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Analysis of back-face strain measurement for adhesively bonded single lap joints using strain gauge, Digital Image Correlation and finite element method
Journal Pre-proof Analysis of back-face strain measurement for adhesively bonded single lap joints using Strain Gauge, Digital Image Correlation and Finite Element Method J. Weiland, M.Z. Sadeghi, J.V. Thomalla, A. Schiebahn, K.U. Schroeder, U. Reisgen PII:
S0143-7496(19)30240-4
DOI:
https://doi.org/10.1016/j.ijadhadh.2019.102491
Reference:
JAAD 102491
To appear in:
International Journal of Adhesion and Adhesives
Please cite this article as: Weiland J, Sadeghi MZ, Thomalla JV, Schiebahn A, Schroeder KU, Reisgen U, Analysis of back-face strain measurement for adhesively bonded single lap joints using Strain Gauge, Digital Image Correlation and Finite Element Method, International Journal of Adhesion and Adhesives, https://doi.org/10.1016/j.ijadhadh.2019.102491. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Elsevier Ltd. All rights reserved.
Analysis of back-face strain measurement for adhesively bonded single lap joints using Strain Gauge, Digital Image Correlation and Finite Element Method J. Weiland1*, M. Z. Sadeghi2, J. V. Thomalla1, A. Schiebahn1, K. U. Schroeder2, U. Reisgen1 1
ISF - Welding and Joining Institute, RWTH Aachen University, Pontstrasse 49, D-52062, Germany
2
SLA - Institute of Structural Mechanics and Lightweight Design, RWTH Aachen University, Wuellnerstrasse 7, D-52062 Aachen, Germany
ABSTRACT
Back-face strain measurement is a widely used method for damage detection of adhesively bonded single lap joints. Often, a simple Strain Gauge is used to monitor in-situ structural adhesives bonds in the field. However, the extrinsic local placement of the Strain Gauge on the strain hot spot of the joint poses a major challenge. Furthermore, finite element method (FEM) simulations do not reproduce the adherents accurately enough due to inaccuracies in the manufacturing process. Therefore, an additional optical measurement methodology is required to precisely analyze and localize the strain hot spots on the adherent. This work deals with the most important theoretical background on the stiffness, strength and fracture behaviour of the single lap joint. Subsequently, the back-face strain along the joint part was simulated by means of FEM. The results were validated and implemented with the results of the Digital Image Correlation (DIC). The strains in the hot spot area were determined from both finite element (FE) and DIC methods. With this knowledge, the Strain Gauge is applied exactly to the location of the strain hot spot. The central result of the paper is the confirmation of the strain hot spot. It is shown that the calculated points and curves can be approximated very well.
Keywords: damage detection, strain measurement, single lap joint, Digital Image Correlation (DIC), Strain Gauge, finite element analysis, A. epoxy/epoxides, B. steels, C. lap-shear, C. fracture mechanics
*
Corresponding author. J. Weiland. Email: [email protected]. Phone: +49 241 80 96275.
I.
INTRODUCTION
Today, adhesively bonded joints cannot be tested 100% non-destructively [1, 2]. This fact is the main motivation for the approach to monitor adhesively bonded joints in order to record the structural behaviour and thus ensure a safe load transmission. Two further complicating factors make it more difficult; on the one-hand are the inaccuracies in the manufacturing process and on the other hand a lack of knowledge in the field of fatigue behaviour and degradation process of the adhesive [3]. These uncertainties are taken into account when designing adhesive joints with high reduction factors and highly conservative safety factors. Through the use of permanent non-destructive structural health monitoring (SHM) methods, structural damages in the adhesive bond can be detected at an early stage. For that task, the back-face strain measurement method can be use. The method is based on an extrinsic sensor concept witch is placed on the back-face of the adherent to measure the strain of adhesively bonded joints. Abe and Satoh [4] start using the back-face strain measurement in the year 1986 to investigate crack formation and propagation in spot-welded joint adherent. Around 1995 several scientists applied the method to adhesively bonded joints and until today, many investigations have been carried out on it [4-14]. All these publications have the same motivation, to detect damage in the adhesive layer on a very efficient way. In order to be able to make predictions about the structural condition of the adhesive bond, the exact location of the strain gauge takes the most significance. For the simple single lap joint different sensor positions are conceivable. Zhang et al. [6] use a measuring point at the end of the overlap. As a result of a crack, the bend at this position increases. The measured longitudinal strains are reduced by the pressure component of the bend. Solana et al. [12] build on this idea. For structural damage monitoring, they concentrate on one measuring point in the area of the largest gradient of the characteristic longitudinal strain curve. Preisler et al. [14] uses the zero strain point in the area of the largest gradient of the longitudinal strain curve for structural damage monitoring. At this point tensile strain and compressive strain cancel each other out due to bending deformation. In the undamaged case there is no
longitudinal strain independent of the load. As soon as a crack occurs within the adhesive bond, the effective overlap length is reduced. As a consequence, the load transfer and the resulting strain distribution shift. Due to the high gradient in the range of compressive strains, there is a high absolute change in the strain here. Especially the use of the zero strain point offers a high potential. A deviation from zero can be directly assigned to a crack and correlates with the crack length. In addition, the generated FEM simulations often only represent an inadequate accuracy of the formation due to inaccuracies existing in manufacturing process [15-17]. Therefore, an additional optical measurement methodology is required to precisely analyze and localize the strain hot spots on the adherent.
