Week 3 Sheet metal Bending challenge

Aim: To conduct a sheet metal bending simulation for three different materials. This is done to come to a conclusion of which element has higher tolerance. In another case, the coefficient of friction is increased and then compared with the Aluminum alloy results. Then we need to refine the mesh for the aluminum alloy plate and run the simulation to compare the results. So there are three cases in this study.

Procedure:

Geometry: The geometry is dragged into space claim and checked if it is free of error.

Connections:

• Contacts: Create two contacts. One between the punch and the plate. Another between the plate and the die. Both the contacts are frictional and have a frictional coeff. of 0.1 and for case 2 is will be 0.19.

Behavior: Auto Asymmetric

Formulation: Augmented Lagrange

Interface: Add offset, no ramping

Mesh:

• Add body sizing to the punch and the die. The element size is 4mm.
• Another body sizing is added to the plate. This element size must be fine as it is the object of interest. So the element size is 1mm / 0.7mm for case 3.
• Also, add a face sizing of 1mm to the faces that are going to in contact with the plate.
• Make sure that the type of element in the workpiece is a tetrahedron by adding the mesh method.

Analysis Setting:

• Number of time step: 10
• End time step: 10s
• Auto Time Stepping: Program Controlled
• Solver type: Direct
• Large Deflection: On (this is to ensure the movement of the punch)

Load Setting:

• Punch Displacement: Add a displacement using tabular data. The punch should be lifted after the 7s.
• Workpiece Displacement: To ensure that the workpiece does not move sideways we fix the workpiece in the z-axis.
• Die Displacement: Keep the die fixed for 0-7s and then add a displacement downwards in 8, 9, and 10th second.

Solution: Plots for total deformation, Von-mises stress, and elastic strain are obtained and compared.

Results & Discussion

Case 1 The arrangement of the image is (Al alloy, Cu alloy, & Mn alloy)

Von-Misses Stress

Aluminum alloy is observed to undergo the least stress and then copper alloy and then magnesium alloy.

The variation of minimum, maximum, and average stress experienced by the sheet metal with time is given below:

Von Mises Stress (MPa)	Aluminum Alloy	Copper Alloy	Magnesium Alloy
Maximum	55.519 MPa	114.87	318.83
Minimum	1.3774e-02	2.7621e-02	9.9453e-002
Average	8.6498	19.514	18.319

Elastic strain

Elastic strain is highest for Copper alloy, then Aluminum alloy, and the lowest for Magnesium alloy.

The variation of minimum, maximum, and average elastic strain experienced by the sheet metal with time is given below:

Elastic Strain (mm/mm)	Aluminum Alloy	Copper Alloy	Magnesium Alloy
Maximum	1.5358e-003	1.7138e-003	1.0037e-002
Minimum	3.5127e-007	4.6127e-07	3.299e-006
Average	3.6646e-004	4.4537e-04	9.4089e-004

Directional Deformation

The variation of minimum, maximum, and average directional deformation experienced by the sheet metal with time is given below:

Directional Deformation (mm)	Aluminum Alloy	Copper Alloy	Magnesium Alloy
Centre	12.992	11.646	11.139
Plate Ends	2.1724	2.8105	2.7188
Average	6.3023	5.2985	5.0526

Case 2

Von mises Stress

The stress significantly increases for F_c 0.19 case. Here the stress is seen to develop along the right edge of the plate too which is not seen in the other case.

The variation of minimum, maximum, and average stress experienced by the sheet metal with time is given below:

Von Mises Stress (MPa)	Aluminum Alloy (f_c = 0.1)	Aluminium Alloy (f_c = 0.19)
Maximum	55.519	154.44
Minimum	1.3774e-02	8.0049e-003
Average	8.6498	19.127

Elastic Strain

The strain is seen to develop in the edges of the plate and the average stress experienced by the plate is greater for 0.19 F_c case.

The variation of minimum, maximum, and average elastic strain experienced by the sheet metal with time is given below:

Elastic Strain (mm/mm)	Aluminum Alloy (f_c = 0.1)	Aluminium Alloy (f_c = 0.19)
Maximum	1.5358e-003	2.5432e-003
Minimum	3.5127e-007	2.317e-007
Average	3.6646e-004	6.2266e-004

Directional Deformation

Due to increases friction coefficient the maximum deflection slightly decreases.

The variation of minimum, maximum, and average directional stress experienced by the sheet metal with time is given below:

Directional Deformation (mm)	Aluminum Alloy (f_c = 0.1)	Aluminium Alloy (f_c = 0.19)
Centre	12.992	12.78
Plate Ends	2.1724	2.2484
Average	6.3023	6.1669

Case 3

Von mises Stress

Maximum von mises stress is seen to increase with mesh refinement also the minimum stress is decreased.

The variation of minimum, maximum, and average stress experienced by the sheet metal with time is given below:

Von Mises Stress (MPa)	Aluminum Alloy (1mm)	Aluminium Alloy (0.7mm)
Maximum	55.519	70.54
Minimum	1.3774e-02	1.6683e-003
Average	8.6498	8.6379

Elastic Strain

Here we observe a high strain zone in the midsection of the plate. this can only be observed when the mesh is refined as it helps considering smaller surfaces. The maximum elastic strain is also seen to increase whereas the minimum elastic strain decreases significantly but the average strain remains about the same.

The variation of minimum, maximum, and average elastic strain experienced by the sheet metal with time is given below:

Elastic Strain (mm/mm)	Aluminum Alloy (1mm)	Aluminium Alloy (0.7mm)
Maximum	1.5358e-003	1.7148e-003
Minimum	3.5127e-007	5.0135e-008
Average	3.6646e-004	3.3945e-004

Directional Deformation

The changes in the deformation in both cases is seen to be almost the same. Please do not consider the contours here as they are obtained for different time steps.

The variation of minimum, maximum, and average directional stress experienced by the sheet metal with time is given below:

Directional Deformation (mm)	Aluminum Alloy (1mm)	Aluminium Alloy (0.7mm)
Centre	12.992	12.808
Plate Ends	2.1724	2.0752
Average	6.3023	6.0038