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1 COLLABORATIVE STUDY WITH 4PB DEVICES IN EUROPE “ROUND ROBIN TEST WITH THREE REFERENCE BEAMS” FINAL REPORT A.C. Pronk [email protected] 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 0.33. 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

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COLLABORATIVE STUDY WITH 4PB DEVICES IN EUROPE “ROUND ROBIN TEST WITH THREE REFERENCE BEAMS”

FINAL REPORT A.C. Pronk [email protected]

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 0.33. 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

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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.

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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 3.2.1 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

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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 factory-adjusted to 120 ... 130 N, but can be adjusted by ZwickService to other (higher) values if required. 3.2.2 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.

3.2.3 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. 3.2.4 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). Figure 3.2.1 Zwick device

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3.3 Cooper device 3.3.1 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 3.3.1 4PB device made by Cooper 3.3.2 Calibration concept No information on a calibration protocol was available at the time of writing. 3.3.3 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 1000th

cycle is captured. A sequential data sampling is used.

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). 3.3.4 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). 3.4 IPC Global device 3.4.1 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 12697-24/26 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. 3.4.1 First generation device with pivot system. Fig. 3.4.2 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

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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 12697-24/26.

Within Europe the common version is UTS018 of which the processing of the data is based on the EN Standards 12697-24/26 (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. 3.4.2 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 3.4.3 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 5th

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.

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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 0.85. Considering shear deflection is not applied in the EN standards, UTS018 calculates only the flexural stiffness. 3.5 DVS/KOAC-NPC & University of Vienna 3.5.1 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.

3.5.2 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. 3.5.3 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

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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 3.5.1 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 3.5.2 Modified DVS 4PB configuration at the University of Vienna (left) and the clamping of the sheets around a beam (right).

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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. Figure 3.5.3 Introduction of an unwanted moment during translation (left) and rotation (right) of the beam in the DVS 4PB device 3.6 University of Coimbra 3.6.1 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 3.6.1 4PB device at the University of Coimbra

February 20, 2009 57

EXAMPLES, 4PB

February 20, 2009 58

EXAMPLES, 4PB

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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 3.6.2 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. 3.6.3 Data collection A total of 32 channels can be read sequentially with a 8 ms time lag (8.10

-6 s) leading to

an interval of 0.256 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 0.256 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 post-processing 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 0.048 Hz at a sample frequency of 100 Hz (see figure 3.6.2).

Figure 3.6.2 Fast Fourier Transform (frequency spectrum) of the measured deflection for an applied load signal at 10 Hz.

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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 3.7.1 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 3.7.1 Cox device

3.7.2 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. 3.7.3 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.

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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 3.8.1 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 3.8.1.

Table 3.8.1 Possible variations with the Wenningsen 4PB device

Test Beam

[mm]

Clamps [mm] Stimulus

width

40…100

height

40…100

length

300…660

inner-inner clamp distance

105…200

outer-outer clamp distance

295…600

inner-outer clamp distance ≥

95

load 0…±12 kN

frequency 0… 60 Hz

deflection 0....±0.25 mm @

60 Hz

0…±1.5 mm @ 10

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

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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 x1 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 EN12697-24 and EN12697-26. 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.

1 2 3

1 32 3 1 real 2

Deflections: W{x },W{x } & W{x }

W{x } W{x }with x L / 2 and x L x W {L / 2} K W{x }

2

3.8.1

Figure 3.8.1 Baustoff-Prüfsysteme Wennigsen device

3.8.2 Calibration concept

No information on a calibration protocol was available at the time of writing.

3.8.3 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.

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 3.9.1 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 3.9.1 ISBS 4PB device

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. 3.9.3 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 20o 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. 3.9.4 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). 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.

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 ALMg4,5Mn (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 = 25 – 30 – 35 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 25 71 3143 II 34 x 30 71 5432 III 34 x 35 71 8625

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 50 6 3125 63 x 50 6 3938 50 x 50 9 4688 63 x 50 9 5906 50 x 50 12 6250 63 x 50 12 7875

As mentioned before the weight of the beams is also important. The weights of the three

reference beams are respectively 1.424 – 1.218 – 1.010 kg. The weights for asphalt

beams are given in table 4.3.

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

400 2.30 2.90 450 2.59 3.26

4.4 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.

Figure 4.1 Dimensions of the accessories Beam I: Filling-in accessory: bottom ---- ; top 7.5 mm 7.5 + 0.0 + 35 + 7.5 = 50 Beam II: Filling-in accessory: bottom 2.5 mm; top 10.0 mm 7.5 + 2.5 + 30 + 10.0 = 50 Beam III: Filling-in accessory: bottom 5.0 mm; top 12.5 mm 7.5 + 5.0 + 25 + 12.5 = 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

Width Beam = 34 mm

50 mm

Width U shape : 63 mm

Beam Height

I = 35 mm

II = 30 mm

III = 25 mm

7,5 mm

Top fill in piece

45 mm

14,5 mm

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 0,336

5. 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.

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

21

140

160

180

200

220

240

260

280

0 10 20 30 40 50 60 70

Frequency [Hz]

Def

lect

ion

[ mm

]

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. = 0

DWW Configuration

Force = 200 N

E = 3 Gpa

j = 30 o

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. 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.

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 pseudo-static 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.

23

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.

Figure 5.3 Back calculated phase lags with the program Bending & Shear

65

66

67

68

69

70

71

72

73

0 2 4 6 8 10

E [

GP

a]

Frequency [Hz]

Beam I-50 Beam I-100 Beam II-50 Beam II-100 Beam III-50 Beam III-100

0

1

2

3

4

5

0 2 4 6 8 10

Ph

ase

lag [

o]

Frequency [Hz]

Beam I-50 Beam I-100 Beam II-50 Beam II-100

Beam III-50 Beam III-100 .

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 1 6.2.1 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 6.2.1.

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 6.2.1. 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 0.21/360 0.6 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.

25

Figure 6.2.1 Back calculated E values and phase lags by participant 1 using his own aluminum reference beam. 6.2.2 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 6.2.2. 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. Figure 6.2.2 Back calculated E modulus and phase lag by participant 1 for reference beam I.

y = -0,2074x

R2 = 0,98

60

65

70

0 10 20 30 40 50

Frequency [Hz]

E [

GP

a]

-8

-7

-6

-5

-4

-3

-2

-1

0

1

Phase lag

[°]

E .

y = -0,1942x

R2 = 0,99

72

77

82

0 10 20 30 40 50

Frequency [Hz]

E [

GP

a]

Ph

ase [°]

E Phase lag

26

6.3 Participant 2 6.3.1 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 6.3.1. Table 6.3.1 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

oC but at 29

oC. This might have an influence on the expected value for

the modulus of aluminum. 6.3.2 Back calculated phase lags for the reference beams The obtained phase lags for the tests with device A (pneumatic) are given in figure 6.3.1. 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 6.3.1 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.

27

Figure 6.3.1 Measured phase lags as function of the frequency for tests with device A. Figure 6.3.2 Measured phase lags as function of the frequency for tests with device B. As shown in figure 6.3.2. 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 6.3.2 are mean values. The standard deviations for the phase lags were quite high as can be seen in table 6.3.2. for test B at 100 micro strain. In figure 6.3.3 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.

28

Figure 6.3.3 Measured phase lags as function of the frequency for tests with device B. Table 6.3.2 Standard deviations for the phase lags [o] in test Beam III-100-B for the interval of cycle 200 to 250.

Frequency 1 2 4 6 8 10 15 20 30 40 50

Stand. Dev. 0,3 0,5 0,3 0,4 0,5 0,3 0,8 0,8 1,5 2,0 2,5 6.3.2 Back calculated moduli for the reference beams The obtained results for the back calculated modulus using the pneumatic device A are given in figure 6.3.3. It’s clear that in general the modulus is too low with respect to the expected value of 71.3 GPa. Because the frequency is below 10 Hz mass inertia forces do not play a role in the back calculation. Participant 2 mentioned problems with the clamping forces and tried to increase the force manually but finally used the automatic protocol as prescribed by the manufacturer. Because the deflection is measured with the aid of a ‘bridge’ a possible non-infinite stiffness of the bending frame should not influence the reading. Nevertheless, it might be an good idea to carry out measurements with a very stiff steel beam (E = 210 GPa) at normal force levels (in order not to damage the frame). If a much lower modulus is back calculated this will be an indication that in spite of the relative deflection measurements the non-infinity stiffness of the frame plays a role in the deflection measure.

Another source for this deviation (besides deviations in the shape of the sinusoidal signals) is an unexpected influence of the help pieces which are used in the clamp devices. Once more this underlines the need of reference (calibration) beams designed for the individual 4PB tool.

It is also possible that due to the clamping system not all of the boundary requirements are fulfilled which may have an influence on the parameters which have to be used in the back calculation.

29

Figure 6.3.3. Back calculated modulus for the tests with device A The shape of the signals with device B were not really sinusoidal above a frequency of 20 Hz. The results for the back calculated modulus of measurements with device B are given in figure 6.3.4. For frequencies below 15 Hz the obtained values are close to the expected value of 71.3 GPa. In table 6.3.3 the standard deviation is given for test Beam III-100-B. For frequencies above 20 Hz the standard deviation increases fast. Figure 6.3.4. Back calculated modulus for the tests with device B Table 6.3.3 Standard deviations for the mean moduli [GPa] in test Beam III-100-B on the interval of cycle 200 to 250.

Frequency 1 2 4 6 8 10 15 20 30 40 50

Stand. Dev. 0,1 0,1 0,1 0,1 0,1 0,1 0,6 1,2 4,2 7,2 9,8

30

6.4 Participant 3 6.4.1 General

Participant 3 measured a nearly constant phase lag with a small variation. In table 6.4.1 the mean values and standard deviations for the applied frequency range from 0 to 10 Hz are given. The standard deviation is very small indicating no frequency dependency. Strange enough the levels of the mean values per test conditions are different. Moreover, the values are negative. The data for deflection and force are collected at the same time. Otherwise an increasing (or decreasing) deviation from nil should occur. A probable cause might be an anti-virus program which was active in the background. This might also explain the “random” differences in the mean value levels. Therefore participant 3 decided to decouple the processing computer from the network and change the configuration into a stand alone unit.

Table 6.4.1 Measured mean phase lags and standard deviations for the frequency range 0-10 Hz Test Configuration Mean [o] Standard Deviation [o] Beam I – 50 m/m -2.35 0.11 Beam I – 100 m/m -2.61 0.08 Beam II – 50 m/m -2.00 0.09 Beam II – 100 m/m -1.49 0.09 Beam III – 50 m/m -1.26 0.05 Beam III – 100 m/m -1.19 0.06

Because aluminum should have a phase lag of zero, it is decided to ignore the

measured phase lags. In the back calculation procedure a phase lag of nil is assumed. Given the low measured phase lags the effect can be ignored.

