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Drop Weight Impact Strength Measurement Method forPorous Concrete Using Laser Doppler VelocimetryAyda Safak Agar Ozbek1; Jaap Weerheijm2; Erik Schlangen3; and Klaas van Breugel4
Abstract: In this study, an experimental configuration that reveals the dynamic response of porous concretes in a drop weight impact test wasintroduced. Through the measurement of particle velocity at the interface, between the impactor and the concrete target, the dynamic responsewas obtained in an easily applicable way. Laser Doppler velocimetry (LDV) was used in monitoring the time history of the particle velocity atthe interface, which was subsequently analyzed to determine the dynamic strengths of the concrete specimens tested. The velocitymeasurements were analyzed using a special reverberation application of the impedance mismatch method. The test results showed thatthe experimental configuration was sufficient to measure the dynamic strengths of porous concretes and a normal concrete with moderatestrength. The method was validated by using impactors having different dynamic impedances in testing the same material and was alsoverified to be precise enough to distinguish between different types of porous concrete mixtures. DOI: 10.1061/(ASCE)MT.1943-5533.0000511. © 2012 American Society of Civil Engineers.
CE Database Subject Headings: Porous media; Concrete; Impact tests; Falling bodies.
Author keywords: Porous concrete; Impact testing; Laser Doppler velocimetry; Drop weight.
Introduction
New monitoring methods used in impact experiments made an ex-tensive contribution to the research on the dynamic properties ofcementitious materials. In the experimental investigation presentedin this study, an easily applicable measurement configuration is de-veloped to determine the particle velocity at the interface betweenthe impactor and the target in a drop weight impact test. The test isapplied on porous concretes using laser Doppler velocimetry(LDV) as the monitoring technique. The velocity measurementswere processed using the reverberation application of the imped-ance mismatch method to quantify the dynamic strengths of theconcretes tested.
This study presents the experimental configuration that has beendeveloped as a part of the research project investigating the use ofporous concrete as an energy-absorbing material for protectivestructures. Porous concrete is a special type of cementitiousmaterial composed of gap-graded aggregates, covered with a thinlayer of cement paste, assembled by the cement paste layers
partially being in contact (Ghafoori and Dutta 1995). Becauseof the high percentage of its mesosize air pores, it has a moderatestatic strength compared with normal concrete while its dynamicperformance is distinctive, which was also investigated in thepioneering work of Jennings and Thomas on safety concrete(O’Neil et al. 2004). Under impact loading, porous concrete frac-tures into small fragments. Although the key feature of the materialthat is aimed to be designed is its property of fracturing into smallsize fragments, quantifying the dynamic strengths of the differentporous concrete mixtures was also essential to be able to betterelaborate the dynamic properties of the material.
Apart from being easily applicable, the experimental configura-tion and the subsequent analysis technique have the advantage ofinvolving the known dynamic-impedance properties and thevelocity measurements of only the impactor. Therefore, the targetspecimen that is being tested is not directly involved in themeasurements or the analysis.
Planar Impact Measurement Techniques
In planar impact experiments, there are various measurementtechniques involved to quantify the velocity and pressure to be ableto define the dynamic performance of a material (Espinosa 2000).Laser interferometry has become generally accepted as a competenttool for monitoring the motion of the surfaces of shocked speci-mens using different experimental configurations. The systemcalled velocity interferometer system for any reflector (VISAR)is the most widely used interferometer configuration for shockprofile measurements (Barker and Hollenbach 1972). It has beeneffectively used in measuring free surface velocity-time historiesin which various materials have been tested and analyzed for hyper-velocity collisions (Grady 1996, 1998; Hereil and Buzaud 2006;Reinhart et al. 1999; Furnish et al. 1999; Hall et al. 1999; Gebbekenet al. 2006; Chhabildas et al. 2002). Particle velocity wave profilesare also captured using electromagnetic velocity gauges embeddedat various depths within the sample to derive the impact stress(Gustavsen et al. 1999). Using piezoresistive manganin stressgauges in measuring the dynamic stress is one of the direct
1Ph.D. Student, Faculty of Civil Engineering and Geosciences, DelftUniv. of Technology, Stevinweg 1, 2628 CN Delft, The Netherlands(corresponding author). E-mail: [email protected]
2TNO, Defence Security and Safety, Rijswijk, The Netherlands; Facultyof Civil Engineering and Geosciences, Delft Univ. of Technology,Stevinweg 1, 2628 CN Delft, The Netherlands. E-mail: [email protected]
3Associate Professor, Faculty of Civil Engineering and Geosciences,Delft Univ. of Technology, Stevinweg 1, 2628 CN Delft, The Netherlands.E-mail: [email protected]
4Professor, Faculty of Civil Engineering and Geosciences, Delft Univ.of Technology, Stevinweg 1, 2628 CN Delft, The Netherlands. E-mail:[email protected]
Note. This manuscript was submitted on May 9, 2011; approved onMarch 7, 2012; published online on March 10, 2012. Discussion periodopen until March 1, 2013; separate discussions must be submitted for in-dividual papers. This paper is part of the Journal of Materials in CivilEngineering, Vol. 24, No. 10, October 1, 2012. © ASCE, ISSN 0899-1561/2012/10-1328-1336/$25.00.
