a combined experimental- numerical technique for ... 4/4-… · numerical technique for determining...

A combined experimental-numerical technique for determining mixed mode

strain energy release ratesSonya A Brown & Liyong Tong

October 18th, 2010

October 18th, 2010

Aim

Single Step 2D Virtual Crack Closure Technique

Hypothesis

( )( )

2 2 2

1 1 1

2

2I u l

II u l

T I II

G F u u a

G F u u aG G G

= − − ∆

= − − ∆

= +

October 18th, 2010

GI (N.mm/mm2) GII (N.mm/mm2) GT (N.mm/mm2)

Global Mesh 0.095731 0.044128 0.139858

Local Mesh 0.095606 0.044095 0.139700

4 Element Case 0.097716 0.044249 0.141965

Initial FEA Validation

October 18th, 2010

Experimentation

Material: Cycom 970/T300 prepreg

Test Machine: Instron 3366

Microscope: Wild‐Heerbrugg Wild M8 (at 9x magnification)

Camera: Canon PowerShot S40 (4.0 MP)

October 18th, 2010

Image Analysis and Linearisation

October 18th, 2010

Applying Test Measurements to Local FEA

u1u (mm) u2u (mm) u1l (mm) u2l (mm) F1 (N) F2 (N)

0.73240 1.5653 0.73460 1.5606 9.7605 ‐8.2623

GI (N.mm/mm2) GII (N.mm/mm2) GT (N.mm/mm2)

0.097078 0.053638 0.150716October 18th, 2010

Global FEA

u1u (mm) u2u (mm) u1l (mm) u2l (mm) F1 (N) F2 (N)

0.64144 1.4837 0.64334 1.4790 8.7134 ‐8.1778

GI (N.mm/mm2) GII (N.mm/mm2) GT (N.mm/mm2)

0.095823 0.041344 0.137167October 18th, 2010

October 18th, 2010

Theoretical Comparison (Small Deflection)

sincos

x i

y i

F PF P

θθ

==

1

1

11 2

y

x

y x

Q F

N FtM F a F s

= −

= −

= − + +

2

2

22 2

y

x

y x

Q F

N FtM F a F s

=

=

= + +

October 18th, 2010

GI (N.mm/mm2) GII (N.mm/mm2) GT (N.mm/mm2)

0.097033 0.021825 0.118858

Theoretical Comparison (Small Deflection)

October 18th, 2010

Results

GI (N.mm/mm2) GII (N.mm/mm2) GT (N.mm/mm2)

Experimental‐Numerical 0.097078 0.053638 0.150716

Global FEA 0.095823 0.041344 0.137167

Theoretical (small deflection) 0.097033 0.021825 0.118858

A04 ‐ P/w = 1.75529 N/mm ‐ θi = 1.63093°

A04 ‐ P/w = 1.63426 N/mm ‐ θi = 1.67254°

GI (N.mm/mm2) GII (N.mm/mm2) GT (N.mm/mm2)

Experimental‐Numerical 0.085239 0.045605 0.130844

Global FEA 0.083638 0.037478 0.121116

Theoretical (small deflection) 0.084126 0.018932 0.103058

October 18th, 2010

Results

GI (N.mm/mm2) GII (N.mm/mm2) GT (N.mm/mm2)

Experimental‐Numerical 0.213534 0.004027 0.217561

Global FEA 0.186029 ‐0.000489 0.185541

Theoretical (small deflection) 0.184508 0.000002 0.184508

A01 ‐ P/w = 2.01443 N/mm ‐ θi = 1.01041°

A02 ‐ P/w = 2.00106 N/mm ‐ θi = 0.95742°

GI (N.mm/mm2) GII (N.mm/mm2) GT (N.mm/mm2)

Experimental‐Numerical 0.292177 ‐0.000252 0.291924

Global FEA 0.282558 0.007734 0.290292

Theoretical (small deflection) 0.272251 0.001316 0.273566

October 18th, 2010

Results

GI (N.mm/mm2) GII (N.mm/mm2) GT (N.mm/mm2)

Experimental‐Numerical 0.141235 0.017671 0.158906

Global FEA 0.105614 0.030016 0.135630

Theoretical (small deflection) 0.105625 0.013064 0.118689

A03 ‐ P/w = 1.66108 N/mm ‐ θi = 1.72973°

October 18th, 2010

Current Limitations and Considerations

• Available experimental displacement data is limited by pixel size‐ High quality camera equipment (e.g. 12 MP+) or laser measurement

apparatus could improve the accuracy

• Manual image analysis‐ Automated Digital Image Correlation software could increase the speed and

accuracy of the analysis

• Differences between ideal modelling and experimentation‐ Further consideration of boundary conditions, initial position, material

properties, etc. in the global finite element model

• Load values of the photos for image analysis‐ To gain the strain energy release rate of the initial crack propagation for any

given specimen, a photo at zero load and a photo just prior to the initial crack propagation would be required

October 18th, 2010

Continuing Research

• Further verification of results via more specimens

• Additional verification of the process using UDCBs loaded at varying angles

• Consideration of the formulation for the simple 4 element case

• Completing theoretical derivations based on beam theory for large deflections and results comparison

Acknowledgements

Prof Liyong Tong and Dr Quantian Luo

October 18th, 2010

October 18th, 2010

Questions?