Modeling of Stress Relaxation Behavior in HDPE and PP Using Fractional Derivatives

Area of Science:

• Materials Science
• Polymer Physics
• Rheology

Background:

• Understanding polymer viscoelasticity is crucial for material performance in demanding applications.
• Stress relaxation experiments provide insights into molecular mobility and material response over time.
• Classical, fractional, and conformable derivative models offer different approaches to describe viscoelastic behavior.

Purpose of the Study:

• To evaluate classical, fractional, and conformable derivatives for analyzing molecular mobility in HDPE and PP.
• To identify the most accurate mathematical model for representing the viscoelastic response of these polymers.
• To utilize statistical methods and optimization techniques for precise material characterization.

Main Methods:

• Stress relaxation experiments were conducted on HDPE and PP at various strain levels.
• Statistical evaluation metrics including R², AAD, and MSE were employed.
• Multivariate Analysis of Variance (MANOVA) and Response Surface Methodology (RSM) were used for model optimization.

Main Results:

• The spring-pot, Fractional Maxwell (FMM), Fractional Voigt-Kelvin (FVKM), and Kohlrausch-Williams-Watts (KWW) models showed effectiveness in describing stress relaxation.
• RSM analysis indicated that model selection significantly impacts results.
• The FVKM model was optimal for HDPE, and the KWW model was optimal for PP.

Conclusions:

• The selection of appropriate mathematical models, guided by statistical optimization, is vital for accurate polymer viscoelasticity characterization.
• Tailored model selection for HDPE and PP enhances predictions of long-term mechanical behavior.
• This framework supports improved polymer processing, product design, and reliability in industrial applications.