Development of the Contact Models to Determine Electrical Contact Resistance Including a Coupled Electro-thermo-mechanical Analysis Considering Temperature-Dependent Material Properties

Abstract

Reliability of the electrical contact or interface is one of the major concerns in many applications such as batteries, solar cells, electrical connectors, MEMS based sensors for hybrid and electric vehicles, electronic devices, employment in mechatronics and so on. Different factors affect the reliability and efficiency of the electrical interface and also vary depending on the application. Electrical contact resistance is one of the most important factors. Electrical contact resistance value is affected by surface imperfection, cold welding or adhesion, vibration, hot-welding, material properties and contact behavior of the interface, organic contaminants, wear debris, various kinds of oxides or thin films and other features as well. Contact mechanics models are widely used to analyze the electrical contact behavior. This dissertation focuses on the development and validation of the contact models to determine the electrical contact resistance, which will be discussed subsequently in the next few paragraphs.

Closed-form finite-element empirical models are available for elastic and elastic-plastic cylindrical, spherical and sinusoidal shaped surfaces in contact. However, some of these models do not consider the effect of interaction with adjacent asperities or require extensive numerical resources because they employ a full 3-D model. Therefore, in this dissertation, a single asperity contact model has been developed, which is more realistic and computationally less expensive. To develop the asperity model, the behavior of an elastic and elastic- perfectly plastic axisymmetric sinusoidal surface in contact with a rigid flat has been analyzed and quantified for a wide range of material properties and asperity sharpness from initial to complete contact (high load). The numerical results agreed well with the Hertz model and the Jackson-Green elastic-plastic spherical contact model at low loads. Empirical equations for elastic and also elastic-perfectly plastic cases are formulated for the contact pressure, contact area, and surface separation. From the current analysis, it is found that it is not any single parameter, but different combinations of material properties and surface geometry that govern the whole contact behavior. The critical value of the amplitude of the sinusoidal asperity below which it will deform completely elastically from initial to complete contact is established. At low values of amplitude normalized by the critical amplitude, it was found that the contact behaved similar to a spherical contact, with the average pressure (hardness) always remaining lower than three times the yield strength. However, at higher values the average pressure increased toward a value as high as six times the yield strength at complete contact. This is a very significant finding as it differs from the conventional theory of hardness. The developed empirical equations are a function of surface roughness and material properties. Therefore, if temperature and scale-dependent material properties are known, these equations should be able to predict temperature and scale-dependent contact behavior.

Greenwood and Williamson (GW model) first developed a rough surface contact model to solve the problem of electrical contact. The original GW model used the Hertz single asperity model and Gaussian distribution of the surface roughness. However, in many of the electrical contact cases, contact deformation surpasses the Hertz small deformation assumtion. For medium to complete contact cases, asperity lateral interactions become very important, and the Hertz model cannot predict this behavior. Besides asperity lateral interaction, the probability distribution function of the surface roughness is critical as not all the surfaces are Gaussian in nature. This work has shown the effect of asperity models to predict asperity interaction behavior. Then the asperity models are applied with different probability distributions of the surface roughness in the framework of the statistical rough surface model. For the elastic case, the newly proposed rough surface models are compared with the Boundary Element Method (BEM) and Persson model that well predicted many of the practical applications. For the elastic-plastic case, electrical contact resistance has been measured between two rough surfaces using a four-wire resistance method. Then the newly proposed rough surface models are compared with the experimental results. Comparisons show that proper choice of the asperity model and the probability distribution function of the surface roughness can effectively model the contact behavior from the very small deformation region to the large deformation region.

Electrical contacts behave in a complicated way, and the effect of temperature makes the contact behavior more complicated. To analyze the temperature-dependent contact behavior, an axisymmetric sinusoidal asperity model of tin has been developed using Finite Element Method (FEM). The axisymmetric sinusoidal model reduces computational expenses and can effectively consider the asperity interaction, which is an important factor for large elastic-plastic deformation. The model considers the temperature-dependent yield strength, thermal conductivity, and resistivity. The effect of the thermal expansion coefficient is also included. For material modeling, the Johnson-Cook material model is employed, which can model the temperature-dependent material behavior from room temperature to melting temperature. Results show that temperature-dependent yield strength has a negligible effect on the electrical contact behavior for the cases analyzed. This work finds that temperature dependent resistivity and thermal conductivity are the key factors that govern the contact mechanism. The present work also confirmed the previous findings that Holm’s electrical contact resistance equation does not work for high-temperature cases. The finite element results have been validated by comparing the results with the voltage-temperature relation provided by the Wiedemann-Franz law. Finally, an equation has been suggested for the electrical contact resistance determination, modifying the equation derived by Greenwood. The equation should be able to predict the contact resistance from room temperature to high-temperature cases. This equation is a function of contact area. This contact area can be determined from the previously developed empirical equation for the contact area of an elastic-plastic axisymmetric wavy asperity.