2. PARTICIPANTS

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1 COLLABORATIVE STUDY WITH 4PB DEVICES IN EUROPE ROUND ROBIN TEST WITH THREE REFERENCE BEAMS FINAL REPORT A.C. Pronk ABSTRACT Determination of the stiffness modulus and fatigue characteristics of a bituminous mix are important factors in pavement design. In the European standards the Four Point Bending test (4PB) is one of the devices permitted for the determination of these properties. The procedures for the back calculation of stiffness modulus and strain from the measured force and deflection are well established. However, large differences exist between several 4PB devices used in Europe. In particular the ways in which the requirements for the boundary conditions are met differ a lot. Moreover no real reference beams were available for checking and calibrating the devices. After the 1 st 4PB Workshop an initiative was started for a collaborative study between thirty participants. The target of the study is to standardize the existing devices with respect to the determination of the stiffness modulus. Three aluminum beams were prepared with different bending beam moments. By changing the height and width of the beams it is possible to simulate asphalt beams with a normal cross section and a stiffness modulus ranging from around 3 GPa to 12 GPa. In this paper the results are discussed 1. INTRODUCTION The introduction of the CEN standards for asphalt mixes and the change to more functional requirements like stiffness modulus and fatigue characteristics have increased the use of several measuring devices, not only in Europe but also world-wide. One of these measuring devices is the (cyclic) four point bending (4PB) test which was already in use in some countries for the determination of stiffness modulus and fatigue life. At the moment the CEN standards for the determination of these two mix characteristics with a 4PB device have to be applied. All the existing 4PB devices meet the requirements in the CEN standard but the results obtained with different 4PB devices may differ a lot. Apparently some aspects are still missing in the standards. At the first European 4PB workshop in Delft an initiative was launched to start a collaborative project for the harmonization of the different 4PB devices at use in Europe with reference beams. This project is aiming results obtained with different 4PB devices will be nearly the same. It should be noted that the project is not aiming at the requirements for asphalt mixes as mentioned in the CEN standards but purely at the desired good functioning of a 4PB device. To achieve this goal, three aluminum reference beams (Tooling plate SALPLAN 5000 ) were made at the Delft University of Technology with a known Young s modulus of 71.3 GPa and a Poisson s ratio of The three beams were shaped in such a way that they simulate asphalt beams with a stiffness modulus of around 3, 6 and 12 GPa, respectively. The reference beams were sent around to each participant with the request to test the reference beams according to a certain protocol. The processed data used by the participant for back calculation were sent to Delft and were used as input for the Excel program Bending & Shear. With this program the exact analytical solution can be obtained including mass inertia effects, overhanging beam ends and the effect of the shear forces on the deflection. The program Bending & Shear is validated and verified with 3D calculations using the program ABAQUS. 2. PARTICIPANTS The interest for this project at the 1 st 4PB workshop in Delft was already big and very soon a number of 30 participating institutes were reached. Afterwards more institutes 1

2 wanted to participate but from a logistic point of a view 30 participants was already too much. During the project one participant hooked off, another participant encountered too much problems and had to hook off also and even one institute brook down. The original target was to finish the whole project within one and a half year with a complete paper for the 2 nd workshop. However, at this moment (2012) not all the results of the remaining participants can be reported. It was agreed that the confidential basic results were sent to the project leader. After discussion the participant decided if these basic results (after a possible correction) can be published. The institutes participating in this project are given in table 1. During the trip of the reference beams through Europe it looks that somebody has put a spell on this project. Several times a participating institute had to pass because the 4PB device was out of order or an own big project was running and the tests couldn t be performed in short term. Table 1. Participating Institutes Institute City Country University of Coimbra Coimbra Portugal University of Minho Guimares Portugal CONSULPAV Casais da Serra Portugal LNEC Lisboa Portugal Vienna University of Technology Vienna Austria The Highway Institute, A.C. Belgrade Serbia University of Belgrade Fact. of Civ. Eng. Belgrade Serbia Wroclaw Univ. of Techn. Inst. Civ. Eng. Wroclaw Poland TPA Instytut Badan Technicznych Pruszkow Poland Centr. Lab. BUDIMEX-DROMEX S.A. Pruszków Poland IBDiM Warsaw Poland Epitem KHT Budapest Hungary TU Braunschweig, Inst. Highway Eng. Braunschweig Germany Dr- Ing Löffler Baustoffprüfung Hannover Germany EMPA Dubendorf Switzerland Elletipi - Material Testing Laboratory Ferrara Italy CST Colas Magny les Hameaux France Shell Global Solutions Petit Couronne France University of Liverpool Liverpool England University of Nottingham Nottingham England Cooper Research Technology ltd Derbyshire England Ooms Nederland Holding Scharwoude The Netherlands Heijmans Rosmalen The Netherlands Asfalt Kennis Centrum Bv Venlo The Netherlands KOAC-NPC Apeldoorn The Netherlands Ballast Nedam Materiaalkunde Nieuwegein The Netherlands BAM Utrecht The Netherlands ZAG Zavod za gradbenistvo Slovenije Ljubljana Slovenia Delft Univ. of Techn. Delft The Netherlands 3. 4PB DEVICES 3.1 General A short description is given of the main devices which are used throughout Europe. There are at least 5 commercial types (Zwick, Cox, Cooper, Freundel and IPC) and 2 home build devices. The description is divided into four paragraphs: General - Calibration concept Data collection Shear deflection correction. 2