A pneumatic actuator was used, which limited the frequency range to 10 Hz. Therefore mass inertia forces play a minor and negligible role in the back calculation procedure. Because no exact values are known only the mass of the beam is are taken into account in the procedure. In this report mean values were used which were measured between the 100

th and 300

th cycle. Except for the frequency of 1 Hz at which the mean value was

taken from the values measured between the 50th

and 75th

cycle. 6.4.2 Back calculated stiffness modulus for the reference beams The back calculated modulus as a function of the frequency is presented in figure 6.4.1 and as function of the applied force in figure 6.4.2 and as a function of the applied deflection in figure 6.4.3. The modulus is back calculated taken into account the deflection due to shear forces. In view of the geometrical dimensions of the reference beams this effect is only marginal (1.5 GPa for beam I; 1.2 GPa for beam II and 0.8 GPa for beam III).

Specially the results for the tests with a strain of 100 m/m the back calculated E values are close to the expected value of 71 GPa. The only exception is test with 50 m/m strain for beam I. An explanation might be found in figure 6.4.3. Because the tests are carried out in the linear elastic range, there should be no dependency on the deflection. However, the measured deflection for beam I at 50 micro strain is clearly an outliner. It looks like that the deflections in the low range (< 0,1 mm) are not measured precisely enough (too low values). Nevertheless the back calculated E values at 100 micro strain are good.

31

65

66

67

68

69

70

71

72

73

0 1 2 3 4 5 6 7 8 9 10

E [

GP

a]

Frequency [Hz]

Beam I-50 Beam I-100 Beam II-50 Beam II-100 Beam III-50 Beam III-100

Figure 6.4.1 Back calculated modulus as a function of the frequency.

Figure 6.4.2 Back calculated moduli as a function of the applied force.

66

67

68

69

70

71

72

0,3 0,5 0,7 0,9 1,1 1,3 1,5 1,7

E [G

Pa]

Force [kN]

Beam III, II, I

e=100 m/m

e=50 m/m

32

66,0

67,0

68,0

69,0

70,0

71,0

0,07 0,09 0,11 0,13 0,15 0,17 0,19 0,21 0,23

Deflection [mm]

E [

GP

a]

Beams I, II, III

tested at 50 m/m

Beams I, II, III

tested at 100 m/m

Figure 6.4.3 Back calculated modulus as a function of the measured deflection.

6.5 Participant 4 6.5.1 General

As by many other participants the variation in the measured phase lag is larger than hoped. In the CEN standard a deviation of 0,5

o is prescribed. Here the phase lags, which

ought to be zero vary from 0,2 to 2,5 o with a mean value of 1,2

o. But at least it is always

a positive number. Because aluminum should have a phase lag of zero, it is decided to ignore the measured phase lags. In the back calculation procedure a phase lag of nil is assumed. Given the low measured phase lags the effect can be ignored.

A pneumatic actuator was used. Also higher frequencies are possible, the tests were performed at a frequency of 10 Hz. Therefore mass inertia forces play a minor role in the back calculation procedure. Nevertheless they are taken into account in the back calculation procedure. 6.5.2 Back calculated stiffness modulus for the reference beams The back calculated modulus as a function of the frequency are presented in figure 6.5.1. and as function of the applied force in figure 6.5.2. The modulus is back calculated taken into account the deflection due to shear forces. In view of the geometrical dimensions of the reference beams this effect is only marginal (1,5 GPa for beam I; 1,2 GPa for beam II and 0,8 GPa for beam III).

It is quite clear from figure 6.5.1 that using a strain of 100 micro strain leads to acceptable values for the given modulus of the reference beams (71 GPa). As expected there is no real evidence of a frequency dependency. For 100 micro strain (closed symbols) the back calculated values vary random around 71 GPa. If a strain of 50 micro strain (open symbols) is applied than in almost all cases a too low value for the modulus is back calculated.

33

In order to explain the differences or to investigate a possible cause for the too low values, the modulus values are also plotted as a function of the applied forces and the applied deflections. These results are given in figure 6.5.2 and 6.5.3

Figure 6.5.1 Back calculated modulus as a function of the frequency.

Figure 6.5.2 Back calculated modulus as a function of the applied force.

In figure 6.5.2 there is again a clear distinction between the measurements at 50 and 100 micro strain with one exception of a measurement with beam I (see question mark; 50 micro strain).

The mean modulus are also plotted as a function of the mean applied deflection. The result is presented in figure 6.5.3.

65

66

67

68

69

70

71

72

73

0 2 4 6 8 10

Frequency [Hz]

E [

GP

a]

Beam I-50 Beam I-100 Beam II-50 Beam II-100 Beam III-50 Beam III-100

65

66

67

68

69

70

71

72

73

0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

E [G

Pa

]

Force [kN]

Beam III II I

e = 50 mm/m

e = 100 mm/m

?

Participant no. 4

34

Figure 6.5.3 Back calculated mean modulus as a function of the applied mean deflection. 6.6 Participant 5 6.6.1 General The device of participant 5 is equipped with a hydraulic actuator. However, the tests performed for this project were limited to a frequency of 10 Hz. Therefore it is not necessarily to include mass inertia forces in the processing of the data. Furthermore no correction for shear deflection is applied in view of the small error (< 5%). Nevertheless this correction is taken into account in this exercise.

The frequency for controlling the bending process is 1 to 2 kHz. For data acquisition (back calculation and fitting data) only 100 points per cycle are stored. According to the participant a Fast Fourier Transform (FFT) is applied to the data. Unfortunately a graph of the obtained frequency spectrum is missing in the reported output. The output does not give the determined amplitudes for deflection and force from the captured data using FFT but calculated values for the amplitudes of stresses and strains. These values are determined per cycle

The deflection is measured with respect to the outer (not moving) supports. If it is an absolute deflection measurement a correction for the non-infinity stiffness of the frame ought to be taken into account. 6.6.2 Back calculated stiffness modulus for the reference beams In figure 6.6.1 the mean values of the stiffness modulus, back calculated with the software of the participant are given as a function of the frequency. The presented values are the mean values over 90 cycles (cycle 10 to 100). The standard deviations are small and given in table 6.6.1.

67

68

69

70

71

72

0,030 0,060 0,090 0,120

Applied deflection [mm]

Mo

du

lus

[GP

a]

Beams I, II, III

tested at 50 m/m

Beams I, II, III

tested at 100

m/m

35

Figure 6.6.1 Mean back calculated moduli by the software of the participant as a function of the applied frequency. Table 6.6.1 Standard deviations [Gpa] for the back calculated moduli (cycle 10 to 100).

50 micro strain 100 micro strain

Freq. I II III I II III

1 0.17 0.31 0.14 0.17 0.10 0.05

2 0.20 0.25 0.25 0.11 0.38 0.06

4 0.11 0.12 0.14 0.09 0.17 0.05

6 0.14 0.12 0.14 0.07 0.08 0.04

8 0.15 0.11 0.08 0.08 0.07 0.05

10 0.16 0.29 0.08 0.05 0.08 0.05

It is obvious that even after correction for the shear deflection the obtained modulus are much too low in view of the expected value of 71.3 GPa. Possible causes will be discussed in paragraph 6.6.4. 6.6.2 Back calculated phase lags for the reference beams In contrast with the back calculated stiffness modulus, the back calculated phase lags are quite reasonable as can be seen in figure 6.6.2. The standard deviations are given in table 6.6.2. Still the range in the back calculated phase lags with respect to the expected value of 0 degrees is a bit too high according to the European CEN standards (0.5 degrees).

36

This value of 0.5 degrees is disputable in view of all the reported phase lags in this project. Figure 6.6.2 Mean back calculated phase lags by the software of the participant as a function of the applied frequency. Table 6.6.2 Standard deviations [o] for the back calculated phase lags (cycle 10 to 100).

50 micro strain 100 micro strain

Freq. I II III I II III

1 0.4 0.6 0.1 0.1 0.1 0.0

2 0.1 0.1 0.1 0.1 0.3 0.0

4 0.1 0.1 0.1 0.0 0.1 0.0

6 0.1 0.1 0.1 0.0 0.1 0.0

8 0.1 0.1 0.1 0.1 0.0 0.1

10 0.1 0.2 0.1 0.1 0.1 0.1

6.6.3 Possible causes or sources for the obtained low stiffness modulus Two possible causes for the deviation of the back calculated stiffness modulus and the expected value of 71.3 GPa are the determination of the amplitudes for the force and the deflection and the frame stiffness. Only a short investigation was possible for which the data for beam I at a frequency of 1 Hz and 50 micro strain are taken. Fortunately the captured data were available. Using the data from cycle 40 to 90 a sine regression was made for the deflection (figure 6.6.3) and force (figure 6.6.4). The fit is quite good. The differences in amplitudes between the values determined by the regression and those

37

based on the maximum peak-peak values in the cycle interval from 40 to 90 is minimal. For the deflection the values are 0.01242 and 0.012515 mm respectively and for the force the values are 0.11670 and 0.11515 kN. Figure 6.6.3 Deflection data and the sine regression for beam I at 1 Hz and 50 μm/m Figure 6.6.4 Force data and the sine regression for beam I at 1 Hz and 50 μm/m

38

Using the standard formulas (no corrections for mass inertia forces and shear deflection) values are obtained for the stiffness modulus using 1) the regression, 2) the peak-peak and 3) the value by the software of the participant and are given in table 6.6.3. Table 6.6.3 Stiffness modulus for beam I at 1 Hz and 50 micro strain using data obtained by sine regression (SR), maximum peak-peak values (PP) and FFT.

Beam I Eback (SR) [Gpa] Eback (PP) [GPa] Eback (FFT) [Gpa] 1 Hz & 50 μm/m 61.7 60.4 62.1

Given the small differences between the values for the stiffness modulus it is clear that the deviation with the expected value of 71.3 GPa is not due to the processing of the captured data.

The other possible source for the deviation is the neglected stiffness of the frame. According to the participant the deflection is measured in the centre (L/2) with respect to the outer supports. In theory there should be no vertical movement or deformation at the outer supports. However it might be possible. It is advised to check this by measuring the deflection also with a ‘deflection bridge’ of which the supports are resting on the beam. In that case the stiffness of the frame has no influence.

