Probabilistic Modeling of Initiation due to Fragment Impact IMEMTS - - PowerPoint PPT Presentation

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Probabilistic Modeling of Initiation due to Fragment Impact

• Dr. Ernie Baker

Warheads Technology TSO e.baker@msiac.nato.int Christiaan Leibbrandt

IMEMTS 2019

Martijn van der Voort Transport and Storage TSO m.vanderVoort@msiac.nato.int

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Overview

• Fragment Impact Testing
• Jacobs-Roslund Initiation Model
• Deterministic initiation response model
• Augmenting deterministic initiation

response model

– Algebraic model: Geometrical aspects of fragment impact – Validation – Implementation in deterministic model

• Probabilistic initiation response model
• Conclusions and recommendations

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Fragment Impact Gun Testing

➢ NATO STANAG 4496, Ed. 1 ➢ Standard test: 253090 m/s

• Alternate test of 183060 m/s

➢ Standard fragment (projectile) geometry ➢ Several loosely defined and undefined characteristics that can affect the test item response

• Velocity variation
• Aim point variation
• Projectile tilt upon impact
• Fragment material characteristics

➢ Develop a probabilistic model that accounts for these variations and conduct an associated case study

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Typical FI Test Setup

NSWC Dahlgren

4.5 meters 3 meters

Test Item Support Table Sabot Stripper Plate TOA Screens ➢ The test item is as close to gun as possible without causing damage to the gun in order to reduce aim point variability. ➢ Fragment velocities are measured using either make/break screens or photographic techniques. ➢ Majority of testing is completed using single stage powder guns Gun

Redstone Test Center

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FI Testing Variation

Velocity, projectile tilt and impact point variation are common ➢ Gun barrel wear ➢ Gun powder variation ➢ Ignition anomalies ➢ Sabot release ➢ Measurement error

GD-OTS USA DGA/EM France

Sabots

AFRL Eglin AFB GD-OTS

High Speed Framing Images

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JACOBS-ROSLUND MODEL

𝑊

𝐷𝑠𝑗𝑢𝑗𝑑𝑏𝑚 = 𝐵

𝑒0.5 ∗ 1 + 𝐶 ∗ 1 + 𝐷 𝑢 𝑒

Deterministic initiation response model VImpact < VCritical : No detonation VImpact > VCritical : Detonation

Symbol Definition Unit VCritical Critical impact velocity for warhead detonation [m/s] Fragment d Fragment critical dimension or diameter [m] B Projectile shape coefficient [-] Warhead t Warhead cover thickness [m] A Explosive sensitivity coefficient [m3/2s-1] C Cover plate protection coefficient [-]

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RESEARCH QUESTION

Bron: MSIAC, NATO

• How can tilted and off-centre fragment

impact variation be implemented in a response model for probabilistic prediction of munitions initiation response?

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INITIATION MODEL DEVELOPMENT

Augment the Jacobs-Roslund model

• Velocity variation: can already account for it
• Aim point variation: match pressure histories with a reduced velocity based on oblique impact
• Projectile tilt upon impact: match pressure histories with a reduced velocity based on oblique

impact

Use previous 3D hydrocode modeling as data set

• 1-D GODLAG hydrocode within Temper for impact velocity and impactor thickness studies
• Use 1-D results to infer new velocity relationships for impact point offset and projectile tilt

Baker et al., “Insensitive Munitions Fragment Impact Gun Testing Technology Challenges” Propellants, Explosives, Pyrotechnics 10.1002/prep.201600045, 2016.

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APPARENT VELOCITY CONCEPT MODEL 𝑊

1 = 𝑊 0 ∗ cos 𝜄 + 𝛾

𝜄 = tan−1(− 𝑌 𝑆2 − 𝑌2)

GEOMETRICAL ASPECTS OF FRAGMENT IMPACT

(β clockwise is negative)

Θ+β

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𝑊

1 = 𝑊 0 ∗ cos 𝜄 + 𝛾

MODEL VALIDATION USING HYDROCODE CALCULATIONS

• Reproduce 3-D pressure histories in 1-D
• Use resulting 1-D impact velocities for

apparent velocity quantification and validation

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MODEL VALIDATION

0,00 2,00 4,00 6,00 8,00 10,00 12,00 0,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00 8,00 9,00 10,00

Pressure [GPa] Time [μs]

