Stiffness and Expansion Estimates for Oriented Short Fiber Composites

Halpin, J. C.

doi:10.1177/002199836900300419

Cited by 824 publications

(304 citation statements)

References 4 publications

Supporting

Mentioning

294

Contrasting

Unclassified

Order By: Relevance

“…The Halpin-Tsai model comes from work by Halpin and co-workers [30,36], and gives the modulus of the material as a function of the modulus of the matrix polymer, E m , and of the filler particles, E f , but also as a function of the aspect ratio by the inclusion of a shape factor. The predicted composite modulus is:…”

Section: Tensile Modulusmentioning

confidence: 99%

Toughening mechanisms of nanoparticle-modified epoxy polymers

Johnsen

Kinloch

Mohammed

et al. 2007

Polymer

862

576

View full text Add to dashboard Cite

An epoxy resin, cured with an anhydride, has been modified by the addition of silica nanoparticles.The particles were introduced via a sol-gel technique which gave a very well dispersed phase of nanosilica particles which were about 20 nm in diameter. Atomic force and electron microscopy showed that the nanoparticles were well dispersed throughout the epoxy matrix. The glass transition temperature was unchanged by the addition of the nanoparticles, but both the modulus and toughness were increased. The measured modulus was compared to theoretical models, and good agreement was found. The fracture energy increased from 100 J/m 2 for the unmodified epoxy to 460 J/m 2 for the epoxy with 13 vol% of nanosilica. The fracture surfaces were inspected using scanning electron and atomic force microscopy, and the results were compared to various toughening mechanisms proposed in the literature. The toughening mechanisms of crack pinning, crack deflection and immobilised polymer were discounted. The microscopy showed evidence of debonding of the nanoparticles and subsequent plastic void growth. A theoretical model of plastic void growth was used to confirm that this mechanism was indeed most likely to be responsible for the increased toughness that was observed due to the addition of the nanoparticles. IntroductionEpoxy polymers are widely used for the matrices of fibre-reinforced composite materials and as adhesives. When cured, epoxies are amorphous and highly-crosslinked (i.e. thermosetting)polymers. This microstructure results in many useful properties for structural engineering applications, such as a high modulus and failure strength, low creep, and good performance at elevated temperatures.However, the structure of such thermosetting polymers also leads to a highly undesirable property in that they are relatively brittle materials, with a poor resistance to crack initiation and growth.Nevertheless, it has been well established for many years that the incorporation of a second microphase of a dispersed rubber, e.g. Hence rigid, inorganic particles have also been used, as these can increase the toughness without affecting the glass transition temperature of the epoxy. Here glass beads or ceramic (e.g. silica or alumina) particles with a diameter of between 4 and 100 μm are typically used, e.g. [9][10][11][12][13][14].However, these relatively large particles also significantly increase the viscosity of the resin, reducing the ease of processing. In addition, due to the size of these particles they are unsuitable for use with infusion processes for the production of fibre composites as they are strained out by the small gaps between the fibres.More recently, a new technology has emerged which holds promise for increasing the mechanical performance of such thermosetting polymers. This is via the addition of a nanophase structure in the polymer, where the nanophase consists of small rigid particles of silica [15][16][17][18]. Such nanoparticle-modified epoxies have been shown to not only increase further the toug...

show abstract

Section: Tensile Modulusmentioning

confidence: 99%

Toughening mechanisms of nanoparticle-modified epoxy polymers

Johnsen

Kinloch

Mohammed

et al. 2007

Polymer

862

576

View full text Add to dashboard Cite

show abstract

“…The most common one's are based on the rule of mixtures (ROM) and can be used to back calculate the intrinsic properties of the reinforcing fibers [2,25,26]. In the case of short fiber semi-aligned composites, the most commonly used models to predict the Young's modulus or the intrinsic Young's modulus, are modified rules of mixtures (mROM) [27], Hirsch model [28], and Halpin-Tsai equations with Tsai-Pagano methods [2,[29][30][31].…”

Section: Introductionmentioning

confidence: 99%

“…The moduli were analyzed from a macromechanical point of view, and their micromechanical aspects were evaluated. The values of the intrinsic Young's moduli of the fibers were obtained by means of Hirsch model [28], and also by means of Halpin-Tsai equations with Tsai-Pagano methods [29][30][31] and then compared, to assess the influence of the aspect ratio of the fibers on the values. By means of Cox-Krenchel equations [32,33] were studied the length efficiency factors, and also were deduced the fiber orientation factors.…”

Section: Introductionmentioning

confidence: 99%

Macro and micromechanics analysis of short fiber composites stiffness: The case of old newspaper fibers–polypropylene composites

Serrano

Espinach²,

Tresserras³

et al. 2014

Materials & Design

View full text Add to dashboard Cite

“…Consequently, Halpin and Tsai [21][22][23] have shown that by grouping terns which pertain to the Poisson effect and particle geometry and also separating terms which depend on the elastic properties of the constituents, the Kemer equations can be generalized to the form:…”

Section: Prediction Of Powder-filled Foam Propertiesmentioning

confidence: 99%