特定位置応力を用いた各種応力集中部の疲労強度・寿命予測法

Title 特定位置応力を用いた各種応力集中部の疲労強度・寿命予_{測法( 本文(Fulltext) )} Author(s) MUHAMMAD AMIRUDDIN BIN AB WAHAB Report No.(Doctoral Degree) 博士(工学) 工博甲第507号 Issue Date 2016-09-30 Type 博士論文 Version ETD URL http://hdl.handle.net/20.500.12099/55516 ※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。

≉ᐃ఩⨨ᛂຊࢆ⏝࠸ࡓྛ✀ᛂຊ㞟୰㒊ࡢ

⑂ປᙉᗘ࣭ᑑ࿨ண ἲ

Fatigue Strength/Life Estimation Method Using

Critical-Distance-Stress Theory

by

MUHAMMAD AMIRUDDIN BIN AB WAHAB

A thesis Submitted to the

Graduate School of Engineering, Gifu University

in Partial Fulfillment of the

Requirements for the degree of

DOCTOR OF ENGINEERING

┠

┠ ḟ

➨㸯❶ ⥴ゝ

………...1 1.1 ◊✲ࡢ⫼ᬒ࡜┠ⓗ………...1 1.2 ᛂຊ㞟୰࡜ᛂຊศᕸ………...3 1.3 ෇Ꮝࢆ᭷ࡍࡿ↓㝈ᖹᯈ࠾ࡼࡧᖏᯈ………...5 1.4 ࡁ⿣ࡢᛂຊศᕸ………...6 1.5 ᛂຊᣑ኱ಀᩘࡢồࡵ᪉………...8 1.6 ࡁ⿣㐍ᒎ≉ᛶ࡜ࡁ⿣㐍ᒎ㝈⏺ᛂຊᣑ኱ಀᩘ⠊ᅖǼKth ………….………....9 1.7 ᚤᑠࡁ⿣ࡢᙉᗘホ౯ἲ………...…………..11 1.8 ≉ᐃ఩⨨ᛂຊἲࡢᙉᗘホ౯ἲ………...……..14 1.9 ᚑ᮶ࡢす㇂ࡢண ᪉ἲ………...……..16

➨

2 ❶ ≉ᐃ఩⨨ᛂຊἲࢆ⏝࠸ࡓᛂຊ㞟୰㒊఩ࡢ

పࢧ࢖ࢡࣝ⑂ປࡢᙉᗘホ౯

……….……...…18 2.1 ⥴ゝ……….18 2.2 ≉ᐃ఩⨨ᛂຊἲ……….18 2.3 ≉ᐃ఩⨨ᛂຊἲࡢపࢧ࢖ࢡࣝ⑂ປᙉᗘண ……….20 2.3.1 ᐇ㦂⿦⨨……….22 2.3.2 ᭷㝈せ⣲ἲ࡟ࡼࡿᛂຊศᕸண ……….25 2.3.3 ≉ᐃ఩⨨ᛂຊἲࢆ⏝࠸ࡓண ⤖ᯝ……….28 2.4 ≉ᐃ఩⨨ᛂຊἲࡢࣇࣞࢵࢸ࢕ࣥࢢ⑂ປᙉᗘホ౯࡟ᑐࡍࡿ㐺⏝ᛶࡢ᳨ウ…….30 2.5 ⤖ゝ……….36

➨

3 ❶ ≉ᐃ఩⨨ἲࢆ⏝࠸ࡓᚤᑠࡁ⿣㒊ࡢ⑂ປࡢᙉᗘ

……...………...37 3.1 ⥴ゝ……….37 3.2 ᚑ᮶ࡢ⑂ປ㝈ண ἲ……….37 3.3 FEM ゎᯒ࡟ࡼࡿᛂຊศᕸࢆ฼⏝ࡍࡿ⑂ປ㝈ண ……….……...38 3.4 ≉ᐃ఩⨨ᛂຊἲࢆ⏝࠸ࡓ⑂ປᙉᗘホ౯ἲࡢ᳨ド……….39 3.4.1 ᐇ㦂᪉ἲ࠾ࡼࡧᐇ㦂᮲௳……….39 3.4.2 ᐇ㦂⤖ᯝ࠾ࡼࡧ≉ᐃ఩⨨ࡢỴᐃ……….40 3.4.3 FEM ゎᯒ࡟ࡼࡿᛂຊศᕸࡢỴᐃ………42 3.4.4 ≉ᐃ఩⨨ᛂຊἲ࡟ࡼࡿホ౯ࡢ᳨ド……….44 3.5 ⤖ゝ……….46

➨

➨

4 ❶ ⤖ゝ……….

47

ཧ⪃ᩥ⊩……….

49

➨

➨

1 ❶ ⥴ゝ

1.1 ◊✲ࡢ⫼ᬒ࡜┠ⓗ

ᶵᲔ㒊ရ࣭ᵓ㐀≀ࡣᏍ㸪ษḞࡁ㸪ẁ࡞࡝ࡢᛴ⃭࡞ᙧ≧ࡢኚ໬㒊ศࢆᣢࡘࡇ࡜ࡀከ࠸㸬 ࡇࡢࡼ࠺࡞ᙧ≧ኚ໬㒊ศ࡛ࡣ࿘ᅖࡼࡾᛂຊࡢ㧗ࡃ࡞ࡿᛂຊ㞟୰ࡀ㉳ࡇࡾ㸪㒊ရࡢ◚ᦆࡸ ◚ቯࡢཎᅉ࡟࡞ࡗ࡚࠸ࡿ㸬ࡇࡢࡼ࠺࡞ᛂຊ㞟୰㒊఩ࡢᙉᗘホ౯࡟ࡣ㸪ᙧ≧࡟ࡼࡗ࡚኱ࡁ ࡃศࢀࡿ࡜௨ୗࡢ 2 ࡘࡢ᪉ἲࡀ⏝࠸ࡽࢀ࡚࠸ࡿ㸬෇Ꮝ㸪ẁ㸪⁁࡞࡝ࡢᙉᗘホ౯࡟ࡣࠕᮦ ᩱຊᏛⓗᙉᗘホ౯ἲࠖࡀ㸪ࡁ⿣ࡸ㗦࠸ษḞࡁ࡞࡝ࡢ᭱኱ᛂຊࡀ↓㝈኱࡜࡞ࡿࡶࡢ࡟ᑐࡋ ࡚ࡣࠕ◚ቯຊᏛⓗᙉᗘホ౯ἲࠖࡀ⏝࠸ࡽࢀ࡚࠸ࡿ㸬 ලయⓗ࡟ࡣ㸪ᶵᲔ㒊ရ㸪ᵓ㐀㒊ᮦ➼ࡢ⑂ປᙉᗘタィ࡟࠶ࡓࡗ࡚ࡣ㸪Fig. 1.1 ࡟♧ࡉࢀࡿ ࡼ࠺࡞୍⯡ࡢᛂຊ㞟୰㒊఩(㸿㒊)࡟ᑐࡋ࡚ࡣ㸪ᛂຊ㞟୰ಀᩘ࡟ᇶ࡙ࡃ⑂ປᙉᗘపୗ⋡ࢆ⏝ ࠸㸪ࡁ⿣ࡸḞ㝗㒊఩(㹀㒊)࡟ᑐࡋ࡚ࡣ㸪ࡁ⿣㐍ᒎ㝈⏺ᛂຊᣑ኱ಀᩘ⠊ᅖࡀ⏝࠸ࡽࢀ࡚ࡁࡓ㸬 ࡋ࠿ࡋ㸪ࡇࢀࡽࡢ 2 ࡘࡢయ⣔ࡀ☜❧ࡋࡓ᫬௦ࡀ࠿࡞ࡾ㞳ࢀ࡚࠸ࡿࡇ࡜࠿ࡽ㸪୧ホ౯ࡢ ◚ᦆ࣓࢝ࢽࢬ࣒㸪ຊᏛホ౯࡜ࡶ࡟ࡎࢀࡀ࠶ࡿࡇ࡜㸪࠶ࡿ࠸ࡣ࠸ࡎࢀࡢᡭἲࡶࡑࡶࡑࡶ◚ ᦆ⌧㇟࡜ຊᏛࣃ࣓࣮ࣛࢱࢆ᫂☜࡟ࡋࡸࡍ࠸ヨ㦂∦࣮࣋ࢫ࡟⪃᱌ࡉࢀࡓࡶࡢ࡛࠶ࡿࡓࡵ㸪 ᐇ㝿ࡢ」㞧࡞ᵓ㐀≀ࡢᙉᗘタィࡸᙉᗘホ౯ࢆ⾜࠺ᢏ⾡⪅࡟࡜ࡗ࡚ࡣᢅ࠸࡟ࡃ࠸Ⅼࡀከ࠸㸬 ࡓ࡜࠼ࡤ㸿㒊ࡢࡼ࠺࡞ᛂຊ㞟୰㒊࡟࠾࠸࡚ࡣᛂຊ㞟୰ಀᩘ࠿ࡽ⑂ປᙉᗘపୗ⋡ࢆண ࡋ㸪 ⑂ປ㝈タィࢆࡍࡿࡇ࡜ࡀከ࠸ࡀ㸪ࡇࡢሙྜ᭱኱ᛂຊࡣFEM ➼࡛ᐜ᫆࡟ồࡵࡽࢀࡿࡶࡢࡢ㸪 ᖹᆒᛂຊࡢᐃ⩏ࡀ࡛ࡁ࡞࠸ࡓࡵᛂຊ㞟୰⋡ࡀᐃ⩏࡛ࡁ࡞࠸ሙྜࡶ࠶ࡿ㸬ࡲࡓ㹀㒊ࡢࡼ࠺ ࡟,ᛂຊ㞟୰㒊఩࡟Ⓨ⏕ࡋࡓᚤᑠࡁ⿣ඛ➃ࡢᛂຊᣑ኱ಀᩘࡶྠᵝ࡟ồࡵࡽࢀࡿࡀ㸪ࡁ⿣㐍 ᒎ㝈⏺ᛂຊᣑ኱ಀᩘ⠊ᅖࡢ⿵ṇ࡟౑࠺➼౯ࡁ⿣㛗ࡉࢆ࡝ࡢࡼ࠺࡟᝿ᐃࡍࢀࡤࡼ࠸࠿࡞࡝ ࡢⅬ࡛࠶ࡿ㸬 ୍᪉㸪㹁㒊ࡢ㗦࠸ษḞࡁ(ඛ➃ࡢ୸ࡳ༙ᚄ ρ = 0)㸪㹂㒊ࡢ᥋ゐ➃ࡲࡓ㹃㒊ࡢ᥋╔➃࡟ࡘ ࠸࡚ࡣ㸪◚ቯຊᏛࡢ⠊␪࡜ࡢ⪃࠼࠿ࡽᛂຊ≉␗ሙࣃ࣓࣮ࣛࢱࢆ⏝࠸ࡓホ౯ἲࡀᑟධࡉࢀ ࡚ࡁ࡚࠸ࡿ(16,17)㸬ࡋ࠿ࡋᛂຊ㞟୰㒊ࡢホ౯࡟ᇶ࡙࠸ࡓρ ≠ 0 ࡟ᑐࡍࡿண ᙉᗘࡣ㸪ρ ࢆᑠ ࡉࡃࡋ࡚࠸ࡃ࡜㹁㒊ࡢண ᙉᗘ࡟₞㏆ࡍࡿࡢ࠿➼ࡀᮍ☜ㄆࡢ୰࡛౑ࢃࢀ࡚࠸ࡿࡢࡀ⌧≧

Fig. 1.1 General structure for fatigue strength evaluation Applied force Adhesive Contact edge Applied force A B C D E Hole Hole A

࡛࠶ࡿ㸬ࡇࢀࡽᑐ㇟㒊఩ࡢᙧ≧࡟ࡼࡗ࡚␗࡞ࡿᡭἲ࡛ᙉᗘホ౯ࡍࡿࡇ࡜ࡣ㸪〇ရࡢᛂຊ

ゎᯒ㸪ᙉᗘホ౯ࢆ⾜࠺ᢏ⾡⪅࡟࡜ࡗ࡚ࡣ኱ࡁ࡞㞀ᐖ࡟࡞ࡗ࡚࠾ࡾ㸪≉࡟᭱㏆ࡢFEM ゎᯒ

ࢆ୰ᚰ࡜ࡍࡿ CAE タィࢶ࣮ࣝࢆά⏝ࡍࡿᢏ⾡⪅࡟࡜ࡗ࡚ၥ㢟࡛ᙉᗘホ౯ἲࡢ⤫୍໬ࡀ

ᮃࡲࢀ࡚࠸ࡿ (18~20)㸬

ࡇࡢ✀ࡢᙉᗘホ౯᪉ἲ࡜ࡋ࡚㸪ୖグ2 ࡘࡢᙉᗘホ౯᪉ἲࡢࣃ࣓࣮ࣛࢱࢆ⤖ࡧ௜ࡅࡓࠕ≉

ᐃ఩⨨ᙉᗘホ౯ἲ(Point method ࠾ࡼࡧ Line method)ࠖࡀᥦ᱌ࡉࢀ࡚࠸ࡿ㸬ࡇࡢ᪉ἲࡣᛂຊ 㞟୰㒊࠿ࡽࡢ≉ᐃࡢ఩⨨㸪ࡲࡓࡣ≉ᐃࡢ⠊ᅖࡢᛂຊࡢᖹᆒ್ࡀᙉᗘࢆつᐃࡍࡿ࡜ぢ࡞ࡍ ᪉ἲ࡛࠶ࡿ㸬ࡑࡢ୰࡛㸪Point method ࡣ≉ᐃࡢ఩⨨࡛ࡢᛂຊࢆᙉᗘホ౯࡟౑⏝ࡍࡿ᪉ἲ㸪 Line method ࡣ≉ᐃࡢ㊥㞳ࡢᛂຊࡢᖹᆒࢆᙉᗘホ౯࡟౑⏝ࡍࡿ᪉ἲ࡛࠶ࡿ㸬 ࡋ࠿ࡋ㸪ࡇࢀࡽࡢ᪉ἲࡢ㐺ᛂᛶ࡟ࡘ࠸࡚ࡣ௒ࡲ࡛࠶ࡲࡾάⓎ࡞㆟ㄽࡣࡉࢀ࡚ࡇ࡞࠿ࡗ ࡓ㸬ࡑࢀࡣ㸪ࡇࢀࡽࡢ᪉ἲࡀಶࠎࡢ㒊ᮦࡢᛂຊ㞟୰㒊௜㏆ࡢᛂຊศᕸࢆᚲせ࡜ࡍࡿࡓࡵ㸪 3 ḟඖࡢ」㞧࡞ᙧ≧ࡢ✀ࠎࡢ᪉ྥࡢᛂຊศᕸࢆ⢭ᗘⰋࡃồࡵࡿࡇ࡜ࡀᅔ㞴ࡔࡗࡓࡓࡵ࡛ ࠶ࡿ㸬ࡋ࠿ࡋ㸪⌧ᅾCAE ᢏ⾡ࡢ㣕㌍ⓗ࡞ྥୖ࡟ࡼࡾ」㞧࡞ᙧ≧ࡢᛂຊศᕸࢆồࡵࡿࡇ࡜ ࡀᐜ᫆࡟࡞ࡗࡓࡓࡵ㸪ᮏᡭἲࡢ᭷ຠᛶࡀ෌᳨ウࡉࢀ࡚࠸ࡿ㸬 ࡑࡇ࡛㸪ᮏ◊✲࡛ࡣ≉ᐃ఩⨨ἲࢆ⏝࠸࡚஧ࡘࡢ⑂ປၥ㢟ࢆ᳨ウࡋࡓ㸬 ➨2 ❶࡛ࡣ≉ᐃ఩⨨ᙉᗘホ౯ἲࡢ☜❧ࢆ┠ⓗ࡜ࡋ㸪ᛂຊ㞟୰㒊఩ࡢపࢧ࢖ࢡࣝ⑂ປ࡟ ᑐࡍࡿ㐺⏝ᛶࢆ᳨ウࡋࡓ㸬࿘▱ࡢ࡜࠾ࡾ㸪ᛂຊ㞟୰㒊఩࡛ࡣ⑂ປᙉᗘࡀⴭࡋࡃపୗࡋ࡚ ࡋࡲ࠺㸬ࡇࢀࡣࠕษḞࡁຠᯝࠖ࡜࿧ࡤࢀ㸪⑂ປ◚ቯࡢ࡯ࡰ100㸣㏆ࡃࢆ༨ࡵ࡚࠸ࡿ㸬㏆ ᖺ࡛ࡣᶵᲔ࣭ᵓ㐀≀ࡢ㛗ᑑ࿨໬㸪ᙧ≧ࡢ」㞧໬ࡀ㐍ࢇ࡛࠾ࡾ㸪ࡲࡍࡲࡍࡇࡢၥ㢟ࡢゎỴ ࡀ㔜せ࡟࡞ࡗ࡚ࡃࡿ㸬 ࡇࡢపࢧ࢖ࢡࣝ⑂ປ࡬ࡢ㐺⏝ᛶࢆ᳨ウࡍࡿࡓࡵ㸪ᮏ◊✲࡛ࡣᖹ⁥ᮦ࡜ᖹᯈ࡟ྛ✀ࡢV ᏐษḞࡁ㸪෇Ꮝࢆ௜୚ࡋࡓሙྜ࡟ᑐࡋ࡚㸪୍⯡ᅽᘏ㗰ᮦSS400 ࢆ⏝࠸࡚ྛ✀ヨ㦂∦ࡢ⑂ ປヨ㦂⤖ᯝࢆ≉ᐃ఩⨨ἲ࡟ࡼࡿᙉᗘண ⤖ᯝ࡜ẚ㍑ࡋࡓ㸬  ➨ 3 ❶࡛ࡣᚤᑠࡁ⿣㒊ࡢ⑂ປᙉᗘホ౯࡟≉ᐃ఩⨨ᙉᗘホ౯ἲࡢ㐺⏝ᛶࢆ᳨ウࡋࡓ㸬ᚤ ᑠࡁ⿣㒊ࡢ⑂ປᙉᗘホ౯ࡣ⥺ᙧ◚ቯຊᏛࢆ⏝࠸ࡓሙྜ㸪ᐇ㝿ࡢᙉᗘ࡜ẚ࡭࡚㐣኱ホ౯࡜ ࡞ࡗ࡚ࡋࡲ࠺㸬ࡇࡢ୙㒔ྜࡢಟṇ࡟ࡣ௬᝿ࡁ⿣㐍ᒎἲ➼ࡢᵝࠎ࡞ಟṇἲࡀᥦ᱌ࡉࢀ࡚࠸ ࡿࡀ㸪௒ᅇࡢ≉ᐃ఩⨨ᙉᗘホ౯ἲࢆ⏝࠸࡚ᐇ㦂࡜ࡢ୧᪉࠿ࡽࡑࡢ⤫୍ᛶࢆ☜ㄆࡍࡿࡇ࡜ ࡛㸪ỗ⏝ⓗᙉᗘホ౯ἲ࡜ࡋ࡚☜❧ࡍࡿࡇ࡜ࢆ┠ⓗ࡜ࡋࡓ㸬ᩘ್ゎᯒ࡛ᛂຊศᕸࢆண ࡋ 㕲㗰ᮦSS400 ࠾ࡼࡧ SKS93 ࡢࡁ⿣ᑟධヨ㦂∦ࢆ౑⏝ࡋ㸪ᐇ㦂⤖ᯝ࡜ண ⤖ᯝࢆẚ㍑ࡋࡓ㸬  ➨  ❶࡛ࡣᮏ◊✲ࡢ⥲ᣓ࡛࠶ࡿ㸬

