FATEPEN Vol I. Analysts Manual 1 .pdf

FATEPEN

Fast Air Target Encounter Penetration

Version 3.0.0 Terminal Ballistic Penetration Model

Volume I—Analyst’s Manual

Prepared by:

Jerome D. Yatteau Richard H. Zernow Gunnar W. Recht

Karl T. Edquist

Applied Research Associates, Inc.

10720 Bradford Road, Suite 110 Littleton, Colorado 80127-4298

Distribution of FATEPEN is limited to U.S. Government Agencies and their contractors only.

Requests for FATEPEN must be referred to the Commander, NSWCDD, Dahlgren, VA 22448-5100

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ARA Project 0175

FATEPEN (Version 3.0.0)

TERMINAL BALLISTIC PENETRATION MODEL

Volume I – Analyst’s Manual

Prepared by:

Jerome D. Yatteau Richard H. Zernow Gunnar W. Recht

Karl T. Edquist

Applied Research Associates, Inc.

10720 Bradford Road, Suite 110

Littleton, Colorado 80127

Prepared for:

Naval Surface Warfare Center, Dahlgren Division 17320 Dahlgren Road

Dahlgren, VA 22448-5500

September 2001 Revised February 2, 2005 i

FOREWORD

Preparation of the FATEPEN (Version 3.0.0) manuals has been funded by the Naval Surface Warfare Center (NSWC), Dahlgren Division, under U.S. Army CBDCOM Contracts DAAA15-94-0005 (Delivery Order 73), DAAM01-97-D-0013 (Delivery Order

33) and DAAD13-01-D-0001 (Delivery Order 10). Mssrs. David L. Dickinson and Thomas L. Wasmund of NSWC, Dahlgren Division provided technical oversight for effort.

ACKNOWLEDGEMENTS

The authors gratefully acknowledge their indebtedness to Rodney F. Recht for his major contributions to the development of FATEPEN and for teaching us how to combine experiment and analysis in developing realistic analytical/empirical engineering models for complex terminal ballistic interactions. Rod’s contributions to FATEPEN include the ballistic limit velocity, residual velocity, and erosion/extrusion-shear mass loss models for compact fragments impacting thin plates. Rod’s numerous contributions advancing the science of terminal ballistics extend well beyond his contributions to FATEPEN and are well known around the world.

The authors also recognize the important contributions to development of the FATEPEN code by Mssrs. James Dunn, Steven Lightsey, and Steven Ford of the Denver Research Institute, Mr. Mike Nagy of Adaptive Technologies, and Mr. Andy Williams of the Naval Research Laboratory for their innovative and resourceful accomplishment of the many impact experiments used in developing and verifying the penetration models .

Finally the authors express their sincere appreciation to Mssrs. David L. Dickinson, Thomas L. Wasmund, and Steven A Hock of the Naval Surface Warfare Center, Dahlgren Laboratory for their vision and long standing commitment to improving weapons effectiveness assessment methodologies, and, in particular, for their sustained sponsorship of improvements to FATEPEN throughout its development history.

ii iii

TABLE OF CONTENTS

Section Page

FOREWORD..................................................................................................................... i

