Tensile Test on a plate with Geometric Discontinuities
TENSILE TEST ON A PLATE WITH HOLE/HOLES
Case 1: In this case, a tensile test is carried out on a plate of the following dimensions:
Length = 300mm
Width = 120mm
Thickness = 30mm
In addition, a hole of 60mm diameter is created at the centre of the plate. The 2d geometry is extruded using the “PULL” option to get a thickness of 30mm. The geometry is prepared on Ansys Space Claim.
The geometry is assigned STRUCTURAL STEEL as the testing material. The properties of structural steel are as follows:
|
Density : |
7.85e-6 kg/mm3 |
|
Young’s Modulus : |
2e+05 MPa |
|
Thermal conductivity : |
0.0605 W/mm ͘C |
|
Specific heat : |
4.34e+05 mJ/kg ͘C |
|
Tensile Yield strength : |
250 MPa |
|
Tensile Ultimate Strength : |
460 MPa |
The geometry is meshed with Tetrahedrons of size 3.5mm to adhere to the node/element limit of the Ansys student edition. Patch Confirming method of meshing is employed.
A mesh metric that identifies elements according to their quality is used to plot a graph of the element quality. It can be seen that most of the elements lie in the high quality region of 0.65-0.9 and very few elements in the lower quality region.
The following boundary conditions are provided in Ansys Mechanical:
- A fixed support on the left surface (120mm*30mm) of the plate.
- A force of 500N on the right surface of the plate in the positive X direction.
The simulation is run in a single step and the results are plotted.
Case 2: In this case, the plate in case 1 is provided with two additional holes of 30mm diameter at a distance of 90mm (either side) from the centre of the plate.
The rest of the dimensions are the same as case 1:
Length = 300mm
Width = 120mm
Thickness = 30mm
The geometry is assigned STRUCTURAL STEEL as the testing material. The properties of structural steel are as follows:
|
Density |
7.85e-6 kg/mm3 |
|
Young’s Modulus : |
2e+05 MPa |
|
Thermal conductivity : |
0.0605 W/mm ͘C |
|
Specific heat : |
4.34e+05 mJ/kg ͘C |
|
Tensile Yield strength : |
250 MPa |
|
Tensile Ultimate Strength : |
460 MPa |
The geometry is meshed with Tetrahedrons of size 3.5mm to adhere to the node/element limit of the Ansys student edition. Patch Confirming method of meshing is employed.
A mesh metric that identifies elements according to their quality is used to plot a graph of the element quality. It can be seen that most of the elements lie in the high quality region of 0.65-0.9 and very few elements in the lower quality region.
The following boundary conditions are provided in Ansys Mechanical:
- A fixed support on the left surface (120mm*30mm) of the plate.
- A force of 500N on the right surface of the plate in the positive X direction.
RESULTS:
The total deformation, Equivalent (Von-Mises) stress and the Maximum Principal Stress for the two cases have been tabulated below.
|
Sl No. |
Particulars (max value) |
Case 1 |
Case 2 |
|
1. |
Total Deformation (mm) |
2.7487e-04 |
2.9719e-04 |
|
2. |
Equivalent Stress (MPa) |
6.0698e-01 |
5.8467e-01 |
|
3. |
Maximum Principal Stress (MPa) |
6.2362e-01 |
6.0101e-01 |
|
|
It can be observed from the above table that the Total Deformation in case of case 2 is 0.2e-04 mm more than in case 1.
The Maximum Principal and Equivalent stresses developed are more in case of the plate with a single hole (case1).
CONCLUSION:
On observing the results obtained from the simulation, the following deductions can be made:
- The regions where maximum and minimum deformations as well as stresses occur are the same in both the cases.
- Maximum stresses in both the cases are observed on the circumference of the hole in the lateral direction. This is because of the stress concentration in the area due to accumulation of stress flow lines in the region.
- Minimum stresses in both the cases are observed on the circumference of the hole in the longitudinal direction where there is a paucity of stress flow lines after they have moved around the sides of the slot.
- Maximum deformation is observed on the edge of the face of application of force. Minimum deformation is observed at the fixed face.
- From an analysis point of view Case 2 will be preferred i.e. the plate with three holes. The presence of smaller diameter holes on either side of the central larger diameter hole, helps to smoothen out the stress flow lines to almost parallel along the longitudinal edges. This reduces stress concentration in the geometry and the Equivalent and Maximum principal stresses in it are lower than in Case1.
- From a manufacturing point of view, Case 1 will be preferred since it involves producing only a single hole of 60mm diameter and hence saves on the machining cost and time that will be involved in Case 2 where two additional 30mm diameter holes are to be produced.