Statistical Analysis of Events of Random Damage in Assessing Fracture Process in Paper Sheets Under Tensile Load

Abstract

This investigation presents an experimental, computational, and data-enabled method to study the statistics of these ERD in the evolution of fracture process in paper sheets, which holds the key to making accurate characterization and evaluation of paper material failure. Firstly, an experimental method based on acoustic emission (AE) monitoring was established to accomplish the acquisition of all possible ERD that represent most physics of fracture process originating from the hierarchical microstructure of paper sheets under the influence of uniaxial tensile load. Then the acquired experimental damage data on characteristics of AE signal (such as timing, quantity, amplitude, magnitude, energy) was integrated as a measurable multivariate D _A based observation windows and multi-scale criteria, which was defined in our previous work. Ultimately entropy S, originated from the Gibbs probabilistic entropy, was obtained and applied to assess the evolving damage states in the evolution of fracture process. The significance of this multivariate (D _A ) and entropy (S) is the application of multi-scale statistical analysis and data-enabled thoughts to deal with the problem of the nonequilibrium damage evolution to macroscopic failure involving multiple space and time scales in paper material, respectively. Particular attention is given to that trajectory of damage states (TDS), S − T relation (when entropy S is correlated with varying tensile strength), is adequate enough to provide a realistic description of whole fracture process. The results evidenced that the multi-scale statistical analysis of ERD in fracture process is equivalent to build a “bridge” to study the connection between micro- and macro-systems. Furthermore, a spectroscopic technique (scanning electron microscope (SEM)) has also been proved to be a powerful method to study morphology of the fractured paper specimen.