In-target radial stress measurements from penetration experiments into concrete by ogive-nose steel projectiles

Int. J. Impact Engng, Vol. 19, No. 8, pp. 715-726, 1997 © 1997 Elsevier Science Ltd Printed in Great Britain. All rights reserved PII:SO734-743X(97)O0008-O 0734-743x/97 $17.00+0.00

~ ) Pergamon

IN-TARGET RADIAL STRESS MEASUREMENTS FROM PENETRATION EXPERIMENTS INTO CONCRETE BY OGIVE-NOSE STEEL PROJECTILES J.K. G R A N t and D.J. FREW¢ ~SRI International, Menlo Park, CA 94025, U,S.A. ~US Army Engineer Waterways Experiment Station, Vicksburg, MS 39180-6199, U.S.A.

(Received 22 August 1996; in revised form 23 December 1996)

S u m m a r y - - W e conducted three penetration experiments of a hardened 4340 steel projectile with a length-todiameter ratio of 7 into concrete targets having an unconfined compressive strength of 43 MPa. The targets were each cast with six flatpack stress gages oriented to measure radial stress and positioned at various depths and radii from the penetration path. The experiments provide researchers with quality data that can be used to validate firstprinciple codes and to better understand the penetration mechanics in brittle, porous materials. Additional tests are recommended at other striking velocities and gage locations to further quantify stress within concrete targets. © 1997 Elsevier Science Ltd.

Keywords: penetration, concrete, stress.

1. INTRODUCTION The problem of predicting the complex interaction of a high-velocity projectile with geologic and structural targets has been of military interest for many years. A number of procedures have been developed over the past 200 years for making such predictions and they generally fall into three categories: (1) empirical approach, (2) analytical approach, and (3) numerical first-principles analysis. Instrumentation and diagnostic techniques have also been developed to evaluate the accuracy and range of application of the various prediction procedures. In the past, instrumentation was limited to the measurements of impact velocity and maximum depth of penetration. The measurements were used to evaluate the accuracy of empirical penetration equations and simple analytical procedures. More comprehensive numerical first-principles procedures have the capability of treating the projectile as a deformable body and for predicting the deformation and disintegration of the target during the penetration process. Evaluation of these numerical procedures requires more elaborate instrumentation and diagnostic techniques. These include on-board data acquisition systems for measuring projectile deceleration and in-target instrumentation for making motion and stress measurements. Ultimately, highresolution diagnostic systems should be developed to measure the state of stress at the projectile-target interface. A number of on-board systems are available and have been used successfully for measuring projectile deceleration. In-target instrumentation is relatively new when applied to the field of projectile penetration. The research described in this paper is an initial attempt to measure the radial stress-time response at selected points in a concrete target during the penetration process. 2. EXPER/MENTS

2.1. Experimental set-up We conducted three penetration experiments on concrete targets with the 3.0-caliber-radius-head, 4340 steel projectile, dimensioned in Fig. 1. An 83-mm smooth-bore powder gun [1] launched the 2.3-kg projectiles to nominal striking velocities of 315 m/s. The projectiles were fitted with sabots and obturators that were aerodynamically stripped before the projectile impacted the target. All three experiments were performed with normal incidence. A Hall Intervalometer system measured the striking velocities, and two orthogonally positioned 10 000-frame-per-second movie cameras were used to measure the pitch and yaw angles. The time of impact was determined by a conductive break screen attached to the front face of the target along the penetration path. The normally closed circuit on the screen is opened when the nose of the penetrator breaks the conductive paint pattern. Thus, zero time in the plots that follow occurs when the circuit is 715

