Investigation of the influence of design parameters onto the cracked lap shear specimen

The Cracked Lap Shear (CLS) specimen allows a mixed-mode loading condition to be generated without a special test fixture using a simple tensile test. The mixed-mode ratio generated is nearly constant over a wide range of crack growth and is representative of the loading conditions in many structural applications of bonded joints. However, this specimen is not standardised, leading to very dissimilar specimen designs in the literature. In this study, the primary design parameter is the sample width in terms of its application for adhesive characterisation, with a typical layup having a 0° layer in contact with the bond line. The results of quasi-static and fatigue tests using varying specimen widths between 5 mm and 40 mm emphasise the specimen width’s influence. Moreover, CLS specimens with the same layup but without an adhesive layer between the adherends are investigated to study the effects of width scaling without a toughened adhesive bond. While the static tests show a linear relationship between specimen width and joint strength, it is different in fatigue tests, where the crack growth rate increases with decreasing specimen width, both for specimens with and without adhesive bond between the joining partners.


Introduction
Adhesive bonds can exploit the lightweight potential of carbon-fibre-reinforced-plastics (CFRP) much better than riveted joints because of the two-dimensional force transmission [1,2].Thus, adhesive bonding technology is attracting attention as a joining technology for aircraft with CFRP fuselages.However, the design of such joints and their certification by the aviation authorities pose challenges.Specifications for bonded joints of primary structures in aviation are addressed in AMC 20-29 [3].According to [2], the only current option to meet the requirements of the aviation authorities is to limit the separation by special design elements, which are referred to as crack-stopper [2,4,5].The Cracked Lap Shear (CLS) specimen is often used in the investigation of such crack-stoppers.The CLS is characterised by a realistic loading of the bonded joint as shear and peel stresses are combined (mixedmode).The stress ratio (mixed-mode ratio, MMR) is almost constant for the CLS [2,5], which is an advantage of this specimen, especially for fatigue tests on crack propagation.Another advantage is that this mixed-mode condition is achieved by applying a tensile load without a special device.This is a particular advantage, as mixed-mode investigations with the Mixed-Mode-Bending (MMB) test system are always influenced by the own weight of the test fixture [6].In [6] the CLS is used for the analysis of fatigue crack growth in bonded joints and advantages in the investigation of crack-stopper elements are mentioned.Studies on different crack-stoppers have been carried out using CLS by [2,4,5].In [2] the adhesive damage behaviour with crack-stopp elements is simulated.Using the finite element method (FEM), whereby the simulated specimen width corresponded to the real specimens tested.In [2], the joining parts are modelled using the equivalent-single-layer approach, which significantly reduces the calculation time of such a FEM model.However, this modelling strategy leads to the fact that adherend damage can only be smeared and damage interaction cannot be represented at all.If these interactions are to be represented in the model, a layer-wise modelling approach is necessary, which, in addition to at least one element per fibre layer over the laminate thickness, also need to provide an element between each fibre layer for the representation of delamination [7].In order to keep the computation time of very fine meshed simulation models reasonable, a simulation model with only one element in width is quite common in the development of material models [8].This is acceptable because the strength of an adhesive bond scales proportionally by the width of the overlap area and the relatively larger proportion of the less load-bearing fringe area at smaller overlap widths does not affect the bond strength [9,10].Since these statements implicitly refer to the static strength for bonded joints with MMR=1 (shear stress only), this study will on the one hand experimentally verify the statements of [9,10] for the CLS specimen and corresponding bonded joints under load MMR≠1 and on the other hand extend them to the fatigue strength of the bonded joints.One objective is to determine the usefulness of test results from wider specimens for the validation of simulations with smaller simulated specimen widths.For this purpose, the CLS specimen is first presented in detail.This is followed by a description of the test scopes (test matrix) and the test fixtures used for this study, after which the results of the static tests and their interpretation are listed.Subsequently, the results of the fatigue investigation are presented.

Material and methods
The material used for the manufacturing of the CFRP panels is the unidirectional prepreg Hexply 8552-IM7(12K)-134-33 % from Hexcel [11].This is a material used in aerospace applications, which is also used in many scientific publications, therefore many material properties can be found in the literature [2,4,8,11,12].The film adhesive investigated is EA 9695 050NW AERO, also known as HYSOL EA 9695 .050PSF NW [13].This adhesive is characterised by high environmental resistance and is used, for example, in CFRP repair bonding.In addition, it is also found in some publications, which means that some material characteristics are available in the literature already [14].