1.2 ᛂຊ㞟୰࡜ᛂຊศᕸ

 ᮏ◊✲࡛ࡣᛂຊ㞟୰ࢆ⏕ࡌࡿ㒊ᮦࡢᙉᗘホ౯ࢆ┠ⓗ࡜ࡋ⑂ປ㝈ண ἲ࡛ࡣ㒊ᮦࡢᛂຊ ศᕸࢆ⏝࠸࡚ᙉᗘண ࢆ⾜࠺㸬ᮏ⠇௨㝆࡛ࡣ㸪ᛂຊ㞟୰ࢆྛ✀ᙉᗘホ౯ἲ࡟㛵ࡍࡿ୍⯡ ஦㡯ࢆ㏙࡭࡚࠾ࡃ㸬 ᶵᲔࡸᵓ㐀≀࡟ᐇ㝿࡟౑⏝ࡉࢀࡿ㒊ᮦࡣ㸪ᶓ᩿㠃ࡢ኱ࡁࡉࡸᙧࡀኚ໬ࡋ࡚࠸ࡿሙྜࡀ ከ࠸㸬ᶵᲔࡸᵓ㐀≀ࡢᏍ㸪ẁ㸪࣮࢟⁁㸪ࡡࡌ㸪࠶ࡿ࠸ࡣᮦᩱ⾲㠃ࡢᑠࡉ࡞യࡸᮦᩱෆ㒊 ࡢ௓ᅾ≀࡞࡝㸪㒊ᮦࡢᙧ≧ࡸᮦ㉁ࡀኚ໬ࡍࡿ㒊ศ࡛ࡣ㏻ᖖᒁ㒊ⓗ࡟ᛂຊࡀ㧗ࡃ࡞ࡿ㸬౛ ࠼ࡤ㸪Fig. 1.1 ࡟♧ࡍࡼ࠺࡟෇Ꮝࢆ᭷ࡍࡿᖏᯈࡀ㍈᪉ྥࡢᘬᙇࡾࢆཷࡅࡿሙྜ࡟ࡣ㸪᭱ᑠ ᩿㠃ࡢᛂຊศᕸࡣ୍ᵝ࡛ࡣ࡞ࡃ࡞ࡾ㸪ᖹᆒᛂຊ࡟ẚ㍑ࡋ࡚✰⦕ࡢᛂຊ್ࡀⴭࡋࡃ㧗ࡃ࡞ ࡿ㸬ࡇࡢࡼ࠺࡞⌧㇟ࢆᛂຊ㞟୰࡜࠸࠺(1)㸬 ᭱ᑠ᩿㠃pq ࡢṇ࿡ࡢ㠃✚(pm,nq)ࢆ A㸪ᘬᙇⲴ㔜ࢆ F ࡜ࡍࢀࡤ㸪᩿㠃 pq ࡢᖹᆒᛂຊ σn ࡣ                σn㸻F/A              㸦1.1㸧 ࡜࡞ࡿ㸬✰⦕mn ࡟⏕ࡎࡿ᭱኱ᛂຊȪmax࡜ᖹᆒᛂຊσn࡜ࡢẚࢆȘ࡜ࡍࢀࡤ㸪 σmax㸻Șσn             㸦1.2㸧 ࡛⾲ࢃࡉࢀࡿ㸪ࡇࡇ࡛Șࢆᛂຊ㞟୰ಀᩘ࡜࠸࠺㸬Șࡣᛂຊ㞟୰㒊࡟࠾ࡅࡿ᭱኱ᛂຊࡀබ ⛠ᛂຊࡢఱಸ࡟㐩ࡋ࡚࠸ࡿ࠿ࢆホ౯ࡍࡿ್࡛࠶ࡿ㸬➼᪉ᛶయ࡛ᙎᛶ㝈ᗘෆ࡛ࡣ㸪Șࡢ್ ࡣᮦᩱࡢ✀㢮࡟㛵ಀ࡞ࡃ㸪㒊ᮦࡢᗄఱᏛⓗᙧ≧࡟ࡼࡗ࡚ࡢࡳᐃࡲࡿࡓࡵ㸪ࡇࢀࢆᙧ≧ಀ ᩘ࡜ࡶ࠸࠺㸬Șࡢ್ࡣᩘ್ィ⟬ࡸ✀ࠎࡢࣁࣥࢻࣈࢵࢡ㸪౽ぴ㸪࠶ࡿ࠸ࡣᩥ⊩࡟ࡼࡗ࡚ồ ࡵࡿࡇ࡜ࡀ࡛ࡁࡿ(1~4)㸬

 Fig. 1.2 ࡟♧ࡍᛂຊ㞟୰ၥ㢟ࡢ FEM ゎᯒ⤖ᯝࡢ୍౛ࢆ Fig. 1.3 ࡟♧ࡍ㸬a/W ࡢቑຍ࡜࡜

ࡶ࡟Șࡢ್ࡣῶᑡࡋ࡚࠸ࡿࡀ㸪ࡇࡢࡇ࡜ࡣ σmax ࡢῶᑡࢆព࿡ࡋ࡚࠸ࡿࡢ࡛ࡣ࡞࠸㸬a/W

ࡢቑຍ࡜࡜ࡶ࡟ σnࡶቑຍࡍࡿ࠿ࡽ σmaxࡣቑຍࡍࡿࡢ࡛࠶ࡿ㸬σmax=Șσn࡛࠶ࡾ㸪σmax=Șσ

࡛࡞࠸ࡇ࡜࡟ὀពࡋ࡞ࡅࢀࡤ࡞ࡽ࡞࠸㸬 n V ma V a 2 W 2 F q p m n V F p m Ȫma x Ȫn

Fig. 1.3 Relationship between Ș and a/W ࡇࡢࡼ࠺࡞ᛂຊ㞟୰ࡀ㉳ࡁࡿᙧ≧ኚ໬㒊ࡣ⥲⛠ࡋ࡚ษḞࡁ࡜ࡶ࿧ࡤࢀࡿ㸬ษḞࡁࡣ◚ ቯࡢ㉳Ⅼ࡟࡞ࡾࡸࡍࡃ㸪≉࡟⑂ປ◚ቯࡢሙྜ㸪࡯࡜ࢇ࡝ࡀษḞࡁࢆ◚ቯࡢ㉳Ⅼ࡜ࡋ࡚Ⓨ ⏕ࡋࡓ⑂ປࡁ⿣ࡢ㐍ᒎ࡟ࡼࡗ࡚㉳ࡇࡿ㸬ࡇࡢࡼ࠺࡟ᛂຊ㞟୰࡟㉳ᅉࡋ࡚⑂ປᙉᗘࡀపୗ ࡍࡿࡇ࡜ࢆษḞࡁຠᯝ࡜࠸࠺㸬ษḞࡁࡣ㏻ᖖࡢᶵᲔࡸᵓ㐀≀࡟࠾࠸࡚㑊ࡅࡽࢀ࡞࠸ࡢ࡛㸪 ษḞࡁຠᯝࡢṇ☜࡞ホ౯ࡣ⑂ປࢆ⪃៖ࡋࡓタィࢆ⾜࠺ୖ࡛୙ྍḞ࡛࠶ࡿ㸬  ๓⠇࡛㏙࡭ࡓࡼ࠺࡟㒊ᮦࡢ◚ቯࡣ୺࡟ᛂຊ㞟୰ࡀ㉳ᅉ࡜࡞ࡾⓎ⏕ࡍࡿ㸬⌧ᅾ㸪㒊ᮦࡢ ⑂ປᙉᗘ࡟ࡣ㸪ᛂຊ㞟୰ࡢ᭱኱Ⅼࡼࡾᑡࡋ㞳ࢀࡓⅬࡲ࡛ࡢᛂຊࡀ㛵ಀࡍࡿ࡜࠸࠺ㄝࡀ᭷ ຊ࡛࠶ࡿ㸬ࡑࡇ࡛㸪ᛂຊࡀ࡝ࡢࡼ࠺࡟ศᕸࡋ࡚࠸ࡿ࠿ࢆ▱ࡿࡇ࡜ࡀᚲせ୙ྍḞ࡛࠶ࡿ㸬 ᮏ◊✲࡛ࡣ㸪ᛂຊศᕸࢆ୺࡟FEM ࡟ࡼࡗ࡚ồࡵࡿ᪉ἲ࡜᥇ࡿࡇ࡜࡜ࡋࡓ㸬ḟ⠇௨㝆࡛ࡣ ྛ✀ᛂຊ㞟୰㒊ࡢᛂຊࢆ♧ࡋ㸪ᚑ᮶ࡢ⑂ປᙉᗘண ἲ࡜ࡑࡢၥ㢟Ⅼ࡟ࡘ࠸࡚㏙࡭࡚࠾ࡃ㸬 St ress conc entr ation fa ct or Ș

Ratio of circular hole diameter to plate width a/W 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 3.0 2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0

1.3 ෇Ꮝࢆ᭷ࡍࡿ↓㝈ᖹᯈ࠾ࡼࡧᖏᯈ

Fig. 1.2 ࡟♧ࡍࡼ࠺࡟ᖹᯈ࡟෇Ꮝࡀ࠶࠸࡚࠸ࡿሙྜ࡟ࡘ࠸࡚⪃࠼ࡿ㸬ࡇࡢᖹᯈࡢᯈᖜ W ࡀ෇Ꮝࡢ┤ᚄ 2a ࡟ẚ࡭࡚༑ศ࡟኱ࡁ࠸ሙྜ࡟ࡣ↓㝈ᖹᯈ࡜⪃࠼ࡿࡇ࡜ࡀ࡛ࡁࡿࡶࡢ࡜ ࡋ㸪y ㍈᪉ྥ࡟୧➃୍࡛ᵝ࡞ᛂຊ σ0ࡀస⏝ࡋ࡚࠸ࡿ࡜ࡍࡿ㸬ࡇࡢࡼ࠺࡞Fig. 1.4 ࡟ᖹᯈࡢ ᛂຊศᕸࡣ㸪✰ࡢ୰ᚰ 0 ࢆཎⅬ࡜ࡋ࡚ᴟᗙᶆ㸦㹰㸪ȟ㸧ࢆ⏝࠸ࢀࡤḟᘧࡢࡼ࠺࡟⾲ࡉࢀ ࡿ(1)㸬   

V

V

V

(

1

3

4

)

c o s

2

T

2

)

1

(

2

2 2 4 4 0 2 2 0

r

a

r

a

r

a

r









T

V

V

V

_T

(

1

3

)

cos

2

2

)

1

(

2

4 4 0 2 2 0

r

a

r

a

_

_



      (1.3)

T

V

W

_T

(

1

3

2

)

sin

2

2

2 2 4 4 0

r

a

r

a

r







σ0㸸ᯈࡢ୧➃࡟స⏝ࡍࡿᘬᙇࡾࡢබ⛠ᛂຊ ᩿㠃pq ࡟⏕ࡎࡿⲴ㔜᪉ྥࡢᆶ┤ᛂຊ σȟࡣ㸪ୖᘧ࡛θ㸻π/2 ࡜࠾ࡅࡤ

)

3

2

(

2

4 4 2 2 0

r

a

r

a 



V

V

_T    (1.4) ࡜⾲ࢃࡉࢀࡿ㸬 ࡇࡢᛂຊࡣ෇Ꮝ⦕m ࡀ᭱኱್ σmax=3σ0࡟㐩ࡍࡿࡀ㸪✰⦕࠿ࡽ㞳ࢀࡿ࡟ᚑࡗ࡚ᛴ⃭࡟ῶ ᑡࡋ㸪σ0࡟㏆࡙ࡃ㸬ࡍ࡞ࢃࡕ㸪r=2a ࡛ σȟ=1.22Ȫ0㸪r=4a ࡛ σȟ=1.04σ0࡜࡞ࡾ㸪✰ࡢࡓࡵ ࡟ᛂຊศᕸࡀ஘ࡉࢀࡿ㡿ᇦࡣ✰⦕௜㏆࡟㝈ࡽࢀࡿࡇ࡜ࡀࢃ࠿ࡿ㸬ࡇࡢሙྜࡢᛂຊ㞟୰ಀ ᩘࡣ㸪Ș=3 ࡛࠶ࡿ㸬  ࡇࡇ࡛㸪✰ࡢᑍἲ࡟ẚ㍑ࡋ࡚ᯈᖜࡀ࠶ࡲࡾ኱ࡁࡃ࡞࠸ሙྜ࡟ࡣ↓㝈ᖹᯈ࡜ࡣ⪃࠼ࡿࡇ ࡜ࡀ࡛ࡁ࡞ࡃ࡞ࡿ㸬ࡑࢀ࡟ࡼࡗ࡚㸪ୖ㏙ࡢㅖ⤖ᯝࢆ㐺⏝ࡍࡿࡇ࡜ࡀ࡛ࡁ࡞ࡃ࡞ࡾ㸪ᛂຊ 㞟୰ಀᩘȘࡣ Fig. 1.3 ࡛⾲ࡋࡓࡼ࠺࡟ a/W ࡢẚ࡟ࡼࡗ࡚ኚ໬ࡍࡿ(1)㸬

1.4 ࡁ

ࡁ⿣ࡢᛂຊศᕸ

ࡁ⿣ඛ➃࡛ࡣᛂຊࡀ↓㝈኱࡜࡞ࡾ㸪≉␗ᛶࢆᣢࡘ࡜࠸࠺ᅔ㞴ࡀ࠶ࡿ㸬ࡇࢀࢆඞ᭹ࡍࡿ ࡓࡵ࡟≉␗ሙࢆ┤どࡋ࡚㸪ࡇࡢᛂຊศᕸࡀᅛ᭷ࡢศᕸᙧࢆᣢࡘࡇ࡜ࢆ✚ᴟⓗ࡟฼⏝ࡋ㸪 ሙࡢಀᩘ࡛࠶ࡿᛂຊᣑ኱ಀᩘࢆ⏝࠸࡚◚ቯࢆグ㏙ࡍࡿ◚ቯຊᏛࡢᴫᛕࡀᥦ᱌ࡉࢀࡓ㸬௨ ୗ࡟ࡑࢀ࡟ࡘ࠸࡚グ㏙ࡍࡿ㸬 ࡁ⿣ࢆ᭷ࡍࡿ㸰ḟඖ≀యࡀ㈇Ⲵࢆཷࡅࡿሙྜࢆ⪃࠼ࡿ㸬ࡁ⿣ࡢኚᙧࡣFig. 1.5 ࡟♧ࡍࡼ ࠺࡞࣮ࣔࢻϨ㸪ϩ࠾ࡼࡧϪ࡜ࡼࡤࢀࡿ୕ࡘࡢ⊂❧࡞ኚᙧᵝᘧ࡟ศ㞳ࡍࡿࡇ࡜ࡀ࡛ࡁࡿ㸪 ࣮ࣔࢻϨࡣ㛤ཱྀ࣮ࣔࢻ࡜࿧ࡤࢀ࡚࠸ࡿ㸬ࡇࢀࡣ㸪ࡁ⿣㠃࡟ᑐࡋ࡚ᑐ⛠࡟ࡁ⿣ࡀ㛤ཱྀࡍࡿ ࡶࡗ࡜ࡶ㔜せ࡞࣮ࣔࢻ࡛࠶ࡿ㸬࣮ࣔࢻϩ࠾ࡼࡧϪࡣ㸪ࡁ⿣㠃࡟ᑐࡋ࡚཯ᑐ⛠࡟ኚᙧࡀ⏕ ࡌࡿ࣮ࣔࢻ࡛࠶ࡾ㸪ࡏࢇ᩿ᆺࡢኚᙧࡀ஧ḟඖ㠃ෆ࡛⏕ࡌࡿ࠿㸪㠃እ࡛⏕ࡌࡿ࠿࡟ᑐᛂࡋ ࡚㸪ࡑࢀࡒࢀ㠃ෆࡏࢇ᩿ᆺ࠾ࡼࡧ㠃እࡏࢇ᩿᪉࡜ࡼࡤࢀ࡚࠸ࡿ(5~7)㸬 y x Ȫ0

(a) ModeϨ (b) Mode ϩ (c)Mode Ϫ

Ȫ0

⌮ㄽゎᯒࡢ⤖ᯝ࡟ࡼࢀࡤ㸪ྛ࣮ࣔࢻ࡟ᑐࡍࡿࡁ⿣㏆ഐࡢᛂຊศᕸࡣḟࡢࡼ࠺࡟࡞ࡿ㸬 ModeϨ㸸     2 3 c o s 2 s i n 2 c o s 2 2 3 s i n 2 s i n 1 2 c o s 2 2 3 s i n 2 s i n 1 2 c o s 2