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opened and it may be 0.050-0.100 ms after the penetrator impact due to the conductive nature of the penetrator body. The concrete targets were cast in ~ 1.37-m-diameter by 1.22-m-long corrugated steel culverts and contained no reinforcement. The concrete was a conventional mix of Portland Type-I cement and natural sand and gravel aggregates, with a nominal maximum aggregate size of 9.5 mm. The water-to-cement ratio was 0.55 and the aggregate-to-cement ratio was 7.12. The mix also included 2.4% by weight of fly ash, Class C, and 0.03% and 0.08% by weight of water-reducing agents, Type A and F, respectively. The targets were cured in the laboratory at ambient temperature and humidity. Test cylinders prepared and cured with the targets had an unconfined compressive strength of 43 MPa at the time of the tests (,~ 80 days after concrete placement). Each target was cast with six flatpack stress gages, spaced circumferentially around the projectile flight path at various depths measured from the front face of the target. Fig. 2 shows a schematic diagram of a typical concrete target with embedded flatpack stress gages. The flatpack gages were 44 mm wide, 3 mm thick, and 1.5 m long. They were held in place at the rear of the target and at the 0.46-m depth from the impact surface with 200-mm-diameter slotted acrylic plates, anchored with threaded steel rods to a wooden plank spanning the rear of the form. The concrete was vibrated internally

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In-target radial stress measurements from penetration experiments Table 1. Gage locations and stress data for the three penetration experiments Test number 1

Gage number

Radial position

(r/rp)

Axial position (Z/rp)

Peak radial stresses (MPa)

Residualstresses (MPa)

ME 44 ME 45 ME 46 ME 47 ME 48 ME 49

2.1 2.2 2.1 2.4 2.6 2.7

4.0 4.0 4.0 4.0 4.0 4.0

154 150 184 159 129 120

15 26 2 24 2

ME 56 ME 57 ME 58 ME 59 ME 60 ME 61

1.5 2.6 2.2 2.1 2.4 3.2

3.8 3.9 3.8 3.0 4.9 5.9

248 119 180 203 135 96

87 3 29 35 5 20

ME 50 ME 51 ME 52 ME 53 ME 54 ME 55

2.1 1.7 2.2 1.4 2.3 3.0

3.9 4.0 3.9 3.9 3.9 4.0

190 195 185 286 159 144

24 7 50 59 6 10

6

during placement to ensure uniform density, taking care not to directly push on the gages or their supports. Some movement of the gages was unavoidable, but no significant strains were introduced. The sensing elements (shown below) are located at the neutral plane of the flatpack package near the front end, so any slight bowing of the flatpacks along their length presented no problem. No shrinkage cracks were visible in the cured targets. Thus, there is no evidence that shrinkage had any effect on the contact between the concrete and the gages. The gage positions and orientations were designed to maximize data return and minimize possible stress shadowing from neighboring gages. Table 1 summarizes the radial and axial gage positions for each target normalized with respect to the projectile radius, rp. The gage radii and depths (r/rp and z/rp) were measured from the projectile flight path and front face of the target, respectively, after the penetration tests were completed by locating the center of the impact crater and the tips of the gages exposed in the crater. The reported locations were determined post-test because the impact points were slightly off-center and the flow of the concrete during target construction had a tendency to shift the gages slightly. The close proximity of the flatpacks to each other and their closeness to the path of the penetrator raises the question of how much they affected the penetration and the stress wave produced by the penetrator. The penetration flow field is dominated by radial compression and tangential tension. The gages are actually quite flexible in bending along their length and so they did not restrict the radial motion of the concrete. The Mylar ® sheathing also limited the extent to which the gages could restrict the tangential tension. Thus, we believe they had minor effect on the penetration and the stress wave. However, post-test inspection of the targets revealed that the craters were affected because the concrete on the outside of the flatpacks did not eject as it apparently would have with no gages present, Because cratering is a relatively long-time phenomenon, this effect does not translate to an effect on the early stress wave. Fig. 2 illustrates the ideal nature of the flatpack stress gages for this experiment. The expected large stress and strain gradients in the radial direction require that the gages have a small dimension in the radial direction - the flatpacks are only 3 m m thick. Also, the inhomogeneous nature of concrete with 9.5-mm aggregates requires averaging over much larger dimensions for stress measurements to be meaningful. The area of the stress elements in the flatpacks (shown below) is ,-~ 325 m m 2 (,-~ 4.5 times maximum aggregate areas).