Cracked Lap Shear (CLS) specimen
Figure 1 shows a detailed sketch of the CLS specimen on the left-hand side at the top a1), where the lap and strap parts can be seen with their multilayered structure, as well as the areas equipped with glass-fibre-reinforced plastic (GFRP) taps.In addition, the film adhesive layer is illustrated in yellow and the artificial crack of 15 mm length in blue.Below a2), the sketch shows the position for the crack length determination.Bottom a3) shows how the specimen deforms under tensile load, generating both shear stresses and peel stresses at the tip of the bonded joint.The ratio of these stress components is described by MMR, which is about 0.7 for the CLS specimen.This corresponds to a shear-dominant stress with about 30 % peel component [2, 4 -6].On the right hand side, figure 1 b) shows a photo of a CLS specimen with a width of 40 mm.

Test plan
To investigate the influence of the specimen width and to check to what extent the statements of [9,10] can also be applied to the fatigue behaviour of CFRP bonded joints under mixed-mode, CLS specimens are tested both in quasi-static and fatigue loading conditions.Specimen widths of 5, 10, 20 and 40 mm are considered.Additionally, CLS specimens without an adhesive layer are tested to investigate the specimen width's influence while excluding the influence of the bonding process quality.The layup for all CFRP parts is [0°, 45°, 90°, -45°]2s which hereafter is labelled as L1.The CLS specimen without an adhesive layer, which has one unified plate (UP) instead of two adherends and is being investigated for the delamination behaviour, is labelled L1-UP.In this configuration, both join partner are laminated together and cured in a single autoclave process to form the component.Specimens with an adhesive layer are produced using secondary bonding and, depending on the surface pre-treatment, are labelled L1-TF for resin-rich surfaces or L1-AG for peel-ply surfaces.Both configurations are treated with Scotch Brite +7447 before bonding.Due to a potential influence of the rotationally non-fixed clamping jaw during fatigue (see Chapter 3.2), specimens were tested both with and without a rotatable clamping jaw.

Specimen width [mm]
static fatigue

Test Set-up and Data Generation
The servo-hydraulic testing machine 8802 from Instron GmbH (Darmstadt, Germany) with a nominal force of 100 kN is used for the tests.It is equipped with hydraulic wedge jaw clamping.The lower clamping jaw is completely fixed and the upper one can rotate around the axis of the hydraulic cylinder.In addition, a Digital Image Correlation (DIC) system from Carl Zeiss GOM Metrology GmbH (Braunschweig, Germany) and an ultrasonic system from Hillger NDT GmbH (Braunschweig, Germany) are integrated into the test setup.Through ultrasound, it is possible to track the crack length and the contour of the crack front across the specimen width.In addition, the crack length at the specimen edges (see figure: 1 a2)) is measured using a magnifying glass (x20) with an integrated ruler (resolution 0.1 mm).In quasi-static testing, a displacement-controlled load is applied at 1 mm/min.The fatigue testing is performed with force-controlled loading at a load level of 425 N per mm of specimen width.This ensures the fatigue load's adjustment in such a manner that all specimen receives the same stress level during fatigue testing.The test frequency for all fatigue tests is 3 Hz.

Quasi-static test results
The following figure 3 a) shows the force-displacement curves of CLS specimen with and without an adhesive layer between the adherends at 4 different specimen widths.Considering the stiffness, it is noted that the stiffness of specimens without an adhesive layer is always slightly higher than the stiffness of specimens with an adhesive layer.The opposite applies for the strength, where the specimens with adhesive layer show a higher ultimate load.If the focus is on the displacement at failure, the specimens without adhesive layer show an almost constant displacement, which decreases minimally when the specimen's width is increased.Specimens with adhesive layer show an identical value of the displacement at failure for 5 mm and 10 mm widths, the 20 mm and 40 mm wide specimens are also almost identical to each other, but compared to narrower specimens they show an increase of about 20 %. Figure 3 b) shows a graph plotting failure load against specimen width, representing the arithmetic mean of the respective configuration.Each dashed line is a straight line connecting the measured values of 5 mm and 40 mm wide specimen.The straight lines illustrate that the proportional increase in failure load as a function of specimen width described in [9,10] also applies to mixed-mode loading.For further clarification the specimens' compliance is calculated as per the method presented in [2] within the range from 2 % to 10 % of the specimen-specific maximum measured force.Even though the calculation model is strongly simplified, the theoretical and measured values are in good agreement.The percentage error for the specimen widths considered is almost constant at an average of -15.8 %.The cause of the deviations in the theoretical compliance is most likely the neglect of the secondary bending of the CLS specimen.The modeling approach described by [2] simplifies the specimen into two cross-sections in series, thus disregarding the secondary bending that occurs in reality (see figure 1 a3)).Other reasons, however, cannot be ruled out.It is further noted that wider specimens facilitate the distinction between different strengths, as material properties are often area-dependent.A wider test area results in more significant differences in the measured values.