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techniques in which the dynamic characteristics of the materials areacquired by doing tests at different stress ranges (Rosenberg 1981;Ishiguchi et al. 2000). Stress gauges work by the same principle asstrain gauges in which the thickness, and therefore the electricalresistance of the gauge, changes as stress is exerted. Accelerome-ters are also used to monitor the impactor and consequently thetarget specimen where the results are compared with laser displace-ment measurements (Sukontasukkul et al. 2004). Contact electricalresistance measurement is conducted to measure the dynamic com-pressive loading between two cementitious surfaces (Luoa andChung 2000). Doppler radar is an alternative technique to obtainvelocity histories (Unosson and Nilsson 2006).
The LDV technique, also known as laser Doppler anemometry(LDA), is a noncontact diagnostic technique, based on the Dopplerprinciple, for measuring instantaneous velocity. The techniquehas been used in various applications after it was first introduced(Yeh and Cummins 1964).The Doppler effect is based on monitor-ing the change in the wavelength of the reflected laser light, whichis a function of the relative velocity of the moving object that thelaser beam meets. The vibrometer used in the measurements is atwo-beam laser interferometer that measures the frequency differ-ence between the internal reference beam and the measuring beam.A Doppler velocimeter system is capable of measuring the motionof a particle or surface that has a rapidly changing velocity. Thisproperty can, therefore, be employed to measure the motion of afree-falling projectile throughout an impact test to obtain the fullvelocity-time history. In research studies in which LDV is used,the velocity signals captured are either differentiated to obtain theacceleration and multiplied by the impactor mass to attain theload-time relationship or used in energy calculations based onthe change in kinetic energy (Wu et al. 1994; Birch and Jones 1990;Hodgkinson et al. 1982). The LDV technique has been selected asthe monitoring technique in the current study to acquire the velocityhistory data of the impact surface.
Outline of the Study
The presented article is structured as follows. The descriptions ofthe LDV test setup and the introduced measurement configurationare followed by the description of the analysis techniques. Theimpedance mismatch method and its reverberation applications thatwere used in the analyses of the impact test results are defined indetail. The results from the experiments that were performed whiletesting the same porous concrete materials with different impactorsare presented for the verification of the experimental configurationand the analysis method. The particle velocity-time histories ob-tained from the tests on different porous concretes and a normalconcrete are also demonstrated. Discussions of the results are thenfollowed by the conclusions.
Experimental Investigations
Materials
To validate the measurement technique samples of porous concreteand a moderate-strength normal concrete were cast. In the porousconcrete mixtures produced for this study, the aggregates were atone standard size range of 4–8 mm. The cement paste content wassignificantly decreased compared with normal concrete mixtures.The aggregate and cement contents of porous concrete are betterexpressed in terms of the aggregate-to-cement ratio by mass, whichwas 5.7 in the mixtures produced. Two types of cement pastes(denoted as cp1 and cp2), two different types of aggregates(crushed basalt and river gravel), and two levels of compaction
were involved in the production. The two compaction techniqueswere machine compaction using an impact hammer while the ham-mer was also rotated and hand compaction using a steel cylinder,which were denoted by high and low, respectively. The summary ofthe compositional properties of the mixtures is given in Table 1.
The preparation of the porous concretes was done following astandardized procedure of first mixing the cement paste separatelyand subsequently mixing the cement paste with the aggregates atprespecified standard durations. Because the fine aggregates areexcluded, the workability of the porous concrete mixture is highlyreduced. Therefore, compaction is required during casting (Crouchet al. 2007). Casting was done in layers in which each 2.5 cm layerwas compacted. Cylindrical specimens that were 83 mm in diam-eter and 170 mm in height were produced.
To verify whether the experimental technique could also be usedfor testing normal concrete, a moderate-strength normal concretemixture was produced. The content of the normal concrete mixture(NC1) is presented in Table 2. Both porous and normal concretespecimens were wrapped with plastic and aluminum foils and keptat 20°C at the laboratory conditions until their testing dates of28 days. Core samples of 60 mm in diameter were then drilled fromthe specimens and cut at the fixed height of 7 cm to be tested in thedrop weight impact test.
