Damage prognosis in metals is a grand challenge that engineers have faced for centuries. The complexity of this problem arises from the interaction of damage mechanisms at multiple scales. For example, a force applied far from a microscopic imperfection can promote the production of defects at the atomic scale. In between, mesoscale attributes (e.g., heterogeneous dislocation density, grain morphology, texture) regulate the exchange of damage across micro- and macro-scales.
Most modelling approaches do not explicitly consider all these length scales and they rely on phenomenological correlations between empirical formulations and macroscopic experiments. This approach is reliable for predictions within the testing conditions of the experiments used for calibration, but the uncertainty is unbound outside these conditions. This lack of predicting power is problematic in critical applications in which the mechanical response should be guaranteed for a large number of working conditions, much larger than the typical experiments required for material certification.
To mitigate modelling uncertainty, leading scientists [1-3] have proposed multiscale approaches validated at various length scales. A key value added by these approaches relies on the lower dependence of damage on loading conditions at smaller scales (e.g., the strength of the interaction between two dislocations is unnafected). Dislocation structures (e.g., cells and persistent slip bands (PSBs)) lay on the verge of sensitivity to loading conditions.
Much research [4] has shown that mesoscale structures (e.g., 1 micron in size) control the stress-strain response under fatigue loading. After an overload, the response depends on the changes of the mesoscale structures and on the crystallographic orientation. A key attribute is that only a few dislocation structures are thermodynamically stable and the same structures arise on myriads of metals. Hence, we argue that the stress-strain response of various single- and poly-crystals after an unknown loading sequence can be bound by models that probe all possible stable structures. Moreover, we hypothesize that the transient behaviour after unexpected events can be reproduced with a parameterized transition between stable structures.
This research proposes to mitigate the uncertainty of assessing overloads by integrating mesoscale mechanical tests and computational modelling. In terms of experimental effort, we will manufacture mesoscale single crystal specimens using Cranfield University proprietary Mesoscale Machining Platform. We will measure the stress-strain response of FCC single- and poly-crystalline specimens of various sizes (50 to 500 microns) after overloads with different intensity and patterns. Additionally, we will characterize mesoscale dislocation structures after overloads in order to identify the evolution of the structures and their morphology at the mesoscale.
In terms of modelling, we will exercise the crystal plasticity model recently developed by the PI [5], which is the state of the art in constitutive models for cyclic loading and has been extensively validated with single- and poly-crystal data for Ni, Cu, and stainless steel. We will propose a physics-based evolution of structures to explain and bind the stress-strain response of single- and poly-crystals after overloads. We will match overload scenarios with their mesoscale structures to predict independently the mechanical response. Finally, we will quantify the role of overloads on microstructurally small fatigue cracks by comparing the crystallographic Fatemi-Socie fatigue indicator parameter (FIP).
[1]Bo, Jiang, Dunne. J. Mech. Phys. Sol. 106 (2017):15-33.
[2]Sweeney, Vorster, Leen, et al. J. Mech. Phys. of Sol. 61 5 (2013):1224-40.
[3]Zhu, Basoalto, Warnken, and Reed. Acta Mat. 60, 12 (2012):4888-4900.
[4]Li, Li, Wang, Zhang, Prog. Mater. Sci. 56 (2011):328-377.
[5]Castelluccio, McDowell, Int. J. Plast. 98 (2017) 1-26.
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