Characterization and modeling of the interplay between grain boundaries and heterogeneous plasticity in titanium

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The strengthening effect of grain boundaries is one of the key components in the development of modern structural materials. This is illustratcd by the intcrisificd research efforts 011 ultra fine grained materials, grain boundary engineering, and nanocrystalline materials over the last decade. The precise nature of the often beneficial effects of grain boundaries, however, have not been understood to a level which would allow for theory guided optimization of microstructures and accelerated alloy development.We propose to combine, improve, and apply recently developed approaches to investigate and quantify the micromechanical behavior of grain boundaries. We will achieve this using a recently developed technique that evaluates indentation topographies to generate a detailed understanding of plastic anisotropy of single crystals. A prominent advantage of the method is its efficiency in generating high quality data that previously could only be generated by careful single and bi-crystal experimentation, which both involve significantly higher amounts of experimental effort. By applying this indentation approach, combined with state of the art characterization and Simulation methods, we will develop a sound understanding of the interplay between grain boundaries and heterogeneous plasticity in titanium polycrystals for the first time.The goals of our research program are: (1) Carry out indentation within the interiors of large grains of a-titanium to effectively collect single crystal data coupled with extensive characterization of the resulting plastic defect fields surrounding the indents. By correlating with models of the indentation, we will arrive at a precise constitutive description of the anisotropic plasticity of single-crystalline titanium. (2) Extend this methodology to indentations close to grain-boundaries, i.e. quasi bi-crystal deformation. (3) Compare the measured characteristics of indentations at grain boundaries to simulated indentations äs predicted by the constitutive model calibrated using the single crystal indentations. This will lead us to qualitative understanding on how different types of grain boundaries modulate the local deformation patterns. (4) Based on this qualitative understanding we will implement a grain boundary transmissivity formulation into our non-local crystal plasticity formulation that fully accounts for all relevant influences from the crystallographic and geometric parameters that describe the boundary and the 3-dimensional relations between deformation Systems on both sides of the interface. (5) This grain boundary aware constitutive model will be validated against the collected indent characteristics. (6) Once the constitutive model has been developed, it will be further validated using data from previously collected high resolution experimental data from a polycrystalline microstructural patch deformed in a bulk specimen.Broad Impact: It is difficult to think of an aspect of material processing that affects society more than being able to reliably predict heterogeneous deformation, which is required before prediction of performance or reliability can be made with physically based confidence. This will be accomplished in a joint research project involving Michigan State University (MSU) and Max-Planck-Institut für Eisenforschung (MPIE) in Düsseldorf, Germany, where mutually useful skills are present which can reach the above goals when integrated into an international cooperative research program. The work will be carried out by 3 Ph.D. students under the guidance of Profs Bieler and Crimp at MSU, and a post-doc and one Ph.D. Student guided by Claudio Zambaldi, Dr. Philip Eisenlohr at MPIE. Extensive exchanges between the two laboratories will occur in order to integrate experimental and analytical methods to reach these goals.