Hongsheng Lu

Microforming: Experimental Investigation of the Extrusion Process for Micropins and its Numerical Simulation Using RKEM

Microforming using a small machine (or so-called desktop machine) is an alternative new approach to those using full-size heavy equipment for manufacturing microparts. Microparts are commonly defined as parts or structures with at least two dimensions in the submillimeter range, which are used extensively in electronics and micromechanical products. However when scaling down a conventional forming process to microscale, the influence of the so-called size effect needs to be considered. The individual microstructure (size, shape, and orientation of grains) and the interfacial conditions show a significant effect on the process characteristics. In this paper, the process of extrusion is investigated to establish it as a viable process for microforming. A forming assembly is fabricated and used in conjunction with a loading substage to extrude micropins with a final diameter of I mm. The effect of grain size is investigated by using workpieces heat treated to produce grain sizes varying from 32 μm up to 211 μm. Two extrusion dies with different roughness are used to study the effect of surface finish. While experiments lead to interesting questions and new discoveries, theoretical or numerical solutions are necessary tools for process optimization. Here, knowing the limits of the current widely used numerical simulation tools [i.e., the Finite Element Method (FEM)], a new method, the Reproducing Kernel Element Method (RKEM), has recently been developed to address the limitations of the FEM (for example, remeshing issue), while maintaining FEMs advantages, e.g., the polynomial reproducing property and function interpolation property. The new RKEM method is used to simulate the microextrusion problem. Its results are compared with that obtained from the FEM and the experiment result. Satisfactory results were obtained. Future directions on the experimental and simulation work are addressed.

Reproducing kernel element interpolation: Globally conforming Im/Cn/Pk Hierarchies

In this work, arbitrarily smooth, globally compatible, I m/C n/P k interpolation hierarchies are constructed in the framework of reproducing kernel element method (RKEM) for multi-dimensional domains. This is the first interpolation hierarchical structure that has been ever constructed with both minimal degrees of freedom and higher order continuity and reproducing conditions over multi-dimensional domains. The proposed hierarchical structure possesses the generalized Kronecker property, i.e., ∂ α Ψ I/(β)/∂x α(x J) = δ IJ δ αβ, |α|, |β| ≤ m. The newly constructed globally conforming interpolant is a hybrid of global partition polynomials (C∞) and a smooth (C n) compactly supported meshfree partition of unity. Examples of compatible RKEM hierarchical interpolations are illustrated, and they are used in a Galerkin procedure to solve differential equations.

A Multi‐scale Simulation of Micro‐forming Process with RKEM

Micro‐forming using meso‐scale press has the potential of bringing up an entire new concept of manufacturing. Compared to macro‐forming process, individual microstructure (i.e., the size, shapes and arrangement of grains) plays an even more critical role in deformation, process variation, interfacial behavior and wear in the micro‐forming process. In this paper, reproducing kernel element method (RKEM) is employed to simulate the micro‐forming process. As a meshfree method, RKEM can handle large deformation of material in the micro‐forming process. The efficiency of RKEM can be improved with using the stabilized conforming nodal integration. Due to the natural conforming of approximation and no requirement of compatible mesh in RKEM, it is easy to remesh the model when moving interfacing (grain boundary) is considered. As the first step of a series investigation, the resulting force of deforming a pin in a micro‐forming process is calculated with RKEM and is compared to the experimental result.