I used ANSYS for mode I and mixed mode crack analysis, J-integral is used to obtain the stress intensity factors. In mode I, one can obtain the KI value using J-int (J=KI2/E, for plane stress condition).
For mixed mode the relation between J and K is J=(KI2+KII2)/E. Since there is no dependence between KI and KII, how do I get KI and KII values from J-integral.?
Hi,
find the below code, which is an example on how to obtain SIF's by J-intergral and stress extrapolation method.
*run this file in Ansys!
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finish
/clear
/units,si
/prep7 !Enters preprocessor
!---PARAMETERS---
W=30e-3 !Parameter to control geometry
hh=0.6*W !Half-height
hc=0.325*W !Hole center
hr=0.25*W !Hole diameter
ch=0.2*W !Crack to hole
h=W/16 !Wide crack faces
!a=10e-3 !Crack length
B=0.5*W
size=W/100
E=200e9 !Young's Modulus
nu=0.3 !Poisson's Ratio
P=1000 !Force
et,1,plane183,,,2 !Specifies element type
!r,thk,7e-3
mp,ex,1,E !Specifies material parameter
mp,nuxy,1,nu
keyopt,1,1,1 !Specifies keyoption
!---GEOMETRY---
k,1,0,0 !Creates keypoints 1 to 9
k,2,1.25*W,0
k,3,1.25*W,hh-h/2
k,4,W-4e-3,hh-h/2
k,5,W-ch,hh
k,6,W-ch-a,hh
k,7,0,hh
k,8,W-4e-3,hh-3*h
k,9,0,hh-3*h
A,1,2,3,4,8,9 !Creates area between specified keypoints, also used to create the coarse mesh
cyl4,W,hc,hr/2 !Creates hole area
A,8,4,5,6,7,9 !Creates area between specified keypoints, also used to create the fine mesh
ASBA,1,2 !Removes hole area from area
lesize,4,size !Refines mesh at close vicinity of crack tip
lesize,5,size
esize,size !Specifies mesh size at fine mesh
kscon,6,size,1 !Collapses mesh at crack tip
amesh,3 !Creates fine mesh
esize,size*5 !Specifies mesh size at coarse mesh
amesh,4 !Creates coarse mesh
Node1=node(W-ch-a,hh,0) !Creates node selections
Node2=node(W-ch-a+2*size,hh,0)
Node3=node(W-ch-a+5*size,hh,0)
Node4=node((W-a)/2,hh,0)
clocal,12,1,w-ch-a,hh,,180 !Creates local coordinate system number 12 at crack tip
csys,0
clocal,13,1,w-ch-a,hh, !Creates local coordinate system number 13 at crack tip
csys,12
nsel,s,loc,x,0,a
nsel,r,loc,y,0
cm,tip,node !Selects nodes and places them in selection 'tip'
cint,new,1 !Specifies new contour integral calculation
cint,type,TSTRESS !Specifies that T-stress is to be calculated
CINT,CTNC,tip !Specifies which nodes that lies on the crack surfaces
cint,norm,12,2 !Specifies that the y-axis is normal to the crack surfaces
CINT,SYMM,ON !Specifies that the model is symmetrical
CINT,NCON,7 !Specifies that seven contours are to be used
cint,new,2
cint,type,sifs
CINT,CTNC,tip
cint,norm,12,2
CINT,SYMM,ON
CINT,NCON,7
cint,new,3
cint,type,jint
CINT,CTNC,tip
cint,norm,12,2
CINT,SYMM,ON
CINT,NCON,7
csys,0
clocal,11,1,W,hc !Create a local system at hole center
csys,11
finish
/solu
!---BOUNDARY CONDITIONS---
csys,0
lsel,s,line,,13
nsll,s,1 !Selects nodes on line 13
d,all,uy,0 !Applies zero displ. at selected nodes, y-dir
nsel,r,loc,x,0 !Selects one node on at end of line 13
d,all,ux,0 !Applies zero displ. at selected nodes, x-dir
clocal,11,1,W,hc
csys,11
nsel,s,loc,x,hr/2
nsel,r,loc,y,270
f,all,fy,-P/B !Applies loading at selected node, bottom of hole
nsel,s,loc,x,hr/2
nsel,r,loc,y,180,360
csys,0
rbe3,node(W,0.2*W,0),all,all !Redistributes force using MPC to hole radius, avoiding stress conc.
allsel,all
solve !Solve problem
finish
/post1
prcint,1,,tstress !Lists results from cint
prcint,2,,k1
prcint,3,,jint
csys,13 !Creates the KCALC
path,1,3,,, !
ppath,1,Node1 !
ppath,2,Node2 !
ppath,3,Node3 !
kcalc,0,,1 !Creates the KCALC
finish
/solu
*get,T_stress,cint,1,,Node1,,1,,tstress !Collects the t-stress from the cint-solution
*get,K_I_CINT,cint,2,,Node1,,1,,K1 !Collects the KI from the cint-solution
*get,K_I_KCALC,KCALC,0,K,1 !Collects the KI from the KCALC
Hi Sajith,
I assume you are working on cracks between 2 different materials and answering.
- As you mentioned, there is no direct relation between KI and KII. I believe you need two parameters to characterize crack-tip stress state. Total energy release rate (equiv to JINT in LEFM) and mode-mixity.
- Now determining mode-mixity is not generally straight forward. There are a lot of approaches. I can suggest some if that is want you are looking for.
Beware, that KI and KII that you get for an interface cracks are not directly mode I and mode II SIF'S.
If you are not working on interface cracks, to my knowledge, I don't see how mixed mode J Integral is involved?
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