➼࡟ࡣ୍㒊 ࡢᮦᩱ࡟ࡘ࠸࡚㸪ὶືᛂຊ᭤⥺ࡢࢹ࣮ࢱ࣮࣋ࢫࡀ‽ഛࡉࢀ࡚࠸ࡿࡀ㸪໬Ꮫᡂศࡸ ⇕ฎ⌮᮲௳ࡶྵࡵ࡚⥙⨶ࡉࢀ࡚࠸ࡿࢃࡅ࡛࡞ࡃ㸪⢭ᗘ㠃ࡢ⿵ൾࡶ࡞࠸㸬ᘏᛶ◚ቯ ࣃ࣓࣮ࣛࢱ࡟㛵ࡋ࡚ࡣ㸪Cockcroft and Latham 1-16)_㸪Ayada 1-17)_{➼ࡢ✚ศᆺᘏᛶ◚ቯ}

᮲௳ᘧࢆጞࡵ࡜ࡍࡿྛ✀ࡢᘏᛶ◚ቯண ࣔࢹࣝ⮬యࡣከࡃࡢࢯࣇࢺ࢚࢘࢔࡟ᐇ ⿦ࡉࢀ࡚࠸ࡿࡀ㸪ࡑࡢࣃ࣓࣮ࣛࢱࡢධຊࡣ࣮ࣘࢨ࣮࡟ࡺࡔࡡࡽࢀ࡚࠸ࡿࡢࡀ⌧ ≧࡛࠶ࡿ㸬 ୖグࡢࡼ࠺࡞≧ἣࢆ㚷ࡳ㸪෭㛫㘫㐀ゎᯒࡢண ⢭ᗘࢆ኱ࡁࡃᕥྑࡍࡿὶືᛂ ຊ᭤⥺ࡸᘏᛶ◚ቯࣃ࣓࣮ࣛࢱ➼ࡢᮦᩱࣃ࣓࣮ࣛࢱࢆ㸪୰ᑠ௻ᴗ⮬㌟࡛⡆౽࠿ࡘ 㧗⢭ᗘ࡟ྠᐃ࡛ࡁࡿࡼ࠺࡞ᡭἲࢆᥦ᱌ࡋࡓ࠸࡜࠸࠺ࡢࡀᮏ◊✲ࡢືᶵ࡛࠶ࡿ㸬 ࡑࡢࡓࡵ㸪ᮏ◊✲࡛ࡣ㸪୰ᑠ௻ᴗ࡛ࡶࡍ࡛࡟ᑟධࡉࢀ࡚࠸ࡿ㸪ࡶࡋࡃࡣᐜ᫆࡟ᑟ ධࡀྍ⬟࡞ᘬᙇヨ㦂ᶵࢆ฼⏝ࡍࡿࡇ࡜࡟╔┠ࡋࡓ㸬 ᘬᙇヨ㦂ࡣ⡆౽࡟ᮦᩱヨ㦂ࡀᐇ᪋࡛ࡁࡿ୍᪉࡛㸪୍ᵝఙࡧ㝈⏺ࢆ㉸࠼ࡓᚋࡣ ヨ㦂∦࡟ࡃࡧࢀࡀⓎ⏕ࡍࡿࡓࡵ㸪㘫㐀ゎᯒ࡛ᚲせ࡜ࡉࢀࡿ1.0 ࢆ㉸࠼ࡿࡼ࠺࡞኱ ࡦࡎࡳᇦࡢὶືᛂຊࢆ┤᥋ⓗ࡟ ᐃࡍࡿࡇ࡜ࡣᅔ㞴࡛࠶ࡿ㸬ࡦ࡜ࡓࡧヨ㦂∦࡟ ࡃࡧࢀࡀ⏕ࡌࡿ࡜㸪ᖹᆒᘬᙇᛂຊ㸦┿ᛂຊ㸧ࡢィ ࡟ᚲせ࡞᩿㠃✚ࡢ ᐃࡀᅔ㞴 ࡟࡞ࡿၥ㢟࡟ຍ࠼㸪ࡓ࡜࠼ᖹᆒᘬᙇᛂຊࡀィ ࡛ࡁࡓ࡜ࡋ࡚ࡶ㸪ࡃࡧࢀᗏࡣከ㍈ ᛂຊ≧ែ࡟ࡉࡽࡉࢀ㸪ィ ࡉࢀࡿᖹᆒᘬᙇᛂຊࡣᮦᩱࡢὶືᛂຊ࡜ࡣ୍⮴ࡋ࡞ ࠸࠿ࡽ࡛࠶ࡿ㸬 ᮏ◊✲࡛ࡣୖグࡢࡼ࠺࡞⫼ᬒ࠿ࡽ㸪ᖹᆒᘬᙇᛂຊ࡟ᑐࡋ࡚᭷㝈せ⣲ἲ㏫ゎᯒ ࡟ᇶ࡙ࡃᛂຊ⿵ṇࢆ㐺⏝ࡍࡿࡇ࡜࡛㸪ࡃࡧࢀⓎ⏕௨㝆ࡢὶືᛂຊ᭤⥺ࢆྠᐃࡍ ࡿᡭἲࡢ㛤Ⓨ࡟ྲྀࡾ⤌ࢇࡔ㸬ࡉࡽ࡟㸪࡜ࡾࢃࡅ◚ቯࡲ࡛ࡢὶືᛂຊ᭤⥺ࢆྠᐃࡍ ࡿࡇ࡜ࡣ㸪◚ቯ㉳Ⅼ࡟࠾ࡅࡿྛ✀ࡢᛂຊᡂศࡸࡦࡎࡳᡂศࡢ㈇ⲴᒚṔࡶྠ᫬࡟

4 ྠᐃ࡛ࡁ㸪ྛ✀ࡢᘏᛶ◚ቯண ࣔࢹࣝࡢࣃ࣓࣮ࣛࢱࢆỴᐃࡍࡿࡇ࡜ࡶྍ⬟࡜࡞ ࡿࡓࡵ㸪◚ቯண ࡟㛵ࡋ࡚ࡶ᳨ドࢆ⾜ࡗࡓ㸬 ᮏ❶࡛ࡣ㸪ࡲࡎ㸪ᘬᙇヨ㦂࡟࠾ࡅࡿࡃࡧࢀⓎ⏕௨㝆ࡢὶືᛂຊྠᐃᡭἲ࠾ࡼࡧ ྛ✀ᘏᛶ◚ቯᇶ‽࡜ࡑࡢࣃ࣓࣮ࣛࢱྠᐃᡭἲ࡟㛵ࡍࡿ㐣ཤࡢ◊✲ࢆᴫほࡋࡓᚋ㸪 ᮏ◊✲ࡢලయⓗ࡞┠ⓗ࡜ᵓᡂ࡟ࡘ࠸࡚㏙࡭ࡿ㸬

Fig. 1-1 Long-term trend of production of forged products in Japan 1-1)

Fig. 1-2 Long-term trend of automobile production volume by Japanese

manufacturers 1-2) ™1000 tons Industrial machinery Transport machine Others Automobile ™10000 Domestic Export Production Overseas production Year Production volume

5

Fig. 1-3 Long-term trend of cold forged products used for passenger cars in Japan 1-4)

Fig. 1-4 Examples of upset fracture 1-6)

Year

Cold forging

Cold forging Cold forging + Finishing

Mass of col d forging parts / 1car [kg] Vertical crack Oblique crack

6

7 1.2 ᪤Ꮡࡢὶືᛂຊྠᐃ᪉ἲ 1.2.1 ᘬᙇヨ㦂  㔠ᒓᮦᩱࢆᑐ㇟࡜ࡋࡓ୍⯡ⓗ࠿ࡘ᭱ࡶ⡆౽࡞ὶືᛂຊྠᐃ᪉ἲࡣ㸪JIS Z 2241 1-18)_{࡟つᐃࡉࢀࡿᘬᙇヨ㦂࡟ࡼࡿࡶࡢ࡛࠶ࡿ㸬㘫㐀⣲ᮦࡢሙྜ㸪Წᮦࡶࡋࡃࡣ⥺} ᮦࡀᨭ⤥ࡉࢀࡿሙྜࡀከࡃ㸪ヨ㦂∦࡟ࡣ㸪෇ᙧ㸪㛗᪉ᙧ➼ࡢ᩿㠃ᙧ≧ࢆ᭷ࡋࡓFig. 1-6 ࡟♧ࡍࡼ࠺࡞ࢲࣥ࣋ࣝ≧ࡢࡶࡢࡀ୍⯡ⓗ࡟฼⏝ࡉࢀࡿ㸬ヨ㦂∦ࡢ୧➃ࢆᘬᙇ ヨ㦂ᶵࡢࢳࣕࢵࢡ࡛ࡘ࠿ࢇ࡛ᘬᙇࢆ୚࠼㸪ヨ㦂∦ᖹ⾜㒊࡟࠾ࡅࡿᶆⅬ㊥㞳ࡢఙ ࡧ࡜ᘬᙇⲴ㔜࠿ࡽྛ✀ࡢᛂຊ࡜ྛ✀ࡢࡦࡎࡳࢆᑟฟࡍࡿ㸬୍⯡࡟㸪ఙࡧࡣࡦࡎࡳ ࢤ࣮ࢪᘧࡢ᥋ゐᘧఙࡧィ࡛ィ ࡉࢀ㸪୍ᵝఙࡧࡢ⠊ᅖෆ࡟࠾࠸࡚ࡣ㸪୍ᵝኚᙧࢆ ௬ᐃࡋᘧ(1-1)࡟ࡼࡗ࡚┿ࡦࡎࡳ㸦ᑐᩘࡦࡎࡳ㸧εTࡀィ⟬ࡉࢀࡿ㸬  _¸ ¹ · ¨ © § 0 ln L L T H                            (1-1) ࡇࡇ࡛㸪L0ࡣኚᙧ๓ࡢཎᶆⅬ㊥㞳㸪L ࡣᶆⅬࡢኚᙧᚋࡢ㊥㞳࡛࠶ࡿ㸬ࡲࡓ㸪ᖹᆒ ᘬᙇᛂຊ㸦┿ᛂຊ㸧σzaveࡣ㸪୍ᵝኚᙧ࠾ࡼࡧረᛶᚋࡢయ✚୍ᐃࢆ௬ᐃࡍࡿࡇ࡜࡟ ࡼࡗ࡚㸪ᘧ(1-2)࡛ィ⟬ࡍࡿࡇ࡜ࡀ࡛ࡁࡿ㸬  (1 ) 0 0 N N zave L L A P A P _{V H} V ˜                    (1-2) ࡇࡇ࡛㸪P ࡣᘬᙇⲴ㔜㸪A0ࡣึᮇ᩿㠃✚㸪A ࡣኚᙧ୰ࡢ᩿㠃✚㸪σNࡣබ⛠ᛂຊ㸪 εNࡣබ⛠ࡦࡎࡳ࡛࠶ࡿ㸬ḟᘧ࡟ࡼࡾεT࠿ࡽᙎᛶࡦࡎࡳεEࢆ㝖ཤࡍࡿࡇ࡜࡛┦ᙜ ረᛶࡦࡎࡳεpࢆ⟬ฟࡍࡿ㸬  E zave T E T P V H H H H                        (1-3) ࡇࡇ࡛㸪E ࡣࣖࣥࢢ⋡࡛࠶ࡿ㸬༢㍈ᛂຊ≧ែ࡛࠶ࢀࡤ㸪ᖹᆒᘬᙇᛂຊ࡜┦ᙜᛂຊ σ ࡀ୍⮴ࡍࡿࡓࡵ㸪┦ᙜᛂຊ̺┦ᙜረᛶࡦࡎࡳࡢ㛵ಀࡀᚓࡽࢀࡿ㸬୍⯡࡟ࡇࢀࢆ ᮦᩱࡢὶືᛂຊ᭤⥺㸦Flow stress curve㸧࡜࿧ࡪ㸬ࡍ࡞ࢃࡕ㸪୍⯡ⓗ࡞ᘬᙇヨ㦂࡛ ࡣ୍ᵝఙࡧࡢ⠊ᅖෆ࡛࠶ࢀࡤ㸪ᘬᙇⲴ㔜࡜ᖹ⾜㒊ᶆⅬ㊥㞳ࡢఙࡧࢆ ᐃࡍࡿࡔ ࡅ࡛ὶືᛂຊ᭤⥺ࡀྠᐃ࡛ࡁࡿ㸬

 ࡑࡢ୍᪉࡛㸪୍ᵝఙࡧ㝈⏺ࢆ㉸࠼ࡓᚋࡣࡃࡧࢀࢆ⏕ࡌࡿࡓࡵ㸪༢㍈ᛂຊ≧ែ࠿ ࡽከ㍈ᛂຊ≧ែ࡬⛣⾜ࡍࡿ㸬ࡑࡢࡓࡵ㸪ఙࡧィᶆⅬ㛫࡟࠾ࡅࡿ୍ᵝኚᙧࡢ௬ᐃࡶ ᡂࡾ❧ࡓࡎὶືᛂຊࡢ ᐃࡣᅔ㞴࡜࡞ࡿ㸬Ⅳ⣲㗰ࡢ୍ᵝఙࡧࡣ㸪Table 1-1 ࡟♧

8

ࡍࡼ࠺࡟㸪㌾㗰ᮦ㸦S10C㸧ࡢሙྜ࡛ࡶࡏ࠸ࡐ࠸ 0.33 ⛬ᗘ࡛࠶ࡿ 1-19)_㸬

Fig. 1-6 JIS14A type tensile test specimen1-18)

Table 1-1 Mechanical properties of carbon steel 1-19)

Japan Y. S. T. S. El. Chemical compositions Germany (DIN) USA (AISI) Forging method Hardness (HB) Draw ing Carbon steel Cold Cold Cold Cold Cold Cold Cold Cold Cold Cold

