Young Stress Analyst Competition

Transcription

1 Young Stress Analyst Competition International Conference on Advances in Experimental Mechanics: Integrating Simulation and Experimentation for Validation (ISEV) The Royal College of Physicians, University of Edinburgh, UK 2011

2 CONTENTS Young Stress Analyst Competition Finalists Identification of the heterogeneous elsto-plastic behaviour of FSW welds at high strain rates Guillaume Le Louëdec LMPF, Arts et Métiers ParisTech, Châlons en Champagne (France)... 1 Failure of sandwich beams with wrinkle defects subjected to static and fatigue loading Martin Leong Siemens Wind Power and Aalborg University (Denmark)... 7 Evaluation of the elastic constants of an orthotropic material in a single test Arnaud Limousin, University of Southampton (UK) Paint coating characterisation for thermoelastic stress analysis Daniel Mulvihill, University of Oxford (UK)... 18

3 Identification of the heterogeneous elastoplastic behaviour of FSW welds at high strain rates G. Le Louëdec 1,2, M.A. Sutton 1, F. Pierron 2 1 :Center for Mechanics, Material and NDE, University of South Carolina, Department of Mechanical Engineering, 300 Main Street, Columbia SC 29208, USA 2 :Laboratoire de Mécanique et Procédés de Fabrication, Arts et Métiers ParisTech, rue Saint Dominique, BP 508, Châlons en Champagne, France lelouede@cec.sc.edu fabrice.pierron@chalons.ensam.fr sutton@sc.edu 1 Introduction Since its invention in 1991, the friction Stir Welding (FSW) process has allowed the use of large aluminium structures in various fields due to the high resistance of the welds produced. In various fields such as automotive and aeronautics these welds hold an important place. However, the high strain-rate mechanical properties used in numerical simulations are still estimates. Indeed, experimental setups used for high-speed measurements such as the Split- Hopkinson Pressure Bar (SHPB) are not suitable for heterogeneous materials. The Virtual Fields Method was introduced by Grédiac [1] in order to solve inverse problems in the materials constitutive parameter identification from full-field measurements. It has already been successfully applied to the identification of constitutive parameters of heterogeneous materials in quasi-static experiments [2]. This work focuses on the identification of elastoplastic properties of AL5456 FSW welds at high strain rate. 2 Experiment and specimen FSW was performed on a AL mm thick plate specimen, at a rotational speed of 480 rpm and a welding speed of 3.4 mm/s. Transverse compressive specimens have been extracted by cutting across the weld. These are 41 mm long cylinders with a diameter of 12.7 mm. Flat surfaces have been machined on each side of the 1

4 specimen to allow the use of 2D digital image correlation [3]. As shown in Fig. 1, the area of interest is mostly focused on the retreating side of the weld. The SHPB experiment (Fig. 2) was performed to obtain a global maximum strain rate of 1500 s -1. The specimen was impacted on the nugget side. The camera used for the image recording is a DRS Imacon 200 (10 bit 1360x1024 array of square pixels) with a 200 mm Nikon lens at a speed of fps. It results in an area of interest of 25x10 mm². Figure 1: Test specimen, with field of view represented by the area containing the vertical lines where the elastic-plastic parameters are identified Figure 2: Diagram of the SHPB test 3 Post-processing Flat field correction is applied to the images, in order to reduce the noise between the different sensors of the camera that is caused by the technology of the camera (light amplifiers) [4]. Then images were processed using 2D-DIC using the software VIC-2D with a 55 pixels subset and a step of 20 pixels. From the displacement fields, VIC-2D was used to calculate strain fields using a least square quadratic fit to each set of 5x5 measurement points. Due to the complex evolution of the displacement fields throughout the weld zone, gradients determined by extrapolation 2