1. Analytical background on the strength of adhesive joints For adhesively bonded joints, a differentiation can be made between adhesive failure and cohesive failure. A purely cohesive failure is assumed for the structural-mechanical analysis of adhesive joints. This internal adhesive strength is strongly related to the stress intensity factors and critical energy release rates for each of the three fracture modes I (traction), II (sliding) and III (tearing). These mechanical parameters determine the failure of the adhesive joint, however the actual fracture mechanism of an adhesive joint is very complex [18] and is usually a combination of mode I and mode II fracture mechanisms. Assuming the surface tension, equation (1) expresses the relationship between the critical energy release rate G1C, the stress intensity factor K1C, and the Young's modulus of the adhesive E for Mode I. 2
G1c =
K1c E
(1)
The above equation applies to brittle and medium-hard materials. It does not make sense for very ductile materials. For general flat stress conditions, equation (1) can be extended for
the case of a combined breaking load. In equation (2), G represents the shear modulus of the adhesive material. 2
Gc =
2
2
K1c K2c K3c + E + 2G E
(2)
The Double Cantilever Beam (DCB) test can be used to determine the energy release rate GIC for Mode I. The End Notched Flexure (ENF) test can be used to determine the energy release rate under Mode II. The Mixed Mode Bending (MMB) is to determine energy release rate at combination of Mode I + II. At most, by the literature, mode III could be considered equivalent to Mode II. [19-21]
2. Analytical background on the stiffness, strength and fracture behaviour of single lap joint The mechanical behaviour of single lap joints was already investigated in the early 1960s. [22] Eichhorn published dimensioning guidelines for metal adhesive bonding in 1979. [22] It is known from Rasche [23] and other publications [3, 24] that the mechanical behaviour is significantly influenced by adhesion of the adhesive to the test adherent, cohesion of the adhesive, ductility of the adhesive, stiffness of the test adherents, geometry of the test adherents and clamping of the test adherent. The main point of attention in the literature is the distribution of the stresses in the adhesive layer, which leads to the failure of the adhesive bonds at the overlapping ends. According to Habenicht [3] and Otto [24], the stress distribution is shown schematic in figure 1. In the case of overlap adhesive bondings, the adhesive is mainly exposed to shear stress (T1). Due to the eccentric application of force, the parts to be joined are deformed at the area of the two overlap ends. This results in a bending moment, which develops stress at the ends on lines of tension / peeling (σ). Additional shear stresses of the adhesive occur due to the adherent elongation (T2), this behaviour is also mainly at the overlap ends. Due to the multi-axial
superimposed stress state, simple overlap bonding fails at the edges of the adhesive layer. [3], [24]
Figure 1. Schematic stress distribution in the adhesive from SLJ according to Habenicht [3] and Otto [24] Due to the typical behaviour of the single lap joint, the joining part on the back-face also undergoes a very characteristic strain curve. This is shown in figure 2 based on Preisler et al. [14]. On one hand, the external force causes a positive change in length of the entire adherent. On the other hand, the eccentric force and the resulting bending moments cause the adherent to bend. This has the consequence for the part expansion on the back-face that there are areas in which compressive expansions exist and areas in which tensile expansions exist. The exact distribution of strain over the overlap length can be seen in figure 2 on the right. There are a few load steps which show the strain as long as there is no damage in the SLJ. The lines of different load steps meet in one point: The zero strain point.
Figure 2. Characteristic back-face strain curve of SLJ adherent, schematic strain curve overall (left) and in the overlap length range for different load cases (right) [14]
II.
MATERIALS AND METHODS
1. Samples Steel and aluminium Single Lap Joints (SLJ) are used for the tensile tests. The adhesive used is Araldite 2015-1 Huntsman Advanced Materials, Basle, Switzerland. The parts to be joined have the dimensions 120 x 25 x 3 mm³. They are joined by a 0.7 mm thick adhesive layer. The limitation to 25 mm, along the test piece, is achieved by PTFE strips to one of the joining parts. The adhesive layer has the dimensions 25 x 25 x 0.7 mm³. For illustration, all relevant dimensions are shown in figure 3.
75 mm
10 mm
25 mm
10 mm
75 mm
3 mm
adhesive layer 0.7 mm
PTFE strips
test specimen
Figure 3. Dimensions of the SLJ
The steel used is S700MC, an alloyed stainless steel. It achieves tensile strengths of ≥ 750 MPa. The aluminium EN AW-7075 T6 used is a high strength hot rolled alloy. It
achieves tensile strengths up to 545 MPa. The stress strain diagrams of the two materials
900
900
800
800
700
700
600
600
Stress [MPa]
Stress [MPa]
can be seen in figure 4.
500 400 300
500 400 300
200
200
100
100 0
0 0
0.05
0.1
0.15
0
Strain [%]
0.05
0.1
0.15
Strain [%]
Figure 4. Stress strain diagrams of S700MC (left) and EN AW-7075 T6 (right)
The adhesive Araldite 2015-1 is a two-component adhesive based on epoxy resin. Curing is carried out for 24 hours at room temperature and for a further 3 hours at 60 °C. The parts to be joined are cleaned for pre-treatment with isopropanol. An ultrasonic bath is available for this purpose. Aluminium samples are pre-treated with a laser. The CL20 laser system from Clean-Lasersysteme GmbH, Herzogenrath, Germany is used for the aluminium adherents with a power of 20 W and a wavelength of 1064 ± 4 nm. Steel samples are irradiated with corundum. The corundum blasting machine is used with a grain size of 150 µm to 210 µm and a pressure of 6 bar. A rough overview over the adherents can be taken in figure 5. There are the two kinds of adherent, steel and aluminium. The view is from the front. There is a number of 5 of each kind of adherents which are tested under tensile tests.
Figure 5. Two adherents steel (top) and aluminium (bottom) from the front with speckle pattern
The fracture behaviour is a cohesive and symmetric one as seen by the fracture pattern in figure 6 for steel and figure 7 for aluminium. It shows that the manufacturing process is suitable to produce samples for the tests.
Figure 6. SLJ with steel adherent
Figure 7. SLJ with aluminium adherent
2. Finite element modelling and parameter estimation In order to simulate the fracture behaviour of SLJ, FE model in Abaqus was developed using surface based-cohesive model approach. In this approach, cohesive connection between the adherents and the adhesive is modelled with a zero-thickness interface which its damage constitutive law is based on the Traction-separation Law (TSL). The constitutive damage response is assigned in the property of the contact interaction between the adherent and adhesive (contact to contact surface). This was successfully implemented for failure behaviour of adhesively bonded joints in a previous work [25]. Constitutive damage law follows TSL which is capable of simulating gradual degradation of the materials based on the simple correlation between the traction (T) and relative displacement (separation ). TSL can have different shapes and the simplest approach is a bilinear softening law.
To capture the most accurate stress-strain field, 3D-symmetry model was developed in Abaqus. Solid elements were used for both adherents and the adhesive layer. Very fine mesh (0.07 mm) were used in the bonded area. The static FE model was carried out under displacement control. The FE mesh and boundary conditions applied in the model is shown in figure 8.
Figure 8. 3D meshing in the FE model developed in the present study
As it was mentioned earlier, symmetry FE model for the SLJ model was developed to reduced the calculation time. The boundary conditions are shown in figure 9 (the symmetry boundary conditions are illustrated in purple).
Figure 9. Boundary conditions for the symmetry FE model
For the onset of damage initiation, the failure index of our single lap joint was computed using quadratic traction:
QUADS Criterion t t
t t
t t
1
(3)
linearized power criterion was considered as shown below:
(4)
Where GI, GII and GIII are the fracture energy values for Mode I, II ,and III respectively [26], while their corresponding subscript values, which are denoted by C, influence the accuracy
of experimental data from fracture tests under Modes I, II, and III. In the present work, the Cohesive Zone Model (CZM) properties used for modelling the adhesive is given in Table 1. The power law used was with power equal to 1.