9  1.2.2 ◳໬๎  ࡯࡜ࢇ࡝ࡢ㘫㐀ຍᕤ࡟࠾࠸࡚㸪⿕ຍᕤᮦ࡟ࡣᘬᙇヨ㦂ࡢ୍ᵝఙࡧࢆ㉸࠼ࡿ኱ ࡦࡎࡳࡀ௜୚ࡉࢀࡿ㸬ࡑࡢࡓࡵ㸪ࡑࡢ⠊ᅖࡢὶືᛂຊࡣ㸪◳໬๎࡜࿧ࡤࢀࡿ㛵ᩘ ࡟ࡼࡗ࡚እᤄண ࡉࢀࡓᚋ㸪CAE ゎᯒ࡟౑⏝ࡉࢀࡿ㸬௦⾲ⓗ࡞◳໬๎㏆ఝ࡟ࡣ㸪 ᘧ(1-4)࡟♧ࡍ⥺ᙧ◳໬๎㸪ᘧ(1-5)࡟♧ࡍ Ludwik ๎ 1-20)_{㸪ᘧ(1-6)࡟♧ࡍ Swift ๎} 1-21)_{➼ࡀ࠶ࡿ㸬}  σ = Y + H εeq                                 (1-4)  σ = Y + C εeqn                                 (1-5)  σ = F (ε0 + εeq)n                           (1-6) ࡇࡇ࡛㸪σ ࡣ┦ᙜᛂຊ㸪Y ࡣึᮇ㝆అᛂຊ㸪H㸪C㸪n㸪F㸪ε0ࡣᮦᩱ࡟ࡼࡗ࡚␗࡞ ࡿࣃ࣓࣮ࣛࢱ࡛࠶ࡾ㸪ࡑࡢ࠺ࡕF ࡣረᛶಀᩘ㸦F ್㸧㸪n ࡣຍᕤ◳໬ಀᩘ㸦n ್㸧 ࡜ࡶ࿧ࡤࢀࡿ㸬࢔࣑ࣝࢽ࣒࢘ྜ㔠ࡢࡼ࠺࡞ࡦࡎࡳࡢቑຍ࡟క࠸ n ್ࡀῶᑡࡍࡿ ഴྥࡀ࠶ࡿᮦᩱ࡟ࡣ㸪ᘧ(1-7)࡟♧ࡍ Voce ๎ 1-22)_{ࢆ㑅ᢥࡋࡓ࡯࠺ࡀᐇ㝿ࡢຍᕤ◳} ໬ᣲື࡟㏆࠸ሙྜࡀ࠶ࡿ㸬  σ = av – bv exp(–cv εeq)                    (1-7) ࡇࡇ࡛㸪av㸪bv㸪cvࡣࣃ࣓࣮ࣛࢱ࡛࠶ࡿ㸬 ࠸ࡎࢀࡢ◳໬๎ࢆ㑅ᢥࡍࡿሙྜ࡟࠾࠸࡚ࡶ㸪ࡑࡢྛࣃ࣓࣮ࣛࢱࡣ୍ᵝఙࡧࡢ ⠊ᅖ࡛ࡢὶືᛂຊࢆ⏝࠸࡚ྠᐃࡉࢀࡿࡓࡵ㸪኱ࡦࡎࡳᇦࡢὶືᛂຊࡢጇᙜᛶࡣ ಖドࡉࢀ࡚࠸࡞࠸㸬

10 1.2.3 %ULGJPDQ ἲࢆ⏝࠸ࡓᛂຊ⿵ṇ᪉ἲ (a) %ULGJPDQ ἲࡢᇶᮏཎ⌮  ࡃࡧࢀⓎ⏕௨㝆ࡢὶືᛂຊࢆ┤᥋ⓗ࡟ྠᐃࡍࡿᡭἲ࡜ࡋ࡚㸪Bridgman 1-23)_ࡀᑟ ฟࡋࡓࡃࡧࢀᗏ࡟࠾ࡅࡿᛂຊศᕸࡢゎᯒ⤖ᯝࢆ฼⏝ࡍࡿ᪉ἲ㸦௨ᚋBridgman ἲ㸧 ࡀ࠶ࡿ㸬࡞࠾㸪㢮ఝࡢゎᯒࡣ㸪Davidenkov ࡽ 1-24)_{࡟ࡼࡗ࡚ࡶ⾜ࢃࢀ࡚࠸ࡿ㸬} Bridgman ࡣ㸪୸Წᘬᙇヨ㦂࡟࠾ࡅࡿࡃࡧࢀᗏ᩿㠃ࡢᛂຊ≧ែࢆ㸪ϸ) ㍈ᑐ⛠ၥ 㢟࡜ࡋ࡚ྲྀࡾᢅ࠺㸪Ϲ) ᮦᩱࡣ von-Mises ࡢ㝆అ᮲௳࡟ᚑ࠺㸪Ϻ) ┦ᙜᛂຊ࡜┦ ᙜࡦࡎࡳࡀࡃࡧࢀ㒊᩿㠃࡟࠾࠸୍࡚ᐃ࡛࠶ࡿ㸪➼ࡢ௬ᐃࡢୗ࡛㸪ึ➼ゎἲ࡟ࡼࡾ ゎᯒࡋࡓ㸬ࡑࢀ࡟ࡼࢀࡤ㸪ࡃࡧࢀᗏ᩿㠃࡟࠾ࡅࡿᆶ┤ᛂຊᡂศࡣḟᘧ࡟ࡼࡗ࡚ồ ࡵࡽࢀࡿ㸬  ¸¸ ¹ · ¨¨ © §   ˜ aR r aR a flow r 2 2 ln 2 2 V V V T                  (1-8)  °¿ ° ¾ ½ °¯ ° ® ­ ¸¸ ¹ · ¨¨ © §    ˜ aR r aR a flow z 2 2 ln 1 2 2 V V                  (1-9) ࡇࡇ࡛σrࡣ༙ᚄ᪉ྥᛂຊ㸪σθࡣ࿘᪉ྥᛂຊ㸪σzࡣᘬᙇ᪉ྥᛂຊ㸪σflowࡣὶືᛂຊ ࢆ♧ࡍ㸬a ࠾ࡼࡧ R ࡣࡃࡧࢀᗏ࡟࠾ࡅࡿ᭱ᑠ᩿㠃༙ᚄ࠾ࡼࡧ᭤⋡༙ᚄ࡛࠶ࡾ㸪r ࡣࡃࡧࢀᗏ᩿㠃୰ᚰ࠿ࡽࡢ༙ᚄ᪉ྥࡢ㊥㞳࡛࠶ࡿ㸬ࡲࡓ㸪σzࢆࡃࡧࢀᗏ᩿㠃࡟ࢃ ࡓࡗ࡚✚ศࡋࡓ್ࡀP ࡜➼ࡋࡃ࡞ࡿࡇ࡜࠿ࡽ㸪ḟᘧࢆᑟฟࡍࡿࡇ࡜ࡀ࡛ࡁࡿ㸬  _{flow zave} R a a R V V ¸ ¹ · ¨ © §  ¸ ¹ · ¨ © §  2 1 ln 2 1 1 _{                  (1-10)}

ᘧ(1-10)ྑ㎶ࡢ σzave ࡟࠿࠿ࡿ㡯ࡀ㸪σzave ࢆ σflow ࡟ᛂຊ⿵ṇࡍࡿಀᩘ㸦௨ᚋ㸪

Bridgman ࡢ⿵ṇಀᩘ࡜⛠ࡍࡿ㸧࡛࠶ࡿ㸬ࡇࡇ࡛㸪σzaveࡣḟᘧ࡛ᐃ⩏ࡉࢀࡿᖹᆒᘬ

ᙇᛂຊ㸦┿ᛂຊ㸧࡛࠶ࡾィ ྍ⬟࡞ᛂຊ࡛࠶ࡿ㸬

 σzave = P/(πa2)                  (1-11)

ࡉࡽ࡟㸪ࡃࡧࢀᗏ᩿㠃✚ࡢኚ໬࠿ࡽ㸪᩿㠃ෆࡢᖹᆒⓗ࡞┦ᙜࡦࡎࡳεeqࡣḟᘧ

11  εeq = 2 ln (A0/A)                   (1-12) ࡇࡇ࡛㸪A0࠾ࡼࡧA ࡣࡃࡧࢀᗏࡢึᮇ࠾ࡼࡧኚᙧᚋࡢ᩿㠃✚࡛࠶ࡿ㸬ࡍ࡞ࢃࡕ㸪 ᘧ(1-10)㸪ᘧ(1-11)࠾ࡼࡧᘧ(1-12)ࡼࡾ㸪୸Წᘬᙇヨ㦂࡟࠾࠸࡚㸪P ࠾ࡼࡧ㸪ࡃࡧ ࢀᗏ࡟࠾ࡅࡿ᫬ࠎ้ࠎࡢ a ࠾ࡼࡧ R ࢆ ᐃࡍࡿࡇ࡜࡛㸪ࡃࡧࢀⓎ⏕௨㝆ࡢ┦ᙜ ࡦࡎࡳ࡜ὶືᛂຊࡢ㛵ಀࢆྠᐃࡍࡿࡇ࡜ࡀ࡛ࡁࡿ㸬Fig. 1-7 ࡟㸪Bridgman ἲ࡟࠾ ࡅࡿᆶ┤ᛂຊศᕸ࠾ࡼࡧ┦ᙜࡦࡎࡳศᕸࡢᶍᘧᅗࢆ♧ࡍ 1-25)_㸬  ࡉࡽ࡟㸪ᘧ(1-8)࠾ࡼࡧ(1-9)࠿ࡽ㸪ከ㍈ᛂຊ≧ែࢆ⾲ࡍᣦᶆ࡜ࡋ࡚ᖹᆒᛂຊ㸦㟼 Ỉᅽ㸧࡜┦ᙜᛂຊࡢẚ࡛ᐃ⩏ࡉࢀࡿᛂຊ୕㍈ᗘ η ࢆḟᘧ࡟ࡼࡗ࡚ᑟฟࡍࡿࡇ࡜ ࡀ࡛ࡁࡿ㸬  _¸ ¹ · ¨ © § _  1 2 ln 3 1 R a m V V K                     (1-13) ࡇࡇ࡛㸪σmࡣᖹᆒᛂຊ㸦㟼Ỉᅽ㸧㸪σ ࡣ┦ᙜᛂຊ࡛࠶ࡿ㸬࡞࠾㸪ୖᘧࡣࡃࡧࢀᗏ ᩿㠃୰ᚰ࡟࠾ࡅࡿᛂຊ୕㍈ᗘࢆ♧ࡋ࡚࠸ࡿ㸬 (b) ࡃࡧࢀᙧ≧ࡢィ ᪉ἲ  Bridgman ࡢ⿵ṇಀᩘࢆỴᐃࡍࡿࡓࡵ࡟ࡣ㸪ࡃࡧࢀᗏ࡟࠾ࡅࡿ᫬ࠎ้ࠎࡢ a ࡜ R ࡢᐇ ್ࡀᚲせ࡜࡞ࡿ㸬ᴮ୪࡜Ọ஭ 1-26), 1-27)_{ࡣ㸪ᘬᙇヨ㦂୰࡟୍᪦ヨ㦂ࢆ୰᩿} ࡋ㸪᫬ࠎ้ࠎࡢ a ࡜ R ࢆᐇ ࡍࡿ᩿⥆ᘬᙇヨ㦂ࢆᥦ᱌ࡋ࡚࠸ࡿ㸬࡞࠾㸪᩿⥆ᘬ ᙇヨ㦂࡟࠾ࡅࡿ R ࡢ ᐃࡣ㸪Fig. 1-8 ࡟♧ࡍࡼ࠺࡟ࡃࡧࢀᗏ࠿ࡽ୍ᐃ㊥㞳 Y0㞳 ࢀࡓX0ࡢ㊥㞳ࢆගᏛ㢧ᚤ㙾࡟ࡼࡾィ ࡋ㸪ᗄఱᏛⓗ࡞㛵ಀ࠿ࡽᑟฟࡉࢀࡿᅗ୰ ࡢᘧࢆ฼⏝ࡍࡿࡇ࡜࡛⾜࠺ 1-26)_{㸬ࡲࡓ㸪ᅵ⏣ࡽ}1-28)_{ࡣ㸪᩿⥆ᘬᙇヨ㦂ࢆᵝࠎ࡞㔠} ᒓᮦᩱ࡟㐺⏝ࡋ㸪┿ࡦࡎࡳ࡛1.0 ࢆ㉸࠼ࡿὶືᛂຊ᭤⥺ࢆྠᐃࡍࡿࡇ࡜࡟ᡂຌࡋ ࡓ㸬ࡋ࠿ࡋ࡞ࡀࡽ㸪ᘬᙇヨ㦂ࢆ୰᩿ࡋ࡚㸪a ࡜ R ࢆ ᐃࡍࡿࡢ࡟ࡣ㸪┦ᙜࡢᡭ㛫 ࢆᚲせ࡜ࡍࡿ㸬ࡲࡓ㸪Fig. 1-8 ࡢࡼ࠺࡞ィ ἲ࡛ࡣ㸪༙ᚄ᪉ྥࡢᇶ‽㊥㞳 Y0ࡢ࡜ ࡾ᪉࡟ࡼࡗ࡚ỴᐃࡉࢀࡿR ࡀ␗࡞ࡗ࡚ࡋࡲ࠺ၥ㢟ࡶ࠶ࡿ㸬 (c) %ULGJPDQ ἲࡢၥ㢟Ⅼ  Bridgman ἲࢆ⏝࠸ࡿ࡟ࡣ㸪᫬ࠎ้ࠎኚ໬ࡍࡿ a ࡜ R ࢆィ ࡋ࡞ࡅࢀࡤ࡞ࡽࡎ㸪 ィ ࡀ↹㞧࡛࠶ࡿၥ㢟ࡀ࠶ࡿ㸬ࡲࡓ㸪ࡃࡧࢀᙧ≧ࡀィ ࡛ࡁࡓ࡜ࡋ࡚ࡶ㸪 Bridgman ἲࡣᘧࡢᑟฟ㐣⛬࡟࠾࠸࡚ከࡃࡢ௬ᐃࢆ⏝࠸࡚࠸ࡿࡓࡵ㸪ᛂຊ୕㍈ᗘ ࡢண ࡸᛂຊ⿵ṇᚋࡢὶືᛂຊ࡟ࡘ࠸࡚ࡣ┦ᙜࡢㄗᕪࡀྵࡲࢀࡿࡇ࡜ࡀ㸪౛࠼ ࡤ㸪Alves ࡜ Jones 1-29)_{㸪La Rosa ࡽ}1-30)_{ࡲࡓࡣBao ࡜ Wierzbicki} 1-31)_{➼࠿ࡽሗ࿌ࡉ}

12

 Mirone 1-32)_{ࡣ㸪ᘬᙇヨ㦂⤖ᯝ࡜ FEM ゎᯒ⤖ᯝ࡜ࢆヲ⣽࡟ẚ㍑ࡍࡿࡇ࡜࡛㸪ᛂ}

ຊ⿵ṇ࡟ࡣࡃࡧࢀ㒊᭤⋡༙ᚄࡀᚲࡎࡋࡶᚲせ࡞࠸ࡇ࡜ࢆᣦ᦬ࡋࡓ㸬ࡲࡓ㸪 Bridgman ἲࡼࡾ㧗⢭ᗘ࡞ᛂຊ⿵ṇࡢᐇ㦂ᘧࢆᥦ᱌ࡋࡓࡀ㸪ࡍ࡭࡚ࡢᮦᩱ࡟㐺⏝ ࡛ࡁࡿಖドࡣ࡞࠸㸬

Fig. 1-7 Stress and strain distributions on Bridgman’s method 1-25)

Fig. 1-8 Measurement method of radius of curvature R in the neck bottom 1-26) °¿ ° ¾ ½ °¯ ° ® ­ ¸¸ ¹ · ¨¨ © §    ˜ aR r aR a flow z 2 2 ln 1 2 2 V V ¸¸ ¹ · ¨¨ © §   ˜ aR r aR a flow r 2 2 ln 2 2 V V V T R a r ) / ln( 2 A0 A eq H z