5 beyond the data field were not used in this study. Acceleration is calculated by time derivation of the displacement field. Both strain fields and acceleration fields are smoothed using an iterative leastsquare smoothing convolution (Savitzky-Gray) method [5] with a 2nd order polynomial over a moving window containing 7 data points (Fig.3-4). Figure 3: Evolution of the smoothed longitudinal strain field over time Figure 4: Evolution of the smoothed longitudinal acceleration field (in m.s -2 ) over time 3.1 The virtual fields method The virtual fields method [1] makes use of the principle of virtual work. Due to the non-linearity of the stress-strain relationship in plasticity, the stress field is written as a non-linear function of the strain field which is dependent on the mechanical parameters to identify. To solve this problem a cost function dependent on the unknown parameters is built up and minimized [6]. Here special virtual fields are used in order to nullify the contribution of the load. Thus only the strain fields and acceleration fields are needed to proceed with the identification. This is a very recent and innovative approach that was already validated in [7] but in elasticity only. This is the first time that such a procedure is applied in elasto-plasticity, and even more challenging, in heterogeneous elasto-plasticity. It should be noted also that though the system to identify is non-linear, there is no need to iterate direct finite element solutions, leading to a very 3

6 computationally efficient solution compared to finite element model updating. 4 Results It has been shown by Sutton and al. [2] that the elastic properties remain constant through the weld. Thus the identification of Young s modulus and Poisson s ratio is performed on the whole specimen in the early stage (2 first images) of the experiment. Results are shown in Table 1. While the identification of the Poisson s ratio is within the expected range, the identified Young s modulus is much lower than expected. This could be explained by the fact that this method makes use of the acceleration. The 2 nd order derivation of the displacement fields used to calculate the acceleration tends to increase the noise significantly, whose contribution is already important in elastic area; while a loss of information results from the smoothing. On the other hand, Poisson s ratio is independent from the acceleration field and only results from the information gathered from the strain field. Reference Identified E (MPa) ν Table 1: Elastic parameters identified by the VFM Figure 5: Identification of the yield stress through the weld The model used for hardening is a simple linear hardening model. The identification is carried out on slices of the specimen, independently from each other (Fig. 1). The results concerning the yield stress are presented in Figure 3. It is interesting to notice that the area with the lowest yield stress is the beginning of the heat- 4

7 affected zone on the retreating side of the specimen, and not the nugget. The identification of the hardening coefficient proved to be very sensitive to noise, thus, so far, accurate identification of it has not been successful. 5 Conclusion In this work, the identification of high-speed mechanical properties of a FSW aluminium weld was investigated. The noise of the displacement field measurement remains a major problem, especially when it comes to the identification of elastic parameters, which explain the error on the identification of the Young s modulus. Nevertheless, it allows a more steady identification when it comes to plastic parameters. Moreover, this method does not make use of the load which measurement remains a major issue in dynamic. Further experiments will be needed to ascertain these results. And the continuous improvement of high-speed camera technology will support the development of this area of research. References [1] M. Grédiac, F. Pierron, S. Avril, E. Toussaint, The virtual fields method for extracting constitutive parameters from full-field measurements : a review, Strain, 42: (2006). [2] M.A. Sutton, J. Yan, S. Avril, F. Pierron, S.M. Adeeb, Identification of heterogeneous constitutive parameters in a welded specimen: uniform stress and virtual fields methods for material property estimation, Exp. Mech. 48: (2008). [3] M.A. Sutton, J. Orteu, H.W. Schreier: Image Correlation for Shape, Motion and Deformation Measurements, Springer, New-York (2009). [4] F. Pierron, M.A. Sutton, V. Tiwari, Ultra high-speed DIC and virtual fields method analysis of a three point ending impact test on an aluminium bar, Exp. Mech. 51: (2010). [5] P.A. Gorry, General least-squares smoothing and differentiation by the convolution (Savitzky-Golay) method, Anal. Chem. 62: (1990). [6] M. Grédiac, F. Pierron, Applying the virtual fields method to the identification of elasto-plastic constitutive parameters, Int. J. Plast. 22: (2006). 5