The expected stiffness for beam I is around 10.86 MN/m. The measured stiffness is around 9.46 MN/m. If the stiffness of the frame is the source the value for the stiffness of the frame will be in the order of 1/(1/9.46 – 1/10.86) = 107 MN/m. This value is quite reasonable. 6.7 Participant 6 6.7.1 General` Participant 6 is one of the few participants who uses a Fast Fourier Transform for the post processing of the data. Although the data are captured sequentially, the phase lag due to this would be in the worst case less than 0.9

o. However, larger phase lags were obtained

as shown in figure 6.7.1. Figure 6.7.1 Phase lags as a function of the applied frequency

0

1

2

3

4

5

6

7

8

0 2 4 6 8 10

Ph

ase

lag [

o]

Frequency [Hz]

Beam I-50 Beam II-50 Beam III-50

Beam I-100 Beam II-100 Beam III-100

39

The tendency of decreasing phase lags with frequency (slope) might still be due to the sequential data captures for force and deflection. However, the positive mean levels of 6

o

(low applied deflections) and 3 o (high applied deflections) for the phase lags are of more

concern. The clamping pressure at the beam is 200 kPa which is not too high. At the moment there is no adequate answer for this deviation. It could be a short coming in the electronic circuits for measuring force and deflections but this doesn’t explain the dependency on the height of the applied signals. Because aluminum is an elastic material it is justified to adopt a zero phase lag in the back calculations. 6.7.2 Back calculated stiffness modulus for the reference beams Due to unforeseen circumstances, the help pieces were not completely suited for the bending frame of participant 6. Nevertheless, participant 6 carried out the tests in order not to disturb the routing planning of the beams. The results are presented in figures 6.7.2 to 6.7.4. The back calculations were carried out using the Excel program “Bending & Shear” taking into account an extra mass of 8,634 kg for the moving frame parts etc.

Probably due to these problems with the help pieces the variation between different tests is rather big (figure 6.7.2). But the variation within one test is very reasonable. No real dependency with the applied frequency is noticed.

The results presented in figure 6.7.3 indicate that a tendency with the force might be present. The back calculated values increase with an increasing force.

A strange result is obtained when the back calculated E values are presented as a function of the applied deflection (figure 6.7.4). No explanation could be found at the moment.

In view of the problem with the help pieces of the reference beams a separate beam of the same material (SALPLAN 5000) might help. This beam should have dimensions and a configuration (shape) which is suited for the bending frame of participant 6.

Figure 6.7.2 Back calculated E values as a function of the applied frequency.

60

65

70

75

80

85

0 2 4 6 8 10

E v

alu

e [

GP

a]

Frequency [Hz]

Beam I-50 Beam I-100 Beam II-50 Beam II-100 Beam III-50 Beam III-100

40

Figure 6.7.3 Back calculated E values as a function of the applied force. Figure 6.7.4 Back calculated E values as a function of the measured deflection.

60

65

70

75

80

85

100 200 300 400 500 600 700 800 900 1000

E v

alu

e [

GP

a]

Force [N]

Beam I-50 Beam I-100 Beam II-50 Beam II-100 Beam III-50 Beam III-100

60

65

70

75

80

85

30 40 50 60 70 80 90 100 110 120

E v

alu

e [

GP

a]

Deflection [m]

Beam I-50 Beam I-100 Beam II-50 Beam II-100 Beam III-50 Beam III-100

41

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

0 10 20 30 40 50 60

Frequency [Hz]

Ph

ase lag

[o

]

Beam III - 50 Beam III - 100 Beam II - 50

Beam II - 100 Beam I - 50 Beam I - 100

6.8 Participant 7 6.8.1 General The device of participant 27 is equipped with a hydraulic actuator capable for frequencies up to 60 Hz. The deflection is measured relatively. The reference points are not located at x = L/6 and x = 5L/6 but closer to the outer supports. Therefore the multiplication factor needed to obtain the absolute deflection in the centre is smaller than 2. Deflections due to shear forces follow another profile than the deflections due to pure bending. However, the error, introduced because the ratios of the shear deflection and bending deflection at these locations are different, is negligible (< 0.04%). The advantage of a relative deflection measurement is that the influence of the non-infinity stiffness for the device is eliminated.

The resolution of the deflection measurement system is 0.00006 mm. This implicate that for a deflection of 0.045 mm (Beam II equivalent to an asphalt beam with a Smix of 9 GPa; 50 µm/m) the deviation can be in the order of 0.13% which is very small.

The correction for inertia effects (moving masses of the device) is done by the use of internal acceleration sensors. The reading of the load cell is adjusted to nil while the device is running without a beam with the use of the measured accelerations and virtual masses. In the processing of the data the weight of the beam has to be taken into account.

The back calculated phase lags are given in figure 6.8.1 as a function of the frequency and in figure 6.8.2 as a function of the applied load.

Figure 6.8.1 Back calculated phase lags as a function of the applied frequency

Up to 40 Hz the phase lag varies between 0 and 1 degree. Beyond 40 Hz the phase lag becomes negative but the absolute value is still small (< 2

o). A similar evolution is

observed for the back calculated E modulus as a function of the frequency (Figure 6.8.2).

42

73

74

75

76

77

0 10 20 30 40 50 60

Frequency [Hz]

Mo

du

lus [

GP

a]

Beam III - 50 Beam III - 100 Beam II - 50 Beam II - 100

Beam I - 50 Beam I - 100

6.8.2 Back calculated stiffness modulus for the reference beams

The calculated centre deflections are corrected for the influence due to shear forces. The back calculated E modulus values, taking into account the mass of the beam are presented in figure 6.8.3 as a function of the applied frequency. In general the back calculated E values are too high compared to the expected value of 71 GPa. Figure 6.7.3 Back calculated E values as a function of the applied frequency.

Again the variation in the back calculated E values is small for moderate frequencies (<

20 Hz). However beyond 20 Hz the back calculated E value increases to 76 GPa at 50 Hz. Very odd is the relative large variation at 60 Hz from 75 GPa for the thinnest beam (25 mm) to 77 GPa for the thickest beam (35 mm).

As mentioned before the correction for the extra moving masses (beam mass excluded) is performed with the aid of acceleration sensors and a virtual mass. The correction is obtained by adjusting the load sensor in a test without a beam. It can be questioned if the right correction can only be obtained when a beam is mounted in the device. 6.9 Participant 8 6.9.1 General The home made device of participant 8 is equipped with a hydraulic actuator with a load capacity up to 50 kN. The maximum frequency is 30 Hz, but due to mechanical problems at the bearings and a low sampling frequency (500 Hz) the forms of the load and deflection signals for frequencies above 10 Hz are not good looking sinusoidal signals.

The deflection is measured in the centre (L/2) absolutely. The clamping device is able to handle specimens with a cross section of 40*40 mm

2 to 100*100 mm

2. The effective

length L can be varied from 240 to 600 mm. For this project the effective length L was taken equal to 430 mm. Only the small fill in help pieces (plates) were used in order to obtain a height of 40 mm.

43

As in the DWW and Vienna devices the mid span is not equal to L/3 but a bit smaller: 142.5 mm. Therefore the parameter A in the calculations is: 143.75 mm.

As most of the other devices rotating clamping frames are used. But instead of servo motors screws are used to fasten the beam in the clamping frame. The moment used to fasten the screws is not yet prescribed but a protocol will be made.

The upper part of the frame device is made of aluminum while the lower part is made out of steel. This may introduce an error because in the analysis (interpretation) it is assumed that the stiffness of the frame is infinite or at least much higher than the beam stiffness. In that case the deflection of the frame due to a load can be ignored compared with the deflection of the beam. Because the deflection is measured absolutely this effect is not been compensated for as is the case for devices with a relative deflection measure. In the future the correction factor Kf will be determined by carrying out tests with a very stiff beam. 6.9.2. Back calculated phase lags for the reference beams The results for the phase lags between force and deflection are given in figure 6.9.2. It is quite clear that the data for the force and deflection are not sampled at the same time. Before the data can be used for the back calculation, especially in case of visco-elastic material, a correction has to be applied. Figure 6.9.1. Phase lags between force and deflection as a function of the frequency.

44

6.9.3 Back calculated stiffness modulus for the reference beams The signal form for frequencies above 10 Hz was not a nice sinusoidal one. The sampling frequency of 500 Hz was too low to obtain good sinusoidal signals for frequencies above 10 Hz as shown in figure 6.9.2 for a frequency of 30 Hz. Figure 6.9.2. Example of the poor sinusoidal signal form at 30 Hz if the sampling frequency is too low.

In general for frequencies below 10 Hz the influences of the inertia forces due to moving masses can be neglected. However, in this case the moving masses are probably rather high. A value of 30 kg had to be adopted in order to get a flat curve. With this value the back calculated stiffness values for frequencies above 6 Hz are nearly constant. The “true” value for the moving masses has to be determined as soon as good sinusoidal signals are obtained for frequencies above 10 Hz. In the back calculation with the program Bending & Shear it is assumed that the phase lag is nil (aluminum reference beams). The correction for shear deflection is taken into account in this program.

The shear deflection can be expressed as: s b

V C.V .

Next to the Poisson ratio of the material (0.33) the coefficient C depends on the geometrical dimensions of the beam (H/L) and is given in table 6.9.1 for the beams in this configuration (L = 430 mm).

Table 6.9.1 Shear correction coefficients C

Height

[mm]

Effective Length

[mm]

Coefficient C

[%]

Beam I 35 430 1.62

Beam II 30 430 1.19

Beam III 25 430 0.95

45

The results of a straight forwards back calculation are presented in figure 6.9.3. Figure 6.9.3. Back calculated stiffness values using a moving extra mass of 30 kg. It’s clear from figure 6.9.3 that this direct back calculation leads to different values depending on the height of the beams. As mentioned before the mass inertia forces do not play a big role in the low frequency range (< 10Hz). Therefore the response of the system in this frequency range can be simplified into two springs in series. Knowing the E value for the reference beams the replacing spring Kb for the beam can be calculated. An estimate for the replacing spring Kf of the frame can be determined. The total measured deflection Vt is the sum of the bending deflection Vb, the shear deflection Vs and the

frame deflection Vf: t b s f

V V V V . For the low frequency range the relation between

deflections and the applied force can be expressed by:

b b f f t b f

V F / K & V F / K & V 1 F / K F / K

In which F is the applied force. It is clear that for a very stiff beam (Kb : Vb 0)

a good estimation for the factor Kf can be established. However, knowing the modulus

for the reference beam (71.7 GPa) a prediction for Kf can be made. The relation between

Kb and the Young’s modulus is:

3

b 2 2

4E B HK

A 3L 4 A

In view of the results obtained with beam I (height 35 mm) this seems to be a plausible explanation for the difference with the expected value of 71.3 GPa. However, for beams II and III the obtained back calculated E values are higher than the expected values. Participant 8 used the help pieces in order to obtain a height of 40 mm for all the beams. This means that for beam I only two sheets of 2.5 mm were used, for beam II 4 sheets of 2.5 mm were used and for beam III 6 sheets of 2.5 mm were used. This in itself would not be a problem if the beams were clamped properly without too much clamping forces. Assuming that the help pieces (at the inner clamps) are rigidly connected to the beam the increase in the apparent stiffness would be 6.5% for beam I, 7% for beam II and 7.4% for beam III. And this can’t explain the observed big differences between the measured values, However, at the time of testing, screws were used which may have led to a much larger increase of the bending moment E.I and in this way to an increase in the replacing spring Kb.

