M. J. Forrestal

Norwegian University of Science and Technology, Trondheim, Sor-Trondelag Fylke, Norway

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Publications (67)67.16 Total impact

  • M. J. Forrestal, T. Børvik, T. L. Warren, W. Chen
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    ABSTRACT: We conducted an experimental study to understand the mechanisms and dominant parameters for 7.62 mm APM2 bullets that perforate 6082-T651 aluminum armor plates at oblique impacts. The 7.62-mm-diameter, 10.7 g, APM2 bullet consists of a brass jacket, lead filler, and a 5.25 g, ogive-nose, hard steel core. The brass and lead were stripped from the APM2 bullets by the targets, so we conducted ballistic experiments with both the APM2 bullets and only the hard steel cores. These projectiles were fired from a rifle to striking velocities between 400 and 1,000 m/s into 20-mm-thick plates at normal impact (β = 0o) and at oblique angles of β = 15o, 30o, and 45o. Measured residual and ballistic-limit velocities for the full bullet and the hard core were within a few percent for normal impact and all oblique angles. Thus, we showed that the perforation process was dominated by the hard steel core of the bullet. In addition, we conducted large strain, compression tests on the 6082-T651 plate material for input to perforation equations derived from a cavity-expansion model for the steel core projectiles. Model predictions were shown to be in good agreement with measured ballistic-limit and residual velocity measurements for β = 0o, 15o, and 30o. We also presented a scaling law for the bullet that showed the ballistic-limit velocities were proportional to the square root of the product of plate thickness and a material strength term.
    Experimental Mechanics 03/2013; · 1.55 Impact Factor
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    ABSTRACT: The electronic industry continues to dramatically reduce the size of electrical components. Many of these components are now small enough to allow shock testing with Hopkinson pressure bar techniques. However, conventional Hopkinson bar techniques must be modified to provide a broad array of shock pulse amplitudes and durations. For this study, we evaluate the shock response of accelerometers that measure large amplitude pulses, such as those experienced in projectile perforation and penetration tests. In particular, we modified the conventional Hopkinson bar apparatus to produce relatively long duration pulses. The modified apparatus consists of a steel striker bar, annealed copper pulse shapers, an aluminum incident bar, and a tungsten disk with mounted accelerometers. With these modifications, we obtained accelerations pulses that reached amplitudes of 10 kG and durations of 0.5 ms. To evaluate the performance of the accelerometers, acceleration-time responses are compared with a model that uses data from a quartz stress gage. Comparisons of data from both measurements are in good agreement.
    International Journal of Impact Engineering 05/2011; 46:56–61. · 1.68 Impact Factor
  • Source
    T. Børvik, M. J. Forrestal, T. L. Warren
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    ABSTRACT: We conducted an experimental and analytical study to understand the mechanisms and dominant parameters for ogive-nose rods and 7.62mm APM2 bullets that perforate 5083-H116 aluminum armor plates. The 20-mm-diameter, 95-mm-long, ogive-nose, 197g, hard steel rods were launched with a gas gun to striking velocities between 230–370m/s. The 7.62-mm-diameter, 10.7g, APM2 bullet consists of a brass jacket, lead filler, and a 5.25g, ogive-nose, hard steel core. The brass and lead were stripped from the APM2 bullets by the targets, so we conducted ballistic experiments with both the APM2 bullets and only the hard steel cores. These projectiles were fired from a rifle to striking velocities between 480–950m/s. Targets were 20, 40, and 60-mm-thick, where the 40 and 60-mm-thick targets were made up of layered 20-mm-thick plates in contact with each other. The measured ballistic-limit velocities for the APM2 bullets were 4, 6, and 12% smaller than that for the hard steel cores for the 20, 40, and 60-mm-thick targets, respectively. Thus, the brass jacket and lead filler had a relatively small effect on the perforation process. In addition, we conducted large strain, compression tests on the 5083-H116 aluminum plate material for input to perforation equations derived from a cavity-expansion model for the ogive-nose rods and steel core projectiles. Predictions for the rod and hard steel core projectiles are shown to be in good agreement with measured ballistic-limit and residual velocity data. These experimental results and perforation equations display the dominant problem parameters. KeywordsAluminum armor plates-Ogive-nose rods-7.62mm APM2 bullets-Experimental study-Perforation equations
    Experimental Mechanics 01/2010; 50(7):969-978. · 1.55 Impact Factor
  • M. J. Forrestal, T. Børvik, T. L. Warren