8 [7] R. Moulart, F. Pierron, S.R. Hallett, M.R. Wisnom, Full-field strain measurement and identification of composites moduli at high strain rate with the virtual fields method, Exp. Mech. 51: (2011). 6

9 FAILURE OF SANDWICH BEAMS WITH WRINKLE DEFECTS SUBJECTED TO STATIC AND FATIGUE LOADING Martin Leong Siemens Wind Power A/S, Denmark and Department of Mechanical and Manufacturing Engineering, Aalborg University, Denmark Introduction Wind turbine blades are sensitive to manufacturing defects, as the blades are designed for both extreme loads and for long fatigue life (>10^8 cycles). A severe type of manufacturing defect is out-of-plane fiber misalignments, or wrinkle defects (Fig. 1), which are commonly found in large composite structures. Figure 1: Full thickness wrinkle in GFRP sandwich face sheet. The objectives of the present research include; 1) characterization of failure mechanisms in composite sandwich beams with wrinkle defects subjected to static loading, 2) identification of a suitable failure criterion, 3) implementation of failure criterion in a numerical model and experimental validation, and 4) investigation of fatigue failure. Investigation of failure mechanisms under static loads Sandwich plates with glass/epoxy composite face sheets and a balsa wood core were manufactured with an artificial wrinkle defect and cut into smaller specimens (Fig. 2), which were then tested to failure when subjected to tension or compression loading. 7

10 Figure 2: Test specimen and wrinkle geometry. The specimens were monitored with strain gauges and Digital Image Correlation (DIC). Due to the inherent variability of the manufacturing of the wrinkles, the height and width of the wrinkles varied between specimens. Generally, specimens with high height to width aspect ratio failed at lower loads than those with low aspect ratio wrinkles. Post mortem inspections with Scanning Electron Microscopy (SEM) revealed that for compressive loading the fracture consisted of layer-wise delaminations through the specimen thickness; Fig. 3 b). Figure 3: a) DIC strain map of out-of-plane normal strain, normalized wrt. to the far field strain. b) Postmortem SEM image at 16 X magnification. 8

11 Selection of failure criterion Several failure criteria capable of predicting interlaminar/delamination failure were considered including the Tsai-Wu, Puck, LaRC and Northwestern University (NU) failure criteria [1]-[3]. The requirements for the selected failure criterion include; 1) it should not require advanced testing to establish material fitting parameters, 2) it should be computationally inexpensive to enable use as a design tool, 3) the formulation should be based on physical argumentation. Finally the NU interfiber/interlaminar failure criterion [3] was chosen. To validate the applicability of the NU criterion for the glass/epoxy composite system, specimens were subjected to comprehensive testing to characterize the failure behavior under combined transverse normal and shear loading. By analyzing the recorded stress-strain curves a method for defining a failure initiation strength was proposed [4]. The comparison between test results and theoretical predictions showed that while the NU criterion performed similar to classical failure theories like Tsai-Wu for the present material system, it was possible to predict the initiation of failure with reasonable accuracy; Fig. 4. Figure 4: Failure envelopes of selected failure criteria, compared to damage initiation strengths from experimental data. Application of NU failure criterion A finite element (FE) model of the sandwich specimens was developed assuming geometrical and material linearity, and the NU criterion was implemented. The FE model was validated by comparing the predicted strain maps with strain maps recorded using DIC (Fig. 3 a)). Prediction of the location of failure initiation using FE together with the NU criterion was in good agreement with the experimental findings as shown in Fig. 5 a) and Fig. 3 b). By plotting the local strain at the predicted failure location vs. the applied stress, it was seen that failure initiation was predicted at the level of applied stress where the stress-strain response started to show non-linear behavior; Fig. 5 b) [5]. 9