3 Next to the differences in the bending beam frames, clamping systems and measures to ensure the required translation and rotation freedoms at the supports, differences in processing and interpreting the raw data are present. One other item is the actuator. Most of the 4PB configurations are equipped with a hydraulic actuator but some configurations are equipped with a pneumatic actuator. The last one limits the frequency range to around 10 Hz. With these configurations it is not possible to meet the requirements in the CEN norm with respect to the required frequency of 30 Hz for fatigue testing. Also the installation of the sensors for measuring the deflection and the load can vary from one configuration to the other. The deflection can be measured with respect to a moveless reference (absolute) or with respect to reference supports which are placed on certain points at the beam (relative). In some devices the reference points are chosen as the two outer supports. In this way the measured deflection should not be influenced by the finite stiffness of the whole bending frame. There is also a difference in the location for the deflection sensor. Instead of placing the sensor peg at the centre of the top or bottom surface of the beam a small nut is then placed at the centre of a side surface ( neutral line ). At last a few sentences are given about the differences introduced by differences in moving masses. For high frequencies it is necessary to correct for mass inertia forces. Normally this is done in the post processing by weighing all the moving masses between the load cell and the beam. In some devices this correction procedure is replaced by a direct correction of the measured force using measured accelerations. A correction for moving masses is not needed in case of (mainly pneumatic) actuators if the frequency of the actuator is limited to 10 Hz. 3.2 Zwick device General The main differences between the Zwick device (figure 3.2.1) and the other ones are: Instead of bearings or rotating rods in the Zwick device elastic hinges are used, which do not have the disadvantages of bearings (e.g. friction, backlash and abrasion). Instead of correcting in the back calculation process for extra moving masses and the mass of the beam this is solved in the Zwick device by measuring the acceleration. The measured force is real-time corrected for these forces. The (practical) advantage is that the determined phase lag between the corrected force and the deflection can be taken equal to the material phase lag. And this leads to a simplification of the interpretation formulas. The mass compensation adjustment is done with a steel reference beam of known weight and Young's modulus. If the density (mass) of the asphalt beam differs much from the reference beam, this difference can be compensated either in the test by changing the mass compensation factor accordingly or by applying the difference of the mass in the back calculation process. A load frame stiffness compensation. Because the stiffness of the frame is not infinite the measured deflection is corrected depending on the mass-compensated force. This is also done in real-time. The loss modulus and the storage modulus are determined directly from the digitized deflection and force data using a Discrete Fourier Transform (DFT) over 5 cycles. This is possible because the inertia forces are incorporated in the measured force. No correction procedure is used for a possible permanent deformation during the data capture which might occur at high temperatures and low frequencies. But this phenomenon is not likely 3

4 to occur in the controlled deflection mode if the deflection is measured in an absolute way (with respect to the moveless frame). Force controlled tests can be carried out with a minimal alteration to the supplied test sequences. In this case the true force (mass compensated load) can be used, and the mean value of deflection can be kept stable. The clamping forces for the device are factoryadjusted to N, but can be adjusted by ZwickService to other (higher) values if required Calibration concept The load and deflection measurement chains are calibrated (statically back traceable) to national standards (German, DKD). Next, the stiffness of the load frame is determined in a 4PB test with a solid steel beam which is much stiffer than the 4PB frame. The stiffness compensation factor is stored in the controller. Finally, the mass compensation factor and system phase lag is determined in a 4PB test with a steel reference beam (elastic phase lag 0 and stiffness is independent on the load frequency) by linearization of the frequency response. The mass compensation factor is stored in the controller. A phase compensation table is used to correct the determined system phase lags. The steel reference beam is also used regularly to verify the 4PB device and the complete measurement chain Data collection Independent on the frequency (range 0.1 to 50 Hz) always 5 sinusoidal cycles are captured. However the number of data points per cycle differs per frequency (151 data points at 0.1 Hz to 200 data points at 50 Hz) Special attention is given to the parallel data sampling for the deflection, force and acceleration. Afterwards each device is calibrated with the aid of a steel reference beam (elastic phase lag 0) and adjusted if necessary Shear deflection correction At the moment no correction for the deflection due to shear is implemented in the software (because it is not mentioned and thus not required in the CEN standards). Figure Zwick device 4

5 3.3 Cooper device General Like the Cox device and the new IPC device, the required horizontal translation freedom at the supports is obtained in the Cooper device (figure 3.3.1) through roll bearings. In the back calculation procedure the inertia forces, due to the weight of the beam, the two inner clamps and the moving masses between load cell and inner clamps, are taken into account. The back calculation is based on the formulas of the CEN standard. No correction is applied for the non-infinite frame stiffness. The default clamping forces are 200 or 300 N. A regression analysis is used for the digitized data of the measured force and deflection signals. No correction procedure is used for a possible permanent deformation during the data capture which might occur at high temperatures and low frequencies. But this phenomenon is not likely to occur in the controlled deflection mode if the deflection is measured in an absolute way (with respect to the moveless frame). A force controlled bending mode is possible. The stiffness modulus and phase lag are back calculated using the formulas in the CEN standard. Figure PB device made by Cooper Calibration concept No information on a calibration protocol was available at the time of writing Data collection The number of data points is 200 per cycle independent on the frequency. Below 100 cycles each cycle is captured, between 100 and 1000 cycles each 100 th cycle is captured and above 1000 cycles each 1000 th cycle is captured. A sequential data sampling is used. 5

6 Therefore a correction procedure has to be applied in the software based on measurements (frequency sweep) with an aluminum beam (expected phase lag is nil) Shear deflection correction At the moment no correction for the deflection due to shear is incorporated in the software (because it is not mentioned and thus not required in the CEN standards). 3.4 IPC Global device General There are two versions of the servo-pneumatic IPC Global 4PB device currently in use. The first generation (Fig 3.4.1) was developed primarily for the US and Australian market based on AASHTO TP8/T321. In 2006 the current device (Fig 3.4.2) was developed. The main difference between the first generation and the current device is that the current device has translation and rotation on all load and reaction points whereas the first device did not provide any obvious translation of the inner load and reaction points. In reality, the translation between the inner load and reaction points is so small that it would be accommodated by the mechanical play in the bearings. The first generation device was predominantly sold as a stand alone servo-pneumatic machine. In 2011 the current device was upgraded for handling beams with a height and width from 50mm to 70mm and an effective length from 300mm to 420mm. In the European standards EN /26 frequencies above 10 Hz are required for testing the beams. For this reason, servo-hydraulic 4PB devices (stand-alone and a jig designed to be incorporated as an accessory into the UTM25/100 servo-hydraulic loading frames) are also available. The loading capacity in the early hydraulic powered stand alone device was 10kN, but the recently released IPC Global EN Standards Tester provides greater flexibility by allowing the application of dynamic loads up to 13.5kN and frequencies ranging from 0.01 up to 60 Hz. Fig First generation device with pivot system. Fig Current device with cross roller slides The Control and Data Acquisition System (CDAS) and associated software have similarly evolved over the past 20 years: initially a 12 bit CDAS operating under DOS and more recently IMACS with the equivalent of a 20 bit acquisition system running IPC 6

