Evaluation of strength-controlling defects in paper by stress concentration analyses

Cellulosic webs, such as paper materials, are composed of an interwoven, bonded network of cellulose fibers. Strength-controlling parameters in these webs are influenced by constituent fibers and method of processing and manufacture. Instead of estimating the effect on tensile strength of each processing/manufacturing variable, this study modifies and compares the point stress criteria and average stress criteria models used to estimate defect-free (i.e., maximum possible) tensile strength and the inherent size of the cumulative effect of strength-limiting defects. The two major modifications to these models were to assume that defect-free tensile strength was unknown and that unnotched tensile strength was reduced by the presence of inherent defects. These modifications allow the calculation of inherent defect size and defect-free tensile strength by characterizing the tensile strength of the web in the presence of stress concentrations associated with holes of different radius. The models were applied to seven paper materials including lightweight, commercial papers, linerboards, and cylinder boards; estimated inherent defect sizes ranged from 0.1 to 1.5 mm. For most materials considered, defect size was larger in the 2-direction than the 1-direction. Actual measured tensile strengths ranged from 59% to over 95% of the estimated defect-free tensile strengths, σ _u .