718

J.K. Gran and D.J. Frew Table 2. Concrete target physical properties

Wet density Water content

2.25 mg/m3 3.00% 2.18 mg/m3 2.68 mg/m~ 81.28% 6.54 % 12.18 % 4.5 km/s 2.7 km/s

Dry density Grain density Volume of solids Volume of water Volume of air Compressional wave speed Shear wave speed

Concrete properties

When performing penetration studies, it is important to fully understand the materials being tested because their properties affect the loading environment that the entire system experiences during the penetration event. In order to better understand the concrete target material, which can have significant variability from batch to batch, it was necessary to perform a series of characterization experiments on samples of the concrete. A total of eight cylinders, 51-mm-diameter and 102-mm-long, were cored and the ends precision ground from a sample disk of the concrete prepared alongside the targets. The average physical properties for the cylinders are presented in Table 2. Quasi-static unconfined compression (UC), triaxial compression (TXC), and uniaxial strain (UX) experiments [1] were performed on the cylinders to determine the stress-strain response and strength of the target material. The results are shown in Fig. 3. The penetration and characterization experiments were conducted ~ 80 days after the concrete targets were cast. Fig. 3(a) shows the results from two uniaxial strain experiments on the target material, plotted as mean normal stress and axial stress versus volumetric strain. The solid lines are from a UX/UX experiment,

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In-target radial stress measurements from penetration experiments

719

where axial load and confining pressure are applied to the specimen in such a way as to hold the radial strain equal to zero during loading, unloading, and reloading. The dashed lines are from a UX/BX experiment, where the radial strain is held at zero during loading and intermediate unload/reload cycles; then the axial strain is held at a constant value during final unloading. Results from the shear phase of three TXC experiments are plotted in Fig. 3(b) as principal stress difference versus axial strain. The experiment is conducted by applying a deviatoric stress to a specimen while maintaining a constant confining pressure. The TXC experiments were conducted at confining pressures (~rc) of 50, 150, and 300 MPa. The character of shear response transitions from 'brittle' at relatively low confining pressure to 'ductile' at relatively high pressure. Fig. 3(c) contains the stress path from the two uniaxial strain experiments and the peak strengths from the TXC experiments. The BX (final unloading) phase of the UX/BX test follows closely the failure data from the TXC experiments. Fig. 3(d) shows the compressibility of the three TXC specimens during application of the confining pressure. The low water content for the 300-MPa TXC experiment (1.96%) may explain its stiffer response compared to the 50- and 150-MPa experiments. 2.3. Stress gage design Radial stresses within the concrete targets were measured with flatpack stress gages. The gages consist of very thin stress-sensing elements sandwiched between layers of insulation inside a protective case. Flatpacks are designed for specific applications, with element areas ranging from < 1-> 1000 mm 2. The width of the gage package is typically ten or more times greater than its thickness, and its length (determined by lead protection requirements) is usually many times greater than its width. This flatpack geometry affords maximum survivability and it minimizes the perturbation the gage raises in the stress field it is trying to measure. The flatpack design used in this work is shown in Fig. 4. The ytterbium (Yb) and constantan elements are piezoresistive materials, i.e. their resistances change under applied stress. These elements are insulated with Teflon® film, and the stainless steel case is welded together at its edges. The overall thickness of the flatpacks was 2.94 mm with a width-to-thickness ratio of 15. The compliance of the gage is minimized by keeping the thickness of the polymeric insulation to a minimum. The natural frequency of this package is ~ 250 kHz. In the flat foil geometry, the Yb element is highly sensitive to the applied normal stress (~ 4.2% change in resistance per 100 MPa), but it can be perturbed significantly by in-plane strains. Constantan is commonly used for strain gages because of its relatively high resistivity and its low sensitivity to normal stress. The stress-sensing area of the flatpack is that of the Yb element; the constantan elements are used to monitor two orthogonal components of the in-plane strain. In acknowledgment of the stress and strain gradients expected in the concrete, consideration was given to the use of smaller elements in order to concentrate the three measurements nearer to a point, but the natural scale of inhomogeneity of the concrete dictated averaging the stress measurement over at least a few 100 mm 2. That the strain sensors were not collocated with the stress sensor also results in slightly

