Analysis on Plates with Holes
Aim:
To perform a static analysis on two plates with holes and compare the results for stress, strain and displacement.
Introduction:
(1) Stress concentration:
Source: https://en.wikipedia.org/wiki/Stress_concentration
The stress and strain concentration locations are the critical structural details to determine the crack initiation and growth life of engineering structures.
A stress concentration is a location in an object where the stress is significantly greater than the surrounding region and occur when there are irregularities in the geometry or material of a structural component that cause an interruption to the flow of stress.
The degree of concentration of a discontinuity under typically tensile loads can be expressed as a non-dimensional stress concentration factor `K_t`, which is the ratio of the highest stress to the nominal stress and it is a function of the geometry of a crack or notch, and not of its size.
`K_t = (sigma_max)/(sigma_(nom))`
(2) Effect of stress concentration on different materials:
For static loading, yielding will typically occur first at a stress concentration and for ductile materials localised plastic deformation can occur causing a redistribution of stress, enabling the component to continue to carry load.
Brittle materials will typically fail at the stress concentration.
However, repeated loading may cause a fatigue crack to initiate and slowly grow at a stress concentration leading to the failure of even ductile materials. Fatigue cracks always start at these spots and so removing such defects increases the fatigue strength.
(3) Effect of holes on a plate:
Holes in structural components will create stress or strain concentrations and hence will reduce the mechanical properties. The majority of service cracks nucleate in the area of stress or strain concentration at the edge of a hole.
Introducing a circular hole in the plate disturbs the uniform stress distribution near the hole, resulting in a significantly higher than average stress.
In general, the rectangular plate having a central hole is a common structure, but stress concentration around the hole makes the material liable to failure across the hole region. For a rectangular plate of finite width, the stress concentration factor is a function of the ratio of hole diameter (D) to the plate width (T).
Case Setup and Procedure:
Model 1:
Length=300mm
Height=120mm
Thickness=30mm
Circular Hole at the center:
Diameter=60mm
Model 2:
Length=300mm
Height=120mm
Thickness=30mm
Circular Hole at the center:
Diameter=60mm
Two holes of 30 mm diameter which are placed 90mm away from the central hole on both sides.
Static analysis was carried out on both the models.
One short side of both the models were fixed and a load of 1000 N was applied such that the plates are stretched to the other side.
The material applied was Alloy Steel for both the plates and Fine mesh was used during meshing. After this, the analysis was carried out.
Results and Explanation:
(1) Comparison of values:
|
S.No |
Parameters |
Model 1 |
Model 2 |
|
1 |
Yield Strength in N/(m^2) |
6.20E+08 |
6.20E+08 |
|
2 |
Stress N/(m^2) |
1.20E+06 |
1.16E+06 |
|
3 |
Strain |
4.55E-06 |
4.34E-06 |
|
4 |
Displacement in mm |
5.24E-04 |
5.67E-04 |
|
5 |
Mass in g |
7.66E+03 |
7.34E+03 |
The screenshots below show a comparison between Stress, Strain and Displacement results for each model.
(2) Case 1 - Plate with hole at the centre:
Explanation:
The stress is the highest at the surface of the hole having a value of 1.203e+06 N/(m^2). The yield strength of this material is 6.2e+08 N/(m^2). We can see that stress is getting distributed to the ends, starting from the hole and the plate will fail at hole surface.
Also strain value is highest at the same spot as stress at the surface of the hole 4.5e-06
Since we have fixed one end of the plate, the other end has a considerable deflection of 5.24e-04 mm due to stretching load of 1000N applied.
(3) Case 2 - Plate with 3 holes:
Explanation:
Compared to the first model, this one has more better stress distribution with maximum value of stress 1.156e+06 N/(m^2) at hole surface. The two smaller holes act as stress relief for this plate and hence this model can be loaded and will remain under safer limits.
Strain is highest with a value of 4.341e-06.
This model has a displacement of 5.666e-04 mm at the free end of plate when stretching load of 1000N is applied.
Inferences:
It can be concluded that the maximum stress occurs at corners of holes in both models.
However, the plate with three holes has more better stress distribution and comparatively lesser stress concentration than the plate with single hole. Hence the second model is less prone to failure than the first one for any material used.
If mass is a consideration, then the plate with more holes is the winner since lesser material is used, which leads to decrease in mass.
Conclusion:
Thus the two plates with holes were modelled and analysed under the given conditions and compared for stress, strain and displacement values.
References:
https://en.wikipedia.org/wiki/Stress_concentration
https://www.sciencedirect.com/science/article/pii/S0020768307003587