12 Figure 5: a) NU failure index and predicted failure location, b) predicted failure initiation. Studies by Vallons et al. [6] have shown that non-crimp fabric composites will display infinite fatigue life when loaded below this failure initiation point, which can then be regarded as an apparent fatigue endurance limit. Fatigue failure Specimens were subjected to tension/compression fatigue loading with a stress ratio R=-1. The minimum endurance limit for all specimens was predicted as proposed, and all fatigue tests were run with equal and constant load amplitude. The tests were stopped after 2*10^6 cycles and the specimens inspected for damage. Preliminary results suggest a correlation between the predicted endurance limit (varies with wrinkle geometry) and the amount of damage inflicted. Thus, specimens with predicted endurance limits close to the applied load failed before 2*10^6 cycles or showed massive damage, while specimens with endurance limits higher than the applied load showed little or no damage after the test; Fig. 6. Figure 6: Selected specimens with high to low endurance limits after 2*10^6 cycles. Summary and conclusions Wrinkle defects represent a significant challenge for wind turbine blade producers, as they can have a catastrophic influence on both static- and fatigue strength. In this research a methodology based on the NU failure criterion has been proposed and partially 10

13 validated to assess if a given wrinkle defect will be critical depending on its size and the loading it is subjected to. References [1] Hinton, M.J., Kaddour, A.S., Soden, P.D., A comparison of the predictive capabilities of current failure theories for composite laminates, judged against experimental evidence, Composites Science and Technology, Vol 62, (2002) [2] Pinho, S.T., Dávila, C.G., Camanho, P.P., Iannucci, L., Robinson, P. Failure models and criteria for FRP under in-plane or three-dimensional stress states including shear non-linearity. NASA Technical Memorandum, TM (2005). [3] Daniel, I.M., Luo, J., Schubel, P.M, Werner, B.T., Interfiber/interlaminar failure of composites under multi-axial states of stress, Composites Science and Technology, Vol 69, (2008). [4] Leong, M., Overgaard, L.C.T., Thomsen O.T., Lund, E, Daniel, I.M. Interlaminar/interfiber failure of unidirectional GFRP used for wind turbine blades. Submitted. [5] Leong, M., Overgaard, L.C.T., Thomsen O.T., Lund, E, Daniel I.M. Investigation of failure mechanisms in GFRP sandwich structures with face sheet wrinkle defects used for wind turbine blades. Under review. [6] Katleen Vallons, Stepan V. Lomov, Ignaas Verpoest, Fatigue and post-fatigue behaviour of carbon/epoxy non-crimp fabric composites, Composites: Part A, Vol 40, (2009) 11

14 Evaluation of the elastic constants of a orthotropic material in a single test by Arnaud Limousin under the supervision of Professor Dulieu-Barton 1. Introduction This paper deals with the identification of the elastic properties of an orthotropic material. The shape of the specimen is a T subjected to a complex state of stress. An analytical solution is not available so an identification procedure is used. This procedure relies on the virtual fields method (VFM) on the condition that the whole strain field is obtained. To achieve this, two optical methods are used, the Grid Method (GM) and Digital Image Correlation (DIC). To determine the four unknown stiffness, the assumptions for the method are as follows: Small strains, Plane stress and strain (classical lamination theory), Linear elastic orthotropic behaviour of the material. The in-plane law for an orthotropic material can be written as follows in the orthotropic axes (see Figure 1) { } [ ] { } (1) Figure 1: orthotropic axes The four stiffness could be identified using standard tests, e.g. a tensile test parallel and perpendicular to the fibres and a shear test. Here the idea is to propose a test specimen that will enable the measurement of all the in-plane stiffness components in just one test. To achieve this, an identification procedure is used. The method relies on the principle of virtual work. This principle is expressed as follows: (2) where : is the volume of the system considered, is the stress tensor, the virtual strain field, the external loads, the virtual displacement field associated to, is the boundary of the system. 12