ACKNOWLEDGEMENTS ................................................................................................. i

1.0 INTRODUCTION .............................................................................................. 1-1

1.1 EXECUTIVE SUMMARY....................................................................... 1-1

1.2 HISTORICAL PERSPECTIVE............................................................... 1-2

1.3 HIGH VELOCITY PENETRATION CHARACTERISTICS..................... 1-6

1.3.1 Compact Fragments................................................................... 1-7

1.3.2 Rod Penetrators ....................................................................... 1-19

1.3.3 Projectiles................................................................................. 1-27

1.3.4 Explosively Formed Fragments................................................ 1-32

1.4 FATEPEN OVERVIEW........................................................................ 1-36

1.4.1 Approach To Model Development............................................ 1-36

1.4.2 Implementation......................................................................... 1-36

1.5 ANALYST’S MANUAL LAYOUT.......................................................... 1-47

1.6 REFERENCES .................................................................................... 1-50

2.0 Penetrator and Target Descriptions.................................................................. 2-1

2.1 PENETRATOR INPUT .......................................................................... 2-1

2.1.1 Material and Hardness ............................................................... 2-1

2.1.2 Shape ......................................................................................... 2-2

2.1.3 Weight and Dimensions ............................................................. 2-3

2.1.4 Equivalent Cylinder Representation........................................... 2-5

2.1.5 Initial Velocity, Orientation, and Angular Momentum ................. 2-6

2.1.6 FATEPEN Penetrator Input for 155-mm Shell Fragments. ...... 2-14 iv

TABLE OF CONTENTS (Cont'd) Section Page

2.2 TARGET INPUT .................................................................................. 2-16

2.2.1 Material and Hardness ............................................................. 2-16

2.2.2 Dimensions............................................................................... 2-17

2.2.3 Orientation................................................................................ 2-20

2.2.4 Location.................................................................................... 2-21

2.3 PENETRATOR AND TARGET MATERIAL PROPERTIES ................ 2-22

2.4 FATEPEN TREATMENT OF LAMINATED PLATES .......................... 2-25

2.5 DEBRIS CLOUD CHARACTERISTICS .............................................. 2-30

2.5.1 Numbers, Sizes, and Shapes of Debris Particles .................... 2-30

2.5.2 Particle Trajectory Distribution ................................................. 2-31

2.5.3 Particle Velocity and Debris Cloud Momentum........................ 2-32

2.5.4 Initialization of Debris Cloud Parameters ................................. 2-33

2.6 REFERENCES .................................................................................... 2-34

3.0 IMPACT CONDITIONS..................................................................................... 3-1

3.1 IMPACT LOCATION AND OBLIQUITY................................................. 3-1

3.1.1 Intercepting Plates of Infinite Lateral Extent............................... 3-1

3.1.2 Intercepting Finite Plates............................................................ 3-4

3.1.3 Travel Distance, Impact Obliquity, and Turning Point Location . 3-7

3.2 IMPACT ORIENTATION (SUBROUTINE ATITUD) .............................. 3-9

3.2.1 Impact Yaw Angle ...................................................................... 3-9

3.2.2 Impact Angle ............................................................................ 3-11

3.3 REFERENCES .................................................................................... 3-12 v

Section Page

4.0 PENETRATOR PRESENTED AREA (Subroutine AFRAG) ............................. 4-1

4.1 ACTUAL PRESENTED AREA (SUBROUTINE APTRUE).................... 4-1

4.2 EFFECTIVE PRESENTED AREA (SUBROUTINE (EFFECTIVEAREA)4-2

4.3 REFERENCES ...................................................................................... 4-5

5.0 BALLISTIC LIMIT VELOCITY AND TARGET DAMAGE.................................. 5-1

5.1 BALLISTIC LIMIT VELOCITIES ............................................................ 5-2

5.1.1 Compact Fragments (Subroutine BALLIM) ................................ 5-3

5.1.2 Rods (Subroutines PRIMLIM and MHYDRO) ............................ 5-9

5.1.3 Projectiles (Subroutine BALLIM) .............................................. 5-13

5.1.4 Transitions Between Compact Fragment and Long Rod Ballistic Limit Velocity Models and Penetration Debris Partitioning for Oblique Impacts (Subroutine PRIMLIM) ............................. 5-15

5.2 SINGLE PENETRATOR HOLE SIZES (SUBROUTINE HOLEDAM) . 5-34

5.2.1 Compact Fragments (Subroutine HOLE) ................................. 5-35

5.2.2 Elongated Penetrators (Subroutine HOLE).............................. 5-38

5.3 SECONDARY PARTICLE EFFECTS (SUBROUTINE HOLEDAM).... 5-46

5.3.1 Secondary Particle Pattern Diameters and Average

Hole Sizes (Subroutine HOLE)................................................. 5-47

5.3.2 Combined Particle Damage (Subroutine PUNCH)................... 5-48

5.4 REFERENCES .................................................................................... 5-60

6.0 PRIMARY FRAGMENT PENETRATION CALCULATIONS............................. 6-1

6.1 EROSION AND EXTRUSION-SHEAR MASS LOSS............................ 6-1

6.1.1 Plug Acceleration Mass Loss Model (Subroutine RESMAS) ..... 6-2

6.1.2 Effective Plate Plug Mass (Subroutine IMPED) ......................... 6-4

6.1.3 Modified Hydrodynamic Penetration Theory (Subroutine

MHYDRO) .................................................................................. 6-8 vi

Section Page

6.1.4 Lateral Erosion Mass Loss Model (Subroutine LATERO)........ 6-20

6.1.5 Application to Projectiles .......................................................... 6-23

6.2 RESIDUAL VELOCITY........................................................................ 6-23

6.2.1 Velocity Loss in Plates (Subroutine VRPLATE) ....................... 6-23

6.2.2 Velocity Loss in Fluids (Subroutines VRFLUID)....................... 6-28

6.2.3 Application to Projectiles .......................................................... 6-30

6.3 RESIDUAL ANGULAR MOMENTUM ................................................. 6-31

6.4 IMPACT FRACTURE, DEBRIS CHARACTERISTICS, AND

CHANGES IN PENETRATOR SHAPE ............................................... 6-31

6.4.1 Impact Fracture or Shatter in Fragments and Rods

(Subroutine SHATR) ................................................................ 6-32

6.4.2 Transverse Shear Deformation and Fracture in Rods

(Subroutine RODSHEAR) ........................................................ 6-45

6.4.3 Application to Projectiles (Subroutine APBRK) ........................ 6-49

6.5 REFERENCES .................................................................................... 6-51

7.0 SECONDARY PARTICLE PENETRATION CALCULATIONS ......................... 7-1

8.0 RESIDUAL DEBRIS CLOUD DESCRIPTION AND PLATE IMPULSE

(SUBROUTINE NEWCLOUD).......................................................................... 8-1

8.1 PRIMARY PENETRATOR..................................................................... 8-1

8.2 BROKEN ROD PIECES ........................................................................ 8-2

8.3 SECONDARY DEBRIS PARTICLES .................................................... 8-2

8.3.1 Representative Penetrator Particles .......................................... 8-2

8.3.2 Representative Plate Particles ................................................... 8-6

8.4 PLATE IMPULSE .................................................................................. 8-7

8.5 FATEPEN OUTPUT ARRAY AND CONTINUATION............................ 8-7

vii

LIST OF FIGURES

Figure Page

1-1. Effects of Increasing Impact Speed on Impact Fracture of Mild Steel Cubes Impacting Flat against 2024-T3 Aluminum Plates (Wr is the Weight of Primary or Largest Penetrator Remnant, W is the Pre-Impact Cube Weight).........................1-3