T

T

T

S

W

T

T

T

S

V

T

T

T

S

V

r K r K r K xy y x Ϩ Ϩ Ϩ ¸ ¹ · ¨ © §  ¸ ¹ · ¨ © §        (1.5) Modeϩ㸸 ¸ ¹ · ¨ © §    ¸ ¹ · ¨ © §   2 3 sin 2 sin 1 2 cos 2 2 3 cos 2 cos 2 sin 2 2 3 cos 2 cos 2 2 sin 2 T T T S W T T T S V T T T S V r K r K r K xy y x ϩ ϩ ϩ          (1.6) ModeϪ㸸  2 cos 2 2 sin 2 T S V T S V r K r K y x ϩ Ϫ      (1.7) ࡲࡓ㸪ᖹ㠃ᛂຊ≧ែ࡛ࡣୖグ௨እࡢࡍ࡭࡚ࡢᛂຊࡣ㸮࡛࠶ࡿࡀ㸪ᖹ㠃ࡦࡎࡳ≧ែ࡛ࡣ ࣮ࣔࢻϨ㸪࣮ࣔࢻϩࡢሙྜ࡟㝈ࡾ σz=Ȥ(σx+σy) Ȥ:࣏࢔ࢯࣥẚ       (1.8) ࡛࠶ࡿ㸬  ࣮ࣔࢻϨ㸪ϩ࠾ࡼࡧϪࡢ࠺ࡕ㸰ࡘ௨ୖྜࢃࡉࡗࡓΰྜ࣮ࣔࢻ࡛ࡣ㸪ᛂຊࡣࡇࢀࡽࡢ㔜 ࡡ࠶ࢃࡏ࡟ࡼࡾồࡵࡽࢀࡿ㸬ࡇࡇ࡛ KϨ㸪Kϩ㸪KϪࢆᛂຊᣑ኱ಀᩘ࡜࠸࠺㸬K ࡀศ࠿ࢀࡤ㸪 ࡁ⿣㏆ഐࡢᛂຊศᕸࢆ≉ᚩ௜ࡅࡿࡇ࡜࡛ࡁࡿࡓࡵ㸪ᛂຊᣑ኱ಀᩘࡣࡁ⿣ࢆ᭷ࡍࡿ㒊ᮦࡢ ᙉᗘࢆ▱ࡿ࠺࠼࡛㠀ᖖ࡟㔜せ࡞ᅉᏊ࡜࡞ࡿ㸬

1.5 ᛂຊᣑ኱ಀᩘࡢồࡵ᪉

ᛂຊᣑ኱ಀᩘK ࢆ⏝࠸࡚ࡁ⿣ࡢⓎ⏕ࡸᡂ㛗ࢆホ౯ࡍࡿ࡟ࡣ㸪ᙜ↛ K ࡢ್ࡀᚲせ࡛࠶ࡿ㸬 ୍⯡࡟స⏝ᛂຊσ ࢆཷࡅࡿ᭷㝈ᯈ୰ࡢࡁ⿣ࡢᛂຊᣑ኱ಀᩘࡣ ) ([ S V a F KϨ ˜              (1.9) ࡜࡞ࡿ㸬ࡇࡇ࡛a ࡣࡁ⿣㛗ࡉ㸪F(ξ)ࡣᙧ≧࡟㛵ࡍࡿ↓ḟඖ㔞ȥ࡟ࡼࡾỴࡲࡿ⿵ṇಀᩘ࡛㸪 ୍⯡࡟1 ࡢ࣮࢜ࢲ࣮࡛࠶ࡿ㸬F(ξ)࡟ࡘ࠸࡚ࡣከࡃࡢ◊✲ࡀ࡞ࡉࢀ࡚࠾ࡾ㸪ࡑࢀࡽࡢᡂᯝࡀ ࣁࣥࢻࣈࢵࢡ(5~7)ࡸᩥ⊩࡟ᥖ㍕ࡉࢀ࡚࠸ࡿ㸬➨3 ❶࡟♧ࡍᚤᑠࡁ⿣㒊ᮦࡢᙉᗘホ౯ἲࡢ᳨ ウ࡛ࡣ㸪Fig. 1.6 ࡟♧ࡍ 3 ࡢᙧ≧࡟㛵ࡍࡿ⿵ṇಀᩘࡢ࠺ࡕ㸪(c)∦ഃࡁ⿣ࡢࡶࡢࢆ⏝࠸ࡓ㸬 (c) Single-crack

(b) Double edge crack (a) Center crack

୰ኸ㒊ࡁ⿣㸸

^

`

2 sec 06 . 0 025 . 0 1 ) (_{[  [}2 _{ [}4 S[ F 㸪ࡇࡇ࡛ȥ=a/W (1.10) ୧ഃࡁ⿣㸸

^

[ [ [ [

`

[ [) 1.1220.561 0.205 0.471 0.109 / 1 ( 2 3 4 F 㸪ࡇࡇ࡛ȥ=a/W (1.11) ∦ഃࡁ⿣㸸 2 cos 2 sin 1 199 . 0 923 . 0 2 tan 2 ) ( 4 S[ S[ S[ S[ [ ¸¹ · ¨ © §   F (1.12)

1.6 ࡁ⿣㐍ᒎ≉ᛶ࡜ࡁ⿣㐍ᒎ㝈⏺ᛂຊᣑ኱ಀᩘ⠊ᅖ ΔK

th Fig. 1.7 ࡢࡼ࠺࡟ࡁ⿣ࢆ᭷ࡍࡿ㒊ᮦ࡟ᛂຊࡀ㈇Ⲵࡉࢀࡓ᫬ࡢࡁ⿣ඛ➃㏆ഐࡢᛂຊศᕸ ࡣ㸪ᛂຊᣑ኱ಀᩘK ࢆ⏝࠸࡚㸪ᘧ(1.5)ࡢࡼ࠺࡟⾲ࡏࡿ㸬ࡇࡢࡼ࠺࡞㒊ᮦࡀ⧞㏉ࡋᛂຊࢆ ཷࡅࡿሙྜ࡟ࡣ㸪⧞㏉ࡋᛂຊࡢ᭱኱್࠾ࡼࡧ᭱ᑠ್ࢆࡑࢀࡒࢀσmax㸪σmin㸪ࡁ⿣㛗ࡉࢆ a ࡜ࡍࡿ࡜ࡁ㸪ᛂຊᣑ኱ಀᩘK ࡢ᭱኱್ Kmax㸪᭱ᑠ್Kminࡣ௨ୗࡢᘧ࡛⾲ࢃࡉࢀࡿ(8)㸬 °¿ ° ¾ ½ a K a K S V S V min min max max

_(1.13) ࡋࡓࡀࡗ࡚ᛂຊࡢኚື⠊ᅖ'σ=σmax㸫σmin ࡟ᑐᛂࡍࡿᛂຊᣑ኱ಀᩘࡢኚື⠊ᅖࡍ࡞ࢃ ࡕᛂຊᣑ኱ಀᩘ⠊ᅖ'K ࡣ㸪 a K K K  'V S ' _{max min} (1.14) ࡜⾲ࢃࡉࢀࡿ㸬 ࡞࠾㸪σmin㸺0 ࡍ࡞ࢃࡕ R㸺0 ࡢሙྜ㸪ᅽ⦰ຊ࡟ࡼࡾࡁ⿣ࡀ㛢ཱྀࡍࡿࡇ࡜ࢆ⪃៖ࡋ࡚㸪 'K㸻Kmaxࡀ୍⯡࡟⏝࠸ࡽࢀࡿ㸬 ࡇࡢࡼ࠺࡟ࡁ⿣ࢆ᭷ࡍࡿ㒊ᮦࡀ⧞㏉ࡋᛂຊࢆཷࡅ࡚ḟ➨࡟ࡁ⿣ࡣᡂ㛗ࡍࡿ࡜㸪ࡸࡀ࡚ 㒊ᮦࡣ◚᩿ࡍࡿ㸬ࡇࡢࡁ⿣ࡢ㐍ᒎࢆ♧ࡍࣃ࣓࣮ࣛࢱࢆ୍ᅇ⧞㏉ࡋᛂຊࢆཷࡅࡿ㛫࡟㐍ᒎ ࡍࡿࡁ⿣ࡢ㛗ࡉ࡜ࡋ࡚㸪ࡁ⿣㐍ᒎ㏿ᗘ da/dN ࡀ⏝࠸ࡽࢀ㸪ࡇࢀ࡜ᛂຊᣑ኱ಀᩘ⠊ᅖ ΔK ࡢ㛵ಀࢆFig. 1.8 ࡢᶍᘧᅗ࡟♧ࡍ㸬 ࡁ⿣㐍ᒎ≉ᛶࡣᛂຊᣑ኱ಀᩘ⠊ᅖࡢኚ໬࡟క࠸኱ࡁࡃ୕ࡘࡢ㡿ᇦ࡟ศࡅ࡚⾲ࡍࡇ࡜ࡀ ࡛ࡁࡿ㸬'K ࡢ኱ࡁ࠸(c)ࡢ㡿ᇦ࡛ࡣ'K ࡢቑຍ࡟కࡗ࡚ da/dN ࡣᛴ⃭࡟ୖ᪼ࡋ㸪Kmaxࡀ㝈 ⏺್࡟㐩ࡍࡿ࡜୙Ᏻᐃ◚ቯࢆ⏕ࡌࡿ㸬ࡇࡢ㝈⏺್ࡣ⑂ປ◚ቯࡌࢇᛶ KIC ࡜ࡼࡤࢀࡿ㸬ࡲ ࡓ'K ࡀᑠࡉ࠸(a)ࡢ㡿ᇦ࡛ࡣ'K ࡢῶᑡ࡟కࡗ࡚ da/dN ࡣᛴ⃭࡟పୗࡋ㸪ࡁ⿣ࡢ㐍ᒎࡀ ஦ᐇୖ⏕ࡌ࡞࠸࡜ぢ࡞ࡉࢀࡿ'K ࡟⮳ࡿ㸬ࡇࡢ'K ࡣࡁ⿣㐍ᒎ㝈⏺ᛂຊᣑ኱ಀᩘ⠊ᅖ'Kth ࡜࿧ࡤࢀࡿ㸬

ࡲࡓ㸪㛫ࡢ'K ࡛࠶ࡿ㡿ᇦ(b)࡛ࡣ'K ࡜ da/dN ࡣ୧ᑐᩘୖ࡛┤⥺ⓗ࡟ኚ໬ࡋ㸪ᘧ(1.15) ࡢࡼ࠺࡟⾲ࡉࢀࡿ㸬

 

_K m C dN da _' (1.15) ୖᘧࡣParis ๎࡜࿧ࡤࢀ㸪ᘧ୰ࡢ C, m ࡣᮦᩱᐃᩘ࡛࠶ࡿ(8)㸬 ᵓ㐀≀ࡀ◚᩿ࡍࡿ࡜ࡁ࡟ࡣᚲࡎࡁ⿣ࡢⓎ⏕㸪㐍ᒎࡀᏑᅾࡍࡿ㸬ࡑࡢࡓࡵࡁ⿣ࡢ≉ᛶࢆ ༑ศ⌮ゎࡍࡿࡇ࡜ࡀ㔜せ࡛࠶ࡿ㸬

Ȫ

₀

Ȫ

r

ߪሺݎሻ ൌ  ξʹπ” ∆Kth ҄

Fig. 1.7 Stress singularity and stress intensity factor at crack tip

1.7 ᚤᑠࡁ⿣ࡢᙉᗘホ౯ἲ

 ᐇ㝿ࡢᶵᲔᵓ㐀≀ࡢ⑂ປᑑ࿨ࡣ㸪ᚤᑠࡁ⿣ࡢẁ㝵ࡀ኱༙ࢆ༨ࡵ࡚࠸ࡿ࡜⪃࠼ࡽࢀࡿࡓ ࡵ㸪ࡇࡢẁ㝵࡛ࡢࡁ⿣ࡢ㐍ᒎᣲືࡢゎ᫂ࡀᵓ㐀≀ࡢ⑂ປᑑ࿨ண ࡟ᚲせ࡛࠶ࡿ㸬ࡋ࠿ࡋ ⥺ᙧ◚ቯຊᏛ࡟ࡼࡿ⑂ປᙉᗘࡢᐇ ࢆࡋ࡚ࡳࡿ࡜㸪ᚤᑠࡁ⿣⠊ᅖ࡛ࡣ㸪㛗࠸ࡁ⿣⠊ᅖ࡜ ྠࡌ⥺ᙧ◚ቯຊᏛࡢྲྀࡾᢅ࠸ࢆ⾜࠺࡜㸪⑂ປᙉᗘࡀ኱ࡁࡵ࡟♧ࡉࢀࡿࡓࡵ㸪ᐇ㝿ၥ㢟࡟ 㐺⏝ࡍࡿࡇ࡜ࡣ༴㝤࡛࠶ࡿ㸬 Fig. 1.9 ࡣ'σ ୍ᐃୗ࡟࠾ࡅࡿᚤᑠࡁ⿣ࡢ㐍ᒎᣲືࡢᶍᘧᅗ࡛࠶ࡿ㸬ࡇࡢሙྜ㸪ࡁ⿣㐍 ᒎ࡟ᚑ࠸'K ࡣቑ኱ࡍࡿ㸬'σ ࡀ㧗࠸࡜ࡁ('σ4)࡟ࡣ㸪኱ࡁ࠸ࡁ⿣ࡢ da/dN㸫'K 㛵ಀ࡟୍ ⮴ࡏࡎ࡟◚ቯ࡟⮳ࡿ㸬'σ ࡀపࡃ࡞ࡿ('σ2㸪'σ3)࡜ࡁ⿣㐍ᒎ࡟కࡗ࡚኱ࡁ࠸ࡁ⿣ࡢ㐍ᒎ ≉ᛶ࡜୍⮴ࡍࡿ㸬'σ2㹼'σ4ࡢሙྜࡣ᭱⤊ⓗ࡟◚ቯ࡟⮳ࡿࡀ㸪ࡁ⿣㐍ᒎึᮇ࡟࠾࠸࡚'K ࡀቑ኱ࡍࡿ࡟ࡶ࠿࠿ࢃࡽࡎ㐍ᒎ㏿ᗘࡀ୍᫬ⓗ࡟పୗࡍࡿ㸬ࡉࡽ࡟ప࠸ᛂຊ('σ1)࡛ࡣ㸪㐍 ᒎ㏿ᗘࡀపୗࡋ⥆ࡅ࡚೵␃࡟⮳ࡿ㸬ࡇࡢࡼ࠺࡟'σ1 ࡜'σ2 ࡢ㛫࡟ࡁ⿣ࡀ㐍ᒎࡋ࡚◚ቯ࡟ ⮳ࡿୗ㝈⏺ࡢᛂຊ⠊ᅖ∆σthࡀᏑᅾࡍࡿ㸬

Stress intensity factor range log(ΔK)

Fatigue cra

ck growth rate log (da/dN)

a ΔKth Kfc da /dN =C(ΔK )m 1 m (a ) (b ) (c )

Fig. 1.8 Relationship between ΔK and da/dN KIC

'Kth

(a) (b)

(c) da/dN = C ('K)m

Stress intensity factor range (' K)

Fatigue cra ck g row th rat e ( da/dN )

Fig. 1.9 Fatigue crack growth rate for various levels in stress amplitude Fig. 1.10 ࡟ࡁ⿣㐍ᒎ㝈⏺ᛂຊ⠊ᅖ∆σthࡢࡁ⿣㛗ࡉa ࡟ᑐࡍࡿ౫Ꮡᛶࢆ♧ࡍ㸬ࡁ⿣㛗ࡉࡀ ༑ศ࡟኱ࡁ࠸ሙྜࡢࡁ⿣㐍ᒎୗ㝈⏺ᛂຊࡣ㸪'K='Kth࡛҄Ỵᐃࡉࢀ㸪ࡁ⿣㛗ࡉࡀᑠࡉࡃ ࡞ࡿ࡟ࡘࢀ࡚∆σthࡣቑ኱ࡍࡿࡀ㸪ᖹ⁥ᮦࡢ∆σw0ࡼࡾࡶᛂຊࡀ㧗ࡃ࡞ࡿࡇ࡜ࡣ࡞࠸㸬 ࡲࡓ㸪⤖ᬗ⢏⛬ᗘࡲࡓࡣࡑࢀ௨ୗࡢࡁࢃࡵ࡚ᚤᑠ࡞኱ࡁࡉࡢࡁ⿣ࡢ㐍ᒎᣲືࡣ㸪⤖ᬗ ⢏⏺ࡸᚤどⓗ࡞⤌⧊࡟኱ࡁࡃᙳ㡪ࡉࢀ㸪㐍ᒎ㏿ᗘࡢࡤࡽࡘࡁࡀ኱ࡁ࠸㸬⌧ᅾ㸪ᚤᑠࡁ⿣ ࡢ㐍ᒎ≉ᛶࡢ⌧㇟ゎ᫂ࡣ㐍ࢇ࡛࠸ࡿࡀ㸪ᐇ㝿ࡢᵓ㐀≀࡟ࡣ⎔ቃࡸᚤどⓗ࡞⤌⧊࡞࡝࡜࠸ ࡗࡓ୙☜ᐃせ⣲ࡀከࡃ㸪ᮍࡔ༑ศ࡞ᙉᗘホ౯ἲࡢᐇ⏝໬࡟ࡣ⮳ࡗ࡚࠸࡞࠸㸬

Fig. 1.10 An example of fatigue strength of SS400 with small crack

0.01 0.05 0.1 0.5 1 5 50 100 500 1000 Crack length a (mm) Stress ∆σ th (MPa)

Linear fracture mechanics Fatigue limit of smooth specimen

'Kth : Constant

∆σw0

Stress intensity factor range 'K

Fatigue cra ck g row th rat e da/dN 'σ1<'σ2<'σ3<'σ4 ' σ4 ' σ3 ' σ2 ' σ1 Final fracture Big crack 'Kth

ୖグࡢࡼ࠺࡟ᚤᑠࡁ⿣ၥ㢟ࡣᵝࠎ࡞せ⣲ࡀ⤡ࡴࡓࡵ㸪᫂☜࡞ண ᪉ἲࡀ☜❧ࡉࢀ࡚࠸ ࡿࢃࡅ࡛ࡣ࡞࠸㸬ࡋ࠿ࡋᚤᑠࡁ⿣ၥ㢟ࢆ◚ቯຊᏛࡢၥ㢟࡜ࡋ࡚⡆༢࡟ᢅ࠺ࡇ࡜ࡢ࡛ࡁࡿ

El Haddad ࡢ᪉ἲࡀᥦ᱌ࡉࢀ㸪ࡑࡢ᭷ຠᛶࡶ☜ㄆࡉࢀ࡚࠸ࡿ(9~12)㸬El Haddad ࡣ㸪ᮦᩱ࡟

ࡣ₯ᅾⓗ࡟Ḟ㝗a0 ࡀᏑᅾࡋ࡚࠸ࡿࡶࡢ࡜௬ᐃࡋ㸪ᐇ㝿ࡢࡁ⿣㛗ࡉa ࡢ௦ࢃࡾ࡟(aa0) ࢆࡁ⿣㛗ࡉ࡜ࡋ࡚ᙉᗘホ౯࡟⏝࠸ࡿ᪉ἲࢆᥦ᱌ࡋࡓ㸬௨ୗ࡟ᘧࢆ♧ࡍ㸬a0ࡣึᮇḞ㝗ᑍ ἲ࡛࠶ࡾ㸪ᘧ1.17 ࡣᘧ 1.14 ࡟ึᮇḞ㝗ᑍἲࢆ⪃៖ࡋࡓࡶࡢ࡛࠶ࡿ㸬 2 0 0 1 ¸¸ ¹ · ¨¨ © § ' ' w th K a V S



a a0



K_th '  ' V S (1.17) ᘧ1.17 ࡟࠾࠸࡚㸪ᐇ㝿ࡢࡁ⿣㛗ࡉa ࡀ El Haddad ࡢ᪉ἲࡀᐃࡵࡿ㛗ࡉ a0࡜ẚ࡭࡚ᑠࡉ ࠸ሙྜࡣ㸪ࡁ⿣㛗ࡉ࡟࠾ࡅࡿᙉᗘホ౯࡟ࡣ㠀ᖖ࡟኱ࡁ࡞ᙳ㡪ࢆ୚࠼ࡿ㸬୍᪉㸪ࡁ⿣㛗ࡉa ࡀEl Haddad ࡢࡁ⿣㛗ࡉa0࡜ẚ࡭࡚༑ศ࡟㛗࠸ሙྜࡣᙉᗘホ౯࡟ᙳ㡪ࡀ࡯࡜ࢇ࡝࡞࠸㸬 ࡘࡲࡾ㸪Fig. 1.11 ࡟♧ࡍ୍౛ࡢࡼ࠺࡟ᚤᑠࡁ⿣⠊ᅖ࡜㛗࠸ࡁ⿣⠊ᅖ࡟⮳ࡿࡍ࡭࡚ࡢࡁ⿣ ⠊ᅖࡢᙉᗘࢆ⤫୍ⓗ࡟ホ౯࡛ࡁࡿ᪉ἲ࡜࡞ࡗ࡚࠸ࡿ㸬

