Micromechanics of Contact and Interphase Layers (Lecture Notes in Applied and Computational Mechanics 30)

Lecture Notes in Applied and Computational Mechanics Volume 30 Series Editors Prof. Dr.-Ing. Friedrich Pfeiffer Prof. Dr.-Ing. Peter Wriggers

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Micromechanics of Contact and Interphase Layers Stanisław Stupkiewicz

Stanisáaw Stupkiewicz Institute of Fundamental Technological Research Polish Academy of Sciences ´ ¸tokrzyska 21 Swie 00-049 Warszawa Poland [email protected] With 76 Figures

Library of Congress Control Number: 2006937129

ISSN 1613-7736 ISBN-
 3-540-49716-1 Springer Berlin Heidelberg New York ISBN-
 978-3-540-49716-5 Springer Berlin Heidelberg New York

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6 6++0' X&CXA.CWR @( CW,.C6R' CA46H C,H H H Y":==+' H +=(+O' @( H B"8PV+VV+OH +"8@:"= @=]P:P B0 V8+ P"OV"8 V+PV B@ +=PV:" @( D+O0+"V=] D=PV:" >V+O:=P [:V8 V8+ V8O++9(:>+@P:B@= 3@:V+ +=+>+@V >B(+=:@7H 2' X6A&6XX.6WX' X__CH CAH H Y"^:"OBP"BD] B0 :@V+O@==] 0Y=V+( Y.@.
= >OV+@P:V+H
6 6++0' X4&A,A.C___' CARRH XCH HH 8==+@ @( H HH \=+]H
@ +\D=@V:B@ B0 V8+ (:1+O+@V O+7:>+P B0 0O:"V:B@ @( [+O YP:@7 PD+O:V] (+0BO>V:B@ >B(+=PH 2' 4W&XXA.X6W' CARAH XXH H 8YH =3623(3 - ,(2.36296923  369= .! (>+VO:+P B0 =:@+O +=PV:":V]H
//+0 &0 :0' 6,E4F&X6R.X,4' CAA4H X4H H
H (+ BY^ +VB' H P8:>BVB' H +O:"' @( HHH [+@H
D8+@B>+9 @B=B7:"= >B(+= 0BO 0O:"V:B@= "B@V"V ""BY@V:@7 0BO [+O +1+"VPH &(+0 2-30 0 .0 .-0
' W46&,CA.,6W' CAASH XSH H YV:(V' @( H OVP"8H VOY"VYO+ "8@7+P (YO:@7 DP+Y(B+=PV:" (+0BO>V:B@ B0 Y
=@ P:@7=+ "O]PV=PH
6 620' 66ECCF&64AR.6S_A' CAASH XRH
H = >O:'
H +@@@' H :(BOB1' @(
H :8:H =PV:"9D=PV:" 8B>B7+@:^V:B@ 0BO =]+O+( "B>DBP:V+PH 920 0 &0
4.+(3' CA&4,4.S_C' X___H X,H HH P8+=]H @+O7] O+=V:B@P @( V8+ +@+O7] >B>+@VY> V+@PBO :@ "B@V:@YY> >+"8@:"PH @ HH @@:@+@ +V =H' +(:VBOP' -+36( &:(.92 .! .+(3' D7+P RR.CC6H "OB[9 :==' +[ BOY=V:P"=+ DDOB"8 0BO >B(+==:@7 V8+ +=PVB9 Z:P"BD=PV:" +8Z:BY:O B0 =B@7 3O+ :T: "B>DBP:V+ >V+O:=PH .,/0 6&0
//+0 &0 -%-%0' C,W&W_A.WW_' X___H WCH
H U=B(:1YP:B@ :@ 8+V+OB7+@+BYP +=PV:" PB=:(P @( 8B>B7+@:^V:B@H
2&0 &0' 6SEWF&XSR.WC6' CAA6H WXH HH +O:@7' HH BB@' @( H
@@(H
D=PV:":V] >B(+= 0BO :@V+O0"+ 0O:"V:B@& DD=:"V:B@ VB P8++V >+V= 0BO>:@7H -60 0 +360' CREXF&XWR.XRC' X__CH WWH
HH :@@:@==] 5V PYO0"+PH 2.0 0 .0 .-0
' XA4&W__.WCA' CASSH W4H H
H O++@[BB( @( HH YH YO0"+ OBY78@+PP @( "B@V"V& @ DB=B7]H -(' WS&SCR.SW_' X__CH WSH H Y+@:@' H BO:@' HH B:@' H +;B@78+' @( H +=+]H =PV:" "B@9 PV@V >+PYO+>+@VP :@  Y.@.
= @+O V8+ >OV+@P:V:" VO@P0BO>V:B@ V+>9 D+OVYO+H 2(/6 6++0' CC&C_RC.C_R4' CARRH

