Phase field modeling of fast crack propagation

Area of Science:

• Continuum mechanics
• Materials science
• Solid mechanics

Background:

• Crack propagation often exhibits singularities, posing challenges for theoretical prediction.
• Elastodynamic effects are crucial for understanding rapid fracture dynamics.
• Phase-field models offer a framework for studying elastically induced phase transitions and fracture.

Purpose of the Study:

• To present a continuum theory for steady-state crack propagation.
• To address the finite-time cusp singularity issue in Grinfeld instability.
• To investigate fracture phenomena using a phase-field model.

Main Methods:

• Developed a continuum theory incorporating elastodynamic effects.
• Utilized a phase-field model for elastically induced phase transitions.
• Performed simulations to validate analytical predictions.

Main Results:

• The theory successfully predicts steady-state crack propagation.
• Elastodynamic effects resolve the Grinfeld instability singularity.
• Simulations confirm analytical predictions for fast crack propagation.

Conclusions:

• The presented continuum theory provides a robust framework for crack propagation.
• Elastodynamic effects are essential for accurate modeling of fracture.
• Phase-field modeling is a viable approach for studying fracture mechanics.