1. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING
6340(Print), ISSN 0976 – 6359(Online) Volume 5, Issue 1, January (2014), © IAEME
AND TECHNOLOGY (IJMET)
ISSN 0976 – 6340 (Print)
ISSN 0976 – 6359 (Online)
Volume 5, Issue 1, January (2014), pp. 98-107
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IJMET
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ESTIMATION OF STRESS INTENSITY FACTOR (SIF) ON CRACK
COMPONENT BY USING FINITE ELEMENT ANALYSIS
M. D. Nikam(1),
G. V. Patil(2),
G. N. Thokal(3),
V. H. Khatawate(4)
1
(Mechanical Engineering, Pillai’s institute of Information and Technology, Mumbai University,
New Panvel, India)
2, 3, 4
(Assistant Professor, Mechanical Engineering, Pillai’s institute of Information and Technology,
Mumbai University, New Panvel, India)
ABSTRACT
Theoretical solutions are available for idealized cases such as Infinite flat plate with edge
crack, central crack etc. However main limitation of these theoretical solutions is they are very
restrictive and while analyzing a normal component, a lot of assumptions go into it. Finite Element
Analysis on the other hand provides good tool to determine Stress Intensity Factor. Cracks generally
initiate at geometric discontinuities (such as notches, holes, weld toes, voids etc.) that induce large
stress (stress concentration). Since crack growth is related to the effective stress intensity factor (SIF)
which is at crack tip, the evaluation of Stress Intensity Factors. The present work would aim to fulfill
this gap and generate more information thereby increased understanding on fracture behavior in 3D
Components. Finite element analysis has been performed to support the results on fracture
parameters like Location and Size of Cracks and results has been compared with available theoretical
solutions. It is concluded that magnitude of critical Stress Intensity Factor can be used as a fracture
criterion for thin Plates. Same procedure has been adapted for Analysis of connecting rod to find
Stress Intensity Factor at various lengths of crack
Keywords: Fracture Mechanics, Finite Element Analysis, Critical Stress Intensity Factor (SIF).
1. INTRODUCTION
Crack extension (i.e., fracture) occurs when the energy available for crack growth is
sufficient to overcome the resistance of the material. The material resistance may include the surface
energy, plastic work, or other types of energy dissipation associated with a propagating crack.
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2. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 5, Issue 1, January (2014), © IAEME
The cause of most structural failures generally falls into one of the following categories:
1. Negligence during design, construction, or operation of the structure.
2. Application of a new design or material, which produces an unexpected (and undesirable) result.
The field of fracture mechanics has prevented a substantial number of structural failures. We
will never know how many lives have been saved or how much property damage has been avoided
by applying this technology, because it is impossible to quantify disasters that don’t happen.[3]
Prime goal of studying is to predict whether a crack is likely to grow or not. If the Stress Intensity
Factor of a crack approaches or exceeds an upper limit of stress intensity factor, the crack may grow.
The upper limit is known as critical stress intensity factor which is a material property. Stress
is a parameter which represent internal loading within the solid and yield stress is the limit on stress,
beyond which the material is regarded to have failed by many designers. Similarly, stress intensity
factor is parameter of measure the severity of stress at the crack tip. The critical stress intensity factor
is limit on SIF, if the SIF exceeds the critical stress intensity factor, the crack may grow.
In order to predict the growth of crack in a component, the designer should find two values:
1.
2.
The SIF determined through analysis for the geometry of the component, crack orientation
and applied load.
The critical SIF determined through experiments for material of component.
If Stress intensity factor exceeds the critical stress intensity factor, the designer should do
something such as reducing the load on the component, modifying the geometry of component, or
choosing the material of higher toughness.
The objective of the work is to estimate whether the variation in SIF can be quantified into a
relation, which will be useful in Damage Tolerance field. The length of the cracks will be varied to
understand the change in SIF due to crack growth.
To find out stress concentrated at crack tip and estimation of stress intensity factor for 2-D
Edge crack and 2-D Central crack. Compare results with theoretical solutions. Apply same procedure
for 3-D crack modelling, SIF calculation and the result validation on Connecting rod. Hence
procedure has developed to analyze Stress Intensity factor to find.
2. STRESS INTENSITY FACTOR (K)
Designers are always interested to know whether a crack is likely to grow or not if the
geometry of crack, loads and other boundary conditions of a structural component are known.
Therefore parameter is available to measure crack effectiveness or crack extension force. The
fracture problem is analyses through different approaches, each approach having its own parameter.
One approach for crack effectiveness is Stress Intensity Factor (SIF).
It is applicable only for Linear Elastic Fracture Mechanics. In comparison to Energy Release
Rate, Stress Intensity Factor (SIF) is simpler for designer and easier for laboratory measurements.
The SIF develops analysis of linear material only, the analysis does not account for plastic
deformation close to the crack tip.