13 1.2.4 ㏫ゎᯒࢆ⏝࠸ࡓ᪉ἲ Bridgman ἲࡣࡃࡧࢀ௨㝆ࡢὶືᛂຊࢆ┤᥋ⓗ࡟ྠᐃ࡛ࡁࡿ཯㠃㸪ࡃࡧࢀᙧ≧ ࡢ ᐃ࡛ R ࡀ୍ព࡟ᐃࡲࡽ࡞࠸ၥ㢟㸪࠾ࡼࡧ⿵ṇ⢭ᗘࡀᝏ࠸࡜࠸࠺ၥ㢟ࢆᢪ࠼ ࡚࠸ࡿ㸬㏆ᖺ࡛ࡣ㸪኱ࡦࡎࡳᇦࡢὶືᛂຊࡢྠᐃ࡟㸪FEM ࡟ࡼࡿゎᯒ⤖ᯝ࡜ᐇ 㦂⤖ᯝࢆ௜ࡁྜࢃࡏࡿ㏫ゎᯒⓗ࡞ᡭἲࡀ⏝࠸ࡽࢀࡿࡇ࡜ࡶከ࠸㸬౛࠼ࡤ㸪Koc ࡜ Štok 1-33)_{ࡣ㸪ᯈᮦヨ㦂∦࡟ᑐࡋ࡚㸪ᘬᙇⲴ㔜࡜ఙࡧࡢ㛵ಀࡀᐇ㦂࡜ FEM ୍࡛⮴} ࡍࡿࡼ࠺࡟㸪Swift ๎㸪Voce ๎ࢆጞࡵ࡜ࡍࡿྛ✀ࡢ◳໬๎ࡢࣃ࣓࣮ࣛࢱࢆྠᐃࡋ ࡚࠸ࡿ㸬Hasegawa ࡽ1-34) _{ࡣα 㯤㖡↝㕌ᯈ㸪ࡾࢇ㟷㖡ㄪ㉁ᯈ࠾ࡼࡧ㧗ᙇຊ㗰ᯈ࡟} ᑐࡋ࡚㸪ᘬᙇⲴ㔜࡜ఙࡧࡢ㛵ಀࡀᐇ㦂࡜ FEM ୍࡛⮴ࡍࡿࡼ࠺࡟㏫ゎᯒࢆ⾜࠸㸪 n ஌◳໬๎ࡢ n ್ࢆࡦࡎࡳ࡟ᑐࡋ࡚⥺ᙧࡲࡓࡣ 2 ḟ㛵ᩘ࡜ࡍࡿࡇ࡜࡛㸪ᐇ㦂࡜ FEM ࡀⰋዲ࡟୍⮴ࡍࡿࡇ࡜ࢆ♧ࡋࡓ㸬Roth ࡜ Mohr 1-35) _{ࡣ㸪㧗ᙇຊ㗰ᯈࡢ㧗㏿}

ᘬᙇヨ㦂⤖ᯝࢆᑐ㇟࡟㸪Swift ๎࡜ Voce ๎࡟㔜ࡳࢆࡘࡅ࡚⥺ᙧ⤖ྜࡋࡓ࠺࠼࡛㸪 ୧⪅ࡢ◳໬๎ࡢࣃ࣓࣮ࣛࢱ࠾ࡼࡧ㔜ࡳಀᩘࢆ㏫ゎᯒ࡟ࡼࡾྠᐃࡋ࡚࠸ࡿ㸬ࡲࡓ㸪 㧗 ࡢኚᙧ᢬ᢠࡢྠᐃ࡟ࡘ࠸࡚㸪Yanagida ࡽ 1-36) _{ࡀ㸪ືⓗ෌⤖ᬗୗࡢὶືᛂຊ} ᭤⥺ࢆ⾲ࡍ㛵ᩘᘧࢆᥦ᱌ࡋ㸪⇕㛫࡛ࡢᅽ⦰ヨ㦂ࡢⲴ㔜࡜ኚ఩ࡢ㛵ಀࢆFEM ࡛෌ ⌧ࡍࡿࡇ࡜ࢆ┠ⓗ࡟㸪㛵ᩘᘧࡢྛࣃ࣓࣮ࣛࢱࢆྠᐃࡋࡓ㸬 ୖグࡢ㏫ゎᯒࡢ஦౛ࡣ㸪࠸ࡎࢀࡶᘬᙇࡶࡋࡃࡣᅽ⦰ヨ㦂࡟࠾ࡅࡿ࣐ࢡࣟ࡞ヨ 㦂Ⲵ㔜࡜ኚᙧ㔞ࡢ㛵ಀࡢࡳࢆFEM ࡛෌⌧ࡍࡿࡇ࡜ࢆ┠ⓗ࡜ࡋ࡚࠾ࡾ㸪ࡃࡧࢀࡢ ኚᙧࡀᐇ㦂࡜୍⮴ࡋ࡚࠸ࡿ࡝࠺࠿ࡲ࡛ࡣ☜ㄆࡀࡉࢀ࡚࠸࡞࠸㸬᭱㏆࡛ࡣ㸪DIC (Digital Image Correlation)➼࡟ࡼࡿࡦࡎࡳศᕸィ ⤖ᯝࢆ฼⏝ࡋ㸪ࡃࡧࢀࡢᙧ≧ ࡲ࡛⪃៖ࡋࡓ㏫ゎᯒⓗ࢔ࣉ࣮ࣟࢳࡶቑ࠼࡚ࡁ࡚࠸ࡿ㸬౛࠼ࡤ㸪Coppieters ࡽ 1-37)

ࡣ῝⤠ࡾ⏝㌾㗰ᯈࢆᑐ㇟࡟㸪ࡃࡧࢀ㒊ࡢࡦࡎࡳศᕸࢆ DIC ࡟ࡼࡾィ ࡋ㸪ࡑࢀ ࢆࡶ࡜࡟ィ⟬ࡍࡿࡃࡧࢀ㒊࡟࠾ࡅࡿෆ㒊௙஦࡜㸪ࡃࡧࢀ㒊࡟ຍࢃࡿእ㒊௙஦ࡢ ẚ㍑࠿ࡽ㸪Swift ๎࡜ Voce ๎ࡢྛࣃ࣓࣮ࣛࢱࢆྠᐃࡋࡓ㸬ࡲࡓ Kim ࡽ 1-38)_ࡣ㸪

௬᝿ኚ఩ሙࢆ฼⏝ࡋࡓ㏫ゎᯒ᪉ἲ࡛࠶ࡿVFM (Virtual Field Method) ࢆ฼⏝ࡍࡿ ࡇ࡜࡛㸪Swift ࡜ಟṇ Voce ࡢࣃ࣓࣮ࣛࢱࢆྠᐃࡋ࡚࠸ࡿ㸬ࡓࡔࡋ㸪ࡦࡎࡳศᕸ඲ యࢆホ౯ᑐ㇟࡜ࡍࡿ᪉ἲࡣ㸪DIC ➼ࡢ㧗ᗘ࡞ィ ⿦⨨ࢆᚲせ࡜ࡍࡿࡔࡅ࡛࡞ࡃ㸪 ᑓ⏝ࡢ࢔ࣝࢦࣜࢬ࣒ࡀᚲせ࡟࡞ࡿ࡞࡝㸪⡆౽࡞ྠᐃᡭἲ࡜ࡣ࠸࠸ࡀࡓ࠸㸬  ࡲࡓ㸪ࡇࢀࡲ࡛ୖࡆࡓ࡯࡜ࢇ࡝ࡢ஦౛ࡣ㸪㛵ᩘ࡜ࡋ࡚ࡢ◳໬๎ࢆ௬ᐃࡋ㸪ࡑࡢ ◳໬๎ࡢࣃ࣓࣮ࣛࢱࢆ㏫ゎᯒࡢྠᐃᑐ㇟࡜ࡋ࡚࠸ࡿࡓࡵ㸪⾲⌧࡛ࡁࡿὶືᛂຊ ᭤⥺ࡣ㑅ᢥࡋࡓ◳໬๎ࡢ⾲⌧⬟ຊ࡟㝈ᐃࡉࢀࡿ࡜࠸࠺ၥ㢟ࢆᢪ࠼࡚࠸ࡿ㸬ࡶࡋ㸪 ᮦᩱࡢຍᕤ◳໬ᣲືࡀ㑅ᢥࡋࡓ◳໬๎ࡢ㛵ᩘ࡜ࡋ࡚ࡢ⾲⌧⬟ຊࢆ㉸࠼ࡓሙྜࡣ㸪 ㏫ゎᯒࢆ⾜ࡗ࡚ࡶᐇ㦂࡜FEM ࡜ࡢㄗᕪࡀᇙࡲࡽ࡞࠸ၥ㢟ࡀ࠶ࡿ㸬  ຍᕤ◳໬ᣲືࡢ⾲⌧࡟◳໬ഃࢆ⏝࠸ࡎ࡟㸪ὶືᛂຊ᭤⥺ࢆከ┤⥺㏆ఝࡍࡿྲྀ ࡾ⤌ࡳࡶ࠶ࡿ㸬Dunand ࡜ Mohr 1-39) _{ࡣపᘏᛶࡢ࢔࣑ࣝࢽ࣒࢘ྜ㔠ᯈࢆᑐ㇟࡟㸪} ᐇ㦂࡟ࡼࡾᚓࡽࢀࡓᘬᙇⲴ㔜࡜ኚ఩ࡢ㛵ಀࡀFEM ࡛෌⌧ࡉࢀࡿࡼ࠺࡟㸪3 ศ๭

14 ࡉࢀࡓከ┤⥺㏆ఝࡢὶືᛂຊ᭤⥺ࡢྛ༊㛫ࡢഴࡁࢆྠᐃࡋࡓ㸬ከ┤⥺㏆ఝࡢὶ ືᛂຊ᭤⥺ࢆ⏝࠸ࡓ㢮ఝࡢྲྀࡾ⤌ࡳࡣ㸪Kajberg ࡜ Lindkvist 1-40)_{࡟ࡼࡗ࡚ࡶ⾜ࢃ} ࢀ࡚࠾ࡾ㸪ࡇࡕࡽࡢศ๭ᩘࡣ 4 ࡛࠶ࡿ㸬୧⪅ࡢ᪉ἲࡣᘏᛶࡢᑠࡉ࠸ὶືᛂຊ᭤ ࡢྠᐃ࡟ࡣ㐺⏝࡛ࡁࡓࡀ㸪౛࠼ࡤ㌾㗰➼ࡢ㧗ᘏᛶᮦᩱ࡟ࡣ㸪ࡼࡾከࡃࡢศ๭ᩘ࡟ ࡋ࡚༊ศ㏆ఝࡋ࡞࠸࡜⾲⌧⬟ຊࡀ୙㊊ࡋ࡚㐺⏝࡛ࡁ࡞࠸㸬

15 1.3 ᘏᛶ◚ቯண ࣔࢹࣝ࠾ࡼࡧࡑࡢࣃ࣓࣮ࣛࢱྠᐃ᪉ἲ 1.3.1 ᘏᛶ◚ቯࡢ࣓࢝ࢽࢬ࣒  㔠ᒓᮦᩱࡢ◚ቯࡣ㸪⣲ᮦࡢ≉ᛶࡸ◚ቯ࡟⮳ࡿ⎔ቃ࡟ࡼࡗ࡚㸪ᘏᛶ◚ቯ㸪⑂ປ◚ ቯ㸪⬤ᛶ◚ቯ㸪ࢡ࣮ࣜࣉ◚ቯ㸪ᛂຊ⭉㣗๭ࢀ࡞࡝࡟኱ูࡉࢀࡿࡀ㸪୺࡟ረᛶຍᕤ ࡟࠾ࡅࡿ㠀ຍᕤᮦࡢ◚ቯ㸦๭ࢀ㸧ࡣ㸪኱ࡁ࡞ኚᙧࢆకࡗࡓᚋ࡟᭱⤊◚᩿࡟⮳ࡿ⌧ ㇟࡛࠶ࡿࡓࡵᘏᛶ◚ቯࡀᨭ㓄ⓗ࡛࠶ࡿ㸬ᘏᛶ◚ቯࡣFig. 1-9 ࡟♧ࡍ࣓࢝ࢽࢬ࣒࡜ ࡋ࡚⌮ゎࡉࢀ࡚࠸ࡿ1-41)_{㸬ረᛶኚᙧࡀ⏕ࡌࡿ࡜ᮦᩱ୰ࡢ௓ᅾ≀㸪➨஧┦⢏Ꮚ㸪⤖} ᬗ⢏⏺࡞࡝ࡢ⏺㠃࡟㌿఩ࡸᒁ㒊ᛂຊࡢᙳ㡪࡛ᚤᑠ✵Ꮝ㸦࣎࢖ࢻ㸧ࡀⓎ⏕ࡍࡿ㸬ኚ ᙧࡢ㐍⾜࡜࡜ࡶ࡟ࡑࡢ✵Ꮝࡀᡂ㛗㸪ྜయࡋ㸪᭱⤊ⓗ࡞◚ቯ࡟⮳ࡿ㸬ࡑࡢ㝿ࡢ◚㠃 ࡣ㸪Fig. 1-10 ࡟♧ࡍࡼ࠺࡞ࢹ࢕ࣥࣉࣝ◚㠃࡜࡞ࡿ 1-42) _{㸬ࡲࡓ㸪ᚤᑠ࣎࢖ࢻࡢᡂ} 㛗ࢆᢚไࡍࡿࡢ࡟㟼Ỉᅽࡀᯝࡓࡍᙺ๭ࡣ኱ࡁࡃ㸪㟼Ỉᅽ࡜࡜ࡶ࡟◚ቯࡦࡎࡳࡀ ቑຍࡍࡿࡇ࡜ࡀ▱ࡽࢀ࡚࠸ࡿ㸦Fig. 1-11㸧1-43)_㸬

Fig. 1-9 Schematic illustration of mechanism of ductile fracture 1-41)

Dislocation

accumulation

Micro hole

generation

Growth

Coalescence

Void

Crack

16

Fig. 1-10 Examples of SEM image of fractured surface 1-42)

Fig. 1-11 Effect of hydrostatic pressure on fracture strain in carbon steel 1-43)

