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
EU project GRD1-2000-25069 contract
G4RD-CT-2000-0396 - ADMIRE
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Objectives

• study of the influence of the mesh type on the
  precision results
• determination of KI values for different
  geometries of finite width
• plates containing cracked circular holes, using
  the finite element method

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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
Mesh used, 1/4 of the plate, coordinates in
m Refined mesh 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 of K/(s(pa)1/2) as function of 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
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with associated precision of 5 if
Range of applicability
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F as a function of a/W and R/W
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3.3 Comparison of results
Error as a function of crack length.
Detail
Precision band for a0.192, and values obtained
using ABAQUS
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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, c1.270mm
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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

• 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
• in the cases where reference values were
  available, good accuracy was obtained, suggesting
• that the results for the other cases are also
  accurate
• in the case of a plate with central hole is not
  very significative the presence of one or two
  small cracks

6 Future developments
implementation of collapsed elements seeking
better modelling of the stress state in the
crack tip regions 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