



ῌ῍   

112ῌ8610  



2ῌ1ῌ1

e-mail: okumura@phys.ocha.ac.jp ! ! "#$%&#'()*+, -./! 01234! 5 &%67*+898
:49, "$%&49, 8 /;<4;,!="4! 5#>$%&'!?@=()A/)&B1 CDEF/GH! 8*+IJKLMNLO,%&, *%! 8-."#$%&# PA#! Q
RSTUSV '()WX/*+YM0

1.  !"#*Z#IJKLMNLO[',9, 4! |B8Z#:T/U/ N\149% G]2 A4 ^_`a':,\/! a34/&Bb5'
G;cG P6 1 dV, ef

49g7



2. +!,-

h;, ?! -a389GB9ijb5G:

wh! =>$9RcVb5Gck;<lmnF41oJp<=>Bq'?+{, ! t@Gv! +!EF75GHIJ&%! 9ij-r:kb5'i/ P6 1 sV,#KLM NOPBQRSTU:VW12,! a>Bq'94&%t@A+uv/w:

! WBG>$B|B s 49&%! Xh;,>$94&%Y r 1/14

lmnF4?+G>Bq'AxB 4$%&'y, ]:! Z[\/*X! >$cz, >Bq'?+t@A+G! =>$9

* a, >$&%RY+G4b5Bc*

44! \4a4C{G|BD/ E/&:|B s0 /&,2) /G! s(r)s0 f1(a/r)%49, }F&'()*+!,-:,X/h49, r a 4H?@1}FGv>$?/wG~G T, -+4! /G<+! >$H W

:}-:t@4, I{?Gb&c#JK>$49B! ~G

s(r)s0(a/r)a(r a)(1)

:X]^*+, |B s(r) >$&%RY+M49:4_ s0 h;! `X Pa,1) ZwB! }#! >$?/wG#bcde{V >$94&%>$^_`fL{* >$ 

f1(a/r) 9XRY:Z>[\/':, !

x+:O){, -4! &'./01

gY+ (rῌa), s(r) :4_ s0 h 

234#56789:;12 <=>?N#/(;,cG , + !"@ABCD49,-4O! >$P~Gf&%|`]^! =X%&@i=X%& P#/-:'W9%j&V k/lm/

B&&Gc|B1QRS49, %! 9W%+B!

4¡:¢1 a m_ij:|B>$944c &%4

, =X%&n( a1/2 49,3) ZwB! 1#>$944|Bo£, ++!,-]"B^_49,}! :pq/¤¥! ¦§¨FL4/J/, ZwB! ©Yª§¨FL«¬/  (1) 1AG3 P9-r
~G­sV 4! `¥1 #o£*#tr,

6 1 IF³~Gb5>$n( PdV 9n( PsV
4! ´:A+1,῍ ±  * * ²

ef x Qy&µ "¶$'()Wz

BUT12034· · (Mark4)· · ML9500F¸Mark4¹º{|

3. `abcd (Gri$th) 89
AxB ! >$P~Gj3u®4Ax
&N¯!v/¥G, 
Gv9wB #u®°\4AxB 
1Fri· Jan· 21· 10:39:46· 2011
»J¼½m³ Page· 1  1 

f2(L/a, W/a, T/a, n)       

% "!&' ( )'* !+

 ,- ./  01$ 2!34
 "56-,'!78"#

9:;,-<=>?!$% ' @&'9"()5

9$%' A)*7<=>?(% !

g

BCDE

 +F!.,1

9

2)

V

sfnf2(L/a, W/a, T/a, n)ῌ Eg/a    !" #$Tn YY% !$(3)

 o (3) ,-bZ%

J #$9 #[  \l$I a "!

$ ] L, W (a), T ( a) S`>!SR,-Vz 4) o (2) !b!$ TYs
XY9'%

 o (2) ^_I

XB

V `



a%



o (2)  +F* sf O4bSX!
4 E, +F()<=>? g, " a ,'%6-,<=>?!GHI';J'-'  KJ }~Nc,-db 9 TFDE%%LM-9 "#'IS`>! a  e$f7

<=>?!