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different times of arrival of the stress wave, but the timing did not have a significant effect on the interpretation of the signals, as described below. The effect of the relative positions of the elements is also believed not to have been significant because the stress gradients in the axial direction were not large. A unique feature of the flatpacks used in this study is the 0.006-mm-thick Mylar ® sheathing applied to the outside of the case. The function of the sheathing was to mitigate the in-plane strain coupled to the gage, as the concrete flowed around the penetrator. Design calculations predicted that the concrete at the gage locations would strain by several percentages. Strain inside the flatpack, as indicated by the measurements shown below, did not exceed 1% and was typically much less, owing largely to the nearly frictionless interface provided by the Mylar ®. The method for interpreting the resistance histories from the flatpacks combines the piezoresistance relations and the constitutive relations for the three elements (two constantan and one Yb) to determine the normal stress and in-plane strain histories that simultaneously satisfy these relations. The desired measurement is the stress normal to the plane of the elements. In overly simplified terms, we can consider one element to be a 'stress' gage, primarily sensitive to the normal stress, but perturbed by the in-plane strains. The other two gages are 'strain' gages, primarily sensitive to their axial strain, but perturbed by transverse strain and normal stress. Then, knowing the sensitivities of each element to the normal stress and in-plane strains and making independent measurements of resistance change in the three elements, we can solve for the normal stress and in-plane strain. Actually, the analytical approach is more complicated than this simplified description because the resistance of each element depends on all of its principal stresses and strains and its plastic strain, so the analysis includes these quantities and each element's constitutive relations as additional equations. Approximate properties of the element materials are available from the results of other work [2], but laboratory calibration tests of the flatpacks are used to determine the best mechanical and piezoresistance coefficients for each gage. A computer program named PIEZOR [3] solves the simultaneous set of non-linear equations. The 18 flatpacks, plus two spares, were individually calibrated in an oil bath by applying quasi-static hydrostatic compression. Strains measured in these calibrations were very small, demonstrating that, by design, the flatpack case stiffness and geometry tend to preserve uniaxial strain conditions. As shown in Fig. 5, the average sensitivity of the flatpacks is matched very well by the nominal uniaxial strain sensitivity of Yb, but there is some variation between the gages. Improved matches for individual flatpacks were obtained by using the PIEZOR model, with slight adjustments to the effective shear modulus of the Yb (a very difficult property to measure). ......L__L.....'.......".............L.....'........'......I............'...._.'.......L....I.............L.....L.....L_?.............!........

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In-target radial stress measurements from penetration experiments Table 3. Penetration data for pitch and yaw Test number

Target length (m)

Striking velocity (m/s)

Pitch/yaw (degrees)

Penetration depth, p (m)

Normalized penetration (p/rp)

1 2 3

1.22 1.22 1.22

320 310 316

0.2U/0.1R 0.0/0.3L 0.4D/0.3R

0.185 0.175 0.157

7.3 6.9 6.2

D = down, U = up, R = right, and L = left

2.4. Stress measurements

Table 3 summarizes the penetration results for the instrumented target experiments. The striking velocity, pitch/yaw, and depth of penetration were nearly the same for all the experiments. Therefore, the stress measurements from all three targets can be combined to evaluate the precision of all the measurements and to provide a comprehensive description of the radial stress field. All 18 flatpacks functioned as planned and provided clear, low-noise signals (resistance histories) for the full duration of interest. As part of the data-reduction process, the significance of three sources of uncertainty in the data interpretation were investigated using the PIEZOR analysis: (a) the effect of timeshifting the constantan resistance histories to coincide with the Yb resistance histories, (b) the difference between the results using the individual gage calibration parameters vs. the results using the nominal properties of Yb, and (c) the magnitude of the correction made in the stress measurement to account for strain in the Yb element. Time shifts of the constantan records produced only negligible differences, but the corrections for the effects of strain and variations among individual gage calibrations proved, at least for some gages, to be significant and so were accounted for in all cases. Recall that the flatpack gages were oriented with their ends pointed toward the impact surface of the target, so the penetrator produced a traveling stress field moving along the length of the gage. At the depth of the majority of the Yb elements (,-~ 100 ram) the time required for the penetrator to travel the roughly 30 mm between elements was a little more than 0.100 ms (assuming a velocity of ,-~ 275 m/s). Thus, the resistance histories of the two constantan elements were shifted, one by +0.100 ms and the other by -0.100 ms to approximate the records of virtual constantan elements collocated with the Yb element. The effect of these shifts is shown for a typical gage (ME 50) in Fig. 6(a). Clearly, the shifting is not important, apparently because the rise time of the stress wave at the gage is relatively long. Nevertheless, the constantan records were shifted +0.100 ms in the interpretation of all the gages. On average, the calibration of the flatpacks was consistent with the nominal Yb uniaxial strain properties. However, the effect of corrections to the PIEZOR model for individual gages was, in some cases, not negligible. An example of the effect, again for the ME 50 gage, is shown in Fig. 6(a). The

