Statistical Analysis of Viscoelastic Creep Compliance of Vinyl Ester Resin

Simsiriwong, Jutima; Sullivan, Rani W.; Hilton, Harry H.; Drake, Daniel A.

doi:10.2514/6.2012-1730

Cited by 6 publications

(3 citation statements)

References 24 publications

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“…More practical, but still operationally difficult, forms of (21) have been formulated in [61], [66], [67], [88] where they have been applied to creep test data. The stochastic functions describing stresses, strains, moduli, etc., are represented by simpler and mathematically more manageable forms consisting of single PDF rather than the 2N distinct PDFs of (21).…”

Section: Statistical and Probability Issuesmentioning

confidence: 99%

Uncertainty in Characterizations of Isotropic Linear Viscoelastic Shear and Bulk Moduli from 1 - D Tensile Experiments

Michaeli¹,

Shtark²,

Grosbein³

et al. 2014

55th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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Previous experiments at constant strain rates, while valuable in their own right, indicated that relaxation experiments at nominally constant strains are more conducive to obtaining data over numerous time decades in order to establish proper moduli/compliances, which cover the entire time range from instantaneous to fully relaxed moduli. The purpose of this paper, then, is to report on a series of relaxation experiments in order to produce high fidelity characterization of the statistical properties of viscoelastic materials, such as relaxation moduli, creep compliances, times to achieve constant strains, etc. Photometric, load cell, extensometers and accelerometer equipment was employed for data harvesting. Beta probability density functions with time dependent parameters were used to best describe the statistics as they answer the need to represent the data in a finite interval. A new analytical protocol for material determination, called the direct numerical calculation of viscoelastic moduli (DVM), has been developed and tested. Various protocols to determine the actual time to complete experimental loading phases are formulated as well as simple dynamic experiments for evaluating instantaneous moduli. Parallel to the above development the instantaneous modulus is determined from separate dynamic experiments and its statistical results are combined with 1 Copyright© the quasi-static experimental statistical data, thus providing time dependent probability density functions covering the entire positive time domain t ≥ 0. The time when the loading cycle ends is calculated from extensometers and its non-trivial influence on the characterization process is evaluated.It is shown that a stochastic elastic/viscoelastic correspondence principle can only be formulated based on integral transforms, since the constitutive relations are no longer of the convolution type. However, its utility for purposes of analysis of stress and strains is severely limited compared deterministic EVCPs because of the complicated non-convolution type constitutive relations.

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Section: Statistical and Probability Issuesmentioning

confidence: 99%

Uncertainty in Characterizations of Isotropic Linear Viscoelastic Shear and Bulk Moduli from 1 - D Tensile Experiments

Michaeli¹,

Shtark²,

Grosbein³

et al. 2014

55th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

View full text Add to dashboard Cite

show abstract

“…The constitutive relationship for an isothermal, isotropic, linearly viscoelastic material can expressed using a Prony series representation as [21][22] ' 0…”

Section: Creep Compliance Using a Prony Seriesmentioning

confidence: 99%

Creep Compliance Characterization of Vapor-Grown Carbon Nanofiber/Vinyl Ester Nanocomposites Using a Central Composite Design of Experiments

Drake

Simsiriwong

Sullivan

et al. 2013

54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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The effects of vapor-grown carbon nanofiber (VGCNF) weight fraction, applied stress, and temperature on the viscoelastic response (creep compliance) of VGCNF/vinyl ester (VE) nanocomposites were studied using a central composite design (CCD). The nanocomposite test articles were fabricated by high shear mixing, casting, curing, and postcuring in an open face mold under a nitrogen environment. Short-term creep/creep recovery experiments were conducted at prescribed combinations of temperatures (23.8 -69.2 o C), applied stresses (30.2 -49.8 MPa), and VGCNF weight fractions (0.00 -1.00 parts of VGCNF per hundred parts of resin, phr) determined from the CCD. The response surface model (RSM) for predicting the creep compliance was 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 -46.5 o C). However, increasing the VGCNF weight fraction for temperatures greater than 50 ºC decreased the creep resistance of these nanocomposites. The latter response may be due to a decrease in the nanofiber-to-matrix adhesion as the temperature is increased. The creep compliance RSM revealed the interactions between the VGCNF weight fraction, stress, and temperature on the creep behavior of thermoset polymer nanocomposites. I. IntroductionNano-reinforced polymer composites have been extensively researched to improve material performance and functionality for a wide variety of applications [1][2][3][4][5][6][7][8][9] . The inclusion of small amounts of nano-fillers can improve such composite properties as interlaminar shear strength, toughness, fatigue life, and corrosion resistance. In particular, nanocomposites with vapor-grown carbon nanofibers (VGCNFs) have been shown to improve the composite mechanical, electrical, and thermal properties 10-13 . However, these efforts have been hindered due to poor VGCNF/matrix adhesion, poor VGCNF dispersion, and VGCNF agglomeration that lead to poor load transfer to the nanofibers 14 . The interfacial adhesion between nanofibers and certain polymers has been improved by oxidizing the nanofiber surfaces 4 .The addition of VGCNFs has also been shown to affect the time-dependent (viscoelastic) response of polymer matrix composites. Nouranian et al. 4 used a full factorial experimental design to compare the effect of the VGCNF type, weight fraction, mixing method, and the use of a dispersing agent on the storage and loss moduli of a VGCNF/vinyl ester (VE) material system. Less than 0.50 phr (parts of VGCNF per hundred parts of resin) increased the storage moduli of the nanocomposites by 20% compared to the storage modulus of the neat VE polymer. Creep, the deformation over time at a constant applied stress, is also influenced by the VGCNF weight fraction. Plaseied and Fatemi 15 performed tensile creep testing and creep modeling of VGCNF/VE nanocomposites at a single weight fraction (0.50 ph...

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“…The upper limits of temperature and stress were selected to promote creep in the linear viscoelastic range and were based on previous research . Additionally, isochronous curves were developed to establish linearity within the temperature and stress design space …”

Section: Design Of Experiments Approachmentioning

confidence: 99%

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

Drake

Sullivan

Lacy

et al. 2015

J of Applied Polymer Sci

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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 (23.8-69.2 C), 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., 23.8-46.5 C). However, increasing the VGCNF weight fraction decreased the creep resistance of these nanocomposites for temperatures greater than 50 C. 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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Statistical Analysis of Viscoelastic Creep Compliance of Vinyl Ester Resin

Cited by 6 publications

References 24 publications

Uncertainty in Characterizations of Isotropic Linear Viscoelastic Shear and Bulk Moduli from 1 - D Tensile Experiments

Uncertainty in Characterizations of Isotropic Linear Viscoelastic Shear and Bulk Moduli from 1 - D Tensile Experiments

Creep Compliance Characterization of Vapor-Grown Carbon Nanofiber/Vinyl Ester Nanocomposites Using a Central Composite Design of Experiments

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

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