Final Presentation No Videos

FEA ANALYSIS OF A PROJECTILE

IMPACTING A PLATE

Final Presentation by Wes Anderson

ORIGINAL PROBLEM

• Elastic steel sphere impacting an elastic-plastic aluminum plate • Normal and 45° impacts considered• Johnson-Cook Damage model applied to the plate

• 1000 x 1000 x 50 mm plate• Constructed of 6061-T6

• 10 mm sphere• Constructed of 1020 Tool

• Sphere velocity was set to 150 kph

JOHNSON-COOK PLASTICITY MODEL

• - new static yield stress• A – yield stress at reference strain and temperature• B – hardening parameter• - cumulative plastic strain• n – cumulative plastic strain exponent• m – temperature dependence exponent

[1], [2], [3]

JOHNSON-COOK DYNAMIC DAMAGE MODEL

• Effective Stress• - Effective plastic strain rate• – obtained from a manually optimized correlation

[1], [2], [3]

MATERIAL PROPERTIES, GEOMETRIES,& PLASTICITY AND DAMAGE PARAMETERS

FOR 6061-T6 ALUMINUMJohnson-Cook Plasticity

A 262 MPa

B 162.1 MPa

n 0.2783

m 1.34

C -

Johnson-Cook Dynamic Damage

d1 -0.77

d2 1.45

d3 0.47

d4 0

d5 1.6

Melting Temp. 651.85

Transition Temp. 20.05

Reference Strain Rate 1

Material Properties10 mm

200 GPa

0.29

8.6e-9

150 kph

50 mm

1000 mm

68.9 GPa

0.33

2.7e-9

ORIGINAL MESHES

Plate Mesh Sphere Mesh

RESULTS: VELOCITIES

Normal Impact 45° Impact

RESULTS: STRESSES

ORIGINAL PROBLEM REFINEMENTS

• Decrease plate thickness• Increase sphere velocity• Give the plate more layers of elements and better mesh the sphere• Examine different materials for the plate and sphere• Make the sphere plastic and apply a damage model

PLATE THICKNESS AND SPHERE VELOCITY

• Plate thickness reduced to 10 mm• Other dimensions kept the same • Infinite length and width to avoid edge effects

• Velocity increased to 1000 m/s• Supersonic • Just below the threshold for “high velocity” small arms• Shockwave not accounted for in analysis

REFINED MESHES

NEW MATERIALS CONSIDEREDPropert

ySteel Lead Titanium Tungsten

ρ(g/cc) 7.83 11.34 4.43 19.3ν 0.29 0.44 0.342 0.28E(GPa) 200 16 113.8 400A(MPa) 792 10.3 1100 1186B(MPa) 510 41.3 1090 1057

n 0.26 0.21 0.93 0m 1.03 1.03 1.1 0.6d1 0.05 0.25 -0.09 5.5d2 3.44 0 0.27 0d3 2.12 0 0.48 0d4 0.002 0 0.014 0d5 0.61 0 3.87 0

• Steel [1]• AISI 4340• Considered for both

plate and sphere• Lead [4], [5]

• Elemental• Considered for the

sphere• Titanium [3], [6]