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    ABSTRACT: We conducted an experimental and analytical study to better understand the mechanisms and dominant parameters for 7.62mm APM2 bullets that perforate 7075-T651 aluminum armor plates. The 7.62-mm-diameter, 10.7g, APM2 bullet consists of a brass jacket, lead filler, and a 5.25g, ogive-nose, hard steel core. The brass and lead were stripped from the APM2 bullets by the targets, so we conducted ballistic experiments with both the APM2 bullets and only the hard steel cores. These projectiles were fired from a rifle to striking velocities between 600 and 1,100m/s. Targets were 20 and 40-mm-thick, where the 40-mm-thick targets were made up of layered 20-mm-thick plates in contact with each other. The measured ballistic-limit velocities for the APM2 bullets were 1% and 8% smaller than that for the hard steel cores for the 20 and 40-mm-thick targets, respectively. Thus, the brass jacket and lead filler had a relatively small effect on the perforation process. Predictions from a cylindrical cavity-expansion model for the hard steel core projectiles are shown to be in good agreement with measured ballistic-limit and residual velocity data. The results of this study complement our previous paper with 5083-H116 aluminum target plates in that the ultimate tensile strength of 7075-T651 is about 1.8 times greater than that of 5083-H116. We also present a scaling law that shows a square root relationship between ballistic-limit velocity and plate thickness and material strength. KeywordsAluminum armor plates-7.62mm APM2 bullets-Experimental study-Perforation equations-Validation
    Experimental Mechanics 01/2010; 50(8):1245-1251. · 1.55 Impact Factor
  • T. L. Warren, M. J. Forrestal
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    ABSTRACT: We present equations that show the effect of radial inertia for incompressible samples that are in dynamic force equilibrium during the split Hopkinson pressure bar test or Kolsky bar test. For steel samples the radial inertia effect can be neglected; however, radial inertia can be important for very soft materials. KeywordsKolsky bar-Radial inertia-Incompressible soft materials
    Experimental Mechanics 01/2010; 50(8):1253-1255. · 1.55 Impact Factor
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    ABSTRACT: The use of aluminium alloys in lightweight protective structures is increasing. Even so, the number of experimental and computational investigations that give detailed information on such problems is limited. In an earlier paper by some of the authors, perforation experiments were performed with 15–30mm thick AA5083-H116 aluminium plates and 20mm diameter, 98mm long, HRC 53 conical-nose hardened steel projectiles. In all tests, initial and residual velocities of the projectile were measured and the ballistic limit velocity of each target plate was determined. In the present paper, an analytical perforation model based on the cylindrical cavity-expansion theory has been reformulated and used to calculate the ballistic perforation resistance of the aluminium plates. In addition, non-linear finite element simulations have been carried out. The target material was modeled with the Johnson–Cook constitutive relation using 2D axisymmetric elements with adaptive rezoning. To allow ductile hole growth, a pin-hole was introduced in the target. The analytical and numerical results have been compared to the experimental findings, and good agreement was in general obtained. A parametric study was also carried out to identify the importance of the different terms of the Johnson–Cook constitutive relation on the perforation resistance of the target. The results indicate that thermal softening cannot be neglected, so an alternative procedure for identification of the material constants in the power-law constitutive relation used in the cavity-expansion theory has been proposed.
    International Journal of Impact Engineering 03/2009; 36(3):426-437. · 1.68 Impact Factor
  • Michael J. Forrestal, Thomas L. Warren
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    ABSTRACT: We developed closed-form perforation equations for rigid, conical and ogival nose projectiles that perforate aluminum target plates at normal impact. An existing cylindrical, cavity-expansion model that was experimentally verified with perforation data into 5083-H131 aluminum armor plates was used as the starting point for the development of the perforation equations. We identified a small parameter in those perforation equations, performed power-series expansions, and obtained closed-form, accurate perforation equations for the ballistic-limit and residual velocities. The closed-form, perforation equations are shown to be very accurate when compared with existing data for 6061-T651 and 5083-H131 aluminum target plates. Our perforation equations display clearly the dominant problem parameters.
    International Journal of Impact Engineering 02/2009; 36(2):220-225. · 1.68 Impact Factor
  • Thomas L. Warren, Michael J. Forrestal
    International Journal of Impact Engineering - INT J IMPACT ENG. 01/2009; 36(8):1079-1079.
  • Michael J. Forrestal, Thomas L. Warren
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    ABSTRACT: We present penetration equations for rigid, ogive-nose, rod projectiles that penetrate aluminum targets at normal impact. Comparisons of depth of penetration data and predictions from a previously published penetration equation derived from spherical, cavity-expansion methods show excellent agreement for striking velocities to 1800 m/s. We then identify a small parameter in the penetration equation, perform a power-series expansion, and obtain approximate penetration equations. These approximate equations are very accurate for striking velocities to 1300 m/s and display clearly the dominant problem parameters.
    International Journal of Impact Engineering. 01/2008;