1-2. Effects of Deformation and Breakup on Fragment Residual Velocity. WAL Fragment Simulating Projectiles Perforating Thin Mild Steel Plates.3 ...................1-8

1-3. Illustration of Extrusion-Shear Mass Loss for Steel Fragment Simulating Projectile (FSP) Perforating a Mild Steel Plate.6,37 ................................................1-9

1-4. FATEPEN Plug Acceleration Non-Fracture Mass Loss Model.8..........................1-10 1-5. Sectioned Aluminum Plate Revealing Penetration prior to Plug Formation in

Thick Plates. ........................................................................................................1-10 1-6. Effects of Increased Impact Obliquity on Fragment Mass Loss, 248-Grain Mild

Steel Cube vs. 3.18-mm 2024. Aluminum Plate; Impact is from Right to Left30 ..1-11 1-7. Penetrator and Plate Plug Trajectory Deflections for Compact Steel Cylinders

Perforating Steel and Aluminum Plates. Impact Obliquity = 45°.6,36 ....................1-12 1-8. High-Velocity, Multiple-Plate Penetration Damage Caused by a 240 Grain Steel

Cube Impacting at 2.56 km/sec1 ..........................................................................1-13 1-9. Double-Exposure Radiograph of 240-Grain Steel Cube after Perforating the

First and Third Plates in 1-81 ...............................................................................1-13 1-10. Debris Cloud and Witness Plate Damage Characteristics for 106 Grain Steel

Spheres after Perforating a 2.4 Mild Steel Shatter Plate at Two Impact Velocities (S = spacing of Witness Plate behind Shatter Plate).21,37....................1-14

1-11. Effect of Spacing behind Shatter Plate on Witness Plate Damage. 6.9 Grain Steel Spheres vs. 2.4 mm Steel Shatter Plate and 0.81mm Steel Witness Plate, V=2100 m/sec.21 ........................................................................................1-16

1-12. Illustration of Impulsive Punch Plate Damage in a 6.4 mm Aluminum Witness Plate Impacted by a Debris Cloud Generated by a 12.7 mm Steel Sphere Perforating a 3.2 mm Steel Plate at 2,260 m/s. Plate Pieces in the Inset were not Perforated.39...................................................................................................1-17

1-13. General Characteristics of High Velocity Multiple Plate Penetration by Compact Fragments............................................................................................................1-18

1-14. Typical Damage to a Plate Impacted by a High Velocity Debris Cloud ...............1-19 1-15. Pre-Impact and Post-Perforation Rod Specimens and CTH Predictions for 12.6 mm Diameter, 4130 Steel Cylinders with Decreasing Lengths Perforating 25.4 mm, 2024-T3 Aluminum Plates at 1850 m/s. Longer Rods Lose More Length and Less Velocity than Equal Diameter Shorter Rods for the Same Impact Conditions.41 ........................................................................................................1-20

1-16. Impact Radiographs for a 4140 Steel Cube and L/D=3 Bars of the Same Cross- Section Impacting 1 mm, 2024-T3 Aluminum Plates. V=2100 m/s.19.................1-21 viii

LIST OF FIGURES (Cont'd) Figure Page

1-17. Recovered Debris from Tests Shown in Figures 1-16.19 .....................................1-22 1-18. Effects of Increasing Impact Yaw on Rod Deformation, Trajectory Deflection, and Post-Impact Tumble Rate. Tungsten Alloy Rods (Rc30, D = 4.75 mm, L/D =

20) vs. 1081 CR Steel Plates (BHN 90 - 110, T/D = 2) Normal Impacts.32,35 ......1-23

1-19. Effects of Increasing Impact Obliquity on Rod Deformation, Trajectory Deflection, and Post-Impact Tumble Rate. Tungsten Alloy Rods Rc30, D = 4.75 mm, L/D = 20) vs. 1081 CR Steel Plates (BHN 90 - 110, T/D = 2).31,32...............1-25

1-20. Three-Dimensional CTH Simulation Results Illustrating Effects of Impact Obliquity on Penetration Pressure Distribution and Offset between Hole Center and Rod Axis. Tungsten Alloy Rod (Rc30, L/D = 10) vs. Mild Steel Plate (θ=45o, T/D = 2), V = 1524 m/s.32 .....................................................................................1-26

1-21. Combined Effects of Impact Yaw and Obliquity on Rod Deformation, Fracture, Trajectory Deflection, and Tumbling. Tungsten Alloy Rod (Rc30, D = 4.26 mm, L/D = 10) vs. A514 Steel Plate (BHN 260, T/D = 1.5).31 .....................................1-27

1-22. The Influence of Penetrator and Target Characteristics upon Ballistic Perforation Resistance (Steel Plate).7 ....................................................................................1-28

1-23. Edge Impact Between a 0.50 cal. AP-M2 Projectile and a 12.7 mm Steel Plate, V = 618 m/s.42 ......................................................................................................1-29

1-24. Recovered 0.50 cal. AP-M2 Projectiles after Ricochet from Steel Plates.43........1-30 1-25. Effect of Impact Velocity and Plate Material on Nose Deformation and Failure.

