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AUTODYN® Explicit Software for Nonlinear Dynamics

Jetting Tutorial Revision 4.3

www.century-dynamics.com

AUTODYN is a trademark of Century Dynamics, Inc. © Copyright 2005 Century Dynamics Inc. All Rights Reserved

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Table of Contents

CHAPTER 1. INTRODUCTION .............................................................................................. 1

CHAPTER 2. JETTING THEORY........................................................................................... 3

§1. Standard Jetting Analysis.........................................................................................................3

§2. Optional Jetting Analysis...........................................................................................................6

CHAPTER 3. SETTING UP A JETTING CALCULATION...................................................... 8

§1. Review of problem setup............................................................................................................8

§2. Review of material models.......................................................................................................14

§3. Jetting definition .......................................................................................................................17

§4. Setting the detonation point ....................................................................................................22

CHAPTER 4. POST PROCESSING DATA FROM A JETTING CALCULATION................ 25

CHAPTER 5. COMPARISONS WITH EXPERIMENT AND OTHER METHODS................. 34

CHAPTER 6. REFERENCES ............................................................................................... 36

Chapter 1. Introduction

1

Chapter 1. Introduction Shaped charges are used in a variety of commercial and defense related applications. The phenomena associated with the high explosive detonation and extreme deformations of the shaped charge casing and liner poses a challenging task for numerical analysis. AUTODYN™ provides the analyst a number of different options for shaped charge design. These options range from using a highly efficient jetting option to the use of the full Euler/Lagrange/Shell processor capabilities within the program. The jetting option, discussed in this tutorial, uses a combined numerical and analytical approach. Two-dimensional finite difference grids (Euler and/or Lagrange) represent components such as the explosive and casings, while shell grids model the liner and other thin components. For the liner, modeled as a thin shell, an additional analytic jetting option is invoked which allows the liner to behave as a shaped charge jet and slug. Although thickness is considered in the shell formulation, the shell thickness is not included in the geometric representation of the shell. Thus, a shell grid is simply a series of nodes joined by linear segments. This representation has two distinct advantages over a regular 2D finite difference grid when modeling shaped charge designs:

•

•

If a full two-dimensional explicit finite difference grid is used to model a thin component, several zones have to be used through the thickness in order to model bending effects accurately. This results in a small time step for the calculation. In such cases bending effects can be modeled more efficiently by a shell formulation which has a stability timestep dependent only on the segment lengths, not on the shell thickness.

If a two dimensional Lagrange grid is used to model the liner, the large cell deformations that occur in the stagnation region during jet formation will cause the run to be terminated early unless substantial rezoning of the grid is performed. AUTODYN has one of the most powerful interactive rezoning capabilities currently available in a finite difference code, so it is possible to carry out a complete analysis in this way. Another approach is to use an Eulerian grid for the definition of the liner. By definition, this avoids any mesh distortion. To accurately perform such an analysis using Euler requires a large, finely zoned mesh. Full Lagrange or Euler analyses are certainly within the capabilities of AUTODYN but another engineering solution is also available, the jetting option, which allows very quick turnaround design calculations.

In the jetting option the liner is modeled as a shell grid, with the explosive modeled with full Lagrange or Euler detail. In this way, the full hydrodynamic equations of motion are used to compute the collapse velocity and angle for each shell mass point. These values are then used in conjunction with an analytic jet formation algorithm to obtain the jet and slug masses and associated velocities.

Chapter 1. Introduction

Section 2 of this tutorial outlines the jetting theory used in AUTODYN. Section 3 shows you how to set up a jetting calculation. The post processing of jetting data is described in section 4. The jetting example used in this tutorial is based on a tested design for a 90 mm charge with an 18 degree conical liner and results of the calculation are compared with experimental data in section 5.

2

Chapter 2. Jetting Theory

3

§1.