46

6.10 Participant 9 6.10.1 General Participant 9 has a 4PB device with a hydraulic actuator capable to apply frequencies up to 30 Hz. From a process control point of view these measurements are of special interest. Normally the desired strain level ought to be reached before the 100

th cycle. At

low frequencies this requirement is no problem as shown in figures 6.10.1 and 6.10.2 for a frequency of 1 Hz.

Figure 6.10.1 Applied force and measured deflection for Beam I at 1 Hz.

Figure 6.10.2 Calculated strain and back calculated stiffness for Beam I at 1 Hz.

0,77

0,78

0,79

0,8

0,81

0,82

0,83

0 20 40 60 80 100

Cycles

Forc

e [k

N]

0,036

0,037

0,038

0,039

0,04

Def

lect

ion [

mm

]

Series5 Series6

94

95

96

97

98

99

100

101

0 20 40 60 80 100

Cycles

Str

ain [

m

/m]

69000

70000

71000

Sti

ffnes

s [M

Pa]

strain Stiffness

47

Quite different is the case if nothing is changed at the process control for higher frequencies. In the figures 6.10.3 and 6.10.4 the same evolutions are given but now for a frequency of 20 Hz. Figure 6.10.3 Applied force and measured deflection for Beam I at 20 Hz. Figure 6.10.4 Calculated strain and back calculated stiffness for Beam I at 20 Hz.

Because for the applied loads in this project the stiffness modulus of aluminum doesn’t depend on the applied stress, it is decided to take the measured and calculated values at cycle 100 or close hereby.

0,77

0,78

0,79

0,8

0,81

0 50 100 150 200 250

Cycle

Fo

rce

[kN

]

0,036

0,037

0,038

0,039

Def

lect

ion

[m

m]Force Deflection

94

96

98

100

0 50 100 150 200 250

Cycles

Str

ain

[

m/m

]

68000

69000

70000

Sti

ffn

ess

[MP

a]

Strain Stiffness

48

As like many other participants, participant 9 also got very often negative phase lags. However, there is no real correlation with frequency or other parameters ( see figure 6.10.5). It is a random variation. There is a tendency that the variation increases with frequency. It should be marked that these phase lags are measured values because no mass inertia forces are taken into account in the data processing. This is advised for frequencies above 10 Hz.

Figure 6.10.5 Measured phase lags for the three beams as a function of the frequency. 6.10.2 Back calculated stiffness modulus for the reference beams The back calculated modulus as a function of the frequency is presented in figure 6.10.6. and as function of the applied force in figure 6.10.7. The modulus is back calculated taken into account the deflection due to shear forces. In view of the geometrical dimensions of the reference beams this effect is only marginal (1,5 GPa for beam I; 1,2 GPa for beam II and 0,8 GPa for beam III). In view of the applied frequencies above 10 Hz it is advised to take into account the mass inertia forces due to the beam and the other moving masses. However, no information was available for these masses (except the beam masses). This might be the reason that for frequencies above 10 Hz the back calculated modulus values are too low.

As clearly shown in figure 6.10.6 only the back calculated E values for beam I and for frequencies below 15 Hz are reasonable to good. The tendency to lower values for higher frequencies is due to the fact that the mass inertia forces are not taken into account. If these masses are in the order of 10 to 20 kg results are obtained which are comparable to the values obtained for frequencies below 10 Hz. In the following figures the results for frequencies above 10 Hz are excluded.

-3

-2

-1

0

1

2

3

0 5 10 15 20 25 30

Ph

ase

lag [

o]

Frequency [Hz]

Beam I-50 Beam I-100 Beam II-50 Beam II-100 Beam III-50 Beam III-100

49

Figure 6.10.6 Back calculated E values as a function of frequency for the 3 beams

60

62

64

66

68

70

72

0 5 10 15 20 25 30 35

E [

GP

a]

Frequency [Hz]

Beam III-50 Beam III-100 Beam II-50

Beam II-100 Beam I-50 Beam I-100

62

64

66

68

70

72

74

0 0,2 0,4 0,6 0,8 1

E v

alu

e [

GP

a]

Force [kN]

Beam III-50 Beam III-100 Beam II-50

Beam II-100 Beam I-50 Beam I-100

50

Figure 6.10.7 Back calculated E values as a function of the applied force.

Figure 6.10.8 Back calculated E values as a function of the required deflection. Although there is a clear difference in the back calculated E values for the three beams

these figures do not give an indication which might be the cause for the differences. 6.11 Participant 10 6.11.1 General Participant 10 used a hydraulic actuator for this project. Measurements were carried out at 1, 2, 4, 6, 8, 10, 15, 20 and 30 Hz. Although frequencies above 10 Hz are used, no corrections for mass forces (except for the beam mass) are included in the back calculation software of this device. Also no correction is applied for the deflection due to shear forces.

The effective beam length is 357 mm and the length between the supports is 119 mm. The sample frequency for the data acquisition, control and calculation purposes is 1024 Hz. However, the data for file recording, which is used in the calculations of the force and deflection amplitudes is only 20 data points per cycle regardless the applied frequency. This is a bit low in view of the data sample frequency of 1024 Hz. Even at 30 Hz it is possible to have much more data points for file recording using this sample frequency. For recording of the data at the applied frequencies, 100 cycles were taken for frequencies up to 2 Hz, 150 cycles for frequencies up to 6 Hz, 200 cycles for frequencies up to 10 Hz and 250 cycles for frequencies up to 30 Hz. The back calculation was performed with the average values over at least 65 cycles. The deflection was measured absolutely in the centre of the beam.

62

64

66

68

70

72

74

0 0,01 0,02 0,03 0,04 0,05 0,06

E v

alu

e [

GP

a]

Deflection [mm]

Beam III-50 Beam III-100 Beam II-50

Beam II-100 Beam I-50 Beam I-100

51

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

0 5 10 15 20

Frequency [Hz]

Phas

e la

g [

o]

Beam I-50 Beam I-100 Beam II-50 Beam II-100 Beam III-50 Beam III-100

6.11.2 Measured phase lags for the reference beams The phase lag as a function of the frequency is given in figure 6.11.1. At first sight there seems to be a time lag (linear decrease with frequency) between the data acquisition for the deflection and the force. However, the decrease becomes higher at increasing frequencies above 10 Hz.

The values at 30 Hz are not plotted because these values range between 9 and 22 degrees. For beam I applying 30 Hz for a strain level of around 50 micro strain, the measured phase lag between force and deflection was 22.1 degrees. If this measure was correct the phase lag for the material (aluminum) has to be 21.6 degrees, which is unrealistic. Therefore the results for a frequency of 30 Hz are not included. It is advised to check in detail the phase lag determination at high frequencies (above 10 Hz). Figure 6.11.1 Back calculated phase lags as function of the applied frequency

An improvement maybe obtained by using a fast Fourier transform (or DFT) on the collected data instead of a sine regression method. Although the decrease in the phase lag and the obtained absolute values for frequencies below 10 Hz are small, in view of the allowed deviation (0.5 degrees) according to the CEN standards a phase lag correction for this frequency range is advised. This can be done by correcting the observed time delay in the pre-processing of the data. In view of the variation in phase lags obtained in this exercise it is recommended to use a (casted) aluminum or steel beam without the kind of help pieces used in this project in order to avoid problems at the clamps. With this beam a frequency sweep for at least 3 deflections can be performed from 0 to 30 Hz. Because of the much higher bending stiffness (E.I) of a beam with standard dimensions (height equal to 50 mm) the forces should be limited. To obtain still a reasonable (measurable deflection value) the width of this beam should be decreased as much as possible. The reduction in width might introduce positioning problems at the clamps. However, the purpose of this beam is only to determine the phase lag correction and not the back calculated modulus. Therefore the beams may have a width at the clamp equal to the width used for asphalt beams. In view of figure 6.11.1 this might help for frequencies up to 20 Hz.

For the determination of the phase lag in e.g. fatigue tests on asphalt beams (30 Hz is prescribed in the CEN standard), it might be necessarily to carry out a more detailed

52

65

70

75

80

0 5 10 15 20 25 30 35

Frequency [Hz]

Modulu

s [G

Pa]

Beam I-50 Beam I-100 Beam II-50 Beam II-100 Beam III-50 Beam III-100

research. For beam I applying 30 Hz for a strain level of around 50 micro strain, the measured phase lag between force and deflection was not negative but positive (+ 22.1 degrees). If this measure was correct the phase lag for the material (aluminum) has to be 21.6 degrees, which is unrealistic. \ 6.11.3 Back calculated modulus for the reference beams In figure 6.11.2 the back calculated values for the modulus of the 3 reference beams are given. These figures are obtained with the software of the 4PB device without correction for shear deflection or moving masses. There is no correlation between the modulus and the applied force or deflection (figure 6.11.3) which might explain the range and deviations.

Figure 6.11.2 Back calculated E values as a function of the applied frequency. The values in figure 6.11.2 are not corrected for moving masses of the bending frame and the shear deflection. The effect of the moving masses is minimal for frequencies up to 10 Hz but will have a substantial influence for frequencies above 20 Hz. Depending on the height length ratio of the beam the value for the back calculated modulus will increase a few percent. Based on an assumption for the moving mass and taking into account the effect of the shear force on the deflection the reported deflections are used in the program “Bending & Shear” for the back calculation of the modulus. The result is given in figure 6.11.4

It is recommended that participant carries out a calibration test with an aluminum (or steel) beam In order to avoid problems with help pieces the following dimensions for a beam of casted aluminum are advised: Height = 50 mm; Widths = 10 and 5 mm. Small help pieces with a height smaller than 50 mm are allowed to overcome clamping problems.

53

65

70

75

80

0 500 Load [N]

Mo

du

lus

[GP

a]

Beam I-50 Beam I-100

Beam II-50 Beam II-100

Beam III-50 Beam III-100

65

70

75

80

0.03 0.07 0.11

Deflection [mm]

Modulu

s [G

Pa]

65

70

75

80

85

0 5 10 15 20 25 30 35

Frequency [Hz]

Modulu

s [G

Pa]

Beam I-50 Beam I-100 Beam II-50 Beam II-100 Beam III-50 Beam III-100

Figure 6.11.3 Back calculated modulus by the software of the manufacturer as a function of the load and deflection.

Figure 6.11.4 Back calculated modulus with the program “Bending & Shear” taking into account moving masses and shear deflection. 6.12 Participant 11 6.12.1 General Unfortunately participant 11 was not able to carry out the tests before September 2012. 6.12 Participant 12

6.13.1 General When the beams arrived at the institute the 4PB device was out of order. It was decided to send the beams to the next participant. Unfortunately the institute didn’t survived and went bankrupt.

