Creep characterization of vapor-grown carbon nanofiber/vinyl ester nanocomposites using a response surface methodology

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AbstractMethodologyMaterial ModelInput DataResultsAcknowledgmentsReferences


Central Composite Design.

The effects of selected factors such as vapor-grown carbon nanofiber (VGCNF) weight fraction, applied stress, and temperature on the viscoelastic responses (creep strain and creep compliance) of VGCNF/vinyl ester (VE) nanocomposites were studied using a central composite design (CCD). Nanocomposite test articles were fabricated by high-shear mixing, casting, curing, and post curing in an open-face mold under a nitrogen environment. Short-term creep/creep recovery experiments were conducted at prescribed combinations of temperature (23.8–69.2C), applied stress (30.2–49.8 MPa), and VGCNF weight fraction (0.00–1.00 parts of VGCNF per hundred parts of resin) determined from the CCD. Response surface models (RSMs) for predicting these viscoelastic responses were developed using the least squares method and an analysis of variance procedure. The response surface estimates indicate that increasing the VGCNF weight fraction marginally increases the creep resistance of the VGCNF/VE nanocomposite at low temperatures (i.e., 23.8–46.5C). However, increasing the VGCNF weight fraction decreased the creep resistance of these nanocomposites for temperatures greater than 50C. The latter response may be due to a decrease in the nanofiber-to-matrix adhesion as the temperature is increased. The RSMs for creep strain and creep compliance revealed the interactions between the VGCNF weight fraction, stress, and temperature on the creep behavior of thermoset polymer nanocomposites. The design of experiments approach is useful in revealing interactions between selected factors, and thus can facilitate the development of more physics-based models.

Author(s): Daniel A. Drake, Rani W. Sullivan, Thomas E. Lacy, Charles U. Pittman, Jr., Hossein Toghiani, Janice L. DuBien, Sasan Nouranian, Jutima Simsiriwong

Corresponding Author: [ Rani W. Sulivan, Ph.D.]

Figure 1. Stages of Creep. (click on the image to enlarge).


To model the viscoelastic behavioral response of the nanocomposites, creep experiments were performed at varying stress levels and temperatures. The creep strain and compliance were modeled using a Prony series representation in conjunction with the Boltzmann superposition principle (BSP). Creep strains and creep compliances were selected at varying times and modeled using a central composite design of experiments approach. This design of experiments approach allowed for the development of response surface models of the creep compliance and creep strain. These are seen in the images below

Material Model

Use a central composite design of experiments approach (Metamodeling) to determine the viscoelastic behavior of vinyl ester nanocomposites.

Input Data

Simulations are not required as this paper is purely experimental.


The creep strain and creep compliance as a function of the vapor-grown carbon nanofiber (VGCNF) weight fraction and temperature are shown below.
Creep Compliance as a Function of Temperature and VGCNF Weight Fraction.
Creep Strain as a Function of Temperature and VGCNF Weight Fraction.


Support from the Center for Advanced Vehicular Systems at Mississippi State University is gratefully acknowledged


D. Drake, R.W. Sullivan, H. Toghiani, S. Nouranian, T.E. Lacy, C. U. Pittman, Jr., J.L. DuBien, J. Simsiriwong. “Creep Compliance Characterization of Vapor-Grown Carbon Nanofiber/Vinyl Ester Nanocomposites Using a Central Composite Design of Experiments,” J. Appl. Polym. Sci., 132, 42162, doi: 10.1002/app.42162.

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