  • S.A. Silling, M.J. Forrestal
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    ABSTRACT: We developed an abrasion model that predicts mass loss and change in nose shape for steel projectiles that penetrate concrete targets. Mass loss data from four sets of experiments with two ogive-nose projectile geometries and concrete targets with limestone and quartz aggregates were used to develop the abrasion model. We plotted post-test mass loss versus initial kinetic energy and found a nearly linear dependence for striking velocities to approximately 1000 m/s. With this linear relationship, we derived a mathematical model that was implemented into the Sandia-developed, Eulerian hydrocode CTH. Predictions from CTH agreed well with experimental observations.
    International Journal of Impact Engineering 01/2007; 34(11):1814-1820. · 1.68 Impact Factor
  • M.J. Forrestal, T.W. Wright, W. Chen
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    ABSTRACT: For a valid split Hopkinson pressure bar (SHPB) or Kolsky compression bar experiment, the sample should be in dynamic stress equilibrium over most of the test duration. In this study, we investigate the effect of radial inertia on elastic samples during a valid SHPB test. We present closed-form equations for the three additional stress components induced by radial inertia for incompressible and compressible, linear elastic samples. These equations should assist in the early experimental designs. As the experiments proceed and more is learned about the sample response, numerical analysis can be used to obtain a more refined account of the sample response and dynamic material strength.
    International Journal of Impact Engineering. 01/2007;
  • D.J. Frew, M.J. Forrestal, J.D. Cargile
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    ABSTRACT: We conducted sets of experiments with three diameters of concrete targets that had an average compressive strength of 23 MPa (3.3 ksi) and 76.2-mm-diameter, 3.0 caliber-radius-head, 13-kg projectiles. The three target diameters were D=1.83D=1.83, 1.37, and 0.91, so the ratios of the target diameters to the projectile diameter were D/d=24D/d=24, 18, and 12. The ogive-nose projectiles were machined from 4340 Rc45 steel and designed to contain a single-channel acceleration data recorder. Thus, we recorded acceleration during launch and deceleration during penetration. An 83-mm-diameter powder gun launched the 13-kg projectiles to striking velocities between 160 and 340 m/s. Measured penetration depths and deceleration-time data were analyzed with a previously published model. We measured negligible changes in penetration depth and only small decreases in deceleration magnitude as the targets’ diameters were reduced.
    International Journal of Impact Engineering 10/2006; 32(10):1584–1594. · 1.68 Impact Factor
  • B. Song, M. J. Forrestal, W. Chen
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    ABSTRACT: We conducted dynamic and quasi-static compression experiments with low-density (ρ = 120kg/m3) epoxy foam specimens. The specimens had a 10.0-mm-square cross-section and a length of 19.3mm. Dynamic experiments were conducted with a modified split Hopkinson pressure bar (SHPB), and the quasi-static experiments were conducted with a hydraulic load frame device (MTS-810). In both cases, the specimens were loaded from one end at a constant velocity. Equally spaced grid lines were marked on the specimens to monitor the deformation history. Digital images taken at equally spaced time intervals gave the positions of each grid line. These images showed that a constant end-face velocity V produced a compaction wave front that traveled at a constant velocity C in both dynamic and quasi-static experiments. We described these results with a shockwave analysis that used a locking solid material model.
    Experimental Mechanics 03/2006; 46(2):127-136. · 1.55 Impact Factor
  • D. J. Frew, M. J. Forrestal, W. Chen
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    ABSTRACT: We present pulse shaping techniques to obtain compressive stress-strain data for elastic-plastic materials with a split Hopkinson pressure bar. The conventional split Hopkinson pressure bar apparatus is modified by placing a combination of copper and steel pulse shapers on the impact surface of the incident bar. After impact by the striker bar, the copper-steel pulse shaper deforms plastically and spreads the pulse in the incident bar so that the sample is nearly in dynamic stress equilibrium and has a nearly constant strain rate in the plastic response region. We present analytical models and data that show a broad range of incident strain pulses can be obtained by varying the pulse shaper geometry and striking velocity. For an application, we present compressive stress-strain data for 4340 Rc 43 steel.
    Experimental Mechanics 04/2005; 45(2):186-195. · 1.55 Impact Factor
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    ABSTRACT: We conducted two sets of penetration experiments with concrete targets that had average compressive strengths of 23 and 39MPa (3.3 and 5.7ksi). The 76.2-mm-diameter, 530-mm-long, ogive-nose projectiles were machined from 4340 RC45 steel and designed to contain a single-channel acceleration data recorder. Thus, we recorded acceleration during launch and deceleration during penetration. An 83-mm-diameter powder gun launched the 13kg projectiles to striking velocities between 140 and 460m/s. Measured penetration depths and deceleration-time data were analyzed with a previously published model. In addition, we compared the results of this study with results obtained from smaller diameter projectiles and this comparison suggested a projectile diameter scale effect.