Test Setup and Instrumentation
The impact tests were carried out using an instrumented dropweight impact test setup. In the experiment, the specimen wasplaced vertically on a steel base structure, which also serves asa steel buffer plate that functions as a wave sink at the impactexperiments. The impactor was dropped from approximately1.2 m to provide striking velocities ranging between 4.0 and4.7 m=s. The results obtained are valid for the impact velocityrange covered in this work. The impact velocity range limits the
Table 1. Compositional Properties of the Porous Concrete Mixtures
Mixture code PRC1 PRC2 PRC3
Aggregate compositionCrushed basalt (2–4 mm) (g) — — —Crushed basalt (4–8 mm) (g) 2,000 — 2,000River gravel (4–8 mm) (g) — 2,000 —Cement paste compositionCement CEM I 52.5 R (g) 351 351 351Silica fume (g) — — —Water (g) 105 105 105Superplasticizer (g) 1.00 1.00 0.97Set retarder (g) — — 1.20Cement paste code cp1 cp1 cp2Compaction Low Low High
Table 2. Compositional Properties of the Normal Concrete Mixture
NC1 composition Amounts (kg)
CEM I 42.5N 3.10Sand, 0.125–0.250 mm 1.32Sand, 0.250–0.500 mm 2.44Sand, 0.500–1 mm 2.82Sand, 1–2 mm 2.82Sand, 2–4 mm 3.76River gravel, 4–8 mm 5.64Water 1.75Superplasticizer 1.8%
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range of strain rate at which the testing is done because impactvelocity determines the initial loading slope. The selection ofthe impactor material and the magnitude of the impact velocity de-termine the pressure applied to the concrete sample. Therefore, byvarying those properties, the input pressure could be controlled.The impactors that were made of either steel or aluminum were110 mm in diameter and 220 mm in height.
A Doppler laser vibrometer was utilized to measure the velocityof the falling impactor. For the purpose of measuring the velocity ofthe interface between the impactor and the target, an easily appli-cable measurement method has been introduced and verified in thisstudy. The impactor diameter (110 mm) was selected to be largerthan the diameter of the target (60 mm) so that there was an outerrim of 25 mm present to take velocity measurements at the inter-face. The point where the laser beam hits the impactor was adjustedto be as close as possible to the specimen perimeter, in the insidelocations of the rim. The laser beam coming from the laser headfollowing a horizontal path was reflected by an angle of 90° froma 45° mirror such that it was directed vertically upward. The re-flected vertical beam hitting the retroreflective sticker attachedto the bottom surface of the impactor rim was then reflectingand following the same path back to the laser head. The capturedparticle velocity-time histories of the interface between the targetand the impactor were subsequently processed to determine theimpact stress applied on the target. The schematic figure showingthe general view of the testing system and an enlarged view ofthe orientations of the retroreflective sticker and the 45° mirrorare presented in Fig. 1.
The photographs of the Doppler vibrometer sensor head and thedrop weight impact test setup are shown in Fig. 2. The bottomsurface of the impactor is also shown in detail in the photographin which the laser light reflected from the retroreflective sticker atthe bottom surface is also visible.
During the test, after the free-falling impactor hits the stationarytarget specimen with the impact velocity, it starts to decelerate asexpected. After its velocity is decreased because of its contact with
the target, the impactor is subsequently brought to rest by a pro-tective chamber, which acts as a stopper (shown in Fig. 1). Theheight of the protective chamber was approximately 2.5 cm shorterthan the specimen height. After the collision with the target, theimpactor was stopped by the protective chamber to protect the tar-get, which had already failed because of the stress waves, frombeing fully crushed by the self-weight of the impactor. This is doneespecially because the sizes of the broken fragments are critical in
Fig. 1. Schematic view of the measurement configuration
Fig. 2. Test setup, laser vibrometer sensor head, and the bottom surfaceof the impactor
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evaluating the feasibility of using porous concretes for safetyapplications and also to protect the 45° mirror that is placed underthe impactor. The mirror was held by a small metal frame attachedto a separate steel structure as shown in Fig. 2 so that it was notaffected by the vibrations of the steel base structure of the dropweight impact tower after the collision. The mirror was fixed atan approximately 5 mm distance from the protective chamber.The horizontal dimensions of the chamber (110 × 120 mm) wereselected to be larger than the cross section (60 mm diameter) of thesample. Therefore, it did not provide lateral confinement duringthe test.