Tungsten Alloy Projectiles vs. Steel and Aluminum Plates44 ...............................1-31 1-26. Uncontrolled Explosive Fragmentation of 155 mm shell......................................1-32 1-27. Close-up of 155 mm Shell Fragment – Cut for Gun Launching...........................1-33 1-28. Example of Explosively Formed Fragments with Size Control by Notching the

Cylinder.19 ............................................................................................................1-33 1-29. Example of Explosively Formed Warhead Fragments Using Shear Control

Notching of Warhead Case.45 ..............................................................................1-34 1-30. Close-up of Fragment No. 3 in 1-28 after Machining Bottom from Gun Launch.451-34 1-31. Example of Explosively Formed Fragments with Size Control by Means of Liner between Explosive and Case...............................................................................1-35 1-32. FATEPEN Overall Penetration Model Flowchart .................................................1-38 1-33. FATEPEN Target Interrogation Flowchart ...........................................................1-39 1-34. FATEPEN Plate Damage Computation Flowchart (Subroutine PLATDAM) .......1-40 1-35. FATEPEN Primary Fragment Penetration Flowchart (Subroutine RESDEB)......1-41 1-36. FATEPEN Larger Secondary Particle Penetration Calculations Flowchart

(Subroutine RESDEB) .........................................................................................1-42 ix

Figure Page

1-37. FATEPEN Smaller Secondary Particle Penetration Calculations Flowchart (Subroutine RESDEB) .........................................................................................1-43

1-39. FATEPEN Penetrator Shapes and Target Structures .........................................1-45 1-40. FATEPEN Debris Cloud Characteristics..............................................................1-45 1-41. Comparisons Between Measured and Predicted Debris Cloud and Witness

Plate Damage, 3.6 Gram Steel Sphere vs. 2.4 mm Copper Shatter Plate and 3.2 mm Aluminum Witness Plate.38 ..............................................................1-48

1-42. Illustration of Analyst’s Manual Equation Number Scheme..................................1-49 2-1. FATEPEN Penetrator Shapes ...............................................................................2-2 2-2. Flat-Nosed and Round-Nosed Cylindrical Penetrators..........................................2-4 2-3. FATEPEN Reference Frame and Initial Velocity Vector Specification ..................2-6 2-4. Pitch, Yaw, and Roll Rotation Sequence for Penetrator Orientation .....................2-8 2-5. Sequential Penetrator Rotations Viewed Along Rotation Axis .................................2-8 2-6. Composite Pitch, Yaw, and Roll Rotation Sequence................................................2-9 2-7. Presented Area vs. Yaw for an L/D=1 Cylinder ...................................................2-10 2-8. Penetrator Precessing About Angular Momentum Vector ...................................2-13 2-9. Plate Thickness and Fluid Thickness (Infinite Lateral Extent Plates) ..................2-18 2-10. Target Plate Dimensions and 3-D Space ............................................................2-19 2-11. Fluid Thickness for Finite Lateral Extent Plates...................................................2-19 2-12. Target Plate Body-Fixed Unit Vectors..................................................................2-20 2-13. Composite Pitch and Yaw Rotation Sequence for Plate Orientation...................2-20 2-14. Plates of Infinite Lateral Extent are Located by Specifying Spacing Along

Z-Axis ..................................................................................................................2-21 2-15. Plates of Finite Lateral Extent are Located by Specifying X, Y, and Z

Coordinates of Center of Impact Face.................................................................2-21 2-16. Equivalent Single Plate Substitution of a Laminated Plate Array ........................2-27 2-17. FATEPEN Debris Cloud Characteristics..............................................................2-31 2-18. Typical Damage to a Plate Impacted by a High Velocity Debris Cloud (Left) and

Illustration of Particle Trajectory Distribution (Right)............................................2-32 3-1. Plates of Infinite Lateral Extent are Positioned Sequentially along the Positive

Z-Axis ....................................................................................................................3-2 3-2. Infinite Plate Crossings Beyond (Left) and Within (Right) theLateral Limits of

Expected Trajectory Deflections ............................................................................3-3 x

Figure Page

3-3. Target Intersection Order for Plates of Infinite Lateral Extent Requires Plate 2 to be Intercepted before Plate 3. Position Vector from Plate 2 to Plate 3 Points “Upstream” and therefore Plate 3 is Missed ..........................................................3-4

3-4. Plates of Infinite Lateral Extent are Missed when Trajectory is Either Parallel to the Next Plate (Left) or when the Position Vector to Interception Point is “Upstream” (right)...................................................................................................3-4

3-5. Finite Plate Target Array. Plate 3 is Closer to Origin than Plate 2, and Plate 3 does not Cross the Z-axis ......................................................................................3-5

3-6. Position Vectors from Point of Interception to Target Verticies when Target is Missed (left) and Hit (right).....................................................................................3-6

3-7. Summation of Angles to Determine Hit or Miss .....................................................3-6 3-8. Trajectory Intersection Geometry, Turning Point Location, and Travel Distance ..3-8 3-9. Gyration Model for Spin-Stabilized Penetrators1 .................................................3-11 3-10. Impact Angle ........................................................................................................3-12 4-1. Effective Presented Area Models...........................................................................4-3 5-1. FATEPEN Plate Damage Characteristics..............................................................5-2 5-2. Ballistic Limit Velocity Correction Factor for High Obliquity Impacts .....................5-9 5-3. FATEPEN Thick Plate Penetration Model ...........................................................5-10 5-4. Illustration of Unconfined and Confined Penetration Depths for

Oblique Impacts ...................................................................................................5-16 5-5. Cosine Interpolation Function in Subroutine INTERP..........................................5-19 5-6. Typical High Obliquity Impact Penetration Geometries6......................................5-28 5-7. Embedment Depth Estimate for Highly Oblique Impacts Using the Projected