+0+O+@"+P

C,R

WRH HH YOV:@H [B9D8P+ (+0BO>V:B@P B0 +=PV:" PB=:(PH
2&0 6(.-0 &0
-+0' ,6&C.XA' CA,WH W,H H @(^+=9B[:+O*^' H =:>"^+ V8+BO+V:"= DO:@":D=+PH 0 &0 &=30 .+(3' CC&W4R.WRX' CASWH 6SH H :==H @ "B@PV:VYV:Z+ >"OB9ZO:=+P 0BO 8+V+OB7+@+BYP PB=:(P V 3@:V+ PVO:@H 2.0 0 .0 .-0
' WXS&CWC.C6R' CARXH 6RH H :==H @V+O0":= BD+OVBOP :@ V8+ >+"8@:"P B0 "B>DBP:V+ >+(:H 0 &0 &=30 .+(3' WCE6F&W6R.W4R' CA,WH 6,H H BO: O+PP' +[ BOZBDBY=BP' H V:B@& V8+ +1+"V B0 PVO:@ 8O(+@:@7H @V+O@= +DBOV  TX__XTC'  
' X__XH RWH H OPVY=BZ:"9DO' H O:77+OP' @( H BO+="H
  9"B@V:@YBYP 0BO>Y=V:B@ 0BO W 3@:V+ (+0BO>V:B@ 0O:"V:B@= "B@V"VH .,/0 &0' XAECF&XR.6X' X__XH R6H H Y"8OP+ XR B0 692 .63 (-
//+( - .,/966(.-+ &-(3' D7+P RA.,SH DO:@7+O' X__SH RAH H +\"+==+@V' HH BB' HH Y@' @( H +O@O(:@:H 8O"V+O:^V:B@' V8+O>B>+"8@:"= +8Z:BYO @( >:"OB>+"8@:"=9P+( "B@PV:VYV:Z+ >B(+= B0 P8D+9>+>BO] Y.@.
= P:@7=+ "O]PV=PH
6 620' 66EAF&WRRW.WR,_' CAASH ,_H HH :Y @( H Y@@+H
VB>:" 0BO"+ >:"OBP"BD+ PVY(] B0 V8+ :@V+O0"+ B0 V[:@@+( >OV+@P:V+ :@ "BDD+O9=Y>:@:Y>9@:":$+":$ 65+69' D7+P R.46H

