Week 10 Bullet penetrating a Bucket Challenge

SIMULATION OF BULLET PENETRATING INTO A BUCKET USING ANSYS WORKBENCH

OBJECTIVE

To simulate bullet penetrating into a bucket for different cases of bucket material,

Case-1: Aluminium Alloy NL

Case-2: Copper Alloy NL

Case-3: Stainless Steel NL

To find out Total deformation and Equivalent stress developed in bucket for each case and compare the results.

1. THEORY

1.1 Bullet Penetration:

A bullet is a projectile, often a pointed metal cylinder, that is shot from a firearm. The bullet is usually part of an ammunition cartridge, the object that contains the bullet and that is inserted into the firearm.

Bullets are made of a variety of materials. Lead or a lead alloy is the traditional bullet core material. Traditional bullet jackets are made of copper or gilding metal, an alloy of copper and zinc. There are many other materials that are used in bullets today, including aluminium, bismuth, bronze, copper, plastics, rubber, steel, tin, and tungsten.

Modern bullets can have many different features. Some of these features concern the shape of the bullet and others the materials of construction. Most bullets look like a cylinder with a pointed end. The cylindrical section to the rear of the bullet is the shank and the pointed section to the front of the bullet is the tip, though the tip may be flat instead of pointed. Bullets can be made of one or more materials.

Bullets made out of only soft material (such as lead) expand on impact causing more damage to the target. Bullets made out of only a harder material (such as steel) penetrate further into thicker targets, but do not expand much. A softer core can be enclosed or partially enclosed in a layer of harder metal called a jacket. This jacket can completely enclose the bullet or it can leave the softer tip exposed for expansion purposes. Varying the amount of jacketing alters the amount of penetration versus expansion.

In this project a truncated cone shaped bucket made of materials like aluminium alloy NL, copper alloy NL and stainless steel NL, is hit with a bullet travelling at a speed of 139000 mm/s. The results are drawn to study the impact of the bullet on the bucket, as well as the behaviour exhibited by the material of the bucket.

2. ANALYSIS SETUP

2.1 Geometry:

Fig.2.1 3D model of bucket and bullet setup.

The given 3D model of bucket and bullet setup assembly is imported into SpaceClaim. It consists of a bucket and a bullet.

2.2 Material Properties:

a. Aluminum Alloy NL.

b. Copper Alloy NL.

c. Stainless Steel NL.

d. Tantalum.

Fig.2.2 Material property details of bucket and bullet.

The material assigned for bullet is tantalum, and for bucket, following materials are assigned for each case,

1. Case-1: Aluminium Alloy NL
2. Case-2: Copper Alloy NL
3. Case-3: Stainless Steel NL

The stiffness behaviour of bullet is chosen as ‘rigid’.

Note: The analysis setup of only case-1 is demonstrated.

2.3 Meshing:

a. Edge sizing of bucket.                                                                                       b. Meshed model

Fig.2.3 Meshing details of bullet and bucket models.

The element size of bucket is refined to 6 mm using edge sizing option. The total number of nodes and elements generated are 4777 and 16746 respectively.

Note: The academic version of software has the problem size limit of 128k nodes or elements.

2.4 Boundary Conditions:

2.4.1 Analysis settings:

Fig.2.4.1 Analysis settings.

In the analysis settings the number of steps considered is 1. The end time specified is 1e-002. The maximum no. of cycles is 1e+07. The maximum energy error is 5. The initial, minimum and maximum time step is set to ‘Program Controlled’.

2.4.2 Boundary condition for bullet penetrating into a bucket:

a. Fixed support.                                                                                              b. Velocity applied to bullet along negative x-axis.

Fig.2.4.2 Boundary conditions for bullet penetrating into a bucket.

The bottom surface of the bucket is fixed. The bullet is directed to hit the bucket with a velocity of 139000 mm/s in negative x-direction.

3. RESULTS AND DISCUSSIONS

3.1 Case-1: Aluminum Alloy NL.

a. Total Deformation.                                                                                                      b. Equivalent (v-m) Stress.

c. Energy Plots

For case-1, the material of the bucket is aluminum alloy NL. From the results, the total deformation of the bullet is 1043 mm, which indicates the distance travelled by the bullet by penetrating through the bucket.