The two impactors used in the tests were made of steel and alu-minum. The material properties of the impactors used are criticalin the sense that they are directly involved in the impact stresscalculations. Using the Young’s modulus of elasticity and thePoisson’s ratio values provided by the manufacturer, the shearand bulk moduli were calculated. With these values, the longitudi-nal wave velocities of the materials of the impactors were calcu-lated adopting Eq. (1). The material properties of the impactorsare presented in Table 3:
Cl ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiK þ 4
3G
ρ
s¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiEð1 − vÞ
ρð1þ vÞð1 − 2vÞ
s(1)
A Polytec OFV 505 laser head and OFV 5000 controller withVD 06 velocity decoder were used in the experiments. The laserlight involved in the measurements was an eye-safe He-Ne laserwith a wavelength of 633 nm. The OFV 5000 controller had a sam-pling frequency capacity of 2 GHz. Measurements with samplingfrequencies of 500 kHz and 400 kHz were taken by using a LeCroyWavesurfer 432 digital oscilloscope. The trigger threshold was setat the velocity of 3 m=s, where the measurement block length andtrigger delay time were set at 2 s and −1 s, respectively. Therefore,the data was saved starting from 1 s before the velocity reached thevalue of 3 m=s until 1 s after that value. This period is sufficient tocapture the whole impact process along with the free fall of theimpactor before the collision.
Measurement and Analysis Techniques
The sampled particle velocity measurements covering the completecollision process were conducted using the Doppler laser velocim-eter. The measurements of particle velocity were then analyzedto be able to obtain the impact stress applied on the samples. Afterthe impactor strikes the target specimen, two compression wavespropagate away from the interface between the impactor and thetarget specimen while the interface itself moves downward withthe particle velocity as a result of the shock wave passing overthe particles. The particle velocity refers to the velocity that aparticle acquires as a result of a shock wave propagating overit with the shock velocity (Drumheller 1998; Asay and Shahinpoor1993).
Impedance Mismatch Method
When analyzing shock waves in solids, it is widely accepted toapproximate compression paths with the Hugoniot curve (alsotermed as Hugoniot). One of the main reasons why it is often em-ployed is that it involves parameters that can easily be measured inan impact experiment (Drumheller 1998). The Hugoniot can berepresented in any two-dimensional plane in which the most usefulrepresentations are either pressure-particle velocity or pressure-specific volume planes. The pressure-particle velocity Hugoniotis not a path that is followed, but rather the locus of all the possiblestates that can be achieved when a single shock wave passesthrough a material at a given initial state (Kanel et al. 2004; Meyers1994). In application, the weak-shock assumption is usually made,which is valid until shock waves are encountered with very largejumps in stress. The weak-shock assumption can be made until ajump in stress of approximately 270 GPa for steel. When thematerial obeys the weak-shock assumption, the response path ofthe compression wave is coincident with the Hugoniot (Drumheller1998). The weak-shock assumption is, therefore, valid for the cur-rent study in which the metal impactors that are involved in theanalyses are exposed to much lower stresses.
The shock wave does not cause the material to move along theHugoniot. Instead, the shock causes the material to jump betweentwo points on the Hugoniot curve. These points are located at theintersections of the Hugoniot curve and the chord, which is namedthe Rayleigh line, connecting the initial state and final shockedstate. The slope of this line is equal to the dynamic impedance(Z) of the material, Z ¼ �ρC, which is one of the main parametersdefining the dynamic properties of a material where ρ and C are thedensity and the related wave velocity of the material, respectively.Hugoniots with slope discontinuities attributable to transition fromelastic to plastic behavior can thus have regions for which the initialstate cannot be connected to the final state with a single Rayleighline. In such cases, the final state is reached by a series of two ormore Rayleigh lines. At moderate pressures, Hugoniots of manymaterials are in their linear range (Drumheller 1998; Kanel et al.2004; Meyers 1994).
The pressure in a shock front follows the Rayleigh line, whichcorresponds to a discontinuity that can also be used in explainingthe planar impact situation. When an impactor strikes a target withan impact velocity, the impact surface between the impactor and thetarget constitutes a discontinuity in particle velocity. The particlevelocity (up) is zero inside the target and is equal to the impactvelocity (ui) inside the flyer plate, and the pressure is the ambientatmospheric pressure (P0). Decomposition of the discontinuitycauses the formation of two shock waves that propagate fromthe impact surface into the impactor and the concrete target, trav-eling in opposite directions (Meyers 1994). The states behind theseshock waves must lie on the corresponding Hugoniots. In mostplanar impact studies, the relationship of pressure versus particlevelocity is analyzed using the main features of a method in whichthe Hugoniot curves are intersected, which is called the impedancemismatch method. The graphical presentation of the impedancemismatch method is illustrated in Fig. 3. The principle of equalpressures and particle velocities at the interface is satisfied atpoint P ¼ P1, up ¼ u1, which is also the intersection of the twoHugoniots (Meyers 1994).
