The existence of residual stresses affects both safety and lifetime. Thus the determination of these stresses is very important. The ESPI (Electronic Speckle Pattern Interferometry) and Hole- Drilling combined method seems to be an appropriate technique for their measurement. The theoretical considerations about the applicability of this method based on computations and preliminary experiments are presented. The experiments on specimens simulating known residual stress distributions were carried out on a professional apparatus. These results were compared and are in good accordance with other conventional methods. The proposed technique can be used for residual stress measurements

Holý,S.

Krempaszky, C.

ŠSedivý, O.

University of Queensland eSpace

5th Australasian Congress on Applied Mechanics, ACAM 2007  
10-12 December 2007, Brisbane, Australia 
Residual Stress Measurement by Electronic Speckle Pattern Interferometry 
 
O. edivý1, C. Krempaszky2, S. Holý1 
 
1Department of Mechanics, Biomechanics and Mechatronics, Faculty of Mechanical Engineering, 
Czech Technical University in Prague, Prague, Czech Republic 
2Christian Doppler Laboratory of Material Mechanics of High Performance Alloys, Lehrstuhl für 
Werkstoffkunde und Werkstoffmechanik, Technische Universität München, Garching, 
Germany 
Abstract: The existence of residual stresses affects both safety and lifetime. Thus the determination of 
these stresses is very important. The ESPI (Electronic Speckle Pattern Interferometry) and Hole-
Drilling combined method seems to be an appropriate technique for their measurement. The 
theoretical considerations about the applicability of this method based on computations and 
preliminary experiments are presented. The experiments on specimens simulating known residual 
stress distributions were carried out on a professional apparatus. These results were compared and 
are in good accordance with other conventional methods. The proposed technique can be used for 
residual stress measurements. 
Keywords: electronic speckle pattern interferometry, residual stresses measurement. 
1 Introduction 
Electronic Speckle Pattern Interferometry (ESPI) is an optical method uti lizing the speckle effect [1,2]. 
By comparing at least three pairs of object images all three point-displacement-components in the 
investigated area can be determined contactlessly [3]. 
The Hole-Drilling method is based on drilling a small hole into an homogenous residual stress field, 
which causes the release of stresses. Corresponding strains are measured on the object surface by 
strain gauges and the directions and magnitude of the principal residual stresses are determined by 
calibration constants [4]. This method is standardized [5]. 
It has been proposed to use ESPI instead of strain gauges in the Hole-Drilling method. The absence 
of strain gauges (no influence of eccentricity, temperature and integration over their lengths), the non-
contact method of full-field measurement by ESPI and time saving represent the advantages of the 
technique. The strains can be determined in all points of the area as first derivatives of displacement 
and when split into more steps, their total magnitude can be arbitrarily large. The differentiation of 
displacement would increase the noise level of the measured values and, because of that, in this work 
a different way of evaluation is used from that employed in conventional Hole-Drilling. 
Recently, preliminary measurements which concentrated on the determination of residual stresses by 
this combined technique, have been provided. Thin specimens with known stress distributions 
simulating a real relieved stress state were examined [6]. 
2 Applicability examination of the proposed method 
2.1 Preliminary e xperiments 
The first experimental part was focused on measurements testing the applicability of professional 2D-
ESPI-sensor Dantec Dynamics Q-300. The strain-stress curves of steel sheets during simple tension 
tests were measured. The results were compared with those from reference strain gauges placed on 
the other side of the samples and good agreement was found, the maximum difference being 1.5% 
[7]. The possibilities for the apparatus were also studied. Further measurements of sample unloading 
from a total deformation of 10% were performed. For these experiments the use of strain gauges 
would be practically impossible if suppression of material relaxation and creep is required. The 
difference between the theoretical linear-elastic material model and real measured data when 
unloaded, is 730 mm/m. This value represents the spring-back difference. 
  