Standard Jetting Analysis

During an AUTODYN computation cycle, the coordinates of each shell mass point are updated from time tn-1 to tn using:

( )

uu f f dt

mxn x

nxsn

xen n

−− − −

=+ +

1 23 2 1 1 1−

( )

uu f f dt

myn y

nysn

yen n

−

− − −

=+ +

1 2

3 2 1 1 1−

x x u dtn nxn n= +− − −1 1 2 . 1 2

y y u dtn nyn n= +− − −1 1 2 . 1 2

)

)

•

•

where

internal shell forces ( f fxs ys,

external forces from the explosive ( )u ux y,

velocity components ( f fxs ys,

mass of the shell point m time step dt With the new coordinates known the jetting analysis proceeds as follows:

When a string of jetting points is created, AUTODYN automatically arranges them in the order in which they are expected to jet (the point closest to the axis is expected to jet first).

Assume that the point j-1 has jetted on a previous cycle and we are testing for jet formation at point j. Also assume that point j+1 exists. We define the angle β to be the slope the segment from j to j+1 at the instant that point j jets.

01 2j+ /


tan( )//

/β01 2 0

1 2

01 2

jj

j

dydx

++

+=

dy y yj j0

1 20

10

+ += −/ j

j

•

dx x xj j0

1 20

10

+ += −/

where the zero subscript indicates values at the instant of jet formation.

The angle β at point j is then computed as an average of the two adjacent segments.

tan( )/ /

/ /β00

1 20

1 2

01 2

01 2

jj j

j j

dy dydx dx

=++

− +

− +

Note that this equation has no geometric interpretation since the jet formation times of the two adjacent segments are different.

The jetting algorithm assumes that, on jetting, the mass point j splits into a slug and a jet according to the theory given by Pugh, Eichelberger and Rostoker in reference [1] . Using this theory, the jet and slug masses and velocities are:

•

m mjetj j

j

=−

.cos( )1

20β

m mslugj j

j

=+

.cos( )1

20β

u u a a bjetj j j j= +0 .(sin( ) cos( ) )j

j

u u a a Bslugj j j j= ⋅ − ⋅0 (sin( ) cos( ) )

where

u u ujx y0 02

02= +( )

4


5

tan( )auu

j xj

yj= − 0

0

b jj

j=−sin( )

cos( )β

β0

01

The mass point j is assumed to split into a slug and a jet at the time that its radius equals the anticipated slug radius, . This radius is related to the slug volume by:

yslugj

•

Vy d d

slugj slug

j j j

=+− +π ( ) .( / /2

01 2

01 2

2)

where

d dx dyj j j0

1 20

1 2 20

1 2 2+ + += +/ /( ) ( )/

•

From the jetting equations, the slug volume is related to the pre-jetting volume (computed for each mass point at the start of the calculation) by

VV

slugj j

j

=+( cos( )1

20β )

•

We can solve these last two equations to give us the slug radius

YVd dslug

jj j

j j=+

+− +

2 1 0

01 2

01 2

( cos( ))( )/ /

βπ

If mass point j-1 or j+1 does not exist, the above equations are still valid if the non-existent point is assigned the same coordinates as point j. These equations are used to determine if jet formation occurs at mass point j during the current cycle. If the radius of point j is less than the computed slug radius at the end of the cycle then a binary search is performed to determine the exact time at which jetting occurs during the cycle. Once point j has jetted, focus switches to point j+1. The logic allows more than one point to jet in a single time step. After mass points have been tested for jetting, the cumulative slug mass and momentum is calculated by summing over all jetted points. From these sums, a mean slug velocity is calculated and assigned to the x-velocity component of each jetted point (the y-velocity component is set to zero). This averaging keeps a stable profile for the slug but has no effect on points that have still to jet.


§2. Optional Jetting Analysis

An optional jetting analysis has been included in AUTODYN which uses post calculation values to provide an improved estimate of the collapse angle, β , and the dependent jetting parameters. The following diagram shows the vector triangle formed by the collapse velocity, , the velocity of the stagnation point, u , and the velocity of the jet relative to the stagnation point,

.

u0

c

ur

a

uc

uruo

ß

uc and are related to u and by: ur jet uslug

uu u

cjet slug

=+

2

uu u

rjet slug

=−

2

From this diagram the following relationship can be obtained:

tan( )cos

sinβ =

−u a

u u ac

0

0

The optional jetting analysis uses the fact that once a calculation is complete, the locus of the stagnation point is defined by the values of ( , ) obtained for each jetted point and thus can be obtained by differentiating this curve. The differentiation is performed by constructing a quadratic through the points j-1, j and j+1 and taking the derivative at point j (except for end points where the derivative is taken at point j-1 or j+1 as required). With u known, the above equation can then be used to obtain new estimates for the collapse angle,

. In general these values will not be the same as those computed during the calculation

t xjet jet

uc

c

β

6


7

and because they yield a more consistent set of data, tend to give better estimates of the jetting parameters.

