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A combined experimental-numerical technique for determining mixed mode
strain energy release ratesSonya A Brown & Liyong Tong
October 18th, 2010
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October 18th, 2010
Aim
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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
= − − ∆
= − − ∆
= +
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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
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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)
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Image Analysis and Linearisation
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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
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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
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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
=
=
= + +
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GI (N.mm/mm2) GII (N.mm/mm2) GT (N.mm/mm2)
0.097033 0.021825 0.118858
Theoretical Comparison (Small Deflection)
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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
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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
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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°
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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
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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
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Acknowledgements
Prof Liyong Tong and Dr Quantian Luo
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Questions?