䛷䜒ᡤヮ䚸䛂◳䛥ヨ㦂䛃䛷䛧䜗䠛

¾ ◳䛥䛰䛡䛷䛿䜒䛳䛯䛔䛺䛔䟿

1 䠊䛂䝘䝜䜲䞁䝕䞁䝔䞊䝅䝵䞁

◳䛥䛃䛿ಙ㢗䛷䛝䛺䛔䠛

¾  ᐃἲ䛾≉ᚩ䜢⌮ゎ䛩䜛䛣䛸䛻䜘䜚䚸䝞䝷䛴䛝ᢚไ䛜ྍ⬟

䇾䝘䝜䜲䞁䝕䞁䝔䞊䝅䝵䞁䇿䛸䛿䠛

䝡䝑䜹䞊䝇◳䛥ヨ㦂 䝘䝜䜲䞁䝕䞁䝔䞊䝅䝵䞁ヨ㦂

୍ᐃⲴ㔜 F 䛷ᅄゅ㗽ᅽᏊ䛻䜘䛳䛶ᢲ㎸ Ⲵ㔜䛸ኚ఩䠄῝䛥䠅䜢ィ 䛧䛺䛜䜙୕ゅ 㗹ᅽᏊ䛻䜘䛳䛶ᢲ㎸

᥋ゐ㠃✚ A 䠄ᑐゅ⥺ d 䛾 㛗䛥䠅䜢ගᏛ㢧ᚤ㙾䛻 䜘䛳䛶ィ 

ͤᡭ㛫䛿䛛䛛䜛䛜䚸ᅽ⑞䛾㠃✚䜢AFM 䠄ᡈ䛔䛿SEM䠅䛷ィ 䛩䜛䛣䛸䜒ฟ᮶䜛

䝡䝑䜹䞊䝇◳䛥 Hv = F / A =1.8544F/d

²

ከ䛟䛾ሙྜ䚸d>10Pm

d

ィ⿦ᢲ㎸◳䛥 H

_IT

= F / A, A = f(h

_c

)

loading

unloading

hmax hs

S =dP dh Pmax

Load, P

Displacement, h hf hc loading

unloading

hmax hs

S =dP S =dhdP dh dP dh Pmax

Load, P

Displacement, h hf hc

᥋ゐᢞᙳ㠃✚䜢䚸඲

ኚ఩䛛䜙ィ⟬䛧䛯᥋ ゐ῝䛥䛛䜙⟬ฟ

ከ䛟䛾ሙྜ䚸d<1Pm

h

_c

◳䛥䛸䛿䠛䠖ゅ㗹䜔⌫䛺䛹䛾ᅽᏊ䜢ᢲ䛧௜䛡䛯䜚䚸䜆䛴䛡䛯䜚䚸ᘬ䛳ᥙ 䛔䛯䜚䛧䛶ヨᩱ䛻ኚᙧ䜢୚䛘䚸䛭䛾ኚᙧ䛜ᑠ䛥䛔䜋䛹◳䛔䛸ุᐃ䛩䜛 ᙉᗘヨ㦂䛾୍✀䚹ᕤᴗⓗ䛻䜒〇ရ᳨ᰝ䛾䛯䜑䛻ᗈ䛟⏝䛔䜙䜜䜛䚹

ᴟ㍍Ⲵ㔜䛷䛒䜛䛣䛸䚸᥋ゐᢞᙳ㠃✚䜢┤᥋ィ 䛧䛺䛔䛣䛸䛻ὀព䛩䜛ᚲせ䛜䛒䜛䟿 䠄ᮦᩱഃ䜒䚸 ᐃഃ䜒䠅

Vickers, Ltd. versus Dr. Berkovich ?