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6.14 Participant 13

6.14.1 General Participant 13 used a device with a pneumatic actuator capable to perform sinusoidal loads up to 30 Hz. The deflection is measured relatively with respect to supports resting on the beam at x = L/6 and x = 5L/6. A 5

th order polynomial was used for the

determination of the amplitudes of the load and deflection sine signals, and the phase lag between force and deflection. This fit is carried out on the data for one cycle. Per frequency 200 data points are captured regardless the frequency. So for a frequency of 30 Hz the sampling frequency is 6 kHz. In this project 100 cycles are applied per frequency. As input for the determination of the modulus the average values over the last 10 cycles are taken. Because a time lag is present between the moments when the force and deflection are captured a correction is applied in the post processing before the back calculations are performed. In this report the uncorrected phase lags are presented in order to give an idea of this phenomenon. In the back calculation procedure no correction is applied for the deflection due to shear forces. In this report the deflection due to shear is taken into account. 6.14.2 Back calculated phase lags for the reference beams The back calculated phase lags are given in figure 6.14.1 as a function of the applied frequency. Figure 6.14.1 Back calculated phase lags as a function of the frequency. The presented values for the phase lags are the uncorrected values. The linear relation of the phase lag with the frequency indicates the presence of a time lag between the moments when the force and deflection are captured. The induced error is eliminated in the post processing before the back calculation procedure leading to a possible error of 0.5 degrees..

55

6.14.3 Back calculated modulus for the reference beams The obtained results for the back calculated modulus’s are given in figure 6.14.2 as a function of the frequency. The back calculated modulus is nearly constant over the whole range. Above 20 Hz the values decrease a bit but this might be due that the moving masses of clamps and plunger are a bit higher than the theoretical ones. It should be noted that for a frequency of 30 Hz the back calculated modulus with the CEN standard formulas is around 0.5% too low. This is due to the fact that the CEN formulas are based on a modified first order approximation of the total solution. The total solution consists out of infinite series. Figure 6.14.2 Back calculated moduli as a function of the frequency. A small difference is observed between the back calculated values for the three different beams. In principal this can’t be due to the non-infinite stiffness of the frame because the deflection is measured relative with the aid of a so called deflection bridge. It might be that the stiffness of this bridge is not high enough. However, the range in values is rather small and the values are very close to the expected value of 71.3 GPa.

6.15 Participant 14 6.15.1 General Unfortunately participant 14 was not able to carry out the tests before September 2012.

56

6.16 Participant 15 6.16.1 General Participant 15 has two different 4PB devices (A and B) with hydraulic actuators capable for a frequency range up to 30 Hz. For both devices a DFT procedure over 5 cycles is used for the back calculation of stiffness modulus and phase lag. No correction for shear deflection is applied. The deflection is measured in the centre with respect to the move less main frame (absolute measure). No information was available about the frequency for data acquisition (sampling). Per frequency around 50 to 100 cycles were carried out. In this report the data of the last recorded cycle are used for the back calculation.

The main difference between the two devices is the clamping method for the beams. In device A a roller system is used with brackets on the beams. The brackets are “glued” to the beams with bitumen. Also the effective length L between the two outer clamps is different (400 mm for device A and 420 mm for device B).

6.16.2 Back calculated phase lags for the reference beams As shown in figures 6.16.1 and 6.16.2 the back calculated (measured) phase lags do not depend on the applied frequency and are very consistent within one test. The values vary from + 0.2 to + 1.3 degrees. In view of the results by other participants this is very reasonable. The allowed deviation in the standard is 0.5 degrees which might be too high.

If possible it is advised to carry out tests with an elastic (steel or aluminum) beam of which the geometry is similar to the geometry of the standard asphalt beams. These tests will be focused on the determination of the phase lag and thus the modulus of this elastic beam is not relevant for these tests. It is possible that the measured deviation is due to the non-infinite stiffness of the frame (see 6.16.3) Figure 6.16.1 Back calculated phase lags for device A

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Figure 6.16.2 Back calculated phase lags for device B 6.16.3 Back calculated stiffness modulus for the reference beams The results of the back calculated stiffness moduli for the two devices are presented in figures 6.16.3 and 6.16.4. In the back calculation the correction for shear deflection is taken into account as well as the moving masses of the frames. Figure 6.16.3 Back calculated stiffness moduli for device A

58

For both devices the back calculated moduli seem to depend on the tested beam. This indicates that the non-infinite frame stiffness might be a source for this effect.

The results obtained with device A beam II and III are close to the expected value but the results with beam I are too low. It should be noted that the clamping of the beams in device A is done by gluing brackets to the beams with bitumen.

For device B the results for beam III are close to the expected value of 71 GPa while the results for beams II and III are a bit too high. The deviations between the tests with a strain of 50 μm/m and 100 μm/m are minimal.

All together it seems that it is worthwhile to investigate the possible influence of a non-infinite frame stiffness. This can be done by using a stiff steel beam.

Another point is the difference in the levels for the back calculated stiffness moduli for both devices. The use of bitumen glue might have a decreasing effect at the back calculated values (device A). In case of device B the differences in back calculated moduli for the three beams indicate an influence of the non-infinite frame stiffness. However, a non-infinite frame stiffness will always have a decreasing effect on the back calculated moduli which is not the case for at least the results obtained for beam II and III. An increasing effect can be caused by a too high clamping force. No information was available about the applied clamping force level. Figure 6.16.4 Back calculated stiffness moduli for device B It is advised to perform tests with 2 or 3 steel beams of which the material modulus is known with a certain accuracy (210 GPa). Given the results for the back calculated phase lags it might be worthwhile to adopt a complex spring for the unknown frame stiffness.

59

6.17 Participant 16 6.17.1 General Unfortunately participant 16 was not able to carry out the tests before September 2012. 6.18 Participant 17 6.18.1 General As other participants, participant 17 encountered problems with the phase lag back calculation. Instead of values in the range of -1

o to + 1

o (which is an acceptable range,

but still twice too high in view of the CEN standards) participant 17 found negative phase lags of which the absolute value increased with increasing frequency. This is shown in figure 6.18.1. Figure 6.18.2 Back calculated phase lags by participant 17 using the software belonging to the 4PB equipment

The negative slope of the ‘line’ indicates that a time lag between the data captures for the force and deflection is not nil. 6.18.2 Back calculated stiffness modulus for the reference beams Participant 17 used the software which was delivered with the 4PB device. The software doesn’t take into account mass inertia effects and deflections due to shear forces. The contribution by the shear forces to the total deflection is negligible in view of the dimensions of the reference beams.

However, mass inertia might play a role moreover because participant 17 has a hydraulic actuator. This enlarge the frequency range up to 60 Hz. Regardless the too low absolute level of the back calculated E modulus, the neglected influence of the mass inertia forces is clearly shown in figure 6.18.2 for increasing frequencies above 10 Hz.

60

The results in figure 6.18.2 have been calculated without taken into account the effect of masses or shear forces.

Another remarkable phenomenon is the high reproducibility per beam. As can been seen in figure 6.18.2 the back calculated values for the two applied deflection (strain) levels for a beam are for nearly the same. It was difficult to choose symbols to indentify different measurements.

A back calculation is also carried out with the Excel program Bending & Shear taking into account only the masses of the reference beams. The results are presented in figure 6.18.3. As expected the same decreasing E modulus values with increasing frequencies are noticed. In figure 6.18.3 also back calculated E values are given for beam I with an applied strain value of 100 m/m taken into account an extra moving mass of 15 kg. The back calculated E modulus values are still much too low but the adoption of this mass might explain the decrease in E modulus values with increasing frequencies. However, according to participant 17 the mass is in the order of 9,5 kg. Figure 6.18.2 Back calculated E values by participant 17 using the software belonging to this 4PB equipment.

When an extra mass of 15 kg is taken into account for the measurement with beam III with an applied strain of 100 m/m and tested at 61 Hz, the back calculated E value is 67,9 GPa which is close to the values back calculated at low frequencies for this beam.

Besides the unknown cause for the deviation in the level for the back calculated E modulus, one suggestion might be to “correct” the measured phase lags according to * = + 0,125.f (with f is applied frequency in Hz) and to use an extra mass of 15 kg in the back calculation procedure.

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Figure 6.18.3 Back calculated E modulus taking into account the mass of the beam and the deflection due to shear force. Note the back calculated E values for beam I if an extra mass of 15 kg is taken into account. 6.19 Participant 18 6.19.1 General Participant 18 has a quite new 4PB device with a hydraulic actuator. Frequencies up to 60 Hz are possible. For each strain level two frequency sweeps are carried out (series A&B).

Instead of (roll) bearings, elastic hinges are used for the required freedoms at the supports. The producer uses steel beams with a mass of 2.9665 kg for calibration of the devices with respect to the mass inertia forces (obtained by acceleration measurements) and phase lag compensation

1. The three steel beams have a beam stiffness E.I similar to

asphalt beams of 450 * 50 * 50 mm3 and with an stiffness modulus in the order of 3, 6

and 12 GPa. These beams are used to determine an internal correction for inertia forces due moving masses during cyclic bending and a phase lag compensation (table 6.19.1). Although the steel beams are measured in a multi-step compression test (pseudo-static), the obtained back calculated stiffness modulus from this test is not meant as a calibration value.

The load cell and deflection sensor are statically calibrated according to international standards. The steel beams are used after this calibration for the dynamic adjustments for

1 As a result of this correction procedure, the difference between the actual mass of an asphalt beam and the

value of 2.892 kg should be the input for the back calculation procedure. This might be a negative value.

62

force and phase lag as described above. The obtained back calculated beam stiffness values (E.I) can be used afterwards as a regular verification for the device.

The deflection is measured absolutely. Using a heavy steel beam a correction factor for the non-infinity stiffness of the 4PB frame is determined and implemented in the software. The data sampling frequency is 10 kHz but only a limited number data points per cycle (150-200) are stored for back calculation purposes. For the determination of amplitudes etc. five consecutive cycles are used. Instead of a sine regression or a Fast Fourier Transform a DFT is used for the determination of amplitudes and phase lags, The DFT is a Fourier Transform for the main (applied) frequency only. It is also called QAM (quadrature demodulation). The DFT is applied to the, for mass inertia forces corrected, load and the measured deflection separately.

Unfortunately the DFT values for the load and deflection do not form an accessible part of the output. Therefore the DFT values for the real and imaginary part of the resolved stiffness (force/deflection), the corrected phase lag and corrected load amplitude are used for recalculating the deflection amplitude. This value can be compared with the maximum peak-peak value for the deflection over five cycles which forms a part of the output. The differences are small. The deviations between the beam stiffness (resolved stiffness, [N/m] based on the ratio of the DFT values for load and deflection and those based on the peak-peak values (PP) are given in figure 6.19.1 ((DFT-PP)/DFT). Up to 20 Hz the deviations are very small indicating a good stable sine. Above 30 Hz the deviations are still acceptable (< 1%) but the range for the applied tests increases. Table 6.19.1 Phase lag composition

Frequency

Compensation

Phase Angle Frequency

Compensation

Phase Angle

Hz [o] Hz [o]

1 0.08 15 -0.325

2 0.06 20 -0.48

4 0.02667 30 -0.75

6 -0.03 40 -1.11

8 -0.11 50 -1.07

10 -0.17 60 (0) 6.19.1 Comparison of beam stiffness [N/m] based on DFT values and peak-peak values. The reported output contain the maximum peak-peak values for the load and deflection during the five captured sinusoidal signals. It should be marked that the reported peak-peak value is the difference between the minimum value and maximum value in these five cycles. Therefore it is not guaranteed that the minimum and maximum values are consecutive extremes. Nevertheless the deviations between the beam stiffness based on the DFT values and those based on the ratios of the peak-peak values for loads and deflections are really small as can be seen in figure 6.19.1 for frequencies up to 20 Hz.

