13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- the reference image becomes P'(x*,y*) in the deformed image and Q(x,y) becomes Q'(x*,y*). DIC is run by comparing group of similar light intensity numbers between the two digital images to track points P and Q. Depending on the use of a first or second order approximation, 6 or 12 unknowns are available and can be found by correlation between the two images. This can be done by minimizing the global residual between the reference image f and the deformed image corrected by the displacement field g(x+u(x)) over the whole region of interest: [ ] (1) ( ) ( )) ( 2 2 g x u x f x dx ∫∫ Ω + − = η In the following, 4-noded elements are considered (i.e. a Q4-DIC approach [11]). The DIC procedure applied herein consists in measuring displacement field discretized with quadratic Q4 elements. The elements size was chosen to be equal to 8 pixels. This value is a good compromise between measurement uncertainly and spatial resolution. Extracting some mechanically meaningful information using the detailed map of displacement can be performed by identifying the amplitudes of relevant reference displacement fields namely, William’s series [13]. These field u=ux+iuy take the following expression in the crack frame (crack tip at the origin, and crack path along the negative x axis) resorting to the complex plane, z=reiθ [ ] (2) ( ) ( ) ( ) ∑= Ω + n n n n n z z u z ψυ ω With, for a mode I regime: (3) 2 exp 2 ( 1) 2 (4 ) exp 2 2 exp 2 2 ( 1) ( ) / 2 (1 ) / 2 ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⎟ − ⎠ ⎞ ⎜ ⎝ ⎛ ⎟+ − + ⎠ ⎞ ⎜ ⎝ ⎛ − ⎟− ⎠ ⎞ ⎜ ⎝ ⎛ − Ω = − θ θ θ κ π μ in n i n n in r z n n n n And a mode II regime: (4) 2 exp 2 ( 1) 2 (4 ) exp 2 2 exp 2 2 ( 1) ( ) / 2 (1 ) / 2 ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⎟ − ⎠ ⎞ ⎜ ⎝ ⎛ ⎟+ − − ⎠ ⎞ ⎜ ⎝ ⎛ − ⎟+ ⎠ ⎞ ⎜ ⎝ ⎛ − Ψ = − θ θ θ κ π μ in n i n n in r i z n n n n Where μ is Lamé’s modulus, and κis a dimensionless parameter dependent on Poisson ratio ν (i.e. υ υ κ + − = 1 3 in plane stress, or 3-4ν in plane strain condition). Amplitudes ω1 and ν1, associated with field Ω1 and Ψ1, are the mode I and II SIFs, KI and KII, respectively. Amplitudes ω0 and ν0 correspond to rigid body translations. Amplitudes ω2 and ν2 give access to the T-stress component, and the rigid body rotation. The crack-tip is located by canceling out amplitude ω-1 of the first supersingular field. 5. Results and discussion Experimental results were obtained from the displacement fields obtained with a mesh size of 8 pixels (1 pixel→44.2 µm), over a region of interest of 2500 x 350 pixels (Figure 4).
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