Andreas Goedecke

Creep Relaxation of an Elastic–Perfectly Plastic Hemisphere in Fully Plastic Contact

A set of finite element simulations was performed to analyze the creep behavior of an elastic-perfectly plastic hemisphere in contact with a rigid flat. This study focuses on the time-dependent stress relaxation of a fully plastic asperity. Assuming a Garofalo (hyperbolic sine) type material creep law, the asperity shows two distinct phases of relaxation. In the first phase, the asperity creeps with an accelerated creep rate and shows a contact area increase similar to that of a cylindrical geometry. In the second phase, no contact area change can be measured and the asperity creeps with a slower rate. Empirical evolution laws for the asperity creep behavior are presented, analyzing the influence of both material and geometrical parameters. The results are interpreted in terms of transient friction.

Discussion and Outlook

With the MIMEAC friction simulation environment fully developed in the previous chapters, it is now time to embed the theory in the scope of engineering system analysis. Chapter 6 focused on the in-depth analysis of the specific transient behavior of dwell time-, velocity- and normal force-dependent friction. In this chapter, in the form of an outlook, it will be demonstrated how the present theory can be used to analyze complex system dynamics.

Fractal Surface Model

The study of the fractal nature of surfaces appearing in engineering problems is a comparatively young field. It started in the 1980s and 1990s of the last century with phenomenological descriptions of fractal surface properties. While many ideas were presented before, Mandelbrot’s influence on the field, especially of his 1982 book The Fractal Geometry of Nature [162], can hardly be underestimated. This monograph collected many ideas from different fields and for the first time presented to a broad audience the baffling concept of a curve that is everywhere continuous, but nowhere differentiable.

Asperity Creep Under Constant Displacement

The main tool in this manuscript is the Finite Element simulation of creep in asperities, which are modeled as elastic-perfectly plastic (i.e. no hardening rule in addition to the creep laws) hemispheres in contact with a rigid flat. A large number of simulations has been performed to analyze the influence of a variety of input parameters. From this pool of simulations, simple empirical laws have been derived, describing the creep behavior of an asperity with a high degree of generality. The resulting creep laws will be presented in Chap. 2 for constant displacement (i.e. stress relaxation).

Generalized Junction Model

The creep laws for spherical asperities under constant displacement (Chap. 2) and constant force (Chap. 3) are generalized for arbitrary transient loading situations. In Chap. 4, the resulting set of Ordinary Differential Equations (ODEs) is presented. In the context of dynamic contact problems, this model constitutes a generalized model for a microscopic contact junction, or asperity.

Asperity Creep Under Constant Force

In Chap. 3, the creep laws for creep in asperities under constant force boundary conditions (i.e. area increase due to sink-in) are presented. These empirical laws can be used not only for analyzing friction, but are of more general value. For example, the behavior of spherical solder connectors (ball grids) under stress and thermal cycling is a long-standing problem in electronics, and creep is believed to play a decisive role. Also, our understanding of the process of sintering could potentially profit from this kind of model [see for example Balluffi et al. (Kinetics of Materials. Wiley, Hoboken, 2005), Chap. 16 or Dutton et al. (J. Am. Ceram. Soc. 75:2146-2154, 2005)].

The MIMEAC Contact Model

Embedding the empirical creep laws of Chaps. 2 and 3 in the fractal contact model of Chap. 5 yields the full MIMEAC (micro-mechanical asperity creep) model, discussed in Chap. 6. The emergence of the transient friction effects from the model will be discussed in depth, together with comparisons with the established models. This chapter takes the viewpoint of a tribologist, discussing the physics of friction.

Robust actuator with micro-hydraulic lever principle

Fast and precise actuators for the millimeter range are increasingly used in a range of applications from semiconductor manufacturing to internal combustion machines. A widely deployed class of such actuators use piezoelectric multilayer stacks due to their high actuation strength and fast movement. Traditionally, the piezo stacks are combined with a mechanical lever to amplify the actuation range. This paper analyzes how robustness and reliability of such an actuator can be improved by replacing the mechanical lever by a fluidic, micro-hydraulic lever.