Table 1: material properties of Araldite 2015 according to Campilho et al. [26] Property
Value
Young modulus (N/mm2)
1850
Poison’s ratio
0.33
Tensile failure strength (N/mm2)
21.63
Shear modulus (N/mm2)
695
Shear failure strength (N/mm2)
17.9
GI (N/mm)
0.47
GII = GIII (N/mm)
4.7
Value of power law parameter
1
3. Experiments and Measuring Equipment Tensile tests are recorded using the strain gauge and Digital Image Correlation (DIC) measurement methods. Both methods are used to investigate surface strain - especially in the zero-strain-point range. GOM Aramis Adjustable is used to acquire the images for the DIC. It is a two-camera-system, so that it can do 3D-analysis of the samples (see also figure 10). The evaluation of the sensor data is done with the help of the program GOM Aramis Professional.
Figure 10. Test assembly as original (left and right) and as a sketch (middle)
Evaluation of the data is done with the help of lines, points and polygons. Polygons are used for the evaluation of strains on an area. This area is staked out equivalent to the area of the strain gauges. Within this area the average strain in longitudinal direction is read out. A section (or line) is used to determine the strain of the positions along the adhesive layer. Along this line, Aramis places arbitrary points at which the strains are determined. Furthermore, the displacement of the adherent is determined with a line that extends over the entire adherent. In order to secure the introduction of force along the parts to be joined, compensation plates are attached to the test adherents. An Instron 5567 tensile testing machine is used for the tests. The set pull rate is 1 mm/min.
III.
RESULTS
1. Force-Displacement – FE and Experiment 12000
10000
Force [N]
8000
6000
4000
2000
0 0
0.05
0.1
0.15 0.2 0.25 Displacement [mm] FE - steel
0.3
0.35
0.4
Experiment - steel
Figure 11. Comparison between FE and experiment (steel adherents)
An example of the result of the steel test samples can be seen in figure 11, where the maximum force is 9123.2 N. The simulation predicts a maximum of 9671.72 N. The average force for the adherents is 9655.4 N. That is just below the maximum predicted by the simulation. The simulation describes a straight gradient up to approximately 0.12 mm. After that the stiffness is a bit higher and is constant to almost the maximum force. After reaching the maximum force with a displacement of 0.28 mm the failure begins and the joint then breaks. An almost linear stress strain curve is detected in the test. A concave tendency is discernible. The stiffness is a bit less than the one predicted by the simulation. The real adherent reaches its maximum at a displacement of 0.31 mm. Overall, the course of the experimental result lags slightly behind the simulation. This can be due to many influences.
On the one hand, settlement phenomena of machine and adherent are possible. Settlement can occur if the clamping on the machine is not tight enough. The adherent slips slightly, which leads to cyclic relaxation and consolidation within a small frame. This is reflected in the evaluation of the samples with DIC. This effect can also be seen in the not quite smooth curve of the experiment. On the other hand, it is possible that the adhesive does not exhibit the ideal stiffness due to exhibits in the simulation because of the inaccuracies in the manufacturing process.
10000 9000 8000
Force [N]
7000 6000 5000 4000 3000 2000 1000 0 0
0.05
0.1
0.15
FE - aluminium
0.2 0.25 0.3 Displacement [mm]
0.35
0.4
0.45
0.5
Experiment - aluminium
Figure 12. Comparison between FE and experiment (aluminium adherents)
For aluminium adherents the maximum force is 8725.8 N. This is just above the maximum of 8698.0 N predicted by the simulation. The average force of the aluminium adherents is 8223.0 N. In figure 12 is an example (with a maximum force of 8022.57 N) of the adherents shown. There is a linear evolution until nearly the maximum force. Then the adherent breaks and the curve does have a falling gradient. Overall, the joint follows the predicted curve very
well. In the simulation, the maximum force is reached with a displacement of 0.38 mm. The real sample reaches its maximum with a displacement of 0.36 mm. This can be due to the same influences as steel. The lower value is just because the maximum force isn’t that much as in the simulation.
2. Back-face strain curve over the adhesive bond As shown in figure 13, different results are obtained for tests and simulations. The strain along the x-axis of the joining part - i.e. along the longitudinal axis - is shown here. The back face strain is evaluated using DIC along a line on the surface. Aramis independently calculates relevant points and interpolates between them. Since only individual points are used for evaluation in this figure, the fluctuations of the measured values are very high. This could be a reason for the deviation between simulation and DIC. The simulation predicts an oscillating curve for the strain. Up to the zero strain point, the values are up to 0.08%. They then assume positive values and become negative again in the last piece. According to Preisler et al. [14], this point can be used to monitor the bond. This zero strain point remains constant at it’s value, almost x = 5,5 mm. In the case of steel, the zero strain point is almost x = 8.4 mm away from the PTFE strip, according to the simulation.
0.2
Technical strain [%]
0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 0
5
10 15 x-position along adhesive [mm] FE - 2000 N
FE - 5000 N
FE - 7000 N
Exp. - 2000 N
Exp. - 5000 N
Exp. - 7000 N
20
25
Figure 13. Typical strain over the adhesive along the x-position of itself (aluminium adherent)
3. Back-face strain at zero-strain-point Figure 14 shows the strains at the zero strain point measured using DIC, DMS and simulation as well as the force curve plotted over the displacement for a specimen with steel adherent. DIC and strain gauges are compared with the simulation as evaluation methods. The curve of the simulation describes an S-stroke, to justify this with the fact that in the simulation no complete failure of the bond is simulated. In addition, the FE results for the strains have been calculated as an average over the area of a strain gauge. Up to a displacement of 0.22 mm, the strain remains almost zero. At this point, a force of approx. 7500 N already acts on the adherent. The strain assumes negative values and asymptotically adapts to a strain of -0.04 % from a displacement of 0.35 mm. The strain gauge describes a similar behaviour, the strain gauge also remains close to zero up to a displacement of 0.22 mm. Subsequently, the strain drops slightly more flatly than the simulation. In order to use the values of the DIC with the values of the strain gauge, a
specific point at the exact strain hot spot was used for evaluation. This gives us an uneven, fluctuating and noisy course of the measurement results, since the natural oscillations caused by irregularities are not averaged by for example an polygon measurement. However, the tendency of the curve can be seen. After a displacement of 0.22 mm, the general tendency decreases until the joint breaks at a displacement of 0.31 mm. At this point, the strain measured by the DIC was -0.06 %. Therefore, the measured values of the DIC are also comparable with the values of the simulation and strain gauges. The actual measured values agree and give a representative statement and confirm the simulation
0.1
12000
0.05
10000
0
8000
-0.05
6000
-0.1
4000
-0.15
2000
-0.2
Force [N]
Technical strain [%]
result.
