Page 132 - Mechanics of Asphalt Microstructure and Micromechanics

124 Ch a p t e r F o u r

(2006) used internally scattered light to obtain a volumetric pattern for imaging and
analysis. 3D volumetric DIC has also been applied to analyze on sandwich structures,
biomaterials, steel powders, metallic alloys, and rock.
4.4.5 Fundamentals of DIC
Using the 2D-DIC as an example, DIC is performed by maximizing a correlation coef-
ficient that is determined by examining pixel intensity array subsets on two or more
corresponding images and extracting the deformation mapping relationship that re-
lates the images. The 2D cross-correlation coefficient r ij is defined as Equation 4-25,
where, F(x i , y j ) is the pixel intensity or the grayscale value at point (x i , y j ) in the un-de-
*
*
*
*
formed image. G(x i , y j ) is the grayscale value at point (x i , y j ) in the deformed image.
–
–
F and G are mean values of the intensity matrices of F and G, respectively.
∑ ∑ ⎡ Fx y −(, ) F ⎤⎡Gx y(, * ) − ⎤
*
G
u ∂ u ∂ v ∂ v ∂ ⎣ ⎣ i j ⎦⎣ i i ⎦
r = ( , , , , ) =− i j (4-25)
1
u v,
ij x ∂ y ∂ x ∂ y ∂ 2 2
∑ ∑ ⎡ Fx y(, j ) − ⎤ G x( , y * i ) G⎤ ⎦
⎡
−
* *
F
⎦ ⎣
⎣
i
i
i j
*
*
The coordinates (x i , y j ) and (x i , y j ) are related by the deformation that occurs be-
tween the two images. If the displacement is perpendicular to the optical axis of the
camera, then the relation between (x i , y j ) and (x i , y j ) can be approximated by a 2D
*
*
transformation according to Equation 4-26, where u and v are translations of the center
of the sub-image in the X and Y directions, respectively. The distances from the center
of the sub-image to the point (x, y) are denoted by Δx and Δy. The correlation coeffi-
cient r ij is a function of displacement components (u, v) and displacement gradients
∂u ∂u ∂v ∂v
, , , and .
∂x ∂y ∂x ∂y
⎧ u ∂ u ∂
*
x u
⎪ x =+ + Δ x + Δ y
⎪ ⎪ x ∂ y ∂
⎨ (4-26)
⎪ y = y v + v ∂ Δ x + v ∂ Δ
+
*
⎪ x ∂ y ∂ y
⎩

4.4.6 DIC in Asphalt Testing and Modeling
Although used widely in the testing of other infrastructure materials such as concrete,
metals, wood, and geomaterials, DIC as a non-contact, full-field, surface displace-
ment/strain measurement technique has seldom been used in characterizing asphalt
materials. The very early use of DIC in asphalt material testing was conducted by Yue
and Morin (1996), where the technology was referred to as digital image processing
(DIP). The authors studied the rutting behavior of AC by comparing the orientations
of aggregate particles in asphalt mixtures before and after mechanical loading tests.
Yue et al. (2003) also used DIP in characterizing other construction materials. Similar
work on AC was done by Chen et al. (2005) in studying experimentally the internal
structure changes in hot mix asphalt (HMA) under wheel load testing. They found
that the rotation of flat and elongated particles contributed significantly to the rutting
of asphalt mixes.
Seo et al. (2002) used DIC in mechanical testing (deformation, strain, and fracture)
of asphalt mixture to determine the accuracy and convenience in comparison to LVDT.