    International Journal of Impact Engineering 05/2003; 28(5):479-497. · 1.68 Impact Factor
  • W. Chen, B. Song, D. J. Frew, M. J. Forrestal
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    ABSTRACT: When a conventional split Hopkinson pressure bar (SHPB) is used to investigate the dynamic flow behavior of ductile metals, the results at small strains (ɛ≲2%) are not considered valid owing to fluctuations associated with the early portion of the reflected signal and the nonequilibrated stress state in the specimen. When small-strain behavior is important, such as in the case of determining the elastic behavior of materials, the accuracy of a conventional SHPB is not acceptable. Using a pulse-shaping technique, the dynamic elastic properties can be determined with a SHPB, as well as the dynamic plastic flow. We present a description of the experimental technique and the experimental results for a mild steel. The dynamic compressive stress-strain curve is composed of a lower strain-rate elastic portion and a high strain-rate plastic flow portion.
    Experimental Mechanics 02/2003; 43(1):20-23. · 1.55 Impact Factor
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    M. J. Forrestal, T. C. Togami, W. E. Baker, D. J. Frew
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    ABSTRACT: We present a Hopkinson bar technique to evaluate the performance of accelerometers that measure large amplitude pulses, such as those experienced during projectile penetration tests. An aluminum striker bar impacts a thin Plexiglas or copper disk placed on the impact surface of an aluminum incident bar. The Plexiglas or copper disk pulse shaper produces a nondispersive stress wave that propagates in the aluminum incident bar and eventually interacts with a tungsten disk at the end of the bar. A quartz stress gage is placed between the aluminum bar and tungsten disk, and an accelerometer is mounted to the free end of the tungsten disk. An analytical model shows that the rise time of the incident stress pulse in the aluminum bar is long enough and the tungsten disk length is short enough that the response of the tungsten disk can be accurately approximated as rigid-body motion. We measure stress at the aluminum bar-tungsten disk interface with the quartz gage and we calculate rigid-body acceleration of the tungsten disk from Newton's Second Law and the stress gage data. In addition, we measure strain-time at two locations on the aluminum incident bar to show that the incident strain pulse is nondispersive and we calculate rigid-body acceleration of the tungsten disk from a model that uses this strain-time data. Thus, we can compare accelerations measured with the accelerometer and accelerations calculated with models that use stress gage and strain gage measurements. We show that all three acceleration-time pulses are in very close agreement for acceleration amplitudes to about 20,000 G.
    Experimental Mechanics 01/2003; 43(1):90-96. · 1.55 Impact Factor
  • M. J. Forrestal, D. J. Frew, W. Chen
    Experimental Mechanics 05/2002; 42(2):129-131. · 1.55 Impact Factor
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    D. J. Frew, Michael J Forrestal, Weinong W Chen
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    ABSTRACT: We present pulse shaping techniques to obtain compressive stress-strain data for brittle materials with the split Hopkinson pressure bar apparatus. The conventional split Hopkinson pressure bar apparatus is modified by shaping the incident pulse such that the samples are in dynamic stress equilibrium and have nearly constant strain rate over most of the test duration. A thin disk of annealed or hard C11000 copper is placed on the impact surface of the incident bar in order to shape the incident pulse. After impact by the striker bar, the copper disk deforms plastically and spreads the pulse in the incident bar. We present an analytical model and data that show a wide variety of incident strain pulses can be produced by varying the geometry of the copper disks and the length and striking velocity of the striker bar. Model predictions are in good agreement with measurements. In addition, we present data for a machineable glass ceramic material, Macor, that shows pulse shaping is required to obtain dynamic stress equilibrium and a nearly constant strain rate over most of the test duration.
    Experimental Mechanics 01/2002; 42(1):93-106. · 1.55 Impact Factor
  • W. Chen, F. Lu, D. J. Frew, M. J. Forrestal
    Journal of Applied Mechanics. 01/2002; 69(3).

Publication Stats

1k Citations
67.16 Total Impact Points

Institutions

  • 2010
    • Norwegian University of Science and Technology
      • Faculty of Engineering Science and Technology
      Trondheim, Sor-Trondelag Fylke, Norway
  • 2007
    • Purdue University
      West Lafayette, Indiana, United States
  • 1982–2007
    • Sandia National Laboratories
      Albuquerque, New Mexico, United States
  • 1992–2000
    • University of Dayton
      Dayton, Ohio, United States
  • 1997
    • University of Missouri
      • Department of Mechanical and Aerospace Engineering
      Columbia, MO, United States