4.1 Detection of defects
The experimental setup according to Fig. 1 is able to detect the type of defect present in different transparent samples tested as follows.
4.1.1 Transparent film
We control a film for optical use. The first stage, we obtained the moiré fringes of the transparent film at initial state shown in Fig. 3a. The moiré fringes are parallel and equidistant straight lines. what explains that this film does not present any anomalies. The second stage, the film has undergoes a small deformation according to the indications of the Fig. 3b; in this case, the moiré fringes obtained are deformed in the area where the deformation was produced; these fringes thus directly materialize the deformation caused on the transparent film.
4.1.2 Glass slide
Figure 4a shows the moiré fringes of a glass plate without defects, however, the moiré fringes of a glass plate about defects such as: hollow, groove, roughness, imprint are collected separately in figures (4b, 4c, 4d and 4e).
Acoording to these figures above, the moiré fringes are deformed in their structure according to the size and position of the defect existing on the surface to be tested. Thus, we can conclude that the moiré fringes materialize the type of defect, and that they can differentiate them distinctly.
4.1.3 Indentation technique
The indentation technique has been investigated and widely applied to detect and to determine the material mechanical properties such as stiffness and hardness, besides, indentation method is also a nondestructive testing method [38].
The principle of the indentation test consists in applying an indenter of known shape (ball, cone, or pyramid) on the surface of the material to be tested. Under the action of the indentation load, the indenter sinks into the material, producing elastic and plastic deformations in the contact area. When the indenter is removed, a redundant indentation remains. The higher the applied load, the larger the size of the indentation [39].
The application of the indentation load can be continuous or discontinuous. In the first case, the residual indentation is observed after the indenter removed using an optical microscope. For continuous indentation, the load applied progressively and the displacement of the indenter tip measured in real time as a function of the load.
The test of instrumented indentation is currently largely used for various applications and to different scales (macro, micro and nanometer). For loads not exceeding 1kgf, the indentation hardness is often called microindentation. Nanoindentation refers to a hardness test with a load less than 1N and the size of the indentation is in the nanometer scale. Currently, Vickers, Knoop indenters are frequently used in microindentation tests [40].
For both microindentation and nanoindentation, considerable care and experience are necessary to obtain good accuracy. Indentation is a good alternative test for brittle materials. Knoop indentation tests are a standard method for material characterization due to the fact that they provide an easy, inexpensive non-destructive and objective method of evaluating basic properties from small volumes of materials [41]. The residual surface deformation after spherical indentations was first investigated using phase-shifting moiré and Twyman-Green interferometry [40]. So, in our work here, we hold of great interest in experimental indentation Knoop tests.
4.1.3.1 Knoop indentation detection
In this part, we will rely on the experimental tests of indentation to predict their effect on the moiré fringes. They were performed with indentor Knoop. We used the first case, where the application of the indentation load is continuous. The image of the print for the various tests of indentation was seen by optical microscope. The tests of indentation were carried out under various loads. Like first step, glass plate serves as the object under study.We take moiré fringes of glass plate before the indentation shown in Fig. 5. The moiré fringes are parallel and equidistant straight lines. After the first step, we applied on the glass plate an indentation using the Knoop indenter. This indentation has magnified by the optical microscope 50x, we respectively collected indentation images with force loads of 0.05 kgf, 0.2 kgf, 0.8 kgf Fig. (6a, 7a, 8a). The topography of the indented surface has described by deformation of the structure of the moiré fringes shown by the figures (6b, 7b, 8b) according to the loads applied respectively.
The results given by the variations of the indentation load show their effect on the shape of moiré fringes. The moiré fringes being deformed at the where the indentation was produced by the application of the indenter, so that as the load icreases the fringes become more and more deformed. It can be observed that moiré fringes react differently according to the variation of the applied indentation load.
4.2 Measurement method of defect
To validate the feasibility of the technique suggested in this work, we propose to evaluate the size of the defect. The special attention is given on the defect created on the surface of the sample of the figures (4a and 4b). Then we consider two states (Fig 9), before and after the creation of the defect.
We consider figure 10 to show the diagram of principle calcul, so we begin with the surface before loading, the light rays coming from point E of grating G of pitch p, arrive at point M on the observation plane. The normal EH of the grating is perpendicular to the sample surface at point H. Point E is projected onto the surface to be inspected at point E', such that the angle HEE' is defined by α.
After loading, the normal undergoes a rotation of angle β to give EH'. EE' it also rotated by an angle β defined by (E'E''). The angle HEE'' is defined by (α + β). The grating lines are numbered starting with line 0 at point A, such as:
AE' = kp and A E'' = mp (1)
k, m: grating lines number, and p: pitch of grating G.
The moiré fringes resulting from the difference (m –k) p such that:
(m - k)p = AE" –AE' = HE" – HE'
HE" – HE'=l tan(α + β) – l tanα (2)
l: the distance between the grating and the sample, is very tall in front of the inspected surface dimensions, therefore:
(m-k) p = np = lβ = l(dz)/(dx)
np = l(dz )/dx (3)
Where Δφ = 2 π n = φob- φref, we can write
n = (Δφ) /(2 π) (4)
Where, φob: object phase (after loading); φref: reference phase (before loading); and n: the fringes number.
Based on Eq. 3 and Eq. 4, hence, we can rewritten :
Δz = dz/dx = pΔφ/(2 π l) (5)
From Eq. 5, we can quantify the defect, however, the plots obtained by matlab software and described in the Fig. 11, present three cases, the first case shows the interfringe curve obtained before the defect creation (Fig. 11a), the second case as shown in Fig. 11b, where the curve of interfringe was obtained after defect creation, but the third case illustrated by Fig. 11c shows the superposition of the previous two curves in order to make comparison between them. In this case, we observe that the difference between them is located in the area where the defect was created. It is represented by dotted rectangle in the interval between 80 and 180 pixels.
To extracted information to characterize the defect, we calculated the phases [42], and their graphs were plotted by the excel software in Fig. 12, as shown. We calculated the phase of the surface before creating the defect (PHIR) and after creating the defect (PHIO) along a horizontal R line (Fig. 9b) on which the defect is located. Both curves show a similar shape and the slight difference at the 75 to 150 pixels. The phase difference between the two states (PHIO-PHIR) determines the defect phase [16, 20, 43]. This phase difference allows us to extract the depth of the current defect; the depth at each point on the probed surface and the width of the defect.
We can see in Fig. 13 the presentation of defect in 2D. The depth is defined by ∆Z along the Z-axis, the defect width defined by X, along the X-axis. The spike of the deformation in depth and given by the deepest Z point. Such that: ΔZ.10− 3 is between 0 and − 0.002.10-3 pixel, and X is between (75 and 150).10− 3 pixel.