0.01

0.05 0.1

0.5 1

5

50

100

500

1000

crack length a mm

T

hre

shol

d S

tre

ss

Ȫ

MPa

linear fracture mechanics fatigue limit of smooth specimen El Haddad equation

Fig. 1.11 Fatigue strength predicted using El Haddad equation for SS400 material

Linear fracture mechanics Fatigue limit of smooth specimen El Haddad equation Crack length a (mm) Stress

Ȫ

w (MPa) (1.16)

1.8 ≉ᐃ఩⨨ᛂຊἲࡢᙉᗘホ౯ἲ

๓㏙ࡢࡼ࠺࡟㸪෇Ꮝࡸࡔ෇Ꮝࡢሙྜ࡟ࡣ㸪ษḞࡁඛ➃ࡢᛂຊࢆᣦᶆ࡜ࡍࡿᛂຊ㞟୰ಀ ᩘȘ࡞࡝ࡢᮦᩱຊᏛⓗᙉᗘホ౯ἲࡀ⏝࠸ࡽࢀࡿ㸬ࡲࡓ㸪ࡁ⿣࡞࡝ࡢඛ➃࡛ࡢᛂຊࡀ↓㝈 ኱࡜࡞ࡾᮦᩱຊᏛⓗ࡟ࡣホ౯ࡍࡿࡇ࡜ࡀ࡛ࡁ࡞࠸ሙྜࡣ㸪ࡁ⿣࿘㎶ࡢᛂຊศᕸࡢẚ౛ᐃ ᩘK ࢆ⏝࠸㸪ࡑࡢ኱ᑠ࡟ࡼࡗ࡚ᙉᗘࢆホ౯ࡍࡿ◚ቯຊᏛⓗᙉᗘホ౯ἲࡀ⏝࠸ࡽࢀ࡚࠸ࡿ㸬 ࡇࡢࡼ࠺࡞ᙉᗘホ౯ἲࡢ⤫୍ࢆ┠ⓗ࡜ࡋ࡚㸪≉ᐃ఩⨨ᙉᗘホ౯ἲࡀᥦ᱌ࡉࢀ࡚࠸ࡿ㸬 ࡇࢀࡣ෇ᏍࡸษḞࡁඛ➃࠿ࡽ࠶ࡿ఩⨨ࡢᛂຊ㸪࠶ࡿ࠸ࡣ≉ᐃ㊥㞳⠊ᅖෆ࡛ࡢᛂຊࡢᖹᆒ ್ࡀ㒊ᮦࡢᙉᗘࢆつᐃࡍࡿ࡜࠸࠺⌮ㄽ࡛࠶ࡾ㸪ࡇࡢ≉ᐃ఩⨨ἲࡣ Point method㸪Line method㸪Area method ࡢ 3 ✀㢮ࡢ᪉ἲ࡟ศ㢮ࡍࡿࡇ࡜ࡀ࡛ࡁࡿ㸬 ௒㸪Fig. 1.12 ࡟♧ࡍࡼ࠺࡟෇Ꮝࢆ᭷ࡍࡿ㒊ᮦ࡟༢㍈ᘬᙇࡾ㈇Ⲵࢆ୚࠼ࡿሙྜࢆ⪃࠼ࡿ㸬 ࡇࡢሙྜ㸪ⅬO ࡛᭱ࡶᛂຊࡀ኱ࡁࡃ࡞ࡿࡀ㸪Point method ࡛ࡣࡇࡢⅬ࠿ࡽ࠶ࡿ≉ᐃࡢ㊥ 㞳rC࡛ࡢᛂຊࡀḞ㝗ࢆ↓どࡋࡓ᫬ࡢᙉᗘ㸪ࡘࡲࡾᖹ⁥ᮦࡢᙉᗘ࡜➼ࡋࡃ࡞ࡿ᫬㸪ࡇࡢ㒊 ᮦࡢᙉᗘࢆᐃࡵࡿ࡜ࡍࡿ᪉ἲ࡛࠶ࡿ㸬ࡲࡓ㸪Line method ࡣ᭱኱ᛂຊࢆ⏕ࡌࡿ㠃࡟ἢࡗ࡚ ࠶ࡿ≉ᐃࡢ㛗ࡉ LCࢆ⪃࠼ࡇࡢ LCෆࡢᛂຊࡢᖹᆒ್ࡀᖹ⁥ᮦࡢᙉᗘ࡜࡞ࡿ᫬㸪ࡇࡢ㒊ᮦ ࡢᙉᗘࢆᐃࡵࡿ࡜ࡍࡿ᪉ἲ࡛࠶ࡿ㸬 Area method ࡛ࡣ㸪᭱኱ᛂຊࢆ⏕ࡌࡿⅬ O ࢆཎⅬ࡜ ࡋࡓ༙ᚄACࡢ༙෇ࢆ⪃࠼㸪ࡇࡢ⠊ᅖෆ࡛ࡢᛂຊࡢᖹᆒ್ࡀᖹ⁥ᮦࡢᙉᗘ࡜➼ࡋࡃ࡞ࡿ᫬㸪 㒊ᮦࡢᙉᗘࢆᐃࡵࡿ࡜௬ᐃࡍࡿ᪉ἲ࡛࠶ࡿ㸬 ᮏ◊✲࡛ࡣ㸪ࡇࡢ㸱ࡘࡢ᪉ἲࡢ୰ࡢ࠺ࡕPoint method ࡟╔┠ࡋ㸪ᮏᡭἲࢆ⑂ປ㝈ᗘ,ప ࢧ࢖ࢡࣝ⑂ປ,ᘬᙇᙉࡉண ࡟㐺⏝ࡋ㸪ᛂຊ㞟୰ࢆ⏕ࡌࡿ㒊ᮦࡢᙉᗘホ౯ࢆ⾜࠺㸬 ࡇࡇ࡛ࡣPoint method ࢆ⑂ປ㝈ᗘண ࡟㐺ᛂࡍࡿሙྜࢆ౛࡜ࡋ࡚㸪≉ᐃ఩⨨ rCࡢ⟬ฟ ἲࢆㄝ᫂ࡍࡿ㸬≉ᐃ఩⨨rCࡣᖹ⁥ᮦࡢ⑂ປ㝈ᗘ࡜㸪ࡁ⿣ᮦࡢࡁ⿣ࡀ㐍ᒎࡍࡿ᭱ᑠࡢᛂຊ ศᕸ⥺ࡢ஺Ⅼ࠿ࡽỴࡵࡿࡇ࡜ࡀ࡛ࡁࡿ㸬↓㝈ᯈ୰ࡢࡀ༑ศ㛗࠸ࡁ⿣࡟ࡘ࠸࡚ࡣ㸪ࡁ⿣ඛ ➃ࡢⲴ㔜㈇Ⲵ᪉ྥࡢᛂຊศᕸࡣᘧ(1.5)࡟ȟ㸻0 ࢆ௦ධࡋ࡚ḟࡢࡼ࠺࡟♧ࡉࢀࡿ(13~17).

 

r K r S V 2  (1.18) ≉ᐃ఩⨨rCࡣᘧ(1.18)ࡢ K ࡟ࡁ⿣㐍ᒎ㝈⏺ᛂຊᣑ኱ಀᩘ⠊ᅖ'Kthࢆ㸪σ(r)࡟ᖹ⁥ᮦࡢ⑂ ປ㝈'σw0ࢆᤄධࡋ㸪r ࡟ࡘ࠸࡚ゎࡃࡇ࡜࡛ồࡵࡿࡇ࡜ࡀ࡛ࡁࡿ㸬 2

2

1

¸¸

¹

·

¨¨

©

§

'

'

wo th C

K

r

V

S

(1.19)

ᛂຊ㞟୰㒊ࡢ⑂ປ㝈ᗘࡣ㸪๓㡯࡛ồࡵࡓ≉ᐃ఩⨨ rC࡛ࡢᛂຊࡀᖹ⁥ᮦ⑂ປ㝈ᗘ 'σw0 ࡜➼ࡋࡃ࡞ࡿᛂຊ࡜ࡋ࡚ண ࡛ࡁࡿ㸬ࡇࡇ࡛ࡣ㸪ࡁ⿣ࡢᛂຊศᕸࡢᘧ(1.5)ࢆ౑⏝ࡋ࡚ㄝ ᫂ࡍࡿ㸬ᘧ(1.5)࡛≉ᐃ఩⨨ rC࡟࠾ࡅࡿᛂຊࡀ⑂ປ㝈'σw0࡜➼ࡋ࠸ࡶࡢ࡜ࡋ࡚ σy࡟ࡘ࠸ ࡚ゎࡃࡇ࡜࡛㸪ࡁ⿣ᮦࡢ⑂ປ㝈ࢆண ࡍࡿࡇ࡜ࡀ࡛ࡁࡿ㸬ࡘࡲࡾ㸪ᘧ(1.5)ࢆ c y r K r K

S

T

T

T

S

V

2 ) 2 3 sin 2 sin 1 ( 2 cos 2 , , _{      } (1.20) ࡜࠸࠺ᙧ࡟ኚᙧࡋ㸪r=rC㸪σy='σw0 ࢆ௦ධࡍࡿࡇ࡜࡛㸪ࡁ⿣ࢆ᭷ࡍࡿᮦᩱࡢ⑂ປ㝈ᗘ σw ࢆồࡵࡿࡇ࡜ࡀ࡛ࡁࡿ(18~20)㸬 r crack rC Δσw0

r

K

r

th

S

V

2

)

(

'

σ

Fig. 1.13 Stress distributions near crack edge

Fig. 1.12 Point, line and area near circular hole in critical distance theory O

LC rC

1.9 ᚑ᮶ࡢす㇂ࡢண ᪉ἲ

S20C ࡟ࡘ࠸࡚ Fig. 1.14 ࡟♧ࡍࡼ࠺࡟ࡁ⿣೵␃⌧㇟ࡢࡓࡵ࡟ษḞࡁᮦࡢ⑂ປ㝈ᗘ࡟ࡣ㸪 ษḞࡁᗏ࡟ࡁ⿣ࡀⓎ⏕ࡍࡿ㝈⏺ࡢᙉᗘ σw1 ࡜೵␃ࡁ⿣ࡀ⏕ࡌࡓࡲࡲ◚᩿࡟⮳ࡽ࡞࠸㝈⏺ ࡢᙉᗘσw2ࡀ࠶ࡿ㸬A ࡢ᭤⥺࡜ B ࡢ᭤⥺ࡢ஺ⅬࢆศᒱⅬ࡜࠸࠺ࡀ㸪ศᒱⅬࡢษḞࡁ༙ᚄ ρ0 ࡣᮦ㉁ᐃᩘ࡜࡞ࡿࡇ࡜ࡀ▱ࡽࢀ࡚࠸ࡿ㸬ࡇࢀࡲ࡛ࡢ᪉ἲࡣ㸪ࡁ⿣Ⓨ⏕㝈⏺σw1ࢆண ࡍࡿ ᪉ἲ࡛࠶ࡗࡓ㸬ࡇࢀ࡟ᑐࡋす㇂ࡣศᒱⅬ࡟࠾ࡅࡿษḞࡁ༙ᚄρ0ࡀᮦᩱ࡟ᅛ᭷࡞್࡜࡞ࡿ ࡇ࡜࡟ὀ┠ࡋ࡚σw2ࡢண ἲࢆ♧ࡋࡓ(21)㸬  ண ࡋࡓ࠸ᙧ≧ࡢ᭤⋡༙ᚄ ρ1ࡀ ρ0ࡼࡾࡶᑠࡉ࠸ሙྜ࡟ࡣ σw2ࡣศᒱⅬࡢ σw1࡟➼ࡋ࠸ ࡓࡵ㸪ษḞࡁ༙ᚄࡔࡅࡀ ρ0࡛௚ࡢᑍἲࡣࡍ࡭࡚࡜ྠࡌ㒊ᮦࡢ σw1ࢆ௚ࡢ᪉ἲ࡟ࡼࡗ࡚ồ ࡵࢀࡤࡼ࠸ࡇ࡜࡟࡞ࡿ㸬  σw1 㸪 σw2,  MPa 0 50 100 150 200 250 1 2 3 4 5

Stress concentration factor Ș ೵␃ࡁ⿣᭷

σw1 σw2 ρ=1.0 mm

Fig. 1.14 S20C Fatigue strength of notched material ρ0=0.5 mm

ศᒱⅬ

A B

Table 1.1(2,22,23)࡟ྛ✀㗰ᮦ࡟ࡘ࠸࡚ࡢρ0ࡢ್ࢆ♧ࡍ㸬

Table 1.1 Critical radius ρ0 for each materials.

Material σB MPa σS MPa σw0 MPa ρ0 mm S10C Carbon steel 372 203 181 0.6 S20C Carbon steel 469 279 211 0.5 S25C Carbon steel 494 297 255 0.5 S35C Carbon steel 600 336 274 0.4 S50C Carbon steel 673 347 265 0.25

S50C Carbon steel refining 1010 858 500 0.1

S50C Carbon steel refining 1246 1132 617 0.1

SNCM26 Nickel-chromium-molybdenum steel 1389 1140 629 0.1

σB: Tensile strength σS: Yield stress σw0: Fatigue limit ρ0: Notch radius

➨

➨

2 ❶ ≉ᐃ఩⨨ᛂຊἲࢆ⏝࠸ࡓᛂຊ㞟୰㒊఩ࡢ

పࢧ࢖ࢡࣝ⑂ປࡢᙉᗘホ౯

2.1 ⥴ ゝ

ᮏ❶࡛ࡣ≉ᐃ఩⨨ᛂຊἲࡢ☜❧ࢆ┠ⓗ࡜ࡋ㸪ᛂຊ㞟୰㒊఩ࡢపࢧ࢖ࢡࣝ⑂ປࡢᙉᗘホ౯࡬ࡢ 㐺⏝ᛶࢆ᳨ウࡋࡓ㸬ᛂຊ㞟୰㒊఩࡛ࡣ⑂ປᙉᗘࡀⴭࡋࡃపୗࡍࡿ㸬ࡇࢀࡣࠕษḞࡁຠᯝࠖ࡜࿧ ࡤࢀ㸪⑂ປ◚ቯࡢ࡯ࡰ 100㸣㏆ࡃࢆ༨ࡵ࡚࠸ࡿ㸬㏆ᖺ࡛ࡣᶵᲔ࣭ᵓ㐀≀ࡢ㛗ᑑ࿨タィ㸪ᙧ≧ࡢ 」㞧໬ࡀ㐍ࢇ࡛࠾ࡾ㸪ࡲࡍࡲࡍࡇࡢၥ㢟ࡀ㔜せ࡟࡞ࡗ࡚࠸ࡿ㸬 ࡇࡇ࡛⾜ࡗࡓᐇ㦂࡛ࡣ㸪౪ヨᮦ࡜ࡋ࡚ᕤᏛⓗ࡟㢖⏝ࡉࢀࡿ㕲㗰ᮦᩱ SS400 ࡢᯈᮦࢆ⏝࠸ࡓ㸬 ヨ㦂∦ᙧ≧࡟ᖹ⁥ᮦ㸪ᖹᯈ࡟V ᏐษḞࡁ㸪෇Ꮝࢆ௜୚ࡋࡓࡶࡢࢆ⏝࠸ࡓ㸬ᛂຊศᕸ࡟ࡘ࠸࡚ࡣ ᭷㝈せ⣲ἲ࡛ண ࡋࡓ㸬ࠕSS400 ࢆ⏝࠸ࡓྛ✀ヨ㦂∦ࡢ⑂ປヨ㦂ࠖ࡜ࠕ≉ᐃ఩⨨ἲ࡟ࡼࡿᙉᗘண  ࠖࢆ⾜࠸㸪ࡇࢀࡽࡢ⤖ᯝࢆẚ㍑ࡋࡓ㸬ࡲࡓ㸪ࣇࣞࢵࢸ࢕ࣥࢢ⑂ປ࡬ࡢ㐺⏝ᛶ࡟ࡘ࠸࡚ࡶ㸪ᐇ 㦂⤖ᯝ࡜ẚ㍑ࡋ᳨ウࡋࡓ㸬

