REVISITING INGLIS THEORY REVISITING INGLIS THEORY BASED ON FINITE ELEMENT BASED ON FINITE ELEMENT
METHODMETHOD
Presented by,
Sachin shewaleSanket kasarAmey Deshpande
Under the guidance of,
Mr.Vinay Patil
Background of the presentationBackground 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.
Evolution of SCFEvolution 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.
• 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
Mathematical model for elliptical hole Mathematical model for elliptical hole developed by Inglis developed by Inglis
PROBLEM SOLUTION MESHING
Inadequate Meshing Inadequate Meshing
Improved MeshingImproved 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.
Section A-A
Zoomed view of sec A-A
Sec A-A
Fine mesh
Circle to EllipseCircle to Ellipse
Modelling elliptical ringModelling elliptical ring
Stress ConvergenceStress Convergence
conservative
start
C=number of refinements
Is C=0 Exit
i=1
erefine, all
i=i+1
Is Is i>C
yes
yes
No
Flow chart of Flow chart of If-Do loopIf-Do loop
No
do
C = 1 C = 2
C = 3
Genuine peak plotGenuine peak plot
Genuine peak
Predicted PeakPredicted Peak
35.846 2.21
38.056 0.999
39.055 0.357
39.412 0.105
39.517 0.027
1/2.2
1/2.8
1/3.4
1/4
Predicted peak value = 39.544 MPa
ANSYS PlotANSYS Plot
(SCF)ansys= (σy)max/ (σ)applied
= 18.8/5 = 3.76
(σy)max
Team WorkTeam Work
• 6 Engineers
• Time Span of 14 days
• No. of Analysis = 400
ResultsResults
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
Graph showing variation in SCF
VARIATION IN ANSYS AND VARIATION IN ANSYS AND THEROTICAL VALUES?THEROTICAL VALUES?
• Theoretical stress values
• ANSYS stress values
Engg. Stress
Engg. Stress = Applied Load/Area
True Stress
True Stress = Applied Load/Instantaneous Area
Estimated value for sigma yEstimated value for sigma y
ConclusionConclusion
• 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.
Future workFuture 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.
THANK YOUTHANK YOU