Presented Area of the Equivalent Unyawed Cylinder6 ........................................5-28 5-8. Illustration of Ballistic Perforation Hole Enlargement in Aluminum and Graphite-

Epoxy Plates Perforated by Compact Steel Cylinders. Shaded Circular Insets in Holes Correspond to the Diameter of the Steel Cylinders. ..................................5-35

5-9. Variations in Ballistic Perforation Hole Sizes with Impact Speed and Plate Thickness for Compact Steel and Aluminum Fragments Perforating 2024 Aluminum Plates. In this Graph, Ds is the Hole Diameter and Dc is the Sphere Diameter or Cube Length15. .................................................................................5-38

5-10. Keyhole Ballistic Perforation Hole Model for Compact and Elongated Fragments............................................................................................................5-39

5-11. Rod/Plate Encounter Geometry ...........................................................................5-41 5-12. Normalized initial contact distance vs. impact yaw , L/D = 16 titanium rods vs.

aluminum plates, T/D = 1.16, V = 1525 m/s, DT/D = 1.84....................................5-44 xi

Figure Page

5-13. Illustration of FATEPEN Debris Cloud Trajectory Distribution and Geometric Area Removal Model for Center Hole Enlargement. ...........................................5-51

5-14. FATEPEN Impulsive Loading Model for Central Hole Enlargement....................5-52 6-1. FATEPEN Plug Acceleration Mass Loss Model .......................................................6-2 6-2. FATEPEN Thick Plate Penetration Model ................................................................6-9 6-3. Modified Hydrodynamic Penetration Phase Diagram. ............................................6-10 6-4. Rigid Rod Penetration in Weak Plates....................................................................6-19 6-5. Superposition of Impact Obliquity and Yaw Effects to Obtain Trajectory

Deflection and Rod Residual Angular Velocity. ...................................................6-24 6-6. Obliquity Effect Residual Velocity Model. ...............................................................6-25 6-7. Transverse loading due to impact yaw (delayed contact)16, 17. ...............................6-26 6-8. Fracture of Tungsten Alloy Cubes Impacting Thin Steel and Aluminum Plates and Corresponding FATEPEN Mode Predicitons.26 ............................................6-34 6-9. Variations in Shatter Velocity with Normalized Plate Thickness for Steel

Cubes.24 ...............................................................................................................6-35 6-10. Effect of Impact Orientation of Impact Fracture of Steel Cubes. .........................6-37 6-11. Impact Fracture Criteria for Non-Flat Impacts. ....................................................6-38 6-12. FATEPEN Three Dimensional Impact Fracture Model ........................................6-39 6-13. Shear Deformation Profiles for L/D = 20 Rods Corresponding to Assumed

Initial Shear Strains of 1 - 4..................................................................................6-46 6-14. Local Plastic Shear Strain Due to Impact Yaw Effect, Delayed Contact Tracking

Force. ..................................................................................................................6-47 6-15. FATEPEN Implementation of the Obliquity Effect, Rod Deformation and

Fracture Models ...................................................................................................6-48 6-16. FATEPEN Implementation of the Yaw Effect Delayed Contact Rod Deformation and Fracture Models ............................................................................................6-49 7-1. FATEPEN Debris Cloud Characteristics...................................................................7-2 xii

LIST OF TABLES

Table Page

2-1 FATEPEN Penetrator Materials .............................................................................2-1 2-2 FATEPEN User-Specified Penetrator Dimensions ................................................2-3 2-3 FATEPEN Armor Piercing Projectile Cores ...........................................................2-5 2-4 FATEPEN Target Materials and Typical Brinell Hardness Values ......................2-17 2-5 FATEPEN Penetrator and Target Material Properties Assigned in Subroutine

MTLPROP............................................................................................................2-24 5-1 Sharp Attack Projectile Ballistic Limit Velocity Parameters .................................5-15 5-2 Compact Fragment Hole Size Empirical Model Parameters ...............................5-37 6-1 Modified Hydrodynamic Penetration Characteristics ...........................................6-11 6-2 Minimum Threshold Fracture, Vc1, and Shatter, Vc2, Speeds for Cubes Impacting

Flat Against 2024 Alumimum Plates....................................................................6-35 6-3 Adjustments to Cube Critical Fracture Speeds for Spheres and Cylinders .........6-36 8-1 FATEPEN Output Array .........................................................................................8-8

1-1

SECTION 1.0

INTRODUCTION

1.1 EXECUTIVE SUMMARY

FATEPEN (Fast Air Target Encounter Penetration) is a set of fast running algorithms that simulate the penetration of spaced target structures by fragments, long rods, and projectiles impacting at speeds up to about 5 km/sec. The model predicts penetrator mass loss, velocity loss, trajectory change, and tumbling throughout a target. The mass loss model includes impact fracture calculations that may transform an incident warhead fragment into a post-impact expanding, multi-particle debris cloud which FATEPEN then tracks through the remaining target structure. FATEPEN also predicts impulsive loading and hole damage to plate structures by single penetrators and multi-particle debris clouds. The primary application of the code has been weapons effectiveness assessments involving air targets and lightly-armored surface targets.

The current development version of FATEPEN is a 32-bit FORTRAN PC code with a Visual Basic graphical user interface. FATEPEN uses the MS-PowerStation 4.0 Professional, FORTRAN 90, compiler and runs under Windows 95 or higher. The terminal interaction models are compiled as a separate Dynamic Link Library (DLL) for easy portability to other calling programs. The current PC version of the code (Version 3.0.0) contains 13,931 lines of FORTRAN and 16,550 lines of Visual Basic. Typical run times with a 166 MHz PC are on the order of 0.02 second for a fragment penetrating a spaced target array comprised of about 10 elements.

