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