Anales28-038 - Pàgina inicial de UPCommons

Anales de Mecánica de la Fractura 28, Vol. 1 (2011)
'(7(50,1$&,Ï1'(/$7(1$&,'$''()5$&785$80%5$/'(32/,3523,/(126(1/$
5(*,Ï1'(75$16,&,Ï1'Ò&7,/)5È*,/
$6DOD]DU-5RGUtJXH]$0DUWtQH]30)URQWLQL
'HSDUWDPHQWRGH&LHQFLDH,QJHQLHUtDGH0DWHULDOHV(VFXHOD6XSHULRUGH&LHQFLDV([SHULPHQWDOHV\
7HFQRORJtD8QLYHUVLGDG5H\-XDQ&DUORV&7XOLSiQVQ0yVWROHV0DGULG(VSDxD
(PDLODOLFLDVDOD]DU#XUMFHV
&HQWUR&DWDOiQGHO3OiVWLFR8QLYHUVLGDG3ROLWpFQLFDGH&DWDOXxD&&ROyQ7HUUDVD(VSDxD
(PDLODQWRQLRPDUWLQH]#XSFHGX
,QVWLWXWRGH,QYHVWLJDFLRQHVHQ&LHQFLD\7HFQRORJtDGH0DWHULDOHV-XDQ%-XVWR
0DUGHO3ODWD$UJHQWLQD
(PDLOSPIURQWL#ILPGSHGXDU
5(680(1
(OSROLSURSLOHQRKRPRSROtPHUR\HOFRSROtPHURDOD]DUHWLOHQRSURSLOHQRFRQZWEDMRFRQGLFLRQHVFXDVLHVWiWLFDV
\Dž&VHHQFXHQWUDQHQUpJLPHQGHWUDQVLFLyQG~FWLOIUiJLO%DMRHVWDVFRQGLFLRQHVVHKDGHWHUPLQDGRODWHQDFLGDGGH
IUDFWXUDXPEUDOSRUGHEDMRGHOFXDOODSUREDELOLGDGGHIUDFWXUDHVQXOD3DUDHOORVHKDXWLOL]DGRXQDQiOLVLVHVWDGtVWLFR
EDVDGRHQHOPRGHORGH:HLEXOOGHSDUiPHWURV3DUDFDGDPDWHULDOVHKDQHQVD\DGRVSUREHWDVFRQGRVGLPHQVLRQHV
GLIHUHQWHV(OSROLSURSLOHQRKRPRSROtPHURSUHVHQWyHQODVSUREHWDVGHPHQRUWDPDxRYDORUHVGHWHQDFLGDGGHIUDFWXUD
XPEUDOXQVXSHULRUHVDORVGHPD\RUWDPDxR(OORREOLJyDODDSOLFDFLyQGHFULWHULRVGHFHQVXUDGHVDUUROODGRVSDUD
PHWDOHVUHGXFLHQGRODVGLIHUHQFLDVDXQ(QHOFDVRGHO FRSROtPHURDOD]DUODWHQDFLGDGGHIUDFWXUDXPEUDOIXH
LQGHSHQGLHQWH GHO WDPDxR 3RU ~OWLPR HO FRSROtPHUR DO D]DU SUHVHQWy WHQDFLGDGHV GH IUDFWXUD XPEUDOHV XQ VXSHULRUHVDORVGHOSROLSURSLOHQRKRPRSROtPHURGHELGRDODSUHVHQFLDGHODIDVHHODVWRPpULFD
$%675$&7
3RO\SURS\OHQHKRPRSRO\PHUDQGDQHWK\HOHQHSURS\OHQHUDQGRPFRSRO\PHUZLWKZWRIHWK\OHQHZHUHZLWKLQWKH
GXFWLOH WR EULWWOH WUDQVLWLRQ UHJLRQ XQGHU TXDVLVWDWLF FRQGLWLRQV DQG DW URRP WHPSHUDWXUH $ VWDWLVWLFDO DQDO\VLV ZDV
SHUIRUPHG XVLQJ WKH SDUDPHWHU :HLEXOO PRGHO WR GHWHUPLQH WKH WKUHVKROG WRXJKQHVV EHORZ ZKLFK WKHUH LV QXOO
SUREDELOLW\ RI IDLOXUH 6DPSOHV ZLWK GLIIHUHQW VL]H ZHUH WHVWHG IRU HDFK PDWHULDO ,Q FDVH RI WKH SRO\SURS\OHQH
KRPRSRO\PHUWKHWKUHVKROGWRXJKQHVVRIWKHVPDOOHUVSHFLPHQVZDV ∼KLJKHUWKDQWKRVHZLWKELJJHUVL]H7KLV
IRUFHGWKHXVHRIGDWDFHQVRULQJFULWHULDEDVHGRQWKHPHWDOOLFILHOGZKLFKUHGXFHGWKHGLIIHUHQFHVXSWR2QWKH
FRQWUDU\ WKH WKUHVKROG WRXJKQHVV RI WKH UDQGRP FRSRO\PHU UHVXOWHG VL]HLQGHSHQGHQW)LQDOO\WKHUDQGRPFRSRO\PHU
VKRZHG WKUHVKROG IUDFWXUH WRXJKQHVV KLJKHU WKDQ WKDW RI WKH SRO\SURS\OHQH KRPRSRO\PHU IRU WKH SUHVHQW RI WKH
HODVWRPHULFSKDVH
3$/$%5$6&/$9(7UDQVLFLyQG~FWLOIUiJLOWHQDFLGDGGHIUDFWXUDXPEUDOSROLSURSLOHQR
,1752'8&&,Ï1
/D FUHFLHQWH GHPDQGD HQ HO PHUFDGR GH SOiVWLFRV FRQ
ILQHV WHFQROyJLFRV H LQJHQLHULOHV GH SUHFLR PRGHUDGR \
