Data driven approach to fatigue crack growth modeling

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Fatigue is a key phenomenon in mechanics, and is responsible for most structural failures. However, the inherent complexity of the problem makes the development of predictive models a non-trivial task and it greatly complicates the identification of the material fatigue constitutive behavior starting from experimental results. Hence, despite the relevance of the problem, a widely accepted model with truly predictive capabilities is still lacking.Aim of the present project is to develop a data driven approach to fatigue crack growth modeling. The adoption of data driven techniques allows to directly embed into the solution of the problem a discrete set of data of experimental or numerical nature. This has the advantage of overcoming the necessity of calibrating analytical fatigue constitutive material relationships. A recent variational phase-field approach to fatigue crack growth proposed by the applicant will be adopted as a reference mechanical model. Then, taking advantage of machine learning and data mining techniques, a data driven procedure will be proposed based on the identification of the numerical constitutive behavior. To this end, a technique involving the interpolation of the material behavior data within sub-clusters of the material space with limited extension will be used. This approach allows to determine a set of combination coefficients that parameterize the numerical (fatigue) constitutive manifold of the material.The procedure will be first studied for a 1D problem and based on a numerically generated material data set. Then, it will be extended to 2-3D and to the employment of experimental data sets. The initial adoption of numerical data allows to precisely estimate the accuracy of the procedure since a reference solution is available, i.e. the results of the numerical simulations adopting available constitutive relationships. The capability of the method will be investigated by simulating standard tests used to characterize the fatigue behavior, such as the compact tension or three-point-bending tests. Here, loading and boundary conditions different that those used to train the numerical manifold detection phase will be adopted.