  1920 /OPQRS N.I

o (3) X f2(L/a, W/a, T/a, n) VR<_

0<=>? T"1U%234V !W= g g'Nc (%

XYS% $+F!,1Z !$ ^7 o (1) bo (4) g

+F5[6\ !+F]Z^77 

'o!h- !

8 78934  1  :7;

 "!' )  A*FGIS`>!);'%  

7<=>? w0%<_=4 E

s20/E S`>%

!V !%+F*

 +F<=>? g   !$ +F<=> T 8o (3) ?@V O XYiwxyj8 4 Y j8(:?!,$% T+#)2E 2 >$ TS`>A$'K QiXYi"5 ,- aI a "57b%Ac7V 2ga <=>?!

'9 8SRJ k¡lb:$'pT

 V +F* sf nj$XBm¢8' £]PQRS34 J <=>?<=>?

1@&  T¤ ¥S

 w0 !"d7N.IGHI o¢! sf HI%'9 ¦<=>?N.!e@f 88 34

T

Ac7V a  T",-#A2

*§X J *   "¨©1A ª,HI +F5[nj% !p V g* )'BhC i7N.!
e'  jDE8k%FG'I

S`>!" a ,'  HI%JV 

4.  +, -./0 *«q(%o (1) i





^7 OPQRS34 ",J!Z^lm  an1/2(s0nsf)  D(w0 a )ῌD(2ga) !K7L TD MN1U

Rr '-(%V !

+F!,1%tm "u*2 

sfῌῌ Eg/a

sf 
(2)

o (1) 8}~Nc¬s  

5)

34

 oi; s0 tmo (2) v$­4 +F*P s(r)ῌῌ Eg/a (a/r) !h-  tm

O4-ao "!&%p !qr'5[P%
F ^ ,s(TE' bS'@&34  Q+ptJ

g !Q+'-JV "!$ uq+F*!NI @& i7  !"#$ s(r) !"u®9u (r a)  a ¯'9' °w%1x ¤ K%%  o (1) i ^7 an1/2

an1/2 !±I

²X 123456%&'()* I-+F*$9%

789:; <=89>?@AB?C*D)EFG?

4 +F<=>?$9%J

HI* ¤ ¦ 8,D2vR  wxy!"
 #$  ^ c"

78#NI SRo,-wxyTU!Vz K ' ( { |c  ! L, W, T    ' - J 2 o  W } ~  X
2

BUT12034· · (Mark4)· · ML9500F¸Mark4¹º~ ¥Sy +F

]8\³z9
8

)g



 

{a´wxy L |a´wxy W !y]$(LT)  2 

34(LW) 

'"!+

  2{



(

E{)81A TK|}bS]µ¶ Vol. 66, No. 2, 2011

Fri· Jan· 21· 10:39:46· 2011»Y¼½ Page· 2EA("

A {" 2a(Ja) *+s0, |jN& E,

PJP0ps20 a2/E &

4P0 

B}& BTU:V/*' TU:V/o?&*~ NOPQ8A
o?&) C@D GC E_B'\

B  C@DFG G C J2g &  _ G (1)  s(r)JKI/῍ r (rK a) '   
n 2 ±w/²W)6'

H KI  4/l I  7) W) KI῏s0῍ aB!  H*~2 NOPQ8A KI  KIC῏῍ EGC u0῏s0 L/E u0  



 

    C@D KIC E

&'

( )

C

   

*+

" ,

d 



-./0/1  23 )  4W 5
6&7   89/: L ; &4<= 

HjYj:MS*'_F

 KIC *c fO"P KI *

#R  KIῌKIC & n2&f T)%*yUV<h$%"6BI s(r)Js0(L/r)a(rK L)(4)! L! "MF #$%"&7&   B(῏a) 1 W%h

XY  4Y+Z[ 

D

D  !"#$%&' EF%&\ 
T\ CG (3) N]

NOPQ8A D(w0 La)῏D(2ga) &F G (2) 
sf῏῍ Eg/L(5)

BI

4

sf *!

  a῏w/2RL G" G (4) G (5) *+,-./ aJ1/2 *]^_`*aF07
s(r)Js0῍ L/r4Irwin-Orowan _g^  bn W%X1 `Sn TU:V/o?

