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LEFM - Mode 1 Stress intensity factors (J-Integral) for inner cracks in pressurized thick-walled cylinders

Hi

During my thesis I am calculating mode 1 stress intensity factors (J-integral) for inner crack in pressurized thick-walled cylinders with ANSYS v13.

The loads are inner pressure on the cylinder bore and gas pressure directly on the crack plane.

I wanted to know why the J-Integral converge along part of the crack front (from the deepest point Phi=90 until Phi=60 degrees, assuming semi-circular crack) when loading the crack plane directly while with the inner pressure the J-integral converge along the whole crack path.

 Best regards

 

 

 

Hi, saley,

if you still have this problem, I can take a look. The J-integral should converge in both cases.   

I hope you're right and I made a mistake.

Cylinder geometry : length=1, outer radius=2, inner radius=1, wall thickness=2-1=1.

Singel inner crack geometry : a=c=0.05 (semi-circular), crack plane perpendicular to the cylinder cross-section.

Material properties : E=200e3 MPa, nu=0.3 (linear, elastic).

Load (surface load) : 608 MPa opening pressure perpendicular to the crack plane.

Analysis type : static.

********************************************

ANSYS macro file :

finish
/clear

!Units : MN,m

/filn,OIC608GAS005ATT1ATC

!a=0.05
!c=0.05
!a/c=1
!a/t=0.05
!L/c=10
!2L=1, length
!Ro=2, outer radius
!Ri=1, inner radius
!t=1, wall thickness
!P=608 MPa, crack pressure

/prep7
 
mp,ex,1,200e3
mp,prxy,1,0.3

et,1,plane183
et,2,solid186

cyl4,0,0,1,0,2,180,0.5
kwplan,-1,8,5,2
cyl4,0,0,1
csys,4
arscale,7,,,0.05,0.05,1,,0,0
adele,7,,,1
adele,8
ldele,19,20,,1
lcomb,17,18,0 
lsbl,12,17,,delete,keep
lsbl,8,17,,delete,keep
kgen,2,13,,,0.01,,,,0
kgen,2,13,,,-0.01,,,,0
kgen,2,13,,,,,0.01,,0
larc,10,12,13,0.01
larc,11,12,13,0.01
lsbl,15,16,,delete,keep
lsbl,12,8,,delete,keep
al,8,16,19,20
vdrag,7,,,,,,17
vptn,1,2
vdele,4,,,1
ldele,17,,,1

ldiv,2,0.5,,2,0
lang,7,14,90,,
lang,4,14,90,,
lang,5,15,90,,
lstr,17,16
asbl,3,24
asbl,24,14
asbl,25,23
asbl,1,21

kscon,13,0.002,1,8,

lesize,8,,,6,,,,,1
lesize,16,,,6,,,,,1

amesh,7

lesize,33,,,20,,,,,1
extopt,aclear,1
vsweep,3

lesize,18,,,10,0.3,,,,1
lesize,40,,,10,0.3,,,,1
lesize,41,,,20,0.05,,,,1
lesize,15,,,40,0.02,,,,1
lesize,7,,,30,20,,,,1

lesize,10,,,5,,,,,1
lesize,1,,,15,,,,,1
lesize,2,,,15,2,,,,1
lesize,4,,,25,2,,,,1
lesize,5,,,25,2,,,,1

lesize,14,,,3,,,,,1
lesize,21,,,6,,,,,1
lesize,23,,,6,,,,,1
lesize,24,,,3,,,,,1

lesize,17,,,20,,,,,1
lesize,12,,,10,,,,,1
lesize,13,,,10,,,,,1
lesize,22,,,20,,,,,1

lesize,3,,,6,,,,,1
lesize,6,,,6,,,,,1
lesize,9,,,3,,,,,1
lesize,11,,,3,,,,,1

mshape,1,3d
vmesh,5

nummrg,node,,,,low

/solu

da,8,symm
da,9,symm
da,7,symm
da,6,symm
da,23,symm
da,16,symm

sfa,15,,pres,608
sfa,22,,pres,608

csys,0

cint,new,1
lsel,s,line,,33
nsll,s,1
cm,CrackFront,node
allsel,all
cint,ctnc,CrackFront
cint,norm,0,2
cint,ncon,20
cint,symm,1
cint,type,sifs
outres,cint,,

eqslv,iter,5

solve

eplot

/output,OIC608GAS005ATT1ATC
/post1
prcint,,1261,k1 !Phi=0
prcint,,1245,k1 !Phi=9
prcint,,1249,k1 !Phi=18
prcint,,1253,k1 !Phi=27
prcint,,1257,k1 !Phi=36
prcint,,1599,k1 !Phi=45
prcint,,1603,k1 !Phi=54
prcint,,1607,k1 !Phi=63
prcint,,1611,k1 !Phi=72
prcint,,1615,k1 !Phi=81
prcint,,26,k1   !Phi=90  
/output,

******************************************** 

The ruslts file :

***** POST1 K1           RESULT LISTING *****

 CrackID =   1  Crack Front Node = 1261                                *****Phi=0 ******
   Contour Values =    144.21       123.43       113.46       101.76   

***** POST1 K1           RESULT LISTING *****

 CrackID =   1  Crack Front Node = 1245                                *****Phi=9 ******
   Contour Values =    146.54       129.33       120.28       109.57   

***** POST1 K1           RESULT LISTING *****

 CrackID =   1  Crack Front Node = 1249                                *****Phi=18 ******
   Contour Values =    145.27       131.48       124.25       115.61   

***** POST1 K1           RESULT LISTING *****

 CrackID =   1  Crack Front Node = 1253                                *****Phi=27 ******
   Contour Values =    145.73       134.86       129.22       122.52   

***** POST1 K1           RESULT LISTING *****

 CrackID =   1  Crack Front Node = 1257                                *****Phi=36 ******
   Contour Values =    147.05       138.79       134.58       129.60   

***** POST1 K1           RESULT LISTING *****

 CrackID =   1  Crack Front Node = 1599                                *****Phi=45 ******
   Contour Values =    148.70       142.74       139.78       136.30   

***** POST1 K1           RESULT LISTING *****

 CrackID =   1  Crack Front Node = 1603                                *****Phi=54 ******
   Contour Values =    150.35       146.34       144.44       142.23   

***** POST1 K1           RESULT LISTING *****

 CrackID =   1  Crack Front Node = 1607                                *****Phi=63 ******
   Contour Values =    151.79       149.36       148.31       147.11   

***** POST1 K1           RESULT LISTING *****

 CrackID =   1  Crack Front Node = 1611                                *****Phi=72 ******
   Contour Values =    152.90       151.63       151.19       150.74   

***** POST1 K1           RESULT LISTING *****

 CrackID =   1  Crack Front Node = 1615                                *****Phi=81 ******
   Contour Values =    153.59       153.04       152.98       152.98   

***** POST1 K1           RESULT LISTING *****

 CrackID =   1  Crack Front Node =   26                                *****Phi=90 ******
   Contour Values =    153.81       153.51       153.58       153.73      

********************************************   

Thanks again

Saley

:)

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