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

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|abstract=  
 
|abstract=  
 
[[Image:CCD_Design.jpg|thumb|300px|right| Central Composite Design. ]]
 
[[Image:CCD_Design.jpg|thumb|300px|right| Central Composite Design. ]]
TThe effects of selected factors such as vapor-grown carbon nanofiber (VGCNF) weight fraction, applied stress, and temperature
+
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
 
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.
 
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.
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Corresponding Author: [Sullivan@ae.msstate.edu Rani W. Sulivan, Ph.D.]
 
Corresponding Author: [Sullivan@ae.msstate.edu Rani W. Sulivan, Ph.D.]
  
|material model= Use a central composite design of experiments ([[Metamodeling]]) to determine the viscoelastic behavior of vinyl ester nanocomposites.
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|material model= Use a central composite design of experiments approach ([[Metamodeling]]) to determine the viscoelastic behavior of vinyl ester nanocomposites.
  
|Input Data= No input data required.  
+
|input deck= Simulations are not required as this paper is purely experimental.
  
 
|animation=
 
|animation=
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{{paper_figure|image=Stages_Of_Creep.jpg|image caption=Figure 1. Stages of Creep.}}
 
{{paper_figure|image=Stages_Of_Creep.jpg|image caption=Figure 1. Stages of Creep.}}
  
|methodology= To model the 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
+
|methodology= 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
  
 
|results=  
 
|results=  
 
<table width="100%" cellspacing="3" cellpadding="5">
 
<table width="100%" cellspacing="3" cellpadding="5">
 
<tr>
 
<tr>
<td colspan="2"> To model the 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.
+
<td colspan="2"> The creep strain and creep compliance as a function of the vapor-grown carbon nanofiber (VGCNF) weight fraction and temperature are shown below.
 
</td>
 
</td>
 
</tr>
 
</tr>
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|acknowledgement=M.A. Tschopp would like to acknowledge funding provided under an NSF graduate fellowship for the initial work. Continued funding for investigating structure-property relationships in grain boundaries under the NEAMS (Nuclear Energy Advanced Modeling and Simulation) program is also acknowledged.  
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|acknowledgement=Support from the Center for Advanced Vehicular Systems at Mississippi State University is gratefully acknowledged  
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|references=
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 +
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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 +
 
  
|references= The initial methodology was used in the following papers:
 
 
}}
 
}}
  
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[[Category: Research Paper]]
 
[[Category: Research Paper]]
 
[[Category: macroscale]]
 
[[Category: macroscale]]
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[[Category: Metamodeling]]
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[[Category: Polymers]]

Latest revision as of 10:43, 12 April 2017

AbstractMethodologyMaterial ModelInput DataResultsAcknowledgmentsReferences

Abstract

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: [Sullivan@ae.msstate.edu Rani W. Sulivan, Ph.D.]


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

Methodology

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.

Results

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.

Acknowledgments

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

References

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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