Reverberation Technique
The experimental configuration in the tests performed for this studywas slightly different from the impact situation described previ-ously, in which there is one interface present. In the tests conductedfor this investigation, a low-impedance target material, like a
Table 3. Properties of the Materials Used in the Impactors
Material properties Steel Aluminum
Elasticity modulus, E (GPa) 200 69Density, ρ ðg=cm3Þ 7.9 2.7Poisson’s ratio, ν 0.28 0.33Shear modulus, G (GPa) 78.1 25.9Bulk modulus, K (GPa) 151.5 67.7Longitudinal wave velocity, Cl ðm=sÞ 5,690 6,155
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porous or normal concrete, is hit by a higher-impedance impactorsuch as steel, while the steel base structure of the setup constitutes asecond interface with the target material and causes the compres-sion wave to reflect back into the specimen. Therefore, the situationin these tests can be considered to be a low-impedance materialthat is impacted while being located between two high-impedancemedia.
A one-dimensional stress wave propagating in different mediacan be presented using a Lagrangian diagram where x is the spatialcoordinate and t is time. Even though the interface between theimpactor and the target moves downward with the particle velocity(up), this should not be observable in the diagram when comparedwith the speed of the wave itself (Zukas 1990). However, becausethe motion of the interface between the impactor and the target ismeasured during the experiments, the displacement of the interfaceis also shown in the diagram given in Fig. 4. In the diagram, timet ¼ 0 corresponds to the instant of collision.
The configuration in which the sample is impacted between twomaterials of higher dynamic impedances has been investigated byseveral researchers (Kanel et al. 2004; Lysne et al. 1969; Kondoet al. 1981). In those experiments, a projectile disc (or impactor)is impacted onto a stationary target, which is also called the rever-beration disc, made of a linear elastic material having a lower dy-namic impedance than the disc that strikes it. The schematicpresentation of the discs is also included in Fig. 4. The target isbacked by a buffer disc, again with a higher dynamic impedance
than itself. With the collision, two compression waves propagateaway from the interface between the projectile disc and the target.The impedance of the target relative to the other two discs is thedetermining factor for how the compression wave is reflected fromthe two interfaces, namely, the interface between the projectile discand one end of the target and the interface between the other end ofthe target and the buffer disc. The reflection and transmission of awave at an interface between two materials depend on the ratio oftheir dynamic impedances,K ¼ ZMAT I=ZMATII. The reflected wavekeeps the sign of the incident wave when the dynamic impedancesof the materials from which it reflects are higher than the dynamicimpedance of the material in which it propagates. Therefore,depending on the relative values of the impedances of the targetand the two discs that are in contact with it, each reflection succes-sively increases the amplitude of the compression wave propagat-ing in the target.
Because the target has a much shorter height compared withthe thicknesses of the projectile and buffer discs, many wave reflec-tions take place after the collision. In the corresponding reverber-ation studies presented in literature, the target is a linear elasticmaterial with a dynamic strength that is sufficient to withstandthe maximum stress that can be applied by that test configurationat that impact velocity. This maximum stress corresponds to theintersection of the Hugoniot curves of the projectile and buffer discmaterials. Therefore, stress continues to increase until that finalvalue is reached through multiple reverberations which is also con-sidered to be a state of equilibrium in pressure (Kanel et al. 2004;Lysne et al. 1969; Kondo et al. 1981). This situation is illustrated inFig. 5, in which the impedance mismatch technique is applied in aspecial manner because of the repetitive reflections and thepresence of two interfaces. Different from the typical impedancemismatch representation illustrated in Fig. 3, in Fig. 5 the two maininclined lines are the Hugoniots of the impactor and the buffer discmaterials, while the lines that travel between those two Hugoniotsrepresent the behavior of the reverberation disc material that iscompacted in between. The Hugoniot lines of the impactor andthe buffer material intersect at stress (Pe) and particle velocity(ue) values that can be considered to be an equilibrium for pressure.The figure also illustrates how the amplitude of a compressiveshock wave in the target specimen increases where the compressivestress is assumued to be positive.
This analysis can also be applied when testing nonlinear mate-rials with dynamic strengths that are not sufficient to withstandthe maximum stress that can be applied by the test configuration.
