A logarithmic-type constitutive model for carbon fiber papers considering Hertz contact effect

Abstract

Porous carbon fiber papers, which are formed by randomly distributed carbon fibers, are commonly used as gas diffusion layers of proton exchange membrane fuel cells. Several key properties of the gas diffusion layers, for example, air permeability, thermal conductivity, and electrical resistance, are inevitably controlled by the strain it experienced, which is always a nonlinear function of the applied compressive stress. In the present study, a logarithmic-type constitutive model is proposed to characterize the nonlinear stress–strain relation of carbon fiber papers under compressive loading. A hexahedral configuration of carbon fibers is adopted as a typical microstructure of carbon fiber papers. Contact and bending deformation of carbon fibers are accounted for with use of Hertz’s contact model and beam bending model, respectively. The logarithmic-type constitutive model is eventually obtained by solving a differential equation considering the variation of structural porosity. The stress–strain curves of the present model and experimental data are compared for a number of commercial gas diffusion layer samples. The comparisons indicate that the present model is capable of predicting the mechanical performance of carbon fiber papers, and may be useful for analytical and numerical analysis of gas diffusion layers and fuel cells.