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RESIDUAL STRAIN AND STRESS ANALYSIS BY SPECKLE
INTERFEROMETRY
COMBINED WITH THE DRILL OF A GROOVE
Guillaume MONTAY, Afaf MARAS, Olivier SICOT,
Emmanuelle ROUHAUD, Manuel FRANÇOIS
Université de Technologie de Troyes (UTT)
Institut Charles Delaunay, LASMIS, FRE CNRS 2848
12, rue Marie Curie, BP 2060, 10010 Troyes
[email protected]
ABSTRACT
In this study a new residual stress determination method in two directions simultaneously is presented. This
method is based on the stresses relaxation during the drill of a groove. This groove is drilled incrementally. The
residual stresses relaxation occurs from the depth drilled and from the length of the groove. Measuring the
surface strain generated by the relaxation, enables to determine the stress gradient in the depth and along the
groove. To measure the surface strain in a direction perpendicular to the groove, a digital speckle pattern
interferometer is used. This method is well adapted when the residual stress field in the structure, varies in the
depth as well as along the surface of the part. It is the case in a welded structure. The method is tested here on
an aluminium plate where a central band has been shot peened.
Introduction
The majority of the measurement methods are able determine a residual stress evolution in one direction only
(generally in depth) [1-5]. In many cases, knowing the residual stress gradient in one direction is not sufficient. In
the case of welding, the residual stress is not homogenous in the depth and along the transverse direction of the
weld. To introduce the complete stress state in a finite element code, for instance, a two dimensional distribution
of residual stresses in the specimen is usually required.
In this study a new residual stress determination method in two directions simultaneously is presented. This
method is based on the stresses relaxation during the drill of a groove. This groove is drilled incrementally. The
residual stress relaxation occurs from the depth drilled and from the length of the groove. Measuring the surface
displacements, generated by the relaxation, enables to determine the stress gradient in the depth and along the
groove. To measure the surface displacements in a direction perpendicular to the groove a digital speckle pattern
interferometer is used. Because of the strong gradients in the volume removed by drilling, piezoresitive strain
gauges do not give enough information to calculate the residual stresses. Full field methods are required.
Various optical techniques can be used, shearography or grating shearography to measure strains and ESPI or
moiré interferometry to measure displacements [6-10]. To measure surface displacement in our situation we have
choose the ESPI with phase shifting. This technique does not require surface preparation and is quite
straightforward to use. An analysis is presented that permits to determine the distribution of residual stresses in
depth and along an axis using a limited set of measurements.
The incremental groove drilling method
The semi destructive incremental groove drilling method (IGDM) is based on the stress relaxation principle. A
small groove is drilled incrementally in the prestressed component. The residual stresses that were present in the
removed volume generate surface displacements.
Y
k
L
X
h
La
Figure 1. Scheme of the structure
The groove is drilled perpendicularly to the prestressed area. The displacement Ux(x, y) is not constant along the
y direction because the residual stresses are not homogenous along y (and along x also).
y
Ux(x,y)
Groove
y
x
Prestressed
area
Figure 2. Scheme of the groove in the prestresses structure
The displacement Ux(x,y) is generated by the relaxation of σx(y,z). More precisely, it is generated by the
contributions with various weights of all the stresses along the groove surface. For the residual stress
computation, we must take in consideration this phenomenon.
Phase shifting applied on the incremental groove drilling method: theory
Electronic Speckle Pattern Interferometry (ESPI) is a widely used technique to measure full-field displacements
on surfaces of many kinds of objects. This method is suitable for in plane displacement measurement and for
rough surface. The speckle interferometer used is a classical two beams interferometer depicted on figure 3.
Miror
Laser
Pin hole
λ = 632,5 nm
k
Camera
Beamsplitter
X
Pin hole
Z
θ
Y
Miror (Pzt)
Figure 3. Classical speckle interferometer
The phase of one beam of the interferometer is shifted with a mirror mounted on a piezo-translator. A set of
r
interference patterns corresponding to the given phase shifts are recorded. K represents the sensitivity vector. In
our setup, five phase steps are recorded; the corresponding speckle patterns are recorded by a CCD camera. For
each phase step, the intensity
I i ( x, y )
of an interference pattern i is given with Eq (1) [11] :
[
]
I i ( x , y ) = I 0 ( x , y ) 1 + γ ( x , y ).cos( φ ( x , y ) + ϕ i )
i = 1,2 ,3,4 ,5
I 0 ( x , y ) is the intensity of the LASER light, γ (x ) describe the contrast and φ ( x , y )
(1)
the optical phase of the
i
wave front, ϕ is the phase shifted of one beam of the interferometer.