2.2 Parameters of ESPI sensor 
The properties of the ESPI sensor and its influence on measured values were also examined. The 
theoretical displacement resolution is about 3x10-3 mm by the designed arrangement, but for real 
measurements, values ten-times this are reasonable. For comparison with strain gauges in the 
investigated area of 8x6 mm2, the minimal  theoretical measurable deformation is 0.4 mm/m. The in-
plane resolution of the apparatus is then 1 mm/m, but also depends on the total displacement. This 
value is equal to the resolution required by ASTM E 837-01 [5]. By comparison to ESPI, stricter 
requirements are imposed on residual stress measurements provided by strain gauges because of the 
effects mentioned in section 1. 
2.3 Displacements relieved by drilling a hole 
The relief of residual stresses by the drilled hole of radius r0 in the coordinate origin of an infinite plate 
loaded by uniaxial homogeneous tension, sx, in x-direction causes displacements which can be 
computed with Kirsch´ equations in Cartesian coordinates x,y [8]: 
( ) ( ) ( )
ú
ú
û
ù
ê
ê
ë
é
+
---
+
+
+
+
=
22
2
022
22
2
0
xx sin41sin41
5cos
2
1,
yx
r


yx

E
ryxu , (1) 
( ) ( ) ( )
ú
ú
û
ù
ê
ê
ë
é
+
-++
+
-
+
+
=
22
2
022
22
2
0
xy cos41cos41
3sin
2
1,
yx
r


yx

E
ryxu , (2) 
where E is Young´s modulus, n Poisson´s ratio and a = arctan (y/x). These equations are valid for 
linearly elastic material and for sx < 50% of yield stress. For aluminum (E = 72.5 GPa, n = 0.35, r0 = 
0.9 mm and sx = 47.25 MPa corresponding to 10% of yield strength), the extreme value of 
displacement on the hole border makes ur = - 1.17 mm. This value is very easily measurable by the 
apparatus. Radial displacements, ur, expressed from (1) and (2) (displacement is proportional to 
intensity), ur (r, a = 0) = ux (x, y = 0) and ur (r, a = p/2) = ux(x, y = 0) are represented in figure 1. 
 
 
 
Figure 1 - ur computed for aluminum (E = 72.5 GPa, n = 0.35), r0 = 0.9 mm and sx = 47.25 MPa 
according to (1) and (2). 
The existing apparatus can be used in the above-mentioned manner for residual stress 
measurements, and in comparison to other apparatus has even better properties on account of its 
larger CCD-chip. The accuracies of similar systems are equivalent to that of Hole-Drilling with strain 
gauges and reach 7.5% for 10% of yield stress [6], comparable with 10% for the conventional Hole-
Drilling method [5]. 
  
3 Stress  displacement relations 
Assuming a 2D-residual stress field at every depth under the surface, the relieved radial displacement, 
ur, at radius, r, on surface from center of a drilled hole of radius, r0, is 
( ) ( ) ( ) ( ) ( ) hrBhrAru 2cos,, minmaxESPIminmaxESPIr +×++×= , (3) 
where smax and smin are the principal stresses acting at depth, h, a is the angle measured 
counterclockwise from smax to the x-axis, AESPI and BESPI are calibration coefficients. Transforming 
displacements u0, u90 and u45 (displacement in counterclockwise angle directions of  0°, 90° and 45° to 
the x-axis) to p, q and t and normal stresses sx, sy and shear stress txy to P, Q and T,  
( ) 2/900 uup += , ( ) 2/900 uuq -=  and ( ) 2/2 45900 uuut -+= , (4) 
( ) 2/yx P += , ( ) 2/yx Q -=  and xyT = . (5) 
Analogously to [9] we get the same expressions for the required principal stresses. 
( ) ú
ú
û
ù
ê
ê
ë
é +
+
×=
ESPI
22
ESPI
minmax 1
,
b
tq
a
pE m  and ( )qt /arctan5.0= . (6) 
Here b is the angle measured clockwise from the x-axis to the maximum principal stress direction, 
aESPI = 2 EAESPI/(1+n) and bESPI = 2EBESPI are coefficients describing the relation between the 
measured displacements and stresses to be determined, which represents the main difference 
regarding [9]. 
A modified, two-dimensional, finite-element computation of the calibration coefficients for hole-drilling 
by the integral method [9] was used. A f ully automated model of step-wise varying stresses over the 
hole-depth was developed for determination of the calibration coefficient matrices (figure 2). For both 
matrices aESPI and bESPI two separate models are necessary (loading corresponding to biaxial stress 
and to pure shear, respectively). In the first model, axisymmetric, four-node, bilinear solid elements, in 
the second one axisymmetric four-node bilinear and Fourier quadrilateral, solid elements with 
nonlinear, asymmetric deformation, were used. 
Maxwells reciprocity theorem states for any isotropic, linearly elastic structure that displacement at 
location 1 due to a unit force at 2 is equal to the displacement at 2 due to a unit force at 1 (i.e. 
the flexibility matrix is symmetric). This property was used to reduce significantly the number of 
computations that deliver matrices whose elements are cumulative sums of the required coefficients. 
 