15 Equation 2 describes the equilibrium of the structure and works for any specimen shape and loading condition. 2. Specimen geometry The geometry proposed is a T-shaped specimen submitted to a tension/bending loading, as shown in Figure 2. The idea is that in the horizontal part, are expected to be mainly involved. In the vertical part, transverse and Poisson s effect will most influence the response of the specimen so that are the main parameters involved. Equation (2) is written with suitable virtual fields to obtain a system of four linear equations. As there are four unknowns stiffness to find, four virtual fields have to be chosen. Figure 2: Four virtual fields from [3] The specimen configuration allows all the stiffness to be derived, provided that the whole strain fields are available. To achieve this, two techniques are used. Both techniques use a CCD camera to captured images before and after deformation. In DIC, a speckle pattern is tracked to obtain deformations. In the Grid Method, the displacement and strain information are carried by the light intensity reflected by a grid attached to the specimen. The phase of the light from both images is computed to obtain the displacement. To obtain the strain field, the displacements are differentiated. 13

16 3. Experimental setup 3.1. Specimen preparation The specimen is water jet cut form a prepreg unidirectional carbon epoxy panel. For the GM, the grid is bonded using white epoxy adhesive, which provides the contrast between the black lines of the grid. For the DIC, the specimen preparation is quite simple. A white and black paint is sprayed over the surface of the specimen to enhance contrast. The paint adheres to the surface and deforms with the specimen Setup The optical setup consists of a CCD camera fixed to a tripod. A suitable L.E.D light provides the intensity over the specimen and no heat comes from it. A tensile testing machine is used. This machine is equipped with a special fixture. This fixture has two cylindrical rods, where the horizontal part of the specimen is located. These two cylinders are not free to rotate. An aligning pin is added to align the specimen with the load direction. For the rest of the test, the aligning pin is removed. Finally, the top part of the specimen is clamped and subjected to a vertical displacement. Tensile grips T-shaped specimen Aligning pin Cylindrical rod Rig Figure 3: the T-shaped specimen in place for a test 14

17 4. Displacement measurement The first step, before loading and image recording the camera system and magnification are adjusted to obtain the minimum possible number of moire fringes. These fringes represent the specimen cross grid. For the second step, a preload of 50N is applied. Two sets of still image are taken to evaluate the performances of the test. From these two images, the displacements and strains are computed. After performing this typical procedure, the load is gradually increased to 1.5 kn with a speed of 2mm/min. 5. Experimental results This section presents the results using a standard tensile test using strips of the carbon epoxy material used to make the T specimen. The results are presented in Table 1. Spc Strain gauge DIC GM VFM E y [GPa] Ave ± ± ± E x [GPa] Ave 9.07 ± ± ± ν xy Ave 0.34 ± ± ± Table 1: Experimental results 15

18 6. Measured displacement and strain fields A FE model was developed using the 2-D four-nodded linear plane element PLANE42. The three measured strain fields are obtained by finite differentiation. These three strain fields are smoothed by using a Gaussian smoothing. Figure 4 and 5 shows the contours of the experimental strains are very much like those from finite elements. The VFM technique was applied to the strains derived from the FE model. Table 1 shows that the elastic constant derived from the VFM applied to the T specimen strains provided values that are very close to those provided by the standard test but in this case only one test is necessary. Figure 4: ε XX contours in strain GM on the right - FE model on the left Figure 5: ε S contours in strain GM on the right - FE model on the left 16

19 7. Conclusion The work has shown that it is possible to obtain accurate elastic constants using the VFM by using a specially designed test. It should be noted that the test was very challenging for the VFM as the material is unidirectional as the strains in one direction are much smaller than the other. In the future, the next step is to apply the VFM by using the strain field obtained by the GM and DIC. References 1. S. Avril and F. Pierron, General framework for the identification of constitutive parameters from full-field measurements in linear elasticity, International Journal of Solids and Structures, vol. 44, (2007) 2. M. Daniel and O. Ishai, Engineering Mechanics of Composite Materials, (1994) 3. M. Grediac and F. Pierron, A T-shaped specimen for the direct characterization of orthotropic materials, International Journal for Numerical Methods in Engineering, vol. 41, (1998) 4. M. Grediac, Importance of full-field measurement techniques for better models in solid mechanics, pages (2004) 5. M. Grediac, The use of full field measurement methods in composite material characterization - interest and limitations, Composites Part A: Applied Science and Manufacturing, 35 (7-8): (2004) 17

