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The use of B-spline interpolation functions in the finite element method (FEM) is not a new subject. B-splines have been utilized in finite elements for many reasons. One reason is the higher continuity of derivatives and smoothness of B-splines. Another reason is the possibility of reducing the required number of degrees of freedom compared to a conventional finite element analysis. Furthermore, if B-splines are utilized to represent the geometry of a finite element model, interfacing a finite element analysis program with existing computer aided design programs (which make extensive use of B-splines) is possible. While B-splines have been used in finite element analysis due to the aforementioned goals, it is difficult to find resources that describe the process of implementing B-splines into an existing finite element framework. Therefore, it is necessary to document this methodology. This implementation should conform to the structure of conventional finite elements and only require exceptions in methodology where absolutely necessary. One goal is to implement B-spline interpolation functions in a finite element framework such that it appears very similar to conventional finite elements and is easily understandable by those with a finite element background. The use of B-spline functions in finite element analysis has been studied for advantages and disadvantages. Two-dimensional B-spline and standard FEM have been compared. This comparison has addressed the accuracy as well as the computational efficiency of B-spline FEM. Results show that for a given number of degrees of freedom, B-spline FEM can produce solutions with lower error than standard FEM. Furthermore, for a given solution time and total analysis time B-spline FEM will typically produce solutions with lower error than standard FEM. However, due to a more coupled system of equations and larger elemental stiffness matrix, B-spline FEM will take longer per degree of freedom for solution and assembly times than standard FEM. Three-dimensional B-spline FEM has also been validated by the comparison of a three-dimensional model with plane-strain boundary conditions to an equivalent two-dimensional model using plane strain conditions.

Friction stir welding (FSW) of steel is often performed with an insert made of polycrystalline cubic boron nitride (PCBN). Specifically, MS80 is a grade of PCBN made by Smith MegaDiamond that has been optimized for the FSW process. The PCBN insert is attached to a tungsten carbide (WC) shank by a compression fitting. However, FSW tools manufactured by this method inevitably fail by fracture in the PCBN. Permanently bonding PCBN to WC would likely solve the fracturing problem and increase the life of PCBN FSW tools to be economically viable. Partial transient liquid phase (PTLP) bonding, a process used to join ceramics with thin metallic interlayers, was proposed as a method to permanently bond PCBN to WC. PTLP bonding is often performed using three layers of pure elements. On heating, the two thin outer interlayers melt and bond to the ceramics. Concurrently, these liquid layers diffuse into the thicker refractory core until solidification has occurred isothermally. A procedure was developed to reduce the number of possible three-layer PTLP bonding setups to a small set of ideal setups using logical filters. Steps in this filtering method include a database of all existing binary systems, sessile drop testing of 20 elements, and a routine that calculates maximum interlayer thicknesses. Results of sessile drop testing showed that the PCBN grade required for this research could only be bonded with an alloy of Ti, Cu, Mg, and Sb. Two PTLP bond setups were tested using this special coating on the PCBN, but a successful bond could not be achieved. However, a PTLP bond of WC to WC was successful and proved the usefulness of the filtering procedure for determining PTLP bond setups. This filtering procedure is then set forth in generalized terms that can be used to PTLP bond any material. Also, recommendations for future research to bond this grade of PCBN, or some other grade, to WC are presented.