Crystal plasticity applied to aggregates under non-symmetric cyclic loadings : Mechanical analysis and model order reduction

The field of mechanics, particularly micromechanics, has undergone great developments. It is well known that plastic flow in a single crystal is anisotropic which may be modeled using phenomenological constitutive laws at the mesoscale. The idea behind the development of micromechanical laws is to relate the behavior of each individual grain, predict evolving plasticity, and in turn account for the macroscopic properties of the structure. Two physical problems have been considered is this thesis i.e. the behavior of materials when they are asymmetrically loaded under cyclic stress or strain based boundary conditions. These loadings cause incremental strain accumulation or mean stress relaxation at the macroscopic scale. Conventional numerical models give an excess of both quantities. In this work it is shown that a mesoscale crystal plasticity finite element approach can give an answer to both problems. Different mechanical states existing in cyclically loaded structures are scrutinized and a micromechanical interpretation is given about their characteristic macroscopic behavior. Statistical results of different constitutive quantities within a polycrystal are also analyzed which give a new insight into what is happening at a local level. More importantly, the focus of this work is to pinpoint critical local regions of failure in the component and to characterize why these regions are prone to damage. The other part of the thesis pertains to big data problems in computational materials science. While solving large scale finite element problems, vast amounts of computational resources are utilized and many a times the evolving results are discarded after studying; not using them for future predictions. In this work it is shown that by utilizing already generated data, new test cases may be predicted from previous simulations. The method employed is called hybrid hyper-reduction which uses an unsupervised machine learning protocol coupled with the gappy POD to run reduced finite element simulations. Low cycle fatigue in a nickel iron based super alloy (Inconel 718) is taken as a test case.