Revisiting Inglis Theory in Finite Element Analysis and ANSYS

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