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calibration of this particular gage is one standard deviation from the average of the full set of calibrations. Thus, this comparison shows a typical effect of using the individual gage calibrations rather than a standard, or average, model when reducing the resistance histories to stress. The effect of strain inside the flatpacks was negligible in most cases because the Mylar ® sheathing was effective at isolating the flatpacks from the axial and circumferential strain within the target. Strain corrections, no matter how small, were made for all gages. An example of a significant strain effect, in flatpack ME 56 at r/rp = 1.5, is shown in Fig. 6(b). Both of the components of strain are tensile. The correction to the stress is ~ 30 MPa and is due almost completely to the axial strain (ez). Note that the circumferential strain (~0) in the flatpack is < 0.2%, even though the strain in the concrete was much larger. Even for this most severe case, the strain-induced perturbation to the stress measurement was only ,,~ 25 MPa, or 10% of the peak stress. As shown below, the gradient in peak stress with depth corresponds to ,-~ 4-20% over the distance between the constantan elements. Thus, an estimate of the effect of the non-collocation of the elements inside the flatpack is 20% of 25 MPa (5 MPa) or 2% of the peak stress. Agreement between records for gages at nominally the same locations is illustrated in Fig. 7. Note that records from different tests are included in all three comparisons. In these plots, the histories from Test 3 have been shifted by +0.050 ms to approximately account for the variance in response times of the TOA screens at the front of the targets. Records for a given location are in good agreement. The overall nature of the stress field determined by the measurements is illustrated in Fig. 8. Each stress record in Fig. 8 is from a gage at depth Z/rp ~ 4.0, but for different radial positions it is in the range 1.4 < rlrp <_ 2.6. The peak stress and residual stress decrease and the rise time lengthens with increasing radial position. The peak stress (~rp~) and residual stress (~rr~s, at t = 1.5 ms) for each gage are listed in the last two columns of Table 1, respectively. Exponential function fits to the complete set of peaks, and residual stresses at Z/rp ~ 4.0 are plotted in Fig. 9(a) and (b). Under the assumption that the data are normally

In-target radial stress measurements from penetration experiments

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distributed about the fits, we determined the standard deviations to be 17.7 MPa for the peak stresses and 15.9 MPa for the residual stresses. Rise time (tr), measured for 10-90% of peak, is plotted in Fig. 9(c) for the 15 measurements at Z/rp .~ 4.0 along with a linear fit to the data. The fit has a slope of 0.036 ms and a standard deviation (for data normally distributed about the fit) of 0.026 ms. Pulse duration, taken as the full width at half the maximum stress (fwhm), is approximately constant with an average of 0.388 ms and a standard deviation of 0.054 ms. The linear fit shown in Fig. 9(d) has a slope of -0.013 ms and a standard deviation of 0.053 ms. Comparisons of stress histories at different depths are shown in Fig. 10. The general trend is that the rise time and fwhm both increase and the peak stress decreases with depth. Although the number of measurements in this set is small, the estimated dependencies on Z/rp are plotted in Fig. 11. The rise time and fwhm at Z/rp .~ 4 are taken to be the average of all 15 gages at that depth, disregarding their slight dependence on radial position; the rise time and fwhm at Z/rp ~ 3, 5, and 6 are from the single gage at each of these depths. To illustrate the dependence of peak stress on depth, we have normalized the measurements at Z/rp ~ 3, 5, and 6 by the exponential fit to the measurements at Z/rp ~ 4, using the specific values of r/rp for each of the three gages at Z/rp ~ 3, 5, and 6. Although these measurements indicate fairly clear trends, additional measurements are needed to better quantify the dependence of the stress histories on z. 3. NUMERICAL PENETRATION MODEL We conducted a pre-test numerical simulation of the penetration event at a striking velocity of 305 m/s (the estimated impact velocity) using the wave propagation code EPIC [4] and compared the computed stresses with the flatpack stress gage records. The analysis was performed in the axisymmetric mode and included accurate representation of the penetrator geometry and the entire concrete target. Element dimensions in the target were of the order of 10 mm x 10 mm, and ~J 10000 degrees of freedom were used. Stress-free boundary conditions were assumed for all target surfaces. The material model we used to simulate the concrete target accounts for the large strains, high strain rates, and the high pressure effects that the concrete experienced during projectile penetration