For frequencies above 30 Hz it might be worthwhile to investigate the applied load and deflection signals in more detail.

6.19.2 Back calculated stiffness modulus for the reference beams Because the separate values for the load and deflection of the DFT analysis are not available (not in the reported output) only the back calculated values according to the soft ware of the manufacturer could be used. It should be noticed that for the back calculation of the stiffness modulus (using the CEN formulas) the real part of the resolved stiffness (DFT value) is first corrected for the non-infinity stiffness of the frame (see Annex

63

-1.5%

-1.0%

-0.5%

0.0%

0.5%

1.0%

0 10 20 30 40 50 60

Frequency [Hz]

Dev

iati

on [

%]

Beam I-50-A Beam I-50-B Beam I-100-A Beam I-100-B

Beam II-50-A Beam II-50-B Beam II-100-A Beam II-100-B

Beam III-50-A Beam III-50-B Beam III-100-A Beam III-100-B

“Frame stiffness”). Although not presented the figures obtained from a back calculation procedure using the peak-peak values are very close to the reported values. The figures in this report are corrected for the shear deflection while this correction is not applied in the software. In view of the lesser heights of the reference beams, compared to the normal dimensions of asphalt beams, the corrections are small. A factor 1.017 for beam I, 1.0125 for beam II and a factor of 1.0087 for beam III.

The results in figure 6.19.2 are close near the expected value of 71.3 GPa. Up to 30 Hz the back calculated modulus are not depended on the frequency. This indicates that in the processing of the ‘raw’ data the compensation for mass inertia effects (based on a beam mass of 2.9665 kg) works fine. In the back calculation the effect of a different beam mass is taken into account according to the CEN formulas. The range in the beam stiffness modulus is not so small as expected but quite satisfactorily for frequencies up to 30 Hz. There is no real relation between the levels and the beam (results for beam I are in the middle). It seems worthwhile to repeat these tests with a reference beams with a height of 50 mm. For the reference beams used here the heights varies from 35 to 25 mm. In order to measure the deflection for these beams, adjustments for the deflection sensor were necessarily. This might have influenced the test.

6.19.3 Back calculated phase lags for the reference beams The phase lag compensation based on the tests carried out by the manufacturer with a steel beam are already small. It should be marked that the phase lag compensation for a frequency of 60 Hz was not mentioned (put to nil in table 6.19.1). Therefore the reported values for this frequency are probably around 1 degree too low. In figure 6.19.3 the results by the software of the manufacturer of the device are given as a function of the frequency. As can be seen in figure 6.19.3 the back calculated value is nearly nil for frequencies up to 40 Hz.

Figure 6.19.1 Deviations between beam stiffness [N/m] based on the DFT values and the P-P values.

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-2.0

-1.0

0.0

1.0

0 10 20 30 40 50 60

Frequency [Hz]

Ph

ase

la

g [

o]

Beam I-50-A Beam I-50-B Beam I-100-A Beam I-100-B

Beam II-50-A Beam II-50-B Beam II-100-A Beam II-100-B

Beam III-50-A Beam III-50-B Beam III-100-A Beam III-100-B

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70

71

72

73

0 10 20 30 40 50 60

Frequency [Hz]

Sti

ffn

ess

mo

du

lus

[GP

a]

Beam I-50-A Beam I-50-B Beam I-100-A Beam I-100-B

Beam II-50-A Beam II-50-B Beam II-100-A Beam II-100-B

Beam III-50-A Beam III-5-A Beam-III-100-A Beam III-100-B

Figure 6.19.2 Back calculated stiffness modulus as a function of the frequency Figure 6.19.3 Back calculated phase lags according to the software of the manufacturer as a function of the frequency

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6.20 Participant 19

6.20.1 General

The device of participant 19 is equipped with a hydraulic actuator (frequency range 1 to 30 Hz). The deflection is measured absolutely with respect to the (move less) frame. The participant glued a separate aluminum pin to the beam at the centre (at half height of the beam; neutral line). It might be possible that at higher frequencies this construction is sensitive for resonance effects. The beam is clamped within a closed frame by servo motors with a constant force. The rotation freedom is accomplished by ball bearings and the horizontal freedom is established by bottom guide rails (sliding) at the outer supports and by top guide rails at the inner supports. A dynamic acquisition is used for processing of the raw data. The amplitudes and phase lag are determined with a sine regression method using the programmed frequency. The PID process control is adjusted with a square signal. According to the participant the displacement signal is a pure sine and the noise in the (white) load signal is around 10N, which is rather high in view of the actual force levels. For the back calculation the participant uses the formulas given in the AASTHO T321-03 (TP8) guide lines. No corrections are applied for the moving masses next to the beam or the possible non-infinity stiffness of the bending frame. For the calculations in this report a moving mass based on figures of similar equipments is used and the formulas for the combination of bending and shear deflections are used.

6.20.2 Back calculated phase lag for the reference beams Figure 6.20.1 Measured phase lags as a function of frequency for the three reference beams. Up to a frequency of 20 Hz the phase lag between force and deflection is very reasonable. The range is from + 0.5 to + 1.5 degrees. However, at the frequency of 30 Hz the phase

66

lag becomes negative and very large. This can be a result of a resonance phenomenon for the aluminum reference pin which was glued to the beam and served as a reference point for the deflection.

6.20.2 Back calculated stiffness modulus for the reference beams Fig. 6.20.2 Back calculated moduli for the reference beams as a function of the frequency.

As shown in figure 6.20.2 the back calculated E moduli are for the low frequencies (< 20 Hz) too low compared with the reference value of 71 GPa. The large variation at 30 Hz is very odd. One explanation might be that the aluminum pin, which served as a reference for the deflection measure and was glued to the beam, was not stiff enough (resonance effects). This explanation is in line with the back calculated values for the phase lags at high frequencies.

The back calculated E values show a small trend to increase with frequency with a constant difference between the three beams. The tests at 50 and 100 micro strain were performed after each other. The results are overlapping each other as can be seen in figure 6.20.2. It’s unlikely that the applications of the adjustments (help pieces) are the cause of the differences in moduli for the three beams. A more realistic explanation might be that the bending frame has a limited stiffness. As a consequence the measured absolute deflection is build up out of a deflection for the bended beam and the deformation of the frame.

The 4PB equipment can be simulated by two springs. One spring resembles the bending stiffness of the beam and is related to the bending stiffness moment E.I. of the beam. The other spring represents the non infinity stiffness of the bending frame. For an ideal system this spring should be infinite. In order to investigate the stiffness of the frame a very stiff steel beam should be tested at the usual force levels. If still a deflection is measured this deflection will represents the deflection due to ‘bending’ of the frame. In

67

this way a correction table can be established for obtaining the correct deflection for the back calculation.

Using the theoretical total deflection based on the reference modulus of 71 GPa and the deflection measurements up to 10 Hz (minor mass influences) figure 6.20.3 is made. The differences between the two deflections (measured minus theoretical) are plotted as a function of the applied forces. The differences can be seen as an indication of the deformation of the frame. It should be marked that the figure is not a proof. It just show that a very small deformation of the frame can have a rather large influence. Figure 6.20.3 Differences in measured and theoretical deflections (based on the reference value of 71 GPa) as a function of the applied forces. 6.21 Participant 20

6.21.1 General Participant 20 has a new 4PB device with a hydraulic actuator similar to the one of participant 18. For more details see chapter 6.19. Two frequency sweep tests (1 & 2) were applied. As mentioned before (chapter 6.19.1) the DFT values for the load and deflection do not form an accessible part of the output for this 4PB device. Therefore the DFT values for the real and imaginary part of the resolved stiffness (force/deflection), the corrected phase lag and corrected load amplitude are used for recalculating the deflection amplitude. This value can be compared with the maximum peak-peak value for the deflection over five cycles which forms a part of the output. As in the case of participant 18 with a similar device the differences are small. See chapter 6.19 for the level of deviations in the resolved stiffness. Even at a frequency of 60 Hz the deviation between the resolved stiffness based on the peak-peak values and the DFT was only 0.2%.

The phase lag compensation is given in table 6.21.1 and in figure 6.21.1. Notice that the phase lag compensation is not determined (yet) for 60 Hz.

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Table 6.21.1 Phase lag composition

Frequency

Compensation

Phase Angle Frequency

Compensation

Phase Angle

Hz [o] Hz [o]

0.1 0.13 8 -0.29

0.2 0.13 10 -0.38

0.5 0.09 20 -0.87

1 0.05 30 -1.31

2 0.00 50 -2

5 -0.15 60 (0) Figure 6.21.1 Phase lag compensation 6.21.2 Back calculated stiffness modulus for the reference beams Because the separate values for the load and deflection of the DFT analysis are not available (not in the reported output) only the back calculated values according to the soft ware of the manufacturer could be used. It should be noticed that for the back calculation of the stiffness modulus (using the CEN formulas) the real part of the resolved stiffness (DFT value) is first corrected for the non-infinity stiffness of the frame (see Annex “Frame stiffness”). This is done in the pre-processing by correcting the measured deflection. The mass of the calibration beam used for this correction procedure was 2.891 kg. As a consequence a negative mass (differences between actual reference beams I, II and III and this value of 2.891 kg) has to be used in the post-processing.

Although not presented, the figures obtained from a back calculation procedure using the peak-peak values are very close to the reported values. The figures in this report are corrected for the shear deflection while this correction is not applied in the software. In view of the lesser heights of the reference beams, compared to the normal dimensions of asphalt beams, the corrections are smaller (factor 1.017 for beam I, 1.0125 for beam II and a factor of 1.0087 for beam III).

The results for test 1 are given in figure 6.21.2. Participant 20 carried out two separate frequency sweeps (1a & 1b) for beams I and II in test 1.