X (῏a 2) Bg& W%

TU:V/

\#¡ B n2&  o B #,-./0/$%& E,

S'(TU:V/ g, W)*XYZ[ L &
*'\

(rK L)(6))'_ b5  456&

7 _c W)YZ[ L 67d'6. (

!

<h S i!`¢@&_ "s a e  * 4e1  k *H *1    23& 89/: 45 
 a

GC )

Nn2

9/: L 

S"~

i#&IJ  KLn2<  Q&  EF G (1) HG S'(TU:V/ g(Fracture toughness) 

>?@A*B C DA 8

'\ B 

5@D KIC  GC 4)

! "  # $%"

c

8*e9

 fg

ῌ k(e/e1)
eῌe1
sJ῍
1/n
e£e1
῎k(e/e1)b<hing) &(8) )  ¤: Cc¥ (unload

2AC

$W%"C2 B

4de¦ Hutchinson, Rice, Rosengren /I§ HRR

C   1

W)B   " ¨f

5. 



 " #:; B_*<h$%S i80jk/l&'+m*:;&s(r)Js0(a/r)1/(1ῌn)

&4nJ1 

(rK a)(9)<h^©ª\   I

c 6n2 NOPQ8`  B_=>J G (7)

2TU:V/o? 4@>p6)_F $%TU:V  h«F<gB g/q _rs*t _ $%uvjwx:TU:¬i­B& h ) ^V/ P *+

` B 

&dy

* %

 KL KIῌKIC *__ JῌJC  2 SA*®
 Cj+  (7)

GJdP/dazz _TU:V/o?& J g

6)&f 1W)Bg5 oG"ep%³ ´µ¶q6d7r

BUT12034· · (Mark4)· · ML9500F¸Mark4¹ºst7. )*+,-./01234
G (9)  k 4 - L1_¯ *~2l°ªm
3Fri· Jan· 21· 10:39:46· 2011»ju¼½² Page· 3  8 (9)  !



&fP L Xij Fi, j, a῍ k(i, j, s)(Xij Xijl(s))1/na" #

(s)

.

234567T)<
(X)

1/n 

= ><&9 $% ?<@97l(1)(d, 0) ,AB 3C* )D 'E/F&G978<   HIJ2 %KC2< !"LM%"#0)O  (9)@N!P$81$%

 i

 UV X  1/n Wm L x]R l(s) tT)<

89 : 2 # ;< 8l(3)(d, 0) ,l(2)(0, d)l(4)(0, d)(13)JRDHV k(i, j, s) =XQH= 2 L D

3 $% 2"@YZ2 iDHV Q2m

 RNV/ [ )F&%&978 G9Q'\(G)*+R d $S,

"S*NO^-&

H A (9) .T*

R

(12)s῎1

3 $%& '()*+,-

/0)1$%

S2 a ix U ym 7

4

 "US V/0 a, V/12@<W3 r

NO ]2 QH-:T)
A

%

_<"S*NOV/a`a#1

4 $% bcSV/12 im A- &

D dX rX a 4Y (9) A5! 6Z7

ff (10)  yzR dO    (9)  r 822 93 [\i,x]^_RA d * A8 "m> efgAhQ &$% Pi" ilm - sM/s0 A d i*

R[\]^_ 0)-:* d/am :l jC%:l@r|}~r"US 

sM

$Sa# 

4

$%  .;¡5¢T£¤k¥D iV=¦VXm D§  ;<sMῌs0(a/d)1/(1ῌn)(10)(10) A5!

§l11)yzR  (12) $%   x 7<  V/12A`.= aJ2 9b

m!*A )D *L A 

A>cdO 0)   d 

L B A(

!"

o2

y7

n

L A (pg$%$%&'()* %?<5S!"

