Mechanical Testing Report: Tensile, Torsion, and Fatigue Analysis
Abstract
This report presents a comprehensive analysis of mechanical behavior under tensile, torsional, and fatigue
loading. Load-extension and stress-strain behavior were investigated to evaluate material properties such
as stiffness, yield strength, and toughness. Flow stress behavior was analyzed to assess strain hardening,
and torsional loading was explored to determine shear modulus and rigidity. Finally, fatigue tests under
varying environmental conditions allowed for comparison of fatigue life and fatigue limits. Graphical
analysis and modeling were used throughout to characterize and interpret material performance.
1. Load-Extension and Stress-Strain Analysis
a. Load vs Extension Plot
A typical load-extension plot was generated from the experimental data. The initial portion of the curve was
linear, indicating elastic behavior, followed by a nonlinear region denoting plastic deformation, and ending
in a sharp drop corresponding to fracture.
Figure 1: Load vs. Extension Curve
b. Stress-Strain Curve (Engineering and True Stress)
Both engineering and true stress-strain curves were plotted. Engineering stress decreases after ultimate
strength due to necking, while true stress continues to rise because it accounts for the decreasing cross-
sectional area during deformation.
Figure 2: Engineering vs. True Stress-Strain Curves
2. Mechanical Properties
Property Value
Stiffness ~3.15 × 10⁶ N/cm
Proportional Limit 259.45 MPa
Elastic Limit 259.45 MPa
Yield Strength 89.70 MPa
Ultimate Strength 4924.69 MPa
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Property Value
Fracture Strength 3907.61 MPa
Resilience 0.0491 MPa
Toughness 2594.47 MPa
• Stiffness: From initial slope of load-extension curve
• Yield Point: Determined using 0.2% offset method
• Toughness: Area under full true stress-strain curve
3. Flow Stress vs Plastic Strain (Strain Hardening)
a. Flow Stress Behavior
The flow stress was plotted against true plastic strain to reveal the hardening effect post-yield.
Figure 3: Flow Stress vs. True Plastic Strain
b. Power Law Model Fit (Hollomon's Equation):
σ = K ⋅ εn
- K ≈ 6.29 × 10⁻⁷ MPa - n ≈ 29.42 (unrealistically high)
c. Conclusion:
The fit was poor. The exponent n was unrealistic, indicating that simple power law models are insufficient.
More complex models such as Voce or Ramberg-Osgood may be required.
4. Torsion Testing
a. Shear Stress vs Shear Strain
Shear stress and strain were computed based on surface conditions and plotted to analyze torsional
deformation.
Figure 4: Shear Stress vs. Shear Strain
• Elastic region was linear
• Post-yield behavior was nonlinear
• No sudden drop: indicates ductile material
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b. Rigidity vs Shear Strain
The shear modulus (G) was calculated at each point as:
τ
G=
γ
Figure 5: Rigidity vs. Shear Strain
• Constant G at low strains confirms elastic behavior
• Decrease in G signifies plastic deformation and microstructural changes
c. Implications:
• Suitable for torsional applications if operated within elastic limits
• Design precautions necessary under cyclic or high-strain torsion
5. Fatigue Testing
a. Test Conditions:
Material Environment
Material A Dry atmospheric conditions
Material B 100°C
Material C Variable thermal cycling
b. S-N Curve Analysis:
Fatigue curves (stress amplitude vs. cycles to failure) were plotted on a log scale.
Figure 6: S-N Curves for All Materials
• Material A: High fatigue strength, fatigue limit ≈ 275 MPa
• Material B: Lower limit (~180 MPa), affected by temperature
• Material C: No fatigue limit, severe degradation under thermal cycling
c. Applications:
• Material A: Ideal for structural components with stable loading
• Material B: Suitable for moderate thermal loads
• Material C: Avoid for cyclic loads under variable thermal conditions
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Conclusion
This comprehensive study of tensile, torsional, and fatigue properties provided key insights: - The material
displays excellent ductility and toughness. - The shear modulus remains stable only in elastic ranges. -
Fatigue strength is highly sensitive to temperature and environmental changes.
Recommendations: - Use power law models cautiously for flow stress modeling. - Always verify fatigue
limits under relevant service conditions. - Consider microstructural effects (like thermal softening and strain
localization) in design.
References 1. Callister, W. D., & Rethwisch, D. G. (2020). Materials Science and Engineering: An Introduction.
Wiley. 2. Dieter, G. E. (1988). Mechanical Metallurgy. McGraw-Hill. 3. ASTM E8 / E8M – 21: Standard Test
Methods for Tension Testing of Metallic Materials. 4. ASTM E466 – 15: Standard Practice for Conducting Force
Controlled Constant Amplitude Axial Fatigue Tests of Metallic Materials.
