Data driven approach to fatigue crack growth modeling
Applied Mechanics, Statics and Dynamics
Final Report Abstract
The research project has developed a new paradigm for variational brittle fracture mechanics that possibly lays the basis for new insights into the fracture mechanics of brittle materials. While solving a brittle fracture mechanics propagation problem, the fracture-related material modeling assumptions are removed. Instead, the governing equations stemming from variational principles are combined with a set of discrete data points, leading to a model-free data-driven method of solution. The proposed framework opens thus the possibility to accounts for the raw material data directly within the solution of the governing boundary value problem. The solution at a given load step of the rate-independent fracture mechanics problem is identified as the point within the data set that best satisfies either the Kuhn-Tucker conditions stemming from the variational fracture problem or global minimization of a suitable energy functional, leading to data-driven counterparts of both the local and the global minimization approaches of variational fracture mechanics. The rate-dependent fracture is studied using the local minimization approach that accounts for the crack propagation speed alone or together with the crack length. In the former case the underlying rate-independent limit is a Griffith-type model, while the latter can involve also R-curve models. The approach developed for the ratedependent fracture mechanics can be straightforwardly adapted to the fatigue case by replacing the time with the number of cycles, the crack-tip speed by the crack growth rate and the crack-tip law of motion with a relationship such as the Paris law or the NASGRO equation. Data-driven fracture mechanics approaches deliver results in excellent agreement with those of their standard fracture mechanics counterparts and they converge to those latter with respect to both the number of points in the data sets and the amplitude of a random noise. Similarly to its analytical counterpart, the data-driven rate-dependent fracture mechanics can be used to regularize the rate-independent approach in the spirit of a vanishing viscosity approach as well as to simulate the fatigue crack growth processes.
Publications
- Data driven fracture mechanics
P. Carrara, L. De Lorenzis, L. Stainier, M. Ortiz
(See online at https://doi.org/10.1016/j.cma.2020.113390)
