XFEM Analysis of Cold

Hole Expansion

Daniel Stockton

2/24/2015

Table of Contents

• Successes:

– Repeat Past XFEM Studies

– Study Mesh Sensitivities

– Cold Expansion with Coarse Mesh

– SIF – Coarse Mesh w/ & w/o Residual Stress

– SIF – Fine Mesh w/o Residual Stress

– Putting Crack into Deformed Mesh

• Next Studies

• Issues

Success:

Repeat of past XFEM Studies

• XFEM Modeling of Mixed-

Mode Cracks in Thin Aluminum

Panels

• 30°, 60° and 90° crack, w.r.t. to

tensile direction, placed in

center

• Displacement until failure

• Abaqus version 6.9

Displacement

Clamped

90° crack 60° crack 30° crack

Success:

Repeat of past XFEM Studies

• XFEM Modeling of Mixed-

Mode Cracks in Thin Aluminum

Panels

Paper’s Results

My Results Abaqus v6.12

90° crack 60° crack 30° crack

Success:

Repeat of past XFEM Studies

1500

1600

1700

1800

1900

2000

2100

2200

2 3 4 5 6 7

Max

Re

acti

on

Fo

rce

, N

Nominal Crack Length, mm

Reaction Force vs Nominal Crack Length

Experimental Results My Simulation Results Paper's Simulation Results

Crack Angle Experimental

Force, N

My Simulation

Force, N

My Error

Paper's Simulation

Force, N

Paper's Error

30° 2162 2071 4.2% 2122 -1.9%

60° 1784 1694 5.0% 1864 4.4%

90° 1695 1601 5.5% 1686 -0.5%

Success:

Study Mesh Sensitivities

• Crack is placed and will jump to next element mesh line along the same

path as the crack.

• XFEM does not work when starting from a mesh line perpendicular to force

direction.

• Why? Because it needs to create two new phantom nodes along the same

direction as the force.

Success:

Study Mesh Sensitivities

• Mesh slightly modified.

• XFEM crack jumps to mesh line not perpendicular to the force.

• Crack propagates as expected.

XFEM Crack Placed XFEM Crack Jumps XFEM Crack Propagates

Success:

Study Mesh Sensitivities

• Basic concept for XFEM is that two new phantom mesh nodes are created

in place of the crack intersection.

• However, a crack along the mesh line will not separate in my experience.

New phantom

nodes

Success:

Study Mesh Sensitivities

• XFEM crack “Short” jump vs “Long” jump, same crack angle.

• Results are impacted to a small degree.

Short vs Long

Crack Angle Experimental Short Jump Error Long Jump Error

Max Force Max Force Max Force

30° 2162 2071 4.21% 2030 6.11%

60° 1784 1694 5.04% 1640 8.07%

90° 1695 1601 5.55% 1543 8.97%

4.21%

5.04%

5.55%

6.11%

8.07%

8.97% 1500

1700

1900

2100

2300

30° Crack 60° Crack 90° Crack

Max

Re

acti

on

Fo

rce

, N

Experimental Reaction Force Short Jump Reaction Force Long Jump Reaction Force

% Error from Experimental Value

Success:

Cold Expansion with Coarse Mesh

• 4% hole expansion.

100 mm

10

0 m

m

6.35 mm

Ø 7.671 mm (Initial)

Ø 7.978 mm (max)

Ø 7.943 mm (Final)

Success:

Cold Expansion with Coarse Mesh

Residual Stresses after 4% Expansion

Success:

Cold Expansion with Coarse Mesh

• Residual Stresses after 4% expansion, Entry and Exit.

-700.00

-600.00

-500.00

-400.00

-300.00

-200.00

-100.00

0.00

100.00

200.00

0 0.01 0.02 0.03 0.04 0.05

Stre

ss (

MP

a)

Distance from Hole (m)

3D - Residual Stresses

Entry Tangential

Exit Tangential

Entry Radial

Exit Radial

Success:

Cold Expansion with Coarse Mesh

• S22, Tangential Stress .

Success:

Stress Intensity Factor, SIF

• Contour integral method used to calculate stress intensity factor

• Each ring is a an individually calculated contour around the crack opening

• Ring is based off of mesh, user specifies # of rings.

• SIF value should converge as the number of rings increase

Converged Value

Ring 1 Ring 2 Ring 3 Ring 4

Ring 1

Ring 2

Ring 3 Ring 4 Ring 5 Ring 6 Ring 7

Success:

SIF – Fine Mesh w/ & w/o Residual Stress

• 1.0 mm crack at Mandrel Entry Edge, both sides

Crack Location

Entry Side Hole Surface

Entry Side Hole Surface

1.0 mm

0.6 mm

6.35 mm

Success:

SIF – With and Without Residual Stress

With Residual Stress

Without Residual Stress

Success:

SIF – With and Without Residual Stress

• Crack Opening comparison

• 5x Deformation Scale

Without Residual Stress With Residual Stress

Crack Opening

Crack Opening

Success:

SIF – With and Without Residual Stress

• Stress intensity factor contour integrals.

Stress intensity factor = 26.2 𝑀𝑃𝑎 𝑚

Stress intensity factor = 8.1 𝑀𝑃𝑎 𝑚

Next Studies

• Low-Cycle fatigue in steps.

– Low-cycle fatigue maximum of 10,000 cycles

• Continue to high-cycle Fatigue correlation.

– XFEM only does low-cycle fatigue

• Al-Li fatigue testing

• Meshing

– Depends on crack size but always difficult with super fine mesh

• Cold Expansion with Fine Mesh

– Static: Large overpenetration except with Reduced Integration

– Implicit: Too slow and large penetration

– Explicit: Too slow

• Equilibrium of Residual Stresses

– If Equilibrium step used then residual stresses shift.

• Deformed Part

– Currently pulled from ODB but orphan mesh.

Issues:

THE END

Thank you