EXPERIMENTAL STUDY OF THE STRESS RELIEF IN PATCHED ALUMINIUM
SPECIMENS
Marie-Pierre Moutrille, Xavier Balandraud, Michel Grédiac
Laboratoire de Mécanique et Ingénierie (LaMI)
Blaise Pascal University (UBP), French Institute for Advanced Mechanics (IFMA)
Campus de Clermont-Ferrand / Les Cézeaux, BP 265
F-63175 Aubière, France
Didier Baptiste, Katell Derrien
Laboratoire d’Ingénierie des Matériaux LIM, UMR CNRS 8006
ENSAM Paris
75013 Paris, France
ABSTRACT
This paper presents an experimental procedure enabling to assess the stress relief in aluminium specimens reinforced by
composite patches. Infrared thermography is used to measure temperature fields during cyclic tensile tests. Temperature
variations are directly linked to the stress variations within the framework of thermoelasticity. Measurements are performed
through the thickness of the aluminium substrate. A data processing is performed to fit the temperature amplitude: a function
based on a one-dimensional model is used for this purpose. The stress transfer relief in the aluminium is observed along the
transfer length, enabling to assess the shear stress in the adhesive.
Introduction
Composite patches are often used to reinforce or to repair damaged structures, especially aeronautical components [1]. The
mechanical properties of the bonded joint between metallic substrate and composite patch clearly influence the quality of the
reinforcement. Objective of this work is to study in detail the mechanical response of such a joint.
The response in terms of strains, displacements and stresses of an adhesive bonded joint and especially the stress transfer
between substrate and adherent has been intensively studied in the literature. Many theoretical and numerical mechanical
models are available [2] [3] for instance. The load transfer from substrate to adherent induces some shear stress
concentrations in the adhesive near the free edges, along the so-called “transfer length”. To the knowledge of the authors, this
shear stress concentration has seldom been experimentally studied whereas many theoretical or numerical studies are
available in the literature. This lack of experimental data has recently led the present authors to use Digital Image Correlation
(DIC) to measure shear strain fields in the adhesive along the transfer length [4].
The aim of the present work is to complete these first results with the experimental evidence of the normal stress decrease in
the aluminium substrate since this decrease reveals the actual relief of the substrate. It is also directly linked to the shear
stress peak in adhesive. Temperature variations measured with an infrared camera are used for this purpose.
Heat diffusion equation
From the principles of thermodynamics, the following heat diffusion equation is obtained for an isotropic material producing
thermoelastic heat sources:
ρC
where
∂σ ii
∂T
− λ∆T = −αT
∂t
∂t
(1)
ρ is the mass density,
α is the coefficient of thermal expansion (CTE)
C is the specific heat capacity,
λ is the thermal conductivity coefficient,
T is the temperature,
σii is the sum of principal stresses.
Under the assumption of adiabatic conditions, obtained in practice with a high level of loading frequency, the conductivity term
is negligible. The following equation is obtained:
∆T = −
αT
(∆σ ii )
ρC
(2)
where
T is assumed to be equal to the room temperature as temperature variations are very low,
∆T is the amplitude of temperature variations during one cycle,
∆σii is the amplitude of the sum of principal stresses during one cycle.
Equation (2) makes it possible to assess the stress variations by measuring temperature variations in the aluminium substrate.
Experimental
Mechanical tests are performed on 4 mm thick plates made of 2024-T3 aluminium. They are reinforced with carbon-epoxy
composite which have been bonded using Redux 312 adhesive. The composite patches are made of three unidirectional plies.
This composite is bonded on both sides of the aluminium specimen to avoid any bending. Those samples have been provided
by the DGA (Direction Générale de l’Armement - Atelier Industriel Aéronautique de Clermont-Ferrand). Figure 1 shows the
geometry of the specimens and the zone observed by the infrared camera:
LOADING
Composites
patches
200 mm
50 mm
24 mm
Observed zone
Aluminium
substrate
4 mm
Figure 1: Specimen geometry
The testing machine is a MTS servohydraulic machine (+/-15kN). The temperature field is captured during the test by an
infrared CEDIP camera which features a focal plane array of 320x240 pixels. The thermal resolution of the camera is about
20mK. Capture frequency of the images is 150 Hz.
