Modeling of Thermal Joint Resistance of Polymer-metal Rough Interfaces

A compact analytical model is developed for predicting thermal joint resistance of rough polymer-metal interfaces in a vacuum. The joint resistance includes two components: i) bulk resistance of the polymer and ii) micro, constriction/spreading resistance of the microcontacts at the interface. Performing a deformation analysis, it is shown that the deformation mode of the polymer asperities is plastic. The required input parameters of the model can be measured in the laboratory and/or found in the open literature. It is observed that the thermophysical properties of the polymer control the thermal joint resistance and the metallic body properties have a second order effect on the thermal joint resistance. A non-dimensional parameter, i.e., ratio of microcontacts over bulk thermal resistances, is proposed as a criterion to specify the relative importance of the microcontacts thermal resistance. The present model is compared with more than 140 experimental data points collected for a selected number of polymers and showed good agreement. Nomenclature A = area, m as = radius of microcontacts, m bL = specimen radius, m E = Young’s modulus, Pa E0 = effective elastic modulus, Pa F = applied load, N Hmic = microhardness, Pa 1Ph.D. Candidate. Department of Mechanical Engineering, University of Waterloo, Waterloo, ON, Canada N2L 3G1. 2Distinguished Professor Emeritus. Department of Mechanical Engineering, University of Waterloo, Waterloo, ON, Canada N2L 3G1. Fellow ASME. 3TEES Associate Research Professor. Department of Mechanical Engineering, Texas A & M University, College Station, Texas 778133123, USA. He = elastic microhardness, Pa h = thermal conductance, W/mK k = thermal conductivity, W/mK k∗ = non-dimensional thermal conductivity, ≡ kp/ks m = combined mean absolute surface slope, [−] ns = number of microcontacts P = apparent contact pressure, Pa P ∗ = non-dimensional pressure, ≡ P/Hmic Q = heat flow rate, W R = thermal resistance, K/W T = temperature, K t = thickness of polymer specimen, m TCR = thermal contact resistance TIM = thermal interface material Y = mean surface plane separation, m Greek γ = plasticity index≡ Hmic/E0m λ = non-dimensional separation≡ Y/√2σ σ = combined RMS surface roughness, m Θ = non-dimensional parameter ≡ Rs/Rb υ = Poisson’s ratio Subscripts 0 = reference value 1, 2 = solid 1, 2 a = apparent b = bulk c = contact e = elastic FM = Fuller Marotta g = glass temperature j = joint mic = micro p = plastic r = real s = solid, micro 1 Copyright c ° 2004 by ASME