Overview
A refined phase-field modeling approach has been developed to address tensile-dominated brittle fracture, specifically introducing a 'shifted energy barrier'. This method aims to manage crack nucleation by mapping the Rankine criterion, applied to the effective stress, onto a state-dependent active-energy threshold. The objective is to enable the prescribed tensile strength to govern crack nucleation, while maintaining existing AT1 model components such as the crack-density functional, stiffness degradation, and degraded stress response.
Research Context
The classical AT1 phase-field model is known to exhibit an intrinsic energy barrier for crack nucleation. This inherent barrier results in a predicted strength that is contingent upon both the fracture toughness and the regularization length. The present work seeks to overcome this dependency for scenarios characterized by tensile-dominated brittle fracture.
Approach
The core of the methodology involves shifting the intrinsic energy barrier found in the classical AT1 phase-field model. This shift is achieved by integrating the Rankine criterion, evaluated on the effective stress, into a state-dependent active-energy threshold. This modification allows the prescribed tensile strength to directly control the initiation of cracking. The existing framework of the AT1 crack-density functional, stiffness degradation, and degraded stress response remains unaltered by this introduction.
Since the active-energy threshold is dependent on the current stress state, the field equations are derived from a restricted variational principle. A microforce formulation was employed to identify the barrier shift as a dissipative resistance. This formulation also establishes a corresponding lower bound for the regularization length.
Findings
- Strength Control and Regularization Length Insensitivity: The formulation allows the prescribed tensile strength to control crack nucleation. Numerical examples indicated that, within an admissible range, the nucleation load exhibited near insensitivity to the regularization length.
- Multiaxial Nucleation Behavior: The predicted multiaxial nucleation states were observed to follow the Rankine envelope.
- Localization Profile in 1D Tension: In one-dimensional tension scenarios, closed-form solutions recovered the prescribed peak strength. These solutions also yielded a cosine-type localization profile. As the introduced shift diminishes, this profile approaches the classical AT1 profile.
- Behavior under Compression: Under conditions of overall compression, crack nucleation continued to be associated with local tensile stress concentrations.
- Transition to LEFM: The formulation successfully captured the transition from strength-controlled failure for small flaws to the Linear Elastic Fracture Mechanics (LEFM) limit for larger cracks.
Why This Matters
The development of a phase-field model that decouples predicted strength from regularization length for tensile-dominated brittle fracture, and one that aligns with prescribed tensile strength and the Rankine criterion for multiaxial states, provides a more robust and predictable computational tool for material failure analysis.