Specimens are subjected to a cyclic tensile loading at a sufficient level of frequency to ensure adiabatic conditions. It is also
required that the ratio between capture frequency and loading frequency is not an entire number. Two levels of frequencies
are chosen according to testing machine performances: 7 and 11 Hz. Specimens are subjected to two different levels of
loading: ∆F=10 or 14 kN and Faverage= 5.2 and 7.2 kN respectively, where ∆F is the amplitude of the cyclic loading and Faverage
is the average of the loading during one cycle.
Several films have been stored for different loading conditions. The temperature field is captured at the edge of the specimen
in the aluminium as shown in Figure 1. The spatial resolution of the measurements is about 100 µm.
Data processing
Discrete Fourier Transform (DFT) is used in to obtain the amplitude of temperature variation at each pixel. As a first approach,
only 1000 pictures are used for this processing. This calculation is performed with the Matlab package. Figure 2 shows the
temperature variation field obtained by DFT during a typical test.
Temperature variations
(°C)
Composite
patches
aluminium
Figure 2: Field of temperature amplitudes during the cyclic loading
For each line in the aluminium zone, the signal is fitted using least square method. The chosen fitting function is similar to the
one obtained from by the shear lag model:
If x<D
f (x) = C
(3)
If x>D
f ( x) = C + A(
BL p
−1
2 BL p
−1
e
e
(e B ( x − D ) − e − B ( x − D ) ) + e B ( x − D ) − 1)
(4)
where
x is the position along the x-axis,
Lp the patch length
and
A, B, C and D are the parameters to be optimized
Note that C and D correspond to the temperature amplitude in the unpatched area and to the location of the left-hand edge of
the patch respectively.
Figure 3 shows an example of fitting for one line of pixels in the aluminium substrate.
Figure 3: Temperature variations fitting
We have noticed that the optimization exhibits similar performances in terms of residuals under all considered experimental
conditions (see Figure 4 bellow).
Results
The experiment has been performed 5 times under the same conditions on the same specimen. Results show that the
experiment is repeatable.
Figure 5 represents temperature amplitude map around the edge of a specimen for different loading conditions.
Figure 4: Temperature amplitude cartography for different loading conditions
It can be noticed that the distribution of temperature variation is the same for all loading conditions. There is however a
difference between both sides of the specimen due to a small shift between the two patches and to the difference of thickness
between the two joints. This difference shows that the two patches do not work exactly in the same way: one of the two
patches gives a maximal reinforcement with a smaller transfer length.
In order to deduce the variations of stresses, coefficient of thermal expansion of this 2024-T3 aluminium must be known (see
-6
-6 -1
equation 2). This value lies between 21.1 10 and 24.7 10 K in the literature. This range leads to an important uncertainty on
stress values. This is the reason for which it is more relevant in a first approach to discuss in terms of stress relief percentage.
Figure 5 shows reinforcement in the aluminium for different conditions.
Delta (F)=10kN
F=7Hz
Delta (F)=10kN
F=11Hz
Stress relief
(%)
Delta (F)=14kN
F=7Hz
Delta (F)=14kN
F=7Hz
Figure 5: Stress relief in the aluminium
The same stress relief map is obtained in all cases. The stress relief for this specimen is about 32%. Unlike the maximum
stress relief, transfer length depends on adhesive layer thickness. The stress transfer length at 95% represents the length
which is necessary to reach 95% of the maximal stress in the composite patch. Figure 6 presents the stress transfer length of
two different samples exhibiting 0.1 and 0.5 mm adhesive layer thickness respectively.
Stress transfer length at 95% (mm)
14
12,6
12
9,2
10
8
6
left-hand side
6,6
5,3
right-hand side
Left hand
side
Righthand
side
4
2
Observed zone
0
nom inal adhesive
thickness 0.1 m m
nom inal adhesive
thickness 0.5 mm
Figure 6: Stress transfer length
Although the nominal adhesive thickness is the same for both patches, stress transfer length is not exactly the same. This
result is in agreement with the observation of a dissymmetry (thickness of adhesive layer). Moreover the smaller the adhesive
layer is, the shorter the stress transfer length is: in the present case the stress transfer length is twice longer when the
adhesive layer is five times thicker.