The v-m stress developed during the impact of bullet is maximum i.e., 1057.3 MPa and later it decreases and reaches a value of 583.64 MPa at time 7.5e-3 s.

From the energy conservation plot, it is observed that the work done graph indicated by green line shows a initial spike which indicates that the bullet has impacted the bucket and later the graph is steady meaning the bullet has penetrated through the bucket and is travelling with constant velocity and later there is again spike in the graph which indicates that the bullet has impacted the other side of the bucket and thereafter the graph is constant which indicates that the bullet has been pushed out of the bucket and is travelling at a constant velocity. The energy error indicated by red line shows that there is negligible energy error.

3.2 Case-2: Copper Alloy NL.

a. Total Deformation.                                                                                                      b. Equivalent (v-m) Stress.

c. Energy Plots

For case-1, the material of the bucket is copper alloy NL. From the results, the total deformation of the bullet is 1399.7 mm, which indicates the distance travelled by the bullet by penetrating through the bucket.

The v-m stress developed during the impact of bullet is maximum i.e., 2805 MPa and later it decreases and reaches a value of 1196.6 MPa at time 1e-2 s.

From the energy conservation plot, it is observed that the work done graph indicated by green line shows an initial spike which indicates that the bullet has impacted the bucket and later the graph is steady meaning the bullet has penetrated through the bucket and is travelling with constant velocity and later there is again spike in the graph which indicates that the bullet has impacted the other side of the bucket and thereafter the graph is constant which indicates that the bullet has been pushed out of the bucket and is travelling at a constant velocity. The energy error indicated by red line shows that there is negligible energy error.

3.3 Case-3: Stainless Steel NL.

a. Total Deformation.                                                                                                       b. Equivalent (v-m) Stress.

c. Energy Plots

For case-1, the material of the bucket is stainless steel NL. From the results, the total deformation of the bullet is 1396.5 mm, which indicates the distance travelled by the bullet by penetrating through the bucket.

The v-m stress developed during the impact of bullet is maximum i.e., 3572 MPa and later it decreases and reaches a value of 2338.2 MPa at time 1e-2 s.

From the energy conservation plot, it is observed that the work done graph indicated by green line shows an initial spike which indicates that the bullet has impacted the bucket and later the graph is steady meaning the bullet has penetrated through the bucket and is travelling with constant velocity and later there is again spike in the graph which indicates that the bullet has impacted the other side of the bucket and thereafter the graph is constant which indicates that the bullet has been pushed out of the bucket and is travelling at a constant velocity. The energy error indicated by red line shows that there is negligible energy error.

3.5 Comparison of Results:

From the table, it is observed that the distance travelled by the bullet by penetrating in and moving out of the bucket is maximum for case-2.

The v-m stress developed for case-3 is maximum compared to other cases, because the value of yield strength and Poisson’s ratio of stainless-steel NL is less compared to other cases.

4. ANIMATION OF RESULTS:

4.1 Case-1: Aluminum Alloy NL.

a. Total Deformation.                                                                                                 b. Equivalent (v-m) Stress.

4.2 Case-2: Copper Alloy NL.

a. Total Deformation.                                                                                               b. Equivalent (v-m) Stress.

4.3 Case-3: Stainless Steel NL.

a. Total Deformation.                                                                                                 b. Equivalent (v-m) Stress.

CONCLUSION

Simulation of bullet penetrating into a bucket was carried out successfully for the following cases of bucket material,

1. Case-1: Aluminium Alloy NL
2. Case-2: Copper Alloy NL
3. Case-3: Stainless Steel NL

The maximum distance travelled by bullet by penetrating in and moving out of the bucket is maximum for case-2.

The v-m stress developed for case-3 is maximum compared to other cases, because the value of yield strength and Poisson’s ratio of stainless-steel NL is less compared to other cases.

Generally, the effect of penetration of the bullet into a metallic object depends upon the thickness and density of the material.