&8S i)D  (12)  ay, s1 ¨ qE

 +,-()*./0123456*0DTA  qEm e3ZT#

45789:;<9 1&e&@N "USr© UJRyzR 45 sªt

UL@A fg&A +,-AB 

e( x 7 V/\r|}~r $%&Ch9  ijk DElm  (10) U cK x 7O*

 v+ A:f<&nF

oG&&LM%"US  !

@N  (10) HI+§l¬*(10) d 

yz

O

R,&* C M@ *­w

pqJK r sR& 2 tuv\]wxyzR{

yzR{87A ®M$Sx¯ °A8r|}~r$%DEl1$%

y 7A«u«

c8

8)

yzR

3

NN L Xij MNO 2 tuD7

N PQ12)&  (10) A§l %

A+  (9) HRR =>?@AB 1&e Qy+(s)

<L  4 "aAL Xij

(1)

(2)

Xij Xiῌ1 j , Xij Xi jῌ1(3)
Xij Xi῍1 j ,(4)

Xij Xi j῍1(11)

0 d iUm JRv"&*

3 +,-/ i± 9 $S²o_t³m

4

BUT12034¸ ¸ (Mark4)¸ ¸ ML9500F¹Mark4º»z{yzR

4 i´m z{yzR g im | lA- &8u}AV/ 2 qE $S´~V/&= &8 ± 10 $S²o_t³ i m (10) d ± 8 $S²o_t³
!

vµ¶· Vol. 66, No. 2, 2011

Fri¸ Jan¸ 21¸ 10:39:46¸ 2011
- ¼½\] Page¸ 4

 4 



     !"# $ % # 

Q

PR"2ST2$'( e 1/1,000 

H$3 1  x U|VW

 !"% # &!"%("# y  !#! VX
=(CYZl%" VX[.\'()*+( ,$"-

 6 0(+( '(%#  6 Z

8. #$%&!#! ?%][.,"## ."%(/$' 6 &^}C_W "%(  5 012$(# 34[.,(%!"2% lE# `arb[

% 0.5 5678 9: ;<=2>".# y ?%# @ 100 !&AB"% CD

2345016 $'( ;K)*%+,-*%./01/$#EF*G+ H$"%( # 

"2;+"% $'( -# $# "

IJ2KLMNOP%&'!"# @Q

%?%c# $Ed'(%)H$!"*%RSE"%(e=%f$($g"%(*+*+# $# "%"+,-TH$U! /$'(VW*%XW$# OJ./(% ¡ (eE¢0) (# 7/89:)*%&;

,Y021"%( 23 9: ;<=4

4<=>?@Ah# @ ¡$BCD"B(# 35!6"*Z[\]8^"%EFG/HH7  +# *+*+i£

/7E_C$5H$(E# @8`a"

b c\9:(;+"%( d<0IJFKLMNOAP QRKSTU*

=>efg7^hig/"?CjkG+)*V IJF7*WX 2BCDEF7*WX6 `""-E# @Y0l%"2 m@nAG

G"%W%

+""%(13) $# oBCf#

CfNpf¤jkHDHl¥ b/$'(  6H

!"mn( ,¦§ eD]8qrs% jk Et( $+ 1 EKG% ¡$H$3Lab c\ojk&Fu"%(*+*+Kg7\vG# [¨p/q 15) (# ©D2ªrw *x# Hy]8q$;8g 5z{

G+( y  [¨ u  x  [¨E2I=!%«G+  @"# 2¨35' Ea2|! jkGw(b c\

9. #$%'(5z{="#  5 }# AB

dh ?%# @+EI!J%AB ds U!

fῌEh((u/(y)2¬eEh((u/(x)2

(14)

"

."%(!!  ­# s&®t?%%5H$"%("B  !"#

](# sN®t"%C_[.uT"AB4 ed~ds/dh  1 E2I!KG%(  #%( ¯ y  [¨ u YZ[\7]^]_?%"%L6MDG@++[`a b:2!( @¯Eh  Es ( +4 eE~Es/Eh 2 1 E2I!