7 Global s UTS Windows software. All in all there are 4 versions of software in the field; UTM2 (DOS) Test F021, UTM4 (Windows) Test 21, UTS (Windows) Test 015 and UTS (Windows) Test 018. The first three are based on US/Australian standards and the last one based on EN /26. Within Europe the common version is UTS018 of which the processing of the data is based on the EN Standards /26 (taking into account the influence of moving masses). In addition, each data point captured is the average of four acquisition samples instead of a single point. So, the captured data is in principle the average of four data points with one period time lag between them. Instead of a Fourier decomposition a refined least square regression method is applied in the UTS Test 018 for the determination of the amplitudes and phase lag. The data for the force and deflection are (according to IPC Global) taken simultaneously. In all cases, the clamping force obtained through servo motors is around 700 N which can be changed by altering the motor current limit (by replacing resistor(s) in the servo motor control board). Instead of measuring the absolute deflection a bridge is used of which the supports are resting on the beam itself. These supports are placed half way between the inner and outer supports (they span 2/3 the distance between the two outer supports). According to IPC Global, by measuring (and controlling) the deflection of the beam with respect to the beam itself, errors due to the compliance of the device and the specimen clamps are eliminated Calibration concept No standard calibration procedure is in place for the 4PB as a system. Of course, similar to the others devices the load cells and other sensors are regularly calibrated but no reference beams with known stiffness are used for calibration. However, reference beams with known stiffness are used as an in-house check. The load cell is calibrated using static loading Data collection In the past, the application software used to run the first generation of 4PB used a 1 khz sampling rate with the following restrictions: for a loading frequency below 1 Hz a maximum of 1000 samples were collected and transferred every 10 th test cycle. For frequencies above 1 Hz the product of data points per cycle times the frequency equals 1000 (e.g. a loading frequency of 5 indicates 200 data points per cycle). The current generation control and data acquisition system, IMACS, is able to capture using 4X over sampling when using the UTS018 test software (i.e. 4 times 200 = 800 data points per cycle). Afterwards 200 mean data point values per cycle are processed. The maximum sampling rate for UTS015 is also 1 khz. For frequencies under 1 Hz, 199 data points are collected every cycle. Between 1 and 2 Hz, a maximum of 99 data points are collected but now for each 2 nd test cycle. Between 2 and 5 Hz a maximum of 99 data points are transferred every 5 th test cycle. And above 5 Hz only 99 data points every 10 th test cycle are captured. A sampling rate of 5 khz is used in the UTS018 configuration. This application is therefore also suited for higher frequencies. At a loading frequency of 60 Hz the number of data points per cycle is 39, Alternatively a special algorithm for determining the number of data points collected per cycle can be used. A servo-hydraulic machine will be required to achieve frequencies above ~20 Hz. UTM2 Test F021, UTM4 Test 21 and UTS015 applications use only raw data to determine the amplitudes. Only UTS018 has the option for a fitting algorithm mentioned above. 7

8 3.4.4 Shear deflection correction Only in the processing of the data obtained with UTM2 Test F021, UTM4 Test 21 and UTS Test 015 a shear deflection correction is applied. Two values are reported: 1) modulus of elasticity which is corrected for shear deflection and 2) flexural stiffness (ignoring the shear deflection). However, a value of 2/3 = 0.67 is applied as a shear correction coefficient k. According to the latest developments the shear deflection correction factor is understood to be approximately Considering shear deflection is not applied in the EN standards, UTS018 calculates only the flexural stiffness. 3.5 DVS/KOAC-NPC & University of Vienna General The DVS (former DWW) 4PB configuration is used in The Netherlands already for a long time (figure 3.5.1) and still in use at some consultants (KOAC-NPC). The concept (configuration) is later on copied and modified by the University of Vienna (figure 3.5.2). The main difference with the other devices is the way in which the horizontal translation and rotational freedoms at the four supports are provided. The two required freedoms are combined into one. It consists of thin steel sheets around the beam with a groove. The supports below and above the beam are also provided with a thin sheet with a groove. A small cylindrical spindle lies in the two grooves (figure 3.5.2) of which the radius is larger than the radius of the spindle. As shown by finite element calculations at the first European 4PB workshop this configuration will introduce a small unwanted moment (reference). The main difference between the DVS device in Vienna and those used in The Netherlands is the fastening of the thin sheets to the beam. In Vienna the sheets are glued to the beam while in The Netherlands a thin layer of bitumen is used (figure 3.5.1). In itself it is a good device for meeting the required translation and rotation freedoms. However, during rotation and translation of the beam, a small unwanted moment is introduced (figure 3.5.3). Clamping is very essential in these two concepts. By good luck trying an optimal torque moment was found of 3 Nm for the Vienna device. For the KOAC-NPC device a torque of 2 Nm is applied. Both in the DVS/KOAC-NPC device as well in the Vienna device the deflection is measured in an absolute way. In the data processing the mass of the beam and other mass inertia forces are taken into account according to the CEN standard Calibration concept At the University of Vienna a calibration procedure is carried out on a quarterly year basis using an aluminum reference beam. The procedure consists of a frequency sweep from 0.1 to 40 Hz and applying 0.1 Hz at the end again with two strain amplitudes (50 & 100 m/m). Between those calibration tests a DELRIN beam is used for routine checking. The DVS devices at KOAC-NPC are regular calibrated with an aluminum reference beam. Also the load cells and LVDT s are at least checked on a yearly basis Data collection For the device at the University of Vienna the number of data points per cycle depends on the frequency. Normally this is around 50 data points per cycle. Also the number of cycles per capture depends on the frequency. For a frequency of 0.1 Hz only 2 cycles are captured during the measure window and at 30 Hz this number is 10 cycles. The 8

9 determination of the force amplitude and the deflection amplitude is performed by a simple regression algorithm in which only a possible (constant) offset is taken into account. In contrast with the IPC processing the data are not averaged before the regression. There is a possibility to check the purity of the signal by plotting the force as a function of the deflection. The data acquisition for the device at KOAC-NPC is a bit different. The window for controlling the bending process depends on the frequency (300 cycles at 30 Hz and 25 cycles at 0.1 Hz). During the opening of this window 4 cycles are captured for the processing of the data. Independent of the frequency 66 data points per cycle are measured, leading to 264 data points for the determination of the force, deflection and phase lag. The determination is performed with a fast Fourier transform. It is not known if a correction is carried out for a change in offset during these 4 cycles. The data for force and deflection are taken sequentially which leads to a small time lag. This is corrected in the electronic software. A frequency sweep using an aluminum beam leads to a phase lag range of 0 o to 0.2 o. Figure DVS 4PB configuration at KOAC-NPC. Note the bitumen between the help clamps and the beam and the spindles above and below the help clamps. Grooves at both sides the beam Figure Modified DVS 4PB configuration at the University of Vienna (left) and the clamping of the sheets around a beam (right). 9