u1 
u2 
u3 
u4 
u5 
F 
r0 
rm 
H
,h
 
 
  ESPI 
Sensor 
Drilling unit  
Sp
ec
im
en
 
 
Figure 2  FEM  Model with load application 
using Maxwells theorem. 
Figure 3  Apparatus arrangement. 
  
4 Experimental part 
4.1 Apparatus 
The designed apparatus used (figure 3) consists of three main parts: ESPI-sensor, drilling unit and stiff 
frame to which different specimens can be attached. The CCD-chip resolution of the sensor camera is 
768 x 576 pixels with a 256-bit color depth. The illumination angle of 28° and laser wavelength of 780 
nm were the same for all experiments. Other sensor properties are described in section 2.2. For 
drilling, a standard pneumatic driven milling machine with mill diameter of 1.8 mm was used. Its 
rotation, radial and tangential feeds are controlled pneumatically by a separate computer which is 
connected by a trigger signal to the ESPI-computer. The measurement and determination of residual 
stresses is fully automatic. 
4.2 Measurement and evaluation procedure 
The apparatus is able to measure displacements, ux and uy, perpendicular to the camera axis, z. For 
each direction four reference, phase-shifted speckle-images are recorded before drilling. After that a 
hole of incremental depth is drilled and another four speckle-images are recorded. By subtracting 
them from the reference images the relieved displacement fields, ux and uy, are determined. The 
second set of images is used as a reference for the following drilling step. 
Within one step, the radial displacement field, ur, is computed from ux and uy. After that the direct and 
inverse Fourier transformations on circles are used to filter signal noise. According to (3) harmonics 0 
and 2 are retained and from corresponding amplitudes the displacements u0, u90 and u45 are computed 
for different radii, rm, (figure 2). The rest of the values below the maximum radius are not utilized. The 
principal residual stresses and their direction are determined by (6). An example of original and filtered 
fields, ur, are shown in figures 4 and 5, where radial displacements are proportional to intensity 
(compare with figure 1). 
  
Figure 4  Radial displacements (unfiltered). Figure 5  Radial displacements (filtered). 
4.3 Specimens and results 
Specimens with constant stress over thickness 
The simplest way to simulate one-dimensional tension was with a conventional tensile sample with 
holes drilled after loading. The behavior of aluminum Al7075 samples was investigated for various 
hole-depths and various stresses. These measurements were compared with strain gauge data and 
with the known stress state. The maximum difference between the ESPI measurement and the known 
stress was 4.5 % for stresses of 10 % of the material yield stress (compare with 7.5% in [6]). 
Another specimen with a known residual stress distribution was a ring and plug with a diametrical 
interference, d, (figure 6). The contact stress, p, between the ring and plug and the radial and 
tangential stresses as a function of radius, R, in the ring are given by the following equations: 
  
( )
2
outin
2
out
2
in
2 RR
RRE
p
-
= ; ÷
÷
ø
ö
ç
ç
è
æ
-
-
= 2
2
out
2
in
2
out
2
in
r 1 R
R
RR
pR  and ÷
÷
ø
ö
ç
ç
è
æ
+
-
= 2
2
out
2
in
2
out
2
in
t 1 R
R
RR
pR . (3) 
 