The improvement of FATEPEN and its extension to new encounter conditions has been the unifying focus of many otherwise independent experimental and analytical efforts to investigate and model high velocity and hypervelocity penetration characteristics for a wide variety of penetrator and target materials and structures. These individual studies and the corresponding FATEPEN improvements are described in detail in the technical reports and papers referenced herein. FATEPEN (Version 3.0.0) is documented, in three volumes as follows:

Volume I – Analysts Manual. The Analysts Guide describes the analytical foundation of FATEPEN and serves to promote more informed decisions regarding its application, to aid in interpreting the output of the code, and as a reference for future improvements. This volume summarizes the development history of FATEPEN, it describes the penetration phenomenology addressed by the code, it provides an overview of the model, it describes penetrator and target input conventions, and it summarizes each of the primary terminal interaction models and algorithms including the principal formulas and the assumptions and limitations associated with their development.

Volume II – User’s Manual. The User’s Guide provides instructions regarding installation of FATEPEN onto a PC, how to activate the code, and includes detailed instructions explanations, and screen displays describing how to use of the code for penetration problems and for component vulnerability analysis. Sample problems are presented to illustrate use of the code and to provide test cases to check installation of the program

1-2

Volume III – Validation Document. The Validation Document presents the results of comparisons between FATEPEN model predictions and numerous test results contained in an expandable terminal ballistics database. The database encompasses a wide range of encounter conditions to thoroughly test the model. Two kinds of comparisons are presented. The first type are “point-by-point” comparisons wherein the exact encounter conditions (impact speed, orientation, impact obliquity, etc.) for a particular test are input to FATEPEN and the predicted results are compared with the corresponding test results. The point-by-point comparison results establish the expected prediction accuracy of the code for various applications (e.g., long rods vs. thick plates, cubes vs. thin plates, etc.). The second kind of comparison deals with variations in model predictions and test results with changes in a single encounter variable such as impact speed, impact obliquity, etc. These “trendline” comparisons reveal basic terminal ballistic penetration behavior and are useful in design and in interpreting weapons effects test results. The juxtaposition of model prediction trends and corresponding test results also serve to confirm the reasonableness of the model predictions even when the point-by-point accuracy statistics might suggest otherwise due to the stochastic nature of some ballistic impacted responses (e.g., impact fracture). Taken together, the two types of comparisons provide a complete picture of model suitability for specific applications.

This volume contains the FATEPEN Analysts Guide

1.2 HISTORICAL PERSPECTIVE

The relative impact velocities between missile warhead fragments and high altitude missile targets have been expected to reach or exceed 5 km/sec since about the mid-1970’s.1* This velocity is well above threshold fracture speeds for common warhead fragments impacting thin plates of aluminum and other aerospace materials. The fragment penetration equations most often used at that time for air target vulnerability assessments were taken from the JTCG Penetration Equations Handbook (JTCG PEH) for Kinetic Energy Penetrators.2,3 These equations indirectly recognize fragment mass loss due to non-fracture and fracture mechanisms, but the fragment residual mass calculations are based on empirical THOR relations obtained by regression analyses of limited steel fragment residual mass data without regard to specific mass loss mechanisms.4 As a result, the mass loss formulas pertain to steel fragments. In the absence of specific impact fracture mass loss data, the JTCG PEH estimates fragment residual masses for impact speeds above the fracture threshold by using the THOR residual mass formula for mild steel plates.

The threshold fracture speeds are estimated for different target materials by adjusting an experimental fracture threshold speed for steel fragments impacting steel plates based on equality of impact pressure. The JTCG PEH impact fracture model does not recognize the sensitivity of the fracture threshold speed to fragment shape and plate thickness.

Figure 1-1 compares normalized fragment residual mass test data with predictions using the JTCG PEH formulas for mild steel cubes impacting aluminum plates with normalized thickness, T/D=0.25. The insets contain post-perforation radiographs of the cubes for selected tests and reveal the effects of increasing impact speed on fragment fracture. It can be seen that the threshold fracture speed in this case is about 1000 m/s. The rapid drop in

* Superscripts denote references listed at the end of each section of the report.

1-3 the fragment residual mass data above the fracture threshold speed is typical of compact fragments. The JTCG PEH THOR formulas properly predict a general downward trend in fragment residual mass with increasing impact speed, but they significantly overestimate the fracture threshold speed and the fragment residual mass above the fracture threshold.

Normalized Residual Weight vs Impact Speed 31 Grain Mild Steel Cubes vs 2024-T3 Aluminum Plates (T/D=0.25)

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0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Impact Speed (m/s)

W r/W

JTCG Pen. Eqs Hbk2.

Test Data (Flat Impacts)14

JTCG PEH Estimated Threshold Fracture Speed = 2167 m/s

THOR Formula for Aluminum Plates4

Modified THOR Formula for Steel Plates

Post-Impact Cube Radiographs

Figure 1-1. Effects of Increasing Impact Speed on Impact Fracture of Mild Steel Cubes

Impacting Flat against 2024-T3 Aluminum Plates (Wr is the Weight of Primary or Largest Penetrator Remnant, W is the Pre-Impact Cube Weight)

The JTCG PEH equations consider only the major residual fragment particle subsequent to perforation. When impact speeds are below to slightly above threshold fracture speed, the primary ballistic threat to air targets by warhead fragments remains fairly well represented by the single largest penetrator remnant throughout the target. However, as revealed by the insets in Figure 1-1, when impact speeds exceed about twice the threshold fracture speed, impact fracture is extensive and the major fragment particle represents only a small fraction of the damage potential of the post-impact debris cloud. Thus, it was recognized that fragment penetration and plate damage predictions for impact speeds above about 2000 m/sec, would require new models to predict the transformation of single fragments into high speed, multi-particle debris clouds as a function of fragment material, shape, and size and target material, thickness and orientation.