60^o l

z

Equivalent cone angle: 70.3

^o a

z d

h

b

65.3^o 77.05^o

h

a d

b 68^o

(b) Berkovich tip (a) Vickers tip

㠃✚㛵ᩘ䛜୍⮴䛩䜛䜘䛖䛻䠄ྠ୍䛾ᢲ㎸䜏῝䛥䛻ᑐ䛩䜛ᢞᙳ 㠃✚䛜➼䛧䛟䛺䜛䜘䛖䛻䠅タィ䛥䜜䛶䛔䜛䚹

1922 E.S. Berkovich, 1950

N.A. Sakharova et al. International Journal of Solids and

䝘䝜䜲䞁䝕䞁䝔䞊䝅䝵䞁◳䛥䛾䝞䝷䛴䛝䛾౛

ᒣᮏ⛉Ꮫᕤල◊✲♫〇ᇶ‽∦䠖 HN-W 䠄༢⤖ᬗ W 䠅

CSM ἲ䛻䛶 12 Ⅼィ 

Nanoindenter G200

㐃⥆๛ᛶ ᐃἲ䠄 CSM ἲ䠅

1 ᅇ䛾ᢲ㎸ヨ㦂䛰䛡䛷㐃

⥆ⓗ䛻᥋ゐ๛ᛶ䛾῝䛥౫ Ꮡᛶ䜢ྲྀᚓྍ⬟䟿

h<50-100nm 䜎䛷䛿 CSM ἲ≉᭷䛾 Artifact

䝘䝜䜲䞁䝕䞁䝔䞊䝅䝵䞁ἲ䛻䛚䛡䜛

◳䛥䛾䝞䝷䛴䛝䛾Ⓨ⏕せᅉ

• ヨ㦂ἲ䛻䛚䛡䜛せᅉ

• ୙㐺ษ䛺ඛ➃⿵ṇ

• ୙㐺ษ䛺ヨ㦂⎔ቃ䠄᣺ື䚸‵ᗘ䚸 ᗘ䛾ኚື➼䠅

• ୙㐺ษ䛺ヨᩱタ⨨

• ୙ ୙㐺ษ䛺⾲㠃఩⨨Ỵᐃ

• 䠄㐃⥆๛ᛶ ᐃἲ䛻䛚䛡䜛䝍䝑䝢䞁䜾⌧㇟䠅

• ヨ㦂᫬㛫ᡈ䛔䛿䜂䛪䜏㏿ᗘ䛾㐪䛔䠄䜂䛪䜏㏿ᗘᙳ㡪䚸䜽䝸䞊䝥䠅

• ᢲ㎸䜏Ⲵ㔜୍ᐃ᫬䛾ᢲ㎸䜏῝䛥䛾㐪䛔䚸䜒䛧䛟䛿䛭䛾㏫

• ᮦᩱഃ䛻䛚䛡䜛せᅉ

• ᮦᩱ䛾ᮏ㉁ⓗ䛺せᅉ

• ⤖ᬗ᪉఩౫Ꮡᛶ

䠎䠊䝡䝑䜹䞊䝇◳䛥䛸䛾 㛵ಀ䛿䠛

୍ᑍἲᖌ (Issun-bōshi) from Google

David and Goliath, a colour lithograph by Osmar Schindler (c. 1888) From Wikipedia

Smaller is Stronger!

䝡䝑䜹䞊䝇◳䛥䛾ᢲ㎸䜏Ⲵ㔜䠄῝䛥䠅౫Ꮡ ᛶ䛾ྂ඾ⓗ⌮ゎ

• (P.21) ୍᪉䚸ᢲ㎸䜏Ⲵ㔜䛻ᑐ䛧䛶◳䛥䛜

ኚ໬䛧䛺䛔䛾䛿䚸䝡䝑䜹䞊䝇◳䛥䛾䜋䛛䚸 䝚䞊䝥◳䛥䜒ྠᵝ䛷䛒䜛䚹 䠄୰␎䠅䜒䛱䜝䜣䚸Ⲵ㔜䛜 ᑠ䛥䛟䛺䜛䛸◳䛥್䛜㧗䛟䛺䜛䛸䛔䛖ሗ࿌䛜䛒䜛䚹ཎᅉ䛿ᮦᩱ䛾ᙎᛶኚ ᙧ䛾๭ྜ䛜኱䛝䛟䛺䜛䛯䜑䛸ゝ䜟䜜䛶䛔䜛䚹䛧䛛䛧䚸ᙎᛶኚᙧ䛿ᅽ⑞䛾

኱䛝䛥䛻ᑐ䛧䛶୍ᐃ䛾๭ྜ䛷䛒䜚䚸ᙎᛶኚᙧ䛾ᙳ㡪䛿୍ᐃ䛷䛒䜛䚹䛧 䛯䛜䛳䛶䚸 ᮏᙜ䛾ཎᅉ䛿ᅽᏊ䛸䛧䛶䛿ඛ➃ 䛾ゅᗘ䛜኱䛝䛛䛳䛯䜚䚸ᖹ㠃䜔෇䛻䛺䛳 䛶䛔䜛䛣䛸䛷䛒䜛䚹ᮦᩱ䛸䛧䛶䛿䚸ヨᩱ⾲