0 0
0.05
FE strain - steel
0.1
0.15 0.2 0.25 Displacement [mm]
DMS - steel
DIC - steel
0.3
0.35
FE force - steel
0.4
Force - steel
Figure 14. Typical strain and force over displacement of one of the test samples
Figure 15 shows the strain measured with DMS and simulation at the zero strain point and the force curve plotted over the displacement for a specimen with aluminium adherent. The
strain gauge is compared with the simulation as an evaluation method. The curve of the simulation describes an approximate S-stroke, which is simulated as a bend at failure. Especially at the beginning, the DMS values are even a bit higher than the ones of the simulation. The curves go apart from a displacement of approx. 0.22 mm, the simulation curve is released in order to drift in a positive direction. The strain gauge assumes a negative gradient at a force of approx. 4500 N. However, the curve of the strain gauge first drops into the negative. The simulation falls below zero at a force of approx. 7400 N. The force of the strain gauge is then reduced to the negative. Both of the curves share approximately the same gradient, so that, because they are gone apart, both are dropping in the negative with a nearly parallel behaviour. This can be observed in the range of approx. 0.3 mm to 0.4 mm. When the joint breaks, the strain gauge indicates a strain of approximately -0.09 %.The measured values of the strain gauge correspond relatively to those of the simulation in the essential areas and give a representative statement.
0.04
10000
0.02
9000
0
8000 7000
-0.04
6000
-0.06 5000 -0.08 4000
-0.1
3000
-0.12 -0.14
2000
-0.16
1000 0
-0.18 0
0.05
0.1
0.15
0.2 0.25 0.3 Displacement [mm]
0.35
0.4
FE strain - aluminium
DMS - aluminium
FE force - aluminium
Force - aluminium
0.45
0.5
Figure 15. Typical strain and force over displacement of one of the test samples
Force [N]
Technical strain [%]
-0.02
IV.
CONCLUSIONS
This paper describes the basic behaviour of single lap joint under load. The back face strain of the joining part is investigated. Due to the eccentric force effect, the bending moment and therefore the bending of the adherents occurs. This results in both positive and negative strain on the back of the adherent. This could be shown by the measured data from the simulation. The generated data of the Digital Image Correlation are consistent with the other measurement data besides from the fluctuations. Attention is drawn to this approach, as it can lead to large fluctuations when looking at individual points, as each of these points offers an increased error potential. If anomalies are present and are detected by some points, the results scatter strongly. Anomalies can be slight soiling or accumulation of paint in the speckle pattern. The comparison of DMS and DIC is only possible if the image correlation is applied accurately, otherwise the accuracy of the methods can vary greatly. The investigations on the zero strain point confirm Preisler et al. [14] statement that this point is suitable for monitoring the joint. To confirm this thesis, further investigations are necessary, especially with damaged adherents and under cyclic loading. Another point of reference for the monitoring of the joint is the consideration of the displacement in z direction. This observation should also be further investigated.
V.
ACKNOWLEDGEMENTS
The IGF-project IGF-Nr. 19909 N / 2, “SmartSHM – Effiziente Zustandsüberwachung struktureller Klebungen” of the research association “DECHEMA Gesellschaft für Chemische Technik und Biotechnologie e.V." is funded within the framework of the industrial collective research programme (IGF) by the Federal Ministry for Economic Affairs and Energy on the basis of a decision by the German Bundestag.
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[4] Abe H, Satoh T. Non-destructive detection method of fatigue crack in spot-welded joints. Yosetsu Gakkai Ronbunshu/Quar J Jap Wel Soc 1986;4:666-73. https://doi.org/10.4271/860601 [5] Shenoy V, Ashcroft IA, Critchlow GW, Crocombe AD, Abdel Wahab MM. Unified methodology for the prediction of the fatigue behavior of adhesively bonded joints. Int J Fatigue 2010;32:1278-88. https://doi.org/10.1016/j.ijfatigue.2010.01.013 [6] Zhang ZH, Shang JK, Lawrence FV. A Backface Strain Technique for Detecting Fatigue Crack Initiation in Adhesive Joints. J Adhesion 1995;49:23-36. https://doi.org/10.1080/00218469508009975 [7] Imanaka M, Haraga K, Nishikawa T. Fatigue-Strength of Adhesive Rivet Combined Lap Joints. J Adhesion 1995;49:197-209. https://doi.org/10.1080/00218469508014356 [8] Curley AJ, Hadavinia H, Kinloch AJ, Taylor AC. Predicting the service-life of adhesively-bonded joints. Int J Fracture 2000;103:41-69. https://doi.org/10.1023/A:1007669219149 [9] Crocombe AD, Ong CY, Chan CM, Wahab MMA, Ashcroft IA. Investigating fatigue damage evolution in adhesively bonded structures using backface strain measurement. J Adhesion 2002;78:745-76. [10] Hadavinia H, Kinloch AJ, Little MSG, Taylor AC. The prediction of crack growth in bonded joints under cyclic fatigue loading. Part I: Experimental studies. Int J Adhes Adhes 2003;23:449-61. https://doi.org/10.1016/S0143-7496(03)00074-5 [11] Kelly G. Quasi-static strength and fatigue life of hybrid (bonded/bolted) composite single-lap joints. Compos Struct. 2006;72:119-29. https://doi.org/10.1016/j.compstruct.2004.11.002 [12] Solana AG, Crocombe AD, Wahab MMA, Ashcroft IA. Fatigue initiation in adhesivelybonded single-lap joints. J Adhes Sci Technol 2007;21:1343-57. https://doi.org/10.1163/156856107782313629 [13] Khoramishad H, Crocombe AD, Katnam KB, Ashcroft IA. Predicting fatigue damage in adhesively bonded joints using a cohesive zone model. Int J Fatigue 2010;32:1146-58. https://doi.org/10.1016/j.ijfatigue.2009.12.013 [14] Preisler A, Sadeghi Z, Adomeit A, Schroeder KU. Damage Assessment in Adhesively Bonded Structures by Using SmartSHM. Struct Health Monit 2015. https://dx.doi.org/10.12783/SHM2015/27