Fatigue test results
At first, the data of the configuration featuring adhesive layer and resin-rich surface (L1-TF) only is given, since both its scatter and amount of specimen are higher.Figure 4 on the left shows the crack length plotted against the load cycles.First, it can be noticed that the scatter for the 5 mm and 20 mm width specimens is comparatively small.Furthermore, the crack length increase is almost linear for all specimens from a crack length of about 20 mm onwards.Concerning the specimen width, however, a clear trend cannot be identified in terms of crack growth rate (slope of the curves), although the crack growth of the 5 mm wide specimens is significantly faster than that of the 40 mm wide specimens, the 10 mm wide specimens show both the second fastest and the slowest crack growth.The fracture surfaces shown in figure 4 on the right hand side indicate that the bonding process and/or surface pretreatment may have had an influence.The fracture surfaces of the 40 mm wide specimen and the neighbouring fracture surface of a 10 mm wide specimen are similar, also their crack growth behaviour.Both fracture surfaces show a decreasing number of fibres pulled out with increasing crack length, whereby the structure of the adherend surface is hardly recognisable.The fracture surface of the 10 mm wide specimen shown on the rightmost is different and the specimen had a substantially faster crack growth.Significantly fewer fibres are visible in the fracture surface of this specimen.The surface structure of the adherend is also widely recognisable.The latter can be interpreted as an indication of adhesion problems.In order to investigate the influence of the specimen width without the influence of the quality of the bonding process, the results of the fatigue tests on CLS specimens without adhesive layer are shown below.
The curves in figure 5 show the crack length over the load cycles in the same colour coding as the results for specimens with adhesive layer.In contrast to specimens with an adhesive layer, those without adhesive layer exhibit rather progressive crack growth instead of a linear increase in crack length.The majority of the specimens show significantly faster crack growth after 2000-3000 cycles than before.In this sample configuration, too, a clear tendency to crack growth in dependence of the specimen width cannot be found.However, the ultrasonic scans shown in figure 5 do have some conspicuous features: the contour of the crack front and thus the area on which the external load is transmitted between the joining partners is obviously differs between the 5 mm and the 40 mm wide specimen.While the crack front of the 5 mm specimen is almost a perfect semicircle, the crack front of the 40 mm specimen is a straight line perpendicular to the loading direction.The fringe area only shows a slight rounding, which matches the statements of [9,10].In addition, it is noticeable that the crack front of the 10 mm wide specimen shows a larger percentage of rounded fringe areas and a course that is not perpendicular to the direction of loading.The bearing condition of the clamping jaws might be the cause for the course that is not perpendicular to the direction of loading.As can be seen in figure 2 a), they are not rotationally fixed.Their hydraulic lines are onesidedly led next to the load frame and therefore subjected to pretensioning.It is assumed that the preloaded lines cause the clamping jaws to rotate during the fatigue process, which in turn induce the specimen to twist beside from the well desired tensile load.An undefined loading condition at the crack tip is the undesired outcome.Hence, a device was integrated into the testing machine to prevent the jaws from rotating.With this configuration of the testing machine, further tests were carried out (see Chapter 2.2).The repetition of the specimens L1-TF with 10 mm and 40 mm width with rotationally fixed jaws showed a highly comparable behaviour to the best performing (slowest crack growth) specimens without fixed jaws.These findings suggest that the that the specimens with significantly faster crack growth probably experienced an additional load due to the rotation of the clamping jaws, resulting in an increased crack growth rate.Graphic illustration to be found in figure 6 a) the diagram on the left.Figure 6 b) display the specimens with the lowest crack growth rate of each configuration.Triangles stand for the measuring points of a 5 mm wide specimen whereas squares represent those of 40mm wide specimens.The different colours stand for different configurations of the specimens, with red being the CLS specimens without adhesive layer (L1-UP), black those with adhesive layer and resin-rich surface (L1-TF) and blue with adhesive layer, too, but peel-ply surface configuration (L1-AG) and fixed clamping jaws.This illustration show a clear distinction between wide and narrow CLS specimens within a single configuration (colour).The wider samples always have a lower crack growth rate than the narrower specimen of the same configuration.