Fig. 3. Graphical presentation of the impedance mismatch method
Fig. 4. Lagrangian diagram for a low-impedance material impacted between two high-impedance media
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In the tests conducted in this research, the targets being eitherporous concrete or normal concrete makes the reverberation pro-cess slightly different. Similar to the case described previously,the target has a small height compared with the impactor andthe steel base structure. Therefore, the shock wave that travelsin the target again makes some reflections before waves that travelin the impactor and the setup reflect back as tension waves from thetop surface of the impactor and the bottom surface of the test setup,respectively. Because of its height, the steel base structure can evenbe considered as a wave sink. However, different from the rever-beration process that occurs when a strong linear elastic material istested, the reverberation situation in the tests performed for thisstudy continues until the stress within the concrete specimenreaches a value that generates substantial inelastic strains in thematerial beyond which further wave propagation within the speci-men can be neglected. The amplitude of the subsequent wavefrontswill be very small (Ramesh 2009). This situation and the relatedwave reverberations can be seen in the impedance mismatch figureillustrated in spots indicated on the Hugoniot of the impactor thatrepresent the points where the Hugoniots of the impactor and thetarget material intersect (i.e., the points where the stress and particlevelocities of the target and the impactor are equal). In the figure,those points eventually come to an equilibrium level that corre-sponds to a constant value of stress (Pe). The velocity values ofthose points are measured by the Doppler laser velocimeter duringthe test when the falling impactor and the target come into contact,and with the subsequent reverberations, the pressure comes to anequilibrium. Because the particle velocity is measured at the inter-face, on the impactor, it reaches an approximately constant valuewhen the pressure reaches equilibrium, as seen in Fig. 6. Thisvelocity value is named equilibrium velocity (ue).
Analysis of Particle Velocity Histories
The particle velocity becoming nearly constant as the pressurereaches equilibrium is shown in the velocity histories measuredduring the tests. In Fig. 7, a typical Doppler laser velocimetry signalfrom a drop weight impact experiment of porous concrete impactedby a steel impactor is given. In the figure, the first part that seemshorizontal corresponds to the free fall of the impactor and has a
Fig. 5. Impedance mismatch graph for a linear elastic reverbera-tion disc; reprinted with permission from Kondo, K., Yasumoto,Y., Sugiura, H., and Sawaoka, A. (1981). Journal of Applied Physics,52(2). Copyright 1981, American Institute of Physics
Fig. 6. Impedance mismatch graph for a concrete target impactedbetween two metals
Fig. 7. Doppler laser velocimetry signal from a drop weight impact test of porous concrete
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slope that is close to the gravitational acceleration. Because of thefriction between the impactor and the setup, the acceleration at thatportion of the curve was measured to be slightly lower than thegravity. After the free-fall part, there is the collision followed bywave reverberations that end up at the equilibrium of the stress thatalso corresponds to a nearly constant particle velocity. The plateaucorresponding to this equilibrium state is clearly observed in all thetests conducted on porous concretes and the normal concrete usinga steel impactor. The last part of the plateau in the figure corre-sponds to the part at which the impactor hits the protective chamber(shown in Fig. 1) that has a shorter height than the specimen,where the particle velocity very rapidly becomes zero. Becausethe particle velocity value that corresponds to equilibrium in pres-sure (i.e., the equilibrium velocity) is extracted from the very be-ginning of the plateau, this last portion of the data has nosignificance. The relative heights of the protective chamber andthe target determine the interval of time before the impactor con-tacts the stopper and therefore the length of the plateau. Along withthe raw data that are measured with the frequency of 400 kHz, thefiltered data with a cutoff frequency of 20 kHz are presented in thefigure.
In Fig. 7, if the time at which the equilibrium velocity is reachedafter the impact is observed, it is shown that this amount is higherthan the amounts of time at which the peak forces are reached in thestudies of very high-speed impact testing in the literature. This iscaused by the low impact velocity and therefore the low strain rateof the drop weight impact test performed. In low-velocity impactstudies, it was presented that the time after impact to reach the peakforce decreased as the velocity of the projectile increased. Forvelocities varying between 26 and 93 m=s, the peak force wasreached at a time range of 0.05–0.60 ms, respectively (Wu et al.1994; Perez-Castellanos et al. 1997). Therefore, the time to reachthe equilibrium velocity in the current study is consistent with theresults presented in the related studies.