• 6Al-4V• Considered for the plate

• Tungsten [7], [8]• Alloy with 0.07 Ni and

0.03 Fe• Considered for the

sphere

SIMULATION RESULTS

• Elastic Spheres• If there is no penetration most reflected off the plate

• Plastic Spheres • Most disintegrated on impact

• Steel and Titanium Plates• No damage from normal impacts

• Summary of the simulations provide in Appendix at the end of the presentation

RESULTS: ELASTIC STEEL NORMALLY IMPACTING ALUMINUM

Stress on the front of the plate Stress on the rear of the plate

RESULTS: ELASTIC STEEL NORMALLY IMPACTING ALUMINUM

Damage inflicted to the plate

• https://youtu.be/Whuspj4wLjQ

RESULTS: ELASTIC LEAD NORMALLY IMPACTING ALUMINUM


RESULTS: ELASTIC LEAD NORMALLY IMPACTING ALUMINUM


• https://youtu.be/cDhCyoJVjtE

RESULTS: ELASTIC TUNGSTEN NORMALLY IMPACTING ALUMINUM


RESULTS: ELASTIC TUNGSTEN NORMALLY IMPACTING ALUMINUM


• https://youtu.be/570yXss2uHg

RESULTS: PLASTIC TUNGSTEN NORMALLY IMPACTING ALUMINUM


RESULTS: PLASTIC TUNGSTEN NORMALLY IMPACTING ALUMINUM


• https://youtu.be/1dFJ3zvBXKA

RESULTS: ELASTIC STEEL IMPACTING ALUMINUM AT 45°


RESULTS: ELASTIC STEEL IMPACTING ALUMINUM AT 45°


• https://youtu.be/6EM_4aubAi8

RESULTS: ELASTIC TUNGSTEN IMPACTING ALUMINUM AT 45°


RESULTS: ELASTIC TUNGSTEN IMPACTING ALUMINUM AT 45°


• https://youtu.be/P4RvmRz-l84

RESULTS: PLASTIC STEEL IMPACTING ALUMINUM AT 45°

Damage inflicted to the plate and sphere

• https://youtu.be/IoM0mhkmzCE

RESULTS: PLASTIC TUNGSTEN IMPACTING ALUMINUM AT 45°

Stress seen in the plate and sphere

• https://youtu.be/ldLrh_dD9ZU

FUTURE WORK/REFINEMENTS

• Alter sphere geometry• Cylinders are used for most examples

• Give the plate additional element layers• Account for the shock wave• Make use of the thermal component of the Johnson-Cook Models

REFERENCES[1] G. Johnson and W. Cook, “A Constitutive Model and Data for Metals Subjected to Large Strains, High Strain Rates, and High Tempertures.”

[2] B. Adams, M. G. D. Geers, J. A. W. an Dommelen, and A. T. M. J. M. Huizinga, “Simulation of ballistic impacts on armored civil vehicles,” Technische Universiteit Eindhoven University of Technology. [Online]. Available at: http://www.mate.tue.nl/mate/pdfs/6290.pdf. [Accessed: 2015].

[3] G. Kay, “Failure Modeling of Titanium-6Al-4V and 2024-T3 Aluminum with the Johnson-Cook Material Model,” pp. 25–30, 2002.

[4] “Lead, Pb,” Matweb Material Property Data. [Online]. Available at: http://www.matweb.com/search/datasheet.aspx?matguid=ebd6d2cdfdca4fc285885cc4749c36b1. [Accessed: 2015].

[5] “Assault Riffle Bullet-Experimental Characterization and Computer (FE) Modeling (Experimental and Applied Mechanics) Part 3,” whatwhenhow RSS. [Online]. Available at: http://what-when-how.com/experimental-and-applied-mechanics/assault-riffle-bullet-experimental-characterization-and-computer-fe-modeling-experimental-and-applied-mechanics-part-3/. [Accessed: 2015].

[6] “ASM Material Data Sheet,” ASM Material Data Sheet. [Online]. Available at: http://asm.matweb.com/search/specificmaterial.asp?bassnum=mtp641. [Accessed: Jun-2015].

[7] “Tungsten, W,” Matweb Material Property Data. [Online]. Available at: http://www.matweb.com/search/datasheet.aspx?matguid=41e0851d2f3c417ba69ea0188fa570e3. [Accessed: 2015].

[8] “Dynamic Fracture of a Tungsten Plate,” Dynamic Fracture of a Tungsten Plate. [Online]. Available at: http://www.jwave.vt.edu/crcd/archives/stprojs98/cbouthie/assignment2.html. [Accessed: 2015].

APPENDIX: SUMMARY OF SIMULATION RESULTS

• SDEG for the plate shown in the upper left screen capture• SDEG – Scalar stiffness degradation variable

• Von Misses stress contours shown for the front and rear of the plate in the top center and top right screen captures

• Velocity over time plot for the sphere show in the bottom right• For the normal impact the z velocity is plotted and for the 45° impact the x velocity

is plotted as well.• Bottom left contains a summary of the result of the impact and the peak Von

Misses stress seen in the simulation.

NORMAL IMPACT OF AN ELASTIC STEEL SPHERE ON AN ALUMINUM PLATE

• Penetration: Full• Damage: All but one impacted elements

destroyed and adjacent elements

either damaged or destroyed• Peak Stress Observed: 376.4 MPa

NORMAL IMPACT OF AN ELASTIC LEAD SPHERE ON AN ALUMINUM PLATE

• Penetration: None• Rebound: None, sphere is still pinned to

the plate by its momentum at the simulation’s conclusion

• Damage: Impacted elements intact but adjacent

elements destroyed• Peak Stress Observed: 373.7 MPa

NORMAL IMPACT OF AN ELASTIC TUNGSTEN SPHERE ON AN ALUMINUM PLATE

• Penetration: Full• Damage: Impacted elements and all adjacent

elements destroyed, only the four

elements directly behind the impacted elements were destroyed in the second

layer• Peak Stress Observed: 345.3 MPa

NORMAL IMPACT OF AN ELASTIC STEEL SPHERE ON A STEEL PLATE

• Penetration: None• Rebound: Sphere reflected back

towards its initial launch point at a greatly reduced velocity

• Damage: None • Peak Stress Observed: 1046 MPa

NORMAL IMPACT OF AN ELASTIC LEAD SPHERE ON A STEEL PLATE

• Penetration: None• Rebound: Sphere reflected back towards its

initial launch point at a greatly reduced velocity


NORMAL IMPACT OF AN ELASTIC TUNGSTEN SPHERE ON A STEEL PLATE

• Penetration: None• Rebound: Sphere still pinned to plate by

its momentum by the conclusion of the simulation


NORMAL IMPACT OF AN ELASTIC STEEL SPHERE ON A TITANIUM PLATE

• Penetration: None• Rebound: Sphere reflects off the plate

with about a 50% drop in speed headed back towards its point of origin.