[15] Da Silva LFM, Campilho RDSG. Advances in Numerical Modelling of Adhesive Joints. Berlin Heidelberg: Springer-Verlag; 2012, p 1-93. http://dx.doi.org/10.1007/978-3-642-236082 [16] Da Silva LFM, Das Neves PJC, Adams RD Wang A, Spelt JK. Analytical models of adhesively bonded joints - Part I: Literature survey. Int J Adhes Adhes 2009;29. https://dx.doi.org/10.1016/j.ijadhadh.2008.06.005 [17] Da Silva LFM, Das Neves PJC, Adams RD Wang A, Spelt JK. Analytical models of adhesively bonded joints - Part II: Comparative study. Int J Adhes Adhes 2009;29. https://dx.doi.org/10.1016/j.ijadhadh.2008.06.007 [18] Da Silva LFM, Pirondi A, Ochsner A. Hybrid Adhesive Joints. 1st ed. Berlin Heidelberg: Springer-Verlag; 2011. https://dx.doi.org/10.1007/978-3-642-16623-5 [19] Bruyneel M, Delsemme JP, Jetteur P, Germain F. Modeling Inter-Laminar Failure in Composite Structures: Illustration on an Industrial Case Study. Appl Compos Mater 2009;16:149-62. https://doi.org/10.1007/s10443-009-9083-9 [20] Da Silva LFM, Dillard DA, Blackman BRK, Adams RD. Testing Adhesive Joints: Best Practices. 2012. https://dx.doi.org/10.1002/9783527647026 [21] Panettieri E, Fanteria D, Danzi F. A sensitivity study on cohesive elements parameters: Towards their effective use to predict delaminations in low-velocity impacts on composites. Comp Struct 2016;137:130-9. https://doi.org/10.1016/j.compstruct.2015.11.011 [22] Eichhorn F, Hahn O, Otto G, Stepanski H. Erarbeitung praktikabler Dimensionierungsrichtlinien für Metallklebverbindungen. 1st ed. Opladen: Westdeutscher Verlag GmbH; 1979. https://doi.org/10.1007/978-3-322-88438-1 [23] Rasche M, Syparek D. Ergebnisse mit Vorsicht behandeln. adh Kleb Dich 2015;59:2631. https://doi.org/10.1007/s35145-015-0585-3 [24] Otto G. Untersuchung der Spannungen, Verformungen und Beanspruchungsgrenzen von Kunststoffschicht und Fügeteil bei einschnittig überlappten Metallklebverbindungen. Dissertation, Aachen; 1978 [25] Sadeghi MZ, Zimmermann J, Gabener A, Schroeder KU. The applicability of J-integral approach in the determination of mixed-mode fracture energy in a ductile adhesive. Int J Adhes Adhes 2018;83:2-8. https://doi.org/10.1016/j.ijadhadh.2018.02.027 [26] Campilho RDSG, Banea MD, Neto JABP, da Silva LFM. Modelling of Single-Lap Joints Using Cohesive Zone Models: Effect of the Cohesive Parameters on the Output of the Simulations. J Adhesion 2012;88:513-33. https://doi.org/10.1080/00218464.2012.660834
S0143-7496(19)30240-4
DOI:
https://doi.org/10.1016/j.ijadhadh.2019.102491
Reference:
JAAD 102491
To appear in:
International Journal of Adhesion and Adhesives
Please cite this article as: Weiland J, Sadeghi MZ, Thomalla JV, Schiebahn A, Schroeder KU, Reisgen U, Analysis of back-face strain measurement for adhesively bonded single lap joints using Strain Gauge, Digital Image Correlation and Finite Element Method, International Journal of Adhesion and Adhesives, https://doi.org/10.1016/j.ijadhadh.2019.102491. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Elsevier Ltd. All rights reserved.
Analysis of back-face strain measurement for adhesively bonded single lap joints using Strain Gauge, Digital Image Correlation and Finite Element Method J. Weiland1*, M. Z. Sadeghi2, J. V. Thomalla1, A. Schiebahn1, K. U. Schroeder2, U. Reisgen1 1
ISF - Welding and Joining Institute, RWTH Aachen University, Pontstrasse 49, D-52062, Germany
2
SLA - Institute of Structural Mechanics and Lightweight Design, RWTH Aachen University, Wuellnerstrasse 7, D-52062 Aachen, Germany
ABSTRACT
Back-face strain measurement is a widely used method for damage detection of adhesively bonded single lap joints. Often, a simple Strain Gauge is used to monitor in-situ structural adhesives bonds in the field. However, the extrinsic local placement of the Strain Gauge on the strain hot spot of the joint poses a major challenge. Furthermore, finite element method (FEM) simulations do not reproduce the adherents accurately enough due to inaccuracies in the manufacturing process. Therefore, an additional optical measurement methodology is required to precisely analyze and localize the strain hot spots on the adherent. This work deals with the most important theoretical background on the stiffness, strength and fracture behaviour of the single lap joint. Subsequently, the back-face strain along the joint part was simulated by means of FEM. The results were validated and implemented with the results of the Digital Image Correlation (DIC). The strains in the hot spot area were determined from both finite element (FE) and DIC methods. With this knowledge, the Strain Gauge is applied exactly to the location of the strain hot spot. The central result of the paper is the confirmation of the strain hot spot. It is shown that the calculated points and curves can be approximated very well.
Keywords: damage detection, strain measurement, single lap joint, Digital Image Correlation (DIC), Strain Gauge, finite element analysis, A. epoxy/epoxides, B. steels, C. lap-shear, C. fracture mechanics
*
Corresponding author. J. Weiland. Email: [email protected]. Phone: +49 241 80 96275.
I.
