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I.

INTRODUCTION

MAGNESIUM is promising for use in transportation applications wherein its high specific strength may be exploited to manufacture lighter machine elements to achieve step changes in performance and fuel efficiency. Also, Mg alloys have densities similar to that of bones in the human body[1] and the fact that Mg2+ is the fourth most abundant cation in humans may offer new frameworks for the fabrication of bioresorbable implants. Despite an array of technological opportunities, the deformation behavior of Mg and its alloys often presents challenges to their widespread utilization. The challenges often emerge from its hexagonally closepacked (HCP) crystal structure that deforms primarily by twinning and basal slip at room temperature. Its anisotropic nature manifests a high cross-resolved shear stress (CRSS) for non-basal (pyramidal and prismatic) slip.[2] Unlike FCC metals that have five slip systems available to accommodate deformation in any configuration, Mg has only two at room temperature, which results in its characteristic lack of ductility. The resulting poor formability of the material often results in premature fracture during manufacturing operations involving plastic deformation.[3] The discontinuous flow (resulting from premature fracture in chips) in Mg is commonly observed in machining,[4] a widely used manufacturing process that is a mainstay of fabrication of metallic components.

During the machining process, the material being machined undergoes plastic deformation in the fanshaped deformation zone, thereby forming the chip (Figure 1(a)). Magnesium often lacks the ability to accommodate plastic deformation to form a continuous chip. As a result, the chip formation process is interrupted by fractures that run through the chip near the fan-shaped deformation zone. Thereafter, as the tool progresses forward, the chip formation process continues and the aforementioned pattern repeats due to which the chip ‘‘flow’’ has been termed discontinuous. Machining is a material removal process that involves advancing a wedge-shaped tool into a workpiece to remove a preset depth of material. Figure 1(a) illustrates a plane-strain prototype of this process in which the wedge-shaped tool advances in a direction that is normal to the cutting edge. In this fabrication process, sheet material in the regime corresponding to the set depths a0 is strained in simple shear as it flows through the fan-shaped deformation zone to become the chip. Thickness ac of the resulting chip depends on material properties of the sheet and the process parameters: V, a (Figure 1(a)). When the material is deformed by shear, the effective strain accumulated by the material in the chip can be determined as a function of the ratio a0/ac and is given by[5] 1 cos a ; 2¼ pffiffiffi 3 sin / cosð/  aÞ

½1

a0 =ac cosðaÞ 1  a0 =ac sinðaÞ

½2

where SAURABH BASU, and SEPIDEH ABOLGHASEM, Graduate Student Researchers, and M. RAVI SHANKAR, Associate Professor, are with the Department of Industrial Engineering, Swanson School of Engineering, Universi