 
Figure 6  Specimen with constant stress over 
thickness. 
Figure 7  Stress distribution in the plug and 
ring.  
During the assembly the plug was cooled down to 160°C by liquid nitrogen and the ring was heated 
to +40°C. The temperature difference of 200°C caused a radius difference, DRin = 0.108 mm between 
both parts, which was sufficient for putting them together (minimal temperature difference 
corresponding to d = 0.05 mm was 84°C). Various strain gauges were installed on the ring, by which 
the assembly symmetry and stress distribution was verified. The experimentally verified stress 
diagram is shown in figure 7 (material Al7075, E = 72.5 GPa, d = 0.05 mm, Rin = 25 mm, Rout = 60 
mm) together with ESPI-measurements (stESPI, srESPI). The maximum difference between them was 
5.1 %. 
Both specimen sides were used for measurements. The chosen thickness was a compromise 
between minimizing the influence of geometrical irregularities and the impact of drilling on one side or 
another. 
Specimen with linearly changing stress over thickness 
Linearly changing stress was simulated on bent, 4.3  mm-thick, aluminum plates. These plates were 
fastened in a four-point-bending device (figure 8) and loaded by adjusting the screw at the base of the 
rig. This causes a plane strain state in the plate, which can be described analytically. Because of the 
lack of a direct force measurement and the non-linear dependence between loading angle and applied 
force, the load was determined by strain gauges attached directly to the upper part of the sample. The 
loading symmetry on the upper and lower surfaces was verified experimentally by strain gauges.  
 
 
F F 
F F 
Load adjustment  
 
 
Figure 8  4-point-bending device. Figure 9  Measured stress distribution in upper 
part of bended plate. 
  
The drilling was done in four 300 mm deep incremental steps up to the depth h = 1.2 mm, equal 
approximately to 1/4 of the plate thickness. An example of the stress distribution and data 
experimentally measured by ESPI for the above-mentioned aluminum, plate thickness t = 4.3 mm, 
width w = 45 mm and bending moment inducing strains ex = 610 mm/m and ey = - 80 mm/m on the  
specimen surface, is shown in figure 9. The maximum difference was 8.2 % for stress in the y-
direction. 
5 Conclusions 
According to the theoretical considerations about the applicability of this method based on basic 
computations and experiments, the existing apparatus can be used for residual stress measurements. 
It is possible to determine casual residual stresses with a relative error of 5 %. It represents a better 
result than the 10% for the conventional Hole-Drilling method which was used as a reference method 
by simple tension experiments. 
Specimens with known internal stresses were designed and their stress distributions were measured 
by ESPI. The algorithm for automatic measurement and evaluation of residual stresses was designed. 
As a further step it is planned to provide measurements on real objects and compare them again with 
strain gauge results. 
Acknowledgements 
The authors gratefully acknowledge the financial support of the grant of the Ministry for Industry and 
Trade of the Czech Republic No. MPO FT-TA/026-T10, the CTU grant 0710712 and the Christian 
Doppler Research Association (CDG). 
References 
[1] DAINTY, J.C.: Laser speckle and related phenomena (Topics in Applied Physics 9), Springer-Verlag, Berlin 
and New York, 1975. 
[2] ARCHOBOLD, E., ENNOS, A.E.: Displacement measurement from double exposure laser photographs. 
Optica Acta, 19, 1972, 253270. 
[3] CLOUD, G. L.: Optical Methods of Engineering Analysis, Cambridge University Press, New York 1995. 
[4] LU, J.: Handbook of Measurement of Residual Stresses, The Fairmont Press, Lilburn 1996. 
[5] ASTM E 837-01: Standard test method for determining residual stresses by the hole-drilling strain gauge 
method, 2001. 
[6] VIOTTI, M. R., KAUFMANN, G. H.: Accuracy and sensitivity of a hole drilling and digital speckle pattern 
interferometry combined techniquie to measure residual stresses, Optics and Lasers in Engineering, 41, 
2004, 297305. 
[7] EDIVÝ, O.: Grundlagen und Anwendung der ESPI für die Analyse elastisch-plastischer 
Werkstoffeigenschaften. Technische Universität Chemnitz, Chemnitz 2003. 
[8] KAIBIRI, M.: Toward more accurate residual-stress measurement by the hole-drilling method: analysis of 
relieved-strain coefficients, Experimental Mechanics, 26, 1986, 1424. 
[9] SCHAJER, G.S.: Measurement of non-uniform residual stresses using the hole-drilling Method. Part II  
Practical application of the integral method, Journal of Engineering Materials and Technology, 110, 1988, 
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