INTRODUCTION
Today, adhesively bonded joints cannot be tested 100% non-destructively [1, 2]. This fact is the main motivation for the approach to monitor adhesively bonded joints in order to record the structural behaviour and thus ensure a safe load transmission. Two further complicating factors make it more difficult; on the one-hand are the inaccuracies in the manufacturing process and on the other hand a lack of knowledge in the field of fatigue behaviour and degradation process of the adhesive [3]. These uncertainties are taken into account when designing adhesive joints with high reduction factors and highly conservative safety factors. Through the use of permanent non-destructive structural health monitoring (SHM) methods, structural damages in the adhesive bond can be detected at an early stage. For that task, the back-face strain measurement method can be use. The method is based on an extrinsic sensor concept witch is placed on the back-face of the adherent to measure the strain of adhesively bonded joints. Abe and Satoh [4] start using the back-face strain measurement in the year 1986 to investigate crack formation and propagation in spot-welded joint adherent. Around 1995 several scientists applied the method to adhesively bonded joints and until today, many investigations have been carried out on it [4-14]. All these publications have the same motivation, to detect damage in the adhesive layer on a very efficient way. In order to be able to make predictions about the structural condition of the adhesive bond, the exact location of the strain gauge takes the most significance. For the simple single lap joint different sensor positions are conceivable. Zhang et al. [6] use a measuring point at the end of the overlap. As a result of a crack, the bend at this position increases. The measured longitudinal strains are reduced by the pressure component of the bend. Solana et al. [12] build on this idea. For structural damage monitoring, they concentrate on one measuring point in the area of the largest gradient of the characteristic longitudinal strain curve. Preisler et al. [14] uses the zero strain point in the area of the largest gradient of the longitudinal strain curve for structural damage monitoring. At this point tensile strain and compressive strain cancel each other out due to bending deformation. In the undamaged case there is no
longitudinal strain independent of the load. As soon as a crack occurs within the adhesive bond, the effective overlap length is reduced. As a consequence, the load transfer and the resulting strain distribution shift. Due to the high gradient in the range of compressive strains, there is a high absolute change in the strain here. Especially the use of the zero strain point offers a high potential. A deviation from zero can be directly assigned to a crack and correlates with the crack length. In addition, the generated FEM simulations often only represent an inadequate accuracy of the formation due to inaccuracies existing in manufacturing process [15-17]. Therefore, an additional optical measurement methodology is required to precisely analyze and localize the strain hot spots on the adherent.
1. Analytical background on the strength of adhesive joints For adhesively bonded joints, a differentiation can be made between adhesive failure and cohesive failure. A purely cohesive failure is assumed for the structural-mechanical analysis of adhesive joints. This internal adhesive strength is strongly related to the stress intensity factors and critical energy release rates for each of the three fracture modes I (traction), II (sliding) and III (tearing). These mechanical parameters determine the failure of the adhesive joint, however the actual fracture mechanism of an adhesive joint is very complex [18] and is usually a combination of mode I and mode II fracture mechanisms. Assuming the surface tension, equation (1) expresses the relationship between the critical energy release rate G1C, the stress intensity factor K1C, and the Young's modulus of the adhesive E for Mode I. 2
G1c =
K1c E
(1)
The above equation applies to brittle and medium-hard materials. It does not make sense for very ductile materials. For general flat stress conditions, equation (1) can be extended for
the case of a combined breaking load. In equation (2), G represents the shear modulus of the adhesive material. 2
Gc =
2
2
K1c K2c K3c + E + 2G E
(2)
The Double Cantilever Beam (DCB) test can be used to determine the energy release rate GIC for Mode I. The End Notched Flexure (ENF) test can be used to determine the energy release rate under Mode II. The Mixed Mode Bending (MMB) is to determine energy release rate at combination of Mode I + II. At most, by the literature, mode III could be considered equivalent to Mode II. [19-21]
2. Analytical background on the stiffness, strength and fracture behaviour of single lap joint The mechanical behaviour of single lap joints was already investigated in the early 1960s. [22] Eichhorn published dimensioning guidelines for metal adhesive bonding in 1979. [22] It is known from Rasche [23] and other publications [3, 24] that the mechanical behaviour is significantly influenced by adhesion of the adhesive to the test adherent, cohesion of the adhesive, ductility of the adhesive, stiffness of the test adherents, geometry of the test adherents and clamping of the test adherent. The main point of attention in the literature is the distribution of the stresses in the adhesive layer, which leads to the failure of the adhesive bonds at the overlapping ends. According to Habenicht [3] and Otto [24], the stress distribution is shown schematic in figure 1. In the case of overlap adhesive bondings, the adhesive is mainly exposed to shear stress (T1). Due to the eccentric application of force, the parts to be joined are deformed at the area of the two overlap ends. This results in a bending moment, which develops stress at the ends on lines of tension / peeling (σ). Additional shear stresses of the adhesive occur due to the adherent elongation (T2), this behaviour is also mainly at the overlap ends. Due to the multi-axial
superimposed stress state, simple overlap bonding fails at the edges of the adhesive layer. [3], [24]
Figure 1. Schematic stress distribution in the adhesive from SLJ according to Habenicht [3] and Otto [24] Due to the typical behaviour of the single lap joint, the joining part on the back-face also undergoes a very characteristic strain curve. This is shown in figure 2 based on Preisler et al. [14]. On one hand, the external force causes a positive change in length of the entire adherent. On the other hand, the eccentric force and the resulting bending moments cause the adherent to bend. This has the consequence for the part expansion on the back-face that there are areas in which compressive expansions exist and areas in which tensile expansions exist. The exact distribution of strain over the overlap length can be seen in figure 2 on the right. There are a few load steps which show the strain as long as there is no damage in the SLJ. The lines of different load steps meet in one point: The zero strain point.
Figure 2. Characteristic back-face strain curve of SLJ adherent, schematic strain curve overall (left) and in the overlap length range for different load cases (right) [14]
II.
MATERIALS AND METHODS
1. Samples Steel and aluminium Single Lap Joints (SLJ) are used for the tensile tests. The adhesive used is Araldite 2015-1 Huntsman Advanced Materials, Basle, Switzerland. The parts to be joined have the dimensions 120 x 25 x 3 mm³. They are joined by a 0.7 mm thick adhesive layer. The limitation to 25 mm, along the test piece, is achieved by PTFE strips to one of the joining parts. The adhesive layer has the dimensions 25 x 25 x 0.7 mm³. For illustration, all relevant dimensions are shown in figure 3.
75 mm
10 mm
25 mm
10 mm
75 mm
3 mm
adhesive layer 0.7 mm
PTFE strips
test specimen
Figure 3. Dimensions of the SLJ
The steel used is S700MC, an alloyed stainless steel. It achieves tensile strengths of ≥ 750 MPa. The aluminium EN AW-7075 T6 used is a high strength hot rolled alloy. It
achieves tensile strengths up to 545 MPa. The stress strain diagrams of the two materials
900
900
800
800
700
700
600
600
Stress [MPa]
Stress [MPa]
can be seen in figure 4.