GH IDFLOLGDG GH UHFLFODGR KD KHFKR GHO SROLSURSLOHQR
33 XQ FDQGLGDWR DWUDFWLYR SDUD QXPHURVDV
DSOLFDFLRQHV /D UD]yQ SULQFLSDO HV TXH HV IiFLOPHQWH
UHFLFODEOH \ SXHGH VHU SURFHVDGR SRU FDVL WRGRV ORV
PpWRGRV LQFOX\HQGR LQ\HFFLyQ VRSODGR \ H[WUXVLyQ
6LQ HPEDUJR VX WHQDFLGDG GH IUDFWXUD QR HV OR
VXILFLHQWHPHQWH HOHYDGD SDUD XQ XVR H[WHQVLYR HQ OD
LQGXVWULD \ HQ OD PD\RUtD GH ODV DSOLFDFLRQHV GH
LQJHQLHUtD 8QD PDQHUD GH DXPHQWDU OD WHQDFLGDG GH
IUDFWXUD GH HVWRV PDWHULDOHV FRQVLVWH HQ LQFRUSRUDU XQD
IDVH HODVWRPpULFD GLVSHUVD HQ OD PDWUL] TXH LQWURGX]FD
PHFDQLVPRV GH GHIRUPDFLyQ TXH DEVRUEDQ HQHUJtD
GXUDQWH OD IUDFWXUD (VWR SXHGH UHDOL]DUVH GH GRV
PDQHUDV PH]FODQGR ItVLFDPHQWH HO 33 FRQ RWURV
SROtPHURVEOHQGVRPHGLDQWHFRSROLPHUL]DFLyQGHO33
FRQRWUDVSROLROHILQDVGHPHQRU7JFRPRHOSROLHWLOHQR
(Q HO FDVR GHO 33 OD FRSROLPHUL]DFLyQ HV SUHIHULEOH
IUHQWHDODVPH]FODVItVLFDVGHELGRDVXEDMDPRMDELOLGDG
>@
(Q DOJXQRV FDVRV HO FRPSRUWDPLHQWR HQ IUDFWXUD GH
PDWHULDOHV EDVH 33 QR HV FRPSOHWDPHQWH IUiJLO QL
HQWHUDPHQWH G~FWLO >@ (Q HVWDV FRQGLFLRQHV ODV
FXUYDV IXHU]DGHVSOD]DPLHQWR VRQ VLHPSUH QR OLQHDOHV
OR TXH LQYDOLGD HO XVR GH OD 0HFiQLFD GH OD )UDFWXUD
(OiVWLFD \ /LQHDO 0)(/ SDUD VX FDUDFWHUL]DFLyQ (VWD
QROLQHDOLGDGVHGHEHELHQDODJHQHUDFLyQGHXQD]RQD
SOiVWLFD HQ HO HQWRUQR GH OD ILVXUD TXH QR SXHGH
FRQVLGHUDUVH SHTXHxD >@ R LQFOXVR DO FUHFLPLHQWR
243
Anales de Mecánica de la Fractura 28, Vol. 1 (2011)
GRQGH)-HVODSUREDELOLGDGGHIDOOR-HVHOYDORUGHOD
WHQDFLGDGGHIUDFWXUDGHODSUREHWDTXHYLHQHGDGDSRU
8
-=
% (: DR )
GRQGH8HVHOiUHDEDMRODFXUYDIXHU]DGHVSOD]DPLHQWR
%:\DVRQHOHVSHVRUHODQFKR\ODORQJLWXGGHJULHWD
LQLFLDOUHVSHFWLYDPHQWH&HVXQSDUiPHWURGHHVFDODP
VH GHQRPLQD IDFWRU GH IRUPD \ -R HV OD WHQDFLGDG GH
IUDFWXUD XPEUDO TXH UHSUHVHQWD HO YDORU PtQLPR GH
WHQDFLGDGSRUGHEDMRGHOFXDOODSUREDELOLGDGGHIDOORHV
QXOD
HVWDEOH GH JULHWD SUHYLD D OD URWXUD LQHVWDEOH > @
$GHPiVODFRQVWUXFFLyQGHODVFXUYDV-5HPSOHDQGROD
0HFiQLFD GH OD )UDFWXUD (ODVWR3OiVWLFD 0)(3 QR HV
SRVLEOH DO QR GHVDUUROODUVH XQ UpJLPHQ FRPSOHWDPHQWH
G~FWLO7RGDVHVWDVFDUDFWHUtVWLFDVHQHOFRPSRUWDPLHQWR
HQ IUDFWXUD GH ORV SROtPHURV XQLGR FRQ XQD
FRQVLGHUDEOH GLVSHUVLyQ HQ ORV YDORUHV GH OD WHQDFLGDG
GH IUDFWXUD FRUUHVSRQGHQ D OD UHJLyQ GH WUDQVLFLyQ
G~FWLOIUiJLO
&RFFRHWDO>@GHPRVWUDURQTXHODDOWDGLVSHUVLyQHQ
ORVYDORUHVGHWHQDFLGDGGHIUDFWXUDGHO33HQODUHJLyQ
GH WUDQVLFLyQ G~FWLOIUiJLO SXHGH VHU WUDWDGD PHGLDQWH
XQD DSUR[LPDFLyQ HVWDGtVWLFD XWLOL]DQGR HO PRGHOR GHO
HVODEyQPiVGpELO>@(VWDWHRUtDSDUWHGHODVVLJXLHQWHV
KLSyWHVLV OD WHQDFLGDG GH IUDFWXUD HV YDULDEOH D OR
ODUJR GHO YROXPHQ GH OD SLH]D \ SDUWLFXODUPHQWH D OR
