Natural Fragmentation using AUTODYN

1. Natural Fragmentation using AUTODYN A Feasibility Study May 2004

2. Computational Slice Donor Explosive VOID COMP B IRON-ARMCO COMPB-IN AIR Acceptor Explosive Casing Goals & Benchmark • Goal • Show capability for sympathetic detonation modelling • Fragmentation of casing • Benchmark • Sympathetic detonation of an acceptor explosive (COMPB-IN) by the explosion of a donor explosive (COMP B) and subsequent fragmentation of the casing.

3. VOID COMP B IRON-ARMCO COMPB-IN AIR Numerical Model for Slice • Feasibility study uses a slice out of the full problem • Full 3-dimensional analysis • Slice of 5 element thick • Explosive(s) and air modelled in Euler • Casing modelled in Lagrange • Exact Euler-Lagrange coupling between explosive(s) and casing

4. VOID COMP B IRON-ARMCO COMPB-IN AIR Numerical Processors • Euler Domain • Modelled by hexagonal cells • Cells remain fixed in space and time • Material can flow from element to element through common faces. • Cells can contain a mixture of different materials • Euler contains 3 materials: • COMP B • COMPB-IN • Air

5. Numerical Processors • Lagrange Domain • Modelled by hexagonal cells • Cells move with material deformation • Casing modelled in Lagrange

6. VOID COMP B IRON-ARMCO COMPB-IN AIR Euler-Lagrange Coupling • Exact Euler-Lagrange Coupling • Outside faces of Lagrange cells of casing act as boundary for Euler flow. • Pressure from Euler is applied to Lagrangian faces • Deforming Lagrangian faces form a new boundary for Euler for next computational cycle.

7. VOID COMP B IRON-ARMCO COMPB-IN AIR Explosive Material Modelling:: JWL Equation of State • Donor Explosive • COMP B outside casing • Forced detonation at outer circumference • Acceptor Explosive • COMPB-IN inside casing • (Possible) sympathetic detonation on compression • Compression by inward motion of casing due to external loading by donor explosive.

8. Casing Material Modelling:: Stochastic Failure • To model fragmentation for symmetric loading and geometry, need to impose some material in-heterogeneity • Materials have inherent microscopic flaws - these flaws are where failure and cracking initiate • An approach to reproducing this numerically is to randomise the failure stress/strain for the material • Each cell in the numerical model will have a different failure strain • This creates ‘weak spots’ in the material • A Mott distribution is used to define the variance in failure stress/strain • Often used in describing the distribution of fragment mass and size for naturally fragmenting warheads

9. Casing Material Modelling:: Stochastic Failure • Mott distribution for stress/strain failure • P is probability of fracture • C and g are constants • g is defined by user • C is calculated such that input failure stress/strain has probability of failure = 0.5 • Distribution Type • Fixed – Same each time • Random Cutoff to prevent zero stress/strain failure Fraction of failure stress/strain

10. Casing Material Modelling:: Stochastic Failure • Casing Material Properties • Standard ARMCO iron • Strength • Johnson & Cook • Failure • Principal Strain – 25 % • Stochastic Variance – 2.0(2.5% - 63.3%)

11. Analysis Results • Donor Explosive - Detonation and Expansion • Pressure distribution

12. Analysis Results • Shockwave Propagation through Casing

13. Analysis Results • Acceptor Explosive - Sympathetic Detonation • Pressure distribution

14. Analysis Results • Acceptor Explosive - Expansion & Subsequent Internal Shockwave Reflections • Pressure distribution

15. Analysis Results • Casing Compression, Expansion and Fragmentation • Donor explosive detonation phase

16. Analysis Results • Casing Compression, Expansion and Fragmentation • Acceptor Explosive Detonation and Expansion phase

17. Analysis Results • Casing Compression, Expansion and Fragmentation • Internal reflection phase