3-D and 1-D model pressure histories for -10° tilted impact

1-D model with v=2342 m/s 1-D model with v=2074 m/s 1-D model with v=1699 m/s 3-D model -10° tilt and 0mm off-centre 3-D model -10° tilt and 12.5mm off-centre 3-D model -10° tilt and 25mm off-centre

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MODEL VALIDATION

1500 1700 1900 2100 2300 2500 2700

Velocity [m/s] Fragment orientation

Average 1-D hydrocode velocities for different fragment impact orientation

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MODEL VALIDATION

1400 1600 1800 2000 2200 2400 2600

Model velocities (V1) and hydrocode velocities

V,hydrocode,avg Model

𝑊

1 = 𝑊 0 ∗ cos 𝜄 + 𝛾

Impact Velocity (m/s)

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MODEL VALIDATION

𝑊

1 = 𝑊 0 ∗ (cos 𝜄 + 𝛾 )3.832

1400 1600 1800 2000 2200 2400 2600

Model velocities (V1) and hydrocode velocities

V,hydrocode,avg Model λ=3,832 (SSD first 8 data points)

𝑊

1 = 𝑊 0 ∗ cos 𝜄 + 𝛾

𝑊

1 = 𝑊 0 ∗ (cos 𝜄 + 𝛾 )λ

Impact Velocity (m/s)

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OFFSET & TILT MODIFIED JACOBS-ROSLUND

𝑊

𝐷𝑠𝑗𝑢𝑗𝑑𝑏𝑚 =

𝐵 𝑒0.5 ∗ ) (co s( 𝜄 + 𝛾) 𝜇 ∗ 1 + 𝐶 ∗ 1 + 𝐷 𝑢 𝑒

(JR Leibbrandt Model)

Symbol Definition Unit VCritical Critical impact velocity for warhead detonation [m/s] Fragment d Fragment critical dimension or diameter [m] θ Angle of tangent at impact point [°] β Fragment’s angle of tilt [°] λ Leibbrandt-coefficient [-] B Projectile shape coefficient [-] Warhead t Warhead cover thickness [mm] A Explosive sensitivity coefficient [m3/2s-1] C Cover plate protection coefficient [-]

MODEL IMPLEMENTATION

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PROBABILISTIC ANALYSIS

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• Input parameters:
• Target explosive: PBXN-9
• Target cover thickness (t): 8.6mm
• Fragment shape (NATO standard cone)
• Fragment critical dimension (d)
• Variables
• Fragment impact velocity (V)
• Fragment tilt
• Fragment aimpoint
• Output
• Critical impact velocity for detonation (Vc)
• Detonation likely or not?

FI Case Study

Example: 155 mm projectile

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• VCritical = 1859 m/s (Deterministic)
• VImpact = 1900 m/s, σ = 30 m/s, no tilt or offset

X (off-centre) [mm] Detonation [%] Center Aimpoint σ = 2,5 73.3 Center Aimpoint σ = 12,5 41.6 Center Aimpoint σ = 25 25.9

PROBABILISTIC INITIATION CASE STUDY

• Now add tilt (β = 0°, σ = 4°) and offset impact position
• Deterministic prediction: 100% Detonation
• Probabalistic prediction: 91% of time detonation

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• VCritical = 1859 m/s (Deterministic)
• VImpact = 1830 m/s, σ = 30 m/s, no tilt or offset

Off-center Impact [mm] Detonation [%] Center Aimpoint σ = 2.5 8.9 Center Aimpoint σ = 12.5 4.2 Center Amipoint σ = 25 2.1

• Deterministic prediction: 0% Detonation
• Probabalistic prediction: 16.6% of time detonation
• Now add tilt (β = 0°, σ = 4°) and offset impact position

PROBABILISTIC INITIATION CASE STUDY

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CONCLUSIONS AND RECOMMENDATIONS

• Tilt and off-centre have influence on munitions response to fragment impact

– Commonly observed angle of tilt during FI testing has some influence – Commonly observed off-centre distance during FI testing has a large influence

• It is possible that munitions “pass” fragment impact tests unjustly due to

testing variation and a small number of tests – Perhaps tilt and off-center impact should be accounted for when reviewing test results

• STANAG 4496 updated March 2019 (STANAG 4496 Ed. 2, AOP-4496 Ed. A)

– Tilt: ±10° tilt recommendation – Off-center distance: Aimpoint accuracy diameter to be defined before testing

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QUESTIONS?