In our case, 5 phase shifts distributed between 0 and 2 are used. Thus, the optical phase is calculated with Eq
(2) :
tan φ ( x , y ) =
− 2( I 4 ( x , y ) − I 2 ( x , y ))
2 I 3 ( x , y ) − I1( x , y ) − I 5 ( x , y )
(2)
This phase is calculated for each pixel of the image to obtain a phase map of the area of interest on the structure.
This phase map is calculated for a state of deformation. The perturbation of the structure generates a new state of
deformation. A second phase map must be measured after the perturbation.
The difference (pixel to pixel) of the two phase maps generates an interference fringe pattern map containing the
displacement information of the material between the two states of deformation, this displacement field is
obtained with Eq (3).
u( x , y ) =
∆φ ( x , y )λ
4π sin θ
(3)
With ∆φ(x,y) is the optical phase difference due to the object deformation, λ=632.8 nm is the wavelength of the
HeNe continuous laser used in our case and θ=45° is the illumination angle (figure 3).
Phase shifting and groove drilling: application on a ultra sonic shot peened band
The test specimen is mounted on a thick T-shape notched plate (Fig 4.). The specimen is a plate in aluminum
(AU4G) which was ultrasonic shot peened on a 4 mm band on one side. In this condition, the maximum residual
stress gradient is at the center of the band and decreases away from this area.
The machining of the groove is performed by a small milling machine with variable rotation speed. The
penetration depth of the milling tool was controlled automatically with a precision of 0.2 µm. we chose here the
minimal rotation speed of 5000 rpm and a feed rate of 1µm/s. The optical system is adjusted to produce an initial
null field, devoid of fringes. The drilling machine is mounted on a YZ translation table and locked when the
position of the drill is adjusted. The drilling system is then removed and the Ux(x,y) displacement field is recorded
by speckle interferometry. The images are captured by a CCD camera connected to a computer. This procedure
is repeated for the subsequent depths drilled.
Figure 4. Photograph of experimental set up
The piezo mirror (a mirror mounted on a piezoelectric transducer PZT) is utilized to introduce phase shifts. The
optical phase distribution is evaluated using a temporal phase shifting method which sequentially acquires 5
phase-shifted images between two steps drilled. The deformed configuration is captured after each drill. Figure 5
represents the phase shift fringes for each step drilled. The length of the groove is always the same, considered
semi infinite with regard to the length of the prestressed area.
Figure 5: Images of fringes pattern for the 9 increments drilled, from 20 µm to 500 µm, obtained with the phase
shifting method.
The width of the groove is 2 mm (40 pixels) and the width of the shot peened area is 4 mm (80 pixels). On these
images, the groove is vertical and the prestressed band is horizontal. The fringes represent the displacement
Ux(x,y). The number of fringes increases as the depth of the groove increases. So the surface displacement
increases as the depth increases, as the residual stress relaxation occurs. We can note a good symmetry in the
fringes patterns. This symmetry in the field of displacement shows that the drill is perpendicular to the surface.
Considering the centre of the shot peened band (of the prestressed area), figure 6 represents the displacement
Ux(x,y=0). Some displacements are difficult to interpret, notably near the groove. In this area (several µm), plastic
effects appear during the residual stress relaxation.
2,5
D is p la c e m e n t ( m ic r o n s )
20
40
80
120
160
200
300
400
500
2
1,5
1
0,5
0
-17
-15
-13
-11
-9
-7
-5
-3
-1
1
3
5
7
9
11
13
15
Position (mm)
Figure 6. Displacement along the centre line of the prestressed area
17
Figure 7 represents a displacement measured for a fixed position of x (x=2.771 mm). This position is far enough
not to be affected by plastic strain. For each increment drilled, the displacement is extracted for 7 positions in the
direction y. We can see the influence of the shot peened area (-1<y<+1) on the value on the displacement. The
displacements decrease while we move away from the prestressed area.
x=2.771
3
2
Y (mm)
1
0
-1
-0,9
20
40
80
120
160
200
300
400
500
-0,8
-0,7
-0,6
-0,5
-0,4
-0,3
-0,2
-0,1
0
-1
-2
-3
Displacement (microns)
Figure 7. Displacement as a function of the y position, x=2,771
Conclusion
A new approach in residual stress analysis based the combination of an optical and a mechanical setup is
proposed. The results obtained confirm the feasibility and the relevance of this approach. The originality of this
technique is the possibility to measure, both the stress profile in depth of the structure, and the stress profile
following the axis of the machined groove. This can be useful to measure the stress gradient in two directions, for
instance in welded joints. Work is currently in progress to obtain the stress field from influence coefficients
calibrated with a finite element model.
References
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