Analysis of a Bullet penetrating a Bucket

Analysis of a Bullet penetrating a Bucket

Objective: To simulate a bullet penetrating a bucket and obtain the Equivalent Stress, Total Deformation and Temperature generated in the bucket. Three simulations are run and in each case the bucket is assigned a different explicit material. The results of all the three cases are compared.

Geometry: The model consists of a bullet almost in contact with an inverted conical bucket of 75mm and 203mm diameter for the smaller and larger circles of the cone respectively.

The bucket is provided a thickness of 5.0mm.

Body Interaction: No contacts are defined for the simulation. Instead a Body Interaction is introduced, the parameters of which are set as per the table below:

Meshing: The bucket is provided with a 6mm element size along its spliting edges. this is done to get more accurate results in the said region as it is area where the bullet impacts the bucket.

The rest of the model is meshed with the default mesh size. Adaptive sizing is turned off.

Analysis Settings: The simulation is run for 1.0E-02s with the maximum number of cycles set to 1E+07.

The energy error is limited to 10% of the energy at reference cycle. The time step safety factor is left to its default value of 0.9.

Boundary Conditions: Two boundary conditions are imposed on the model-a fixed support at the base thickness of the bucket to constrain its motion and an imposed velocity of 139000mm/s on the bullet in the negative X-direction.

Material Definition: The bullet is assigned \"Tantalum\" as the working material, the properties of which have been tabulate below:

The bullet is assigned a Rigid behaviour so stresses and strains are not computed for the bullet.

For this challenge, the bucket is assigned three different explicit materials.

Aluminium Al 1100-O

In this case the bucket is assigned Al 1100-O as the working material which includes the Steinberg Guinan Strength model and Shock EOS Linear model for failure modelling.

Steel 1006

In this case, the bucket is assigned Carbon Steel 1006 as the working material which includes Johnson Cook and Shock EOS Linear parameters for failure modelling:

Tungsten

In this case the bucket is assigned Tungsten as the working material which includes the Steinberg Guinan Strength model and Shock EOS Linear parameters for failure modelling.

The simulations are run and the results are plotted.

Results:

The Total Deformation, Equivalent Stress and Temperature obtained from the runs have been tabulated below:

SR No	Particular	Case1	Case2	Case3
1.	Total Deformation (mm)	1390	2353.5	2760.2
2.	Equivalent Stress (MPa)	234.35	526.68	2209.5
3.	Temperature Generated (degree Celsius)	253.64	556.41	2655.1
4.	Equivalent Elastic Strain	2.164	2.5977	2.1365

1) Total Deformation: The highest deformation is observed in case3 where Tungsten is used as the working material.

Case1

Case2

Case3

The green, blue and red lines indicate the respective maximum, average and minimum Total Deformations computed for the model.

2) Equivalent Stress: On using Tungsten as the working material, the stress in the bucket increases by a factor of 5-10.

Case1

Case2

Case3

The green, blue and red lines indicate the respective maximum, average and minimum Equivalent Stress computed for the model.

3) Temperature Generated: The temperature generated is highestDue to the impact of the bullet and the resulting strain, is highest when Aluminium is assigned to the bucket.

Case1

Case2

Case3

The green, blue and red lines indicate the respective maximum, average and minimum Temperature generated in the model.

4) Equivalent Elastic Strain: The highest elastic strain is observed when Steel is used as the working material for the bucket. One of the failed elements exhibit the maximum elastic strain.

Case1

Case2

Case3

The green, blue and red lines indicate the respective maximum, average and minimum Equivalent Elastic Strain in the model.

Inference:

Both the simulations terminate successfully with the energy errors being within the designated target of 10% of reference cycle energy for all the cases.

Case1 Case2

Case3

From the results obtained, the follwoing inferences can be drawn:

• The Total Deformation in case1 is the same as the distance that is traversed by the bullet in 0.01s. For the other two cases the maximum deformation is observed on one of the fragments of the failed elements.
• The highest stress is observed in case of Tungsten (Case3) indicating that Tungsten offered the maximum resistance to the incoming bullet than the other two materials. Had the bullet been provided an initial velocity (instead of imposed velocity) and had the bucket been a solid one instead of a hollow one, the bullet would have penetrated the least if the bucket was made up of Tungsten.
• The region of development of stress and strain also differs. In case1, highest stress and strain is developed at the sharp end of the failed material (still in contact with the parent body). In case2 and case3, the highest stresses are recorded at the base of the bucket. The stress from the bullet impact is transfered to the base in the form of shock waves. The highest strain in these cases is found in one of the fragments of the failed elements.
• The high stress developed in case3 also leads to high strain and consequently internal energy in the model. Since internal energy is a function of temperature, Case3 also exhibits the highest temperature in the model.

Energy summary of Case1

Energy summary of Case2

Energy summary of Case3