STRESS INTENSITY FACTOR DETERMINATION USING THE FINITE ELEMENT METHOD

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STRESS INTENSITY FACTOR DETERMINATIONUSING THE
FINITE ELEMENT METHOD 
Paulo F P de Matos, Pedro M G P Moreira,Paulo M
S T de Castro
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Objectives
determination of KI values for different
geometries of finite width plates containing
cracked circular holes, using the finite element
method study of the influence of the mesh type
on the precision results
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• Cases

Plate with central crack
Plate with central hole and 2
symmetricral cracks
Plate with central hole and 1 crack
Dimensions
Dimensions
Dimensions
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1.1 Plate with central crack
Details of meshes
a) Very coarse mesh
b) Coarse mesh
c) Refined mesh qnp
d) Refined mesh qnp details
Meshes data
Number of elements
Mesh type
Mesh used, 1/4 of the plate, coordinates in m
300
very coarse
600
coarse
1704
refined
1704
refined and qnp
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1.2 Plate with central hole and 2 symmetrical
cracks
Details of meshes
a) Very coarse mesh
b) Coarse mesh
c) Refined mesh qnp
d) Refined mesh qnp details
Meshes data
Number of elements
Mesh type
206
very coarse
554
coarse
1900
refined
Mesh used, 1/4 of the plate, coordinates in m
1900
refined and using qnp
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1.3 Plate with central hole and 1 crack
Details of meshes
a) Very coarse mesh
b) Coarse mesh
c) Refined mesh qnp
d) Refined mesh qnp details
Meshes data
Mesh used, 1/4 of the plate, coordinates in m.
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2.1 Plate with central crack, results using
ABAQUS
sy stress very coarse mesh, 300 elements
sy stress coarse mesh, 600 elements
sy stress refined mesh qnp, 1704 elements
Non-dimensional KI
Non-dimensional KI as a function of mesh type
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2.2 Plate with central crack, analytical results
Non-dimensional KI and F
KI Pa m-3/2
F
2,2809E07
1,07238
Tada
2.3 Comparison of results
Error of K/(s(pa)1/2) as function mesh type
Error
Mesh type
-0,609
very coarse
-0,434
coarse
-0,039
refined
0,092
refined and qnp
Error of K/(s(pa)1/2) as function mesh type
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3.1 Plate with central circular hole and two
symmetrical cracks results using ABAQUS
3.1.1 - Influence of elements size
sy. Very coarse mesh with 206 elements. ESx
0.3175 mm.
sy. Coarse mesh with 554 elements. ESx 0.15875
mm.
sy. Refined mesh with 1900 elements. ESx
0.084667 mm.
Non-dimensional KI
ESx element size along x
Non-dimensional KI as a function of mesh type
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3.1.2 - Stress distribution as a function of the
crack size
sy. Crack size, c0.127 mm
sy. Crack size, c0.254 mm
sy. Crack size, c0.762 mm
Non-dimensional KI
Non-dimensional KI as a function of crack size
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3.2 Analytical results for KI
.
F as a function of a/W and R/W
Range of applicability
K Pa.m(1/2)
F
y
j
g
d
a
a mm
9140343
0,8549
0,7992
1,0696
0,192
1
0,20216
2,527
10319855
0,9418
0,8772
1,0737
0,192
1
0,21232
2,654
with associated precision of 5 if
12727240
1,0641
0,9741
1,0924
0,192
1
0,25296
3,162
14326509
1,1119
0,9969
1,1153
0,192
1
0,2936
3,67
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3.3 Comparison of results
Error as a function of crack length.
Precision band for a0.192, and values obtained
using ABAQUS
Detail
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4.1 Plate with central circular hole and one
crack results using ABAQUS
4.1.1 - Stress distribution as a function of the
crack size
sy. Crack size, c0.127mm
sy. Crack size, c0.256mm
sy. Crack size, c0.762mm
sy. Crack size, c1.27mm
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K/(s(pa)1/2) as a function of crack length
4.2 KI/(s(pa)1/2) results for one and two
cracks
Progress of KI/(s(pa)1/2) as function of crack
size
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5 Conclusions
stress intensity factors for 2D finite width
cracked plates subjected to remote tensile loads
were determined using ABAQUS finite element
software. Small values of crack length were
considered, because of their importance for
EIFS studies in the cases where reference values
were available, good accuracy was obtained,
suggesting that the results for the other cases
are also accurate it was found that, for the
standard case of a rectangular plate with centre
crack subjected to remote tensile stress, the
accuracy of a refined mesh of 8 node
isoparametric elements is of the same order as
the accuracy obtained using the quarter node
point technique
6 Future developments
implementation of collapsed elements seeking
better modelling of the stress state in the
crack tip regions modelling of the influence
of cold-working parameters upon the residual
stress field around circular holes of finite
width plates, and resultant stress intensity
factors more realistic modelling of cracks
using 3D finite elements in particular, the
problem of curved cracked fronts will be
addressed, and 2D simplifications should be
evaluated