Chapter 3. Setting Up A Jetting Calculation

§1.


Review of problem setup

Cycle zero of a sample jetting calculation has been included on the tutorial diskette. Activate AUTODYN on your workstation and load this file with has ident “JETTNG”. (This model is similar to the “INTER3” Interaction Tutorial Model. See the Interaction Tutorial for details on setting up this problem.)

The calculation is based on a tested design for a 90 mm charge with an 18 degree conical liner (results are compared with the experimental data in section 5). A majority of the input for the calculation has already been generated. This allows us to skip over the standard input required for most calculations (geometry, material assignments, etc.) and focus on the special input required for a jetting calculation (jetting points and explosive burn). The input units used are (cm, gm, µsecs). Before we proceed to input the remaining data, take some time to review the problem as it has previously been set up. Choose the “Modify” option from the main menu followed by “View”, “Gridplot” & “Matplot” to view the four subgrids that have been generated and the associated material assignments.

8


9

Gridplot of shaped charge model

Material Location Plot


Enter the subgrid menu and view the zoning, material allocations and boundary conditions for each subgrid. The following figures illustrate the four subgrids.

Liner (Shell subgrid, copper, constant thickness of 2mm)

10


11

Explosive (Euler subgrid, Octol and initial void regions)


Case (Lagrange subgrid, steel)

12


13

Detonator (Lagrange subgrid, aluminum)


Viewing all of the subgrids together using View Gridplot (available from the Global/Subgrid menu) and turning on the Mirror option (F5 function key) produces the following plot of the entire system:

Once you are familiar with the subgrid data, proceed to the “Global” menu and “Review” the “Material” data for the problem.

§2. Review of material models

14


15

AUTODYN uses only the reference density for copper. A shell subgrid containing jetting points is automatically treated as a string of mass points with no material strength.


16


17

A JWL equation of state for the explosive is defined. The data was extracted from the material library (EXPLOS) supplied with AUTODYN which contains JWL parameters for most conventional explosives.

Note: You must specify a JWL equation of state if you wish to use the burn logic included in AUTODYN. If you do not have JWL parameters for a particular explosive, you can model the explosive as a gamma law gas by setting the first two terms in the JWL equation of state to zero.

You should now be familiar with the problem setup, so we will proceed to complete the definition of the problem.

§3. Jetting definition


Our first task is to define which points are to be jetting points. We do this by moving to the “Global”, “Subgrid” (choosing LINER), “Options”, “Jetting” menu. To set our jetting points we enter the data as above.

AUTODYN allows one string of jetting points to be defined at the start of a calculation. These points must be a consecutive string of nodes within a shell subgrid. It is not necessary (or usually desirable) to define all nodes of the shell subgrid to be jetting nodes. However, all nodes of a subgrid containing jetting points will automatically be treated as mass points with no strength. When a string of jetting points is defined, AUTODYN automatically numbers the points in the order in which they are expected to jet (the point closest to the axis is expected to jet first etc.). If we wish to redefine a string of jetting points we must first “Clear” any existing points. You can only “Define” and “Clear” jetting points at the start of a calculation. However, you can use the “Reduce” option at any time to remove unjetted points from the end of the string. This might be useful if an ill behaved late jetting point were to adversely influence the jetting of an adjacent point.

18


19

The Jetting menu is displayed with the following options: Reduce Reduce the number of points in the current string of jetting points •

•

•

•

Clear Clear all jetting points

Setwrap Set wrapup to occur when jetting completed

View View the current jetting points

We set Setwrap to “Yes” in order to wrapup (stop) the calculation when all the specified jetting points have jetted.


We now select “View” to check that the points have been assigned correctly.