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Figure 6.21.2 Back calculated stiffness modulus as a function of the frequency for test 1. The results for beam II and III in test 1 are satisfactorily in view of the expected reference value of 71.3 GPa. The results for beam I are a bit to high. It should be mentioned that special measures had to be taken for the positioning of the deflection sensor. Before a test with another beam this had to be carried out and may have induced these deviations. This effect was more noticed in the results for test 2 (figure 6.21.3). Here only the results for beam I 6.21.3 Back calculated phase lags for the reference beams The phase lag compensation based on the tests carried out by the manufacturer with a steel beam are already small. It should be marked that the phase lag compensation for a frequency of 60 Hz was not determined (put to nil in table 6.21.1). Therefore the reported values for this frequency are probably around 1 degree too low. In figures 6.21.4 and 6.21.5 the results by the software of the manufacturer of the device are given as a function of the frequency. As can be seen in both figures the values are nearly nil for frequencies up to 40 Hz. Only the results for beam II at 100 micro strain in test 2 deviate more but the phase lags are less than 0.7 degrees. Once more it should be emphasized that no phase compensation for a frequency of 60 Hz was established in the calibration. I are far too high.

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Figure 6.21.3 Back calculated stiffness modulus as a function of the frequency for test 2. Figure 6.21.3 Back calculated phase lags according to the software of the manufacturer as a function of the frequency for test 1.

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Figure 6.21.3 Back calculated phase lags according to the software of the manufacturer as a function of the frequency for test 2. 6.22 Participant 21

6.22.1 General Participant 21 has a new 4PB device with a hydraulic actuator similar to the one of participant 18. For more details see chapter 6.19. Two frequency sweep tests (1 & 2) were applied up to a frequency of 40 Hz. Per frequency 3 readings were obtained. In this report the mean values of these 3 readings are used. The standard deviation was for all frequencies less than 0.02 GPa. The standard deviation in phase lags was around 0.01 degrees.

As mentioned before (chapter 6.19.1) the DFT values for the load and deflection do not form an accessible part of the output for this 4PB device. Therefore the DFT values for the real and imaginary part of the resolved stiffness (force/deflection), the corrected phase lag and corrected load amplitude are used for recalculating the deflection amplitude. This value can be compared with the maximum peak-peak value for the deflection over five cycles which forms a part of the output. As in the case of participant 18 with a similar device the differences are small. See chapter 6.19 for the level of deviations in the resolved stiffness

The phase lag compensation is given in table 6.21.1 and in figure 6.21.1. Notice that the phase lag compensation is not determined (yet) for frequencies above 40 Hz. For frequencies below 10 Hz the phase lag compensation is nearly constant in contrast for similar devices by other participants. It’s recommended to check this compensation again including frequencies above 40 Hz.

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Table 6.22.1 Phase lag composition

Frequency

Compensation

Phase Angle Frequency

Compensation

Phase Angle Frequency

Compensation

Phase Angle

Hz [o] Hz [o] Hz [o]

1 0.21 6 0.22333 20 0.16

2 0.20 8 0.21 30 0

4 0.22 10 0.25 40 -0.53

15 0.205 Figure 6.22.1 Phase lag compensation 6.22.2 Back calculated stiffness modulus for the reference beams Because the separate values for the load and deflection of the DFT analysis are not available (not in the reported output) only the back calculated values according to the soft ware of the manufacturer could be used, taking the mean value of 3 recordings per frequency. It should be noticed that for the back calculation of the stiffness modulus (using the CEN formulas) the real part of the resolved stiffness (DFT value) is first corrected for the non-infinity stiffness of the frame (see Annex “Frame stiffness”). This is done in the pre-processing by correcting the measured deflection.

Although not presented, the figures obtained from a back calculation procedure using the peak-peak values are very close to the reported values. The figures in this report are corrected for the shear deflection while this correction is not applied in the software. In view of the lesser heights of the reference beams, compared to the normal dimensions of asphalt beams, the corrections are smaller (factor 1.017 for beam I, 1.0125 for beam II and a factor of 1.0087 for beam III). The results for test 1 are given in figure 6.22.2. Participant 21 carried out two separate frequency sweeps (1 & 2). In figure 6.22.3 the results are given for test round 2.

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Figure 6.22.2 Back calculated stiffness modulus as a function of the frequency for test 1. Figure 6.22.3 Back calculated stiffness modulus as a function of the frequency for test 2. 6.21.3 Back calculated phase lags for the reference beams The phase lag compensation based on the tests carried out by the manufacturer with a steel beam are already small. In figures 6.22.4 and 6.22.5 the results by the software of the manufacturer of the device are given as a function of the frequency. As can be seen in both figures the values are very close to nil for frequencies up to 40 Hz.

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Figure 6.22.4 Back calculated phase lags according to the software of the manufacturer as a function of the frequency for round 1. Figure 6.22.5 Back calculated phase lags according to the software of the manufacturer as a function of the frequency for round 2.

6.22.4 Extra measurements with the beams II and III 90o degrees turned

Participant 21 carried out also tests with beam II and III in which the height and width

were changed (90o degrees turning of the sample). Thus instead of a height of 30 mm and

a width of 34 mm, beam II was tested as a beam with height 34 mm and a width of 30

mm.

As can be seen in figure 6.22.5 the back calculated modulus are a bit too low in this

special test upset. It’s not known if the help pieces are used in these tests ( positioning of

the neutral axis at a height of 25 mm in the clamping device). Nevertheless, the results

are not too bad.

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Figure 6.22.5 Modulus obtained for beam II and III in tests where the beams were

turned over 90o degrees.

6.23 Participant 22 6.23.1 General Participant 22 uses a pneumatic actuator which limited the frequency to a maximum of 10 Hz. In the software no correction for mass inertia forces are applied. A correction coefficient of 2/3 is applied for the influence of shear forces. However, this factor should be 0.85 which is used in this report. According to general information about this 4PB device a simple sine regression is performed on the raw data. The deflections are measured relatively using reference points at the top of the beam (X = L/6 and 5L/6). In this way the possible influence of a non-infinity stiffness of the frame is eliminated. 6.23.2 Back calculated phase lags for the reference beams

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Figure 6.23.1 Back calculated phase lags by participant 22 using the software belonging to the 4PB equipment As shown in figure 6.23.1 the measured phase lags are negative but near to nil. There is no evidence of a frequency dependency. Also the variations are small. All together it might be attractive to introduce a mean correction term of + 1 degree before processing the data. Another option might be to use a (fast) Fourier Transform. 6.23.3 Back calculated stiffness modulus for the reference beams In spite of the limited horizontal translation freedom at the inner clamps, the results for the back calculated moduli (figure 6.23.2) are very acceptable (using a shear coefficient of 0.85). There is a trend that at lower deflections (open symbols) the back calculated moduli is lower than at higher deflections (filled symbols). At forehand there is no explanation why the differences between the back calculated moduli seem to depend on the bending stiffness moment (E.I). Figure 6.23.2 Back calculated moduli as a function of the frequency 6.24 Participant 23 6.24.1 General Unfortunately participant 23 was not able to carry out the tests before September 2012.

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6.25 Participant 24 6.25.1 General A pneumatic actuator was used, which limited the frequency range to 10 Hz. Therefore mass inertia forces play a minor role in the back calculation procedure. Nevertheless the masses according to the participant are taken into account in the back calculation with the Excel program Bending & Shear. Per frequency and per strain level three separate test of 300 cycles were carried out. Measures were taken at cycle 100, 150 and 200. So for each test condition 9 measures are available. In this paragraph only the mean values of the 9 measures are given.

Like many other participants, participant 11 encountered problems with the phase lag determination. When extreme outliners are omitted an increasing positive phase lag with frequency was obtained as shown in figure 6.12.1. In view of the general trend for all measurements it can be concluded that a post correction of the form * = + 0,5.f (with the frequency f in Hz and the measured phase lag in

o) is usefully.

6.25.1 Back calculated stiffness modulus for the reference beams The back calculated modulus as a function of the frequency are presented in figure 6.12.2. The modulus is back calculated taken into account the deflection due to shear forces. In view of the geometrical dimensions of the reference beams this effect is only marginal (1,5 GPa for beam I; 1,2 GPa for beam II and 0,8 GPa for beam III). The mean back calculated E modulus for all test conditions is 70,7 GPa which is very close to the “target” value of 71 GPa. In view of the many measurements per test condition, a mean standard deviation of 0,9 GPa and a maximum standard deviation of 1,7 GPa per test condition it can be concluded that for calibration with a reference beam of known stiffness modulus that value should be back calculated within at least 2 %. Given the target value of 71 GPa the range of allowable back calculated values is than from 69,5 to 72,5 GPa.

It is worthwhile to investigate if this value of 2 % can be adopted in the CEN standards.

0

1

2

3

4

5

0 2 4 6 8 10

Frequency [Hz]

Phas

e la

g [

o]

Beam I-50 Beam I-100 Beam II-50 Beam II-100 Beam III-50 Beam III-100 .

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Figure 6.25.2 Back calculated modulus as a function of the frequency.

6.26 Participant 25 6.26.1 General Unfortunately the PID (process control) for the 4PB device of participant 25 was not working well. Following the given protocol of maximal 300 load applications (cycles) per frequency, the required steady state (constant deflection) couldn’t be reached. This was clearly indicated by the large fluctuations in the (calculated) mean values for the stresses and strains. Moreover, the raw data is not accessible and the output consists, next to peak-peak and mean values for the calculated stress and strain, only out of a back calculated stiffness modulus and a phase lag (between force and deflection).

Participant 25 carried out 10 repetition tests for each frequency. The back calculation procedure is based on the pseudo-static bending case without a correction for shear deflection. The deflection is measured relative with the reference support points on the beam at x = L/5 and x = 5L/6. A pneumatic actuator is used with a very limited range from 6 to 10 Hz. Given these facts the back calculated E values in this particular case are not corrected for the influence of the shear deflection. The procedure for fitting the measured raw data is not known. Probably a kind of a simple linear sine regression of the form: .sin( )Y A t + Shift is used. Due to the fact that the steady state was not reached within the 300 cycles, unrealistic values (above 60

o) were sometimes produced

for the phase lag. Also the number of cycles to reach the steady state increases with frequency. This may indicate that the sample frequency is not high. Furthermore the assumed low sample frequency may also be the cause that the system converges faster in tests with higher deflection amplitudes. Therefore in this paragraph only the results in the last cycle for the tests with a strain amplitude of 100 micro strain are reported.

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6.26.2 Phase lag

Figure 6.26.1 gives the mean phase lags for cycle 300 as a function of the frequency.

Figure 6.26.1. Phase lags in cycle 300 for the tests with a amplitude of 100 micro strain as a function of the frequency.

In these tests with a strain amplitude of 100 micro strain the steady state is nearly reached after 300 cycles (minor fluctuations in the mean values). The values in figure 6.26.1 are very acceptable. 6.26.3 Back calculated stiffness modulus for the reference beams As mentioned before no correction is applied for the output of the back calculated modulus values. So, the output values for the modulus should be lesser than the expected value of 71 GPa. Again only the output for cycle 300 in the tests with a 100 micro strain amplitude are reported in this paragraph (figure 6.26.2.) The results presented in figure 6.26.2 for the back calculated modulus are, like the phase lags in figure 6.26.1, acceptable. Specially because the steady state was not yet obtained in cycle 300. The main disadvantages of the device are the large number of cycles before the steady state is reached and the (assumed) low sampling frequency. It is recommended to improve, if possible, the sampling frequency (number of data points per second). However, to get a more detailed insight it is advised to carry out long lasting tests with aluminum (or plastic) beams in order to obtain the required number of cycles before the steady state is reached. The results obtained in this project indicate that this number may depend on the height of the deflection amplitude.