20 Observations on the frictional behaviour of interfaces undergoing reciprocating sliding Daniel M. Mulvihill Department of Engineering Science, University of Oxford Introduction Reciprocating sliding can be a common occurrence in frictional joints which form part of dynamic structures. The coefficient of friction and the tangential contact stiffness of such interfaces are important parameters in characterising joint behaviour: as the energy dissipated in frictional damping, and the overall stiffness of the structure will be dependent on them. Presently, models of the vibration response of jointed structures are not sufficiently accurate due to a failure to correctly model the interface properties such as friction and contact stiffness. This work aims at developing a better understanding of each of these parameters in reciprocating sliding. First, a commonly observed phenomenon whereby the friction force varies (usually increases) during the sliding phase of individual fretting cycles is investigated, and, second, some combined modelling and experimental work is performed which is aimed at developing an improved physical understanding of tangential contact stiffness in real fretting interfaces. Results and Discussion The phenomenon of increasing friction during sliding (or hook effect) is contrary to the Amontons/Coulomb model of friction which predicts a constant friction force as sliding proceeds (Fig. 1a). An in-line fretting test (Figs. 1b and 1c) involving an abrupt increase in amplitude during the test was used to show that the effect is a result of wear-scar interaction effects. The material used for the test was the nickel alloy Udimet 720 and the normal pressure was 70 MPa. Microslip (a) Gross slip/sliding δ app (a) (b) Tangential force 2Q (b) (a) (b) Commonly observed friction response Coulomb friction Load cell response Q Specimen Hydraulic Minimum friction force piston Maximum Hydraulic friction force actuator Friction variation range Fretting pads Cast iron block δ (Pad & specimen thickness = 10mm) Normal force P Pad Q R 8 Q 10 Q Q 8 12 Normal force P Hydraulic piston Load cell Specimen 2δ app Hydraulic actuator Fretting pads Cast iron block (Pad & specime thickness = 10m Normal force P Pad R 2δ slip 19 Base Specimen Base K t 2δ actual Fig. 1: (a) Schematic hysteresis loops (b) Pad-specimen geometry (c) Testing machine The result of this test is shown in Fig. 2. No increase in friction is observed for cycle N=10, whereas, a distinct increase in observed in cycle N=400. This suggests that the friction variation is caused by wear-scar interactions rather than a velocity effect. Further, the loop recorded eight cycles after the increase in amplitude (N=400+8, shown in red) shows an increase in friction force only up to the position where the old wear-scar would have ended followed by a drop off in friction force as new unworn surface is encountered. After a further five cycles (N=400+13), this transient feature has disapeared and a conventional hook feature develops. These results point strongly towards wear-scar interaction effects as the cause of the friction variation. 18

21 Q/P E Linear displacement δ (mm) a N=10, 2δ=1 app =1 mm mm N=400, 2δ=1 app =1 mm mm N=400+8, (during ramp up up period) N=400+13, 2δ=1.6 app =1.6 mm mm Fig. 2: Frictional hysteresis loops derived from the in-line fretting test. A pair of rotational fretting tests where results from a continuous ring type contact (with no wearscar ends) could be compared to a segmented ring type contact (with wear-scar ends) were then carried out to determine whether these interaction effects originate from interaction of the wear-scar ends, or whether such interaction occurs throughout the nominal contact area at local peaks and troughs. A new experimental rig designed to adapt conventional in-line test machines for rotational fretting was designed and built for this purpose. The pads and specimens for this test are shown in Fig. 3a, while Fig. 3b shows a schamatic of the test rig. The test pressure was 30 MPa and the material was again Udimet 720. b c (a) (b) Fig. 3: (a) Rotational fretting pads and specimens (b) Schematic of rotational fretting rig Results (Fig. 4) show that the friction variation occurs whether or not wear-scar ends are present. (a) N = N = q a /p a 0 q a /p a Segmented Ring Segmented Ring -0.8 Continuous Ring -0.8 Continuous Ring -1-1 Angular displacement δ θ (Degrees) Angular Displacement δ θ (Degrees) Fig. 4: Hysteresis loops from rotational fretting test: (a) cycles , (b) cycles (b) 19