ODUJR GHO IUHQWH GH JULHWD OD WHQDFLGDG GH IUDFWXUD
HVWi JREHUQDGD SRU HO SXQWR R OD UHJLyQ TXH SUHVHQWH
PHQRU YDORU GH WHQDFLGDG GH IUDFWXUD D OR ODUJR GHO
IUHQWH GH JULHWD /RV YDORUHV H[SHULPHQWDOHV SXHGHQ
DMXVWDUVHDXQPRGHORGH:HLEXOOGHSDUiPHWURVHQHO
TXHVHREWLHQHXQYDORUPtQLPRGHWHQDFLGDGGHIUDFWXUD
RWHQDFLGDGXPEUDO>@(VWHSDUiPHWURHVXQYDORU
VHJXUR GH GLVHxR \D TXH SRU GHEDMR GHO PLVPR OD
SUREDELOLGDG GH IDOOR HV QXOD R OD SUREDELOLGDG GH
VXSHUYLYHQFLDHVGHO
3DUD DMXVWDU OD FXUYD GH GLVWULEXFLyQ D ORV SXQWRV
H[SHULPHQWDOHV ORV SDUiPHWURV GH :HLEXOO -R P \ &
IXHURQFDOFXODGRVVLJXLHQGRHOVLJXLHQWHSURFHGLPLHQWR
/RVYDORUHVGHWHQDFLGDGIXHURQRUGHQDGRVGHPHQRU
DPD\RU\VHOHVDVLJQyXQQ~PHURGHRUGHQDFDGD
YDORUL
/D SUREDELOLGDG DFXPXODWLYD IXH FDOFXODGD
XWLOL]DQGRHOVLJXLHQWHHVWLPDGRU
)- ≈ 3L =
L 1
GRQGHLHVHOLpVLPRYDORUGH-\1HOQ~PHURWRWDOGH
GDWRV
/D IXQFLyQ GH SUREDELOLGDG HF VH DMXVWD D XQD
OtQHDUHFWDWRPDQGRGRVYHFHVORJDULWPRV
/RV SROtPHURV VHPLFULVWDOLQRV FRPR HO 33 \ VXV
FRSROtPHURV WLHQHQ XVRV HVWUXFWXUDOHV UHHPSOD]DQGR HQ
PXFKDV RFDVLRQHV D ORV WUDGLFLRQDOHV PHWDOHV /D
LPSRUWDQFLDGHGHWHUPLQDUGHPDQHUDILDEOHODWHQDFLGDG
GHIUDFWXUDGHHVWRVSROtPHURVHQUpJLPHQGHWUDQVLFLyQ
VH DSR\D HQ HO KHFKR GH TXH SDUD HVWRV PDWHULDOHV OD
WUDQVLFLyQ VH HQFXHQWUD SUy[LPD D OD WHPSHUDWXUD
DPELHQWHRODVROLFLWDFLyQHQVHUYLFLRSXHGHUHVXOWDUHQ
XQDYHORFLGDGGHGHIRUPDFLyQHQHOUDQJRGHWUDQVLFLyQ
/D LQFHUWLGXPEUH HQ OD GHWHUPLQDFLyQ GHO YDORU GH OD
WHQDFLGDG GH IUDFWXUD KDFH TXH H[LVWDQ IDOORV
LQHVSHUDGRV TXH SRQHQ HQ ULHVJR OD LQWHJULGDG
HVWUXFWXUDO GHO FRPSRQHQWH 3RU HOOR HO REMHWLYR GHO
SUHVHQWH WUDEDMR HV GHWHUPLQDU OD WHQDFLGDG GH IUDFWXUD
XPEUDO GH XQ33KRPRSROtPHUR\GHXQFRSROtPHURDO
D]DUHWLOHQRSURSLOHQRHQODUHJLyQGHWUDQVLFLyQG~FWLO
IUiJLO $GHPiV VH HYDOXDUi HO HIHFWR GHO HWLOHQR HQ HO
YDORUGHODWHQDFLGDGGHIUDFWXUDXPEUDO
ª § ·º
OQ «OQ¨
¸» = P ⋅ OQ (- - R ) P ⋅ OQ (& - R ) ¬ © 3 ¹¼
(OSDUiPHWURGHHVFDODPHVODSHQGLHQWHGHODUHFWD\
&SXHGHFDOFXODUVHDSDUWLUGHODRUGHQDGDHQHORULJHQ
- VH REWLHQH FRPR HO YDORU TXH SURSRUFLRQD HO PHMRU
DMXVWHGHORVSXQWRVH[SHULPHQWDOHVDODHFXDFLyQ
352&(',0,(172(;3(5,0(17$/
/RV PDWHULDOHV HVWXGLDGRV IXHURQ XQ SROLSURSLOHQR
KRPRSROtPHUR 33 \ XQ FRSROtPHUR DO D]DU HWLOHQR
SURSLOHQR (35 SURFHVDGRV SRU PROGHR SRU LQ\HFFLyQ
/D 7DEOD UHFRJH HO FRQWHQLGR HQ HWLOHQR HO SHVR
PROHFXODU 0Z HO tQGLFH GH SROLGLVSHUVLGDG α OD
WHPSHUDWXUD GH WUDQVLFLyQ YtWUHD 7J \ HO tQGLFH GH
FULVWDOLQLGDGχF
$352;,0$&,Ï1 (67$'Ë67,&$ 0e72'2
'(:(,%8//
7DEOD 3DUiPHWURV HVWUXFWXUDOHV \ SURSLHGDGHV
WpUPLFDVGHORVPDWHULDOHVHVWXGLDGRV
/RV PDWHULDOHV TXH SUHVHQWDQ XQ FRPSRUWDPLHQWR HQ OD