724

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experiments. The model was developed by Holmquist, Johnson, and Cook [5] and fits to the recommended mechanical properties for a concrete with an unconfined compressive strength of ,,~ 35 MPa [4]. This fit was compared with results from the quasi-static tests conducted on specimens of the concrete used in the penetration experiments and found to be an adequate representation of the target material for the purpose of evaluating the credibility and consistency of the measurements. The EPIC simulation predicted a normalized depth of penetration (P/rp) of 7.0 which compared well with the average experimental result of 6.8. The EPIC predictions of radial stress at a normalized depth (Z/rp ~ 4) and radii (rlrp ~ 1.5, 2.0, 2.5, and 3.0) are compared with the experimental radial stress-time histories in Fig. 12. Zero time for the simulation was the first contact of the target by the penetrator. For comparison purposes, the experimental gage records were shifted +0.050 ms (Tests 1 and 2) or +0.100 ms (Test 3) to align the times of arrival of the stress wave at the stress gages. Overall, the simulation shows good agreement with the experimental data. The peak and residual stress levels at a depth z/rp ~ 4 for the simulation and experiments are also in good agreement, as shown in Fig. 9(a) and (b).

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Fig. 11. Dependenceof radial stress on depth. 4. Conclusions The experimental results presented in this paper provide a credible and useful description of the stresses in a concrete target during penetration by a steel, ogive-shaped nose projectile. The reliability of the measurements is a result of the care for and attention to detail used in the design, fabrication, and calibration of the stress gages, the fabrication of the concrete targets, the execution of the experiments, and the analysis of the results. The good comparisons between the simulation and experiments demonstrate that the data are consistent both in character and magnitude. Thus, the penetration experiments into concrete presented in this paper provides researchers with a high-quality set of data that can be used to evaluate first-principle codes and prediction methods.

726

J.K. Gran and D.J. Frew I

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Acknowledgements--The authors wish to gratefully acknowledge the funding and support given for this work by Mr Mike Giltrud, Defense Special Weapons Agency, and the assistance in performing the experiments by several staff members at SRI and Waterways Experiment Station. The views expressed in this article are those of the authors and do not reflect the official policy or position of the Department of Defense or the U.S. Government.

REFERENCES 1. Frew, D. J., Cargile, J. D. and Ehrgott, J. Q., WES geodynamics and projectile penetration research facilities, Proceedings from the 1993 ASME Winter Annual Meeting, New Orleans, AMD-171, 1-8 November 1993. 2. Chen, D. Y., Gupta, Y. M. and Miles, M. H., Quasi static experiments to determine material constants for the piezoresistance foils used in shock wave experiments, Journal of Applied Physics, 1 June 1984, 55(11). 3. Gran J. K. and Seaman, L., Analysis of Piezoresistance Gauges for Stress in Divergent Flow Fields. ASCE Journal of Engineering Mechanics, January 1997, 123(1). 4. Johnson, G. R., Stryke, R. A., User Instructions for the 1994 Version of the EPIC Code, Alliant Techsystems, Inc., Minnesota, 1994. 5. Holmquist, T. J., Johnson, G. R. and Cook, W. H., A computational constitutive model for concrete subjected to large strains, high strain rates, and high pressures, Proceedings of the 14th International Symposium on Ballistics, Quebec City, Canada, September 1993.