Note that we have not included the first and last two nodes of the shell subgrid in the string of jetting points. The first node is on the axis of symmetry and is therefore not able to jet. Instead we have already assigned a boundary condition which fixes this node in its starting position:

20


21

Fixed node on axis

The last two nodes have been omitted because from past experience of similar geometries, these nodes will probably receive a smaller impulse from the explosive than other nodes and consequently are likely to lag behind during the liner collapse. The nodes will probably not jet, but more importantly the averaging of segment quantities (length, angle) used to determine jet parameters would cause the node (if included) to adversely effect the jetting of the adjacent nodes.

Note: If you are unsure whether or not to include such nodes, include them initially and then use the “Reduce” option to remove them later if necessary. You cannot add nodes later.

Since we have elected to have the calculation terminate automatically after the last point jets, the wrapup time and cycle limit have already been set to large values so that they will not stop the calculation.


§4. Setting the detonation point

Our next task is to set up the detonation of the explosive. We do this by moving to the “Global”, “Options”, “Explode” menu which has the following options:

Node Define an detonation point •

•

•

•

•

Plane Define a detonation plane

Delete Delete detonation points/planes

Review Review the detonation points/planes specifications

View View all detonation points/planes

Choose the “Node” option to define a single point detonation at the coordinates shown above. After entering this data we are asked if we wish to limit the range of influence of the detonation point we have defined. This is useful if, for example, we want to detonate around a wave shaper which we may define by multiple detonation points with different detonation times. However, this is not required for the present analysis. Enter “no”. Choose the “View” option to check that the detonation point has been defined correctly:

22


23

Detonation point

The rest of the problem data has already been setup, so that we are now ready to proceed with the analysis. For further details on specifications of the interaction of the various subgrids (Euler/Lagrange coupling) please refer to the Interaction Tutorial.

We return to the main menu by pressing <Tab> a number of times. We “Save” the data and then “Execute” the calculation. On most machines the calculation will take less than one hour to complete. The problem wraps up when the last specified jetting point has jetted around 35 microseconds.


Final cycle, t= 35.5 microseconds

We save this last cycle and exit to the main menu by selecting Wrapup.

24

Chapter 4. Post processing Data From A Jetting Calculation

25


Once a calculation is complete we can post process jetting data to produce graphical and printed output of the jetting variables. In our sample calculation, jetting is complete by cycle 373. The save file for this cycle is included on the diskette for this tutorial. Return to the main menu and load this file (Ident “JETTNG”, cycle 373). Then select “Post proc.”, ”Jetting”.

A jetting summary plot appears showing the jet velocity as a function of the cumulative jet mass and the following menu is presented.

Variables Define new variables for the horizontal and vertical axes •

•

•

•

•

Analysis Define the type of analysis to be performed on the jetting data

Numpts Limit the number of jetting points to be included in the plot

Zoom Zoom in to a portion of the plot

Reset Reset the window to show the entire plot


•

•

Examine Determine (X, Y) coordinates of any position

Output Output a jetting summary to a disk file

The default variables of jet velocity (vertical axis) and cumulative jet mass (horizontal axis) can be changed by variables from the following list:

Variable Definition

X-ZERO Initial X coordinate

Y-ZERO Initial Y coordinate

LIN.MASS Initial liner mass

LIN.THICK Initial liner thickness

T-JET Time of jet formation

X-JET X coordinate of jet formation

Y-JET Radius Y of jet formation (i.e. slug radius)

UX-JET X component of collapse velocity at jet formation

UY-JET Y component of collapse velocity at jet formation

DX-JET DX of segment at jet formation

DY-JET DY of segment at jet formation

BETA Liner angle at jet formation

ANGLEA Angle A in the jetting equations

U-ZERO Collapse speed at jet formation

U-JET Jet velocity

U-C Velocity of the stagnation point

U-REL Velocity of jet relative to stagnation point

SLUG MASS Slug mass

JET MASS Jet mass

CUM J MASS Cumulative jet mass

CUM J KE Cumulative jet kinetic energy

Jetting Variables For example, in the following plot the horizontal variable has been changed to “X-ZERO”.

26


27

The jetting theory given in section 2 describes two types of jetting analyses - the standard analysis and an optional analysis. We can select which of these we wish to use with the “Analysis” option. The default is to use the standard analysis. We now select the optional analysis. Notice that the analysis type is shown in the top right corner of the plot window:


The “Numpts” option allows us to exclude some of the later jetting points from the plot if we wish. There are a total of 21 jetting points for our calculation. You have the option of plotting data from a lesser number if you choose.