 
' OP^[' CAASH ,6H H O B^ @( H VYD+V= 0BO>:@7 DOB"+PP+PH -60 0 &0 (0' 6_&X,C.W_W' CAA,H ,4H H ) Y==+O @( H YH @ V8+ DP+Y(B9+=PV:" 8]PV+O+P:PH
6 6++0 620' WAEWF&XSW.XRC' CAACH # ,SH H BZ OOV+@P:V+P :@ 9D8P+ ==B]PH 2(/6 6++0 620' XA&CW4A.CWS6' CAAWH AXH H VPY:^YH Y""+PP:Z+ PVO+PP9:@(Y"+( >OV+@P:V:" VO@P0BO>V:B@P @( PPB":V+( VO@P0BO>V:B@ DP+Y(B+=PV:":V] :@ Y.
=.: ==B]PH
6 6++0' XR&4,4.S_C' CARAH AWH H VPY:^YH BOD8B=B7] @( "O]PV==B7OD8] B0 V8+O>B+=PV:" Y.
=.: >OV+@P:V+ @=]^+( ] V8+ D8+@B>+@B=B7:"= V8+BO]H 2-30 /0 -360 6+3' C4&C_W.C_,' CAR6H A6H H VPY@' +(:VBOPH &/ ,.2= 62(+3H >O:(7+ @:Z+OP:V] O+PP' CAA,H A4H H VPY:^YH YD+O9 +=PV:":V] +1+"VP @( PVO+PP9:@(Y"+( >OV+@P:V:" VO@P0BO>V:B@P :@ Y.
=.: ==B]PH
6 6++0' X6&X_R.XXS' CARSH

CA_

+0+O+@"+P

ASH H VBBO'
H +O8O(V' @( H +OZ+:==+OH :"OB>+"8@:"= >B(+==:@7 B0 PYD+O+=PV:":V] :@ P8D+ >+>BO] ==B]PH 0 &=3(19 ' C&XRR.XAX' CAASH ARH H VBBO' HH 7BY(P' HH @V"8+Z' HH O:@PB@' @( H BH 8D+ >+>BO] ==B]P' OV & +@+O= DOBD+OV:+P @( >B(+=:@7 B0 P:@7=+ "O]PV=PH &0 620' W,&WAC.6XA' X__SH A,H HH Y< @( H B^@: 0BO  8=09PD"+ [:V8 B9 Y@(O] :>D+O0+"V:B@PH -60 0 .+0 62960' WS&W4SA.W4RA' CAAAH AAH H +(+OP+@H +36((6=
-(3.62./= ,(-63H +"8@:"= @:Z+OP:V] B0 +@9 >O+

' D7+P A,R.AA6' B@(B@' CA,RH OB"H

@PV@H +"8H @7OPH C_XH H +VO]+>BO] ==B]PH
2&0 6++0 620' 6AE6F&RS4.RRR' X__6H C_6H H +VO]+>BO] ==B] V8+O>B>+"8@:"= +8Z:BYOH
DD=:"V:B@ VB PVOY"VYO+ "B>DY9 VV:B@ ] H &0 620' W,&4C_.4X6' X__SH C_SH H :+VO^< @(
H YO@:+OH O7+ (+0BO>V:B@ 0O:"V:B@= "B@V"V >+"8@:"P& "B@V:@YY> 0BO>Y=V:B@ @( Y7>+@V+( 7O@7:@ VO+V>+@VH .,/0 6&0
//+0 &0 -%-%0' CRREW.6F&W4C.W,C' CAAAH C_RH H :VV+O: @( H @^BVVBH +@+O:" @( @B@97+@+O:" "Y:"9VB9>B@B"=:@:" VO@9 P:V:B@P @( V8+:O V[:@PH
6 620' 6SECF&XX4.XWR' CAA,H C_,H H OY"8@:"+O V 3@:V+ PVO:@ [:V8 +(7+ +1+"VPH
6 &0' CXA&CWA.CSX' CAA,H C_AH H :@B[:"^H 2(6(.- - 2 .! 62(+3H B8@ :=+]  B@P' @"H' +[ BOB(+=P B0 DP+Y(B+=PV:":V] @( V8+:O PD+9 ":3"V:B@P 0BO PB>+ P8D+ >+>BO] ==B]PH 920 0 &0
4.+(3' CW&XC.4_' CAA6H CCXH H @:+"+>BO] ==B]PH 920 0 &0
4.+(3' CR&C,4.X_4' CAA,H CCWH H @:+":" (O:Z:@7 0BO"+ 0BO "B8+O+@V D8P+ VO@P0BO>V:B@PH -60 0 -%-% (0' WX&C,64.C,4,' CAA6H CC6H HH :"+H B@V:@YY> >+"8@:"P @( V8+O>B(]@>:"P B0 D=PV:":V] :@ O+=V:B@ VB >:"OBP"=+ (+0BO>V:B@ >+"8@:P>PH @
HH
O7B@' +(:VBO' .-36(696(: 196(.-3 (- +36((6=' D7+P XW.RAH   O+PP' >O:(7+' PPH' CAR4H CC4H H B(O:7Y+^ @( HH OB[@H 8+ V8+O>= +1+"V (Y+ VB PVO+PP9:@(Y"+( >O9 V+@P:V+ 0BO>V:B@ :@ 9Y
=: P:@7=+ "O]PV=PH 6++0 2-30
' CC
&C6R.C4_' CA,_H