Standard annealed material Fr ac ture strain Pressure [MPa] 㽢100

17 1.3.2 ྛ✀ࡢᘏᛶ◚ቯண ࣔࢹࣝ  ᘏᛶ◚ቯண ࣔࢹࣝࡣ㸪୺࡟ᚤᑠ࣎࢖ࢻࡢᡂ㛗࠾ࡼࡧྜయ㐣⛬ࢆ⪃៖ࡋ࡚ ᵝࠎ࡞ほⅬ࠿ࡽከᩘࡢࣔࢹࣝࡀᥦ᱌ࡉࢀ࡚࠸ࡿ㸬ࡇࡇ࡛ࡣ㸪௦⾲ⓗ࡞ᘏᛶ◚ቯண  ࣔࢹࣝ࡟ࡘ࠸࡚㸪⌮ㄽ⫼ᬒ࡜㸪ࡑࡢࣔࢹࣝᘧࢆ♧ࡍ㸬࡞࠾㸪CM, CRT, CCL, CAࡣ ྛᘏᛶ◚ቯண ࣔࢹࣝ࡟࠾ࡅࡿᮦᩱᅛ᭷ࡢࣃ࣓࣮ࣛࢱ࡛㸪㝈⏺ࢲ࣓࣮ࢪ್࡜࿧ ࡤࢀࡿ㸬 (a) ࣎࢖ࢻࡢᡂ㛗࠾ࡼࡧྜయ᮲௳࡟ᇶ࡙ࡃࣔࢹࣝ  McClintock 1-44)_{ࡣ෇ᰕ≧ࡢ࣎࢖ࢻࡢ࠶ࡿࣘࢽࢵࢺࢭࣝࡀつ๎ⓗ࡟୪ࢇ࡛࠸ࡿᮦ} ᩱࢆ⪃࠼㸪࣎࢖ࢻࡢึᮇ┤ᚄࡀ࣎࢖ࢻࡢᖹᆒ㛫㝸ࡲ࡛ᡂ㛗ࡋࡓẁ㝵࡛◚᩿ࡀ⏕ ࡌࡿ࡜ࡋࡓ⌮ㄽゎᯒ࡟ࡼࡾ㸪ḟᘧࡢ᮲௳ᘧࢆᥦ᱌ࡋ࡚࠸ࡿ㸬  M f C d n n _»»_¼ º « « ¬ ª _  ¿ ¾ ½ ¯ ® ­ _{ } 

³

H H V V V V V V1 2 1 2 4 3 2 ) 1 ( 3 sinh ) 1 ( 2 3       (1-14) ࡇࡇ࡛㸪dε ࡣ┦ᙜረᛶࡦࡎࡳቑศ㸪εfࡣ◚᩿┦ᙜረᛶࡦࡎࡳ㸪n ࡣຍᕤ◳໬ᣦᩘ㸪 σ1࠾ࡼࡧσ2ࡣ୺ᛂຊ㸪σ ࡣ┦ᙜᛂຊ࡛࠶ࡿ㸬

 Rice and Tracy 1-45)_{ࡣMcClintock ࡜ࡣ␗࡞ࡾ⌫ᙧࡢ࣎࢖ࢻࢆ௬ᐃࡋ㸪㧗ᛂຊ୕}

㍈ᗘሙ࡟࠾ࡅࡿ࣎࢖ࢻࡢᡂ㛗ࢆࣔࢹࣝ໬ࡋࡓ㸬ࡑࡢ⤖ᯝ࠿ࡽᖹᆒᆶ┤ᛂຊσmࡀ ᘬᙇഃ࡟ቑຍࡍࡿ࡟ࡘࢀ࡚◚ቯ㝈⏺ࡀᛴ㏿࡟ᑠࡉࡃ࡞ࡿࡇ࡜ࢆ᫂ࡽ࠿࡟ࡋࡓ㸬 ࡇࡢࣔࢹࣝࡣḟᘧ࡛⾲ࡉࢀࡿ㸬 

³

_¸ ¹ · ¨ © § f RT m _{d C} H H V V 2 3 exp                      (1-15) (b) ᛂຊ㈇ⲴᒚṔ࡟╔┠ࡋࡓࣔࢹࣝ

 ຍᕤ᫬ࡢᛂຊ㈇ⲴᒚṔ࡟╔┠ࡋࡓࣔࢹࣝ࡜ࡋ࡚㸪Cockcroft and Latham 1-16)_ࡣ㸪

࣎࢖ࢻࡢ⏕ᡂ࠾ࡼࡧᡂ㛗࡟୚࠼ࡿᙳ㡪ࢆ᭱ࡶᙳ㡪ࢆ୚࠼ࡿᛂຊࢆ᭱኱୺ᛂຊ࡜ ௬ᐃࡋ㸪௨ୗࡢ⌧㇟ㄽⓗ࡞ࣔࢹࣝࢆᥦ᱌ࡋ࡚࠸ࡿ㸬  CL f C d

³

H Vmax H                        (1-16) ࡇࡇ࡛㸪σmaxࡣ᭱኱୺ᛂຊ࡛࠶ࡿ㸬ࡇࡢࣔࢹࣝࡣ㸪ᘬᙇ㸪ࡡࡌࡾ㸪᭤ࡆ㸪ᢲࡋฟ ࡋ,࠾ࡼࡧᅽᘏࡢ◚ቯண ࡟᭷ຠ࡛࠶ࡿ࡜ࡉࢀ࡚࠸ࡿ㸬

18  ࡲࡓ㸪Ayada 1-17)_{ࡣࢩ࢙ࣈࣟࣥࢡࣛࢵࢡࡢ◊✲࡟࠾ࡅࡿᐇ㦂⤖ᯝࢆࡶ࡜࡟㸪ᛂ} ຊ୕㍈ᗘࡢࡦࡎࡳ࡟ᑐࡍࡿ✚ศ್ࡀ㸪࠶ࡿ㝈⏺್࡟㐩ࡍࡿ࡜◚ቯࡍࡿ࡜࠸࠺ḟ ᘧࡢࣔࢹࣝࢆᥦ᱌ࡋ࡚࠸ࡿ㸬  A f _m C d

³

H H V V _{                       (1-17)} (c) ᵓᡂᘧ࡟࣎࢖ࢻࡢᙳ㡪ࢆ⤌ࡳ㎸ࢇࡔࣔࢹࣝ  Gurson 1-46) _{ࡢ㝆అ᮲௳ᘧ࡟௦⾲ࡉࢀࡿࡼ࠺࡟㸪㐃⥆యࡢረᛶᵓᡂᘧ࡟ᚤᑠ࣎} ࢖ࢻࡢᙳ㡪ࢆ┤᥋ྲྀࡾ㎸ࢇ࡛ィ⟬ࢆ⾜࠺ࣔࢹࣝࡶ࠶ࡿ㸬࣎࢖ࢻయ✚⋡ࡢኚ໬ࢆ ࣎࢖ࢻࡢ⏕ᡂ࡜ᡂ㛗ࡢ࿴࡜ࡋ࡚⾲ࡍᦆയⓎᒎᘧ࡛⾲⌧ࡋ㸪ຍᕤ୰࡟ࡑࡢ࣎࢖ࢻ య✚⋡ࡀᮦᩱᅛ᭷ࡢ㝈⏺್࡟㐩ࡋࡓ᫬Ⅼ࡛◚ቯࢆุᐃࡍࡿࡶࡢ࡛࠶ࡿ㸬 (d) ᛂຊ୕㍈ᗘ࡟ᑐࡍࡿ◚᩿┦ᙜࡦࡎࡳࢆࡋࡁ࠸್࡜ࡋࡓࣔࢹࣝ  ຍᕤ୰ࡢᖹᆒᛂຊ୕㍈ᗘ࡜◚᩿┦ᙜࡦࡎࡳ࡜ࡢ㛵ಀ࡟╔┠ࡋࡓࣔࢹࣝࡶ࠶ࡿ㸬 Bao ࡜ Wierzbicki 1-47)_{ࡣ㸪ᅽ⦰㸪ࡏࢇ᩿㸪ᘬᙇࡏࢇ᩿࠾ࡼࡧᘬᙇࡢ」ᩘࡢᛂຊ≧} ែࢆኚ໬ࡉࡏࡓᐇ㦂ࢆ⾜࠸㸪ᐇ㦂⤖ᯝ࡜ྠᵝࡢFEM ゎᯒࡢ⤖ᯝ࠿ࡽ㸪ᖹᆒᛂຊ ୕㍈ᗘ࡟ᑐࡍࡿ◚ቯ┦ᙜࡦࡎࡳࡢኚ໬ࢆㄪᰝࡋ㸪Fig. 1-12 ࡟♧ࡍࡼ࠺࡟ᩚ⌮ࡋ ࡚࠸ࡿ㸬᭱㏆࡛ࡣ㸪ᖹᆒᛂຊ୕㍈ᗘ࡟ຍ࠼㸪ᛂຊ≧ែࢆ⾲ࡍᣦᶆ࡜ࡋ࡚Lode ゅ ࡶ⪃៖ࡋ㸪Fig. 1-13 ࡟♧ࡍࡼ࠺࡟㸪ᖹᆒᛂຊ୕㍈ᗘ࡜ᖹᆒ Lode ゅT ࡟ᑐࡋ࡚◚ ᩿┦ᙜࡦࡎࡳࢆ୕ḟඖ⾲⌧ࡋ࡚◚ቯࢆண ࡍࡿࣔࢹࣝࡶ࠶ࡿ1-48)㸬

19

Fig. 1-12 Relationship between equivalent strain to fracture and average stress

triaxiality on 2024-T351 aluminum alloy 1-47)

20 1.3.3 ᘏᛶ◚ቯࣃ࣓࣮ࣛࢱࡢྠᐃ᪉ἲ ࠸ࡎࢀࡢ◚ቯ᮲௳ࢆ⏝࠸ࡿ࡟ࡋ࡚ࡶᘏᛶ◚ቯண ࣔࢹࣝ୰࡟ࡣ1 ಶ࡞࠸ࡋࡣ㸪 」ᩘࡢࣃ࣓࣮ࣛࢱࡀᏑᅾࡍࡿࡓࡵ㸪◚ቯࢆక࠺ఱ࠿ࡋࡽࡢᮦᩱヨ㦂࡟ࡼࡗ࡚㸪ࡇ ࢀࡽࢆ஦๓࡟ྠᐃࡋ࡚࠾࠿ࡡࡤ࡞ࡽ࡞࠸㸬ከࡃࡢࣔࢹࣝ࡟࠾࠸࡚㸪ྛࣔࢹ࡛ࣝᐃ ⩏ࡉࢀࡿᦆയ್㸦ࢲ࣓࣮ࢪ್㸧ࢆ◚᩿ࡲ࡛ࡢࡦࡎࡳ࡛✚ศࡍࡿᙧ࡟࡞ࡗ࡚࠸ࡿࡓ ࡵ㸪ࣃ࣓࣮ࣛࢱࢆྠᐃࡍࡿࡓࡵ࡟ࡣ㸪◚ቯࡲ࡛ࡢᛂຊ࡜ࡦࡎࡳࡢ㈇ⲴᒚṔࡀ᫂☜ ࡟࡞ࡗ࡚࠸ࡿᚲせࡀ࠶ࡿ㸬  ྜྷ⏣ࡽ 1-49)_{ࡣ㸪ษḞ௜୸Წᘬᙇヨ㦂ࢆ⏝࠸ࡓ㝈⏺ࢲ࣓࣮ࢪ್ࡢྠᐃἲࢆᥦ᱌} ࡋ࡚࠸ࡿ㸬ษḞ௜୸Წᘬᙇヨ㦂࡛ࡣ㸪ኚᙧ㒊ࢆษḞ㒊࡟㞟୰࡛ࡁࡿࡓࡵࡃࡧࢀ㒊 ࡢᑍἲィ ࡀᐜ࡛᫆࠶ࡾ㸪ึᮇษḞ༙ᚄࢆኚ࠼ࡿࡇ࡜࡛⡆౽࡟ᛂຊ୕㍈ᗘࡢ㈇ ⲴᒚṔࢆኚ࠼ࡽࢀࡿ࣓ࣜࢵࢺࡀ࠶ࡿ㸬ྜྷ⏣ࡽࡢ⏬ീゎᯒ௜ᘬᙇヨ㦂ࢩࢫࢸ࣒ࢆ Fig. 1-14 ࡟♧ࡍ㸬ࡃࡧࢀ㒊ࢆ CCD ࣓࡛࢝ࣛ᧜ᙳࡋ㸪⏬ീゎᯒ࡟ࡼࡾ᫬ࠎ้ࠎࡢ a ࡜ R ࢆィ ࡋ㸪1.2.3 ⠇࡛♧ࡋࡓ Bridgman ἲࢆ฼⏝ࡋ࡚㸪ࡃࡧࢀᗏ᩿㠃୰ᚰ࡟ ࠾ࡅࡿᛂຊ୕㍈ᗘ࠾ࡼࡧ┦ᙜࡦࡎࡳࡢᒚṔࢆィ ࡍࡿ㸬 ࡇࡢ᪉ἲ࡛ྠᐃࡉࢀࡓ 3 ✀㢮ࡢ㗰ᮦࡢ Ayada ࡢ㝈⏺ࢲ࣓࣮ࢪ್ࢆ Fig. 1-15 ࡟♧ࡍ㸬ྠᐃࡉࢀࡿ㝈⏺ࢲ ࣓࣮ࢪ್ࡣᛂຊ୕㍈ᗘ࡟ᑐࡋ୍࡚ᐃ࡛ࡣ࡞࠸ࡇ࡜ࡀศ࠿ࡿ1-50)_㸬  ྜྷ⏣ࡽࡢ᪉ἲࡣ㸪ᘬᙇヨ㦂⤖ᯝ࠿ࡽ┤᥋ᛂຊࡸࡦࡎࡳࡢᒚṔࢆ ᐃ࡛ࡁࡿ୍ ᪉࡛㸪ᛂຊࡢホ౯࡟Bridgman ἲࢆ฼⏝ࡋ࡚࠸ࡿࡓࡵ㸪ྠᐃ⢭ᗘࡢ㠃࡛ࡣㄢ㢟ࡀ ࠶ࡿ㸬

21

Fig. 1-15 Relationship between critical damage value of Ayada model and stress

triaxiality at fracture on 3 type of carbon steel 1-50)