10 3.5.3 Shear deflection correction At the moment no correction for the deflection due to shear is incorporated in the software used by consultants (because it is not mentioned and thus not required in the CEN standards). Only in research projects at the Delft University of Technology a correction on the deflection is applied. EXAMPLES, 4PB EXAMPLES, 4PB February 20, February 20, Figure Introduction of an unwanted moment during translation (left) and rotation (right) of the beam in the DVS 4PB device 3.6 University of Coimbra General Like the DVS device the 4PB device at the University of Coimbra is a self made design (figure 3.6.1). The way in which the requirements for the translation and rotation freedoms at the supports are fulfilled is very similar to the one used in the DVS device. Instead of clamping frames with a separate rotation axis, rollers (bearings) are used between the beam and the supports. In the Coimbra device the radius of the roller is 0.5 mm bigger than the radius of the groove in which the roller moves. Also a lubricant is used to minimize friction. In the DVS device the radius of the roller is 5 mm and the radius of the groove is 15 mm. In case of horizontal translation a small (undesirable) moment is introduced in this last solution. Another difference is the clamping itself. This is achieved by pneumatic actuators with a constant force. In the DVS device springs have been used. Like in the other devices a PID process control with a feed-forward speed loop is used.. Figure PB device at the University of Coimbra 10

11 Although the device is driven by a hydraulic actuator the frequency is limited from 0.1 to 10 Hz. The deflections are measured in an absolute way. A big research advantage is the horizontal freedom of the support. The length between the two outer supports can be varied between 270 and 450 mm and the distance between the two inner supports from 110 to 150 mm. The maximum widths and heights for the beams are 90 and 80 mm. The back calculation formulas are based on the formulas for the pseudo-static case. In view of the limited frequency range no corrections have to be applied for the influences of moving masses Calibration concept The load cell response is controlled every three month using a calibrated load cell. The LVDTs are also controlled every three months using a calibrate measurement device, using the manufacturer calibration table as a reference. A general check up of the monitoring and acquisition system is made every year by a hardware supplier, using a general check up reference for this kind of systems. However, a calibration using a reference beam in order to check the output (stiffness modulus and phase lag) is not yet in the procedure. Only a beam made of PVC is used regularly to check if anything has changed Data collection A total of 32 channels can be read sequentially with a 8 ms time lag ( s) leading to an interval of ms between two readings. The sample frequency is 500 Hz. Therefore the interval between two captures is 2 ms. In view of the interval of ms the sample frequency could even be 3800 Hz. At the moment the highest test frequency is 10 Hz which means a period time of 100 ms. Therefore at the highest sample frequency 50 data captures (readings) per cycle are obtained. A first order recursive filter is applied to minimize noise in the signal. In the postprocessing a Fast Fourier Transform is applied to determine the amplitudes and phase difference between force and deflection. In contrast with most other institutes the University of Coimbra compares the amplitudes of the analog signals and those obtained by Fourier Transform ( purity check on the signals). For a frequency of 10 Hz the step frequency is Hz at a sample frequency of 100 Hz (see figure 3.6.2). Figure Fast Fourier Transform (frequency spectrum) of the measured deflection for an applied load signal at 10 Hz. 11

12 3.6.4 Shear deflection correction At the moment no correction for the deflection due to shear is incorporated in the software (because it is not mentioned and thus not required in the CEN standards). 3.7 Cox device General Only one version of the 4PB Cox device is made (figure 3.7.1). The device is mainly sold in Canada and the USA. Only a few devices are operational in Europe. As many of the other devices the horizontal translation freedom at the supports in the 4PB Cox device is established with ball bearings. Separate bending frames in which the beams are clamped by servo motors ensure the required rotation freedom at the supports. Although the two inner supports are connected to each other they can move independently of each other. There is a stop at the end of the frame to avoid that the beam can slide away. An absolute deflection with respect to the moveless main frame is measured using a bridge resting on the outer reference supports. The deflection sensor measures the deflection in the centre of the beam. Because the Cox device is normally used for low frequencies ( < 10 Hz) no corrections are needed nor applied for the influence of mass inertia forces on the bending. Figure Cox device Calibration concept An aluminum beam is used for the calibration of the phase lag. If the phase lag for this elastic beam is not equal to nil, the value can be adjusted electronically Data collection The deflection and force signal are captured at the same time. The sample frequency rate is 1 or 2 khz and 100 data points per cycle are captured, regardless the applied load frequency. For each cycle the amplitudes and phase lag are determined. Instead of a regression method a (Fast) Fourier Transform is used. This feature creates the possibility for a check on the purity of the sinusoidal signal but this is only carried out in the adjustment phase of a test. 12

13 3.7.4 Shear deflection correction At the moment no correction for the deflection due to shear is implemented in the software (because it is not mentioned and thus not required in the CEN standards). 3.8 Baustoff-Prüfsysteme Wennigsen device General This device is one of the few devices for testing beams with different dimensions with respect to height, length and width. Also the length between the two inner supports can be varied as shown in table Table Possible variations with the Wenningsen 4PB device Test Beam [mm] width height length Clamps [mm] inner-inner clamp distance outer-outer clamp distance inner-outer clamp distance 95 Stimulus load 0 ±12 kn frequency 0 60 Hz deflection 0...± Hz 0 ± Hz A hydraulic actuator allows to perform the tests in force controlled mode and in deflection controlled mode up to a frequency of 60 Hz. As in other new devices the required rotation freedom is obtained through clamping frames (figure 3.8.1) which can rotate freely. To have the test beam always fixed symmetrical to the neutral axis, the distances of the track rolls inside the clamping frame (ring, see detail in figure 3.8.1) are controlled with motors, separately for the top and the bottom support. The required horizontal translation freedom is assured by support rolls. This system is comparable with the ones used in the device at the University of Vienna. Separate grinded and hardened metal plates are glued on the test beam. The test beam is clamped by support rolls for a free horizontal motion in X-direction. Grinded and hardened metal plates are glued on the test beam to prevent any indentation of these rolls and to enable the free horizontal motion with load. The default clamping force is 150 to 250 N. The applied force is measured with a transducer located between the hydraulic actuator and the 4PB testing equipment. The inertia forces of the moving masses of the support rings and the piston rods are compensated inside the machine with the aid of an acceleration transducer. In this way no correction for mass inertia forces is needed in the back calculation procedure. The absolute deflection is measured, not with one sensor in the centre but with two extra sensors which are placed symmetrically around the centre. Based on the deflection profile for pure bending of a beam a mean value for the centre deflection is calculated (equation 3.8.1). According to the manufacturer this procedure avoids a possible necessary correction due to the non-infinite 13