+0+O+@"+P

CAC

CCSH H H B(O:7Y+^' HH BZ+]' H Y+@:@' H H +=+7O:@' H (+' @( H BO:@H =PV:" "B@PV@VP B0 V8+ >B@B"=:@:" C, >OV+@P:V+ B0  Y.@.
= ==B]H
6 6++0 620' 6CECCF&WW_R.WWC_' CAAWH CCRH
H H B]VYO(H OV+@P:V:" VO@P0BO>V:B@ P  V]D:"= D8P+ VO@P0BO>V:B@ :@ PB=:(PH @ H +:V^ @( H YO@Y==' +(:VBOP' .+( 66 &=3(3' ZB=Y>+ WW' D7+P WCR.W,_H
"(+>:" O+PP' +[ BO+ XRX B0 692 .63 (- &=3(3' D7+P CXC.CAXH DO:@7+O' +O=:@' CA,RH CXSH HH 8:+=(H O:+@VV:B@ (+D+@(+@"+ B0 V8+ DP+Y(B+=PV:" +8Z:BO B0 P:@7=+ "O]PV=P B0 Y.
=.: :@ V+@P:B@H 0 &0 &=30 .+(3' 6W&,SA.,A4' CAA4H CXRH HH :>B @( HHH Y78+PH .,/966(.-+ -+36((6=H DO:@7+O9+O=7' +[ BOOV+@P:V+ D=V+PH 920 0 &0
4.+(3' XWECF&C_R.CXS' X__6H CWXH H VYD+"8@:"P B0 "B@V"V @( :@V+OD8P+ =]+OPH  +9 DBOVP XTX__4' @PV:VYV+ B0 Y@(>+@V= +"8@B=B7:"= +P+O"8' OP[' X__4H CWWH H VYDPH .,/0 6&0
//+0 &0 -%-%0' CACEWWF&W444.W4,C' X__XH

CAX

+0+O+@"+P

CW6H H VYDV:B@ :@ V8+ V8:@93=> 8](OB(]@>:" =YO:"V:B@ O+7:>+H @ H ]' +(:VBO' 2.0 8 -60 .-!0 .- 2(.+.%= (- -9!692(-% 2.333 8??$' D7+P SA4.R_X' ]BO7' +@>O+@B=B7:"= >B(+= B0 0O:"V:B@ ""BY@V:@7 0BO PYPYO0"+ D=PV:" (+0BO>V:B@ :@ >+V= 0BO>:@7H @ H
HH OV:@P @( HHH B@V+:OB OJY+P' +(:VBOP' .-66 &-(3' B=:( +"8@:"P @( :VP
DD=:"V:B@P' D7+P CRA.C,S' BO(O+"8V' X__XH =Y[+O
"(+>:" Y=:P8+OPH CW,H H VYDB(+= B0 O+= "B@V"V O+ +ZB=YV:B@ [:V8 ""BY@V 0BO Y=< D=PV:" (+0BO>V:B@ :@ >+V= 0BO>:@7H -60 0 +360' CAEWF&WXW.W66' X__WH CWAH H VYD+"8@:"= >B(+= B0 PVO+PP9 :@(Y"+( >OV+@P:V:" VO@P0BO>V:B@P :@ P8D+ >+>BO] ==B]PH 620 (0 -%0
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
@@(H B=]"O]PV==:@+ P8D+9>+>BO] >V+O:=P& +1+"V B0 "O]PV==B7OD8:" V+\VYO+H 0 &0 &=30 .+(3' 6A&R_A.RWR' X__CH C4_H H O(:' H +(+O' @( H O:+(O:"8H Z=YV:B@ B0 V8+ O+= "B@V"V O+P' DO+PPYO+ (:PVO:YV:B@P @( "B@V"V V+>D+OVYO+P (YO:@7 P=:(:@7 "B@V"V +V[++@ O+= >+V= PYO0"+PH 2' X__&44.SX' CAASH