Critical dam

age

value

C

A

22 1.4 ᮏㄽᩥࡢ┠ⓗ࡜ᵓᡂ  ᮏㄽᩥ࡛ࡣ㸪ᘬᙇヨ㦂࡟࠾࠸࡚◚᩿ࡲ࡛ࡢὶືᛂຊ᭤⥺ࢆ┤᥋ⓗ࡟ྠᐃࡍࡿ ᪂ࡋ࠸ᡭἲࢆᥦ᱌ࡍࡿࡇ࡜ࢆ┠ⓗ࡜ࡍࡿ㸬1.2 ⠇࡛㏙࡭ࡓࡼ࠺࡟㸪ᘬᙇヨ㦂࡟࠾ ࠸࡚Bridgman ἲࢆ⏝࠸ࢀࡤ㸪◚᩿ࡲ࡛ࡢὶືᛂຊ᭤⥺ࢆ┤᥋ⓗ࡟ྠᐃ࡛ࡁࡿࡀ㸪 ึ➼ゎἲ࡛ࡢ௬ᐃࡀᡂ❧ࡋ࡞࠸࡜⢭ᗘࡀᝏ໬ࡍࡿၥ㢟ࢆᢪ࠼࡚࠸ࡿ㸬୍᪉㸪㏫ゎ ᯒⓗ࡞᪉ἲ࡛ࡣ㸪ከࡃࡢሙྜ࡛◳໬๎ࡢࣃ࣓࣮ࣛࢱࢆྠᐃᑐ㇟࡜ࡋ࡚࠾ࡾ㸪ྠᐃ ࡉࢀࡿὶືᛂຊ᭤⥺ࡣ㑅ᢥࡋࡓ◳໬๎࡟౫Ꮡࡋ࡚ࡋࡲ࠺ၥ㢟ࡀ࠶ࡿ㸬  ࡑࡇ࡛㸪ᥦ᱌ࡍࡿᡭἲ࡛ࡣBridgman ࡢᛂຊ⿵ṇࡢ⪃࠼᪉ࢆ㋃くࡋ㸪ᐇ㦂࠿ࡽ ᚓࡽࢀࡿᖹᆒᘬᙇᛂຊࢆὶືᛂຊ࡟⿵ṇࡍࡿࡀ㸪ࡑࡢ⿵ṇಀᩘࡢỴᐃ࡟FEM ࡜ ᭱㐺໬ᡭἲࢆ⏝࠸ࡓ㏫ゎᯒࡢᡭἲࢆ㐺⏝ࡍࡿ㸬ࡇࡢᡭἲ࡛࠶ࢀࡤ㸪◳໬๎࡟౫Ꮡ ࡍࡿࡇ࡜࡞ࡃ┤᥋ⓗ࡟ὶືᛂຊࢆྠᐃ࡛ࡁ㸪ࡲࡓ㸪ᐇ㦂⤖ᯝ࡜FEM ゎᯒ⤖ᯝࡀ ୍⮴ࡍࡿࡼ࠺࡟⿵ṇಀᩘࢆỴᐃࡍࡿࡓࡵ㸪⢭ᗘ㠃࡛ࡶBridgman ἲ࡟ᑐࡋ࡚ᨵၿ ࡀᮇᚅ࡛ࡁࡿ㸬◳໬๎ࢆ௬ᐃࡍࡿሙྜ࡟ẚ࡭࡚ࣃ࣓࣮ࣛࢱᩘࡣከࡃ࡞ࡿࡀ㸪ᛂຊ ⿵ṇಀᩘࢆࣃ࣓࣮ࣛࢱ࡜ࡍࡿࡇ࡜࡛㸪ࡑࡢ᥈⣴⠊ᅖࡣ⤠ࡾ㎸ࡴࡇ࡜ࡀ࡛ࡁࡿ㸬 Fig. 1-16 ࡟ᥦ᱌ᡭἲࡢᴫᛕᅗࢆ♧ࡍ㸬ᥦ᱌ᡭἲࡢ୺࡞≉ᚩࢆ௨ୗ࡟ࡲ࡜ࡵࡿ㸬  1) ᘬᙇヨ㦂࡟࠾࠸࡚㸪ࡃࡧࢀⓎ⏕࠿ࡽ◚᩿࡟⮳ࡿࡲ࡛ࡢ኱ࡦࡎࡳᇦࡢὶືᛂ ຊ᭤⥺ࢆ◳໬๎࡟౫Ꮡࡏࡎ࡟ྠᐃࡍࡿ  2) Bridgman ἲࡢᛂຊ⿵ṇࡢ⪃࠼᪉ࢆ㋃くࡋ㸪ᛂຊ⿵ṇ㔞ࡢỴᐃ࡟ FEM ࡜᭱ 㐺໬ᡭἲࢆ฼⏝ࡋࡓ㏫ゎᯒࢆ㐺⏝ࡍࡿ㸬  3) ᭱㐺໬࢔ࣝࢦࣜࢬ࣒࡟ࡣ㏲ḟ㏆ఝᛂ⟅᭤㠃ἲࡢ୍✀࡛࠶ࡿ SRSM2-3)_ࢆ᥇ ⏝ࡍࡿ㸬ࡇࢀࡣ㸪ᑡ࡞࠸ヨ⾜ᅇᩘ࡛᭱㐺໬ࢆᚓࡿࡇ࡜ࡀ࡛ࡁࡿ㸬  ୖグࡢᡭἲࢆᥦ᱌ࡍࡿࡢ࡟㝿ࡋ㸪᳨ドࡍ࡭ࡁㄢ㢟ࢆิグࡍࡿ㸬  1) ᖹᆒᘬᙇᛂຊࢆ ᐃྍ⬟࡞ᘬᙇヨ㦂ࢩࢫࢸ࣒ࡢᵓ⠏  2) ᥦ᱌ᡭἲ࡟ࡼࡿᛂຊ⿵ṇ㔞ࡢጇᙜᛶࡢ᳨ド  3) ᥦ᱌ᡭἲࡀ㐺⏝ྍ⬟࡞ᮦᩱࡢ᫂☜໬ 1) ࡟㛵ࡋ࡚ࡣ㸪ྜྷ⏣ࡽࡀ㛤Ⓨࡋࡓ⏬ീゎᯒ௜ᘬᙇヨ㦂ࢩࢫࢸ࣒ࢆ฼⏝ࡍࡿ㸬ࡇ ࡢࢩࢫࢸ࣒࡟㸪ࡃࡧࢀ఩⨨ࡀ᫂☜࡞ษḞ୸Წᘬᙇヨ㦂ࢆ⤌ࡳྜࢃࡏࡿࡇ࡜࡛㸪Ᏻ ౯࠿ࡘᖹ᫆࡟ᛂຊ⿵ṇࡢ࣮࣋ࢫ࡜࡞ࡿᖹᆒᘬᙇᛂຊࢆィ ࡍࡿࡇ࡜ࡀ࡛ࡁࡿ㸬2) ࡜ 3) ࡟㛵ࡋ࡚ࡣ㸪ጞࡵ࡟ FEM ࡢゎᯒ⤖ᯝࢆ௬᝿ࡢᐇ㦂⤖ᯝ࡜ぢ❧࡚ࡓᩘ್ᐇ 㦂ࢆ㏻ࡌ᳨࡚ドࢆ⾜࠺㸬2) ࡟㛵ࡋ࡚ࡣ㸪ึᮇษḞ༙ᚄࢆኚ໬ࡉࡏࡓ㸪ࡍ࡞ࢃࡕ ከ㍈ᛂຊ≧ែࢆኚ໬ࡉࡏࡓ」ᩘࡢᘬᙇヨ㦂ࡢ⤖ᯝ࠿ࡽྠ୍ࡢὶືᛂຊ᭤⥺ࡀྠ ᐃ࡛ࡁࡿ࠿࡝࠺࠿㸪3) ࡟㛵ࡋ࡚ࡣ㸪࠶ࡽ࠿ࡌࡵタᐃࡋࡓ␗࡞ࡿຍᕤ◳໬ᣲືࡢ

23 ὶືᛂຊ᭤⥺ࡀࡑࢀࡒࢀྠᐃྍ⬟࠿࡝࠺࠿㸪࡜࠸࠺ほⅬ᳨࡛ドࢆᐇ᪋ࡍࡿ㸬᳨ド ᚋ㸪ᐇ㝿ࡢᮦᩱ࡟ᥦ᱌ᡭἲࢆ㐺⏝ࡋ㸪ᐇၥ㢟࡛ࡢ㐺⏝ᛶࢆ᳨ドࡍࡿ㸬  ࡲࡓ㸪1.3 ⠇࡛㏙࡭ࡓࡼ࠺࡟㸪◚᩿ࡲ࡛ࡢὶືᛂຊ᭤⥺ࢆྠᐃࡍࡿࡇ࡜࡜㸪ྛ ✀ࡢᘏᛶ◚ቯண ࣔࢹࣝࡢࣃ࣓࣮ࣛࢱࢆྠᐃࡍࡿࡇ࡜࡜ࡣ㸪◚᩿ࡲ࡛ࡢᛂຊ࡜ ࡦࡎࡳࡢ㈇ⲴᒚṔࢆྠᐃࡍࡿ࡜࠸࠺ព࿡࡟࠾࠸࡚ࡣ㸪➼౯࡞ၥ㢟࡛࠶ࡿ࡜࠸࠼ ࡿ㸬ᮏᡭἲ࡛ࡣ㸪ὶືᛂຊ᭤⥺ࡀྠᐃ࡛ࡁࡓ᫬Ⅼ࡛㸪FEM ࡢ࣏ࢫࢺฎ⌮࡟ࡼࡗ ࡚௵ពࡢሙᡤ࡟࠾ࡅࡿྛ✀ࡢᛂຊࡸࡦࡎࡳࡢᒚṔࢆᢳฟྍ⬟࡜࡞ࡾྛ✀ࡢᘏᛶ ◚ቯࣃ࣓࣮ࣛࢱࡀྠᐃྍ⬟࡜࡞ࡿ㸬ࡋ࠿ࡋ࡞ࡀࡽ㸪ྠᐃࡉࢀࡓࣃ࣓࣮ࣛࢱࡀᐇ⏝ ၥ㢟࡟᭷ຠ࡛࠶ࡿ࠿࡝࠺࠿ࡣ㸪ᐇドᐇ㦂ࢆ㏻ࡌ࡚ὀព῝ࡃ᳨ドࡍࡿᚲせࡀ࠶ࡿ㸬 ࡑࡇ࡛㸪ᮏㄽᩥ࡛ࡣ㸪㘫㐀ࡢึᮇᕤ⛬࡛ከ⏝ࡉࢀࡿᤣ㎸ࡳヨ㦂ࡢ⾲㠃๭ࢀࢆᑐ㇟ ࡟ࡋࡓᐇドᐇ㦂ࢆ⾜࠸㸪ࡑࡢ᭷ຠᛶࢆ᳨ドࡋࡓ㸬  ᮏㄽᩥࡣ 5 ❶࡛ᵓᡂࡉࢀ࡚࠾ࡾ㸪ࡑࢀࡒࢀࡢ❶࡛ྲྀࡾୖࡆࡿෆᐜࡣ௨ୗࡢ㏻ ࡾ࡛࠶ࡿ㸬  ➨ 1 ❶ࡣᗎㄽ࡛࠶ࡾ㸪᪤Ꮡࡢὶືᛂຊ᭤⥺ࡢྠᐃᢏ⾡࠾ࡼࡧᘏᛶ◚ቯࡢ࣓࢝ ࢽࢬ࣒ࡸྛ✀ࡢᘏᛶ◚ቯண ࣔࢹࣝࢆᴫほࡍࡿ࡜࡜ࡶ࡟㸪ᮏㄽᩥ࡛ྲྀࡾᢅ࠺◊ ✲ࡢ┠ⓗ࠾ࡼࡧ఩⨨࡙ࡅࢆ᫂☜࡟ࡋ࡚࠸ࡿ㸬  ➨2 ❶࡛ࡣ㸪ษḞ୸Წᘬᙇヨ㦂࡟ᑐࡋ࡚ FEM ࡜᭱㐺໬ᡭἲࢆ฼⏝ࡋࡓ᪂ࡋ࠸ ᛂຊ⿵ṇἲࢆᥦ᱌ࡍࡿ࡜࡜ࡶ࡟㸪ᩘ್ᐇ㦂࠾ࡼࡧᐇ㝿ࡢ㕲㗰ᮦᩱࢆᑐ㇟࡜ࡋࡓ ᐇ㦂ࢆ㏻ࡌ࡚㸪ᥦ᱌ࡍࡿᛂຊ⿵ṇἲࡢጇᙜᛶ࡜㸪ᚑ᮶ᢏ⾡࡛࠶ࡿBridgman ἲ࡜ ࡢẚ㍑ࢆ⾜ࡗ࡚࠸ࡿ㸬  ➨ 3 ❶࡛ࡣ㸪ຍᕤ◳໬ᣲືࡢ␗࡞ࡿ 3 ✀㢮ࡢ㔠ᒓᮦᩱ࡟ᑐࡋ࡚㸪ᥦ᱌ᡭἲ࡟ ࡼࡾྛὶືᛂຊ᭤⥺࠾ࡼࡧ 2 ✀㢮ࡢᘏᛶ◚ቯ᮲௳ᘧࡢ㝈⏺ࢲ࣓࣮ࢪ್ࢆྠᐃࡋ ࡚࠸ࡿ㸬ࡲࡓ㸪Bridgman ἲࢆ฼⏝ࡋࡓሙྜࡢ㝈⏺ࢲ࣓࣮ࢪ್ࡢྠᐃ⤖ᯝ࡜ࡢẚ ㍑ࢆ⾜࠸㸪ࡑࡢᕪ␗࡟ࡘ࠸࡚ࡢ⪃ᐹࢆࡋ࡚࠸ࡿ㸬  ➨4 ❶࡛ࡣ㸪Ⅳ⣲㗰 S45C ࢆᑐ㇟࡟㸪෭㛫㘫㐀ࡢึᮇᕤ⛬࡛ከ⏝ࡉࢀࡿᤣ㎸ࡳ ࡢ๭ࢀண ࡟ྲྀࡾ⤌ࡴ㸬ษḞ௜ࡁ୸Წᘬᙇヨ㦂ࡢࡳ࡛ࡣ㸪Ỵᐃ࡛ࡁࡿᘏᛶ◚ቯࣃ ࣓࣮ࣛࢱࡢᛂຊ୕㍈ᗘ⠊ᅖࡀ༑ศ࡛࡞࠸ࡓࡵ㸪3 Ⅼ᭤ࡆヨ㦂ࡶᐇ᪋ࡋ㸪ᣦᩘ㛵ᩘ ᆺࡢᘏᛶ◚ቯண ࣔࢹࣝࡢࣃ࣓࣮ࣛࢱࢆỴᐃࡍࡿ㸬෇ᰕࡢ➃㠃ᣊ᮰ᅽ⦰ヨ㦂࡛ ࡢᅽ⦰㝈⏺࡟ࡼࡾ㸪Ỵᐃࡋࡓᘏᛶ◚ቯࣃ࣓࣮ࣛࢱࡢጇᙜᛶࢆ᳨ドࡋࡓ㸬  ➨5 ❶ࡣ⥲ᣓ࡛࠶ࡾ㸪ᮏ◊✲࡛ᚓࡽࢀࡓᡂᯝ࡟ࡘ࠸࡚ࡲ࡜ࡵ࡚࠸ࡿ㸬

24 Fi g. 1 -1 6 Sc he ma tic dia gr am of pr op ose d str ess co rr ec tion me tho d Post-ne ckin g Equivalent stress Equivalent stress min ) ( 1 2 1 o ¸ ¸ ¹ · ¨ ¨ © § 

¦

n _i i i i P Max P F n e x a F εeq = 2ln( a0 /a ) εu εf Standard tensile test εeq = 2ln( a0 /a ) σzave I σu εu εf Stress corre ction FEM (L S-DYNA) Standard tensile test 㽢 㽢 σzave = P /( πa 2) xI σzave N σflow N xN Error eva lu atio n Notched round-bar tensile test w ith image analy sis Initial (I nitial:2 a0 ) 2a CCD camera P _P

Error

e

a

0

-a

T ensile load i

P

)

