Publications

The primary goals of the present study are to: (1) determine how and why MEMS-scale friction differs from friction on the macro-scale, and (2) to begin to develop a capability to perform finite element simulations of MEMS materials and components that accurately predicts response in the presence of adhesion and friction. Regarding the first goal, a newly developed nanotractor actuator was used to measure friction between molecular monolayer-coated, polysilicon surfaces. Amontons law does indeed apply over a wide range of forces. However, at low loads, which are of relevance to MEMS, there is an important adhesive contribution to the normal load that cannot be neglected. More importantly, we found that at short sliding distances, the concept of a coefficient of friction is not relevant; rather, one must invoke the notion of 'pre-sliding tangential deflections' (PSTD). Results of a simple 2-D model suggests that PSTD is a cascade of small-scale slips with a roughly constant number of contacts equilibrating the applied normal load. Regarding the second goal, an Adhesion Model and a Junction Model have been implemented in PRESTO, Sandia's transient dynamics, finite element code to enable asperity-level simulations. The Junction Model includes a tangential shear traction that opposes the relative tangential motion of contacting surfaces. An atomic force microscope (AFM)-based method was used to measure nano-scale, single asperity friction forces as a function of normal force. This data is used to determine Junction Model parameters. An illustrative simulation demonstrates the use of the Junction Model in conjunction with a mesh generated directly from an atomic force microscope (AFM) image to directly predict frictional response of a sliding asperity. Also with regards to the second goal, grid-level, homogenized models were studied. One would like to perform a finite element analysis of a MEMS component assuming nominally flat surfaces and to include the effect of roughness in such an analysis by using a homogenized contact and friction models. AFM measurements were made to determine statistical information on polysilicon surfaces with different roughnesses, and this data was used as input to a homogenized, multi-asperity contact model (the classical Greenwood and Williamson model). Extensions of the Greenwood and Williamson model are also discussed: one incorporates the effect of adhesion while the other modifies the theory so that it applies to the case of relatively few contacting asperities.

In a recent paper, Starr and Segalman demonstrated that any Masing model can be represented as a parallel-series Iwan model. A preponderance of the constitutive models that have been suggested for simulating mechanical joints are Masing models, and the purpose of this discussion is to demonstrate how the Iwan representation of those models can yield insight into their character. In particular, this approach can facilitate a critical comparison among numerous plausible constitutive models. It is explicitly shown that three-parameter models such as Smallwood's (Ramberg-Osgood) calculate parameters in such a manner that macro-slip is not an independent parameter, yet the model admits macro-slip. The introduction of a fourth parameter is therefore required. It is shown that when a macro-slip force is specified for the Smallwood model the result is a special case of the Segalman four-parameter model. Both of these models admit a slope discontinuity at the inception of macro-slip. A five-parameter model that has the beneficial features of Segalman's four-parameter model is proposed. This model manifests a force-displacement curve having a continuous first derivative.

It is shown that for any material or structural model expressible as a Masing model, there exists a unique parallel-series (displacement-based) Iwan system that characterizes that model as a function of displacement history. This poses advantages both in terms of more convenient force evaluation in arbitrary deformation histories as well as in terms of model inversion. Characterization as an Iwan system is demonstrated through the inversion of the Ramberg-Osgood model, a force(stress)-based material model that is not explicitly invertible. An implication of the inversion process is that direct, rigorous comparisons of different Masing models, regardless of the ability to invert their constitutive relationship, can be achieved through the comparison of their associated Iwan distribution densities.

The Lubkin solution for two spheres pressed together and then subjected to a monotonically increasing axial couple is examined numerically. The Deresiewicz asymptotic solution is compared to the full solution and its utility is evaluated. Alternative approximations for the Lubkin solution are suggested and compared. One approximation is a Pade rational function which matches the analytic solution over all rotations. The other is an exponential approximation that reproduces the asymptotic values of the analytic solution at infinitesimal and infinite rotations. Finally, finite element solutions for the Lubkin problem are compared with the exact and approximate solutions.

Abstract not provided.