28


29

If “Output” is selected a summary of the jetting data for the current analysis type will be output to a disk file. If the standard jetting analysis is currently being used the data will be written to the file “JETOUT.STD”. If the optional analysis is being used the data will be written to the file “JETOUT.OPT”. Data output to these two files for our current problem is reproduced on the following pages.


Standard Jetting Analysis (JETOUT.STD)

SHAPED CHARGE JETTING ANALYSIS STANDARD JETTING ANALYSIS

LINER MASS = 2.3025E+02 JET MASS = 3.1015E+01

LINER MOMENTUM = 2.3619E+01 JET MOMENTUM = 1.8521E+01

LINER KINETIC ENERGY = 6.1329E+00 JET KINETIC ENERGY = 6.0509E+00

J X-ZERO Y-ZERO LIN.MASS LIN.THICK

1 5.0000E-01 5.5200E-01 1.4405E+00 2.0000E-01

2 9.8236E-01 7.0873E-01 3.4098E+00 2.0000E-01

3 1.4647E+00 8.6545E-01 4.3845E+00 2.0000E-01

4 1.9471E+00 1.0222E+00 5.2765E+00 2.0000E-01

5 2.4295E+00 1.1789E+00 6.1685E+00 2.0000E-01

6 2.9118E+00 1.3356E+00 7.0605E+00 2.0000E-01

7 3.3942E+00 1.4924E+00 7.9525E+00 2.0000E-01

8 3.8765E+00 1.6491E+00 8.8446E+00 2.0000E-01

9 4.3589E+00 1.8058E+00 9.7366E+00 2.0000E-01

10 4.8413E+00 1.9625E+00 1.0629E+01 2.0000E-01

11 5.3236E+00 2.1193E+00 1.1521E+01 2.0000E-01

12 5.8060E+00 2.2760E+00 1.2413E+01 2.0000E-01

13 6.2884E+00 2.4327E+00 1.3305E+01 2.0000E-01

14 6.7707E+00 2.5895E+00 1.4197E+01 2.0000E-01

15 7.2531E+00 2.7462E+00 1.5089E+01 2.0000E-01

16 7.7355E+00 2.9029E+00 1.5981E+01 2.0000E-01

17 8.2178E+00 3.0596E+00 1.6873E+01 2.0000E-01

18 8.7002E+00 3.2164E+00 1.7765E+01 2.0000E-01

19 9.1825E+00 3.3731E+00 1.8657E+01 2.0000E-01

20 9.6649E+00 3.5298E+00 1.9549E+01 2.0000E-01

21 1.0147E+01 3.6865E+00 9.9973E+00 2.0000E-01

J X-JET Y-JET T-JET ANGLEA U-ZERO

1 5.5835E-01 4.3991E-01 6.0152E+00 2.7340E+01 1.4529E-01

2 1.0763E+00 4.7659E-01 7.7687E+00 2.2040E+01 1.7147E-01

3 1.5976E+00 5.3638E-01 8.9941E+00 2.2710E+01 1.8367E-01

4 2.1294E+00 5.8591E-01 1.0239E+01 2.3370E+01 1.9908E-01

5 2.6621E+00 6.3316E-01 1.1460E+01 2.3909E+01 2.0818E-01

6 3.1965E+00 6.7543E-01 1.2621E+01 2.3924E+01 2.2346E-01

7 3.7356E+00 7.1514E-01 1.3821E+01 2.4448E+01 2.3213E-01

8 4.2729E+00 7.5446E-01 1.4991E+01 2.4721E+01 2.3687E-01

9 4.8135E+00 7.8965E-01 1.6165E+01 2.4924E+01 2.4099E-01