500 400 300
500 400 300
200
200
100
100 0
0 0
0.05
0.1
0.15
0
Strain [%]
0.05
0.1
0.15
Strain [%]
Figure 4. Stress strain diagrams of S700MC (left) and EN AW-7075 T6 (right)
The adhesive Araldite 2015-1 is a two-component adhesive based on epoxy resin. Curing is carried out for 24 hours at room temperature and for a further 3 hours at 60 °C. The parts to be joined are cleaned for pre-treatment with isopropanol. An ultrasonic bath is available for this purpose. Aluminium samples are pre-treated with a laser. The CL20 laser system from Clean-Lasersysteme GmbH, Herzogenrath, Germany is used for the aluminium adherents with a power of 20 W and a wavelength of 1064 ± 4 nm. Steel samples are irradiated with corundum. The corundum blasting machine is used with a grain size of 150 µm to 210 µm and a pressure of 6 bar. A rough overview over the adherents can be taken in figure 5. There are the two kinds of adherent, steel and aluminium. The view is from the front. There is a number of 5 of each kind of adherents which are tested under tensile tests.
Figure 5. Two adherents steel (top) and aluminium (bottom) from the front with speckle pattern
The fracture behaviour is a cohesive and symmetric one as seen by the fracture pattern in figure 6 for steel and figure 7 for aluminium. It shows that the manufacturing process is suitable to produce samples for the tests.
Figure 6. SLJ with steel adherent
Figure 7. SLJ with aluminium adherent
2. Finite element modelling and parameter estimation In order to simulate the fracture behaviour of SLJ, FE model in Abaqus was developed using surface based-cohesive model approach. In this approach, cohesive connection between the adherents and the adhesive is modelled with a zero-thickness interface which its damage constitutive law is based on the Traction-separation Law (TSL). The constitutive damage response is assigned in the property of the contact interaction between the adherent and adhesive (contact to contact surface). This was successfully implemented for failure behaviour of adhesively bonded joints in a previous work [25]. Constitutive damage law follows TSL which is capable of simulating gradual degradation of the materials based on the simple correlation between the traction (T) and relative displacement (separation ). TSL can have different shapes and the simplest approach is a bilinear softening law.
To capture the most accurate stress-strain field, 3D-symmetry model was developed in Abaqus. Solid elements were used for both adherents and the adhesive layer. Very fine mesh (0.07 mm) were used in the bonded area. The static FE model was carried out under displacement control. The FE mesh and boundary conditions applied in the model is shown in figure 8.
Figure 8. 3D meshing in the FE model developed in the present study
As it was mentioned earlier, symmetry FE model for the SLJ model was developed to reduced the calculation time. The boundary conditions are shown in figure 9 (the symmetry boundary conditions are illustrated in purple).
Figure 9. Boundary conditions for the symmetry FE model
For the onset of damage initiation, the failure index of our single lap joint was computed using quadratic traction:
QUADS Criterion t t
t t
t t
1
(3)
linearized power criterion was considered as shown below:
(4)
Where GI, GII and GIII are the fracture energy values for Mode I, II ,and III respectively [26], while their corresponding subscript values, which are denoted by C, influence the accuracy
of experimental data from fracture tests under Modes I, II, and III. In the present work, the Cohesive Zone Model (CZM) properties used for modelling the adhesive is given in Table 1. The power law used was with power equal to 1.
Table 1: material properties of Araldite 2015 according to Campilho et al. [26] Property
Value
Young modulus (N/mm2)
1850
Poison’s ratio
0.33
Tensile failure strength (N/mm2)
21.63
Shear modulus (N/mm2)
695
Shear failure strength (N/mm2)
17.9
GI (N/mm)
0.47
GII = GIII (N/mm)
4.7
Value of power law parameter
1
3. Experiments and Measuring Equipment Tensile tests are recorded using the strain gauge and Digital Image Correlation (DIC) measurement methods. Both methods are used to investigate surface strain - especially in the zero-strain-point range. GOM Aramis Adjustable is used to acquire the images for the DIC. It is a two-camera-system, so that it can do 3D-analysis of the samples (see also figure 10). The evaluation of the sensor data is done with the help of the program GOM Aramis Professional.
Figure 10. Test assembly as original (left and right) and as a sketch (middle)
Evaluation of the data is done with the help of lines, points and polygons. Polygons are used for the evaluation of strains on an area. This area is staked out equivalent to the area of the strain gauges. Within this area the average strain in longitudinal direction is read out. A section (or line) is used to determine the strain of the positions along the adhesive layer. Along this line, Aramis places arbitrary points at which the strains are determined. Furthermore, the displacement of the adherent is determined with a line that extends over the entire adherent. In order to secure the introduction of force along the parts to be joined, compensation plates are attached to the test adherents. An Instron 5567 tensile testing machine is used for the tests. The set pull rate is 1 mm/min.
III.
RESULTS
1. Force-Displacement – FE and Experiment 12000
10000
Force [N]
8000
6000
4000
2000
0 0
0.05
0.1
0.15 0.2 0.25 Displacement [mm] FE - steel
0.3
0.35
0.4
Experiment - steel
Figure 11. Comparison between FE and experiment (steel adherents)
An example of the result of the steel test samples can be seen in figure 11, where the maximum force is 9123.2 N. The simulation predicts a maximum of 9671.72 N. The average force for the adherents is 9655.4 N. That is just below the maximum predicted by the simulation. The simulation describes a straight gradient up to approximately 0.12 mm. After that the stiffness is a bit higher and is constant to almost the maximum force. After reaching the maximum force with a displacement of 0.28 mm the failure begins and the joint then breaks. An almost linear stress strain curve is detected in the test. A concave tendency is discernible. The stiffness is a bit less than the one predicted by the simulation. The real adherent reaches its maximum at a displacement of 0.31 mm. Overall, the course of the experimental result lags slightly behind the simulation. This can be due to many influences.
On the one hand, settlement phenomena of machine and adherent are possible. Settlement can occur if the clamping on the machine is not tight enough. The adherent slips slightly, which leads to cyclic relaxation and consolidation within a small frame. This is reflected in the evaluation of the samples with DIC. This effect can also be seen in the not quite smooth curve of the experiment. On the other hand, it is possible that the adhesive does not exhibit the ideal stiffness due to exhibits in the simulation because of the inaccuracies in the manufacturing process.
10000 9000 8000
Force [N]
7000 6000 5000 4000 3000 2000 1000 0 0
0.05
0.1
0.15
FE - aluminium
0.2 0.25 0.3 Displacement [mm]
0.35
0.4
0.45
0.5
Experiment - aluminium
Figure 12. Comparison between FE and experiment (aluminium adherents)
For aluminium adherents the maximum force is 8725.8 N. This is just above the maximum of 8698.0 N predicted by the simulation. The average force of the aluminium adherents is 8223.0 N. In figure 12 is an example (with a maximum force of 8022.57 N) of the adherents shown. There is a linear evolution until nearly the maximum force. Then the adherent breaks and the curve does have a falling gradient. Overall, the joint follows the predicted curve very
well. In the simulation, the maximum force is reached with a displacement of 0.38 mm. The real sample reaches its maximum with a displacement of 0.36 mm. This can be due to the same influences as steel. The lower value is just because the maximum force isn’t that much as in the simulation.