Critical Stress Intensity Factor of a material depends on many factors, such as
1. Heat treatment which control the yield stress of material.
2. Speed of the crack.
3. Temperature of specimen.
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3. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 5, Issue 1, January (2014), © IAEME
4. Process of manufacturing (as cast or rolled).
5. Orientation of crack with respect to the grains at the crack tip. [4]
3. ESTIMATION OF STRESS INTENSITY FACTOR
Analytical calculations are performed using Irwin's formula and 2D finite element analyses
(FEA) are conducted in parallel using ANSYS. Methodology followed to find out Stress Intensity
Factor for a two dimensional and three dimensional components is as follows. In theoretical
Solution, Initially stress intensity factor for both central and edge crack of plate component is
estimated. Stress intensity factor for Mode I fracture KI, has the following form:
K = σ × f(α)
Where, σ = Applied stress
a = Crack length and
f(α) = A non-dimensional function depending on the size and geometry of the crack, size and
geometry of the structural component, and the type of loading.
Elastic modulus i.e. young’s Modulus , Poisson’s ratio, Crack length, point loads and
boundary conditions as per problem statement are require for Finite Element Analysis of Crack
Propagation.
Material Properties:
Density
Young's modulus
Poisson’s ratio
Element shape
Element type
Material
: 7850 kg/mm^3
: 200000 MPa
: 0.30
: Tetra, Hex, Penta
: Solid
: Steel (generic)
Model:
The dimension of Edge crack plate is 100×50mm and Centre crack plate is 200×50 mm and both
plates is modeled using BLC4 command.
Plate Dimensions:
1. Dimensions
: 100×50×5m
Crack Location
: Edge
Crack Dimensions : 10%W to 60%W (W=50mm)
2. Dimensions
: 200×50×5mm
Crack Location
: Center Area Loc.
Crack Dimensions : 10%W to 60%W (W=50mm)
Symmetric Distribution
Mesh:
a) PLANE82 is a higher order version of the 2-D, four node element (PLANE42) has used for
Central crack plate.
b) PLANE183 is a higher order 2-D, 8-node or 6-node element has used for central crack.
PLANE183 has quadratic displacement behavior and is well suited to modeling irregular meshes has
used for Edge crack plate.
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4. ANALYSIS OF STRESS INTENSITY FACTOR
Stress intensity factors are a measure of the change in stress within the vicinity of the crack
tip. Therefore, it is important to know the crack direction and crack propagating in engineering
component. The stress intensity factor is compared with the critical stress intensity factor (KIc) to
determine whether the crack will propagate in the component or it will not propagate.
4.1 Theoretical Stress Intensity Factor (SIF)
Dimensional analysis can be used to show that the stress intensity factor for Mode I fracture
K , has the following form:
I
K=σ
*f (α)
Where, σ = Applied stress
a = Crack length and
f (α) = A non-dimensional function depending on the size and geometry of the crack, size and
geometry of the structural component, and the type of loading. [3]
Theoretical solutions are available for idealized cases such as Infinite flat plate with edge
crack, central crack etc. However main limitation of these theoretical solutions is that they are very
restrictive and while analyzing a normal component, a lot of assumptions go into it. Ansys on the
other hand provides good tool to determine SIF.
4.2 Finite Element Analysis (FEA)
Material Properties
Code Name (Internal)
Modulus of Elasticity (E)
Poisson's Ratio
Yield Strength
Element used
Density
Young's modulus
Plate Dimensions
1) Dimensions
Crack Location
Crack Dimensions
2) Dimensions
Crack Location
Crack Dimensions
: GTS-65-02 CI
: Fe Rest, C 2.0-2.6, Si 0.90-1.60, Mn 0.40-0.50 (Wt.
%)
: 180 GPa
: 0.32
: 380MPa
: Plane183
: 7400 kg/m³
: 180000MPa
: 100×50×5mm
: Edge
: 10%W to 60%W (W=50mm)
: 200×50×5mm
: Center Area Loc.
: 10%W to 60%W (W=50mm)
Symmetric Distribution
4.2.1 Pre-Processing
PLANE183 is a higher order 2-D, 8-node or 6-node element. PLANE183 has quadratic
displacement behavior and is well suited to modeling irregular meshes (such as those produced by
various CAD/CAM systems). This element is defined by 8 nodes or 6 nodes having two degrees of
freedom at each node: translations in the nodal x and y directions.
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5. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
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Figure 4.3: Mesh model
In Model file dimension of Edge crack plate is 100×50mm and Centre crack plate is 200×50
mm and both plates is modeled using BLC4 command.
Figure 4.4: Edge-Cracked plate
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Figure 4.5: Stress intensity close to the crack tip in edge crack.
4.2.3 Post-Processing
It displays result graphically. Graphics displays are perhaps the most effective way to review
results. In the plate model the stress intensity is shown in red color, there is a sharp rise in stress in
the vicinity of crack. And similarly following the steps for central crack stress intensity factor can be
estimated.