22 Cross-Correlation Function (CCF) The presence of the friction variation even when macroscopic wear-scar ends are absent suggests that the wear-scar interaction is occuring at local peaks and troughs. After testing, the worn surface topography of each fretting pair was scanned using a focus variation microscope, and these surface images (Fig. 5a) revealed the existence (and size) of many such local peaks and troughs distributed throughout the contact area. A cross/auto correlation analysis of the continuous ring wear-scars was also carried out to obtain more quantitative information. The cross-correlation result for the continuous ring wear-scar pair of Fig 5a is shown in Fig 5b. This shows that the wear-scars are highly correlated for an interval of angles corresponding to the test configuration and are uncorrelated outside this region. The correlation angle allows an estimate for the dominant feature size to be obtained. This feature size was found to be similar in size, (though somewhat larger for higher pressures) to the applied fretting stroke angle of Fig. 5b also shows the crosscorrelation function for the pre-test ground surface which shows no correlating features. (a) (b) Cross-correlation angle = 18.5º (predicts a feature size of 9.25 ) Worn Pad and pad specimen and specimen surfaces wear scar pair Unworn ground ground surfaces pad and specimen surfaces Relative angular position Δθ (Degrees) Fig. 5: (a) Post-test wear-scar topography (b) Cross correlation function In addition, a simple one degree-of-freedom model involving an idealised surface peak interacting with surface grooves of varying steepness was developed to allow a physical explanation for how local wear-scar features interact to produce the type of friction behaviour observed. Indeed, hysteresis loops from the model show similar friction variation behaviour during sliding as is often measured experimentally. To investigate the tangential contact stiffness of interfaces undergoing fretting wear, Digital Image Correlation (DIC) measurments were compared to finite element (FE) model predictions. The setup of the FE model of the pad-specimen experiment is outlined in Fig. 6a for nominal contact areas of 20, 40, 60 and 80 mm 2. Fig. 6b compares tangential contact stiffness measurments derived from the elastic FE model (80 mm 2 contact area with homogenious bulk properties of Ti-6Al-4V) to experimental DIC results. It can be seen that the FE results were significantly stiffer than the experimental result. This indicates that the interface behaves as a compliant layer where the extra compliance probably results from issues such as wear debris, oxide layers and surface roughness. Another FE model, this time incorporating a compliant elastic interface layer (Fig. 6a), was then tuned (via the elastic properties of the layer) to match the experimental result (Fig. 6c). It was found that for a 100 μm layer, a youngs modulus of 2.29 GPa was required. Thus, under fretting wear 20

23 conditions, the interface behaves like a 100 microns thick layer of polystyrene. This model together with experimental data was used to show that the tangential contact stiffness of fretting interfaces in likely to be proportional to nominal contact area (Fig. 6d). This linearity results from the high compliance of the interface in relation to the substrate. (a) (b) (c) (d) Fig. 6: (a) Model setup and FE mesh geometry (b) comparison of DIC and FE tangential contact stiffness results (c) FE model tuned to represent experimental results (d) tangential contact stiffness versus nominal contact area for both DIC and FE (tuned). Conclusion In conclusion, the friction variation (hook effect) commonly observed in gross slip fretting tests in the literature arises predominantly from the interaction of local wear-scar features distributed over the nominal contact region. The tangential contact stiffness of real fretting interfaces is much less stiff than the substrate material would predict due to factors such as wear debris. This high compliance of the interface leads to a linear dependency of tangential contact stiffness upon nominal contact area. These findings have important implications for researchers attempting to develop models of dynamic structures involving frictional joints. 21