NORMAL IMPACT OF AN ELASTIC LEAD SPHERE ON A TITANIUM PLATE




NORMAL IMPACT OF AN ELASTIC TUNGSTEN SPHERE ON A TITANIUM

PLATE




NORMAL IMPACT OF A PLASTIC STEEL SPHERE ON AN ALUMINUM PLATE


before disintegrating, the tracked node flies back the way it came

• Damage: None to the plate, sphere fails in all elements

• Peak Stress Observed (plate): 342.2 MPa

NORMAL IMPACT OF A PLASTIC LEAD SPHERE ON AN ALUMINUM PLATE





NORMAL IMPACT OF A PLASTIC TUNGSTEN SPHERE ON AN ALUMINUM

PLATE

• Penetration: Partial• Damage: One impacted element failed

along with all 1st layer elements adjacent to the impacted elements, no damage done to the 2nd layer. Sphere did not survive the impact.


NORMAL IMPACT OF A PLASTIC STEEL SPHERE ON AN STEEL PLATE





NORMAL IMPACT OF A PLASTIC LEAD SPHERE ON AN STEEL PLATE

• Penetration: None• Rebound: Sphere disintegrates upon

impact, and the tracked node stops dead at the plate surface.



NORMAL IMPACT OF A PLASTIC TUNGSTEN SPHERE ON AN STEEL PLATE

• Penetration: None• Rebound: Sphere breaks up upon

impact but rebounds off the plate enough for the debris to move back the way it came at a much slower speed.


• Peak Stress Observed (plate): 1042 MPa

NORMAL IMPACT OF A PLASTIC STEEL SPHERE ON AN TITANIUM PLATE


impact but rebounds off the plate enough for the debris to move back the way it came at a much slower speed.



NORMAL IMPACT OF A PLASTIC LEAD SPHERE ON AN TITANIUM PLATE

• Penetration: None• Rebound: Sphere breaks up upon impact

but rebounds off the plate enough for the debris to retain most of their speed.



NORMAL IMPACT OF A PLASTIC TUNGSTEN SPHERE ON AN TITANIUM

PLATE


impact but rebounds for a bit before coming to a halt.


• Peak Stress Observed (plate): 1118 MPa

45° IMPACT OF AN ELASTIC STEEL SPHERE ON AN ALUMINUM PLATE

• Penetration: None• Damage: High damage to the left two of

the impacted elements and light damage to the elements above and below them, with moderate damage to the elements behind the right side impacted elements.

• Peak Stress Observed: 330.6 MPa

45° IMPACT OF AN ELASTIC LEAD SPHERE ON AN ALUMINUM PLATE

• Penetration: None• Rebound: Relatively minor changes in x

velocity and significant slow down in z• Damage: none• Peak Stress Observed: 344.8 MPa

45° IMPACT OF AN ELASTIC TUNGSTEN SPHERE ON AN ALUMINUM PLATE

• Penetration: Full• Rebound: Minimal x velocity variation,

large loss in z velocity • Damage: All four impacted elements

destroyed, as well as the two above and below. Elements to the left and right of the impact have also been damaged

• Peak Stress Observed: 367.0 MPa

45° IMPACT OF A PLASTIC STEEL SPHERE ON AN ALUMINUM PLATE

• Penetration: None• Rebound: Sphere fragments glance off

the plate loosing most of their z velocity and a bit of their x velocity

• Damage: no damage to the plate, a few fragments of the sphere survive


45° IMPACT OF A PLASTIC LEAD SPHERE ON AN ALUMINUM PLATE

• Penetration: None• Rebound: Sphere fragments loose a bit

of x velocity and most of z velocity as they dissipate

• Damage: no damage to the plate, the sphere breaks up on impact


45° IMPACT OF A PLASTIC TUNGSTEN SPHERE ON AN ALUMINUM PLATE

• Penetration: None• Rebound: Sphere rebounds loosing only

a small amount of x velocity • Damage: Slight damage to the plate

elements above and below the two impacted damage on the right, no damage to the sphere but it does flatten out


Final Presentation No Videos

Documents

Transcript of Final Presentation No Videos