Measurements of a Multicomponent Variate in Assessing Evolving Damage States in a Polymeric Material

Abstract

This paper presents a novel approach in assessing material damage resulted from micro- and mesostructural variations. We measured acoustic signals of randomly generated microscopic events (RGMEs) due to these variations and extracted the acoustic signals that represent the most physical essence of the RGME. To integrate the components of the measurements, we defined a variate D such that it establishes the spectrum of the RGME amplitude. We then employed Gibbs probabilistic entropy s to quantify the spectrum. When correlated with the applied stress, we proposed a novel s-σ relationship. This relationship depicts the evolving state of RGME as the stress field varies. We evidenced that entropy can be used to assess the material's damage states such that if the current stress level does not exceed the previous maximum, damage is in the states of “not-yet-the-maximum” by being either in “equientropy” or “vertical increment” processes using a sample polymer material. We also evidenced that the essence of the well-known Kaiser effect is its “memory” of damage. The significance of this variate or is that it takes into account the effects of the RGME on the material macroscopic behavior. A broader merit of our proposed approach lies within its great practical potential that connects the micro- and macrobehaviors of the materials through a set of simple mechanical tests.