14 frame stiffness (leading to an extra vertical translation motion of the beam during loading). This concept is an extension of the relative deflection measurement used in other devices. The factor K depends on the distance L, the distance A between the outer and inner support and the location x 1 of the sensor on the beam. The back calculation of stiffness modulus and phase lag is performed with the formulas given by the CEN standards EN and EN The inertia forces due to the mass of the beam and the mass of the metal plates fixed to the beam are taken into account. Deflections: W{x },W{x } & W{x } W{x 1} W{x 3} with x2 L / 2 and x3 L x1 W real{l / 2} K W{x 2} Figure Baustoff-Prüfsysteme Wennigsen device Calibration concept No information on a calibration protocol was available at the time of writing Data collection The measured force and deflection signals are simultaneously sampled with a frequency of 2400 Hz. Above a frequency of 30 Hz all sampled data are recorded, e.g. the number of data points per cycle for an applied frequency of 50 Hz is 48 (50*48=2400). For frequencies lower than 30 Hz the recorded data for processing (interpretation) is reduced to at least 80 points per cycle. 14

15 3.8.4 Shear deflection correction At the moment no correction for the deflection due to shear is implemented in the software (because it is not mentioned and thus not required in the CEN standards). 3.9 ISBS device General The ISBS device is a home made device with a hydraulic actuator capable for cyclic loads up to 50 kn with a maximum frequency of 30 Hz. Like some other devices beams of various sizes can be tested (from 40*40*240 up to 100*100*600 mm 3 ). The mid span length can be varied from 80 to 200 mm. Rotation freedom at the supports is assured by bearings and the required horizontal freedom at the outer supports is allowed by sliding bearings. As in the case of the older IPC device (figure 3.4.1) no sliding bearings are present at the inner supports. The bottom part of the load frame is made of stainless steel (figure 3.9.1) but the upper part is made of aluminum. The lower stiffness of the upper part makes it necessarily to correct for the non-infinite stiffness of the whole load frame in relation with the stiffness of the beam. The beam is clamped into closed steel frames by adjusting screws while the vertical force in the test device is controlled to avoid the introduction of clamping bending loads. In the future a protocol will be made using a torque wrench. The deflection is measured absolutely in the centre of the beam at the bottom with a LVDT ( 5 mm) with respect to the moveless lower part of the frame. The load is measured with a load that is placed outside the climate chamber. The total mass of moving parts between the load cell and the beam is 12.5 kg. The PID values for the control circuit are defined manually. Figure ISBS 4PB device 15

16 3.9.2 Calibration concept Three aluminum beams are used for the calibration of the device. The total measured deflection is the summation of a deflection due to the non-infinite stiffness of the upper part of the load frame, the deflection due to bending and the deflection due to shear. In the present calibration protocol the shear deflection is ignored. The response of the device is modeled as the response of two serial springs. The first spring represents the stiffness of the load frame and the second the stiffness of the beam. For a perfect 4PB device the value for the first spring ought to be infinite. Knowing the stiffness of the reference beam (and thus a good estimate for the second spring) the value for the first spring (representing the load frame) can be established. Afterwards measured deflections are corrected for this influence. These problems can be avoided by a relative measure in which a deflection is measured with respect to supports which are resting on the beam Data collection The deflection and force signal are not captured at the same time which introduces a certain time lag (phase lag) between the force and deflection. This phase lag depends on the applied frequency. For an elastic specimen the phase lag increased from 3 o at 1 Hz up to 20 o at 20 Hz. Using these results a correction protocol is defined for the measured phase lags. The present maximum sampling frequency of 500 Hz is rather low for frequencies above 10 Hz (20 data per cycle). At one hand controlling the test (pure constant sine wave shape) is troublesome and at the other hand the determination of amplitude and phase lag by regression fitting is not so accurate. Per cycle a regression is performed using the Excel Solver option on the measured data in that cycle Shear deflection correction At the moment no correction for the deflection due to shear is implemented in the software (because it is not mentioned and thus not required in the CEN standards). 4. REFERENCE BEAMS 4.1 General The ideal material for reference beams would be a material with the same range of possible stiffness modulus (2-20 GPa) and with the same density as an asphalt mix (around 2300 kg/m 3 ). In that case the beams can have the same shape as asphalt beams. Such a material could be Acetal. Acetal (POM) is a crystalline thermoplastic polymer which is strong and rigid and which has an excellent dimensional stability, a low coefficient of friction, a good abrasion and impact resistance, and a low moisture absorption. There are two groups within the Acetal resins: Homopolymers and Copolymers. Depending on the manufacturing process and additives a range of stiffness modulus from 3 to 9 GPa can be covered. However, the stiffness modulus of these materials can vary from batch to batch and only a mean value can be given by the producer. Also the stiffness modulus depends slightly on the temperature and frequency. Therefore this material is not suited as a real reference material. Nevertheless, the material is very well suitable for a round robin test. Two other materials are steel and aluminum. The stiffness modulus for steel is around 210 GPa. This implies a large reduction in the dimensions of the reference beam in order to get the same bending stiffness (EI) as for the asphalt beams. The stiffness modulus of aluminum is around 71 GPa and the required reductions of the dimensions can be less. Therefore the reference beams are made of aluminum. 16

17 4.2 Material The reference beams were cut from casted aluminum plates (Tooling plate Salplan 5000 ; thickness 25, 30 and 35 mm). The material is based on an alloy of ALMg 4,5 Mn (3.3547; 5083; H112). After casting a special heat process is applied. Finally the plates are milled on both sides and sealed with a coating. The flatness tolerance is 0.15 mm/m. Therefore, no further milling has to be applied for the reference beams. Other advantages are the high homogeneity, free of stress and shape stability. The stiffness modulus is close to 71.3 GPa, the Poisson s ratio 0.33 and the density is 2660 kg/m 3,which is close to the density of asphalt mixes. 4.3 Dimensions of reference beams The relevant parameter in the back calculation of the 4PB measurements is the product of the stiffness modulus E and the moment I = BH 3 /12 of the beam. In most cases the height of the asphalt beams is 50 mm. The width may vary from 50 to 63 mm. Due to the restriction in the CEN standards that the minimal values for the width and the height of the beam should be at least three times the maximum grain size in the asphalt mix, 4PB tests with larger values for the height and width will occur. The stiffness modulus for asphalt varies with the temperature and frequency. A common range is from 6 GPA to 12 GPa. These values are 12 to 6 times lower than the stiffness modulus of the chosen aluminum alloy. To get the same EI values the product of BH 3 /12 has to be scaled down with a factor of 6 to 12. Several values for H and B are possible. Taking into account the weight of an asphalt beam two equations for H and B can be obtained. However, in view of the thicknesses of the aluminum tooling plates, the following dimensions were chosen: Width B = 34 mm and Height H = mm. Given the variations in 4PB devices the length L was taken as 450 mm. For these values the product EI for the three beams is given in table 4.1. Table 4.1 The bending stiffness EI of the three reference beams Beam B x H [mm 2 ] E [GPa] EI [GNm 2 ] I 34 x II 34 x III 34 x Taking three values for the asphalt stiffness modulus, table 4.2 gives the bending stiffness for beams with 1) a width of 50 mm and a height of 50 mm and 2) a width of 63 mm and a height of 50 mm. Thus, with respect to bending stiffness the three chosen dimensions of the reference beams cover a reasonable range of bending stiffness of asphalt beams. Table 4.2 Range of bending stiffness for two types of asphalt beams. Asphalt Beam Smix [GPa] EI [GNm 2 ] Asphalt Beam Smix [GPa] EI [GNm 2 ] 50 x x x x x x As mentioned before the weight of the beams is also important. The weights of the three reference beams are respectively kg. The weights for asphalt beams are given in table

