Mechanical Property Extrapolation for Friction Correction

Overview

This project provides a Python-based solution for extrapolating compressive stress-strain data to ideal frictionless conditions (m=0) using linear regression over multiple specimen geometries. The method corrects for friction effects in mechanical testing by analyzing data from specimens with different diameter-to-height ratios.

Features

• Data Cleaning: Removes duplicate strain values and averages corresponding stresses
• Common Range Identification: Finds overlapping strain ranges across multiple datasets
• Cubic Spline Interpolation: Creates smooth stress-strain curves for consistent comparison
• Linear Extrapolation: Extrapolates stress to m=0 condition at each strain point
• Quality Assessment: Calculates R² values to evaluate extrapolation reliability
• Visualization: Generates comprehensive plots of results and analysis
• Data Export: Saves corrected frictionless curve to CSV format

Theoretical Background

The method assumes linear relationship between stress (σ) and diameter-to-height ratio (m = d/h) at constant strain:

σ(ε, m) = A(ε)·m + σ₀(ε)

Where:

• σ(ε, m) = measured stress at strain ε and geometry m
• A(ε) = slope representing friction sensitivity
• σ₀(ε) = extrapolated stress at m=0 (frictionless condition)

By measuring specimens with different m values and extrapolating to m=0, we obtain the ideal frictionless stress-strain curve.

Installation Requirements

pip install numpy pandas matplotlib scipy

Usage

1. Prepare Input Data

Create CSV files containing experimental stress-strain data:

• data_m1.csv: Data for m = 0.504032 (Al20)
• data_m2.csv: Data for m = 0.678161 (Al15)
• data_m3.csv: Data for m = 0.988142 (Al10)

Each CSV should have two columns: Strain and Stress (MPa)

2. Run the Script

python interpolation.py

3. Output Files

• friction_corrected_curve.csv: Contains the extrapolated frictionless curve
• Visual plots: Four-panel visualization of results

Code Structure

Main Functions:

clean_duplicate_strain(data)

• Removes duplicate strain values by averaging corresponding stresses
• Returns sorted, cleaned data

interpolate_stress(strain_data, stress_data, target_strains)

• Performs cubic spline interpolation to common strain points

get_common_strain_range(all_data)

• Identifies overlapping strain range across all datasets

extrapolate_to_m0(m_values, all_data, num_points=50)

• Main extrapolation function
• Returns extrapolated stress at m=0 and statistical details

plot_results(...)

• Generates comprehensive visualization:
  • Original and extrapolated curves
  • Linear extrapolation at sample strains
  • Slope variation with strain
  • R² quality metrics

save_results(...)

• Exports results to CSV format

Output Description

Data Output (CSV):

• Strain: Common strain points
• Stress_m0_MPa: Extrapolated stress at m=0
• Slope_dSigma_dm: Sensitivity of stress to geometry
• R_squared: Quality of linear fit at each strain

Visual Output (4-panel plot):

1. Top-left: Original stress-strain curves and extrapolated m=0 curve
2. Top-right: Linear extrapolation at selected strain values
3. Bottom-left: Variation of slope (dσ/dm) with strain
4. Bottom-right: R² values indicating extrapolation quality

Example Results

Extrapolation Statistical Summary:
==================================================
Mean R²: 0.9743
Min R²: 0.9214 at strain 0.127
Max R²: 0.9987 at strain 0.358
Mean slope: 145.67 MPa
Output strain range: 0.070 to 0.470

Interpretation Guidelines

1. High R² (>0.95): Reliable extrapolation, linear assumption valid
2. Low R² (<0.90): Potential issues with data or linear assumption
3. Slope magnitude: Indicates friction sensitivity
4. Corrected curve: Represents ideal frictionless material response

Applications

• Material property characterization
• Friction effect quantification in compression testing
• Comparative analysis of lubricant effectiveness
• Finite element model calibration
• Quality control in mechanical testing

Limitations and Assumptions

1. Linear relationship between stress and m (valid for small m variations)
2. Similar deformation mechanisms across different geometries
3. Consistent testing conditions and material homogeneity
4. Adequate number of geometry variations (minimum 3 recommended)

Future Improvements

• Non-linear extrapolation models
• Uncertainty quantification
• Batch processing for multiple materials
• Integration with FEM software
• Real-time monitoring during testing

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This tool was developed for academic research in mechanical property characterization and friction correction in materials testing.