Dynamic crack tip equation of motion: high-speed oscillatory instability

Area of Science:

• Fracture Mechanics
• Materials Science
• Nonlinear Dynamics

Background:

• Understanding dynamic crack propagation is crucial for material failure analysis.
• Existing models often simplify the complex nonlinear behavior at the crack tip.
• The influence of the near-tip nonlinear zone on dynamic crack motion requires further investigation.

Purpose of the Study:

• To propose a novel dynamic crack tip equation of motion.
• To incorporate principles of causality and scaling for near-tip nonlinear zones.
• To investigate high-speed crack instabilities and inertial effects.

Main Methods:

• Developing a dynamic crack tip equation of motion based on autonomy, symmetry, and causality.
• Utilizing scaling arguments for the near-tip nonlinear zone.
• Applying approximate analysis for the fully dynamic regime and comparing with experimental data.

Main Results:

• The proposed equation aligns with known results in the quasistatic regime.
• A prediction of high-speed oscillatory instability with a characteristic scale determined by the nonlinear zone.
• Experimental corroboration of predicted instabilities and emergent crack tip inertialike effects.

Conclusions:

• The new dynamic crack tip equation provides a robust framework for analyzing crack motion.
• Causality and the nonlinear zone's scale are key factors in dynamic fracture.
• The study demonstrates crack tip inertialike effects in high-speed dynamic fracture.