2.2 ≉ᐃ఩⨨ᛂຊἲ

ᮏ◊✲࡛ࡣᥦ᱌ࡍࡿ≉ᐃ఩⨨ᛂຊἲࢆ⏝࠸ࡓ⑂ປ㝈ホ౯ἲࡣ㸪Fig. 2.1 ࡟♧ࡍࡼ࠺࡟ᖹ⁥ᮦ ࡜ࡁ⿣ᮦࡢ୧ᴟ➃ࡢᛂຊศᕸࢆ⏝࠸ࡿ㸬ᖹ⁥ᮦࡢ⑂ປ㝈 ∆σw0࡜㸪ࡁ⿣㐍ᒎୗ㝈⏺ᛂຊᣑ኱ಀ ᩘ⠊ᅖ ∆Kth࡛ࡢᛂຊศᕸࡢ஺Ⅼ࡟ᑐᛂࡍࡿࡁ⿣ඛ➃࠿ࡽࡢ㊥㞳rC㸦Point method㸧㸪࠶ࡿ࠸ࡣ ᅖࡲࢀࡓ㠃✚ࡀ➼ࡋࡃ࡞ࡿ఩⨨LC㸦Line method㸧ࢆồࡵ㸪ホ౯ᑐ㇟࡜ࡍࡿ㒊ᮦࡢᛂຊศᕸ࠿ࡽ ồࡲࡿᖹᆒ್࡟࡞ࡗࡓ࡜ࡁ㸪⑂ປ㝈ࢆᐃࡵࡿ᪉ἲ࡛࠶ࡿ. rC࡜LCࡢ఩⨨ࡣ௨ୗࡢࡼ࠺࡟ồࡵࡽ ࢀࡿ. rC=(∆Kth /Δσw0)2/2 π (Point method) (2.1) LC=2(∆Kth /Δσw0)2/π (Line method) (2.2)

(a) Point method

(b) Line method

Fig. 2.1 Derivation of critical distance rC and LC Crack r σ ߪሺݎሻ ൌ  ξʹπ” ∆Kth Δσw0 rC Crack r σ ߪሺݎሻ ൌ  ξʹπ” ∆Kth Δσw0 LC S1 S2

2.3 ≉

≉ᐃ఩⨨ᛂຊἲ࡟ࡼࡿపࢧ࢖ࢡࣝ⑂ປᙉᗘண 

๓㏙ࡢ≉ᐃ఩⨨ᛂຊἲࡣ㸪ࡑࡶࡑࡶ⑂ປ㝈ண ࡢࡓࡵࡢࡶࡢ࡛࠶ࡿࡀ㸪ࡇࡢ᪉ἲࡶ㸪㟼ⓗᙉ ᗘσB㸦ᘬᙇᙉࡉ㸧㸪KIC㸦ᖹ㠃ࡦࡎࡳ◚ቯࡌࢇᛶ್㸧㸪 ࠾ࡼࡧᖹ⁥ᮦࡢప⧞㏉ࡋᩘ㡿ᇦࡢ⑂ປ≉ ᛶࡀศ࠿ࢀࡤ௵ពࡢᙧ≧㸪ᛂຊศᕸୗࡢ㒊ᮦࡢ㟼ⓗᙉᗘ㸪ప⧞㏉ࡋᩘ㡿ᇦࡢ⑂ປᙉᗘ࣭ᑑ࿨ࡢ ホ౯࡟㐺⏝࡛ࡁࡿ࡜⪃࠼ࡽࢀࡿ㸬ලయⓗ࡟ࡣ㸪Fig. 2.2 ࡟♧ࡍࡼ࠺࡟๓㏙ࡢ∆σw0 (ᖹ⁥ᮦࡢ⑂ ປ㝈)࡜∆Kth㸦ࡁ⿣㐍ᒎ㝈⏺ᛂຊᣑ኱ಀᩘ⠊ᅖ㸧࠿ࡽᐃࡲࡿ⑂ປ㝈࡟ᑐࡍࡿ≉ᐃ఩⨨rC㸪࠾ࡼࡧ σB࡜KIC࠿ࡽᐃࡲࡿ㟼ⓗᙉᗘ࡟ᑐࡍࡿ≉ᐃ఩⨨rC͛ࢆồࡵ㸪⦪㍈࡟ࡣᛂຊ㸪ᶓ㍈࡟ࡣ≉ᐃ఩⨨ ࢆྲྀࡾ㸪 2 ࡘࡢⅬࢆ┤⥺࡛⤖ࡧ㸪ᐇᵓ㐀㒊ᮦࡢప⧞㏉ࡋᩘ㡿ᇦࡢ⑂ປᙉᗘ࡟ࡣ㸪ࡇࡢ┤⥺ୖ࡟ ࠶ࡿࡶࡢ࡜௬ᐃࡋ࡚㸪పࢧ࢖ࢡࣝᇦࡢᙉᗘࢆồࡵࡿ᪉ἲ࡛࠶ࡿ㸬ᮏ◊✲࡛ࡣ㸪పࢧ࢖ࢡࣝᇦࡢ ⑂ປᙉᗘࢆ➨୍㏆ఝ࡜ࡋ࡚┤⥺⿵㛫ࡋ࡚ồࡵ㸪ࡑࡢ᭷ຠᛶࢆ᳨ウࡍࡿ㸬 ࡲࡎ㸪ண ࡋࡓ࠸ᙧ≧ࡢヨ㦂∦ࡢ᭷㝈せ⣲ἲゎᯒ࡛ồࡵࡓᛂຊศᕸ⥺࡜2 Ⅼࢆ⤖ࢇࡔ┤⥺ࡢ ஺Ⅼ࠿ࡽ࠶ࡿ≉ᐃ఩⨨࡛ࡢᛂຊσ ࢆồࡵࡿ㸬ࡘࡂ࡟ᖹ⁥ᮦヨ㦂∦࡟㛵ࡍࡿపࢧ࢖ࢡࣝ S-N ᭤⥺ ࢆ⏝࠸࡚㸪ࡇࢀ࡜ྠࡌᛂຊ࡟ᑐࡍࡿᑑ࿨ࢆษḞࡁᮦࡢ⑂ປᑑ࿨࡜ࡋ࡚ᐃࡵࡿ㸬  ලయⓗ࡟௨ୗ࡟ㄝ᫂ࡍࡿ㸬Fig. 2.2 ࡢ⦪㍈࡟ࡣᛂຊ㸪ᶓ㍈࡟≉ᐃ఩⨨ࢆ⾲ࢃࡍ㸬ᕥୗࡢ  Ⅼࡣ㧗ࢧ࢖ࢡࣝ⑂ປ࡟ࡼࡿ≉ᐃ఩್rC࡛㸪ྑୖࡢ Ⅼࡣ㟼ⓗᙉᗘ࡟ᑐࡍࡿ≉ᐃ఩⨨rC࡛͛࠶ ࡿ㸬ࡇࢀࡽࡢⅬࢆ⤖ࡪ஧Ⅼ㙐⥺ࡣண ⥺࡛࠶ࡾ㸪పࢧ࢖ࢡࣝ⑂ປᙉᗘࡣࡇࡢ㛫࡟Ꮡᅾࡍࡿ࡜௬ ᐃࡍࡿ㸬ࡑࡢ௬ᐃࡋࡓண ⥺࡜ண ࡍࡿษḞࡁᮦ࡟ᑐࡋ࡚㸪ᖹᆒᛂຊσnࢆ୚࠼ࡓ࡜ࡁࡢᛂຊศ ᕸ⥺㸦㸦ᅗ୰ࡢ◚⥺㸧࡜ࡢ஺Ⅼ࠿ࡽᛂຊ್σ ࡀồࡲࡿ㸬 

Fig. 2.2 Critical distances and stress range rC͛ F F F F

Critical distance

St

ress range

rC σ σB ∆σw0

(

∆

K

th

)

(K

IC

)

Cycling loading F F F F

ࡇࡢ್࡜Fig. 2.3 ࡟♧ࡍᖹ⁥ᮦࡢ S-N ᭤⥺࡜ࡢ஺Ⅼ࠿ࡽ◚᩿ࢆ⏕ࡌࡿ⧞㏉ࡋᅇᩘ N ࡀᐃࡲࡿ㸬

ḟ࡟Fig. 2.4 ࡟♧ࡍࡼ࠺࡟㸪㈇Ⲵᛂຊࡢ್ࢆኚ࠼ࡓ᫬ࡢᛂຊศᕸ⥺࠿ࡽ㸪ࡑࡢ㈇Ⲵᛂຊ σn࡟ᑐ

ࡍࡿ◚᩿ᑑ࿨࠿ࡽᐃࡲࡿⅬࢆࣉࣟࢵࢺࡋ࡚㸪S-N ᭤⥺ࢆண ࡍࡿ.

Fig. 2.3 Determination of N from smooth specimen S-N curve of smooth specimen

Fig. 2.4 Plotting using average stress σn and N on S-N curve σB

∆σ

w0

σ

N

Number of cycle to failure Nf

St res s ran ge σ σn

N

St res s ran ge σ

Number of cycle to failure Nf F F

F F

2.3.1 ᐇ

ᐇ㦂⿦⨨

ヨ㦂∦࡟⧞㏉ࡋⲴ㔜ࢆ୚࠼㸪㈇Ⲵᛂຊσ ࡜◚᩿࡟⮳ࡿ⧞㏉ࡋᅇᩘ N ࡢ㛵ಀࢆᖹ⁥ᮦ㸪V Ꮠษ Ḟࡁ࠾ࡼࡧ෇Ꮝヨ㦂∦࡟ᑐࡋ࡚⑂ປ㝈ᗘࢆㄪ࡭ࡓ㸬ヨ㦂ᶵࡣᓥὠ〇సᡤ〇10t 㟁ẼἜᅽࢧ࣮࣎ ᘧ᣺ື⑂ປヨ㦂ᶵ㸦ࢧ࣮࣎ࣃࣝࢧ࣮EHF-EA10 ᙧ㸪 4830 ᆺไᚚ⿦⨨㸧ࢆ౑⏝ࡋࡓ㸬እほ෗┿ ࢆFig. 2.5 ࡟♧ࡍ㸬Ἔᅽ※ࡼࡾⓎ⏕ࡋࡓἜᅽࡣ㸪ࢧ࣮࣎ᘚ࡟ࡼࡗ࡚ὶἜ㔞ࢆㄪᩚࡋ࢔ࢡࢳ࢚ࣗ ࣮ࢱ࡟ὶධࡋヨ㦂∦࡟⧞㏉ࡋⲴ㔜ࢆ୚࠼ࡿ㸬ヨ㦂∦࡟ຍ࠼ࡽࢀࡿ㈇Ⲵࡣ࣮ࣟࢻࢭ࡛ࣝ㟁Ẽಙྕ ࡟ኚ᥮ࡉࢀ㸪ࢥࣥࢺ࣮ࣟࣛ࡟㏦ࡽࢀ㸪┠ᶆࡢ್࡟࡞ࡿࡼ࠺ࢧ࣮࣎ᘚࢆไᚚࡍࡿ㛢࣮ࣝࣉไᚚࡀ ⾜ࢃࢀ࡚࠸ࡿ㸬 ヨ㦂᮲௳࡟ࡘ࠸࡚ࡣⲴ㔜ไᚚ࡜ࡋ㸪ṇᘻἼࢆᛂຊẚR㸻0 ࡛୚࠼ࡓ㸬⧞㏉ࡋ㏿ᗘࡣ 20Hz ࢆタ ᐃࡋ㸪᭱኱⧞ࡾ㏉ࡋᩘࡣN㸻5™106ᅇ࡜ࡋࡓ㸬ࢥࣥࢺ࣮ࣟࣛ࡟ࡢヨ㦂᮲௳࡜ヨ㦂Ⲵ㔜ࢆධຊࡋ㸪 ┠ᶆࡢⲴ㔜࡟ᑐࡍࡿኚືࡢ࣑ࣜࢵࢺࢆヨ㦂Ⲵ㔜࡟ᑐࡋ࡚2 kN ⛬ᗘ࡟タᐃ㸪ヨ㦂∦ࡀ◚᩿ࡍࢀ ࡤ┤ࡕ࡟⮬ື೵Ṇࡍࡿ㸬 Table 2.1 ࡟౪ヨᮦ SS400 ࡢᖹ⁥ヨ㦂∦࡟ࡘ࠸࡚㸪௨๓⾜ࢃࢀࡓูࡢ◊✲࡛ᚓࡽࢀ࡚࠸ࡿ㟼ⓗ ࠾ࡼࡧ⑂ປᙉᗘ≉ᛶࢆ♧ࡍ(20)㸬Fig. 2.6 ࡟ᐇ㦂࡟⏝࠸ࡓヨ㦂∦ࡢᙧ≧ᑍἲࢆ♧ࡍ.

Fig. 2.5 General view of fatigue testing apparatus ∆σw0 (MPa) ∆Kth (MPa㺃m1/2) σB (MPa) KIC (MPa㺃m1/2) 305 6.7 448 39.5 Hydraulic unit Testing machine Servo controller Load cell Specimen Hydraulic actuator

(a) Smooth specimen

(b) V-notch specimen

(c) Circular hole specimen Fig. 2.6 Dimensions of specimens

ྠ⾲ࡢᙉᗘ≉ᛶ್ࢆ⏝࠸࡚㸪㟼ⓗ᮲௳࠾ࡼࡧ⑂ປ㝈࡛ࡢ≉ᐃ఩⨨rC͛࠾ࡼࡧrCࡣᘧ(2.1),(2.2) ࡼࡾ㸪

r

C

͛= (∆K

IC

/Δσ

B

)

2

/2 π = 1.240 mm (㟼ⓗ᮲௳)

r

C

㸻(∆K

th

/Δσ

w0

)

2

/2 π= 0.077 mm (⑂ປ㝈)

4 mm or 10 mm 60ror 120r 8-ȭ10 8-ȭ10 8-ȭ10 15

2.3.2 ᭷

᭷㝈せ⣲ἲ࡟ࡼࡿᛂຊศᕸண 

 ᮏண ἲ࡛ࡣ㸪ษḞࡁࡸ෇Ꮝ㏆ഐࡢᛂຊศᕸ⥺ࢆ฼⏝ࡋ࡚࠸ࡿ㸬ᮏ◊✲࡛ࡣᕷ㈍ࡢ㟼ⓗ㝜ゎ

ἲ᭷㝈せ⣲ࢯࣝࣂ࣮ࡢNX NASTRAN ࢆ⏝࠸࡚ᛂຊศᕸࢆィ⟬ࡋࡓ㸬

ヨ㦂∦ᙧ≧ࡢᗄఱᏛⓗᑐ⛠ᛶࢆ⪃៖ࡋ㸪1/4 ࣔࢹ࡛ࣝ⾜ࡗࡓ㸬V ᏐษḞࡁ࠾ࡼࡧ෇Ꮝヨ㦂∦

࡟ᑐࡍࡿィ⟬ࣔࢹࣝࡢ౛ࢆFig. 2.7 ࡟♧ࡍ㸬୚࠼ࡓᖹᆒᛂຊࡣ 200 MPa ࠿ࡽ 450 MPa ࡢ⠊ᅖ࡛

࠶ࡿ㸬ィ⟬᮲௳ࢆTable 2.2 ࡟♧ࡍ㸬ᖹ㠃ᛂຊࢆ௬ᐃࡋ㸪ᯈཌࡣᐇ㦂࡛⏝࠸ࡓ౪ヨᮦ࡜ྠᵝ㸪5 mm

࡟タᐃࡋࡓ㸬ᮦᩱࡣ⥺ᙧᙎᛶయࢆ௬ᐃࡋ㸪ࣖࣥࢢ⋡࡜࣏࢔ࢯࣥẚࡣ㕲㗰ᮦᩱࡢ୍⯡ⓗࡢ್࡜ࡋ ࡓ㸬

(a) V-notch specimen (1/4 region)

(b) Circular hole specimen (1/4 region) Fig. 2.7 Finite element meshes

Element type 2-Dimensional 6 node triangular element (PLANE183)

Element model Plane stress condition

Material property Linear elastic body Young's modulus 210 GPa

Poisson's ratio 0.3

V ᏐษḞࡁࡢゅᗘࡀ 60°࠾ࡼࡧ 120°ࡢヨ㦂∦࡟ᑐࡍࡿᛂຊศᕸࢆ Fig. 2.8 ࡟♧ࡍ㸬ᖹ⁥ᮦࡢ㧗 ࢧ࢖ࢡࣝ⑂ປ࠾ࡼࡧ㟼ⓗᙉᗘࡢྛ≉ᐃ఩⨨࡜㸪⑂ປ㝈࠾ࡼࡧ㟼ⓗᙉᗘࢆࣉࣟࢵࢺࡋ㸪୧Ⅼࢆ┤

⥺࡛⤖ࢇ࡛࠸ࡿ㸬ࡇࡢᅗ࠿ࡽྛᛂຊ᣺ᖜ࡟ᑐࡍࡿ⑂ປ㝈ࢆㄞࡳྲྀࡗࡓ㸬ࡲࡓ㸪෇Ꮝ4 mm ࠾ࡼ

ࡧ10 mm ࡢヨ㦂∦࡟ᑐࡍࡿᛂຊศᕸࢆ Fig. 2.9 ࡟♧ࡍ㸬ྠࡌࡃྛᛂຊ࡟ᑐࡍࡿ⑂ປ㝈ࢆࡇࡢᅗ

ࡼࡾᐃࡵࡓ㸬

(a) 60° V-notch specimen

(b) 120° V-notch specimen Location r (mm) St re ss σ (MP a) Location r (mm) St re ss σ (MP a) (KIC) (KIC) σB σB (∆Kth) (∆Kth) Assumed relationship between ∆Kth and KIC 200MPa 250MPa 300MPa 350MPa 400MPa 450MPa 60r 120r Assumed relationship between ∆Kth and KIC 250MPa 300MPa 320MPa 335MPa 350MPa 370MPa 0.01 0.1 1 10 100 0.01 0.1 1 10 100 1000 800 600 400 200 0 500 400 300 200 100 0 ∆σw0 ∆σw0

(a) 4 mm circular hole specimen

(b) 10 mm circular hole specimen

Fig. 2.9 Stress distributions for circular hole specimen Location r (mm) St re ss σ (MP a) Location r (mm) St re ss σ (MP a) (KIC) (KIC) σB σB (∆Kth) (∆Kth) ∆σw0 Assumed relationship between ∆Kth and KIC 200MPa 250MPa 300MPa 350MPa 400MPa 450MPa Assumed relationship between ∆Kth and KIC 300MPa 325MPa 350MPa 375MPa 400MPa 600 500 400 300 200 100 0 0.01 0.1 1 100 600 500 400 300 200 100 0 700 0.01 0.1 1 10 100 ∆σw0