]RQD GH WUDQVLFLyQ G~FWLOIUiJLO VRQ GLItFLOHV GH
FDUDFWHUL]DU \D TXH QR HV SRVLEOH DSOLFDU ORV PRGHORV
EDVDGRV HQ OD WHRUtD (OiVWLFR/LQHDO 0)(/ QL
WDPSRFR DTXHOORV EDVDGRV HQ OD WHRUtD (ODVWR3OiVWLFD
0)(3 (Q HVWRV FDVRV HV SRVLEOH DSOLFDU OD
DSUR[LPDFLyQ HVWDGtVWLFD EDVDGD HQ HO PRGHOR GH
:HLEXOOGHWUHVSDUiPHWURV3:(VWHPRGHORVHULJH
SRUODVLJXLHQWHH[SUHVLyQ
­° ª - − - º P ½°
R
)- = − H[S ®− «
» ¾
−
&
R ¼ °
°̄ ¬
¿
ZW
HWLOHQRD
0Z
NJPROE
αE
7J
ž&F
χ F
G
33
(35
D
0HGLGDSRUUHVRQDQFLDPDJQpWLFDQXFOHDU501
0HGLGDSRUFURPDWRJUDItDGHH[FOXVLyQGHWDPDxRV6(&
F
0HGLGDSRUDQiOLVLVWpUPLFRPHFDQRGLQiPLFR'07$
G
0HGLGDSRUFDORULPHWUtDGLIHUHQFLDOGHEDUULGR'6&
E
/RVHQVD\RVGHWUDFFLyQVHOOHYDURQDFDERDWHQGLHQGRD
ODV GLUHFWULFHV GH OD QRUPD $670 ' >@ D XQD
YHORFLGDGGHVROLFLWDFLyQGHPPPLQ\DWHPSHUDWXUD
244
Anales de Mecánica de la Fractura 28, Vol. 1 (2011)
DPELHQWH /DV SUREHWDV HUDQ GH WLSR KDOWHULR FRQ
GLPHQVLRQHVHQOD]RQDOLEUHHQWUHPRUGD]DVGH[[
PP /D WDEOD PXHVWUD ORV YDORUHV PHGLRV MXQWR FRQ
ODVFRUUHVSRQGLHQWHVGHVYLDFLRQHVVWiQGDUGGHOPyGXOR
GHHODVWLFLGDG(HOFRHILFLHQWHGH3RLVVRQνODWHQVLyQ
GHFHGHQFLDσ<\ODGHIRUPDFLyQGHFHGHQFLDε<
SDUD HO 33 FRQ HVSHVRUHV GH \ PP
UHVSHFWLYDPHQWHWRPDQGRGLIHUHQWHVYDORUHVGH-
250
200
33
(35
(*3D
±
±
ν
±
±
σ<03D
±
±
ε<03D
±
±
Fuerza (N)
7DEOD3URSLHGDGHVPHFiQLFDVGH33\(35
150
100
PP0
50
/RV HQVD\RV GH WHQDFLGDG VH UHDOL]DURQ VREUH SUREHWDV
QRUPDOL]DGDV GH IOH[LyQ 6LQJOH (GJH 1RWFK %HQG
6(1% >@FRQHVSHVRUHVGH\PPVLHQGRODV
GLPHQVLRQHV WRWDOHV GH [[ PP \ [[
PP UHVSHFWLYDPHQWH 6H XWLOL]y XQ GLVSRVLWLYR GH
IOH[LyQ HQ WUHV SXQWRV FRQ XQD OX] GH FXDWUR YHFHV HO
DQFKRGHODSUREHWD/DORQJLWXGGHODHQWDOODLQLFLDOIXH
GH\PPSDUDODVSUREHWDVFRQHVSHVRUHVGH
\PPGHHVSHVRUUHVSHFWLYDPHQWH&RQD\XGDGHXQD
FXFKLOOD VH LQVHUWy XQD JULHWD DILODGD HQ HO FHQWUR GH OD
HQWDOODKDVWDFRQVHJXLUXQDORQJLWXGILQDODGHPP
SDUD ODVPXHVWUDVGHPPGHHVSHVRU\GHPP
SDUD ODV SUREHWDV GH PP GH HVSHVRU /RV HQVD\RV GH
IUDFWXUD VH UHDOL]DURQ HQ XQD PiTXLQD HOHFWURPHFiQLFD
XQLYHUVDOGHHQVD\RVPHFiQLFRV076$OOLDQFH5)
HQODTXHODIXHU]DVHPLGLyFRQXQDFpOXODGHFDUJDGH
± N1 /DV FRQGLFLRQHV GH HQVD\R IXHURQ WDOHV TXH
DPERV PDWHULDOHV VH HQFRQWUDURQ HQ UpJLPHQ GH
WUDQVLFLyQG~FWLOIUiJLOHVGHFLUDž&\EDMRFRQWURO
GHSRVLFLyQDXQDYHORFLGDGGHPPPLQ'HELGRDOD
QDWXUDOH]D DOHDWRULD GHO FRPSRUWDPLHQWR HQ IUDFWXUD VH
OOHYDURQ D FDER ∼ HQVD\RV SDUD FDGD PDWHULDO \
FRQGLFLyQ
B=6.35 mm
B=9 mm
0
0
0,5
1
1,5
2
Desplazamiento (mm)
)LJXUD 7tSLFDV FXUYDV IXHU]DGHVSOD]DPLHQWR GH
SUREHWDVGH33FRQ\PPGHHVSHVRU
D
PP
E
5(68/7$'26<',6&86,Ï1
3ROLSURSLOHQRKRPRSROtPHUR33
3DUD HO SROLSURSLOHQR KRPRSROtPHUR 33 ORV UHJLVWURV