10 5.3570E+00 8.2424E-01 1.7349E+01 2.5264E+01 2.4483E-01

11 5.9005E+00 8.5635E-01 1.8520E+01 2.5410E+01 2.5016E-01

12 6.4473E+00 8.8566E-01 1.9787E+01 2.5769E+01 2.5294E-01

13 6.9923E+00 9.1529E-01 2.1012E+01 2.6038E+01 2.5288E-01

14 7.5425E+00 9.4029E-01 2.2309E+01 2.6194E+01 2.5328E-01

15 8.0877E+00 9.6926E-01 2.3681E+01 2.6363E+01 2.4888E-01

16 8.6338E+00 9.8645E-01 2.5093E+01 2.6378E+01 2.4443E-01

17 9.2075E+00 9.8684E-01 2.6759E+01 2.7063E+01 2.3850E-01

18 9.7561E+00 1.0067E+00 2.8659E+01 2.7220E+01 2.2596E-01

19 1.0326E+01 9.7675E-01 3.0794E+01 2.7540E+01 2.1527E-01

20 1.1023E+01 8.6705E-01 3.4372E+01 3.0449E+01 2.0239E-01

21 1.1784E+01 8.0866E-01 3.9478E+01 3.6267E+01 1.8242E-01

30


31

J BETA U-C U-REL U-JET JET MASS CUM J MASS

1 2.9230E+01 2.9737E-01 2.6430E-01 5.6166E-01 9.1715E-02 9.1715E-02

2 2.8985E+01 3.5126E-01 3.2800E-01 6.7925E-01 2.1355E-01 3.0526E-01

3 2.9366E+01 3.7201E-01 3.4550E-01 7.1751E-01 2.8169E-01 5.8695E-01

4 3.0541E+01 3.8871E-01 3.5963E-01 7.4834E-01 3.6601E-01 9.5296E-01

5 3.1168E+01 3.9901E-01 3.6771E-01 7.6672E-01 4.4521E-01 1.3982E+00

6 3.1997E+01 4.1755E-01 3.8549E-01 8.0304E-01 5.3633E-01 1.9345E+00

7 3.2876E+01 4.2301E-01 3.8929E-01 8.1231E-01 6.3682E-01 2.5713E+00

8 3.3102E+01 4.2910E-01 3.9398E-01 8.2307E-01 7.1772E-01 3.2890E+00

9 3.3573E+01 4.3083E-01 3.9520E-01 8.2603E-01 8.1213E-01 4.1012E+00

10 3.3955E+01 4.3331E-01 3.9641E-01 8.2972E-01 9.0620E-01 5.0074E+00

11 3.4693E+01 4.3375E-01 3.9699E-01 8.3075E-01 1.0241E+00 6.0315E+00

12 3.5816E+01 4.2561E-01 3.8926E-01 8.1487E-01 1.1736E+00 7.2051E+00

13 3.6320E+01 4.2010E-01 3.8362E-01 8.0371E-01 1.2924E+00 8.4976E+00

14 3.7699E+01 4.0586E-01 3.7165E-01 7.7750E-01 1.4819E+00 9.9794E+00

15 3.8535E+01 3.9051E-01 3.5794E-01 7.4845E-01 1.6430E+00 1.1622E+01

16 3.9821E+01 3.7123E-01 3.4195E-01 7.1317E-01 1.8534E+00 1.3476E+01

17 4.4475E+01 3.2483E-01 3.0315E-01 6.2798E-01 2.4165E+00 1.5892E+01

18 4.6904E+01 2.9136E-01 2.7518E-01 5.6654E-01 2.8138E+00 1.8706E+01

19 5.1336E+01 2.5226E-01 2.4445E-01 4.9671E-01 3.5005E+00 2.2207E+01

20 6.3806E+01 1.8840E-01 1.9444E-01 3.8284E-01 5.4598E+00 2.7666E+01

21 7.0726E+01 1.5934E-01 1.5581E-01 3.1515E-01 3.3487E+00 3.1015E+01


Optional Jetting Analysis (JETOUT.OPT)