㠃䛻ຍᕤᒙ䛜䛒䛳䛶ᴟ⾲㠃䛰䛡䛜ຠᯝ 䛧䛶䛔䜛䛯䜑䛷䛒䛳䛶䚸ᮏ ᮏ㉁ⓗ䛻䛿ᙳ㡪 䛺䛔䛸⪃䛘䜛䜉䛝䛷䛒䜛䚹

◳䛥䛾ྡⴭ䟿

Nix & Gao (1998)

䛂◳䛥䛾┦ఝ๎䛾◚䜜䛃䛿 Artifact 䛷䛿䛺䛔䟿

Ref.: W.D. Nix and H. Gao, J. Mech. Phys. Solids, 46 (1998) 411.

h h H

H ₀ 1 ^*

Citation=1509 㻌 䠄 Sep, 2014)

Nix-Gao 䝰䝕䝹

h h H

H ₀ 1 ^*

Indentation size effect (ISE)䜢䛂ᗄఱᏛⓗ䛻ᚲせ䛺㌿఩䛃䛾䝁䞁䝉䝥䝖䜢ᑟධ䛧䛶ㄝ᫂

H䠖῝䛥h䛻䛚䛡䜛◳䛥䚸H

₀

䠖↓㝈῝䛥䠄䝞䝹䜽䠅䛻䛚䛡䜛◳䛥䚸

h*䠖ᅽᏊᙧ≧䚸䛫䜣᩿๛ᛶ⋡䚸H

₀

䛻౫Ꮡ䛩䜛≉ᛶ㛗䛥

a r

h

T T

s Ref.: W.D. Nix and H. Gao, J. Mech. Phys. Solids, 46 (1998) 411.

2

3

a

V S

h s ba s

b a

h ,

tan T

Fe-Cr ஧ඖ⣔ྜ㔠䛻䛚䛡䜛 Hv-H ₀ ┦㛵

R. Kasada, K. Sato, Y. Sakamoto, K. Yabuuchi, A. Kimura, to be submitted.

Hv _0.1 [GPa] = 0.8 x H ₀ [GPa]

Hv [kgf/mm

²

] = 0.8 x H

₀

/0.0108

Hv- [GPa] = 0.0108 x Hv [kgf/mm

²

] (unit change) x (surface

area→projected area)

Pile up effect is a possible reason of the difference between Hv and H

₀

.

For Fe-Cr alloys,

᏶඲䛻୍⮴䛧䛺䛔䛾䛿䚸䝟䜲䝹䜰䝑䝥䛸 㛵ಀ䛧䛶䛔䜛䚹

䠏䠊䜲䜸䞁↷ᑕᮦ䛾ホ౯

ἲ䛿䠛 ^{ヨ㦂๓䛾≧ែ}

ヨ㦂୰䛾≧ែ

ཌᥭ䛢䛾⓶䛾◳䛥䜢ୗᆅ䛾㇋⭉䛾ᙳ㡪䜢ཷ䛡䛪䛻 䜜䜛䛾䛛䠛

非公開

䜲䜸䞁↷ᑕ䛧䛯ᮦᩱ䛾䝘䝜䜲䞁䝕䞁䝔䞊䝅䝵䞁

◳䛥䛻ᙳ㡪䜢ཬ䜌䛩ㅖᅉᏊ䜢య⣔໬

b-1) Surface roughness b-2) Residual hardened layer b) Surface preparation factors

c) Microstructural complexity factors

c-1) Boundaries c-2) Inhomogeneity

a) Indentation system factors

a-2) Tip rounding

a-1) System compliance

d) Indented material factors e) Ion-irradiation-specific factors d-2) Indentation size effect (ISE)

d-1) Pile-up effect (PUE)

e-2) Softer substrate effect (SSE) e-3) Implanted-ion effect (IIE) e-1) Damage gradient effect (DGE) Indentor-tip

a-3) Tapping (CSM) a-4) Tip configuration

a-5) Determination of touch-down

Nix-Gao 䝰䝕䝹䛸」ྜ◳䛥䝰䝕䝹䛻ᇶ䛵䛟

䜲䜸䞁↷ᑕᮦ䛾䝞䝹䜽ᙉᗘண ἲ䜢㛤Ⓨ

Fe-1.4Mn h_c

H₀^irr

H₀^unirr

Unirradiated Substrate Effect

Indentation Size Effect

Fe-1.4Mn

DGE ホ౯ྍ⬟䛺䝰䝕䝹

ͤ ISE 䛸 DGE 䛾⥺ᙧ࿴䜢᝿ᐃ

) / 1 (

) ( ) 1

( )

(

2 2

0 d h

h dH h h

H h

H

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