An explicit solution of the Alekseevski–Tate penetration equations

Walters, William P.; Williams, Cyril L.; Normandia, M. J.

doi:10.1016/j.ijimpeng.2006.09.057

Cited by 11 publications

(17 citation statements)

References 5 publications

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“…The modeling equation is numerically solved, though explicit solution for the model was developed more recently [3].…”

Section: Introductionmentioning

confidence: 99%

Effects of high pressure strength of rock material on penetration by shaped charge jet

Huang

2012

AIP Conference Proceedings

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Abstract. Perforating of oil/gas well creates communication tunnel between reservoir and wellbore. Shaped charges are widely used as perforators in oilfield industry. The liners of the charges are mostly made of powder metal to prevent solid slug clogging the entrance hole of well casing or locking the hole in perforating gun. High speed jet from the shaped charge pierces through perforating gun, well fluid, well casing, and then penetrates into reservoir formation. Prediction of jet penetration in reservoir rock is critical in modeling of well production. An analytical penetration model developed for solid rod by Tate and Alekseevskii is applied in this work. For better results, strength of formation rock at high pressure needs to be measured. Lateral stress gauge measurements in plate impact tests are conducted. Piezoelectric pressure gauges are imbedded in samples to measure the longitudinal and transverse stress simultaneously. The two stresses provide Hugoniot and material compressive strength. Indiana limestone, a typical rock in perforation testing, is selected as target sample material in the plate impact tests. Since target strength effect on penetration is more important in late stage of penetration when the strength of material becomes significant compared to the impact pressure, all the impact tests are focused on lower impact pressure up to 9 GPa. The measurements show that the strength increases with impact pressure. The results are applied in the penetration calculations. The final penetration matches testing data very well.

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“…The modeling equation is numerically solved, though explicit solution for the model was developed more recently [3].…”

Section: Introductionmentioning

confidence: 99%

Effects of high pressure strength of rock material on penetration by shaped charge jet

Huang

2012

AIP Conference Proceedings

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“…However, due to the nonlinear nature of the equations, the penetration was obtained implicitly as a function of time, so that an explicit functional dependence of the penetration on material properties was not obtained. Walters and Williams [4,5, 6] obtained the velocities, length, and penetration as an explicit function of time by employing a perturbation solution of the nondimensional Alekseevski-Tate equations. Algebraic equations were obtained for a third-order perturbation solution which showed excellent agreement with the exact solution of the Tate equations for tungsten heavy alloy rods penetrating a semi-infinite armor plate.…”

Section: Introductionmentioning

confidence: 99%

“…However, due to the nonlinear nature of these equations, the exact solution yields the penetration as an implicit function of time. An accurate, explicit solution to these equations, for each of the pertinent variables (penetration velocity, penetrator length, penetrator velocity, and penetration depth) was obtained by Walters and Williams [4,5,6] using a perturbation technique.…”

Section: Introductionmentioning

confidence: 99%

“…Then one can calculate V 0 , V 1 , V 2 , V 3 , and the corresponding U, P, and λ expressions. These expressions are given in Walters and Williams [4,5,6] through the third order. The emphasis of the current paper is to exploit the influence of the target parameters on the rod penetration so the final expression for penetration is given below.…”

Section: Introductionmentioning

confidence: 99%

“…The emphasis of the current paper is to exploit the influence of the target parameters on the rod penetration so the final expression for penetration is given below. Analogous equations for the rod velocity, penetration velocity, and rod length may be found in [4,5,6]. .…”

Section: Introductionmentioning

confidence: 99%

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The Influence of Armor Material Parameters on the Penetration by Long-Rod Projectiles

Walters

Williams

2006

Volume 4: Fluid Structure Interaction, Parts a and B

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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. REPORT DATE (DD-MM-YYYY)September 2006 ARL-RP-129 SPONSOR/MONITOR'S ACRONYM(S) 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) SPONSOR/MONITOR'S REPORT NUMBER(S) DISTRIBUTION/AVAILABILITY STATEMENTApproved for public release; distribution is unlimited. SUPPLEMENTARY NOTESA reprint from the 2006 ASME Pressure Vessels and Piping Conference Proceedings, 23-27 July 2006, Vancouver, BC. ABSTRACTThe Alekseevski-Tate equations have long been used to predict the penetration, penetration velocity, rod velocity, and rod erosion of long-rod projectiles or kinetic energy penetrators (1). These nonlinear equations were originally solved numerically, then by the exact analytical solution of Walters and Segletes (2, 3). However, due to the nonlinear nature of the equations, the penetration was obtained implicitly as a function of time, so that an explicit functional dependence of the penetration on material properties was not obtained. Walters and Williams (4-6) obtained the velocities, length, and penetration as an explicit function of time employing a perturbation solution of the non-dimensional Alekseevski-Tate equations. Algebraic equations were obtained for a third-order perturbation solution which showed excellent agreement with the exact solution of the Tate equations for tungsten heavy alloy rods penetrating a semi-infinite armor plate. The current report employs this model to rapidly assess the effect of increasing the impact velocity of the penetrator and increasing the armor material properties (density and target resistance) on penetration. This study is applicable to the design of hardened targets. SUBJECT TERMS ABSTRACTThe Alekseevski-Tate equations have long been used to predict the penetration, penetration velocity, rod velocity, and rod erosion of long-rod projectiles or kinetic-energy penetrators [1]. These nonlinear equations were originally solved numerically, then by the exact analytical solution of Walters and Segletes [2,3]. However, due to the nonlinear nature of the equations, the penetration was obtained implicitly as a function of time, so that an explicit functional dependence of the penetration ...

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Approximate solutions of the Alekseevskii–Tate model of long-rod penetration

Jiao

Chen

2017

Acta Mech. Sin.

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An explicit solution of the Alekseevski–Tate penetration equations

Cited by 11 publications

References 5 publications

Effects of high pressure strength of rock material on penetration by shaped charge jet

Effects of high pressure strength of rock material on penetration by shaped charge jet

The Influence of Armor Material Parameters on the Penetration by Long-Rod Projectiles

Approximate solutions of the Alekseevskii–Tate model of long-rod penetration

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