Data Analysis of Tensile Test

Introduction

• Presenter: Camille Zube

• Purpose of Video: Instruction on how to perform data analysis for a tensile test.

Overview of Mechanical Parameters

• Key mechanical parameters to calculate from the stress-strain curves include:

  • Young's Modulus: Measure of the stiffness of a material.

  • Yield Strength: The stress at which a material begins to deform plastically.

  • Tensile Strength: Maximum stress a material can withstand while being stretched.

  • Fracture Strength: The stress at which a material fails and breaks.

  • Elongation at Break: Measure of how much a specimen can stretch before breaking.

  • Strain Hardening Exponent: Describes how a material hardens with deformation.

Data Description

• Data is provided in CSV format with three columns:

  1. Timestamp

  2. Displacement Value

  3. Force

Displacement

• Displacement: Change in gauge length measured during the test, denoted as ΔL.

• Basis of displacement measurement is the zeroing of transducers and length gauge prior to testing.

Force Measurement

• Force measurement: Taken in kilonewtons (kN) using a force transducer.

Preparation Before Calculations

• **Measurements Needed:

  1. Thickness:** Measured at three points: 1.17 mm, 1.18 mm, and 1.29 mm.

  2. Width: Measured across three points. Average values must be used for calculations.

  3. Effective Length: Straight section of the specimen, typically 70 mm for the dog bone shape.

• Cross-sectional area (
  A): Calculated as Thickness × Width.

Engineering Stress and Strain Calculations

Engineering Strain

• Definition: Ratio of change of length to initial length, calculated as follows:
  $ext{Engineering Strain} = rac{ ext{Displacement}}{L_0}$

• Excel Tip: Use dollar signs for absolute references to maintain cell references when copying formulas.

Engineering Stress

• Definition: Calculated using the force (converted to newtons) divided by the original area:
  $ext{Engineering Stress} = rac{ ext{Force}}{ ext{Original Area}}$

• Data unit conversion:

  • Force from kN to N by multiplying by 1000.

  • Area in square millimeters to retain consistency with stress in megapascals (MPa).

Data Visualization

• Graphing: Plot the graphs for:

  • Engineering Stress vs. Engineering Strain

  • True Stress vs. True Strain afterwards (following calculations).

True Stress and True Strain Calculations

• True Stress: Calculated using the current length and current cross-sectional area. $ext{True Stress} = rac{ ext{Force}}{A}$

  • Given that volume remains constant, employs the formula:
    $L<em>0 imes A</em>0 = L<em>{inst} imes A</em>{inst}$

• True Strain: Calculated as:
  $ext{True Strain} = ext{ln}\bigg( rac{L<em>{inst}}{L</em>0}\bigg)$

Young's Modulus Calculation

• Determined as the slope of the linear region of the engineering stress-strain curve.

• To perform linear regression on the elastic region.

• Example calculation results in: $14,450 ext{ MPa (or 14.4 GPa)}$

Yield Strength Calculation

• Determined at the point of plastic deformation initiation through:

  • Drawing a 0.2% offset line: The slope remains constant, and only intercept shifts down.

  • Estimate the yield strength from the graph, resulting in approximately 89 MPa.

Tensile Strength and Fracture Strength

• Tensile Strength: Found as the maximum stress value from the engineering stress curve:

  • Resulting max stress is 140 MPa.

• Fracture Strength: The last point before abrupt drop in stress, estimated at about 110-150 MPa.

Elongation at Break

• The elongation at break measures how much the sample can stretch before breaking, noted as 0.4 in this analysis.

Strain Hardening Exponent Calculation

• Based on the true stress and strain relationship focusing on the plastic region:

  • Employ logarithmic transformation for fitting an exponential curve.

• Execute a linear regression to find the slope, which yields the strain hardening exponent.

Reporting Instructions

• Ensure all data and graphs are properly labeled with units.

• Include all intermediate calculations in the report.

• Illustrate the engineering stress-strain for all samples for comparison.

Conclusion

• Follow through the discussed procedures to produce a comprehensive analysis from tensile testing data, ensuring to validate each calculation and maintain proper documentation.