To be able to obtain the stress from the particle velocity mea-surements, conservation of the linear momentum law is used. Theconservation law is actually the principle behind the impedancemismatch calculations in which the stress is calculated using theequilibrium velocity and the slope of the Hugoniot of the impactor,which is the dynamic impedance (that is equal to the density multi-plied by the related wave velocity). According to the conservationequation, the pressure P applied to the target material is determinedby the linear momentum transferred by the impactor to the targetper unit time as shown in Eq. (2)
P − P0 ¼ ρ0Cðui − ueÞ (2)
where P, P0, ρ0, C, ui, and ue are the shock pressure, initial pres-sure, initial density, wave velocity, impact velocity, and equilibriumvelocity, respectively. For shock waves traveling in solids, theshock pressure P is much greater than the initial pressure P0, whichis the ambient atmospheric pressure. Therefore, the P0 is usuallyneglected and removed from the conservation equations involvingsolids (Kanel et al. 2004; Meyers 1994). As the equilibrium inpressure is reached, while the stationary target material with zerovelocity reaches an approximately constant particle velocity corre-sponding to the equilibrium in pressure, the impactor with the im-pact velocity decelerates down to the same velocity (Kanel et al.2004). Therefore, the analyses of the particle velocity histories weredone by first extracting the impact and equilibrium velocitiesfrom the experimental graph as in Fig. 7 and then by using thoseto determine the stress through impedance mismatch and thereforeconservation of linear momentum calculations.
Because the concretes that were tested in the experiments havefailed and reached their dynamic strength values, the stress that is
calculated is also the dynamic strength of the specimen tested. Thekey feature of this technique is that the stress is calculated usingthe dynamic-impedance properties of only the impactor and thatthe properties of the target are not involved in the calculations.Therefore, while all the information is obtained from the well-defined metal drop weight, the target can be an unknown material.
Results and Discussion
The particle velocity histories were measured for three differenttypes of porous concretes and one mixture of normal concrete.All the specimens that were tested failed during the impact. There-fore, the stress values calculated using the equilibrium velocitiesobtained from the experiments [from Eq. (2)] are the dynamicstrengths of the specimens.
Measurements were conducted to demonstrate how the pro-posed experimental technique can be used on porous and normalconcretes. In the first series, two different types of porous concreteswere tested by impacting each type with two different types ofimpactors (steel and aluminum). The purpose of performing thesetests was validating the consistency of the technique by testing thespecimens from the same mixture with two different impactors hav-ing different dynamic impedances. In the tests, it was proved thatthe same dynamic strength values were obtained using differentimpactors. The wave histories obtained from the tests on porousconcretes with different strengths and a normal concrete were alsodemonstrated to show the distinctions between results of differentmixtures.
Impact Test Results of Porous Concretes Tested withDifferent Impactors
In the first series of tests, each of the two types of porous concreteswas tested by using steel and aluminum impactors of the same geo-metric size. The dynamic impedances of steel and aluminum werecalculated [with Eq. (1)] using the material properties provided bythe manufacturer. The results of the first series of tests are presentedin Table 4. The averages of the dynamic strength results were 26.26(with an SD of 2.61 MPa) and 25.48 MPa (SD = 1.71 MPa) forPRC1 tested with steel and aluminum impactors, respectively.The average results for PRC2 were 21.84 (SD = 2.22 MPa)and 22.93 MPa (SD = 1.29 MPa), again for steel and aluminumimpactor tests, respectively. The results obtained for the same mix-ture, when tested with two impactors having different dynamicimpedances, were consistent for both porous concrete mixtures.This validates that the measurement principle holds irrespectiveof the type of metal selected for the impactor. From the comparisonof the test results obtained with steel and aluminum impactors, itcan be said that as the dynamic impedance of the impactorincreases, equilibrium velocity is also higher and the differencebetween impact velocity and the equilibrium velocity is lower.However, both impactors are suitable for testing porous concretebecause the dynamic impedance for both aluminum and steelare much higher than that of porous concrete. The static strengthsof PRC1 and PRC2 were 15.9 and 13.1 MPa, respectively. There-fore, the dynamic increase factor (DIF), which is the ratio of thedynamic strength to the static strength under uniaxial compression,was 1.60 and 1.73 for the two porous concretes, respectively.
Particle Velocity-Time Histories Measured for DifferentPorous Concretes and Normal Concrete
The typical particle velocity-time history curves for two types ofporous concretes (PRC1 and PRC3) having different static
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strengths and a moderate-strength normal concrete (NC1) using asteel impactor are demonstrated in Fig. 8.
The average static compressive strengths of the PRC1, PRC3,and NC1 mixtures were 15.9, 34.8, and 26.4 MPa, respectively.