IXHU]DGHVSOD]DPLHQWRGHODVSUREHWDVFRQ\PP
GH HVSHVRU IXHURQ QR OLQHDOHV \ WRGDV ODV SUREHWDV VH
URPSLHURQ GH PDQHUD LQHVWDEOH DQWHV GH DOFDQ]DU HO
SODWHDXGHFDUJDPi[LPD)LJXUD
PP
)LJXUD6XSHUILFLHVGHIUDFWXUDWtSLFDVGHSUREHWDVGHO
33FRQHVSHVRUHVGHD\EPP
/DV)LJXUDVD\EPXHVWUDQODVVXSHUILFLHVGHIUDFWXUD
SDUD ODV SUREHWDV GH \ PP GH HVSHVRU
UHVSHFWLYDPHQWH 7RGDV HOODV SUHVHQWDURQ FUHFLPLHQWR
LUUHJXODU GH ILVXUD SHUR HQ QLQJ~Q FDVR HO DYDQFH
VXSHUy HQ SURPHGLR HO OLJDPHQWR UHPDQHQWH
LQFLDO/RVUHVXOWDGRVGHWHQDFLGDGYDULDURQHQWUH\
N-P \ HQWUH \ N-P SDUD ODV SUREHWDV
FRQ\PPGHHVSHVRUUHVSHFWLYDPHQWH$VXYH]
ORV FRUUHVSRQGLHQWHV YDORUHV GH WHQDFLGDG GH IUDFWXUD
PHGLR IXHURQ GH \ N-P UHVSHFWLYDPHQWH /DV
)LJXUDV D \ E PXHVWUDQ OD HYROXFLyQ GH OD UHJUHVLyQ
OLQHDOGHODIXQFLyQGHSUREDELOLGDGDFXPXODWLYDHF
(O Q~PHUR GH HQVD\RV SDUD GHWHUPLQDU OD WHQDFLGDG GH
IUDFWXUD XPEUDO HQ OD UHJLyQ GH WUDQVLFLyQ G~FWLOIUiJLO
GHO 33 IXH GH SUREHWDV SDUD ODV PXHVWUDV FRQ PPGHHVSHVRU\GHSUREHWDVSDUDODVPXHVWUDVFRQ
PPGHHVSHVRU(QpVWH~OWLPRFDVRKXERTXHGHVFDUWDU
SUREHWDVGHODVLQLFLDOPHQWHHQVD\DGDVGHELGRDOD
SUHVHQFLDGHSRURVHQODUHJLyQGHURWXUDFRQWDPDxRV
VXSHULRUHV D μP (VWRV GHIHFWRV VH JHQHUDURQ
GXUDQWHHOSURFHVRGHLQ\HFFLyQVLHQGRPiVSUREDEOHVX
DSDULFLyQFXDQWRPD\RUHVHOHVSHVRUGHODSUREHWD
245
Anales de Mecánica de la Fractura 28, Vol. 1 (2011)
2
(a)
SUREDELOLGDG WHQLHQGR HQ FXHQWD WRGRV ORV GDWRV SHUR
XWLOL]DQGR XQ FULWHULR GH H[FOXVLyQ DO DMXVWDU ORV
SDUiPHWURVGHODIXQFLyQGLVWULEXFLyQ/DQRUPD$670
( >@ HVWDEOHFH UHTXHULPLHQWRV HQ UHODFLyQ D ODV
GLPHQVLRQHV GH ODV SUREHWDV HVWDEOHFLHQGR XQ YDORU
OtPLWH GH - SDUD HYLWDU ORV HIHFWRV GH SpUGLGD GH
UHVWULFFLyQHQHOSODQRHVWDGRPL[WRWHQVLRQDO\GHHVWD
PDQHUD FRQVHJXLU XQ IUHQWH GH JULHWD UHFWR (O YDORU
Pi[LPRGH--OLPHVLJXDOD
PP0
B= 6.35 mm
N= 60
1
Ln(Ln(1/(1-P )))
0
i
-1
m= 1.443
-2
C= 9.262 kJ/m
2
- OLP =
-3
J=J
0
J = 6.53
min
-10
0
2
R = 0.7249
-6
J =0
0
2
2
R = 0.9879
-8
-6
-4
-2
R = 0.8837
0
2
Ln(J-J )
0
2
PP0
B= 9 mm
N= 32
(a)
PP0
B= 6.35 mm
N´= 60
1
0
Ln(Ln(1/(1-P )))
0
-1
-1
i
i
2
(b)
1
Ln(Ln(1/(1-P )))
(O WUDWDPLHQWR HVWDGtVWLFR D UHDOL]DU HQ XQ FRQMXQWR GH
GDWRV HQ HO TXH H[LVWHQ YDORUHV TXH QR FXPSOHQ HO
FULWHULR GH WDPDxR GHILQLGR SRU OD HFXDFLyQ HV HO
PLVPRTXHHOGHVFULWRHQHOSURFHGLPLHQWRH[SHULPHQWDO
DH[FHSFLyQTXHORVGDWRVFHQVXUDGRVVRQUHHPSOD]DGRV
SRU-OLPHF>@
-4
-5
(: − D )σ<
-2
m= 1.69
C= 8.235 kJ/m
-3
2
-2
m= 1.707
-3
C= 7.056 kJ/m
2
-4
-4
J =J
0
-5
J =5.195
min
-10
-6
-4
-2
J =J
0
2
R = 0.9835
-8
-5
0
2
R = 0.6354
-12
J =0
0
2
R = 0.8967
0
2
J =5.95
min
-6
4
J =0
0
R = 0.6543
-10
0
R = 0.9333
2
2
R = 0.8794
2
-8
-6
Ln(J-J )
-4
-2
0
2
4