Beginning in 1978, the Naval Surface Warfare Center, Dahlgren Division, (NSWC) funded a series of experimental and analytical efforts to expand the available penetration database for impact speeds between about 1500 and 5000 m/sec. An initial test program of 18 shots

1-4 provided preliminary observations regarding the effects of fragment shape, size, and impact speed on penetration of a spaced plate array representing a typical air target.1 These and other tests provided the experimental basis behind the 1981-82 development of the multiple plate fragment penetration model and a computer code called Fast Air Target Encounter (FATE).5 FATE was developed for applications involving steel fragments penetrating thin aluminum and/or steel plates at very high velocities. The code incorporated previously developed formulas for the primary fragment residual mass and velocity calculations.3,6.7.8 Most of the new models in FATE were associated with predicting the formation, dispersion, penetration, and plate damage associated with a multi-particle debris clouds. When the impact speed exceeded an empirical impact fracture threshold velocity, the penetrator was presumed to fracture into a velocity-dependent, number of identical debris particles. Impact fracture of the plate plug was predicted independently using similar models. In 1982 several new algorithms were added to FATE to compute kill probabilities for avionics components exposed to multi-particle debris clouds; the new version of the code was called FATE-1.9 In 1983 the penetration equations in FATE-1 were expanded to predict the size of the largest or primary penetrator debris particle and its penetration and damage independently of the other plate and penetrator debris particles. The improved version of the code was named FATE-2.10

FATE, FATE-1 and FATE-2 were coded in HP-BASIC for execution on a HP-9845B desktop computer. The BASIC version of FATE-2 was translated into FORTRAN at NSWC for execution on the center’s VAX computers. In the process, the component kill probability algorithms were removed and an option to utilize JTCG PEH THOR formulas for the primary fragment penetration calculations was added for comparisons with the FATE equations.

The NSWC FORTRAN version was named FATEX and included a text-menu based user interface which greatly improved the usability of the code.11 The VAX FORTRAN version of FATEX was later converted at ARA to Microsoft FORTRAN Version 3.51 for use on MS- DOS personal computers. The THOR penetration calculation option was not included in the MS-DOS version of FATEX.

During the period from 1984-90, additional experiments and analyses were performed at the Naval Research Laboratory (NRL), Denver Research Institute (DRI) and Applied Research Associates, Inc. (ARA) to expand the high-speed impact database and to improve the penetration model. Approximately 750 impact fracture tests were conducted during this period, and the results were used to develop a comprehensive impact fracture model for steel, tungsten alloy, aluminum, and depleted uranium cubes impacting a variety of metallic plate materials.12,13,14

Parallel efforts under sponsorship by the Raytheon Company, the Naval Weapons Center (NWC), and the Naval Surface Warfare Center, Dahlgren Laboratory (NSWC) led to development of a penetration code called FPIIM (Fragment Penetration and Impact Initiation Model) which simulated multiple-spaced plate penetration by steel, tungsten alloy, or depleted uranium compact fragments.15,16 FPIIM included expanded primary fragment residual mass and velocity models and recognized fragment mass loss due to shock-erosion, extrusion shear, lateral erosion, and impact fracture. The FPIIM impact fracture calculations utilized the MS-DOS FATEX impact fracture model for steel cubes and extended the model to approximate impact fracture for other fragment materials by adjusting the steel cube threshold fracture speed based on equality of impact pressure.12

1-5

FPIIM monitored the mass, velocity, and orientation of the primary residual fragment throughout the plate array, but did not consider secondary particles.

In 1988, the intact FPIIM and MS-DOS FATEX codes were linked for sequential execution to form the original FATEPEN code.17 In this first version of FATEPEN, the user could exercise an option to use FPIIM for the primary fragment penetration calculations through the entire plate array and then store the results for subsequent use by FATEX in the debris cloud penetration and damage calculations. This initial version of FATEPEN was cumbersome and inefficient, and, in 1989-90, the code was completely restructured and streamlined, and the user interface was substantially improved. The generalized steel cube fracture model14 was extended to non-steel fragment materials and also installed along with an additional secondary penetrator particle size and improvements to the plate damage calculations. The new version of FATEPEN was named FATEPEN2 and was released in January of 1991.18 The naming convention for new releases of the code was later revised, and FATEPEN2 is now referred to as FATEPEN (Version 2.0).

Since its original release in 1991, several experimental and analytical efforts have been accomplished to improve FATEPEN penetration models. This work has been sponsored by the NSWC, the Air Force Armament Laboratory (AFATL), and by the Raytheon Company.

These later model enhancements include: new impact fracture models for bar fragments,19 cylinders and spheres,20 multi-particle, synergistic effects on plate damage,21 impact fracture and penetration models for tantalum fragments, an improved lateral erosion mass loss model, new residual mass and velocity models for laminated plates, and 3-D fragment tumbling and trajectory deflection models.22 These FATEPEN improvements led to the release of FATEPEN (Version 2.4 and Version 2.4R for Raytheon) in April of 1994.

