The problem of understanding and modeling the complicated physics underlying the action and response of the interfaces in typical structures under dynamic loading conditions has occupied researchers for many decades. This handbook presents an integrated approach to the goal of dynamic modeling of typical jointed structures, beginning with a mathematical assessment of experimental or simulation data, development of constitutive models to account for load histories to deformation, establishment of kinematic models coupling to the continuum models, and application of finite element analysis leading to dynamic structural simulation. In addition, formulations are discussed to mitigate the very short simulation time steps that appear to be required in numerical simulation for problems such as this. This handbook satisfies the commitment to DOE that Sandia will develop the technical content and write a Joints Handbook. The content will include: (1) Methods for characterizing the nonlinear stiffness and energy dissipation for typical joints used in mechanical systems and components. (2) The methodology will include practical guidance on experiments, and reduced order models that can be used to characterize joint behavior. (3) Examples for typical bolted and screw joints will be provided.
Geometric features with characteristic lengths on the order of the size of the contact patch interface may be at least partly responsible for the variability observed in experimental measurements of structural stiffness and energy dissipation per cycle in a bolted joint. Experiments on combinations of two different types of joints (statically determinate single-joint and statically indeterminate three-joint structures) of nominally identical hardware show that the structural stiffness of the tested specimens varies by up to 25% and the energy dissipation varies by up to nearly 300%. A pressure-sensitive film was assembled into the interfaces of jointed structures to gain a qualitative understanding of the distribution of interfacial pressures of nominally conformal surfaces. The resultant pressure distributions suggest that there are misfit mechanisms that may influence contact patch geometry and also structural response of the interface. These mechanisms include local plateaus and machining induced waviness. The mechanisms are not consistent across nominally machined hardware interfaces. The proposed misfit mechanisms may be partly responsible for the variability in energy dissipation per cycle of joint experiments.
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.
A classical mechanistic model was developed to capture the existence of pre-sliding tangential deflection (PSTD) in contacting polysilicon and coated polysilicon surfaces. For the purposes of modeling asperity friction, experiments have shown, and been supported through detailed finite element analyses, that frictional forces developed through tangential sliding scale linearly through a material parameter known as the junction strength. A junction strength model coupled with a discrete quasi-static contact mechanics analysis, using contacting surface descriptions sampled by AFM from actual polysilicon surfaces, predicts inelastic tangential displacements that are qualitatively consistent with observed PSTD response. The simulations imply that the existence of PSTD depends not only on the spatial characteristics of contacting surfaces, but also on the local loading characteristics.
The generalized momentum balance (GMB) methods, explored chiefly by Shabana and his co-workers, treat slap or collision in linear structures as sequences of impulses, thereby maintaining the linearity of the structures throughout. Further, such linear analysis is facilitated by modal representation of the structures. These methods are discussed here and extended. Simulations on a simple two-rod problem demonstrate how this modal impulse approximation affects the system both directly after each impulse as well as over the entire collision. Furthermore, these simulations illustrate how the GMB results differ from the exact solution and how mitigation of these artifacts is achieved. Another modal method discussed in this paper is the idea of imposing piecewise constant forces over short, yet finite, time intervals during contact. The derivation of this method is substantially different than that of the GMB method, yet the numerical results show similar behavior, adding credence to both models. Finally, a novel method combining these two approaches is introduced. The new method produces physically reasonable results that are numerically very close to the exact solution of the collision of two rods. This approach avoids most of the non physical, numerical artifacts of interpenetration or chatter present in the first two methods.
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.