(x

_i

F

1 i n i 2 i 3 i i

Ex

pe

riment

FEM

a

f

㽢

SRSM 䠄LS-OPT 䠅 C orrected flow stress σflo wI = xI σzave I Frac tu re Post-ne ckin g

25 ཧ⪃ᩥ⊩ 1-1) ㏆␥㘫ᕤရ஦ᴗඹྠ⤌ྜ㸸http://www.kintan.jp/forging.html. 1-2) ᪥ᮏᨻ⟇ᢞ㈨㖟⾜㸸௒᭶ࡢࢺࣆࢵࢡࢫ㸪No.083 (2005). 1-3) ౛࠼ࡤ㸪᳃ୗᛅ᫭㸸⮬ື㌴⏕⏘࡟࠾ࡅࡿረᛶຍᕤᢏ⾡ࡢⓎᒎ㸪ረᛶ࡜ຍᕤ㸪 52-600 (2011), 101-107. 1-4) ᪥ᮏረᛶຍᕤᏛ఍⦅㸸ረᛶຍᕤᢏ⾡ࢩ࣮ࣜࢬ 4 㘫㐀, ࢥࣟࢼ♫ (1995), 12. 1-5) ⃝㎶ᘯ㸪ྜྷᮧ㇮἞㸸㔠ᆺタィࡢᕤኵ࠶ࢀࡇࢀረᛶ࡜ຍᕤ㸪40-464(1999)㸪 857-862. 1-6) ᪥ᮏረᛶຍᕤᏛ఍⦅㸸ረᛶຍᕤᢏ⾡ࢩ࣮ࣜࢬ 4 㘫㐀, ࢥࣟࢼ♫ (1995), 150. 1-7) ▼ᕝᏕྖ㸪㧗ᰗ⪽㸪ྜྷ⏣ె඾㸪‮ᕝఙᶞ㸪ఀ⸨ඞᾈ㸪ụ⏣ᐇ㸸෭㛫ከẁᢲ ࡋฟࡋᡂᙧ࡟࠾ࡅࡿෆ㒊Ḟ㝗ࡢண 㸪ረᛶ࡜ຍᕤ, 42-488 (2001), 949-953. 1-8) ᑠᆏ⏣ᏹ㐀㸪㔠Ⅱ⌼㸸ᙺ❧ࡘ㘫㐀ࢩ࣑࣮ࣗࣞࢱ㸪ረᛶ࡜ຍᕤ㸪39-454(1998)㸪 1107-1111. 1-9) ⸨ᕝ┿୍ᮁ㸸⮬ື㌴⏘ᴗ࡟࠾ࡅࡿ㘫㐀ᢏ⾡ࡢ㐍໬࡜ࡑࡢᒎᮃ㸪ረᛶ࡜ຍᕤ㸪 52-600(2011)㸪148-152. 1-10) ⥲ົ┬㸸୰ᑠ௻ᴗࡢࡶࡢ࡙ࡃࡾᇶ┙ᢏ⾡ࡢ㧗ᗘ໬࡟㛵ࡍࡿἲᚊ, ᖹᡂ༑ඵ ᖺᅄ᭶஧༑භ᪥ἲᚊ➨୕༑୕ྕ. 1-11) ୰ᑠ௻ᴗᗇ㸸http://www.chusho.meti.go.jp/keiei/sapoin/index.html. 1-12) ⏘ᴗ➇தຊ᠓ㄯ఍ COCN㸪HPC ᛂ⏝◊✲఍㸸⏘ᴗ➇தຊ᠓ㄯ఍ 2011 ᖺᗘ ◊✲఍᭱⤊ሗ࿌(2012). 1-13) ≉ᐃ㠀Ⴀ฼άືἲே CAE ᠓ヰ఍㸸http://www.cae21.org/ 1-14) ≉ᐃ㠀Ⴀ฼άືἲே㠀⥺ᙧ CAE ༠఍㸸http://www.jancae.org/ 1-15) ≉ᐃ㠀Ⴀ฼άືἲே CAE ᨭ᥼ࢿࢵࢺ㸸http://www.caesn.org/

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1-24) Davidenkov, N. N., Spiridonova, N. I.: Proc. ASTM, 46 (1946), 1147-1158. 1-25) J.W.Hancock and A.C.Mackenzie: On the mechanisms of ductile failure in

high-strength steels subjected to multi-axial stress-states, Journal of the Mechanics and Physics of Solids, 24 (1976) ,147-160. 1-26) ᴮ୪ၨኴ㑻㸪㛗஭ᑑ㸸෇࿘ษḞᘬᙇヨ㦂࡟ࡼࡿረᛶኚᙧ㝈⏺ࡢホ౯, 㕲࡜ 㗰, 91-2 (2005), 285-291. 1-27) ᴮ୪ၨኴ㑻㸪㛗஭ᑑ㸸᩿⥆ᘬᙇヨ㦂࡟ࡼࡿᒁᡤࡃࡧࢀ௨㝆ࡢ┿ᛂຊ-┿ࡦ ࡎࡳ⥺ᅗࡢホ౯, 㕲࡜㗰, 91-9 (2005), 712-718. 1-28) ᅵ⏣⣖அ㸪஭ୖᛅಙ㸪ᴮ୪ၨኴ㑻㸸ᵝࠎ࡞㔠ᒓᮦᩱࢆ⏝࠸ࡓ᩿⥆ᘬᙇヨ㦂 ࡜ Bridgman ࡢᘧ࡟ࡼࡿ◚᩿┤๓ࡲ࡛ࡢ┿ࡢᛂຊ-ࡦࡎࡳ㛵ಀࡢ᥎⟬, ᪥ ᮏ㔠ᒓᏛ఍ㄅ, 76-10 (2012) 579-586.

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1-31) Bao, Y., Wierzbicki, T.: On the cut-off value of negative triaxiality for fracture. Engineering Fracture Mechanics, 72 (2005), 1049-1069.

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1-33) Koc, P., Štok, B.: Computer-aided identification of the yield curve of a sheet metal after onset of necking, Computational Materials Science 31 (1) (2004), 155-168. 1-34) Hasegawa, K., Chen, Z., Nishimura, K., Ikeda, K.: Determination of True Stress– Strain Curves of Sheet Metals in Post-Uniform Elongation Range, Materials Transactions, 50 (2009), 138-144.

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1-37) Coppieters, S., Cooreman, S., Sol, H., Van Houtte P., Debruyne, D.: Identification of the post-necking hardening behavior of sheet metal by comparison of the

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internal and external work in the necking zone, Journal of Materials Processing Technology, 211 (3) (2011) 545-552.

1-38) Kim, J.H., Serpantié, A., Barlat, F., Pierron, F., Lee, M.G.: Characterization of the post-necking strain hardening behavior using the virtual fields method, International Journal of Solids and Structures, 50 (2013), 3829–3842.

1-39) Dunand, M., Mohr, D.: Hybrid experimental-numerical analysis of basic ductile fracture experiments for sheet metals, International Journal of Solids and Structures, 47 (2010), 1130-1143.

1-40) Kajberg, J., Lindkvist, G.: Characterisation of materials subjected to large strains by inverse modelling based on in-plane displacement fields, International Journal of Solids and Structures, 41 (2004), 3439-3459.

1-41) ᑠᆏ⏣ᏹ㐀㸸㘫ᅽຍᕤ࡟࠾ࡅࡿኚᙧ㐣⛬࡜Ḟ㝗Ⓨ⏕㸪ረᛶ࡜ຍᕤ㸪17-187 㸦1976㸧㸪627. 1-42) ▼ᕝᏕྖ㸸෭㛫㘫㐀࡟࠾ࡅࡿᮦᩱࡢ๭ࢀண 㸪ረᛶ࡜ຍᕤ㸪53-620 (2012) 790-794. 1-43) ᑠ㜰⏣ᏹ㐀㸪⥥㇂ᬗᘅ㸪㛵ཱྀ⚽ኵ㸸෭㛫ረᛶຍᕤ᮲௳࡟࠾ࡅࡿⅣ⣲㗰ࡢᘏ ᛶ◚ቯ㸪➨2 ሗ㔠ᒓ⤌⧊ࡢᙳ㡪㸪᪥ᮏᶵᲔᏛ఍ㄽᩥ㞟㸪43-376 (1977) 4463-4473.

1-44) McClintock, F.A.: A criterion for ductile fracture by the growth of holes. ASME Journal of Applied Mechanics 35 (1968), 363-371.

1-45) Rice, J.R., Tracey, D.M.: On the ductile enlargement of voids in triaxial stress fields, Journal of the Mechanics and Physics of Solids 17 (1969), 201-217. 1-46) Gurson, A.L.: Continuum Theory of Ductile Rupture by Void Nucleation and

Growth: Part I—Yield Criteria and Flow Rules for Porous Ductile Media, Journal of Engineering Materials and Technology, 99 (1977), 2.

1-47) Bao, Y., Wierzbicki, T.: On fracture locus in the equivalent strain and stress triaxiality space, International Journal of Mechanical Sciences, 46 (2004), 81-98. 1-48) Bai, Y., Wierzbicki, T.: A new model of metal plasticity and fracture with pressure and Lode dependence, International Journal of Plasticity, 24 (2008), 1071-1096. 1-49) Yoshida, Y., Yukawa, N., Ishikawa, T.: Determination of ductile damage

parameters by notched round bar tension test using image analysis, Proc. of 8th NUMIFORM, (2004), 1869-1874.

1-50) ྜྷ⏣ె඾㸸ᘏᛶ◚ቯ᮲௳ᘧ࡜ᘏᛶ◚ቯࣃ࣓࣮ࣛࢱỴᐃἲ㸪ረᛶ࡜ຍᕤ㸪57-669 (2016) 940-944.

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➨㸰❶ ษḞ௜୸Წᘬᙇヨ㦂ࢆ⏝࠸ࡓὶືᛂຊྠᐃᡭἲࡢ㛤Ⓨ

_ 2.1 ⥴ゝ ➨㸯❶࡟࡚♧ࡋࡓࡼ࠺࡟㸪ᘬᙇヨ㦂࡟࠾࠸࡚ࡦ࡜ࡓࡧヨ㦂∦࡟ࡃࡧࢀࡀ⏕ࡌ ࡿ࡜ࡃࡧࢀ㒊ࡣከ㍈ᛂຊ≧ែ࡟ࡉࡽࡉࢀࡿࡓࡵ㸪᫬ࠎ้ࠎࡢᘬᙇ㍈᪉ྥࡢᖹᆒ ᛂຊ㸦௨ᚋ㸪ᖹᆒᘬᙇᛂຊ࡜⛠ࡍࡿ㸧σzave = P/A ࡣࡑࡢᙳ㡪ࢆཷࡅ࡚㸪ᮦᩱࡢὶ ືᛂຊ σflowࡼࡾ㧗ࡵ࡟ィ ࡉࢀ࡚ࡋࡲ࠺㸬 Fig. 2-1 ࡣ୸Წᘬᙇヨ㦂࡟࠾ࡅࡿ㸪 ὶືᛂຊ࡜ᖹᆒᘬᙇᛂຊࢆ♧ࡋࡓᶍᘧᅗ࡛࠶ࡿ㸬 ᮏ❶࡛ࡣ㸪ࡇࡢᖹᆒᘬᙇᛂຊࢆὶືᛂຊ࡟⿵ṇࡍࡿ᪂ࡋ࠸᪉ἲࢆᥦ᱌ࡍࡿ㸬⏬ ീゎᯒࢆ⏝࠸ࡓษḞ௜୸Წᘬᙇヨ㦂ࢆᐇ᪋ࡋ㸪ᚓࡽࢀࡿᖹᆒᘬᙇᛂຊ σzave࡟ᑐ ࡋ࡚FEM ゎᯒ࡜᭱㐺໬ᡭἲ࡟ࡼࡿ㏫ゎᯒࢆ฼⏝ࡍࡿࡇ࡜࡛ᛂຊ⿵ṇ㔞ࢆỴᐃࡍ ࡿ㸬ࡇࡢ᪉ἲ࡟ࡼࡾ◚᩿࡟⮳ࡿࡲ࡛ࡢὶືᛂຊࢆ㸪ྠᐃࡍࡿࡇ࡜ࡀྍ⬟࡜࡞ࡿ㸬 ᮏᡭἲࡢጇᙜᛶࢆ᳨ドࡍࡿ┠ⓗ࡛㸪FEM ゎᯒ࡟ࡼࡿษḞ௜୸Წᘬᙇヨ㦂ࡢᩘ ್ᐇ㦂ࢆᐇ᪋ࡋ㸪࠶ࡽ࠿ࡌࡵタᐃࡋࡓṇゎࡢὶືᛂຊ᭤⥺㸦௨ᚋ㸪ཧ↷ὶືᛂຊ ᭤⥺σref࡜⛠ࡍࡿ㸧ࡀ෌⌧࡛ࡁࡿ࠿ࢆ᳨ドࡋࡓ㸬ࡲࡓ㸪ᐇᮦᩱࢆ⏝࠸ࡓᐇ㦂࡛ࡣ㸪 㧗ᘏᛶᮦᩱ࡛࠶ࡿ୍⯡ᵓ㐀⏝㗰ᮦࡢษḞ௜୸Წᘬᙇヨ㦂࡟ᮏᡭἲࢆ㐺⏝ࡋ࡚◚ ᩿ࡲ࡛ࡢὶືᛂຊ᭤⥺ࡢྠᐃࢆヨࡳࡓ㸬ࡲࡓ㸪ᩘ್ᐇ㦂࠾ࡼࡧᐇ㦂࡟࠾࠸࡚㸪ᮏ ᡭἲ࡜୪⾜ࡋ࡚ึ➼ゎἲ࡟ᇶ࡙ࡃྂ඾ⓗ࡞ᛂຊ⿵ṇἲ࡛࠶ࡿ Bridgman ἲ 1-23)_࡛ ࡶᛂຊ⿵ṇࢆᐇ᪋ࡋ㸪ᛂຊ⿵ṇ⢭ᗘࡢẚ㍑ࢆ⾜ࡗࡓ㸬

Fig. 2-1 Difference between the average tensile stress and the material flow stress in