During 1994-95, under sponsorship by the Army Research Laboratory (ARL), portions of the FATEPEN code were modified to improve computational flow and the improved FORTRAN code was translated into the C programming language for installation in the Modular UNIX-based Vulnerability Estimation Suite (MUVES).23 The improved version of the FORTRAN code, FATEPEN (Version 2.5.0) was released in June, 1995.24

Several enhancements to the FATEPEN penetration model have been accomplished since the release of Version 2.5.0. These include the addition of two additional tungsten alloys to the fragment material catalog and generalization of the shape effects model to recognize the effects of all aspect ratios (rods, bars, and platelets) on impact fracture characteristics,25 determination of FATEPEN fragment input parameters for explosively formed fragments,26 the addition of fluids to the target catalog,27,29 the installation of long rod residual mass and velocity models for thin and thick plates,28,29 further improvements to the high obliquity impact mass and velocity loss models,30,31 the installation of new lateral loading and response models for long rod penetrators,31,32,33 the addition of graphite epoxy fiber reinforced composite panels to the FATEPEN target catalog,34 and the addition of projectile penetration equations for pointed AP and non-AP projectiles.2,34

The FATEPEN user interface has been steadily improved along with the penetration models. The original HP-BASIC version of FATE utilized DATA statements to describe penetrator and target input parameters.5 The user could input new encounter conditions simply by changing the appropriate DATA statements. Output was printed directly to a printer. During its translation to the FORTRAN language, NSWC replaced the DATA

1-6 statements with a text-menu based user interface, which greatly enhanced its usability.11 The NSWC user interface was retained in the translation to Microsoft FORTRAN and through the merger of FATE and FPIIM to form FATEPEN.

During 1995-97, as part of a Phase II SBIR study to develop a missile battery damage prediction methodology, the user interface was redesigned and converted to a graphical user interface using Microsoft Visual Basic to run under the Windows operating system.35 In the process, the FATEPEN penetration algorithms were completely separated from the user interface and converted from MS FORTRAN Version 5.1 to MS FORTRAN PowerStation, Version 4.0. The penetration algorithms are now compiled as a Dynamic Link Library (DLL) to facilitate their use in other programs. In developing the new FATEPEN GUI, a Component Vulnerability Analysis Tool (CVAT) pre- and post-processor was developed to be included as an option. The CVAT enables a user to easily generate and store multiple structural and functional models representing components. The CVAT will automatically generate the associated Pk/h tables corresponding to user-defined ranges and increments in fragment threats, impact locations, and attack aspects. The CVAT calls the FATEPEN DLL for all penetration calculations.

1.3 HIGH VELOCITY PENETRATION CHARACTERISTICS

Most air and ground targets are highly complex structures comprised of a very large number of spaced and non-spaced elements involving diverse metallic and non-metallic materials and geometries (plates, tubes, wires, angles, fluid-filled containers, etc.). Current practice is to represent the actual target structures, intersected along a particular shotline, by an array of spaced and non-spaced plates. The material, thickness, and orientation of the representative plates relative to the shotline are determined by the corresponding properties of the actual structures at the point or over the area of intersection. The latter are usually obtained from computer codes that pass shot lines or volumes through highly detailed and realistic geometric descriptions of the target.

Representation of complex target structures by spaced plates is appealing first of all because it affords a general approach that can be applied to all targets. Plates also provide an accurate approximation to target ballistic resistance when the penetrator is small relative to the surfaces being impacted so that the variations in target thickness and curvature over the contact area are likewise small. Finally, representation by plates is recommended by practical considerations in that most current analytical/empirical penetration models pertain to plate impacts and nearly all terminal ballistic test data are associated with plate structures either because they were the actual structures of interest or because they provided a reasonable economical approximation.

Predicting penetration characteristics for a series of spaced plates requires models to predict ballistic perforation damage and models to predict transformations that may occur in the penetrator as a result of the impact. The penetration models must be general enough to recognize the changes that occur in the penetrator from impact to impact. The latter will generally include changes in the penetrator mass and shape, and its linear and angular velocity vectors. Plate damage and penetrator impact transformations depend on the material, thickness, and orientation of the plate and the material, shape, weight, orientation, and velocity of the penetrator. In predicting penetration characteristics, FATEPEN

1-7 distinguishes between compact penetrators, long rod penetrators and pointed projectiles as follows.

1.3.1 Compact Fragments

For this discussion, compact fragments are considered to be regular solids (spheres, cylinders, and rectangular parallelepipeds) with aspect ratios, L/D (Length/Diameter), less that about 2. Pre-formed warhead fragments are typically cubes or rectangular parallelepipeds. Elongated fragments (rods), projectiles, and irregular or explosively formed fragments are discussed in Sections 1.3.2 – 1.3.4.

Residual Velocity. Figure 1-2 compares post-perforation residual velocity measurements and model predictions versus impact velocity for compact steel cylinders impacting thin steel plates. Fragment velocity loss depends on both the strength and inertial characteristics of the penetrator and target plate. However, the sensitivity to strength properties diminishes with increasing impact speed as the ratio of material strength to impact or penetration pressure approaches zero. For impact speeds up to and slightly above the ballistic limit velocity, V50 (minimum perforation velocity), plate strength and fragment shape significantly affect fragment residual velocity (i.e., for impact speeds below the knee of the predicted Vr curve in Figure 1-2).