Discussion
The static results confirm the statements of [9,10] that the failure load of a bonded joint scales proportionally to the specimen respectively overlap width.Although the number of specimens within a configuration is very small, a linear relationship is visible (see figure 3 b)).For specimens without an adhesive layer, it is evident that the displacement at failure is unaffected by the specimen width.This does not apply for specimens with an adhesive layer.They show an elongation at failure of 0.5 % in relation to the free length of the specimen (200 mm) for specimens up to 10 mm width, and 0.625 % for specimens of 20 mm and 40 mm width, which is 25 % higher than the elongation at failure of narrower specimens.The cause for the varying elongation at failure could not be identified.
The fatigue test results demonstrate that even details such as the arrangement of hydraulic lines can be a disturbing factor in the tests.Regardless of whether the clamping jaws are rotationally fixed or not, a difference between very narrow (5 mm) and wider (40 mm) CLS specimens is noted in test results.This is probably due to the change in stress state from narrow with a plane stress state to wider specimens with a plane strain stress state.Ultrasonic scans on specimens without adhesive layer underpin this assumption.The scans evince a different contour of the crack front depending on the specimen width.For the validation of material models in the FEM, the use of different specimen widths between laboratory tests and simulation model is accordingly not recommended at the current state of knowledge.Nevertheless, further experiments are necessary for the statistical validation of the observations.Furthermore, numerical simulations and/or analytical analysis could help to identify the cause for the different crack growth rates.

Summary
The CLS specimens were tested under static and fatigue loading.Specimens with and without adhesive layer between the joining partners were tested in 4 different specimen widths.The statements of [9,10] regarding the proportionally scaling failure load of a bonded joint could be confirmed for mixed-mode loading with MMR of approx.0.7 [2, 4 -6] under quasi-static loading.The static results have also shown that the specimen width has an influence on the elongation at break for specimens with an adhesive layer.It is further observed that wider specimens facilitate the distinction between different configurations due to their increased measured values.
The fatigue tests show a possible influence of the bonding process on the results, although the surface pre-treatment was carried out with great care.Specimens of the same configuration (L1-TF-10mm) had very different crack growth rates.Even the specimens without an adhesive layer did not present a clear trend in terms of specimen width.However, corresponding ultrasound scans supported the assumption that, at least in some tests, an unintentional rotation of the jaws had occurred, resulting in an undefined loading condition during the test.Therefore, some tests were carried out with nonrotating clamping jaws.The results of the test series (L1-TF) showed that the 10 mm wide and the 40 mm wide test specimens behaved identically.In addition, another configuration (L1-AG) was tested with 5 mm and 40 mm wide specimens.These were also examined with rotation-fixed jaws and showed a significant difference between the crack growth rates, with the 5 mm wide specimens displaying significantly faster crack growth.The same trend presents itself when only the respective specimen of a configuration with the slowest crack growth is considered.This approach appears reasonable since specimens that showed faster crack growth were probably additionally twisted, thus favouring faster crack growth.Considering only the specimens with slower crack growth, the crack growth rate is higher for 5 mm wide specimen compared to 40 mm wide specimen, for specimen with and without an adhesive layer between the adherends, regardless of whether the jaws are rotationally fixed or not.Because of this, it can be deduced with regard to the use of different specimen widths between laboratory tests and numerical simulation that identical geometries should be considered.Therefore, in terms of time-efficient FEM models, the use of narrow specimens in the laboratory test is recommended.

Figure 1 :
Figure 1: a1) detailed sketch side view, a2) sketch unloaded side view, a3) sketch loaded CLS with stress at the crack tip, b) CLS photo with details of the clamping area and dimensions.

Figure 2 :
Figure 2: a) overview of the test set-up, b) detailed view of clamped CLS with DIC system and ultrasonic system.

Figure 3 :
Figure 3: a) Force-Displacement-Curves from quasi-static CLS with (black) and without (red) adhesive bond line, b) Failure Load-Sample-width diagram.

Figure 4 :
Figure 4: Crack length-load cycle diagram of CLS with adhesive bond line, corresponding crack surfaces.

Figure 5 :
Figure 5: Crack length load cycle diagram of CLS without adhesive bond line, corresponding ultrasonic scans.

Figure 6 :
Figure 6: a) Crack length load cycles diagram of CLS with and without rotational-fixed clamping jaws, b) 5 mm and 40 mm CLS of each configuration with the slowest measured crack growth rate with cycles shifted to the onset.

Table 2 :
Comparison of measured and calculated compliance between 2 % and 10 % of the maximum load.