29 2.2 ᐇ㦂᪉ἲ 2.2.1 ౪ヨᮦ࠾ࡼࡧヨ㦂∦ᙧ≧ ୍⯡ᵓ㐀⏝㗰ᮦࡢ SS400 ୸Წ࠿ࡽᘬᙇヨ㦂∦ࢆ๐ࡾฟࡋ㸪ᐇ㦂࡟౑⏝ࡋࡓ㸬 SS400 ୸Წࡢ໬Ꮫ⤌ᡂࢆ Table 2-1 ࡟♧ࡍ㸬ᘬᙇヨ㦂࡟ࡣ Fig. 2-2 ࡟♧ࡍ࡜࠾ࡾ㸪 4 ✀㢮ࡢษḞ௜୸Წᘬᙇヨ㦂∦࡜ 1 ✀㢮ࡢᖹ⁥୸Წᘬᙇヨ㦂∦ࢆ౑⏝ࡋࡓ㸬ᖹ⁥ ୸Წᘬᙇヨ㦂࡟࡚ィ ࡋࡓᶵᲔⓗ≉ᛶ್࠾ࡼࡧ୍ᵝఙࡧࡢ⠊ᅖ࡛ྠᐃࡋࡓSwift ๎ࡢࣃ࣓࣮ࣛࢱࢆTable 2-2 ࡟♧ࡍ㸬ࡇࡇ࡛㸪εpࡣ┦ᙜረᛶࡦࡎࡳ࡛࠶ࡿ㸬ษḞ ௜୸Წᘬᙇヨ㦂∦ࡣ㸪ษḞᙧ≧ࢆ௜୚ࡍࡿࡇ࡜࡛ࡃࡧࢀⓎ⏕఩⨨ࡀᐃࡲࡾィ  ࡀᐜ᫆࡟࡞ࡿ㸬ࡲࡓ㸪ึᮇษḞ༙ᚄR0ࢆኚ໬ࡉࡏࡿࡇ࡜࡛㸪ࡃࡧࢀ㒊࡟Ⓨ⏕ࡍ ࡿᛂຊࡢ㈇ⲴᒚṔࢆኚ໬ࡉࡏࡓヨ㦂ࡀྍ⬟࡜࡞ࡿ㸬」ᩘࡢᛂຊ㈇ⲴᒚṔࡢᘬᙇ ヨ㦂⤖ᯝ࠿ࡽྠࡌὶືᛂຊ᭤⥺ࡀᚓࡽࢀࢀࡤ㸪ᡭἲࡀጇᙜ࡛࠶ࡿ࡜ุ᩿࡛ࡁࡿ㸬

Fig. 2-2 Notched round bar specimens (a)㹼(d) and a smooth round bar specimen (e)

30

Table 2-1 Chemical compositions of SS400 (mass %)

C Si Mn P S

0.07 0.16 0.6 0.024 0.041

Table 2-2 Mechanical properties of SS400

Tensile strength Yield strength Uniform elongation F* n* ε0*

473MPa 357MPa 19% 788MPa 0.19 0.002 *Approximated using σ = F(ε0 + εp)n for εp = 0.1 - 0.19

31 2.2.2 ᘬᙇヨ㦂᪉ἲ

4 ✀ࡢษḞ௜ᘬᙇヨ㦂∦࡟ᑐࡋ࡚ࢡࣟࢫ࣊ࢵࢻ㏿ᗘ࡛ 3 mm/min ࡢ㏿ᗘ࡛⏬ീ ゎᯒᘬᙇヨ㦂ࢆ⾜ࡗࡓ㸬ᘬᙇ㛤ጞ࠿ࡽ◚᩿ࡲ࡛ࡢࡃࡧࢀ㒊ࡢኚᙧࡢᵝᏊࢆ CCD ࣓࢝ࣛ (Point Grey Research ♫, GRAS-20S4M) ࡛ື⏬᧜ᙳࡋ㸪ྜྷ⏣ࡽ1-49)_ࡀ㛤Ⓨ

ࡋࡓ⏬ീゎᯒࢩࢫࢸ࣒࡟ࡼࡗ࡚᭱ᑠ᩿㠃༙ᚄa ࡜㸪ᚋ㏙ࡢ Bridgman ἲ࡛ᚲせ࡜ ࡞ࡿࡃࡧࢀᗏࡢ᭤⋡༙ᚄR ࢆ㐃⥆ⓗ࡟ ᐃࡋࡓ㸬࡞࠾㸪ᮏࢩࢫࢸ࣒࡛ࡣ㸪R ࡣࡃ ࡧࢀᗏ࡟࠾ࡅࡿ⏬ീ㍯㒌ࢆ෇ᘼ࡟᭱ᑠ஧஌㏆ఝࡍࡿࡇ࡜࡛Ỵᐃࡋ࡚࠸ࡿ㸬ྛᘬ ᙇヨ㦂⤖ᯝ࠿ࡽ௨ୗࡢ2 ✀㢮ࡢ᭤⥺ࢆᚓࡓ㸬ࡑࡢ୍ࡘࡣ㸪ᖹᆒᘬᙇᛂຊ σzave̺┦ ᙜࡦࡎࡳεeq᭤⥺࡛࠶ࡾ㸪ᛂຊ⿵ṇࡢᇶ‽࡜࡞ࡿ᭤⥺࡛࠶ࡿ㸬୸Წ࡛࠿ࡘ➼᪉ⓗ ࡞ኚᙧࢆࡍࡿ࡜௬ᐃࡍࡿ࡜㸪σzaveࡣḟᘧ࡛ィ⟬࡛ࡁࡿ㸬 σzave = P/(πa2)                          (2-1) ┦ᙜࡦࡎࡳεeqࡣ㸪ࡃࡧࢀᗏ᩿㠃ෆ࡟ศᕸࡍࡿࡦࡎࡳࢆ㸪ḟᘧ࡛ᖹᆒⓗ࡟ホ౯ࡋ ࡓࡶࡢ࡛࠶ࡿ㸬  εeq = 2 ln (a0/a) (2-2) ࡶ࠺୍᪉ࡣ㸪ᘬᙇⲴ㔜 P̺ࡃࡧࢀᗏ᩿㠃༙ᚄኚ໬(a0-a)᭤⥺࡛࠶ࡾ㸪ᚋࡢ㏫ゎᯒ ࡢྠᐃᑐ㇟࡜࡞ࡿ㸬

32 2.3 ᩘ್ᐇ㦂᪉ἲ ᥦ᱌ᡭἲࡢጇᙜᛶࢆ᳨ドࡍࡿ┠ⓗ࡛㸪FEM ࡟ࡼࡿᩘ್ᐇ㦂ࢆᐇ᪋ࡋࡓ㸬㍈ᑐ ⛠࠿ࡘࡃࡧࢀᗏ᩿㠃ᑐ⛠ࢆ௬ᐃࡋ㸪㍈ᑐ⛠せ⣲࡟࡚Fig. 2-3 ࡟♧ࡍࡼ࠺࡟ヨ㦂∦ ⦪᩿㠃ࡢ1/4 㡿ᇦࢆࣔࢹࣝ໬ࡋࡓ㸬ࡃࡧࢀᗏ࡟࠾ࡅࡿ௦⾲せ⣲ᑍἲࡣ 0.1 mm ࡛ ࠶ࡿ㸬ᮦᩱࡣᙎረᛶయ࡛ von-Mises ࡢ㝆అ᮲௳࡟ᚑ࠺࡜௬ᐃࡋࡓ㸬FEM ゎᯒࢯ ࣝࣂ࡟ࡣLS-DYNA971 (Livermore Software Technology Corporation)ࢆ⏝࠸㸪ୖ➃ ⠇Ⅼ࡟ᙉไኚ఩ࢆ୚࠼ࡿࡇ࡜࡛㸪ᘬᙇヨ㦂ゎᯒࢆ⾜ࡗࡓ㸬

ᩘ್ᐇ㦂࡟౑⏝ࡍࡿཧ↷ὶືᛂຊ᭤⥺σrefࡣ㸪ᘧ(2-3)࠾ࡼࡧ(2-4)࡟♧ࡍ࡜࠾ࡾ㸪

Swift ࠾ࡼࡧ Voce ๎࡟ᚑ࠺ σ(swift)

ref 㸪σ (voce) ref ࡢ2 ✀㢮ࢆ⏝ពࡋࡓ㸬  σ(swift) ref = 830 (εp + 0.002)0.22 (MPa)     (2-3)   σ(voce)

ref = 602.7㸫338.0e-12.9εp (MPa)     (2-4) ୧⪅ࡣ୍ᵝఙࡧࡢ⠊ᅖෆ࡛ࡣ࡯ࡰ୍⮴ࡋ㸪ࡃࡧࢀⓎ⏕௨㝆࡟㐪࠸ࢆ♧ࡍࡼ࠺࡟ ࣃ࣓࣮ࣛࢱࢆㄪᩚࡋ࡚࠶ࡿ㸬ࡲࡓᘬᙇヨ㦂ゎᯒ⤖ᯝ࠿ࡽ2.2.2 ⠇ࡢᐇ㦂࡜ྠᵝ࡟㸪 σzave-εeq᭤⥺࠾ࡼࡧP̺(a0-a)᭤⥺ࢆ㸪ᇶ‽᭤⥺࠾ࡼࡧྠᐃᑐ㇟᭤⥺࡜ࡋ࡚సᡂࡋ

ࡓ㸬ࡃࡧࢀᗏࡢ᭤⋡༙ᚄR ࡟ࡘ࠸࡚ࡣ㸪ࡃࡧࢀᗏ㏆ഐࡢ⠇Ⅼᗙᶆࢆ෇ᘼ㏆ఝࡋ㸪 ᘬᙇኚ఩0.1 mm ࡈ࡜࡟ᢳฟࡋࡓ㸬

33 2.4 ᛂຊ⿵ṇ᪉ἲ 2.4.1 %ULGJPDQ ἲ࡟ࡼࡿᛂຊ⿵ṇ㸦ᚑ᮶ἲ㸧 Bridgman ࡢᛂຊゎᯒ 1-23)_{࡟ࡼࢀࡤ㸪୸Წᘬᙇヨ㦂࡟࠾ࡅࡿࡃࡧࢀᗏ᩿㠃࡟࠾} ࡅࡿྛᛂຊᡂศࡣᘧ(2-5)࠾ࡼࡧ(2-6)࡛⾲ࡉࢀࡿ㸬                                  (2-5)                                   (2-6)  ࡇࡇ࡛σrࡣ༙ᚄ᪉ྥᛂຊ㸪σȟࡣ࿘᪉ྥᛂຊ㸪σzࡣᘬᙇ᪉ྥᛂຊ㸪r ࡣࡃࡧࢀᗏ᩿ 㠃୰ᚰ࠿ࡽࡢ༙ᚄ᪉ྥࡢ㊥㞳࡛࠶ࡿ㸬ࡲࡓ㸪σzࢆࡃࡧࢀᗏ᩿㠃࡟ࢃࡓࡗ࡚✚ศࡋ ࡓ್ࡀP ࡜➼ࡋࡃ࡞ࡿࡇ࡜࠿ࡽ㸪ᘧ(2-7)ࢆᑟฟࡍࡿࡇ࡜ࡀ࡛ࡁࡿ㸬                                  (2-7) 

ᘧ(2-7)ྑ㎶ࡢ σzave࡟࠿࠿ࡿ㡯ࡣ㸪σzaveࢆ σflow࡟ᛂຊ⿵ṇࡍࡿᣊ᮰ಀᩘ㸦௨ᚋ㸪

Bridgman ࡢ⿵ṇಀᩘ࡜⛠ࡍࡿ㸧࡛࠶ࡾ㸪᫬ࠎ้ࠎࡢ R ࡜ a ࠿ࡽỴᐃࡍࡿࡇ࡜ࡀ ࡛ࡁࡿ㸬ᐇ㦂⤖ᯝ࠾ࡼࡧᩘ್ᐇ㦂⤖ᯝ࠿ࡽᚓࡽࢀࡿ σzave-εeq᭤⥺࡜ Bridgman ࡢ ⿵ṇಀᩘ࡜ࡢ✚ࢆ࡜ࡗ࡚ᛂຊ⿵ṇࢆᐇ᪋ࡋσflow-εeq᭤⥺ࢆᚓࡓ㸬 °¿ ° ¾ ½ °¯ ° ® ­ ¸ ¸ ¹ · ¨ ¨ © § _{ }  ˜ aR r aR a flow z 1 ln ₂2 2 2 V V ¸ ¸ ¹ · ¨ ¨ © § _{ } ˜ aR r aR a flow r ln ₂2 2 2 V V V _T zave flow R a a R V V ¸ ¹ · ¨ © §  ¸ ¹ · ¨ © §  2 1 ln 2 1 1

