Multiscale modeling of Ti/TiB composites

Titanium and its alloys have broad applications in the industry due to their high specific strength and chemical resistance. However, they suffer from low elastic modulus, wear resistance, and strength at elevated temperatures. To overcome these issues, several reinforcements, including long fibers (continuous fibers), short fibers (discontinuous fibers or whiskers), and particulates, have been used to produce titanium metal matrix composites (TMCs). Titanium boride whiskers (TiBw) are one type of reinforcement that have shown promising results in improving the wear behavior, hardness, high-temperature strength, and elastic modulus of titanium. Besides the stated benefits, TiB has a similar density and thermal expansion coefficient to titanium, which minimizes the residual stresses during production or at high temperatures. TiB is produced by in-situ reactions of titanium with compounds that contain boron ( e.g., TiB2). The produced TiB whiskers are monocrystalline and have a low lattice mismatch with titanium, which results in a clean and well-bonded semi-coherent interface. Because of these characteristics, Ti/TiB composites are good candidates for applications in the automotive, aerospace, and biomedical industries. TiB is not a naturally occurring compound, and many of its properties can only be obtained indirectly. Numerous experimental studies have been conducted during the last two decades to examine the microstructure and material properties of Ti/TiB. A few of them have gone further and used analytical methods to estimate the material properties of TiB whiskers. To design Ti/TiB composites, especially for applications in extreme conditions, the material properties of titanium, titanium boride, and their interface are needed at various temperatures. Due to the inaccessibility of TiB whiskers and the infeasibility of conducting costly experiments to obtain their properties indirectly, computational techniques could be an alternative method to derive the required properties. Theoretical predictions and computer-aided engineering are indispensable to designing materials for specific purposes. Computational materials science, a fast-growing research field, helps researchers to study the physical behaviors of materials that sometimes cannot be easily investigated in laboratories. At each length scale, there is an appropriate mathematical formulation to model materials. Those models can be linked together in a multiscale framework to predict and explain phenomena we can observe in the real world. This research aims to use computational materials science and computational mechanics techniques in multiscale modeling of Ti/TiB composites. At the smallest scale, i.e., the molecular scale, we use density functional theory (DFT) to investigate the interface between Ti/TiB. For investigations at finite temperatures, firstly, we develop interatomic potentials for B-B and Ti-B bonds based on a series of properties obtained from DFT. Then, the developed potentials are used in molecular dynamics (MD) simulations to study the temperature dependence of the material properties of TiB and cohesive zone parameters for Ti/TiB interfaces at the nanoscale. At last, we incorporate the cohesive zone model parameters in macroscale simulations and perform finite element analysis (FEA) to assess the failure strength Ti/TiB composites.