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Analysis of Plate with a hole in HyperWorks

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Static stress concentration factor calculation for a plate with centre hole subjected to axial loading in tension using FEA software

Title: Static stress concentration factor calculation for a plate with centre hole subjected to axial loading in tension using FEA software

Problem Statement: Find the stress concentration factor of a Rectangular plate of dimension 60*30 mm2 with a hole in the centre of diameter 5 mm. Material is Cast Iron. An axial load of 300N is applied on the circumference of the circular centre hole and three sides of the rectangular plate are fixed.

Properties: Elastic Modulus(N/mm2): 1.20*105,Poisson’ s Ratio: 0.28 and Density (tonne/mm3): 7.20*10-9.

Modelling:

A)

Geometry of the component
Figure 1: Geometry of the component
Material Properties of the component
Figure 2: Material Properties of the component
Meshing of Plate
Figure 3: Meshing of Plate

Static stress concentration factor calculation for a plate with centre hole subjected to axial loading in tension using FEA software

Constraint and force application
Figure 4: Constraint and force application
Figure 5: Imputing thickness of the plate
Figure 6: Running analysis on Optistruct
Figure 7: Finishing of analysis

B) Loading and boundary Condition

Figure 8: 3 edges shown in black are completely constrained
Figure 9: Axial force of 300N is applied in z-direction in red arrow

Result and Analysis
Mesh Properties:
2D Mesh
Element size: 1.000
Mesh Type: Quads and Trias
Linear static analysis

Static stress concentration factor calculation for a plate with centre hole subjected to axial loading in tension using FEA software

Figure 10: Deformation Plot for 5mm Thickness
Figure 11: Stress Plot for 5mm Thickness

Stress Concentration:
A stress concentration (often called stress raisers or stress risers) is a location in an object where stress is concentrated. An object is stronger when force is evenly distributed over its area, so a reduction in area, e.g., caused by a crack, results in a localized increase in stress. A material can fail, via a propagating crack, when a concentrated stress exceeds the material’s theoretical cohesive strength. The real fracture strength of a material is always lower than the theoretical value because most materials contain small cracks or contaminants (especially foreign particles) that concentrate stress. Fatigue cracks always start at stress raisers, so removing such defects increases the fatigue strength.

Stress concentration factor:
Stress concentration factor (Kt), is a dimensionless factor that is used to quantify how concentrated the stress is in a material. It is defined as the ratio of the highest stress in the element to the reference stress.

SCF(Kt)= Max stress/Remote stress

Reference stress is the total stress within an element under the same loading conditions without the stress concentrators, meaning the total stress on the material where the material is free from holes, cuts, shoulders or narrow passes.

Aspect Ratio(A/H) is the Area by Thickness ratio

Analysis of Plate with a hole in HyperWorks

Calculation:

Area of plate (a) = 16*80-(π/4)d^2 = 1780.36 mm2
Thickness of plate (h) = 5 mm
(a/h) = 356.07 mm
Maximum Stress: 3.554*102N/mm2
Reference Stress: 2.768*102 N/mm2

Stress concentration factor = Max stress/Remote stress
= 3.554/2.768= 1.284

Result Table:

Sr No. Aspect Ratio(A/H) Max. Displacement(mm) Max. Stress(N/mm2) SCF
1 356.07 8.437*10-2 3.554*102 1.284
2 237.38 1.231*10-2 9.300*101 1.280
3 178.04 4.777*10-3 4.309*101 1.273
4 142.43 2.728*10-3 2.505*101 1.264

Conclusion
When the value of Aspect Ratio decreases, Maximum Displacement decreases, Maximum stress decreases and so is Stress Concentration Factor.

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Analysis of Plate with a hole in HyperWorks

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