18 Table 4.3 Weights [kg] for several asphalt beams with a height of 50 mm using a representative density value of 2300 kg/m3. Length [mm] Width = 50 mm Width = 63 mm Accessories Due to the smaller width and the different height of the reference beams, accessories have to be used in the clamp devices at the supports of the several 4PB devices. The chosen shape is given in figure 4.1. Most devices are capable to handle beams with a width of 63 mm and a height of 50 mm. In order to avoid a stiffening of the reference beam at the support a U shape with a height of 45 mm was chosen, with a little top filling-in piece for the clamping of the beam. The accessories are made of stainless steel (density of 7800 kg/m3). For the length of the U shape (long the beam) and the other accessories a value of 10 mm is taken which is the common length for beam clamping. The effect of the length of the clamping device on the bending profile is not yet investigated. For beams II & III filling-in accessories at the bottom are needed to ensure that the neutral line is at the same level as the axis of the clamping frame with the servo motors. This is based on a normal height of 50 mm for asphalt beams. In this way the mid line of the aluminum reference beams is 25 mm above the bottom of the clamping U frame. 14,5 mm Width Beam = 34 mm Top fill in piece 45 mm Beam Height I = 35 mm II = 30 mm III = 25 mm 50 mm 7,5 mm Width U shape : 63 mm Figure 4.1 Dimensions of the accessories Beam I: Filling-in accessory: bottom ---- ; top 7.5 mm = 50 Beam II: Filling-in accessory: bottom 2.5 mm; top 10.0 mm = 50 Beam III: Filling-in accessory: bottom 5.0 mm; top 12.5 mm = 50. Another important point is the effect of the accessories on the bending beam moment. In case of a complete rigid connection (specially at the inner supports) between the accessories and the beam the effect would be much bigger than was expected on 18

19 forehand. Instead of an E value of 71 GPa a value of 77 GPa or more can be back calculated for the aluminum reference beams. Fortunately, the connection is quite loose and the stiffening effect can be ignored. Only when the clamping forces are extremely high the effect of the accessories can be seen in the bending profile of the beam. Nevertheless it is highly recommended to use in future reference beams that have a height equal to the normal height of the asphalt beams used in that 4PB equipment. The required reduction in the width of the reference beam will become much more and will lead to a thickness of 5 to 10 mm. 4.5 Masses In the back calculation the mass of the beam and the masses of the (moving) accessories at the two inner supports are needed if inertia forces are taken into account. The figures are given in table 3.4. Table 4.4 Masses of reference beams and moving accessories Beam Weight [kg] Accessories (2) [kg] I 1,424 0,283 II 1,218 0,310 III 1,010 0, PROCESSING OF DATA 5.1 Determination of amplitudes and phase lags The time of recording the analog signals on e.g. paper has long gone and today all analog signals are digitized. The number of data points per cycle can vary from 50 to 500. This depends on the applied frequency and the sample frequency. In principle here are two main techniques for the determination of the amplitudes and phase lags. Both method have there advantages and disadvantages. The first one is a simple regression using e.g. the least squares method. An example of an extended regression is given by the following equation: Y A B t C Sin 2 f t where A, B, C and are the regression coefficients, t is the time and f is the applied frequency. The term A+Bt is applied for the possibility that the offset of the signal increases or decreases during the capture of the data. Given the short measure window for data capturing, a linear relation for a possible change in the offset is sufficient. Sometimes the frequency f is also considered as a regression coefficient. In case the fitted frequency deviates too much of the planned frequency this can be seen as a warning signal. By subtracting the obtained values of the phase lags in the force and deflection signal the system phase lag difference between force and deflection can be obtained. The second method is the (Fast) Fourier Transform (FFT) in which the digitized signal is decomposed in frequency components. One advantage of this method is that a direct determination of the phase lag between the force and the deflection for the applied frequency is possible. Another advantage is the possibility to show a frequency spectrum which gives the opportunity to judge the purity of the applied sinusoidal signal. It should be noted that all frequency components for the calculation of the dissipated energy per cycle have to be used. 19