2.3.3 ≉

≉ᐃ఩⨨ᛂຊἲࢆ⏝࠸ࡓண ⤖ᯝ

Fig. 2.10 ࡟ 60°࠾ࡼࡧ 120°ࡢ V ᏐษḞࡁࡀ࠶ࡿヨ㦂∦ࡢᐇ㦂⤖ᯝ࡜≉ᐃ఩⨨ᛂຊἲ࡟ࡼࡿண  ⥺ࢆ♧ࡍ㸬ྠᅗ࡟ࡣᖹ⁥ᮦࡢ⑂ປ◚ቯ⤖ᯝࡶཧ⪃ࡋ࡚ేグࡋࡓ㸬⧞㏉ࡋᩘࡀ 100࠿ࡽ 103ࡲ ࡛⦆ࡸ࠿࡟ῶᑡࡋ㸪103࠿ࡽ 106ࡲ࡛ᛴ⃭࡟ῶᑡࡍࡿഴྥࡀࡳࡽࢀࡓ㸬103࠿ࡽ 105పࢧ࢖ࢡࣝ 㡿ᇦ࡟ࡼࡾ⑂ປண ᙉᗘࡣ≉ᐃ఩⨨ᛂຊἲࢆᐇ㦂⤖ᯝࡼࡾࡶᑡࡋ㧗ࡵࡢ್࡜࡞ࡗ࡚࠸ࡿࡀ㸪ࡑ ࡢᕪࡣ10㸣௨ୗ࡟ᢚ࠼ࡽࢀⰋዲ࡞ண ⤖ᯝ࡜ゝ࠼ࡿ㸬ࡋ࠿ࡋ㸪ࡸࡸ༴㝤ഃ࡟ண ࡋࡓ⤖ᯝ࡜࡞ ࡗࡓ㸬  

(a) 60° V-notch specimen Number of cycle to failure Nf

Number of cycle to failure Nf

100 101 102 103 104 105 106 107 100 101 102 103 104 105 106 107 Predicted S-N curve V-notch 60° Smooth specimen Predicted S-N curve V-notch 120° Smooth specimen St res s ran ge σ (MP a) 500 450 400 350 300 250 200 150 100 50 0 120r 500 450 400 350 300 250 200 150 100 50 0 St res s ran ge σ (MP a) 60r

Fig. 2.11 ࡟෇Ꮝ 4 mm ࠾ࡼࡧ 10 mm ࡢヨ㦂∦࡟ᑐࡍࡿᐇ㦂⤖ᯝ࡜㸪≉ᐃ఩⨨ᛂຊἲ࡟ࡼࡿண  ⥺ࢆ♧ࡍ㸬ྠᅗ࡟ࡣᖹ⁥ᮦࡢ⑂ປ◚ቯ⤖ᯝࡶཧ⪃ࡋ࡚ేグࡋࡓ㸬෇Ꮝ4 mm ࡢሙྜ࡟ࡣ⧞㏉ ࡋᩘࡀ100࠿ࡽ104ࡲ࡛⦆ࡸ࠿࡟ῶᑡࡋ㸪104࠿ࡽ105ࡲ࡛ᛴ⃭࡟ῶᑡ㸪105࠿ࡽ106ࡲ࡛⦆ࡸ࠿ ࡟ῶᑡࡋࡓ㸬ࡲࡓ෇Ꮝ10 mm ࡢሙྜ࡟ࡣ⧞㏉ࡋᩘࡀ 100࠿ࡽ103ࡲ࡛⦆ࡸ࠿࡟ῶᑡࡋ㸪103࠿ࡽ 106ࡲ࡛ᛴ⃭࡟ῶᑡࡋࡓ㸬103࠿ࡽ 105పࢧ࢖ࢡࣝ㡿ᇦ࡟ࡘ࠸࡚ࡣ㸪୍㒊㸪ᐇ㦂⤖ᯝ࡜ண ್ࡀ 㞳ࢀ࡚ࡿ࡜ࡇࢁࡀ࠶ࡿࡶࡢࡢ㸪⑂ປண ᙉᗘࡣ≉ᐃ఩⨨ᛂຊἲࢆ⏝࠸࡚Ⰻዲ࡞ண ࢆᚓࡿࡇ࡜ ࡀ࡛ࡁ࡚࠸ࡿ㸬

(a) 4 mm circular hole specimen

(b) 10 mm circular hole specimen

Fig. 2.11 Predicted and experimental by obtained S-N curves for circular hole specimen Number of cycle to failure Nf

100 101 102 103 104 105 106 107 Predicted S-N curve Circle 4 mm Smooth specimen Predicted S-N curve Circle 10 mm Smooth specimen St res s ran ge σ (MP a) St res s ran ge σ (MP a) 500 450 400 350 300 250 200 150 100 50 0 500 450 400 350 300 250 200 150 100 50 0 100 101 102 103 104 105 106 107 Number of cycle to failure Nf

2.4 ≉

≉ᐃ఩⨨ᛂຊἲࡢࣇࣞࢵࢸ࢕ࣥࢢ⑂ປᙉᗘホ౯࡟ᑐࡍࡿ㐺⏝ᛶࡢ᳨ウ

୍⯡࡟ࣇࣞࢵࢸ࢕ࣥࢢ⑂ປࡣ㸪㧗⧞㏉ࡋᩘ㡿ᇦ㸦పᛂຊ᣺ᖜ㸧࡜㸪ప⧞㏉ࡋᩘ㡿ᇦ㸦㧗ᛂຊ ᣺ᖜ㸧ࡢ2 ẁ S-N ᭤⥺ࢆ♧ࡍ㸬ᶵჾࡢᙉᗘタィ࡟㝿ࡋ࡚᭱ࡶᜍࢀࡽࢀ࡚࠸ࡿࡢࡣ๓⪅ࡢ㧗⧞ࡾ ㏉ࡋᩘ㡿ᇦ࡛ࡢ⑂ປᙉᗘ࡛࠶ࡿࡀ㸪ࡇࢀ࡟ࡘ࠸࡚ࡣ㸪᥋ゐ➃ᛂຊ≉␗ሙ࡛ࡢࡁ⿣Ⓨ⏕ᙉᗘࡢண  (24~27)㸪᥋ゐ➃㒊࡟Ⓨ⏕ࡋࡓࡁ⿣ࡢ㐍ᒎ≉ᛶࢆ⏝࠸ࡓࣇࣞࢵࢸ࢕ࣥࢢ⑂ປ㝈ࡢண (27~28)㸪᥋ゐ ➃㒊ࡢᦶ⪖ࢆ⪃៖ࡋࡓ㧗⧞ࡾ㏉ࡋᩘ㡿ᇦࡢࣇࣞࢵࢸ࢕ࣥࢢ⑂ປᙉᗘホ౯ἲ(29~31)ࡀᥦ᱌ࡉࢀ࡚ ࠸ࡿ㸬ࡋ࠿ࡋⓎ㟁ࣉࣛࣥࢺ౑ࢃࢀࡿᅇ㌿ᶵᲔࡢᙉᗘタィ࡟࠾࠸࡚ࡣ㸪㟁ຊ㟂せኚື࡟ᰂ㌾࡟ᑐ

ᛂࡍࡿࡓࡵ㸪DSS(Daily Start Stop)㐠㌿࡟ᑐࡍࡿᛶ⬟ࡶせồࡉࢀࡿࡼ࠺࡟࡞ࡗ࡚ࡁࡓ㸬ࡓ࡜࠼ࡤ㸪

Fig. 2.12 ࡟♧ࡍ࢞ࢫࢱ࣮ࣅࣥື⩼ࡢྲྀ௜ࡅ㒊➼࡛ࡣ㸪⿦⨨ࡢ㉳ື㸪೵Ṇࡢ⧞㏉ࡋ࡟ࡼࡿపࢧ࢖ ࢡࣝ⑂ປ㡿ᇦࡢࣇࣞࢵࢸ࢕ࣥࢢ⑂ປ࡟ᑐࡍࡿᙉᗘホ౯ࡢ㧗⢭ᗘ໬ࢆᅗࡽ࡞ࡅࢀࡤ࡞ࡽ࡞࠸㸬 ࡇࡇ࡛ࡣ㸪ప⧞㏉ࡋᩘ㡿ᇦ࡟࠾ࡅࡿࣇࣞࢵࢸ࢕ࣥࢢ⑂ປᙉᗘࢆ㸪≉ᐃ఩⨨ᛂຊホ౯ἲࢆ⏝࠸ ࡚ண ࡟ࡘ࠸࡚㏙࡭ࡿ㸬ᐇ㦂⤖ᯝ࡟ࡘ࠸࡚ࡣ௨๓㸪ู㏵⾜ࢃࢀࡓࢹ࣮ࢱ(30,31)࡜ẚ㍑ࡋ㸪ࡇࡢ᪉ ἲࡢ㐺⏝ᛶࢆ᳨ウࡋࡓ㸬᥋ゐ➃㏆ഐࡢᛂຊศᕸࡣ㸪Fig. 2.13 ࡟♧ࡍࡼ࠺࡟ᛂຊ≉␗ሙࢆ࿊ࡋ㸪 ᛂຊศᕸࡣ஧ࡘࡢᛂຊ≉␗ሙࣃ࣓࣮ࣛࢱH ࡜ࡑࡢḟᩘȢࢆ⏝࠸࡚㸪᥋ゐ➃࠿ࡽࡢ㊥㞳 r ࡟ᑐࡋ ࡚ḟᘧ࡛⾲ࡉࢀࡿ㸬 O V H /r (2.3)

High cycle fatigue

Low cycle fatigue Time t Str e ss σ

Fig. 2.13 Stress distribution near contact edge ࡇࡇ࡛≉␗ᛶࡢ⛬ᗘࢆ⾲ࢃࡍᣦᩘλ ࡣ㸪Fig. 2.14 ࡟♧ࡍ஫࠸࡟᥋ゐࡍࡿ஧ࡘࡢ≀య 1 ࡜ 2 ࡢ ᥋ゐゅᗘ θ1㸪θ2㸪ࣖࣥࢢ⋡㹃1㸪㹃2㸪࣏࢔ࢯࣥẚ ν1㸪ν2࠾ࡼࡧ᥋ゐ㠃ࡢᦶ᧿ಀᩘμ ࡼࡾゎᯒⓗ ࡟ồࡲࡿ㸬ࡇࡢࡼ࠺࡟ィ⟬ࡉࢀࡓ㹆࡜ λ ࢆ㸪ࡁ⿣Ⓨ⏕㝈⏺ᛂຊ≉␗ሙࡢᙉࡉ HC࡜ẚ㍑ࡍࡿࡇ ࡜࡟ࡼࡾ㸪௵ពࡢ᥋ゐ᮲௳࡟࠾ࡅࡿࣇࣞࢵࢸ࢕ࣥࢢࡁ⿣Ⓨ⏕ࢆண ࡍࡿࡇ࡜ࡀ࡛ࡁࡿࡶࡢ࡜⪃ ࠼ࡓ㸬

Fig. 2.14 Geometry of contact edge and stress singularity parameter

ࡇࡢࡁ⿣Ⓨ⏕㝈⏺ᛂຊ≉␗ሙࡢᙉࡉ HCࢆ㸪ୖグ≉ᐃ఩⨨ᛂຊἲࢆ㐺ᛂࡋ࡚ồࡵ࡚ࡳࡿ࡜㸪

ࡇࡇ࡛ᑐ㇟࡜ࡋࡓNi-Mo-V 㗰ᮦ࡟ࡘ࠸࡚ࡣ㸪ᖹ⁥ᮦࡢ⑂ປ㝈 σw0 = 360 MPa ࡜ࡁ⿣㐍ᒎ㝈⏺ᛂ

ຊᣑ኱ಀᩘ⠊ᅖ∆Kth = 6 MPa·m1/2 ࡀࡍ࡛࡟ᚓࡽࢀ࡚࠾ࡾ(24,25,26)㸪H ࡜Ȣࡢ㛵ಀࡣ Fig. 2.15 ࡟♧

ࡉࢀࡿ㸬

H=f(F)

Intensity of stress singularity H Order of stress singularity Ȣ

Ȫ= H/rȢ St re ss  Ȫ

Distance from the adherent edge r

Contact edge Contact edge Contact Surface P F Frictional coefficient ȣ

F Intensity of stress singularity Order of stress singularity Ȣ=f (E1,E2, ν1,ν2, θ1,θ2,ȣ)

0 0.1 0.2 0.3 0.4 0.5 0

200 400

Fig. 2.15 Fretting fatigue crack initiation criteria using stress singularity parameters derived from critical distance theory

ᩥ⊩(26)࡟ࡼࡿ࡜㸪Fig. 2.16 ࡟♧ࡍ᭷㝈せ⣲ゎᯒࣔࢹࣝ࡟ࡼࡾ㸪᥋ゐ➃ゅᗘࡀ 90°ࡢሙྜ㸪ቃ

⏺㠃࡟ᑐࡋ࡚ゅᗘ65°ࡢ㠃࡟ἢࡗࡓᛂຊ⠊ᅖ ΔσθࡣFig. 2.17 ࡢࡼ࠺࡟ศᕸࡋ࡚࠸ࡿ㸬ࡇࢀࡽࡢ

ࡇࡢྥᛂຊศᕸ࡟࠾ࡅࡿ≉ᐃ఩⨨ࡣ㸪ᘧ(2.1)ࡼࡾ rC = 0.11mm ࡜ồࡵࡽࢀ㸪ࡑࡢ఩⨨ࡢᛂຊ್

ࢆ⏝࠸࡚ࣇࣞࢵࢸ࢕ࣥࢢᙉᗘࢆホ౯ࡍࡿ㸬

Fig. 2.16 Contact model for initiation of fretting fatigue crack Line method

Point method

Order of stress singularity Ȣ

In te ns ity o f st re ss si ngu la ri ty H Contact pressure P Contact edge Axial load σa Pad Contact surface Specimen

Fig. 2.17 Calculated stress distributions near the contact edge (σa㸻100 MPa, Wedge angle 90°)

ࡇࡢ≉ᐃ఩⨨ᛂຊἲ࡟ࡘ࠸࡚࣮࢜ࢲ࣮ࡀ 105⛬ᗘࡢప⧞㏉ࡋᩘ㡿ᇦࡢࣇࣞࢵࢸ࢕ࣥࢢ⑂ປᙉ ᗘ࣭ᑑ࿨ホ౯࡬ࡢ㐺⏝ᛶࢆ᳨ウࡋࡓ㸬ᐇ㦂࡛⏝࠸ࡓࣇࣞࢵࢸ࢕ࣥࢢ⑂ປヨ㦂἞ලࢆFig. 2.18 ࡟ ♧ࡍ㸬ヨ㦂∦ࡣཌࡉ20 mm㸪ᖜࡣ 10 mm ࡛㸪ࣃࢵࢻࡣ 10 mm ᖜࡢ㠃࡟ᡤᐃࡢᅽຊ࡛ᢲࡋ௜ࡅ ࡽࢀ࡚࠸ࡿ㸬 ప⧞㏉ࡋᩘ㡿ᇦ࡟࠾࠸࡚ࡣ㸪ᦶ⪖࡟ࡼࡿᙧ≧ኚ໬ࢆ⪃៖ࡍࡿᚲせࡀ࡞࠸ࡓࡵ㸪㒊ရ࡝࠺ࡋࡢ ᥋ゐึᮇ࡟࠾ࡅࡿᛂຊศᕸࢆィ⟬ࡍࡿࡇ࡜࡟ࡼࡗ࡚๓⠇࡜ྠᵝࡢ᪉ἲ࡛⑂ປᙉᗘࡀホ౯࡛ࡁ ࡿ. ᩥ⊩(24~26)ࡼࡾFig. 2.19 ࡟ヨ㦂࡟⏝࠸ࡓ Ni-Mo-V 㗰ࡢᖹ⁥ᮦ S-N ᭤⥺(R= -1) ࢆ♧ࡍ㸬ࡲࡓ㸪 Fig. 2.20 ࡟ྠᮦࡢ⑂ປࡁ⿣㐍ᒎ≉ᛶࢆ♧ࡍ㸬ࡇࢀࡽࡢᶵᲔⓗ≉ᛶࡼࡾ㸪ࡇࡢᮦᩱࡢྛࠎࡢ≉ᐃ ఩⨨ࡣࡑࢀࡒࢀrC = 0.011 mm and rC’= 2.13 mm ࡜ồࡲࡿ㸬ࡇࢀࡽࡢ≉ᐃ఩⨨࡜ࡑࢀ࡟ᑐᛂࡍࡿ ᛂຊࢆFig. 2.21 ࡟ࣉࣟࢵࢺࡋ࡚㸪୧Ⅼࢆ┤⥺࡛⤖ࢇࡔ㸬 ࡘࡂ࡟㸪᭷㝈せ⣲ἲ࡛ゅᗘ65rࡢ㠃࡟ἢࡗ࡚ᘬᙇᛂຊ σa=200 MPa ࢆィ⟬ࡋࡓ㸬ᛂຊศᕸࢆ Fig.2.21 ࡟◚⥺࡛♧ࡍ㸬ࡇࡢ◚⥺࡜ 2 Ⅼࢆ⤖ࢇࡔ┤⥺ࡢ஺Ⅼ࠿ࡽ㸪ᛂຊࡣ 490 MPa㸪≉ᐃ఩⨨ ࡣ0.12 mm ࡜ᐃࡲࡿ㸬ࡉࡽ࡟ Fig. 2.19 ࠿ࡽ 490 MPa ࡟ᑐࡍࡿ⑂ປᑑ࿨ࡣ 105࡜ㄞࡳྲྀࡿࡇ࡜ࡀ ࡛ࡁ㸪ࡇࡢ࡜ࡁ୚࠼ࡓᘬᙇᛂຊσa=200 MPa ࡜㸪⑂ປᑑ࿨ 105ࡢⅬࢆFig. 2.22 ࡟ࣉࣟࢵࢺࡍࡿ㸬 ࡉࡽ࡟㸪ูࡢ σaࡢ್࡛ྠᵝ࡟ᛂຊศᕸࢆồࡵ㸪ࡇࡢ࡜ࡁ୚࠼ࡓ σa࡜ࡑࡢᛂຊ࡟ᑐᛂࡍࡿ⑂ປ ᑑ࿨ࡢⅬࢆࣉࣟࢵࢺࡍࡿ㸬ࡇࢀࡽࡢ2 Ⅼࢆ┤⥺࡛⤖ࡧ㸪Fig. 2.22 ࡢపࢧ࢖ࢡࣝ㡿ᇦ࡟◚⥺࡟♧ ࡍ㸬ྠᅗ࡟࠾࠸࡚ࡣ㸪ᐇ㦂⤖ᯝࡢഴྥࢆண ࡛ࡁ࡚࠾ࡾ㸪ࡸࡸ㐣ᑠᛂຊ࡟ホ౯ࡍࡿഴྥࡀ࠶ࡿ ࡀ㸪ᥦ᱌ࡋࡓ≉ᐃ఩⨨ᛂຊἲࢆ⏝࠸ࡓࣇࣞࢵࢸ࢕ࣥࢢ⑂ປᑑ࿨ホ౯ࡢጇᙜᛶࡀ☜ㄆ࡛ࡁࡓ㸬ྠ ᅗ࡟ࡣ㸪௨๓࡟⾜ࢃࢀࡓᩥ⊩(26~31)࠿ࡽࣇࣞࢵࢸ࢕ࣥࢢᦶ⪖ࢆ⪃៖ࡋࡓ࡜ࡁ࡜ࡋ࡞࠸࡜ࡁࡢ㧗ࢧ ࢖ࢡࣝ㡿ᇦࡢS-N ᭤⥺㸦୍Ⅼ㙐⥺࠾ࡼࡧ஧Ⅼ㙐⥺㸧ࡶేグࡋ࡚࠸ࡿ㸬 σa σa

