Transverse elastic moduli

Person 2 Calculate the elastic modulus transverse to the fiber direction, Ea-... 

EXPERIMENTAL AND THEORETICAL VALUES FOR ELASTIC MODULUS TRANSVERSE TO THE CHAIN IN THE CRYSTALLINE REGION,... 

Material Density (g/cm ) Tensile strength (GPa) Elastic modulus (axial) (GPa) Elastic modulus (transverse) (GPa)... 

Elastic modulus transverse to the Property based on test data fiber direction... 

In many isotropic materials the shear modulus G is high compared to the elastic modulus E, and the shear distortion of a transversely loaded beam is so small that it can be neglected in calculating deflection. In a structural sandwich the core shear modulus G, is usually so much smaller than Ef of the facings that the shear distortion of the core may be large and therefore contribute significantly to the deflection of a transversely loaded beam. The total deflection of a beam is thus composed of two factors the deflection caused by the bending moment alone, and the deflection caused by shear, that is, S = m + Ss, where S = total deflection, Sm = moment deflection, and Ss = shear deflection. 

The geometry and structure of a bone consist of a mineralised tissue populated with cells. This bone tissue has two distinct structural forms dense cortical and lattice-like cancellous bone, see Figure 7.2(a). Cortical bone is a nearly transversely isotropic material, made up of osteons, longitudinal cylinders of bone centred around blood vessels. Cancellous bone is an orthotropic material, with a porous architecture formed by individual struts or trabeculae. This high surface area structure represents only 20 per cent of the skeletal mass but has 50 per cent of the metabolic activity. The density of cancellous bone varies significantly, and its mechanical behaviour is influenced by density and architecture. The elastic modulus and strength of both tissue structures are functions of the apparent density. 

The implication of Eq. (6.21) is that the criterion is dependent mainly on the ratio of the energies for longitudinal splitting and transverse cracking, and is relatively insensitive to crack length and the elastic modulus. It is also noted from experimental study that crack speed has a pronounced effect on the toughness ratio, Rl/Ri, and thus the crack deflection phenomenon. 

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). 

The Halpin-Tsai equations represent a semiempirical approach to the problem of the significant separation between the upper and lower bounds of elastic properties observed when the fiber and matrix elastic constants differ significantly. The equations employ the rule-of-mixture approximations for axial elastic modulus and Poisson s ratio [Equations. (5.119) and (5.120), respectively]. The expressions for the transverse elastic modulus, Et, and the axial and transverse shear moduli, Ga and Gf, are assumed to be of the general form... 

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. 

Here, and Ey are the axial and transverse elastic modulus of the driveshaft material, and Vxy and Vy are the axial and transverse Poisson s ratios, respectively (see Section 5.4.3.1 for more information). 

Figure l visualizes the influence of overall chain rigidity produced by variation of the PHB-content x in the copolymer on the elastic modulus parallel and transverse to the applied injection flow. 

Figure 1. Elastic modulus of PET/xPHB copolymers in function of x determined in the direction parallel ( ) and transverse to the flow ( ).

Abbreviations ffp, tensile strength (nominal) elongation at break E, elastic modulus MD, machine direction TD, transverse direction and DR, draw ratio. 

The value of the elastic modulus, often called the Reuss bound, is identical to that for transverse loading on a fibre composite, and gives a value for the elastic modulus normal to the layers. In both of these equations, E, E and Ep are the elastic moduli of the ceramic, matrix and particles, respectively, and Vc (equal to 1.0), Vm and Vp are the corresponding volume fractions. 

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. ... 

As is known from transverse displacement of coal body in plastic area, the horizontal displacement in plastic area has hnear increasing relationship with the plastic area width, Poisson s ratio of coal, and has inverse proportion with elastic modulus of coal ... 

In many isotropic materials, the shear modulus G is high compared to the elastic modulus E, and the shear distortion of a transversely loaded beam is so small that it can be neglected in calculating deflection. In a structural sandwich the core shear modulus G, is usually so much smaller than Efof... 

Halpin-Tsai theory is used for prediction elastic modulus of unidirectional composites as function of aspect ratio. The longitudinal stiflfiiess, transverse modulus, are expressed in the following general form ... 

The Mori-Tanaka model is uses for prediction an elastic stress field for in and around an ellipsoidal reinforcement in an infinite matrix. This method is based on Eshebly s model. Longitudinal and transverse elastic modulus, Ejj and for isotropic matrix and directed spherical reinforcement are ... 

Transverse tensile strength Tensile elastic modulus, E Shear modulus, G (calculated) Density... 

FIGURE 41.8. Elastic modulus at 25 °C of PET/xPHB copolymers as a function of x in the direction transverse to the fiow during processing after [50]. 

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