2. Back-face strain curve over the adhesive bond As shown in figure 13, different results are obtained for tests and simulations. The strain along the x-axis of the joining part - i.e. along the longitudinal axis - is shown here. The back face strain is evaluated using DIC along a line on the surface. Aramis independently calculates relevant points and interpolates between them. Since only individual points are used for evaluation in this figure, the fluctuations of the measured values are very high. This could be a reason for the deviation between simulation and DIC. The simulation predicts an oscillating curve for the strain. Up to the zero strain point, the values are up to 0.08%. They then assume positive values and become negative again in the last piece. According to Preisler et al. [14], this point can be used to monitor the bond. This zero strain point remains constant at it’s value, almost x = 5,5 mm. In the case of steel, the zero strain point is almost x = 8.4 mm away from the PTFE strip, according to the simulation.
0.2
Technical strain [%]
0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 0
5
10 15 x-position along adhesive [mm] FE - 2000 N
FE - 5000 N
FE - 7000 N
Exp. - 2000 N
Exp. - 5000 N
Exp. - 7000 N
20
25
Figure 13. Typical strain over the adhesive along the x-position of itself (aluminium adherent)
3. Back-face strain at zero-strain-point Figure 14 shows the strains at the zero strain point measured using DIC, DMS and simulation as well as the force curve plotted over the displacement for a specimen with steel adherent. DIC and strain gauges are compared with the simulation as evaluation methods. The curve of the simulation describes an S-stroke, to justify this with the fact that in the simulation no complete failure of the bond is simulated. In addition, the FE results for the strains have been calculated as an average over the area of a strain gauge. Up to a displacement of 0.22 mm, the strain remains almost zero. At this point, a force of approx. 7500 N already acts on the adherent. The strain assumes negative values and asymptotically adapts to a strain of -0.04 % from a displacement of 0.35 mm. The strain gauge describes a similar behaviour, the strain gauge also remains close to zero up to a displacement of 0.22 mm. Subsequently, the strain drops slightly more flatly than the simulation. In order to use the values of the DIC with the values of the strain gauge, a
specific point at the exact strain hot spot was used for evaluation. This gives us an uneven, fluctuating and noisy course of the measurement results, since the natural oscillations caused by irregularities are not averaged by for example an polygon measurement. However, the tendency of the curve can be seen. After a displacement of 0.22 mm, the general tendency decreases until the joint breaks at a displacement of 0.31 mm. At this point, the strain measured by the DIC was -0.06 %. Therefore, the measured values of the DIC are also comparable with the values of the simulation and strain gauges. The actual measured values agree and give a representative statement and confirm the simulation
0.1
12000
0.05
10000
0
8000
-0.05
6000
-0.1
4000
-0.15
2000
-0.2
Force [N]
Technical strain [%]
result.
0 0
0.05
FE strain - steel
0.1
0.15 0.2 0.25 Displacement [mm]
DMS - steel
DIC - steel
0.3
0.35
FE force - steel
0.4
Force - steel
Figure 14. Typical strain and force over displacement of one of the test samples
Figure 15 shows the strain measured with DMS and simulation at the zero strain point and the force curve plotted over the displacement for a specimen with aluminium adherent. The
strain gauge is compared with the simulation as an evaluation method. The curve of the simulation describes an approximate S-stroke, which is simulated as a bend at failure. Especially at the beginning, the DMS values are even a bit higher than the ones of the simulation. The curves go apart from a displacement of approx. 0.22 mm, the simulation curve is released in order to drift in a positive direction. The strain gauge assumes a negative gradient at a force of approx. 4500 N. However, the curve of the strain gauge first drops into the negative. The simulation falls below zero at a force of approx. 7400 N. The force of the strain gauge is then reduced to the negative. Both of the curves share approximately the same gradient, so that, because they are gone apart, both are dropping in the negative with a nearly parallel behaviour. This can be observed in the range of approx. 0.3 mm to 0.4 mm. When the joint breaks, the strain gauge indicates a strain of approximately -0.09 %.The measured values of the strain gauge correspond relatively to those of the simulation in the essential areas and give a representative statement.
0.04
10000
0.02
9000
0
8000 7000
-0.04
6000
-0.06 5000 -0.08 4000
-0.1
3000
-0.12 -0.14
2000
-0.16
1000 0
-0.18 0
0.05
0.1
0.15
0.2 0.25 0.3 Displacement [mm]
0.35
0.4
FE strain - aluminium
DMS - aluminium
FE force - aluminium
Force - aluminium
0.45
0.5
Figure 15. Typical strain and force over displacement of one of the test samples
Force [N]
Technical strain [%]
-0.02
IV.
CONCLUSIONS
This paper describes the basic behaviour of single lap joint under load. The back face strain of the joining part is investigated. Due to the eccentric force effect, the bending moment and therefore the bending of the adherents occurs. This results in both positive and negative strain on the back of the adherent. This could be shown by the measured data from the simulation. The generated data of the Digital Image Correlation are consistent with the other measurement data besides from the fluctuations. Attention is drawn to this approach, as it can lead to large fluctuations when looking at individual points, as each of these points offers an increased error potential. If anomalies are present and are detected by some points, the results scatter strongly. Anomalies can be slight soiling or accumulation of paint in the speckle pattern. The comparison of DMS and DIC is only possible if the image correlation is applied accurately, otherwise the accuracy of the methods can vary greatly. The investigations on the zero strain point confirm Preisler et al. [14] statement that this point is suitable for monitoring the joint. To confirm this thesis, further investigations are necessary, especially with damaged adherents and under cyclic loading. Another point of reference for the monitoring of the joint is the consideration of the displacement in z direction. This observation should also be further investigated.
V.
ACKNOWLEDGEMENTS
The IGF-project IGF-Nr. 19909 N / 2, “SmartSHM – Effiziente Zustandsüberwachung struktureller Klebungen” of the research association “DECHEMA Gesellschaft für Chemische Technik und Biotechnologie e.V." is funded within the framework of the industrial collective research programme (IGF) by the Federal Ministry for Economic Affairs and Energy on the basis of a decision by the German Bundestag.
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