Distance from the adherent edge r (mm)

St re ss Ȫ (MP a)

Fig. 2.18 Fretting fatigue test apparatus

103 104 105 106 107 108

100 1000

Fig. 2.19 S-N Curve of Ni-Mo-V steel smooth specimen

Estimated cycle to failure

Number of cycle to failure Nf

St res s ran ge σa (MP a) σB = 705 MPa ∆σw0 = 360 MPa Specimen

Pad Strain gage B

Screw Press plate Strain gage A 20 10 10 40

1 10 100 10−12

10−10 10−8 10−6

Fig. 2.20 Crack propagation rate of Ni-Mo-V steel

0.01 0.1 1 10

100 1000

Fig. 2.21 Derivation of specific distance in low cycle fatigue region and estimation of low cycle fretting fatigue life fatigue

Crac k pro pa gat io n ra te da /d N, m /c ycl e

Stress intensity factor range ∆K, MPa·m1/2 da/dN=C(∆K)m R=0 St re ss σ (M Pa ) Distance r (mm) σa = 200 MPa σB (KIC) (∆Kth) ∆σw0 705 360 1000 100 Stress distribution obtained by FEM 0.01 0.1 1 10

103 ₁₀4 ₁₀5 ₁₀6 ₁₀7 ₁₀8

100 500 1000

Number of cycles to failure N_f

S tr e s s am pl it u de σa ( M pa) Plane specimen

Fretting (Low cycle)

Fretting (Ultra high cycle)

Experimental Smooth specimen

Fig. 2.22 Estimated and experimental fretting fatigue S-N Curves a: Prediction from(30,31) b: Prediction from(30,31)

2.5 ⤖

⤖

ゝ

ᛂຊ㞟୰㒊఩ࡢపࢧ࢖ࢡࣝ⑂ປ࡟ᑐࡍࡿ≉ᐃ఩⨨ᙉᗘホ౯ἲࡢ㐺⏝ᛶࢆ᳨ウࡋࡓ㸬௦⾲ⓗ࡞ ୍⯡ᅽᘏ㗰ᮦSS400 ࢆ౪ヨᮦ࡜ࡋ㸪ᖹ⁥ᮦヨ㦂∦࡜ྠヨ㦂∦࡟ V ᏐษḞࡁࢆ୧ഃ࡟௜୚ࡋࡓࡶ ࡢ㸪෇Ꮝࢆ୰ኸ࡟௜୚ࡋࡓࡶࡢࡢ⑂ປヨ㦂⤖ᯝࢆᚓ࡚㸪≉ᐃ఩⨨ᛂຊἲ࡟ࡼࡿᙉᗘண ⤖ᯝ࡜ ẚ㍑ࡋࡓ㸬ࡉࡽ࡟ప⧞㏉ࡋᩘ㡿ᇦࡢࣇࣞࢵࢸ࢕ࣥࢢ⑂ປᙉᗘ࡟ᑐࡍࡿ≉ᐃ఩⨨ᛂຊἲࡢ㐺⏝ᛶ ࡟ࡘ࠸࡚ࡶண ⢭ᗘࢆ᳨ドࡋ㸪௨ୗࡢ⤖ㄽࢆᚓࡓ㸬 (1) ᖹ⁥ᮦࡢ⑂ປ㝈࡜㸪ࡁ⿣㐍ᒎୗ㝈⏺ᛂຊᣑ኱ಀᩘ⠊ᅖ࠿ࡽᐃࡲࡿ⑂ປ㝈࡟ᑐࡍࡿ≉ᐃ఩⨨㸪 ࠾ࡼࡧ◚᩿ᙉᗘ࡜㸪◚ቯ㠌ᛶ್࠿ࡽᐃࡲࡿ㟼ⓗᙉᗘ࡟ᑐࡍࡿ≉ᐃ఩⨨ࡢ୧Ⅼࢆ┤⥺࡛⤖ࡧ㸪 ప⧞㏉ࡋᩘ㡿ᇦࡢ⑂ປᙉᗘࡣࡇࡢ┤⥺ୖ࡟࠶ࡿ࡜௬ᐃࡋ㸪᭷㝈せ⣲ἲ࡟ࡼࡿᛂຊศᕸࢆ฼ ⏝ࡍࡿ≉ᐃ఩⨨ᙉᗘホ౯ἲࢆᥦ᱌ࡋࡓ㸬 (2) ࣮࢜ࢲ࣮ࡀ 103 㹼 105ࡢపࢧ࢖ࢡࣝᇦ⑂ປᙉᗘ࡟ࡘ࠸࡚㸪V ᏐษḞࡁ௜ࡁヨ㦂∦࡟࠾ࡅࡿ ᐇ㦂್ࡣ㸪ண ್ࡼࡾ10 %⛬ᗘప࠸ᛂຊ್࡜࡞ࡗࡓ㸬ᐇ㦂್࡜ࡢᕪࡣண ⢭ᗘ࡜ࡋ࡚ࡣ࡯ ࡰ༑ศ࡜⪃࠼ࡿࡀ㸪ᐇ㝿ࡢタィ࡟㐺⏝ࡍࡿሙྜ㸪ࡸࡸ༴㝤ഃࢆண ࡋ࡚࠸ࡿ࡜࠸࠺Ⅼࢆ⪃ ៖ࡋ࡚㐺⏝ࡍ࡭ࡁ࡛࠶ࡿ࡜ゝ࠼ࡿ㸬 (3) ୍᪉㸪෇Ꮝ௜ࡁヨ㦂∦࡟࠾࠸࡚ࡣ㸪ண ᛂຊ್ࡣᐇ㦂್ࡼࡾࡶࡸࡸపࡃ㸪ࡑࡢᕪࡶ 10 %௨ ෆ࡛࠶ࡗࡓ㸬ᙉᗘࢆᏳ඲ഃ࡟ண ࡛ࡁ࡚࠸ࡿ࡜࠸࠺Ⅼ࡛ࡣ㸪V ᏐษḞࡁᙧ≧࡟ẚ࡭࡚Ⰻዲ ࡞ண ࡀ࡛ࡁࡓ㸬 (4) ప⧞㏉ࡋᩘ㡿ᇦࡢࣇࣞࢵࢸ࢕ࣥࢢ⑂ປᙉᗘ࡟ᑐࡍࡿ≉ᐃ఩⨨ᛂຊἲࡢ㐺⏝ᛶ࡟ࡘ࠸࡚ࡣ㸪 Number of cycles to failure Nf

St re ss a m pl itud e σa (MP a) (a) (b)

   

➨

➨

3 ❶ ≉ᐃ఩⨨ᛂຊࢆ⏝࠸ࡓ

ᚤᑠࡁ⿣㒊ᮦࡢ⑂ປᙉᗘホ౯ἲ

3.1 ⥴ ゝ

➨ 2 ❶࡛ࡣ㸪ྲྀࡾᢅ࠸ࡀ⡆౽࡞ Point method ࡟╔┠ࡋ㸪෇Ꮝ㸪ษḞࡁ࡟ࡘ࠸࡚≉ᐃ఩⨨ ᛂຊἲ࡛⑂ປ㝈ࢆண ࡍࡿ᪉ἲࢆᥦ᱌ࡋ㸪ࡑࡢ᭷ຠᛶࢆ᳨ウࡋ࡚ࡁࡓ㸬ᮏ❶࡛ࡣ㸪ᚤᑠࡁ ⿣㒊࡟㛵ࡋ࡚ྠᵝ࡞≉ᐃ఩⨨ᛂຊホ౯ἲ࡟㸪ࡁ⿣ᮦࡢFEM ゎᯒ࡛ᚓࡽࢀࡓ≉ᐃ఩⨨࡛ࡢᛂ ຊ್ࢆ⏝࠸ࡿ⡆౽࡞ண ἲࡢ㐺⏝ᛶࢆ♧ࡍࡇ࡜ࢆ┠ⓗ࡜ࡋ㸪㕲㗰ᮦᩱSS400 ࡜ SKS93 ࢆ౪ ヨᮦ࡜ࡋ࡚ᐇ㦂ⓗ࡟᳨ド㸪ᚑ᮶ἲ࡟ࡼࡿண ࡜ࡶẚ㍑ࡋࡓ㸬ᶵᲔ㒊ရࡸᵓ㐀≀࡟㢖⏝ࡉࢀ ࡿᮦᩱ࡜ࡋ࡚㸪ᮏ◊✲࡛ࡣ◚ቯ㠌ᛶ್ࡸ S-N ≉ᛶࡀ␗࡞ࡿᵓ㐀⏝ᅽᘏ㗰ᯈ SS400 ࠾ࡼࡧྜ 㔠ᕤල㗰SKS93 ࢆ㑅ᐃࡋࡓ㸬

3.2 ᚑ᮶ࡢ⑂ປ㝈ண ἲ

⥺ᙧ◚ቯຊᏛ࡟ࡼࡾ㸪ᛂຊᣑ኱ಀᩘࢆ⏝࠸࡚ࡁ⿣ࡢⓎ⏕ࡸᡂ㛗ࢆホ౯ࡍࡿ࡜ࡁ㸪㠃ෆ㛤 ཱྀᙧࡢ᭷㝈ᑍἲࡁ⿣ᵓ㐀࡟ᑐࡍࡿᛂຊᣑ኱ಀᩘ KIࡣ㸪ḟᘧ࡛♧ࡉࢀࡿ㸬             KϨ V Sa˜F([) ࡇࡇ࡛⿵ṇ㡯 F(ξ)ࡣ㸪୍ᵝᘬᙇᛂຊ㈇Ⲵࡢ∦ഃࡁ⿣ᮦ࡟㛵ࡍࡿ↓ḟඖ㔞 ξ ࡟ࡼࡾỴࡲࡿ ⿵ṇಀᩘ࡛㸪ヨ㦂∦ᖜW ࡟ᑐࡍࡿ┦ᑐࡁ⿣㛗ࡉ ξ = a / W ࢆ⏝࠸࡚ィ⟬ࡉࢀࡿ(5㹼7)_㸬      

c o s

2

2

s i n

1

199

.

0

923

.

0

2

tan

2

)

(

4

S[

S[

S[

S[

[

¸

¹

·

¨

©

§ 



F

         ࡋ࠿ࡋࡇࡢ⥺ᙧ◚ቯຊᏛ࡟ࡼࡿ⑂ປ㝈ண ࡟࠾࠸࡚ࡣ㸪ᚤᑠࡁ⿣㡿ᇦ࡟࡞ࡿ࡜ᖹ⁥ᮦࡢ ⑂ປ㝈Δσw0ࡼࡾࡶ㧗ࡃ࡞ࡿ࡜࠸࠺୙㒔ྜࡀ⏕ࡌ࡚ࡋࡲ࠺㸬 ࡇࡢၥ㢟ࢆపῶࡍࡿࡓࡵࡢ⑂ປ㝈ண ἲ࡜ࡋ࡚㸪El Haddad ࡢ᪉ἲࡀᗈࡃ⏝࠸ࡽࢀ࡚࠸ࡿ㸬 ࡇࡢண ἲࡣ㸪᭱ึ࠿ࡽᮦᩱ࡟ࡣ₯ᅾⓗ࡟Ḟ㝗 a0ࡀᏑᅾࡋ࡚࠸ࡿࡶࡢ࡜௬ᐃࡋ㸪ᐇ㝿ࡢࡁ ⿣㛗ࡉa ࡢ௦ࢃࡾ࡟( a + a0 )ࢆࡁ⿣㛗ࡉ࡜ࡋ࡚㸪௨ୗࡢᘧ࡛⾲ࡉࢀࡿ◚ቯຊᏛⓗᙉᗘホ౯ἲ ࡛࠶ࡿ(10)㸬         V_E

Δ

K_th/ S(aa₀)       ࡁ⿣㛗ࡉa ࢆ 0 ࡟₞㏆ࡍࡿ࡜㸪⑂ປ㝈ࡣ Δσw0࡟₞㏆ࡍࡿࡇ࡜࠿ࡽa0ࡣḟᘧ࡛♧ࡉࢀࡿ㸬            2 0 0 1 ¸¸ ¹ · ¨¨ © § w th K a

V

S

ԥ ԥ ࡇࡢண ᘧࡣ㸪ࡁ⿣㛗ࡉ a ࡀ₯ᅾⓗḞ㝗㛗ࡉ a0࡜ẚ࡭࡚ᑠࡉ࠸ሙྜ㸪ᙉᗘホ౯࡟ࡣ㠀ᖖ ࡟኱ࡁ࡞ᙳ㡪ࢆ୚࠼㸪a ࡀ a0ࡼࡾ༑ศ㛗࠸ሙྜࡣᙉᗘホ౯࡟ᙳ㡪ࡀ࡯࡜ࢇ࡝࡞࠸ࡶࡢ࡛࠶ ࡿ㸬 ୍⯡࡟ࡇࡢࡼ࠺࡞ࡁ⿣ࢆ᭷ࡍࡿ㒊ᮦࡢ⑂ປ㝈㸦⪏ஂ㝈㸧ࡢண ࡣ㸪ୖグ࡛ィ⟬ࡉࢀࡓᛂ ຊᣑ኱ಀᩘࡢ⠊ᅖ ΔK ࡀ㸪ᮦᩱ≉᭷ࡢࡁ⿣㐍ᒎୗ㝈⏺ᛂຊᣑ኱ಀᩘ⠊ᅖ ΔKth࡟⮳ࡗࡓ࡜ࡁ (3.1) (3.2) (3.4) (3.3)

Δ

Δ

   

3.3 FEM ゎ

ゎᯒ࡟ࡼࡿᛂຊศᕸࢆ฼⏝ࡍࡿ⑂ປ㝈ண ἲ

ࡇࡇ࡛ࡣᮏ◊✲࡛ᥦ᱌ࡍࡿ᪉ἲ࡟ࡘ࠸࡚㏙࡭ࡿ㸬 Fig. 3.1 ࡟♧ࡍࡼ࠺࡟㸪ᙎᛶ FEM ゎᯒ࡛ᮦᩱࢆ⥺ᙧᙎᛶయ࡜௬ᐃࡋ࡚ᚓࡽࢀࡓᛂຊศᕸ ࡟ᇶ࡙࠸࡚㸪⑂ປ㝈ࡢண ࢆ⾜࠺᪉ἲࢆ௨ୗ࡟㏙࡭ࡿ㸬 ࡲࡎ≉ᐃ఩⨨ rCࢆỴᐃࡍࡿᚲせࡀ࠶ࡾ㸪ࡇࢀࡣ༑ศ㛗࠸ࡁ⿣ᮦࡢࡁ⿣㐍ᒎ㝈 ΔKth࡜ࡑࡢᮦ ᩱࡢᖹ⁥ᮦࡢ⑂ປ㝈Δσw0ࡼࡾḟᘧ࡛ồࡵࡿࡇ࡜ࡀ࡛ࡁࡿ㸬        2 2 1 ¸¸ ¹ · ¨¨ © § ' ' wo th c K r

V

S

_{                        } ࡘࡂ࡟ᡤᐃࡢࡁ⿣㛗ࡉࢆタᐃࡋࡓ㒊ᮦ࡟ࡘ࠸࡚㸪ᘬᙇ㈇Ⲵ࡜ࡋ࡚ᛂຊ᣺ᖜ σn ࢆタᐃࡋ࡚ ᙎᛶᘬᙇኚᙧࡢ FEM ゎᯒࢆ⾜࠸㸪ࡁ⿣ඛ➃ᘏ㛗⥺ୖࡢ≉ᐃ఩⨨ rC࡟࠾ࡅࡿᛂຊ σ ࢆồࡵ ࡿ㸬Point method ࡛ࡣ㸪ᖹ⁥ᮦࡢ⑂ປ㝈 Δσw0࡜≉ᐃ఩⨨ rC࡜ࡢ஺Ⅼ࡟ᛂຊศᕸ᭤⥺ࢆ୍⮴ ࡉࡏࡿ᫬ࡢᛂຊ⠊ᅖࢆࡁ⿣ᮦࡢ⑂ປ㝈࡜ᐃࡵ࡚࠸ࡿ㸬ࡼࡗ࡚㸪ࡇࡢ࡜ࡁ≉ᐃ㒊ᮦ࡟୚࠼ࡓ ᖹᆒᛂຊσn࡟≉ᐃ఩⨨ࡢᛂຊσ ࡟ᑐࡍࡿᖹ⁥ᮦࡢ⑂ປ㝈 Δσw0ࡢẚࢆ஌ࡌ࡚㸪ᡤᐃࡁ⿣㛗ࡉ ࡢ㒊ᮦࡢ⑂ປ㝈σwࡢண ್ࢆᚓࡿ㸬    

V

V

V

V

w0 n w ԥ               

r

c

Distance from crack

Stress distribution

Prediction by FEM

Magnified by

ԥ

σ

w0

/ σ

ԥ

σ

w0

σ

(3.5) (3.6)

r

C

Distance from crack tip

Stress distribution

Prediction by FEM

Magnified by

Δ Δ

Δσ

w0

/

σ

Δσw0 σ

St

re

ss

   

3.4 ≉

≉ᐃ఩⨨ᛂຊἲࢆ⏝࠸ࡓ⑂ປᙉᗘホ౯ἲࡢ᳨ド

ࡣࡌࡵ࡟≉ᐃ఩⨨ rCࢆồࡵࡿࡓࡵᖹ⁥ᮦ࠾ࡼࡧࡁ⿣ᮦࡢ⑂ປヨ㦂ࢆ⾜ࡗࡓ㸬ࡘࡂ࡟ࡁ⿣ ᮦࡢᘬᙇ㈇ⲴୗࡢFEM ゎᯒ࡛⾜࠸ᛂຊศᕸࢆồࡵ㸪ணࡁ⿣ᮦࡢ⑂ປ㝈ᗘࢆண ࡋ㸪ᚑ᮶ண  ἲ࡜ࡶẚ㍑ࡋᮏண ἲࡢ⢭ᗘࢆ᳨ドࡋࡓ㸬