KG%(X# NlOK[\h\4 e~

eE/ed  1 EI!KG% P# ed  1/50 $'E#
E h  E s @++ 50 GPa  MPa $'(#

ῌ (2
(2 ῐ
῎
ῒ
῏ 2 ¬
ΐu~0
(y2ῑ
῍ (x̃

(15)

$v+#  +([ x 14)

 5 1 °D. Katti ±wi²³ 0 ´xµ y%)!"% V"%(zAG 0.5 5678
cd +,/Y0µ ?"~BF*BUT12034¶ ¶ (Mark4)¶ ¶ ML9500F·Mark4¸¹

x̃~x/῔ e

 6 0 y  !#!
aNlrb[.

(16)

V{|$[¨} }`5Fri¶ Jan¶ 21¶ 10:39:46¶ 2011º8»¼½^ Page¶ 5

  

 1/1,000 !LM>

e/895XYZ

!!" #$%&'  
 xy/5XYZ

  !! [

gh 67

[

g

D

 #$% '()*123 4563 7

89:;5<=>?@5AB'(CD5E/
FGHIJKLM&N

()$  7 *+ #,-./ ,012 15, 16)  34),- 4) 5 6 7 7 y8

10. FGHOPQRSTU
xy/8&'  e  1 %D EFLM&

0 2# ῌxῌ9a: ;% <5

' KE=  (14) BU UGH2>IJ!> 1"14#$?%&('@Aῌ% < H 6 F + $  G(BKLM >N

B+C! e  1 %D EF y80 G>2  } 18R&' H(!) wHC 18)  (12) l=uy( y80ῌ)ῌu0῍ r̃/L ,!&syy( y80ῌ)ῌs0῍ L/r̃(17)

 2 OPQ+/3K0R+ +,34
PQ+#%3SG(!# JC 

!*2H17)  r̃  (16) !

 8  TN P UR>24#$2>I- r  /G+  >VW#Hll+,

(17) ! (6) .J! /3K0LM

1N <H% Be/XJ l 2 Y%! 1 %PD QR*ST

U! 34¡ PQ+  8 7 (a), (b) 

D UH   V2% "#$%&'(4#$ >2/¡ ¢Z*[ £2)*+,-.!/0!*+

¤*+ \]  Y¥ ¤

ON.J e

1/4W 1/e

1/4!QRST34+!M #QR2> 5XYZ
1/῍ e ST34[!M !P! 

>
¦ 9 *  &' (12) 8R&'+, ( x §! y §\

! \] (^!+,675XYZ [H&'  +2+  9   6 

3_`a$ 15) $b.cd!e/ST>2/£¨]©XJ ©+ #2>895XG( sh `:PHC 89

$% t` !A£¨]© >2/£e/fg;hij ah !+ ¨]© 6>2/K^ lª_: «`>f!LMC ¬ e/© 64&?£¨]

!  (2) % shῌ῍ Ehgh/ah !  Eh ! gh ©`> : 4&?2>- !ª_©«`g<D4!H5XG(k=e/89 >!5X&?YZ [ > (10) @A+ !A!+,LM l  (17) BG(&(/3K0mVd nopqr

Hb #$%  (14) YZ[!= a{ ©C> ©,R2> V.W0H+5XY/0/3 nopqr 6s4: s0῍῍ e L/d  sh t

7Z3 [0HX+CD !/0!*2 ¬ou+ !A4vw !LMC !A '(\]Y/0 [0H&3 [0HX s0 xy/5XG( sF ! (sF 8 s0), sF 8

+CD !!^3 '()*,_b  e῍1/4῍ d/L sh ! ! (5) z{@A +*2H '()*`abc

+  sFῌ῍ Ehg/L 2> xy/5XYZ [g<def ^­  ¦*(d/ah)gh ! 4~C d  1 G(B®,R = 1"1bc!a{|}! gῌe