Ln(J-J )
0
0
)LJXUD$MXVWHGHODIXQFLyQGHSUREDELOLGDGHF
GHO33FRQDPP\EPPGHHVSHVRU
2
/RV YDORUHV GH WHQDFLGDG GH IUDFWXUD XPEUDO REWHQLGRV
SDUD ODV SUREHWDV GH 33 GH \ PP GH HVSHVRU
IXHURQ \ N-P UHVSHFWLYDPHQWH /D
GLVFUHSDQFLD GH HVWRV UHVXOWDGRV FRQ HO HVSHVRU SXHGHQ
GHEHUVH D GRV PRWLYRV (O SULPHUR GH HOORV SDUWH GH OD
KLSyWHVLV GH OD DSUR[LPDFLyQ HVWDGtVWLFD HO SXQWR GH
PHQRU WHQDFLGDG GH IUDFWXUD D OR ODUJR GHO IUHQWH GH
JULHWDFRQWURODODIUDFWXUDIUiJLOSRUWDQWRXQDSUREHWD
VH URPSH FXDQGR VH DOFDQ]D HO YDORU GHO IDFWRU GH
LQWHQVLGDG GH WHQVLRQHV FUtWLFR HVODEyQ PiV GpELO HQ
GLFKRSXQWR>@'HDFXHUGRFRQ+HHUHQVHWDO>@
OD Pi[LPD WHQVLyQ DIHFWDUi D XQ YROXPHQ PD\RU GHO
PDWHULDOHQXQDSUREHWDFRQXQDILVXUDTXHDYDQ]DTXH
HQXQDSUREHWDFRQXQDILVXUDHVWDFLRQDULDDXPHQWDQGR
DVtODSUREDELOLGDGGHIUDFWXUDIUiJLO\SXGLHQGRVHUHVWH
DYDQFH GHSHQGLHQWH GHO HVSHVRU (O VHJXQGR PRWLYR VH
GHEH D TXH ODV SUREHWDV GH PHQRU HVSHVRU PP
SXHGHQ QR HVWDU HQ FRQGLFLRQHV GH GHIRUPDFLyQ SODQD
3DUD HYLWDU HVWRV HIHFWRV HQ OD GHWHUPLQDFLyQ WHQDFLGDG
GHIUDFWXUDXPEUDOVHXWLOL]DQHVWUDWHJLDVGHFHQVXUDGH
GDWRV eVWDV FRQVLVWHQ HQ UHDOL]DU HO FiOFXOR GH OD
(b)
PP0
B= 9 mm
N´= 32
1
i
Ln(Ln(1/(1-P )))
0
-1
m= 1.860
-2
C= 8.016 kJ/m
2
-3
-4
J=J
0
-5
J =5.10
min
-10
J =0
0
2
-8
0
2
R = 0.9575
R = 0.6360
-6
-4
-2
0
2
R = 0.9161
2
4
Ln(J-J )
0
)LJXUD $MXVWH GH ODV IXQFLRQHV GH SUREDELOLGDG GHO
33FRQFHQVXUDGHGDWRVVHJ~QFULWHULRGHWDPDxRHF
SDUDSUREHWDVFRQD\EPPGHHVSHVRU
/DV )LJXUDV D \ E PXHVWUDQ OD HYROXFLyQ GH OD
UHJUHVLyQ OLQHDO GH OD IXQFLyQ GH SUREDELOLGDG
246
Anales de Mecánica de la Fractura 28, Vol. 1 (2011)
DFXPXODWLYDHFSDUDHO33FRQHVSHVRUHVGH\
PPUHVSHFWLYDPHQWHWRPDQGRGLIHUHQWHVYDORUHVGH-
\WHQLHQGRHQFXHQWDHOFULWHULRGHWDPDxRGHILQLGRSRU
ODHFXDFLyQ/RVYDORUHVGH-GHO33GHODVSUREHWDV
FRQ \ PP GH HVSHVRU WUDV WHQHU HQ FXHQWD OD
H[FOXVLyQGHGDWRVVHJ~QHOFULWHULRGHWDPDxRVRQ
\N-PUHVSHFWLYDPHQWH/DVGLIHUHQFLDVHQ-FRQ
HO HVSHVRU IXHURQ GHO \ HO KHFKR GH XQ DOFDQ]DU
XQLIRUPLGDGHQHOYDORUSXHGHVHUGHELGRDTXHHOYDORU
GH-OLPHFHVWiGHVDUUROODGRSDUDPHWDOHV>@\PX\
SUREDEOHPHQWHGHEHQVHUUHGHILQLGRVSDUDSROtPHURV
/DV)LJXUDVD\EPXHVWUDQODVVXSHUILFLHVGHIUDFWXUD
FDUDFWHUtVWLFDV SDUD ODV SUREHWDV GH \ PP GH
HVSHVRUUHVSHFWLYDPHQWH6HREVHUYDXQD]RQDGHFODUD
GHIRUPDFLyQ SOiVWLFD ]RQD EODQTXHFLQD SUy[LPD D OD
HQWDOOD \ SHTXHxRV FUHFLPLHQWRV HVWDEOHV GH JULHWD FRQ
ORQJLWXGHV Pi[LPDV GH ∼ μP /RV UHVXOWDGRV GH
WHQDFLGDG YDULDURQ HQWUH \ N-P \ HQWUH
\ N-P SDUD ODV SUREHWDV FRQ \ PP
GH HVSHVRU UHVSHFWLYDPHQWH $ VX YH] ODV
FRUUHVSRQGLHQWHVWHQDFLGDGHVGHIUDFWXUDPHGLDVIXHURQ
GH\N-PUHVSHFWLYDPHQWH/DV)LJXUDVD