34 2.4.2 ㏫ゎᯒ࡟ࡼࡿᛂຊ⿵ṇ㸦ᥦ᱌ἲ㸧 (a) ὶືᛂຊ᭤⥺ࡢࣃ࣓࣮ࣛࢱ⾲⌧

 ᮏᥦ᱌ἲ࡛ࡣ㸪ྠᐃᑐ㇟᭤⥺࡛࠶ࡿ㸪P̺(a0-a)᭤⥺ࡀ FEM ゎᯒ࡛෌⌧ࡉࢀࡿ

ࡼ࠺࡟㸪㏫ゎᯒ࡟ࡼࡗ࡚σzaveࢆ⿵ṇࡍࡿ㸬㏫ゎᯒ࡟౑⏝ࡍࡿσflow-εeq᭤⥺ࡣ㸪ᐇ 㦂࠾ࡼࡧᩘ್ᐇ㦂࠿ࡽᚓࡽࢀࡿ σzave-εeq᭤⥺ࢆᇶ‽᭤⥺࡜ࡋ࡚㸪Fig. 2-4 ࡢࡼ࠺ ࡟ᐃ⩏ࡋࡓ㸬ࡍ࡞ࢃࡕ㸪୍ᵝఙࡧࡢ⠊ᅖෆ࡛ࡣᖹ⁥୸Წᘬᙇヨ㦂∦࡟ࡼࡿσzaveࡢ  ᐃ್ࢆṇ್࡜ࡋ㸪ࡑࢀ௨㝆ࡢࡦࡎࡳ⠊ᅖ࡟ࡘ࠸࡚ࡣ N ಶࡢ༊㛫࡟ศ๭ࡋࡓከ ┤⥺㏆ఝ࡛⾲⌧ࡋࡓ㸬ྛ┦ᙜࡦࡎࡳ࡟ᑐᛂࡍࡿὶືᛂຊ σflowIࡣᘧ(2-8)ࡢࡼ࠺࡟ ᑐᛂࡍࡿᖹᆒᘬᙇᛂຊσzaveI࡟x = xI㸦I = 1,2,͐,N㸧ࢆ஌ࡌࡿᙧ࡛⾲⌧ࡋࡓ㸬 ) , 2 , 1 , 1 0 ( x I N xI zaveI I I flow V d d  V                 (2-8) ) , 2 , 1 ( 1 I N I flow I flow dV   V                     (2-9) ࡇࡇ࡛㸪x ࡣ Bridgman ࡢ⿵ṇಀᩘ࡟ᑐᛂࡍࡿ᭱㐺໬ィ⟬ࡢタィኚᩘ࡛࠶ࡿ㸬ᮏ ㄽᩥ࡛ࡣ㸪୍⯡ⓗ࡟ຍᕤ㌾໬ࡀ⏕ࡌ࡞࠸࡜ࡉࢀࡿ෭㛫࠿ࡘ‽㟼ⓗ࡞᮲௳ୗ࡛ࡢ ኚᙧࢆᑐ㇟࡜⪃࠼㸪ᘧ(2-9)ࡢᣊ᮰᮲௳ࢆ௜୚ࡋࡓ㸬ࡍ࡞ࢃࡕ㸪ᅗ୰ࡢ⥙࠿ࡅ㡿ᇦ ࡀࡇࡢὶືᛂຊ᭤⥺ࡢᐃ⩏ᘧࡀ⾲⌧ࡋ࠺ࡿ⠊ᅖ࡜࡞ࡿ㸬┦ᙜࡦࡎࡳ༊㛫ࡢศ๭ ࡣ㸪εuӌεeqӌ0.5 ࡢ⠊ᅖ࡛ࡣ 0.05 㛫㝸㸪0.5 ӌ εeq ӌ εfࡢ⠊ᅖ࡛ࡣ0.1 㛫㝸࡜ࡋ ࡓ㸬ࡇࡇ࡛㸪εuࡣ୍ᵝఙࡧ㝈⏺ࡢ┦ᙜࡦࡎࡳ㸪εfࡣ◚᩿᫬ࡢࡃࡧࢀᗏ࡟࠾ࡅࡿᖹ ᆒ┦ᙜࡦࡎࡳ࡛࠶ࡾ㸪◚᩿᫬ࡢࡃࡧࢀᗏ᩿㠃༙ᚄࢆaf࡜ࡍࡿ࡜㸪εf = 2 ln(a0/af)࡛ ࠶ࡿ㸬౛࠼ࡤᩘ್ᐇ㦂⤖ᯝࢆᑐ㇟࡜ࡋࡓᛂຊ⿵ṇࡢሙྜ㸪σref࠾ࡼࡧR0࡟ࡼࡽࡎ εu = 0.2㸪εf = 1.2 ࡜௬ᐃࡍࡿ࡜㸪Ỵᐃࡍ࡭ࡁタィኚᩘࡣ x1㹼x13ࡢ13 ಶ࡛࠶ࡿ㸬 (b) ㏫ゎᯒࡢ᪉ἲ  ㏫ゎᯒࡢྠᐃᑐ㇟᭤⥺ࡣ㸪๓㏙ࡢ㏻ࡾ㸪◚᩿ࡲ࡛ࡢ P̺(a0-a)᭤⥺࡜ࡋࡓ㸬ࡇ ࡢ᭤⥺࡟ࡣ୍ᵝఙࡧ௨㝆ࡢσflowࡢ᝟ሗࡀከࡃྵࡲࢀࡿ㸬Fig. 2-5 ࡣྠᐃᑐ㇟᭤⥺ ࡟࠾ࡅࡿᘬᙇⲴ㔜ࡢᐇ㦂ⅬPi࡜㏫ゎᯒࡢⲴ㔜ࡢィ⟬ⅬFi(x)㛫ࡢㄗᕪ࡟㛵ࡍࡿᶍ ᘧᅗ࡛࠶ࡿ㸬ᘧ(2-10)࡟ᐃ⩏ࡋࡓ Pi࡜ Fi(x)ࡢ㛫ࡢᖹᆒ஧஌ㄗᕪ e ࡢ᭱ᑠ໬ࢆ┠ ⓗ㛵ᩘ࡜ࡋ࡚㸪x ࡢ᭱㐺್ࢆồࡵࡿ㸬ࡇࡇ࡛㸪n ࡣᑐ㇟᭤⥺ࡢศ๭ᩘ࡛࠶ࡿ㸬ᮏ ◊✲࡛ࡣ㸪ከኚᩘ࠿ࡘ኱つᶍࣔࢹ࡛ࣝࡢ㏫ゎᯒࢆ⾜࠺ࡓࡵ㸪x ࡢ᭱㐺್ࡢ᥈⣴࡟㸪 GA 2-2)_{➼࡟௦⾲ࡉࢀࡿ኱ᇦⓗ᭱㐺໬ᡭἲ࡛ࡣ࡞ࡃ㸪Stander ࡽ࡟ࡼࡗ࡚㛤Ⓨࡉࢀ}

ࡓ㏲ḟ㏆ఝᛂ⟅᭤㠃ἲࡢ୍✀࡛࠶ࡿSRSM (Successive Response Surface Method)

2-3) _{ἲࢆ౑⏝ࡋࡓ㸬ྠἲࡣᒁᡤ᭱㐺໬࡟㐺ࡋࡓ≉ᚩࡀ࠶ࡿ㸬᭱㐺໬ࢯࣇࢺ࢚࢘࢔}

࡟ࡣ㸪LS-OPT4.2 (Livermore Software Technology Corporation)ࢆ౑⏝ࡋࡓ㸬Fig.

35 ⏬ࢆ౑⏝ࡋ࡚ᘬᙇヨ㦂ゎᯒࢆᐇ᪋ࡍࡿ㸬ḟ࠸࡛ᛂ⟅᭤㠃ࢆసᡂࡍࡿࡀ㸪ྠᐃᑐ㇟ ᭤⥺࡟ᑐᛂࡍࡿィ⟬Ⅼࡈ࡜࡟ᛂ⟅᭤㠃Fi(x) ࢆసᡂࡋ㸪ᘧ (2-10)࡛ᐃ⩏ࡋࡓ e ࡢ 㛵ᩘࡢ᭱㐺໬ࢆᐇ᪋ࡍࡿ㸬 min ) ( 1 2 1 o ¸ ¸ ¹ · ¨ ¨ © § _

¦

n i i i i P Max P F n e x                    (2-10) ᛂ⟅᭤㠃 Fi(x) ࡣ x ࡟㛵ࡍࡿ୍ḟከ㡯ᘧ࡛࠶ࡿ㸬ࡲࡓ e ࡢ᭱ᑠ್ࡢ᥈⣴࡟ࡣ㸪

ASA 2-4) _{(Adaptive simulated annealing)ἲࢆ⏝࠸ࡓ㸬ᐇ㦂࡜ゎᯒ⤖ᯝࡢㄗᕪࡀ༑ศ}

ᑠࡉࡃ࡞ࡿࡲ࡛㸪ࣃ࣓࣮ࣛࢱ x ࡢ᥈⣴㡿ᇦࢆ⛣ື㸪⦰ᑠࡉࡏ࡚⧞㏉ࡋィ⟬ࢆᐇ ᪋ࡋࡓ㸬࡞࠾㏫ゎᯒ࡛ᐇ᪋ࡍࡿᘬᙇヨ㦂ゎᯒࡣ㸪σflow-εeq᭤⥺ࢆ㝖࠸࡚2.3 ⠇ࡢᩘ

್ᐇ㦂࡜ྠ୍ࡢ᮲௳࡛ᐇ᪋ࡋࡓ㸬

36

Fig. 2-5 Error between experimental and computed curve

Fig. 2-6 Flowchart of optimization method

Change in radius a

₀

-a

Te

nsile load

P,

F

i

P

)

( x

i

F

1 i

n

i

2 i

_i

₃

i

Sampling

Perform tensile test analysis

Creation of metamodels

Optimization

Evaluation

Move or/and contract

the region of interest

Start

End

OK

NG

Computed curve

Experimental curve

37 2.5 ⤖ᯝ࡜⪃ᐹ 2.5.1 ᩘ್ᐇ㦂ࢆᑐ㇟࡜ࡋࡓᛂຊ⿵ṇ࡜ࡑࡢ⪃ᐹ ᩘ್ᐇ㦂⤖ᯝࢆ⏝࠸ࡓ᳨ドࡢࣇ࣮ࣟࢳ࣮ࣕࢺࢆ Fig. 2-7 ࡟♧ࡍ㸬Bridgman ἲ ࠾ࡼࡧ㏫ゎᯒᡭἲࡑࢀࡒࢀ࡛ᛂຊ⿵ṇࡉࢀࡓ σflow ࡢྠᐃ⤖ᯝ࡜ᩘ್ᐇ㦂࡟ධຊ ࡋࡓσrefࢆẚ㍑ࡋ㸪ࡑࡢ෌⌧ᛶࢆホ౯ࡋࡓ㸬 Fig. 2-8 ࡟ࡣ㸪ᩘ್ᐇ㦂⤖ᯝ࠿ࡽᘧ(2-1)࠾ࡼࡧ(2-2)ࢆ⏝࠸࡚ σzave-εeq᭤⥺ࢆィ ⟬ࡋࡓ౛࡜ࡋ࡚㸪σ(swift) ref ࢆ౑⏝ࡋࡓሙྜࡢヱᙜ⤖ᯝࢆ♧ࡍࡀ㸪᫬ࠎ้ࠎࡢ᩿㠃✚࠿ ࡽσzaveࢆィ⟬ࡋࡓ࡜ࡋ࡚ࡶ㸪ࡑࢀࡽࡣσ(swift) ref ࡼࡾࡶᖖ࡟㧗ࡃ࡞ࡾ㸪R0ࡀᑠࡉ࠸࡯ ࡝㢧ⴭ࡛࠶ࡿ㸬ࡇࢀࡣ㸪R0 ࡀᑠࡉ࠸࡯࡝୍㍈ᛂຊ≧ែ࠿ࡽእࢀ࡚ከ㍈ᛂຊ≧ែ ࡢᙳ㡪ࡀ኱ࡁࡃ࡞ࡿࡓࡵ࡜⪃࠼ࡽࢀࡿ㸬 (a) Bridgman ἲ࡟ࡼࡿᛂຊ⿵ṇ  σzave-εeq᭤⥺࡟ᑐࡋ࡚㸪2.4.1 ⠇ࡢᡭ㡰࡟ᚑ࠸ Bridgman ἲ࡟ࡼࡿᛂຊ⿵ṇࢆᐇ ᪋ࡋࡓ⤖ᯝࢆFig. 2-9 ࡟♧ࡍ㸬σ(swift) ref 㸪σ (voce) ref ࡝ࡕࡽࢆ౑ࡗࡓሙྜ࡟࠾࠸࡚ࡶ㸪ᛂຊ ⿵ṇࡉࢀࡓσflowࡣR0࡟㛵ࢃࡽࡎ࠾࠾ࡴࡡ1 ᮏ࡟㔜࡞ࡗࡓ㸬ࡋ࠿ࡋ࡞ࡀࡽ㸪εeqࡲ ࡓࡣεpࡀ኱ࡁࡃ࡞ࡿ࡜σ(swift) ref ࠾ࡼࡧσ (voce) ref ࠿ࡽ஋㞳ࡋ㸪᭱኱࡛Swift ๎ࡢሙྜ࡛ 12% ⛬ᗘ㸪Voce ๎ࡢሙྜ࡛ 16%⛬ᗘὶືᛂຊࢆ㐣኱࡟ホ౯ࡍࡿ⤖ᯝ࡜࡞ࡗࡓ㸬Fig. 2-10 ࡟㸪εf = 1.2 ᫬Ⅼ࡛ࡢ㸪Bridgman ἲ࡟ࡼࡿண ࡜ᩘ್ᐇ㦂⤖ᯝࡢࡃࡧࢀᗏ᩿㠃 ࡟࠾ࡅࡿྛᛂຊᡂศศᕸࡢ౛ࢆ♧ࡍ㸦R0 = 20mm㸪ཧ↷ὶືᛂຊ᭤⥺ࡣ σ(swift) ref 㸧㸬 ᘧ(2-5)㸪(2-6)࠾ࡼࡧ(2-7)ࡢ Bridgman ἲ࡛ண ࡋࡓᛂຊศᕸࡣ㸪ᩘ್ᐇ㦂ࡢᛂຊ ≧ែࢆ༑ศ෌⌧࡛ࡁ࡚࠸࡞࠸㸬ࡑࡢࡓࡵὶືᛂຊࢆ㐣኱࡟ホ౯ࡋࡓ࡜⪃࠼ࡽࢀ ࡿ㸬 (b) ㏫ゎᯒ࡟ࡼࡿᛂຊ⿵ṇ  ḟ࡟㸪2.4.2 ⠇ࡢᡭ㡰࡟ᚑ࠸㏫ゎᯒ࡟ࡼࡿᛂຊ⿵ṇࢆᐇ᪋ࡋࡓ⤖ᯝ࡟ࡘ࠸࡚♧ ࡍ㸬 Fig. 2-11 ࡣ⧞㏉ࡋィ⟬࡟ࡼࡿタィኚᩘࡢᒚṔࡢ౛࡛࠶ࡾ㸪Fig. 2-12 ࡣᛂຊ ⿵ṇ⤖ᯝࡢᒚṔࡢ౛࡛࠶ࡿ㸦R0 = 3mm㸪ཧ↷ὶືᛂຊ᭤⥺ࡣ σ(swift) ref )㸬8 ᅇ┠ࡢ⧞ ㏉ࡋィ⟬⤊஢᫬Ⅼ࡟࠾࠸࡚㸪࠸ࡎࢀࡢxIࡶ┿್࡟཰᮰ࡋ࡚࠸ࡿ㸬ᛂຊ⿵ṇ⤖ᯝ ࡶ8 ᅇ┠ࡢ⧞㏉ࡋィ⟬⤊஢᫬Ⅼ࡛ࡣ㸪σ(swift) ref ࡟୍⮴ࡋ࡚࠸ࡿࡇ࡜ࡀศ࠿ࡿ㸬௚ࡢ ࡍ࡭࡚ࡢ⤌ྜࡏ࡟ࡘ࠸࡚㸪8 ᅇ┠ࡢ⧞㏉ࡋィ⟬ᚋࡢ σflow-εeq᭤⥺ࡢྠᐃ⤖ᯝࢆ㔜 ࡡ࡚⾲♧ࡋࡓࡶࡢࡀFig. 2-13 ࡛࠶ࡿࡀ㸪ྠᐃࡉࢀࡓ σflow-εeq᭤⥺ࡣR0࡟࠿࠿ࢃ ࡽࡎ1 ᮏ࡟㔜࡞ࡾ㸪࠿ࡘ σ(swift)

ref ࠾ࡼࡧσ(voce) ref ࡜ࡑࢀࡒࢀ୍⮴ࡋࡓ㸬Fig. 2-14 ࡣ㸪ᩘ

್ᐇ㦂࡟ࡼࡿྠᐃᑐ㇟᭤⥺࡜㏫ゎᯒ࡛ྠᐃࡋࡓσflow-εeq᭤⥺ࢆ⏝࠸ࡓP̺(a0-a)

᭤⥺ࡢゎᯒ⤖ᯝࢆẚ㍑ࡋࡓࡶࡢ࡛࠶ࡿࡀ㸪ヨ㦂∦ᙧ≧ࡸཧ↷ὶືᛂຊ᭤⥺ࡀ␗ ࡞ࡗ࡚࠸࡚ࡶᩘ್ᐇ㦂⤖ᯝࢆ⢭ᗘⰋࡃ෌⌧࡛ࡁ࡚࠸ࡿࡇ࡜ࡀศ࠿ࡿ㸬ࡍ࡞ࢃ ࡕ㸪ᩘ್ᐇ㦂ࡢ⤖ᯝ࡟㏫ゎᯒࢆ⏝࠸ࡓᛂຊ⿵ṇࢆ㐺⏝ࡍࡿࡇ࡜࡛㸪ཧ↷ᛂຊ᭤