For estimation of crack in 3D component same procedure has been followed. We have taken
Connecting rod as sample case study for this work to find out stress intensity factor. Which is explain
in next chapter.
5. CRACK PROPAGATION ANALYSIS OF CONNECTING ROD
It is a part of the engine, which is subjected to millions of repetitive cyclic loadings. It should
be strong enough to remain rigid under loading, and also be light enough to reduce the inertia forces
which are produced when the rod and piston stop, change directions and start again at the end of each
stroke.
5.1 Hypermesh
Connecting rod mode is made by using CATIA V5 software. Meshing of connecting rod is
done using HyperMesh v12.0. The problem is to find Stress intensity factor of Cracked Connecting
rod and this is solved by using ANSYS software.
5.1.1 Material Properties
Density
Young's modulus
Poisson’s ratio
Element used
Material
: 7.85e-06 kg mm^-3
: 200000 MPa
: 0.3
: Solid 187 and Solid 186
: Steel (generic)
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6340(Print), ISSN 0976 – 6359(Online) Volume 5, Issue 1, January (2014), © IAEME
5.1.2 Mesh
Meshing of connecting rod by using Hypermesh software.
Warpage aspect ratio
:5
Square angle
: 600(>=900)
Jacobian
: 0.7
Quadrilateral faces
: Min angle is less than 450
: Max angle is greater than 135
Total No. of element
: 9557
Order
: 2nd order element critical shape
Force
: 14000N
Element
A) Solid 187
: Tetrahedron
: 4 faces
:
B) Solid 186
: Hexa-Dominants
: 6 faces
C) Surf 154
: Penta
: 5 faces
: Solid 187- tetra-3mm
: Solid 187-tetra-1mm
: Solid 186 –Hex dominant - 0.2mm
Figure 5.1 Connecting rod mesh view
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8. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
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Figure 5.2 Crack meshing of connecting rod (close view)
6. RESULT AND DISCUSSION
Theoretical calculations and Ansys simulation results are compared with each other as shown
in Table 6.1 for edge crack and central crack.
Table 6.1: Comparison of Theoretical and APDL SIF result in Edge and central crack
Comparison of Theoretical and APDL SIF result Comparison of Theoretical and APDL
in Edge crack
SIF result in Central crack
Crack length Theoretical SIF
APDL SIF
Theoretical SIF
APDL SIF
(mm)
5
18.76
18.7275
11.33
11.26
10
30.72
30.5070
16.26
16.01
15
45.25
45.3899
20.45
19.76
20
66.70
66.7738
24.71
24.07
25
100.20
99.8654
29.63
29.15
30
156.33
155.9892
35.74
35.16
Figure 6.1 Comparison of Theoretical and
APDL SIF result in Edge crack
Figure 6.2 Comparison of Theoretical and
APDL SIF result in Central crack
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9. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
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For Edge crack the variation in SIF value in between Theoretical and APDL SIF is ranging in
between -0.1% to 0.8%. From figure 6.1 we can observe as crack length increase, stress intensity
factor also increases.
For Centre crack the variation in SIF value in between Theoretical and APDL SIF is ranging
in between 0.6% to 3.4% from figure 6.2.
Form Table 6.1 it has been observed that values of Stress intensity factor increasing as crack
length increases. This stress intensity factor is compared with the critical stress intensity factor KIc
(the capacity) to determine whether crack will propagate or not. According to basic Fracture
Mechanics theory if actual crack SIF is greater than this critical value it results in crack propagation.
Variation of stress intensity factor with respective crack length in connecting rod is observed
elliptical in nature inside the connecting rod from figure 5.6.
Figure 5.6: Severity of crack propagation in the connecting rod with respect to distance.
7. CONCLUSION
Theoretical values of Stress Intensity Factor and the values of Stress Intensity Factor by using
ANSYS for central and horizontal crack are compared and analyze results for plate two dimensional
components. Using the same Methodology for connecting rod (3D component) we estimated the
Stress intensity factor and finding out the severity of crack in connecting rod. Hence by inference if
we employ the same process we should achieve reasonable accuracy. If Stress intensity factor
exceeds the critical stress intensity factor, the designer should reduce the load on the component,
modifying the geometry of component, or choosing the material of higher toughness.
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[1]
[2]
“SIFs of part-through mode I crack for uniform crack surface Pressure” G. S WANG the
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“Evaluation of mode I stress intensity factors for edge cracks from 2-D V-notches using
composition of constituent SIF weight functions” L.S. Teh, F.P. Brennan. International
Journal of Fatigue 29 (2007) 1253–1268
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6340(Print), ISSN 0976 – 6359(Online) Volume 5, Issue 1, January (2014), © IAEME
[3]
“Fracture mechanics-Fundamentals and Applications” by T.L.Anderson published by Taylor
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