An estimation of the shear stress in the adhesive is obtained using a shear lag model:
τ xy ( x) = −es
dσ xx
dx
(5)
where
τxy is the shear stress in the adhesive
es is the thickness of the aluminium substrate,
σxx is the longitudinal stress in the aluminium substrate.
In our case we make the assumption that:
σ xx = ∆σ ii
(6)
Longitudinal stresses in the aluminium are calculated first. Therefore it is necessary to choose a value for CTE. This value is
chosen in the range of value of the literature and in agreement with the known level of stress in the unpatched area.
Then the shear stress distribution is obtained in the adhesive by derivation of the longitudinal stress (equation 5) for each
column of pixels in the substrate. It is considered that this procedure is correct near the adhesive joint. This is the reason why
the five closest columns from the adhesive are used to obtain the shear stress distribution in the adhesive. Figure 7 presents
the shear stress distribution in both adhesive joints of a specimen subjected to a tensile loading amplitude of 10kN at a
frequency of 11Hz. The nominal adhesive thickness of the specimen is 0.5 mm.
Figure 7: Shear stress in the adhesive joints
A significant difference between both sides of the specimen is observed. It is in agreement with the results above. The longer
the transfer length is the lower the maximum shear stress is.
Maximum shear stress for two different specimens can be compared at the same loading conditions. These results are
compared with a theoretical result (shear lag model) considering nominal material properties and dimension of the specimens.
Material properties used for this calculation are given below:
Longitudinal composite young modulus: 130500 MPa;
Aluminium young modulus: 73100 MPa;
Adhesive shear modulus: 1600 MPa.
Maximum shear stress in the adhesive joint (MPa)
The Figure 8 presents those results.
50
45
44,9 45,2
43,25
40
35
28,3
30
25
20,1
left-hand side
19,68
20
right-hand side
theoretical value
15
10
5
0
nominal adhesive
thickness 0.1 mm
nominal adhesive
thickness 0.5 mm
Figure 8: Maximum shear stress in adhesive joints of two different specimens
The maximum shear stress calculated in the adhesive with experimental results is closed from the theoretical result for the first
case (specimen with nominal thickness of adhesive equal to 0.1 mm). The relative difference between experimental and
theoretical data is less than 5%. There is moreover a very low difference between both sides of the specimen (less than 1%).
Level of shear stress in this case is very high for this material since the nominal ultimate shear strength given by the suppliers
is 40MPa.
The second specimen (specimen with nominal thickness of adhesive equal to 0.5 mm) clearly exhibits a dissymmetry as it was
presented in previous figure (Figures 4, 5, 6 and 7). Nevertheless, it is interesting to note that maximum shear stress in the
left-hand side is the same as the theoretical maximum shear stress. All these observations highlight the difficulty to obtain
adhesive layers with regular thickness and perfectly symmetric specimens.
Conclusions
Infrared thermography seems to be an appropriate technique for measuring stress relief in aluminium patched specimens.
Fields of temperature amplitude and relief are not really dependent on loading conditions. The experimental technique and
data treatment give repeatable results.
The main observation is the asymmetric effect of both composite patched on both side of the sample to avoid bending.
Although maximum reinforcement is the same (about 30% of stress relief under the composite patch), stress transfer length is
very sensitive to geometric parameters such as thickness of adhesive layer.
By choosing a representative CET and considering one-dimensional shear lag model, we obtain an estimation of the shear
stress in the adhesive. When the adhesive layer is thin, the maximum shear stress is very high (more than 40 MPa).
Acknowledgments
The authors acknowledge financial support from the French Ministry of Research (ACI ECD 058) and DGA (Direction Générale
de l’Armement - Atelier Industriel Aéronautique de Clermont-Ferrand) for providing specimens.
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