20 A third method is the Discrete Fourier Transform (DFT). This method is based on the multiplication of the measured signals with a sine and cosine signal with known amplitude and the same applied frequency. An integration is applied over n periods leading to two components (in phase and out phase). 5.2 Problems with the phase lag determination In general the determination of the amplitudes yields no problems. However, the determination of the phase lag is more complex. The data capture for the force and deflection signals need to be taken at exactly the same time. Another restriction is the processing electronics which should be tuned for both signals. A last item which was noticed in practice is the presence of other software (e.g. anti-virus software packages) on the computer. Therefore it is advised to use a stand alone computer with, if desired, only processed data output to a network. The correct determination of the phase lag can be checked by stiffness measurements with an elastic beam made of stainless steel or aluminum. The phase lag between force and deflection must be nil (or at least between -0,5 < < +0,5 according to the CEN standard). When an increasing or decreasing phase lag with frequency is noticed it will be probably caused by a time lag between the force and deflection captures (sequential sampling instead of parallel sampling). If the error can be localized it is advised to introduce a patch in the software rules. A more or less constant deviation from zero often indicates the presence of other operating software packages on the computer, even if they operate in the background. But it might also be that the processing electronics for the force and deflection signals are not tuned properly. A timely software patch might be applied to subtract or add the mean value for this deviation. It is also advised to carry out a check on the purity of the applied sinusoidal signals or the presence of current deviations in the power supply. 5.3 Phase lag correction All participants processed their data with their own software packages. In those cases where negative (system) phase lags appear, the data were corrected using either a linear correction of the form * = + a.f (for increasing or decreasing phase lags with frequency f) or by adding a constant if the system phase lag differs consequently positive (or negative) from nil. Sometimes it was only possible to apply the correction to the back calculated data for the material phase lag. Normally the difference between the system phase lag and the material phase lag is small. 5.4 Mass correction In theory the moving masses should be taken into account for the determination of the stiffness modulus and phase lag. But this is not the case in all (commercial) developed software. Sometimes only the mass of the beam is taken into account. According to the CEN norm all the influences of moving masses on the bending process should be taken into account. Of course at low frequencies the influences of these mass inertia forces are negligible (fig. 5.1). If the masses are known the influences of moving masses are taken into account in this paper. In the back calculation procedure only the (modified) first term of the infinite exact solution is taken. For higher frequencies (> 30 Hz) the exact value for the moving mass is not enough and a virtual mass has to be added in order to obtain the correct modulus. 5.5 Shear deflection correction Pure bending of a beam is not possible because the beam has a finite height and width. However, the influence of the occurring shear forces in the cross sections of the beam is 20

21 Deflection [mm] small if the ratio of the height over length (H/L) is small. For the configuration of the beams used in asphalt research the shear deflection is around 3-5 % of the deflection due to pure bending. So, in general the influence might be neglected. However, next to the importance of the shear deflection in the calibration test, the shear deflection doesn t contribute to the occurring horizontal strain in the beam. And by neglecting the shear deflection an error of 3 to 5 % is introduced in the back calculated strain. In this paper a shear correction is applied on the data. In contrast with the value of 2/3 used as the shear correction coefficient in the IPC software a value of 0.85 is used. This value is based on 1D and 3D finite elements calculations Mass beam = 2,7 kg ; Mass frame etc. = 5 kg Mass beam = 2,7 kg ; Mass frame etc. = 0 Mass beam = 0 ; Mass frame etc. = DWW Configuration Force = 200 N E = 3 Gpa j = 30 o Frequency [Hz] Figure 5.1 Influence of moving masses on the deflection as a function of the applied frequency 5.6 Damping coefficient In the CEN standard it is allowed to introduce a correction for system losses (damping). These system losses lead in almost all the cases to back calculated stiffness modulus which are too high. In other words, a part of the force is lost due to friction etc. and doesn t contribute to the real bending of the beam. In this paper no damping term is used while this term should be determined for each 4PB configuration separately using calibration measurements at several frequencies. Although the stiffness modulus (71 GPa) and phase lag (0 o ) of the reference beams are known, due to the different required beam dimensions (height, width and length) in different 4PB equipments, the reference beams in this project are not really suited as beams for calibration of an equipment. However, the outcome of this project may lead to suggested extended calibration measurements, especially when the results of the back calculation are quite different from the expected values. 21

22 5.7 Clamping problems As mentioned before, in order to be able using the reference beams in each 4PB equipments, clamping accessories of stainless steel are used in the clamping frames at the supports. These accessories introduce a deviation of the bending stiffness (EI) along the beam. When the beams were designed it was not investigated what the effect of the stainless steel accessories would be on the bending. However, it turned out using pseudostatic calculations that the effect could be much bigger than expected. In the worst case the back calculated stiffness modulus can be 10 % higher (78 GPa instead of 71 GPa). But this only occurs when the accessories and the beam are rigidly connected to each other and can be considered as one part. It is also possible to carry out an analytical calculation in which the accessories are not rigidly connected to the beam but still form a part of the bending beam. This case can be considered as the bending stiffness for three beam parts which rest frictionless on each other. In that case, so assuming that the accessories bend also, the influence is 2 to 3 % (73 GPa instead 71 GPa). Because it is not known how the applied clamping forces will influence the combined clamping stiffness and these forces differ for each 4PB device, the target value for the back calculated E value will be between 71 and 73 GPa. It should be noticed that the target E value is back calculated taking into account the deflection due to shear. In some data processing procedures no correction is applied for the shear deflection. In those cases the target value range changes to lower values. The change depends on the height over length ratio of the beam. In this case the changes are small, from 0.7 % for the beam with a height of 35 mm to 1.3 % for the beam with a height of 25 mm. These percentages are calculated for an effective length of 400 mm. In asphalt research the height of the beams is 50 mm or more. The error introduced by not taking into account shear forces (pseudo-static bending) is then 2.8 %. However, when the height of future reference beams is changed to 50 mm or more the contribution of the shear deflection will increase (depending on the height over length ratio). 5.8 Back calculation of E modulus All the participants use their own back calculation procedures and report their findings in a short note. Next to these notes all the (raw) data in the form of deflections, forces and phase lags are send to the coordinator. The coordinator uses these data in a back calculation program Bending & Shear (Excel program). Given the input (E modulus; phase lag) this program calculates the exact response on a loading at an arbitrary frequency. Mass inertia forces and overhanging beam ends are taken into account. The program has been checked with finite element calculations. By using the Solver option in Excel it is possible to back calculate the required E value in order to obtain the measured response. Because the phase lag determination is still tricky, it is decided to pre set the phase lag at 0 degrees. For the determination of the E value this has no influence. Examples of back calculated E values and phase lags are given in figures 5.2 and 5.3. The results presented in figure 5.2 give the impression that for low forces, there is too much play in the accessories and the clamping forces should have been increased. But this is only one of the possibilities. The increasing back calculated phase lags with the applied frequency in figure 5.3 are most probably due to a small time lag between the moments at which the deflections and forces are measured. 22

23 Phase lag [o] E [GPa] Beam I-50 Beam I-100 Beam II-50 Beam II-100 Beam III-50 Beam III Frequency [Hz] Figure 5.2 Back calculated E values with the program Bending & Shear; Beam I: 450*35*34 ; Beam II: 450*30*34 ; Beam III: 450*25*34 mm 3-50: strain value 50 m/m; - 100: strain value 100 m/m. Beam I-50 Beam I-100 Beam II-50 Beam II-100 Beam III-50 Beam III Frequency [Hz] Figure 5.3 Back calculated phase lags with the program Bending & Shear 23