When the locations of the plateaus with respect to the impact veloc-ity are compared, the distinctions between the two porous concretemixtures (PRC1 and PRC3) with different static strengths can alsoclearly be made in terms of their dynamic strengths. The dynamicstrengths of the PRC1 and PRC3 samples, having the particlevelocity-time histories presented in Fig. 8, were found to be40.1 and 67.2 MPa [using Eq. (2)], respectively. To be able to verifywhether the experimental technique can be used for a moderate-strength normal concrete or not, tests were also performed on anormal concrete. As in the impact tests of porous concrete samples,in normal concrete testing the plateau was very clearly observed, asseen in Fig. 8, and the samples were completely fractured duringthe test. The dynamic strength was found to be 60.2 MPa for thenormal concrete (NC1) sample in Fig. 8.
Conclusions
In the study presented in this article, an experimental configurationfor determination of the dynamic response of porous concretes in adrop weight impact test was introduced. The dynamic response wasobtained through the measurement of the particle velocity at theinterface between the impactor and the concrete target. Usingthe particle velocity measurements in the subsequent analyses,the dynamic strengths of porous concretes and normal concretecould be obtained. The results derived from this work can besummarized as follows:• The motion of the interface (i.e., the particle velocity at the inter-
face between the impactor and the concrete specimen) could bemonitored accurately by using the experimental configurationintroduced. The laser Doppler velocimetry technique was usedfor monitoring the particle velocity at the interface, measured atthe bottom surface of the impactor.
• The velocity measurements were analyzed using a special rever-beration application of the impedance mismatch method,in which a nonlinear and low-dynamic-impedance target mate-rial is stressed between two materials with higher impedances tobe able to obtain the dynamic strengths of the concretes.
• The testing technique was applied on porous concretes havingdifferent dynamic strengths and was proved to be sufficientin testing porous concrete. It was also validated that the
Table 4. Results of Impact Tests on Porous Concretes Tested with Different Impactors
Mixture code Impactor Sample no.Impact
velocity (ui) (m=s)Particle velocity at pressureequilibrium (ue) (m=s)
Δ Particle velocity(Δu) (m=s)
Dynamic strength[from Eq. (2)] (MPa)
PRC1 Steel 1 4.46 3.90 0.56 25.17PRC1 Steel 2 4.34 3.72 0.62 27.86PRC1 Steel 3 4.30 3.67 0.63 28.31PRC1 Steel 4 4.34 3.73 0.61 27.42PRC1 Steel 5 4.33 3.84 0.49 22.02PRC1 Aluminum 1 4.58 2.91 1.67 27.75PRC1 Aluminum 2 4.59 3.08 1.51 25.09PRC1 Aluminum 3 4.65 3.13 1.52 25.25PRC1 Aluminum 4 4.52 2.94 1.58 26.24PRC1 Aluminum 5 4.56 3.17 1.39 23.09PRC2 Steel 1 4.43 3.95 0.48 21.57PRC2 Steel 2 4.40 3.88 0.52 23.37PRC2 Steel 3 4.47 4.02 0.45 20.22PRC2 Steel 4 4.49 3.94 0.55 24.72PRC2 Steel 5 4.55 4.12 0.43 19.33PRC2 Aluminum 1 4.46 3.03 1.43 24.19PRC2 Aluminum 2 4.49 3.07 1.42 23.56PRC2 Aluminum 3 4.54 3.28 1.26 20.85PRC2 Aluminum 4 4.34 2.93 1.41 23.43PRC2 Aluminum 5 4.41 3.11 1.30 22.63
Fig. 8. Particle velocity-time histories for PRC1, PRC3, and NC1 samples
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measurement technique could be used on normal concrete,provided that a high-dynamic-impedance impactor such as steelis used in testing.
• The measurement technique was proved to be consistent by test-ing the same type of porous concrete specimens using both steeland aluminum impactors. The results showed that although thedynamic impedance of the impactor was varied, the same stressresults were obtained.
• The testing configuration can be used to test a large number ofsamples in a short time (e.g., 20–25 samples in a working day).The laser Doppler velocimetry technique provides additionalfunctionality because it is a noncontact monitoring method inwhich no sensors are installed on the target samples or theimpactor.
• The experimental configuration and the subsequent analysistechnique also have the advantage of involving only the well-known dynamic-impedance properties and the velocity mea-surements of the impactor, while the target specimen that istested is not directly involved in the measurements or theanalysis.
Acknowledgments
This project was funded by the Netherlands Ministry of Defence.The authors would also like to acknowledge the EngineeringDynamics Section of the Faculty of Mechanical, Materials andMaritime Engineering at Delft University of Technology forproviding the laser Doppler velocimetry equipment. The authorswould also like to thank Ger Nagtegaal and Gerard Timmers fortheir contributions to establishing the test setup.
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