+0+O+@"+P

CAW

C4CH H +(@V> @( H
+]OV@+H
+=>8B=^ 0O++9+@+O7] 0Y@"V:B@ 0BO  Y.
=.: P8D+ >+>BO] ==B]H -60 0 .-' (-0 &0' 6_&CRR.CAW' X__4H # C4XH H :VV@+OH O:ZV+ "B>>Y@:"V:B@H X__6H # C4WH H :VV@+O @( H BZ +>BO] ==B]P :@ V+@9 P:B@T"B>DO+PP:B@ V8+O>B>+"8@:"= =B(PH 2-30
 0 -%0 60 &0' CXC&6,.44' CAAAH # C46H H :VV@+O @( H BZ OV+@P:V:" VO@P0BO>V:B@P :@ >B9 (+=:@7 B0 P8D+ >+>BO] ==B] DB=]"O]PV=PH -60 0 +36((6=' CS&CX6W.CXS,' X___H # C44H H :VV@+O' H BZ @' @( H
H +(H @ V8+ V8+BO] B0 V8+ 0BO>V:B@ B0 >OV+@P:V+H 2-30
 0 6+3' CAR&C4_W.C4C4' CA4WH C4,H HH 8:V+8BYP+ @( HH
O"8O(H 8+ DOBD+OV:+P B0 O@(B> PYO0"+P :@ "B@V"VH 2.0 0 .0 .-0
' WCS&AR.CXC' CAR_H C4AH HH :==:PH O:V:B@= @( O+=V+( >+V8B(P 0BO V8+ BZ+O== DOBD+OV:+P B0 "B>9 DBP:V+PH @
:-3 (-
//+( &-(3' ZB=Y>+ XC' D7+P C.R,H
"(+>:" O+PP' +[ BO+@V 0BO>Y=V:B@ B0 =O7+ (+0BO>V:B@ :>D"V9"B@V"V DOB=+>P [:V8 0O:"V:B@H .,/0 62960' WR&WCA. WWC' CAA_H CSRH H PY@7' H Y@VPY' H B;:>' H VPY>+O>@@ @( H Y>+OVH +V+O>:@V:B@ B0 V8+ 8:V D=@+ "8O"V+9 O:PV:"P :@ V8+ . D8P+ VO@P0BO>V:B@ :@(Y"+( ] PVO+PP :@ :.4
=.X@.6O. 6B.XO.C+H
6 620' 4_&CRW4.CR6_' X__XH

&7


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
=: ==B] CCX' CXA' CW,' C6X' C4W "Y:"9VB9>B@B"=:@:" VO@P0BO>V:B@ CXA' C4W' CR, "Y:"9VB9BOV8BO8B>:" VO@P0BO>V:B@ CCX' CWS' CRR Y@
= ==B] C4W' CS_ (:PP:DV:B@

CXC' CW,' C6_

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

C_W' CC,' C4W

CAS

@(+\

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

"8>:( 0"VBO CXA' CWW P8+>BO] +1+"V C_4 PV"