῍1/2 ah >2/ DC d/ah  100, e

 7 1 " 1  ! >     #  , -     b P 5 ] $( y8¯L)  6d: ¬= u0 °= 45G(± !,-./²

6

BUT12034· · (Mark4)· · ML9500F¸Mark4¹º f

 8 xy/8R&'

6: !347$Z*³4 67:eYLM´µ¶ Vol. 66, No. 2, 2011

Fri· Jan· 21· 10:39:46· 2011»¼½op Page· 6/9]^bc1]^Sa¦r/sl§¨G$ Q©¦rtu  x ©5gªv & «C l0 ¬b3 R$ T$«C l 0  9 w¦r­l§/ r/l 0 e100 
0 #V3% / r/l0
ej100  0 ¦r"#x$ y® 18 N4¯° z {±$$ $6:>) =>s% tKu? …eK/L=N$ 33% Q6

 =N4:>"v?% @ABRtuN?%tu?":>CDwJ% (n, m) '8Q6
tu?

k̄mek/lm S'$ 01S

Q6N4P'% Kxk #"E f n, myz(n, m)

$6"
$ F n, m=$6Q6F'G

o3 S'$/ 10 01]^1]^ ­  G F 0 $6Q6P>
K/k ²³ $  K ´3 k l>V$ y® 19
N4¯° z {±$50163{-H12H

S4% H4 ,-12| I9+J$ 
JK N?LM3 !bc11]^
NW} $ 1~% 6G Fn, m OP 3

   d a L L   

 !

QR! S8?
VWX"Y

"#$

 !

$ 016T"'- 32-UU%Z [\!'$ 33% 2]^bc1]^N?Z \11. 

k4# 12 _q"!$% &'()*+ ,-.#"% /#01234#$ 5% 0
1678+ ,9!:6#]^011]^>k
: : 
G"

`s % 3$ 01Ua  s wJ"p9$ 33% ?3@0A

D # N4% |"-!

B% 01 +3 C)?DE?

 G bcLq!#"% y <=;<=>!

F  G +#"% H6"

L#$ d% 

32-CV$ Z #  Z

 !I"  JKLM3 #3

N?O"$ > % 01% P' 

U%  !

"8-$&  (CU:V ? W

% ghQ

C t% li $ N?)X % *+,YZ[@\1!$  "# $ ! %! &#'()*]^-;D<= ._3N?$19)+,-./0#D$ > %  G tu?

$6%' &  Q6 R'>

S4% T ?ef % '01" U

1]^/ 10 N?% 0`12Sabc
X n, m  (q, r) d3

X n, m e(2np/N, mL) N?$4f5g6$6

N % h75g2:Q6

M% ne0, 1, 2, i, Nj1, me1, 2, i, M $bc Xn, m  Xn, mῌ1
Xn, m  Xnῌ1, m

kl6

kl6

m(n, m) '8$6n o3%(n, m) '8$6p9:qp9: lm  m r;3m(n, m) '8Q6n%
L, (n, m) '8Q6

lm e2mL sin(p/N) <J

12 |9.P}Xµ T¶&(CU:V~

BUT12034· · (Mark4)· · ML9500F¸Mark4¹º K/k V3

ALM3C"/ 10 #$y% 501N? 1 N4 !'
k

3

!% e" 10 jky#24l: '$ mn % 501 K/k e 10 jk#$20) E% K/k6!' % 01 2 op'X. ¡ 3¢: $  w

J% £q3  3lJ (;)¤¥LM
7

Fri· Jan· 21· 10:39:46· 2011
»¼½LM Page· 7





K/k



    !"  %&#$

'

(#  )*+   #  /012M

x[BE"J y\  z] ,  /3ND
" R {< 45oSTp ^94;01^ _<`A ]^hSijk1l

$,-

YZ tuvwY"

17#  K/k/3$mno |01 }J an~cMb RZ*S c01

J.RdU?

e



 N .

