A crystal plasticity based methodology for modeling fatigue crack initiation and estimating material coefficients to predict fatigue crack initiation life at micro, nano and macro scales

Fatigue failure is a dominant mechanism that governs the failure of components and structures in many engineering applications. In conventional engineering applications due to the design specifications, a significant proportion of the fatigue life is spent in the crack initiation phase. In spite of the large number of works addressing fatigue life modeling, the problem of modeling crack initiation life still remains a major challenge. In this work, a novel computational methodology based upon crystal plasticity formulations has been developed to predict crack initiation life at macro, micro and nano length scales. The crystal plasticity based constitutive model has been employed to model the micromechanical deformation and damage accumulation under cyclic loading in polycrystalline metals. This work provides a first of its kind, fundamental basis for employing crystal plasticity formulations for evaluating a quantifiable estimate of fatigue crack initiation life. A semi-empirical energy based fatigue crack initiation criterion s employed to allow for accurate modeling of the underlying microstructural phenomenon leading to the initiation of cracks at different material length scales. The results of the fatigue crack initiation life prediction in case of polycrystalline metals such as Copper and Nickel demonstrated that the crack initiation life prediction using the proposed methodology yielded an improvement of more than 30% in comparison to the existing continuum methodologies for fatigue crack initiation prediction and more than 80% improvement compared to the existing analytical models. The computational methodology developed in this work also provides a first of its kind technique to evaluate the fatigue crack initiation coefficient in the form of energy dissipation coefficient that can be used at varying length scales. The methodology and the computational framework proposed in this work, are developed such that experimental inputs are used to improve computational model performance and the closed loop feedback system enables the modeling of micro, macro and nano scale mechanisms very well. The computational models for the representative material microstructures were built by creating randomized Voronoi tessellations of the representative region that allows for reducing the need for extensive testing which is the major challenge in crack initiation predictions in engineering structures. In order to facilitate the use of the model for engineering applications, an analytical expression for fatigue crack initiation prediction using macro-scale loading conditions has been developed. The analytical model developed for fatigue crack initiation using macro-scale conditions has been validated using benchmark data in the literature to allow for the identification of the material co-efficients necessary to predict the fatigue crack initiation life while considering surface finish, grain size and crack size. The computational modeling and prediction of fatigue crack initiation life in nanostructured graphene reinforced materials is also studied by creating an effective interface method based computational model. The results of the model prediction showed good agreement with the trend of fatigue crack initiation life compared with the experimental results. This work lays the foundation for linking micromechanical plastic deformation to the nano-scale phenomenon while simultaneously providing a tool for engineers predicting crack initiation in macro-scale applications