3.4.1 ᐇ㦂᪉ἲ࠾ࡼࡧᐇ㦂᮲௳

⑂ປヨ㦂࡟⏝࠸ࡓᖹ⁥ᮦヨ㦂∦ࡢᑍἲࡣ㸪ᖜ 30 mm㸪ᖹ⾜㒊㛗ࡉ 100 mm㸪ᯈཌࡉ 5mm ࡛࠶ࡿ㸬ࡁ⿣㐍ᒎୗ㝈⏺ᛂຊᣑ኱ಀᩘΔKthࢆồࡵࡿࡓࡵ㸪Fig. 3.2 ࡟♧ࡍ∦ഃ࡟ࡁ⿣ࢆ⏕ࡌ ࡉࡏࡓヨ㦂∦ࢆ⏝࠸ࡓ㸬 ᚤᑠࡁ⿣ヨ㦂∦ࡢ〇స᪉ἲࢆ㏙࡭ࡿ㸬ࡣࡌࡵ࡟ᖜ 32 mm ࡢᖹ⁥ヨ㦂∦ࡢ∦ഃ࡟㛗ࡉ 2 mm ࡢ▴ᙧ≧ࢫࣜࢵࢺࢆ࣡࢖࣮ࣖᨺ㟁ຍᕤᶵ࡛ຍᕤࡋ࡚࠾ࡁ㸪ࡇࢀ࡟᭱኱ᘬᙇᛂຊ 200 MPa ࡢ 20 Hz ࡢᘬᙇṇᘻἼࢆ୚࠼࡚ࡁ⿣ࢆ⏕ࡌࡉࡏ㸪ᛂຊࢆ㐺ᐅᑠࡉࡃࡋ࡞ࡀࡽࡁ⿣ࢆ㐍 ᒎࡉࡏࡓ㸬ࡑࡢᚋ㸪ྠᅗ࡟♧ࡍࡼ࠺࡟タᐃࡋࡓ࠸ࡁ⿣㛗ࡉ a ࡟࡞ࡿࡼ࠺࡟࣡࢖࣮ࣖᨺ㟁ຍ ᕤ࡛ࢫࣜࢵࢺഃࢆษ᩿ࡋ㸪඲యࡢᖜࡀ28 mm ࡟࡞ࡿࡼ࠺࡟཯ᑐഃࢆຍᕤࡋ∦ഃࡁ⿣ヨ㦂∦ ࢆ〇సࡋࡓ㸬 ∦ഃࡁ⿣ヨ㦂∦ࡣ㸪ヨ㦂᮲௳࡜ࡋ࡚㸪Ⲵ㔜ไᚚ࡛ᛂຊẚ R: 0 ࡢṇᘻἼࢆ⧞㏉ࡋ㏿ᗘ f : 20Hz ࡛୚࠼ࡓ㸬2 ✀㢮ࡢ㕲㗰ᮦᩱ SS400 ࠾ࡼࡧ SKS93 ࡛ヨ㦂∦ࢆ〇సࡋࡓ㸬⧞㏉ࡋᩘ 1×107ᅇ࡟㐩ࡍࡿ᭱኱ࡢᛂຊࢆ⑂ປ㝈࡜ࡋࡓྛᮦᩱࡢᶵᲔⓗ≉ᛶࢆTable 3.1 ࡟♧ࡍ㸬

Fig. 3.2 Single - small -crack specimen Table 3.1 Mechanical properties of steels used

Material SS400 SKS93

Young’s modulus 206 GPa 210 GPa

Poisson’s ratio 0.30 0.30

Ultimate tensile strength: σB 448 MPa 543 MPa

Fatigue limit: Δσw0 305 MPa 342 MPa

   

3.4.2 ᐇ

ᐇ㦂⤖ᯝ࠾ࡼࡧ≉ᐃ఩⨨ࡢỴᐃ

SS400 ࠾ࡼࡧ SKS93 ࡢ⑂ປࡁ⿣㐍ᒎヨ㦂ࡢ⤖ᯝࢆ Fig. 3.3 ࡟♧ࡍ㸬ᅗ୰ࡢ○༳ࡣࢢࣜࢵࢺ 㛫㝸0.1 mm ࡢࢡࣛࢵࢡࢤ࣮ࢪ(ඹ࿴㟁ᴗ〇㸪KV - 5C)ࢆ⏝࠸࡚ ΔK ₞ῶヨ㦂ࢆ⾜ࡗࡓ⤖ᯝ࡛ ࠶ࡿ㸬ࡲࡓᇞ࡜□༳ࡣ㸪ࢢࣜࢵࢺ㛫㝸 0.1 mm ࡜ 1 mm ࡢࢡࣛࢵࢡࢤ࣮ࢪ(ྠ♫〇㸪KV - 25B) ࢆ⏝࠸࡚᣺ᖜⲴ㔜ࢆ୍ᐃ࡜ࡋࡓ᫬ࡢࡁ⿣㐍ᒎヨ㦂ࡢ⤖ᯝࢆ⾲ࡍ㸬 ࡇࡢᅗ࠿ࡽ㸪୧ᮦᩱ࡜ࡶᛂຊᣑ኱ಀᩘ⠊ᅖࡀ኱ࡁ࠸⠊ᅖ࡛ࡣParis ๎㸸           da/dN c'Km    (3.7) ࡟ᚑ࠺┤⥺㛵ಀࡀ⌧ࢀ࡚࠸ࡿ㸬SS400 ࡛ࡣ㸪ࡁ⿣㐍ᒎ㏿ᗘࡣᛂຊᣑ኱ಀᩘ⠊ᅖࡀ⣙ 8 MPa·m1/2௨ୗ࡟࡞ࡿ࡜ᛴ࡟పࡃ࡞ࡾ㸪ᛂຊᣑ኱ಀᩘ⠊ᅖࡀ 6.7 MPa·m1/2௨ୗ࡛ࡣ㸪ࡁ⿣ࡢ 㐍ᒎࡣぢࡽࢀ࡞ࡃ࡞ࡗࡓ㸬ࡋࡓࡀࡗ࡚ SS400 ࡟ᑐࡍࡿࡁ⿣㐍ᒎୗ㝈⏺ᛂຊᣑ኱ಀᩘ⠊ᅖ ΔKthࡣ6.7 MPa·m1/2࡜ࡋࡓ㸬ྠᵝ࡟㸪SKS93 ࡟ࡘ࠸࡚ࡣ 8.1 MPa·m1/2࡜ᐃࡲࡗࡓ㸬 ࡘࡂ࡟≉ᐃ఩⨨ࡢỴᐃ࡟ࡘ࠸࡚㏙࡭ࡿ㸬Table 3.2 ࡟ᖹ⁥ヨ㦂∦ࢆ⏝࠸࡚ồࡵࡓ⑂ປ㝈 Δσw0㸪ࡁ⿣ヨ㦂ࢆ⏝࠸࡚ồࡵࡓࡁ⿣㐍ᒎ㝈⏺ᛂຊᣑ኱ಀᩘ⠊ᅖ ΔKthࢆᘧ(4)࡜(5)࡟௦ධࡍࡿ ࡜㸪ྛᮦᩱࡢ≉ᐃ఩⨨rC࡜El Haddad ࡢ₯ᅾࡁ⿣㛗ࡉ a0ࡀTable 3.2 ࡢࡼ࠺࡟ồࡵࡽࢀࡿ㸬

Table 3.2 Critical distance and potential crack length

Material SS400 SKS93

Critical distance rC 0.077 mm 0.089 mm Potential crack length a0 0.154 mm 0.179 mm

    10-4 10-5 10-6 10-7 䕕 ԥσ=Const 䕿 ԥK- Decreasingprocedure 100 ₁₀1 ₁₀2 10-4 10-5 10-6 10-7 䕕 ԥσ=Const 䕿 ԥK- Decreasingprocedure 100 ₁₀1 ₁₀2 1 2 3 4 5 678910 20 30 405060708090100 10−10 10−8 10−6 10−4 100 ₁₀1 ₁₀2 10-4 10-5 10-6 10-7 10-8 10-9 10-10 10-11

䕿 䠣䡎䡅䡀 interval 0.1mm䠈K-decreasing procedure

䕕 䠣䡎䡅䡀 interval 1mm䠈ԥσ = const

ڹ 䠣䡎䡅䡀 interval 0.1mm䠈ԥσ = const

(a) Material: SS400

  (b) Material: SKS93

Stress intensity factor range ΔK (MPa㺃m1/2) Fatigue crack growth ra te da/dN (mm/cycle)

Stress intensity factor range ΔK (MPa㺃m1/2)

Fatigue crack growth r

ate

da/dN

(mm/cycle)

Grid interval 0.1 mm, ΔK-decreasing procedure

Grid interval 1 mm, Δσ = Const

Δσ = Const

ΔK-decreasing procedure

Grid interval 0.1 mm, Δσ = Const

10-4

10-5

10-6

10-7

   

3.4.3 FEM ゎᯒ࡟ࡼࡿᛂຊศᕸࡢỴᐃ

⥺ᙧ◚ቯຊᏛ࡛ᑟ࠿ࢀࡿᛂຊศᕸ࡜ẚ㍑ࡍࡿࡓࡵ㸪Fig. 3.2 ࡜ྠ➼࡞ Fig. 3.4 ࡟♧ࡍࡁ⿣ ᵓ㐀FEM ゎᯒࣔࢹࣝࢆ⏝࠸࡚㸪ᛂຊゎᯒࢆ⾜ࡗࡓ㸬ゎᯒ᮲௳࡜ࡋ࡚㸪ᮦᩱࡣ⥺ᙧᙎᛶయࢆ ௬ᐃࡋ㸪せ⣲ࢱ࢖ࣉࡣ 2 ḟඖ 8 ⠇Ⅼᅄゅᙧ 2 ḟせ⣲࡜ࡋ㸪ᖹ㠃ᛂຊ࡛ィ⟬ࡋࡓ㸬ᯈࡢཌࡉ ࡣ5 mm㸪࣓ࢵࢩࣗࢧ࢖ࢬ࡜ࡋ࡚ࡢ 1 ㎶ࡢ㛗ࡉࡣ 0.01 mm ࡛࠶ࡿ㸬ྛᮦᩱࡢࣖࣥࢢ⋡࡜࣏࢔ ࢯࣥẚࡣ⾲1 ࡢ್ࢆタᐃࡋࡓ㸬Fig. 3.5 ࡟ࡁ⿣㛗ࡉ a = 0.10 mm(ᚤᑠࡁ⿣㸧㸪ࡁ⿣㛗ࡉ a = 5 mm(㛗ࡁ⿣)࡟ࡘ࠸࡚ FEM ࡟ࡼࡿᛂຊศᕸ࡜⥺ᙧ◚ቯຊᏛ࠿ࡽィ⟬ࡋࡓࡶࡢࢆ♧ࡍ㸬ࡇࢀ ࡽࡢᛂຊศᕸࢆẚ㍑ࡍࡿ࡜㸪≉࡟ᚤᑠࡁ⿣ࡢሙྜ࡟ࡣࡁ⿣ඛ➃ࡈࡃ㏆ഐ(r < 0.02 mm)࡛ࡣⰋ ࠸୍⮴ࢆぢࡿࡀ㸪ࡑࢀࢆ㉸࠼ࡓ⠊ᅖ࡛ࡣ㸪⥺ᙧ◚ቯຊᏛ࡛ィ⟬ࡋࡓᛂຊศᕸࡣFEM ᛂຊゎ ᯒ⤖ᯝ࡜ẚ㍑ࡋ࡚࠿࡞ࡾపࡃ࡞ࡾ㸪ࡑࡢᕪࡣࡁ⿣ඛ➃࠿ࡽࡢ㊥㞳࡜࡜ࡶ࡟ᣑ኱ࡋ0.1 mm ௜ ㏆࡛ࡣ⣙༙ศࡢ್ࢆ♧ࡋ࡚࠸ࡿ㸬ࡇࢀࡣᑠつᶍ㝆అ᮲௳ࢆ‶ࡓࡉ࡞࠸࡜㐺⏝࡛ࡁ࡞࠸⥺ᙧ ◚ቯຊᏛࡢၥ㢟Ⅼࢆ෌☜ㄆࡋࡓࡶࡢ࡛࠶ࡾ㸪๓❶࡛㏙࡭ࡓண ἲࡢಟṇࡢᚲせᛶࡀ⌮ゎ࡛ ࡁࡿ㸬 㻞㻤 㻝㻞㻜㻌

Fig. 3.4 Finite element model with small crack a



28

    0 0.1 0 100 200 0 0.02 0.04 0.06 0.08 0.1 200 Distance r (mm) S tr ess σ (M P a) 100

Linear fracture mechanics FEM 0 (a) a: 0.10 mm , σ: 100 MPa 0 0.1 0 500 1000 1500

Linear fracture mechanics FEM 500 1000 1500 0 0.02 0.04 0.06 0.08 0.1 S tr ess σ (MPa ) Distance r (mm) 0 (b) a: 5 mm , σ:100 MPa

    5 10 15 [u10+6_] 300 310 320 330

3.4.4 ≉ᐃ఩⨨ᛂຊἲ࡟ࡼࡿホ౯ࡢ᳨ド

ᮏ❶࡛ᥦ᱌ࡍࡿ≉ᐃ఩⨨ᛂຊホ౯ἲࡣ㸪ࡁ⿣㛗ࡉ0.10㸪0.50㸪1.00㸪5.00㸪10.00 mm ࡟ᑐ ࡋ࡚᭷㝈せ⣲ἲ࡛ィ⟬ࡉࢀࡿ≉ᐃ఩⨨ࡢᛂຊࢆ⏝࠸ࡿ㸬ᖹᆒᛂຊσnࢆ100 MPa ࡜ࡋ࡚ゎᯒ ࡋࡓ⤖ᯝ࠿ࡽ≉ᐃ఩⨨ࡢᛂຊσ ࢆồࡵ㸪(3.6)ᘧ࡟ᚑࡗ࡚⑂ປ㝈 σwࢆண ࡋࡓ㸬 ヨ㦂᮲௳ࡣᮦᩱ࡟ࡼࡽࡎ㸪3.4.1 ⠇࡛㏙࡭ࡓࡶࡢ࡜ྠᵝ࡛࠶ࡿ㸬㈇Ⲵᛂຊࡣᖹ⁥ᮦࡢ⑂ປ 㝈ࢆᇶ‽࡜ࡋ࡚㸪ࡁ⿣ᮦࢆ⏝࠸ࡿヨ㦂࡛ࡣࡑࢀࡼࡾప࠸ᛂຊࢆタᐃࡋ㸪⧞㏉ࡋᩘࡀ 1×107 ᅇࢆ㉸࠼ࡓ࡜ࡁࡢ᭱ࡶ኱ࡁ࠸ᛂຊࢆ⑂ປ㝈࡜ᐃࡵࡓ㸬Fig. 3.2 ࡢ᪉ἲ࡛〇సࡋࡓᚤᑠࡁ⿣ヨ 㦂∦ࢆ⏝࠸࡚㸪⑂ປ㝈㏆ഐࡢࡳࡢ 3㸪4 Ⅼࡢᐇ㦂⤖ᯝ࠿ࡽ⑂ປ㝈ࢆồࡵࡓ㸬SKS93 㗰ࡢ,ࡁ ⿣㛗ࡉ0.112 mm ࡟㛵ࡍࡿ S-N ⥺ᅗࢆ Fig. 3.6 ࡟♧ࡍ㸬

Fig. 3.6 Experimental results of fatigue limit of cracked      specimens (SKS93 Steel, Cracked length 0.112 mm)

ࡇࡢ࡜ࡁ㸪⑂ປ㝈σwࡣ310 MPa ࡜ồࡲࡿ㸬ࡇࡇ࡛ᥦ᱌ࡍࡿ≉ᐃ఩⨨ᛂຊホ౯ἲ࡟ࡼࡿ⑂ ປ㝈ண ⤖ᯝ㸪El Haddad ࠾ࡼࡧ⥺ᙧ◚ቯຊᏛ࡟ࡼࡿண ⤖ᯝࢆྛᮦᩱ࡟ᑐࡋ࡚ Fig. 3.7 ࡟ ♧ࡍ㸬    Table 3.3 ࡟ྛࡁ⿣㛗ࡉ࡟ᑐࡍࡿ᭷㝈せ⣲ィ⟬࡛ồࡵࡓ≉ᐃ఩⨨࡟࠾ࡅࡿᛂຊẚ Δσw0 / σ ࡜㸪 ࡁ⿣ᮦࡢ⑂ປ㝈ண ್ σwࢆ♧ࡍ㸬ేࡏ࡚ Table 3.2 ࡢ a0ࢆᘧ(3)࡟௦ධࡋ࡚ᚓࡓ El Haddad ࡢண ್σEࡶ♧ࡍ㸬 ࡇࡇ࡛ᥦ᱌ࡍࡿ≉ᐃ఩⨨ᛂຊホ౯ἲ࡟ࡼࡿ⑂ປ㝈ண ⤖ᯝ㸪El Haddad ࠾ࡼࡧ⥺ᙧ◚ቯຊ Ꮫ࡟ࡼࡿண ⤖ᯝࢆྛᮦᩱ࡟ᑐࡋ࡚Fig. 3.7 ࡟♧ࡍ㸬๓⪅஧ࡘࡢホ౯ἲ࡟ࡘ࠸࡚ࡣ Table 3.3 ࡢྛⅬࢆ㏻ࡿࢫࣉࣛ࢖ࣥ᭤⥺࡛㐃⥆ⓗ࡟♧ࡋ࡚࠸ࡿ㸬 ࡁ⿣㛗ࡉ10 mm ࡢሙྜ࡟ࡘ࠸࡚ࡶ௒ᅇࡢ᪉ἲ࡟ࡼࡿண ⑂ປᙉᗘࢆ Table 3.3 ࡟グ㍕ࡋ࡚ ࠸ࡿࡀ㸪ヨ㦂∦ࡢᖜ28 mm ࡟ᑐࡍࡿ┦ᑐⓗ࡞ࡁ⿣㛗ࡉࡣ 1/3 ௨ୖ࡟࡞ࡗ࡚࠾ࡾ㸪ࡶࡣࡸ㒊 ศⓗ࡟⏕ࡌ࡚࠸ࡿࡁ⿣࡜࠸ࡗࡓྲྀࡾᢅ࠸ࡣᅔ㞴࡟࡞ࡗ࡚࠾ࡾ㸪ண ᛂຊ್ࡣ┦ᙜᑠࡉࡵ࡟ Fig. 3.7 ࡟ࡣࣉࣟࢵࢺࡋ࡚࠸࡞࠸㸬ࡲࡓ㸪ࡁ⿣㛗ࡉࡀ 0.1mm ௨ St ress range Δ σn (MP a) 300 330 320 310 106    107 Number of cycle to failure Nf