[Paper Review] Study of the Fracturing Behavior of Thermoset Polymer Nanocomposites via Cohesive Zone Modeling

Yao Qiao, Marco Salviato|arXiv (Cornell University)|Jul 21, 2018

Mechanical Behavior of Composites38 references16 citations

TL;DR

This study investigates the fracturing behavior of thermoset polymer nanocomposites using cohesive zone modeling and size effect law (SEL) to quantify the influence of the nonlinear Fracture Process Zone (FPZ). It demonstrates that LEFM leads to errors exceeding 150% in fracture energy estimation due to non-negligible FPZ effects, and shows that a bi-linear cohesive law provides superior accuracy—especially for graphene-reinforced nanocomposites—while the initial cohesive response remains unchanged by nanofillers.

ABSTRACT

This work proposes an investigation of the fracturing behavior of polymer nanocomposites. Towards this end, the study leverages the analysis of a large bulk of fracture tests from the literature with the goal of critically investigating the effects of the nonlinear Fracture Process Zone (FPZ). It is shown that for most of the fracture tests the effects of the nonlinear FPZ are not negligible, leading to significant deviations from Linear Elastic Fracture Mechanics (LEFM) sometimes exceeding 150% depending on the specimen size and nanofiller content. To get a deeper understanding of the characteristics of the FPZ, fracture tests on geometrically-scaled Single Edge Notch Bending (SENB) specimens are analyzed leveraging a cohesive zone model. It is found that the FPZ cannot be neglected and a bi-linear cohesive crack law generally provides the best match of experimental data.

Motivation & Objective

• To critically assess the impact of the nonlinear Fracture Process Zone (FPZ) on the fracture behavior of thermoset polymer nanocomposites.
• To quantify deviations from Linear Elastic Fracture Mechanics (LEFM) due to finite, non-negligible FPZ effects in nanocomposite fracture tests.
• To evaluate the effectiveness of the Size Effect Law (SEL) and cohesive zone modeling in re-analyzing existing literature data on nanocomposite fracture.
• To determine whether a linear or bi-linear cohesive law better captures the experimental fracture response across varying specimen sizes and nanofiller contents.
• To investigate how graphene nanoplatelet modification alters the cohesive behavior, particularly in the initial and post-peak regions of the cohesive law.

Proposed method

• A large dataset of mode I fracture tests from the literature on thermoset nanocomposites was compiled and analyzed using the Size Effect Law (SEL) to assess deviations from LEFM.
• The SEL was applied with a characteristic length scale derived from the FPZ size, enabling the identification of structural size effects and non-linear FPZ contributions.
• Cohesive zone modeling was employed using both linear and bi-linear cohesive laws to simulate the load-displacement response of geometrically scaled Single Edge Notch Bending (SENB) specimens.
• The linear cohesive law was tested with both LEFM-calculated and SEL-corrected fracture energy values to compare predictive accuracy.
• A bi-linear cohesive law was fitted to experimental data from Mefford et al. on graphene-reinforced thermoset nanocomposites across multiple sizes and filler contents.
• The model parameters were calibrated to minimize error between predicted and experimental peak load, with error thresholds used to evaluate model performance.

Experimental results

Research questions

• RQ1 To what extent do non-linear Fracture Process Zone (FPZ) effects invalidate the assumptions of Linear Elastic Fracture Mechanics (LEFM) in thermoset polymer nanocomposites?
• RQ2 How significant are the errors in fracture energy estimation when LEFM is applied to nanocomposite fracture tests with varying specimen sizes and nanofiller contents?
• RQ3 Does a bi-linear cohesive law provide a better fit to experimental data than a linear cohesive law for nanocomposite fracture behavior across different scales?
• RQ4 How does graphene nanoplatelet reinforcement affect the cohesive stress–displacement response, particularly in the initial and post-peak regions of the cohesive law?
• RQ5 Under what conditions does nanomodification significantly alter the fracture toughness, and when can it be considered negligible?

Key findings

• The double logarithmic plots of normalized strength versus normalized size show excellent agreement with the Size Effect Law (SEL), confirming that most nanocomposite fracture data fall in the transitional range where LEFM is inadequate.
• LEFM-based fracture energy estimation leads to errors of up to 156% due to non-negligible FPZ effects, particularly for small specimens and high nanofiller content.
• The bi-linear cohesive law provides a highly accurate description of fracture behavior, with errors in predicted structural strength less than 7% across all tested sizes and graphene contents.
• A linear cohesive law with SEL-corrected fracture energy yields reasonable agreement (errors ≤30%), but performs worse than the bi-linear model.
• Nanomodification via graphene nanoplatelets does not alter the initial portion of the cohesive law (up to ~20 µm crack opening), indicating that toughening mechanisms are active only at larger displacements.
• The increase in total fracture energy with higher graphene content is entirely attributable to a change in the slope of the second (post-peak) segment of the bi-linear cohesive law, indicating energy dissipation through mechanisms like crack deflection and bridging at larger crack openings.