Competing Weibull and stress-transfer influences on the specific tensile strength of a bonded fibrous network

We present the results of an experimental study into the influence of areal density on the tensile strength of paper. Our data illustrate a non-linearity in the relationship between tensile strength and areal density that gives rise to a weight dependent maximum of specific tensile strength. A model is derived showing that this maximum can be attributed to the competing effects of a non-linear increase in the efficiency of stress transfer and hence strength with network weight, and the increased Weibull probability of reduced strength with increasing cross-sectional area of the network. We propose that two Weibull moduli may be required to account for the orthotropic nature of network structure and its contribution to strength.