\ E PXHVWUDQ OD HYROXFLyQ GH OD UHJUHVLyQ OLQHDOGHOD
IXQFLyQGHSUREDELOLGDGDFXPXODWLYDHFSDUDHO(35
FRQ HVSHVRUHV GH \ PP UHVSHFWLYDPHQWH
WRPDQGR GLIHUHQWHV YDORUHV GH - /RV YDORUHV GH
WHQDFLGDGGHIUDFWXUDXPEUDOREWHQLGRVSDUDODVSUREHWDV
GH (35 GH \ PP GH HVSHVRU IXHURQ \ N-P UHVSHFWLYDPHQWH /RV YDORUHV GH - SDUD HVWH
PDWHULDO IXHURQ LQGHSHQGLHQWHV GHO HVSHVRU VLHQGR
LQQHFHVDULDODXWLOL]DFLyQGHFULWHULRVGHFHQVXUD
&RSROtPHURDOD]DU(35
/DV FXUYDV IXHU]DGHVSOD]DPLHQWR GH ODV SUREHWDV GH
(35 FRQ \ PP GH HVSHVRU IXHURQ QR OLQHDOHV \
WRGDV URPSLHURQ GH PDQHUD LQHVWDEOH DQWHV GH DOFDQ]DU
HOSODWHDXGHFDUJDPi[LPD)LJXUD
250
200
2
(a)
EPR
B= 6.35 mm
N= 58
150
0
Ln(Ln(1/(1-P )))
100
-1
i
Fuerza (N)
1
EPR
50
B= 6.35 mm
m= 2.508
-2
C= 20.60 kJ/m
2
-3
B= 9 mm
-4
0
0
0,5
1
1,5
2
2,5
3
3,5
4
Desplazamiento (mm)
-5
)LJXUD&XUYDVIXHU]DGHVSOD]DPLHQWRFDUDFWHUtVWLFDV
GHSUREHWDVGH(35FRQ\PPGHHVSHVRU
J =J
0
J =8.5
min
0
2
-6
-8
J =0
0
2
2
R = 0.9638 R = 0.9303
R = 0.6076
-6
-4
-2
0
2
4
Ln(J-J )
D
0
2
(b)
EPR
B= 9 mm
N= 56
1
-1
i
Ln(Ln(1/(1-P )))
0
PP
E
m= 1.951
-2
C= 12.509 kJ/m
2
-3
-4
-5
J =J
0
J =8.58
min
-6
-10
J =0
0
2
-8
0
2
2
R = 0.9877 R = 0.9118
R = 0.6626
-6
-4
-2
0
2
4
Ln(J-J )
0
PP
)LJXUD $MXVWH GH ODV IXQFLRQHV GH SUREDELOLGDG GHO
(35SDUDSUREHWDVFRQD\EPPGHHVSHVRU
)LJXUD6XSHUILFLHVGHIUDFWXUDWtSLFDVGHSUREHWDVGHO
(35FRQHVSHVRUHVGHD\EPP
247
Anales de Mecánica de la Fractura 28, Vol. 1 (2011)
(IHFWRGHOFRQWHQLGRGHHWLOHQR
SURFHVVLQJ DQG DSSOLFDWLRQV HGLWDGR SRU +DQVHU
3XEOLVKHUV0XQLFK
/DWDEODUHFRSLODORVYDORUHVGHWHQDFLGDGGHIUDFWXUD
XPEUDO GHO 33 \ (35 PHGLGRV HQ SUREHWDV FRQ
HVSHVRUHVGH\PPGHHVSHVRU'RVFRQFOXVLRQHV
VH REWLHQHQ GHO DQiOLVLV GH OD SUHVHQWH WDEOD(QSULPHU
OXJDUHOYDORUGH-HVXQSDUiPHWURLQGHSHQGLHQWHGHO
WDPDxR SDUD XQ PLVPR PDWHULDO /DV GLIHUHQFLDV PiV
VLJQLILFDWLYDV VH REWXYLHURQ HQ 33 FRQ GLVFUHSDQFLDV
GHO (Q VHJXQGR OXJDU HO PDWHULDO FRQ FRQWHQLGR
HQ HWLOHQR (35 SUHVHQWy YDORUHV GH - XQ PiV
DOWRVTXHORVGHOSROLSURSLOHQRKRPRSROtPHUR33(VWH
HVXQUHVXOWDGRHVSHUDEOHWHQLHQGRTXHODIDVHHWLOpQLFD
HVLQWURGXFLGDSDUDJHQHUDUPHFDQLVPRVGHGHIRUPDFLyQ
TXHDEVRUEDQHQHUJtDGXUDQWHODIUDFWXUD>@
>@)DVFH/$)URQWLQL30$VVHVVPHQWRILPSDFW
WRXJKQHVV RI 33(ODVWRPHULF 3RO\ROHILQH EOHQGV
-RXUQDO RI 0DFURPROHFXODU 6FLHQFH 3DUW %3K\VLFV
%SS
>@*UHLQ & .DXVFK + + %HJXHOLQ 3 +
&KDUDFWHUL]DWLRQ RI WRXJKHQHG SRO\PHUV E\ /()0
XVLQJ DQ H[SHULPHQWDO GHWHUPLQDWLRQ RI WKH SODVWLF
]RQH FRUUHFWLRQ 3RO\PHU 7HVWLQJ SS
>@&RFFR5*7HQDFLGDGGHIUDFWXUDHQODUHJLRQGH
WUDQVLFLyQ GXFWLOIUiJLO GH SROtPHURV 7HVLV
'RFWRUDO$UJHQWLQD
7DEOD9DORUHVGHODWHQDFLGDGGHIUDFWXUDXPEUDOHQ
N-P - REWHQLGRV HQ SUREHWDV GH \ PP GH