SHAPED CHARGE JETTING ANALYSIS OPTIONAL JETTING ANALYSIS

LINER MASS = 2.3025E+02 JET MASS = 3.2447E+01

LINER MOMENTUM = 2.3619E+01 JET MOMENTUM = 1.8554E+01

LINER KINETIC ENERGY = 6.1329E+00 JET KINETIC ENERGY = 6.0362E+00

J X-ZERO Y-ZERO LIN.MASS LIN.THICK

1 5.0000E-01 5.5200E-01 1.4405E+00 2.0000E-01

2 9.8236E-01 7.0873E-01 3.4098E+00 2.0000E-01

3 1.4647E+00 8.6545E-01 4.3845E+00 2.0000E-01

4 1.9471E+00 1.0222E+00 5.2765E+00 2.0000E-01

5 2.4295E+00 1.1789E+00 6.1685E+00 2.0000E-01

6 2.9118E+00 1.3356E+00 7.0605E+00 2.0000E-01

7 3.3942E+00 1.4924E+00 7.9525E+00 2.0000E-01

8 3.8765E+00 1.6491E+00 8.8446E+00 2.0000E-01

9 4.3589E+00 1.8058E+00 9.7366E+00 2.0000E-01

10 4.8413E+00 1.9625E+00 1.0629E+01 2.0000E-01

11 5.3236E+00 2.1193E+00 1.1521E+01 2.0000E-01

12 5.8060E+00 2.2760E+00 1.2413E+01 2.0000E-01

13 6.2884E+00 2.4327E+00 1.3305E+01 2.0000E-01

14 6.7707E+00 2.5895E+00 1.4197E+01 2.0000E-01

15 7.2531E+00 2.7462E+00 1.5089E+01 2.0000E-01

16 7.7355E+00 2.9029E+00 1.5981E+01 2.0000E-01

17 8.2178E+00 3.0596E+00 1.6873E+01 2.0000E-01

18 8.7002E+00 3.2164E+00 1.7765E+01 2.0000E-01

19 9.1825E+00 3.3731E+00 1.8657E+01 2.0000E-01

20 9.6649E+00 3.5298E+00 1.9549E+01 2.0000E-01

21 1.0147E+01 3.6865E+00 9.9973E+00 2.0000E-01

J X-JET Y-JET T-JET ANGLEA U-ZERO

1 5.5835E-01 4.3991E-01 6.0152E+00 2.7340E+01 1.4529E-01

2 1.0763E+00 4.7659E-01 7.7687E+00 2.2040E+01 1.7147E-01

3 1.5976E+00 5.3638E-01 8.9941E+00 2.2710E+01 1.8367E-01

4 2.1294E+00 5.8591E-01 1.0239E+01 2.3370E+01 1.9908E-01

5 2.6621E+00 6.3316E-01 1.1460E+01 2.3909E+01 2.0818E-01

6 3.1965E+00 6.7543E-01 1.2621E+01 2.3924E+01 2.2346E-01

7 3.7356E+00 7.1514E-01 1.3821E+01 2.4448E+01 2.3213E-01

8 4.2729E+00 7.5446E-01 1.4991E+01 2.4721E+01 2.3687E-01

9 4.8135E+00 7.8965E-01 1.6165E+01 2.4924E+01 2.4099E-01

10 5.3570E+00 8.2424E-01 1.7349E+01 2.5264E+01 2.4483E-01

11 5.9005E+00 8.5635E-01 1.8520E+01 2.5410E+01 2.5016E-01

12 6.4473E+00 8.8566E-01 1.9787E+01 2.5769E+01 2.5294E-01

13 6.9923E+00 9.1529E-01 2.1012E+01 2.6038E+01 2.5288E-01

14 7.5425E+00 9.4029E-01 2.2309E+01 2.6194E+01 2.5328E-01

15 8.0877E+00 9.6926E-01 2.3681E+01 2.6363E+01 2.4888E-01

16 8.6338E+00 9.8645E-01 2.5093E+01 2.6378E+01 2.4443E-01

17 9.2075E+00 9.8684E-01 2.6759E+01 2.7063E+01 2.3850E-01

18 9.7561E+00 1.0067E+00 2.8659E+01 2.7220E+01 2.2596E-01

19 1.0326E+01 9.7675E-01 3.0794E+01 2.7540E+01 2.1527E-01

20 1.1023E+01 8.6705E-01 3.4372E+01 3.0449E+01 2.0239E-01

32


33

21 1.1784E+01 8.0866E-01 3.9478E+01 3.6267E+01 1.8242E-01

J BETA U-C U-REL U-JET JET MASS CUM J MASS

1 4.0313E+01 2.1884E-01 1.9949E-01 4.1833E-01 1.7105E-01 1.7105E-01

2 2.7329E+01 3.7191E-01 3.4620E-01 7.1811E-01 1.9029E-01 3.6134E-01

3 2.5492E+01 4.2625E-01 3.9367E-01 8.1992E-01 2.1342E-01 5.7476E-01

4 2.7388E+01 4.3171E-01 3.9727E-01 8.2898E-01 2.9571E-01 8.7047E-01

5 2.7578E+01 4.4874E-01 4.1108E-01 8.5982E-01 3.5044E-01 1.2209E+00

