A Constitutive Model for the Mechanical Behavior of Single Crystal Silicon at Elevated Temperature
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A Constitutive Model for the Mechanical Behavior of Single Crystal Silicon at Elevated Temperature H.-S. Moon*, L. Anand*, and S. M. Spearing+ * Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA + Department of Aeronautics and Astronautics Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA ABSTRACT Silicon in single crystal form has been the material of choice for the first demonstration of the MIT microengine project. However, because it has a relatively low melting temperature, silicon is not an ideal material for the intended operational environment of high temperature and stress. In addition, preliminary work indicates that single crystal silicon has a tendency to undergo localized deformation by slip band formation. Thus it is critical to obtain a better understanding of the mechanical behavior of this material at elevated temperatures in order to properly exploit its capabilities as a structural material. Creep tests in simple compression with n-type single crystal silicon, with low initial dislocation density, were conducted over a temperature range of 900 K to 1200 K and a stress range of 10 MPa to 120 MPa. The compression specimens were machined such that the multi-slip or orientations were coincident with the compression axis. The creep tests reveal that response can be delineated into two broad regimes: (a) in the first regime rapid dislocation multiplication is responsible for accelerating creep rates, and (b) in the second regime an increasing resistance to dislocation motion is responsible for the decelerating creep rates, as is typically observed for creep in metals. An isotropic elasto-viscoplastic constitutive model that accounts for these two mechanisms has been developed in support of the design of the high temperature turbine structure of the MIT microengine. INTRODUCTION The design of the MIT microengine is limited in part by the capabilities of Si as a structural material at temperatures higher than its brittle-to-ductile transition temperature (BDT), 900 K. In order to circumvent this limitation, it has been proposed to reinforce the Si with CVD SiC in strategic locations to create a Si/SiC hybrid microengine turbine spool. The feasibility of this hybrid turbine spool design has been investigated by a series of finite element analyses involving primitive material models [1, 2, 3]. While this has confirmed the potential of the Si/SiC hybrid microturbine structure for improving engine efficiency, as well as maintaining structural integrity, the thermomechanical structural analyses conducted thus far have not addressed the following three specific questions: 1) Can the upper yield point of Si be relied upon for designing a part that is to be in service at temperatures higher than the BDT? 2) Can the creep-limited service life of a part be reliably estimated? 3) Will stress concentrations such as fillet radii be susceptible to localized deformations?
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