Assessment of statistical responses of multi-scale damage events in an acrylic polymeric composite to the applied stress

• This paper assesses the statistical ensembles of random damage of an acrylic polymeric composite under pure tension and bending.
• The correlations among the across multi-variate were analyzed.
• Damage mechanisms in statistical ensembles were identified using Andrews plot and principal component analysis.

Assessments of the statistics of damage ensemble are essential steps to develop accurate modeling and predictions of material failures. Events of random damage constitute a damage system that resides in the microstructures of the materials. Characterization and evaluation of such a system involve assessing the evolving the cascading damage events from hierarchical microstructures of the solids, and there currently lacks an experimental means to do so. To address this need, we established an approach to acquire the events of random damage (ERD) by employing a measureable multi-variate DA defined in our previous work based on acoustic emission. It was found that the responsive events of random damage created by pure tension and three-point bending correlated strongly across all multiscale column vectors of DA in spacetime. The correlation strength is much stronger under tension than that under bending, and much stronger in early loading stages across the column scale vectors of the DA variate. ERD were found to be in clear distinct statistical populations by Andrews' exploratory data analysis plots under tension and bending, and in different stages of loading, which suggests that damage mechanisms are not only “physical”, but also “statistical”. Furthermore, our data showed that the strongly coupled multiscale column vectors of DA can be transformed orthogonally to becoming decoupled principal components, PCs, which may facilitate the constitutive modeling. However, a PC indexes nearly evenly all scale vectors of DA, which implicates, in conjunction with the findings of correlation and Andrews' plot, can be unidirectional, bi-directional, and or interwoven, but is a complicated index variable to describe the cascading multiscale damage events in evolving hierarchical microstructures of semicrystalline polymers.