Indications

The analysis presented in this article is based on four main components:

• Theoretical Analysis: This component focuses on the theoretical framework, using Linear Elastic Fracture Mechanics (LEFM) and Paris’ law. The results are saved in files with the .lefm extension for comparison with other methods.

• Elastic Simulations: This component includes simulations of linear elastic problems. The results are saved in files with the .elastic extension for comparison with other methods.

• Phase-Field Simulations: This component involves simulations using phase-field energy-controlled schemes. The results are saved in files with the .pff extension for comparison with other methods.

• Reference Data: This component consists of additional data from articles or other references. This data is saved in files with the .databib extension.

For all the simulations and calculations the following units system is considered:

Quantity	Unit
Length	\(mm\)
Force: \(P\)	\(kN\)
Area	\(mm^2\)
Energy	\(kN \cdot mm\)
Young’s modulus: \(E\)	\(kN/mm^2\)
Poisson’s ratio \(\nu\)	dimensionless
Energy release rate: \(G\)	\(kN/mm\)
Crack length	\(mm\)
Crack area	\(mm^2\)
Stiffness \(K\)	\(kN/mm\)
Compliance \(C\)	\(mm/kN\)
Paris constant \(n\)	dimensionless
Paris constant \(C_\text{Paris}\)	\(mm^{(2+3n)/2} / \text{cycle} \cdot {kN}^n\)

All 2D simulations are performed using quadrilateral elements under plane strain conditions.