Subject: Finite Element Analysis (FEA) of Specimens Under Axial Tension – Lab Results
Hi Professor Stapleton,
I hope this email finds you well! I am writing to report a summary of the results of the Finite Element
Analysis lab where specimens were subjected to axial tension in Ansys. In this lab, we set out to observe
the deformation, stress and strain behaviors of Aluminum, Copper, Steel and Titanium and compare these
results to hand calculations.
The data for the stress, strain and deformation of each material was collected both under standard and
realistic boundary conditions to provide comprehensive insights into each material’s behaviors under
axial tension. The detailed breakdown of the results with the hand calculations and percent error are in
Tables 1-4 at the end of this email.
When analyzing the differences between the fixed end boundary condition and realistic boundary
conditions, variations were observed across the materials. For Aluminum and Titanium, the maximum
stress and strain values increased under realistic boundary conditions, whereas the total deformation
decreased when compared to the fixed end condition. In contrast, Steel exhibited a decrease in all
parameters – maximum stress, strain, and deformation under realistic conditions compared to the fixed
end condition. Lastly, copper increased in all parameters when subjected to realistic boundary conditions.
Another observation was the error in total deformation across all materials when comparing FEA results
and hand calculations. This discrepancy suggests that the software's material meshing, and algorithms
capture details that our simplistic hand calculations may overlook. This leads me to believe that tools like
Ansys offer a more comprehensive and realistic analysis, especially for boundary conditions and complex
geometries like the dog bone.
Upon comparing the rectangular samples to the dog bone samples, it's clear that geometry plays a
significant role in stress distribution – see Figure 1. The reduced section in the dog bone tends to
concentrate stress, making it different from the rectangular samples. As a result, the reduced section
experiences a higher strain rate which can lead to earlier plastic deformation and/or fracture when
compared to the rectangular samples.
Our analysis implies the significance of the relationship between material properties and material
geometry. The loading effects in the dog bone sample emphasize the importance of geometrical
considerations in material testing. Given these insights, I recommend that the ASME standards are
followed when testing materials to ensure consistent, reproducible, and reliable results. Also, ensure that
the design considerations of any project account for the stress concentrations in materials with complex
geometries. Lastly, I recommend using FEA software like Ansys to refine our predictions instead of
simply using equations and hand calculations.
Please let me know if you have any questions and if I can clarify anything further!
Best,
Kevin Diaz-Salvador
Subject: Finite Element Analysis (FEA) of Specimens Under Axial Tension – Lab Results
Aluminum
Maximum
Deformation (mm)
Maximum Strain
Experimental
Calculation
2.1007
Hand Calculation
Error (%)
4.23
101
0.047392
0.0704225
48.6
Maximum Stress
3.3648
5.00
48.6
(GPa)
Table 1 – Comparison of Experimental and Hand Calculations for Aluminum under Fixed End
Conditions
Copper
Maximum
Deformation (mm)
Maximum Strain
Experimental
Calculation
0.6777
Hand Calculation
Error (%)
1.3636
101
0.015421
0.0227273
47.4
Maximum Stress
1.6963
2.5
47.4
(GPa)
Table 2 – Comparison of Experimental and Hand Calculations for Copper under Fixed End Conditions
Titanium
Maximum
Deformation (mm)
Maximum Strain
Experimental
Calculation
1.5519
Hand Calculation
Error (%)
3.125
101
0.035937
0.0520833
44.9
Maximum Stress
3.4499
5
44.9
(GPa)
Table 3 – Comparison of Experimental and Hand Calculations for Titanium under Fixed End Conditions
Steel
Maximum
Deformation (mm)
Maximum Strain
Experimental
Calculation
1.8663
Hand Calculation
Error (%)
3.75
101
0.041046
0.0625
52.3
Maximum Stress
8.2092
12.5
52.3
(GPa)
Table 4 – Comparison of Experimental and Hand Calculations for Steel under Fixed End Conditions
Subject: Finite Element Analysis (FEA) of Specimens Under Axial Tension – Lab Results
Figure 1 – Stress Concentration in the Narrowed Section of Dog Bone Sample under Axial Tension