Multiscale Modeling of Materials Using Machine Learning

Project Overview

This project focuses on optimizing the microstructural properties of copper heat pipes to enhance their performance. By integrating machine learning (ML)-derived constitutive models with finite element analysis (FEA), we explored the impact of grain size on stress handling and thermal efficiency. The concept of multiscale modeling was central to connecting the grain-scale microstructure to the larger, component-level material behavior.

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Objectives

1. Analyze the effect of grain size on the strength and heat resistance of copper heat pipes.
2. Develop a custom user material (UMAT) subroutine based on an ML-derived stress-strain relationship.
3. Validate the UMAT model against experimental and simulation results.

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Methodology

1. Multiscale Modeling

• Micro to Macro Connection:

  • Simulated grain-scale behavior using the VPSC (Visco-Plastic Self-Consistent) code.
  • Integrated grain-scale data (stress, strain rate, grain size) into the macroscale FEA model using the UMAT subroutine.

• Purpose:

  • To understand how microstructural features like grain size influence macroscale material properties (e.g., stress, strain, and thermal conductivity).

2. Data Generation

• VPSC Simulation Setup:

  • Generated 76 datasets using vpsc7.exe for 19 grain sizes (5–95 µm) at 4 strain rates (10⁻² to 10⁻⁵).
  • Each dataset contained stress-strain data for different combinations of grain size and strain rate.

• Dataset Concatenation: Combined all datasets for ML training and analysis.

3. Machine Learning Model

• Polynomial Regression (Degree 2):
  • Modeled stress as a function of strain, strain rate, and grain size.
  • Derived the following stress equation:

    Stress = 115.87 + 581.17 * Strain + 24694.13 * Strain Rate + 1168663.06 * Grain Size 
             - 1368.07 * Strain² + 12543.13 * Strain * Strain Rate 
             - 29095.13 * Strain * Grain Size - 2102507.11 * Strain Rate² 
             - 9820971.89 * Strain Rate * Grain Size + 8222685370.00 * Grain Size²
    

  • Achieved R² = 0.948.

4. UMAT Code Development

• Integrated the ML-derived stress equation into the UMAT subroutine in Abaqus.

• Differentiated the equation to compute:

  • Stress Flow (sf)
  • Strain Tensor Update

• Enhanced the UMAT to include plastic strain adjustments for dynamic stress-strain calculations.

5. Validation

• Compared stress-strain plots from the UMAT model against VPSC simulation results.
• Result: Close match, validating the ML-based approach.

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Simulation Details

• Component: Hollow copper pipe.

  • Inner Diameter: 8 mm
  • Outer Diameter: 10 mm
  • Length: 100 mm

• FEA Setup:

  • Applied radial load to simulate real-world conditions.
  • Two scenarios:
    1. With Microstructure: Grain size incorporated using the UMAT.
    2. Without Microstructure: Uniform material response.

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Multiscale Insights

• Grain Size Effect:

  • Smaller grain sizes increased stress due to the Hall-Petch effect, improving material strength.
  • Enhanced the strain rate sensitivity, reflecting realistic material behavior under varying loads.

• Integration of Scales:

  • By incorporating grain-scale behavior into the macroscale FEA model, the simulation accurately captured localized stress variations.
  • The multiscale approach highlighted the interdependence of microstructure and component performance, bridging the gap between material science and engineering applications.

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Key Findings

1. Smaller grain sizes increased material strength due to the Hall-Petch effect.
2. Incorporating microstructure led to localized stress variations, improving accuracy in simulations.
3. Thermal Performance:
   • Smaller grains reduced heat resistance, enabling faster heat transfer without damaging the pipe.

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Conclusion

The integration of microstructural details like grain size into FEA simulations:

• Improved stress and heat transfer predictions.
• Highlighted the importance of multiscale modeling in optimizing material performance.

This study demonstrates the potential of combining machine learning with FEM to achieve realistic and efficient material design.

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Technologies and Tools Used

• Programming: Fortran
• Simulation: Abaqus, VPSC
• Machine Learning: Python (Polynomial Regression)
• Software: Ansys for custom material definition

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Visual Results

Stress-Strain Curves

1. With Microstructure:

   • Stress levels significantly increased with smaller grain sizes.

2. Without Microstructure:

   • Uniform stress distribution observed.

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Feel free to explore the code and dataset in this repository for further insights.