HVSHVRUGH33\(35
%PP
33
(35
>@*UHOOPDQQ : &KH 0 $VVHVVPHQW RI
WHPSHUDWXUHGHSHQGHQW IUDFWXUH EHKDYLRU ZLWK
GLIIHUHQW IUDFWXUH PHFKDQLFV FRQFHSWV RQ H[DPSOHV
RI XQRULHQWHG DQG FROGUROOHG SRO\SURS\OHQH
-RXUQDORI$SSOLHG3RO\PHU6FLHQFHSS
>@$QGHUVRQ 7 / )UDFWXUH 0HFKDQLFV
)XQGDPHQWDOVDQG$SSOLFDWLRQVQGHG&5&3UHVV
%RFD5DWRQ)/SS
&21&/86,21(6
(OSROLSURSLOHQRKRPRSROtPHUR\HOFRSROtPHURDOD]DU
HWLOHQRSURSLOHQR FRQ XQ ZW GH HWLOHQR VH
HQFXHQWUDQ HQ OD UHJLyQ GH WUDQVLFLyQ G~FWLOIUiJLO EDMR
FRQGLFLRQHV FXDVLHVWiWLFDV \ D WHPSHUDWXUD DPELHQWH
3RU HOOR VH KD HYDOXDGRODLQIOXHQFLDGHOWDPDxR\GHO
FRQWHQLGRHQHWLOHQRHQODWHQDFLGDGGHIUDFWXUDXPEUDO
HQ HVWH UpJLPHQ XWLOL]DQGR HO PRGHOR GH :HLEXOO GH SDUiPHWURV(QHOFDVRGHOSROLSURSLOHQRKRPRSROtPHUR
OD WHQDFLGDG GH IUDFWXUD XPEUDO SUHVHQWy YDORUHV ∼
PD\RUHVHQODVSUREHWDVFRQPHQRUHVSHVRUHVGHFLUGH
PP IUHQWH D PP GH HVSHVRU (VWDV GLIHUHQFLDV
REOLJDURQ D XWLOL]DU FULWHULRV GH FHQVXUD EDVDGRV HQ
DTXHOORVGHVDUUROODGRVSDUDPHWDOHVORTXHUHGXMRHVWDV
GLIHUHQFLDVD∼(QHOFDVRGHOFRSROtPHURDOD]DU
QR VH REVHUYDURQ GLIHUHQFLDV HQWUH ORV YDORUHV GH OD
WHQDFLGDG GH IUDFWXUD XPEUDO PHGLGRV HQ SUREHWDV FRQ
GLVWLQWDV GLPHQVLRQHV SHUR Vt HQ ORV YDORUHV GH OD
WHQDFLGDGGHIUDFWXUDPHGLD3RU~OWLPRODWHQDFLGDGGH
IUDFWXUDXPEUDOGHOFRSROtPHURDOD]DUSUHVHQWyYDORUHV
GH WHQDFLGDG ∼ VXSHULRUHV D ORV GH SROLSURSLOHQR
KRPRSROtPHUR SXHVWR TXH HO HWLOHQR HV XQD IDVH
HODVWRPpULFD LQWURGXFLGD SDUD JHQHUDU PHFDQLVPRV GH
GHIRUPDFLyQGXUDQWHHOSURFHVRGHURWXUD
>@ &RFFR 5 * )URQWLQL 3 0 3pUH] ,SLxD - (
7KUHVKROG WRXJKQHVV RI SRO\PHUV LQ WKH GXFWLOH WR
EULWWOH WUDQVLWLRQ UHJLRQ E\ GLIIHUHQW DSSURDFKHV
(QJLQHHULQJ )UDFWXUH 0HFKDQLFV >@ SS
>@$670 ( 6WDQGDUG WHVW PHWKRG IRU
GHWHUPLQDWLRQ RI UHIHUHQFH WHPSHUDWXUH 7 IRU
IHUULWLFVWHHOVLQWKHWUDQVLWLRQUDQJH
>@ +HHUHQV - =HUEVW 8 6FKZDOEH . + 6WUDWHJ\
IRU FKDUDFWHUL]LQJ IUDFWXUH WRXJKQHVV LQ WKH GXFWLOH
WR EULWWOH WUDQVLWLRQ UHJLPH)DWLJXHDQG)UDFWXUHRI
(QJLQHHULQJ 0DWHULDOV DQG 6WUXFWXUHV >@
SS
>@/DQGHV-'0F&DEH'((IIHFWRIVHFWLRQVL]H
RQ WUDQVLWLRQ EHKDYLRXU RI VWUXFWXUDO VWHHOV
:HVWLQJKRXVH5'&HQWHUSDSHU'0HWDO3
>@$670 ' 6WDQGDUG WHVW PHWKRG IRU WHQVLOH
SURSHUWLHVRISODVWLFV
>@+DOH*(5DPVWHLQHU)-IUDFWXUHWRXJKQHVVRI
SRO\PHUV DW VORZ VSHHG ,Q )UDFWXUH PHFKDQLFV
WHVWLQJ PHWKRGV IRU SRO\PHUV DGKHVLYHV DQG
FRPSRVLWHV'50RRUH$3DYDQ-*:LOOLDPV
HGLWRUV (OVHYLHU 6FLHQFH /WG DQG (6,6 7KH
1HWKHUODQGVSS
$*5$'(&,0,(1726
/RV DXWRUHV GHVHDQ DJUDGHFHU DO 0LQLVWHULR GH
(GXFDFLyQ OD ILQDQFLDFLyQ D WUDYpV GHO 0$7
\D5(362/SRUHOVXPLQLVWURGHPDWHULDO
5()(5(1&,$6
>@0RRUH ( 3 3RO\SURS\OHQH KDQGERRN ±
3RO\PHUL]DWLRQ
FKDUDFWHUL]DWLRQ
SURSHUWLHV
248