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Figure 6.26.2. Back calculated modulus in cycle 300 for the tests with a amplitude of

100 micro strain as a function of the frequency.

6.27 Participant 26

6.27.1 General Due to several circumstances participant 26 was not able to perform the tests correctly. The obtained results were a factor of 10 lower than the expected values. Because the equipment of participant 26 will be replaced in short time by a new device, it was suggested that the beams will be send again to participant 26 when the new device has arrived. The consequence is that no results of participant 26 are available for this project.

6.28 Participant 27 6.28.1 General The device of participant 27 is equipped with a hydraulic actuator capable for frequencies up to 60 Hz. However, in this project the applied frequency range is limited to 20 Hz. The deflection is measured relatively. The reference points are not located at x = L/6 and x = 5L/6 but closer to the outer supports. Therefore the multiplication factor needed to obtain the absolute deflection in the centre is smaller than 2. Deflections due to shear forces follow another profile than the deflections due to pure bending. However, the error introduced because the ratios of the shear deflection and bending deflection at these locations are different, is negligible (< 0.04%). The advantage of a relative deflection measurement is that the influence of the non-infinity stiffness for the device is eliminated.

The resolution of the deflection measurement system is 0.00006 mm. This implicate that for a deflection of 0.045 mm (Beam II equivalent to an asphalt beam with a Smix of 9 GPa; 50 µm/m) the deviation can be in the order of 0.13% which is very small.

Another detail is the correction for inertia effects (moving masses of the device) by the use of internal acceleration sensors. But due to the applied frequency range (maximum 20

81

Hz) the effect is negligible. The back calculated phase lags are given in figure 6.28.1 as a function of the frequency and in figure 6.28.2 as a function of the applied load.

Figure 6.28.1 Back calculated phase lags as a function of the applied frequency

There is no real visual dependency between phase lag and applied frequency (or beam). The scatter is less than 1 degree. Strange enough the back calculated phase lags seem to be dependent on the applied loads as illustrated in figure 6.28.2. No explanation is yet found. Nevertheless, the variation is rather small but consistently above 0 degrees. Although correcting the back calculated phase lags by adding 0.5 degrees seems attractive without a plausible cause this is not advised. Figure 6.28.2 Back calculated phase lags as a function of the applied load.

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6.28.2 Back calculated stiffness modulus for the reference beams Firstly the calculated centre deflections are corrected for the influence due to shear forces. The back calculated E modulus values, taking into account the mass of the beam are presented in figure 6.28.3 as a function of the applied frequency. The variation is of 2 GPa is small (3%). There is no consistent dependency with the frequency (up to 20 Hz). Compared to the expected value for the stiffness of 71 GPa for the reference beam the back calculated values are consistently a bit too high. However, this can be caused by the use of the help pieces, which can introduce a stiffening effect on the response. In the annex “Influence of accessories on bending beam moment” this effect is simulated for a static load. In case of beam III more little sheets between the beam and the help frame are used lowering the stiffening effect when the help pieces can slip over each other. This might explain why the results for beam III are nearer the expected value of 71.3 GPa. The default clamping force was between 150 and 250 N.

As mentioned before mass inertia forces do not play an important role in the low frequency range (20 Hz). Although the back calculated values are a bit too high the obtained values are reasonable. In view of the possible influence of the help pieces it will be worthwhile to repeat the measurements without the aid of the help accessories. Given the possibilities of the clamping device of the used apparatus this is possible.

In figure 6.28.4 the back calculated E values are given as a function of the applied load. It seems that for each beam the back calculated E value depends on the applied value. Without further information and testing no explanation can be given. Figure 6.28.3 Back calculated E values as a function of the applied frequency.

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Figure 6.28.4 Back calculated E values as a function of the applied load 6.29 Participant 28 6.29.1 General Participant 28 carried out a program with several repetitions (table 6.29.1) using two similar devices. The applied frequency sweep started at 0.1 Hz and ended at 30 Hz. Before demounting the beam for the following repetition or new test, again tests at 10 Hz and 0.1 Hz were carried out in order to check the repeatability within one frequency sweep. The two devices are equipped with hydraulic actuators with a frequency range from 0.1 to 30 Hz. For the back calculation 64 data points per cycle for all frequencies are used in combination with a Fourier transform (FFT).

Unfortunately the output didn’t contain the phase lag between the force and deflection signals. Also the received Excel file contained rounded figures (3 digits) for the force and deflection amplitudes. Nevertheless the back calculated values using these figures are in agreement with the reported values by the participant. In the back calculation program of the participant no correction for the deflection due to shear forces is applied. The corrections for the reference beams are very small (table 6.29.2). In this report the modulus are back calculated taking into account the influence of the shear deflection.

Table 6.29.1 Test program by participant 28; number of repetitions

Actuator 1 Actuator 2 Beam 50 m/m 100 m/m 50 m/m 100 m/m

I 2 2 4 2 II 4 4 - - III 2 2 - -

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6.29.2 Back calculated phase lags by the participant The back calculated phase lags by the participant are in good agreement with the expected value of 0 degrees. No correction has to be applied for a time delay between the moment at which the force and deflection are captured. The results as found by the participant are given in the figures 6.29.1. (actuator 1) and 6.29.2. (actuator 2). It should be mentioned that the values are rounded up on one digit. For actuator 1 there seems to be a significant but very small difference between the tests with a strain amplitude of 50 micro strain and those with a strain amplitude of 100 micro strain. For actuator 2 the phase lags are positive for both applied strain amplitudes.

Table 6.29.2 Shear correction coefficients Vs/Vb

Beam I Beam II Beam III

Coefficient [%] 1.88 1.38 0.96 Figure 6.29.1. Phase lags reported by participant for actuator 1 as a function of frequency. Figure 6.29.2. Phase lags reported by participant for actuator 2 as a function of frequency.

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6.29.3 Back calculated stiffness modulus for the reference beams Although overall the back calculated modulus are close to the expected value of 71.3 GPa the deviations in the results for the repetition measurements are odd. See for example the results for actuator 1 at a frequency of 20 Hz and a strain amplitude of 50 micro strain (figure 6.29.3). In total four repetitions were carried out. The first two repetitions lead to values between 72 and 73 GPa but the third and fourth repetitions gave values around 69 GPa. It should be marked that the results for the frequencies 10 and 0.1 Hz at the end of a frequency sweep didn’t differ from the results for the same frequencies at the start of the frequency sweep. Therefore it’s more plausible that these differences are due to the demounting and mounting of the beams between the repetitions. Strange enough the deviations were smaller when a strain amplitude of 100 micro strain was applied. The same phenomenon was also noticed for the measurements using actuator 2 (figure 6.29.4).

The results as given in this report are corrected for the influence of the shear deflection. The influences are small (table 6.29.2). Comparing the back calculated modulus by the participant and the modulus in this report lead to similar (mean) values for beam I and II (table 6.29.3). Only for beam III the back calculated modulus in this report are around 0.5% lower than those reported by the participant. It should be marked that this is probably due to the small numbers of digits which were available for the back calculation ion this report. Table 6.29.3 Difference in mean back calculated modulus by the participant and the results used in this report.

Actuator 1 Actuator 2 Beam 50 mm/m 100 mm/m 50 mm/m 100 mm/m

I +1.75% +2.05% +2.14% +2.08% II +0.85% +1.02% - - III -0.55% -0.49% - -

Figure 6.29.3 Back calculated modulus as a function of the frequency for actuator 1

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Figure 6.29.4 Back calculated modulus as a function of the frequency for actuator 2

6.30 Participant 29

Participant 29 encountered serious problems with the 4PB software at the time the beams

arrived. The problems couldn't be solved in due time. Therefore it was decided to send

the beams to the next participant on the list. When the problems are solved it will be

reconsidered to send the beams again to participant 29 for retesting. Another problem was

the length (450 mm) of the reference beam in relation with the limited space in the

climate cabinet. Once again it seems that a witch had put a spell on this project.

6.31 Participant 30 6.31.1 General Unfortunately participant 30 was not able to carry out the tests before September 2012.

7. CONCLUSIONS & RECOMMENDATIONS

It is highly recommended that each device is calibrated with its own reference beam. The geometrical dimensions should be chosen in such away that at least the height is equal to the height of the normal asphalt beams.

Help pieces (adapters) are not recommended for the design of a reference beam. It is advised to have at least 3 reference beams covering a wide range of E.I

values. The E.I. values should be taken in such a way that the comparable E.I value for an asphalt beam leads to a stiffness modulus in the range of 3 GPa to 12-20 GPa.

In spite of precautions it appeared that the phase lag determination is a difficult item. In the CEN standards an inaccuracy of maximum 0.5

o is prescribed which

requirement is hard to fulfill. Therefore it is advised to enlarge the interval at least to 1

o in the next version of the CEN standard.

Calibration with an elastic material (phase lag = 0o) over a wide range of

frequencies is highly recommended. In this way errors caused by a time lag in the

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captures for the deflection and force can be detected and a correction protocol can be established for each 4PB device separately.

Corrections for mass inertia effects are not necessary for frequencies below 10 Hz.

It is recommended to correct for the influence of shear forces on the total measured deflection. At this moment this influence is not covered in the CEN standards.

In principle it is possible to back calculate the E modulus with a high fidelity (inaccuracy of 1 %) comparable with the phase lag determination. But in practice this range is too narrow. It is suggested to increase the inaccuracy level to 3%. Therefore a 4PB device in this project is functioning well if the back calculated E value is within 3 % of the target value of 71 GPa (69-73 GPa).

It remains possible to calibrate each 4PB device separately by introducing a damping factor for each individual device (see CEN standards). This option enables a device dependent correction parameter. Even if the back calculated E value is much too low and the cause can not be established, the introduction of a negative damping factor might help. However, extended calibration tests are highly recommended in that case.

Normally the clamping force (which not contributes to the bending process) should be taken as small as possible. But in the case that accessories have to be used, it might be that bigger clamping forces are needed (especially at low deflection levels) in order to avoid unwanted play or space in the accessories. Just one more reason to use beams especially made for the 4PB device under consideration.

If in spite of all efforts it is not possible to meet the 4PB requirements as mentioned in the CEN standard, it might be possible to use a specific device dependent damping factor. However, to establish this factor extended calibration tests are necessary.

8. ACKNOWLEDGEMENT The author would like thank all the participants for their enthusiasm, the manufacturers for their contributions and many others who make this project ‘work’.