6 2.9277E+01 4.5495E-01 4.1769E-01 8.7264E-01 4.5093E-01 1.6718E+00

7 3.0542E+01 4.5422E-01 4.1584E-01 8.7006E-01 5.5168E-01 2.2235E+00

8 3.0809E+01 4.5986E-01 4.2009E-01 8.7995E-01 6.2408E-01 2.8476E+00

9 3.1391E+01 4.5972E-01 4.1957E-01 8.7929E-01 7.1258E-01 3.5602E+00

10 3.1798E+01 4.6161E-01 4.2019E-01 8.8180E-01 7.9764E-01 4.3578E+00

11 3.3514E+01 4.4855E-01 4.0924E-01 8.5779E-01 9.5767E-01 5.3155E+00

12 3.4745E+01 4.3839E-01 3.9969E-01 8.3808E-01 1.1066E+00 6.4221E+00

13 3.5053E+01 4.3487E-01 3.9562E-01 8.3049E-01 1.2066E+00 7.6287E+00

14 3.7208E+01 4.1112E-01 3.7583E-01 7.8695E-01 1.4449E+00 9.0736E+00

15 3.8369E+01 3.9217E-01 3.5925E-01 7.5142E-01 1.6294E+00 1.0703E+01

16 4.0239E+01 3.6736E-01 3.3899E-01 7.0635E-01 1.8909E+00 1.2594E+01

17 4.5345E+01 3.1836E-01 2.9857E-01 6.1692E-01 2.5070E+00 1.5101E+01

18 4.8930E+01 2.7846E-01 2.6653E-01 5.4499E-01 3.0468E+00 1.8148E+01

19 5.3644E+01 2.4003E-01 2.3701E-01 4.7704E-01 3.7985E+00 2.1946E+01

20 6.7180E+01 1.7598E-01 1.8929E-01 3.6527E-01 5.9835E+00 2.7930E+01

21 8.4477E+01 1.2213E-01 1.4776E-01 2.6990E-01 4.5175E+00 3.2447E+01

Chapter 5. Comparisons with Experiment and other Methods


As mentioned earlier, the calculation used in this tutorial is based on a tested design for a 90mm shaped charge with an 18 degree conical liner. The following two figures compare the experimental data with the calculated jet velocity versus cumulative jet mass using the standard and the optional analyses respectively.

AUTODYN vs Experimental Data

0.00E+00

1.00E-01

2.00E-01

3.00E-01

4.00E-01

5.00E-01

6.00E-01

7.00E-01

8.00E-01

9.00E-01

0.00E+00 5.00E+00 1.00E+01 1.50E+01 2.00E+01 2.50E+01 3.00E+01 3.50E+01 4.00E+01

Cumulative Jet Mass

U-J

ET

U-JET -StandardU-JET -OptionalU-JET -Experimental

AUTODYN Comparison with Experiment

This test was one of a number that were used in a comparative investigation of various analytic and numerical shaped charge liner collapse models. The results of this investigation were published in reference[2].

34


35

There are considerable discrepancies between the results of individual models and the lack of experimental data on parameters such as the collapse velocity makes it impossible to say which model best predicts such parameters. However, in all cases the AUTODYN results fall within the spread of the other results and compare favorably with the experimental data for jet velocity as a function of cumulative jet mass.

Chapter 6. References

36

Chapter 6. References

[1] Pugh, Eichelberger, Rostoker.

“Theory of Jet Formation by Charges with Lined Conical Cavities”. J. Appl. Physics, Vol 23, No 5. 1952

[2] Dullum, Haugstad, Gustavsson, Nordell & Arvidsson.

“A comparison Investigation Of Various Analytical And Numerical Shaped Charge Liner Collapse Models” Proc. 9th International Symposium On Ballistics, R.A.R.D.E., Shrivenham, England, April, 1986

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