24 6 BACK CALCULATION 6.1 Introduction For the back calculation of the modulus value E of reference beams the Excel program Bending & Shear (Pronk, 2007) is used in an iterative way. The measured values for the applied force and deflection were used as fixed figures. By changing the modulus value a perfect match between measured and calculated deflection is found (solver option). This leads to slight different answers compared to the determination of the modulus value by the modified first order approximation (CEN standard). For 4PB devices of which the frequency range is limited to 10 Hz (e.g. pneumatic actuators) the influence of inertia forces by moving masses can be ignored. Nevertheless, if the weight of the masses is known, these inertia forces are taken into account. Another point of concern is the phase lag. In the CEN standards an accuracy of 0,5 o is required. The phase lag for the beams ought to be zero because aluminum is an elastic material in the applied stress/strain range. However, very often phase lags are measured above 2 o and even negative phase lags occur. Given the fact that the priority of this project is aimed at the back calculation of the modulus, the back calculation of the phase lag is omitted. In the back calculation a zero value for the phase lag is adopted. This doesn t influence the height of the back calculated value for the modulus. The participants have been given a random number. Only the participant knows which paragraph in this chapter deals with his or her measurements. 6.2 Participant General Unfortunately participant 1 encountered problems with the interpretation of the measurements after the beams were already sent away to the next participant. Back calculation of the E modulus taking into account inertia forces (frequency range up to 40 Hz; moving masses in the order of 20 kg) gave too high values in the order of 80 GPa. This was due to the introduction of a new system which was not calibrated yet. Also the PID adjustment appeared to be not right at the time of the tests. Afterwards participant 1 calibrated the new system with their own aluminum beam. This beam had a height of 50 mm and a width of 9.73 mm. Therefore no help pieces were needed. The results of those tests are given in figure The back calculated E modulus is around 69.8 GPa in the low frequency range. These values are very acceptable because in the back calculation procedure used by participant 1 the contribution of shear deflection to the total (measured) deflection is not taken into account. However, there is a tendency to lower back calculated values at higher frequencies. It might indicate that not all the moving masses are taken into account. An exercise in which the back calculated E value is fixed at 70 GPa leads to an extra mass of around 10 kg. The back calculated phase lags in figure are nice examples of an unwanted time lag between the captures of the deflections and the forces. A trend line through zero indicates that at e.g. a frequency of 1 Hz the phase lag is 0,21 o. Therefore the time lag between the captures is 0.21/ ms. However, it should be marked that there might be other explanations for this frequency dependency of the phase lag. At higher frequencies there is strong interaction between the measured phase lag and the weight of the extra moving masses. 24

25 E [GPa] E [GPa] Phase lag [ ] Phase [ ] y = -0,2074x R 2 = 0, Frequency [Hz] E Figure Back calculated E values and phase lags by participant 1 using his own aluminum reference beam Back calculated stiffness modulus for the reference beams As mentioned above the results of participant 1 are not correct with respect to the E modulus due to several causes. Nevertheless, one figure for the results obtained with beam I is shown in figure The same trends are found as in the results of the measurements with their own reference beam which were carried later on when the equipment was tuned and calibrated. As many other participants participant 1 used the back calculation formulas as given in the CEN standards. The mass inertia forces are taken into account in those formulas. But the interpretation procedure uses a modified first order approximation instead of the complete solution. However, it is unlikely that this can explain the light tendency to lower back calculated E values at higher frequencies. One option is that participant repeats the tests after all participants have carried out the tests with the three reference beams. 82 E Phase lag 77 y = -0,1942x R 2 = 0, Frequency [Hz] Figure Back calculated E modulus and phase lag by participant 1 for reference beam I. 25

26 6.3 Participant General Participant 2 owns two devices, an old one with a pneumatic actuator (A; 0 10 Hz) and a newer version equipped with a hydraulic actuator (B; 0 60 Hz). During the testing problems were encountered with both software and hardware. It was also obtained that the climatic cabinet fan could affect the load cell reading and consequently the modulus results etc. Due to several other problems, mainly clamping problems, not all the beams could be tested at all frequencies and strain levels. This underlines once again the need for calibration beams designed for an individual device without help pieces or adapters at the clamps. An overview is given in table Table Overview of the tests performed by participant 2. Strain Device A Device B Beam I 50 μm/m No No 100 μm/m No No Beam II 50 μm/m Yes No 100 μm/m No No Beam III 50 μm/m Yes Yes 100 μm/m Yes Yes Next to the clamping problems the participant encountered problems with the shape of the sinusoidal waves. For device A (pneumatic) the wave shape was poor for frequencies above 8 Hz and for device B (hydraulic) the limit for good sinusoidal wave shapes was 20 Hz. The deflection is measured relative with a bridge of which the supports rest on the beam between the outer and inner support. Unfortunately the mass of the bridge is not known and is not included in the processing. Per frequency 100 cycles are carried using device A and 300 cycles when device B was used. For this project the mean values of the force and deflection amplitudes for the interval of cycle 50 to 90 in case of the measurements with device A and for device B the mean value for the interval from 200 to 250 cycles are taken for the back calculation procedure. The program Bending & Shear was used for the back calculation procedure including the correction for shear deflection. Furthermore it should be noticed that the tests were not carried out at a room temperature of 20 o C but at 29 o C. This might have an influence on the expected value for the modulus of aluminum Back calculated phase lags for the reference beams The obtained phase lags for the tests with device A (pneumatic) are given in figure Although it was possible to carry out tests with frequencies up to 30 Hz with this device, the wave shapes of the desired sinusoidal signals for frequencies above 10 Hz were far away from sinusoidal. As clearly shown in figure there is no relationship with the frequency which would implicate a time lag between the captures for the force and deflection data. Nevertheless the deviations from a phase lag of zero degrees is rather large. It is recommended that participant 2 will carry out tests with an elastic (aluminum or steel) beam with dimensions equal to the normal used asphalt beams in order to check if a correction on the phase lag is necessarily in the pre-processing of the data. 26

27 Figure Measured phase lags as function of the frequency for tests with device A. Figure Measured phase lags as function of the frequency for tests with device B. As shown in figure the results for frequencies below 15 Hz are close to the expected value of 0 degrees. Beyond a frequency of 20 Hz the wave shapes of the signals got deformed and couldn t be consider to be pure sinusoidal of shape. This may have influenced the determination of the phase lags for the deflection and force signals. It should be noted that the given values in figure are mean values. The standard deviations for the phase lags were quite high as can be seen in table for test B at 100 micro strain. In figure the values for frequencies above 15 Hz are omitted. There is no direct relation with the frequency in this interval. It s recommended that the procedure for the determination of the phase lag will checked for inconsistencies. 27

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