1. REVISITING INGLIS THEORY
BASED ON FINITE ELEMENT
METHOD
Presented by,
Sachin shewale
Sanket kasar
Amey Deshpande
Under the guidance of,
Mr.Vinay Patil

2. Background of the presentation
• Project deals with calculation of SIF under influence of various
parameters.
• SIF is the concept evolved during the development of fracture
mechanics.
• Fracture mechanics treats crack as a discontinuity and early work on
discontinuity is related with stress concentration factor.

3. Evolution of SCF
• Leonardo Da Vinci proposed flaws to be the root cause of failure.
• Presence of flaw in a material focuses the stress at particular portion
and this stress concentration causes failure.
• This concept was extended by Inglis giving a mathematical formula
for stress concentration factor.

4. Mathematical model for elliptical hole
developed by Inglis
• Inglis approximated crack as an extremely flat ellipse.
• His analysis began with circular hole and then compressing it to
form an ellipse .
Fig. Elliptical hole in flat plate

5. Inadequate Meshing
PROBLEM SOLUTION MESHING

6. Improved Meshing
Since we are more concerned about stress distribution at the
vicinity of circular hole, ring is modeled around the hole and
regular mesh is generated in that ring zone as shown in fig.
Sec A-A
Section A-A
Fine
mesh
Zoomed view of sec A-A

7. Circle to Ellipse

8. Modelling elliptical ring

9. Stress Convergence
conservative

10. Flow chart of If-Do loop
start
C=number of
refinements
yes
Is C=0 Exit
No
i=1
C=1 C=2
yes
erefine, all
do No i=i+1
IsIs
i>C C=3

11. Genuine peak plot
Genuine peak

12. Predicted Peak
Predicted peak value = 39.544 MPa
35.846 2.21 1/2.2
38.056 0.999
1/2.8
39.055 0.357
1/3.4
39.412 0.105 1/4
39.517 0.027

13. ANSYS Plot
σ
( y)max
(SCF)ansys= (σy)max/ (σ)applied
= 18.8/5
= 3.76

14. Team Work
• 6 Engineers
• Time Span of 14 days
• No. of Analysis = 400

15. Results
RATIO (b/a) ANSYS SCF THEROTICAL SCF [Ref4]
1 circular hole 3.76 3
. . .
. . .
0.75 4.44 3.66
. . .
. . .
0.5 5.8628 5
. . .
. . .
0.25
. . .
. . .
0.02 Flat Elliptical Hole 110.83 101

16. Graph showing variation in SCF

17. VARIATION IN ANSYS AND
THEROTICAL VALUES?
• Theoretical stress values Engg. Stress
Engg. Stress = Applied Load/Area
• ANSYS stress values True Stress
True Stress = Applied Load/Instantaneous Area

18. Estimated value for sigma y

19. Conclusion

20. • From the graph value of stress at x=0, is 12360 MPa it is
clearly shows that estimated values of Stress in y direction are
increasing as we collapse circle to ellipse to form crack .
• Hence reaching stress singularity and our work is correlating
with Inglis theory.

21. Future work
• 2-D crack modelling and SIF calculation.
• 2-D Inclined crack modelling and SIF calculation.
• 3-D crack modelling and SIF calculation
• 3-D Inclined crack modelling and SIF calculation.(if time
permits).
• Crack Tip Plasticity.

22. THANK YOU