Researchers have developed a powerful new method to simulate and predict how cracks form and grow in engineering materials under repeated loading.

The study, recently published in the International Journal of Fatigue, is the work of IMDEA Materials Institute’s Miguel Castillón, and Profs. Javier Segurado and Ignacio Romero.

It introduces a novel fatigue crack–propagation framework that combines the strengths of Linear Elastic Fracture Mechanics (LEFM) with the rapidly advancing phase-field fracture (PFF) approach.

Fracture mechanics and fatigue analysis are two fundamental theories for understanding the failure of materials and structures.

While fracture mechanics provides a theoretical framework to study the conditions for quasistatic crack propagation, fatigue analysis focuses on the behaviour of materials under cyclic loading conditions.

Traditional phase-field fatigue models estimate fatigue life by simulating loading cycles one by one, a process that becomes extremely slow and computationally expensive when cracks take millions of cycles to develop.

In contrast, the new method requires only a single monotonic simulation while still predicting fatigue life with high accuracy. Moreover, this approach can be directly applied to different materials without the need to repeat simulations for each case, offering greater flexibility and efficiency compared to conventional methods.

“The core of this new methodology lies in the development of novel energy (crack length)-controlled solvers that robustly trace the complete quasi-static equilibrium path of a cracked body, including complex snap-back instabilities, in a single simulation,” the paper’s authors explain.

The technique works via the numerical evaluation of the derivative of the sample’s compliance with respect to the crack area.  

To retrieve this compliance the framework relies on a PFF-FEM (Finite Element Method) simulation, controlled imposing a monotonic crack growth.

This information is then used together with Paris’ law, a standard engineering rule for fatigue prediction, to determine how the crack will propagate over time.

Because the simulation does not need to follow each cycle, it can rapidly evaluate long-term fatigue problems, including high-cycle and ultra-high-cycle fatigue, without additional computing cost.

“The proposed framework leverages the energy-controlled simulation to directly compute the evolution of the specimen’s compliance and its derivative with respect to the crack length,” state the authors.

“This avoids the need for computationally expensive cycle-by-cycle simulations, as the fatigue life can be directly integrated using Paris’ law from the compliance data of a single quasi-static analysis.”

“This significantly reduces computational cost compared to cycle-by-cycle methods and avoids extensive calibration work required by other phase-field fatigue models,” they conclude.

The framework was first validated against analytical solutions and also showed high levels of agreement with experimental data resulting from realistic test cases featuring unknown and curved crack paths.

All files needed to reproduce the results of this paper are available on GitHub (Phase-Field Fatigue Paper repository ) and can also be explored via the project website (Phase-Field Fatigue Documentation).

All simulations were carried out using the PhaseFieldX package (PhaseFieldx Github repository), with its documentation and usage examples available at (Phasefieldx Documentation), ensuring full reproducibility, transparency, and easy adaptation to different materials and geometries.