5 fN|01 ghijck5EF

456

0#g  hi+j^1#18#  Hk`#

el05;01#

9:50#-#mnoHp   qq rs E1-';$<    !"#!$%&'(0#tuvp wx Z  D  O



N

M

) *+,-./'    .$01
K/k

yT1 9jzD1#%54{

 ;501=>  ;16# 10 ? @A2 4B50# ;$< 0+ 1!$!23
425  671!  3 C   /01'1?< .  & D#E
F"G1 <!'1 -53 #01 H;01

$D I 41$3  ?< 8 '9:" ;<=>?$

@A3!5

12. BCD
J "EFGH.I3$JKL!51M/N

1 #OPQRSTU@3$KLMN" O%  &' P#(Q R ) *S+01 O, O%  T
U V-$() *S+01 $# .O% "1 /0 FWX"
Y"S ZO% [61?
?23\45 ]6 78^9 :_
01`;23-35a H\J

<=>/3?@; \D/3

; 3 bcde <C1
(de Gennes)

ND1

5ABf

DEF\#GghijckHI

J-0#21) K

LM O%

lAm'D1

 O;5n-0# KP01Q1#/3  RZ45
oSTp 4581 VWXYZ[\[RST

UU V3 EFGH.I3]^L*_5 " -22) K qrsD1`abcdWA- ?@X5  nP /I1 ^efgD 5
8

BUT12034» » (Mark4)» » ML9500F¼Mark4
¼½2n

O]

|}Xc"61}/

e ;1~!

")p )p # $p x1spqrs1) u W %1  1920 ;;  /< W   X
1\>1 & & 05'
%'5ND }J. E.
"gc \' ' ( } f2) H0 ' ) e *D#  s0 B1 Ee *D1ND1 O  }E + ' 
+ 91   H; + }Dc+ }' 1   ,BFWX"Y"? btc n *D  BP + 'H;*D?
 
3) T. L. Anderson: Fracture MechanicsῌFundamentals and Applications(CRC Press, Boca Raton, FL, 1995).
4)  o3Up 1$3  o¡3Bp 1S45 <
7P  ? }N. Goldenfeld: Lectures on Phase Transitions and the Renormalization Group (Addison Wesley, 1992) 2  o3Up  5) K. Okumura: Europhys. Lett. 67 (2004) 470.
6)  3 KLMN"01 ¢(  dc~£M
KLMN"? ¤-¥E#KLMN" }¦ 7?#<¤-§ ^q ¦ u1 1FῌE(u1/a)2a2¨su1 a©ga

(18)

31  u1 /014uª ¡sῌEu1/a «=  ' a 4u¢ (2) >1 (P. G. de Gennes: Europhys. Lett. 13 (1990) 709
¬#(  ­ K®cv-37) £I ¤¯¥ ¤- 61 ¦.   T
 dctM\ ° P o§¨O% }©&Tp o ¨O% }©&)p 
¤-ª«5 ±/ r ¦² q
2 B¬­ 91*D1   T 5 }"g  3 g0NDH®¯ "g I W8) Y. Aoyanagi and K. Okumura: J. Phys. Soc. Jpn. 78 (2009) 034402.
9) R. B. Emlet: Biol. Bull. 163 (1982) 264.
10) S. Nakagawa and K. Okumura: J. Phys. Soc. Jpn. 76 (2007) 114801.
11) ° 4 ³ 8  1 sM/s0  1   ±  ² £ I  (n) /  ,log(d/a) ¨0.25 ³Z 01  ¤-´)Qµ }¶@´  2 µ 3T¶_
 ? ¤-E£¤-1'01
$3 ²3 .·=>D
12) P ° 4 ¸ x ¹ y ¹º1£I·¸M C
¹1#E ° 4 ¸/\17 }0 < ¤- ª« xº20l ? ¤- ª« xº20l /<¸, \5 ¤-'01  #E ¢ (9) d 2x]» Vol. 66, No. 2, 2011

