Modulus continued transverse

The transverse modulus (Mt) and many other properties of a long fiber resin composite may be estimated from the law of mixtures. The longitudinal modulus (Ml) may be estimated from the Kelly-Tyson equation (8.5), where the longitudinal modulus is proportional to the sum of the fiber modulus (Mp) and the resin matrix modulus (Mm)- Each modulus is based on a fractional volume (c). The constant k is equal to 1 for parallel continuous filaments and decreases for more randomly arranged shorter filaments. 

We will see in Section 5.4.2 that the elastic modulus of a unidirectional, continuous-fiber-reinforced composite depends on whether the composite is tested along the direction of fiber orientation (parallel) or normal to the fiber direction (transverse). In fact, the elastic modulus parallel to the fibers, Ei, is given by Eq. (1.62), whereas the transverse modulus, 2, is given by Eq. (1.63). Consider a composite material that consists of 40% (by volume) continuous, uniaxially aligned, glass fibers (Ef =16 GPa) in a polyester matrix (Em = 3 GPa). 

Assume that the conductivity of a undirectional, continuous fiber-reinforced composite is a summation effect just like elastic modulus and tensile strength that is, an equation analogous to Eq. (5.88) can be used to describe the conductivity in the axial direction, and one analogous to (5.92) can be used for the transverse direction, where the modulus is replaced with the corresponding conductivity of the fiber and matrix phase. Perform the following calculations for an aluminum matrix composite reinforced with 40 vol% continuous, unidirectional AI2O3 fibers. Use average conductivity values from Appendix 8. 

Compute the modulus of elasticity of a composite consisting of continuous and aligned carbon fibres of 60 % weight fraction in an epoxy resin matrix under (a) longitudinal and (b) transverse loading. The modulus of elasticity of the carbon fibres is 290 GPa and the density is 1785 kg m. The elastic modulus of the resin is 3.2 GPa and its density is 1350 kg m. ... 

High modulus melt-spun PE from Hoechst Celanese Certran has a modulus of about 40 GPa (common unreinforced engineering TPs have a modulus in the range 2.3 to 3 GPa) showed a longitudinal modulus of 37 GPa for imidirectional fiber and 110 MPa longitudinal strength, a transverse modulus of 3.9 GPa and transverse strength 28 MPa. The process continues to be applied to all melt-spun fibers. 

The following account begins with an outline of the various methods used to determine the modulus in the chain direction and transverse to the chain for measurements at the molecular level, as well as the overall modulus in the direction of the fibre axis. It continues with a comparison of the experimental values at the molecular level, with a range of theoretical calculations based on the assessment of the intramolecular and inter-molecular forces. It concludes with an attempt to reconcile the behaviour of bulk materials in their various forms—anisotropic and isotropic, semicrystalline and amorphous—with their behaviour at the molecular level. 

A composite material consists of 55% (by volume) continuous, uniaxially aligned, S-glass fibres in a matrix of epoi. Such a composite is found to have a tensile strength transverse to the fibres a- = 25 MPa and shear strength parallel to the fibres t 2 = 55 MPa. The tensile strength and modulus of the fibres are 1900 MPa and 86 GPa, and of the matrix are 60 MPa and 2.4 GPa, respectively. The composite is to be subjected to tensile stress in a direction inclined at 2(P to the iSbre axes. Predict the stress at failure and determine the mode of failure. 

An interpolation procedure applied by Halpin and Tsai [17,18] has led to general expressions for the moduli of composites, as given by Eqs. (2.18) and (2.19). Note that for = 0, Eq. (2.18) reduces to that for the lower hmit, Eq. (2.8), and for = infinity, it becomes equal to the upper limit for continuous composites, Eq. (2.7). By empirical curve fitting, the value of = 2(l/d) has been shown to predict the tensile modulus of aligned short-fiber composites in the direction of the fibers, and the value of = 0.5 can be used for the transverse modulus. Other mathematical relationships for modulus calculations of composites with discontinuous fillers include the Takaya-nagi and the Mori-Tanaka equations [20]. 

While the examples above used Young s modulus, many other parameters may be substituted. These include other moduli, rheological functions such as creep, stress relaxation, melt viscosity, and rubber elasticity. Each element may itself be expressed by temperature-, time-, or frequency-dependent quantities. It must also be noted that these models find application in composite problems as well. For example, a composite of continuous fibers in a plastic matrix can be described by Figure 10.6a if deformed in the direction of the fibers, and by Figure 10.66 if deformed in the transverse direction. 

Thus, to a first approximation, the modulus is given by the modulus of the fiber times its volume fraction. However, in the transverse direction the fibers are discontinuous, while the matrix retains its continuity. The Takayanagi model Figure 10.6b and equation (10.8) hold. Then... 

It is assumed that the use of such a nanocomposite as a matrix in continuous fiber-reinforced composites will definitely improve the matrix-related properties, such as interlaminar fracture toughness, transverse tensile strength and modulus, as well as interlaminar shear strength. The same should be true for polymer-based tribomaterials, in which such a nanoparticle-modifled resin is used in combination with friction and wear improving fillers, such as short carbon fibers, PTFE particles, and graphite flakes. 

For a continuous and aUgned fiber-reinforced composite, modulus of elasticity in the transverse direction... 

For continuous and aligned composites, rule-of-mixtures expressions for the modulus in both longitudinal and transverse orientations were developed (Equations 16.10 and 16.16). In addition, an equation for longitudinal strength was also cited (Equation 16.17). 

Derive a generalized expression analogous to Equation 16.16 for the transverse modulus of elasticity of an aligned hybrid composite consisting of two types of continuous fibers. 

For polymers reinforced with continuous fibers, the situation can be reversed. Long, thin fibers support tensile loading much more effectively than they support compressive loading. Tensile stresses straighten and stiffen the fibers, whereas fibers loaded in compression buckle, with a concurrent loss of stiffiiess. Tlius, the tensile compliance in the direction of the fiber reinforcement should be less than the compressive compliance in the fiber direction. In the transverse direction, the compliance for tension and compression should behave more like pure resin, which has a higher compressive modulus. 

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