Fri» Jan» 21» 10:39:46» 2011
½c iªv Page» 8
 
 (9)   10) ! x " y " #$%$&'(
') *+ ,-.$ (9) /013) H. J. Gao, B. H. Ji, I. L. Jager, E. Artz and P. Fratzl: Proc. Natl. Acad.
Sci. U.S.A. 100 (2003) 5597.
14) 1!' ! "#$$0%2 ((1!&'345 $6 
1!34()* +78,ῌ-$"#9:
T. Sumitomo, H. Kakisawa, Y. Owaki and Y. Kagawa: J. Mater. Res.
23 (2008) 3213.
15) K. Okumura and P.-G. de Gennes: Eur. Phys. J. E 4 (2001) 121.
16) Y. Hamamoto and K. Okumura: Phys. Rev. E 78 (2008) 026118.
17) ῍ e  a/L 0;./0<1=(1>  ?
29: 3@AB4CD2E45,F  G1
(69:18) Y. Aoyanagi and K. Okumura: Phys. Rev. E 79 (2009) 066108.
19) Y. Aoyanagi and K. Okumura: Phys. Rev. Lett. 104 (2010) 038102; featured in, P. Ball: Nat. Mater. 9 (2010) 190.
20) M. S. Alam, M. A. Wahab and C. H. Jenkins: Mech. Mater. 39 (2007)
145.
21) H7 8I 9:;<JK= 62 (2007) 634.
22) L>?@;<JM NOPABQ LCD.;<JM NOPABQ R 2 
abcdm
vfm@


H7

8EI

F@

<ῌSDT ;<ῌ GHIF@JU.J VJ;<R?K<ῌWXLY Z[\]^_WXM
`NO;<J$Pabcd.efD;<JWXgQ hR$S
 T `NO;<JUVb$WXMJW$3@iX:
iYZ[UjWX\g 

N2010 ] 7 k 31 9l^_`Q
Toughening Materials by Exploiting Soft῍Hard Combination
ῌFrom Nacre to Spider Webs
Ko Okumura
abstract:

Tough materials found in nature tend to have characteris-tic internal structures. For example, nacre which covers the surface of pearl possesses a layered structure composed of soft andhard elements.

Nacre is not only beautiful but also strong! We

review here a simple view on the toughening mechanism of nacre,
together with that of spider webs which are also made up of softand hard elements, i.e., hard radial threads and soft spiral threads.
We begin our discussion with a review on the standard fracture
mechanics, putting stress on dimensional analysis.


neofJg<pJWXq 169ῌ8555 hrijkstl 3ῌ4ῌ1
nhrJJwpJxWXq 113ῌ8656 hri-rs:y 7ῌ3ῌ1e-mail: uesu93@waseda.jpu
e-mail: yokota@bioeng.t.u-tokyo.ac.jpu

zn 2 >op ,D{D;qGr|s}tu~ :p 2 vwpxD,^.zyW'hN2 ( z{[ |[ }; ~'e4d] -;q?$D-7(1!$9:0 ;q$R1>W[;q $  'r(hNu LG:$ (:1$ TjWX~"#'

1. 

?$'7y? Ps , y|V Ms , y῎ xs Y ::xUs}tu&

H, ;. X $

s&¦'.Uj¡¢£§' ¨';qd] -;q (:;u?K?¤($¥© Z ^A^\ª1;q5a'&5«^¬¦P/b $w­?u ~R' 09?y,D{Dz>p§ ®@gy¯y$LG:

$!? Nz{? |s ?Q3)$  2{E, |:¥¤ yh'1) y$ ~6' :(°$2?¨±$' $??$42

''>© T$ª«²³ T PsῌH  MsῌE -TsP2 {D´µ¬¶ (SPM) y­ nm T·D40$|V |V? 7 ¡$| $$0! 1 SPM 0®¯

z{ ?? 7(0e4d]

°±?G3@ ¸0

-;qWX$LG:$02)

?

?>s!1s$s& 0 
G:$¢£¤1:

²9:8

¹R?%²9hN³´($9:4) ¶·;q¸I ¹iº5 Gº» i zn 2 >opµ¬¶?

BUT12034» » (Mark4)» » ML9500F¼Mark4¼½῍f

6 

Uj¡¢µW! :9Fri» Jan» 21» 10:39:46» 2011
^½\. Page» 9