Equations Kelly, Tyson

One of the best ways to tlioronghly examine the variable effecting the composite properties is to examine the Kelly-Tyson eqnation for tensile strength, as follows [27-31]  

The interfacial shear strengtli can be fnrther defined as follows  

Anotlier important variable to consider is the fiber orientation. This is affected by many variables such as tire injection molding conditions, fiber length, resin viscosity and part tliickness. The fiber orientation can be determined experimentally by optical metliods [44], or it can be estimated from fire modulus of the molded part as follows [45-47]  

In the above, the variable R is the radius between center to center fiber spacing, while r is the fiber radius. The shear modulus (Gm) can be approximated as E /3. The matrix modulus is effected by the level of crystallinity and it is important that the samples are fully crystallized to ensure reproducibility. The value of p for 30wt% glass-fiber-reinforced PET has been calculated as 3.15 x 10 . Using the mathematical analysis shown above, the orientation function of the glass fiber 

Pi operty Example 1 Example 2 Example 3 Example 4 Example 5 

The interfacial shear strength can be further defined as follows  

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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. 

Since the contribution of the resin matrix is small in a strong composite, the second term in the Kelly-Tyson equation can be disregarded. Thus, the longitudinal modulus is dependent on the reinforcement modulus, which is independent of the diameter of the reinforcing fiber. 

Tensile Strength. Composite tensile strength (a ) are often predicted from the Kelly-Tyson equation for discrete uniaxially aligned fiber reinforced composites, modified to accoimt for the non-uniaxial orientations of thermoplastic composites [24]. 

Properties of filler can be compared with the stress applied to the filler particle. In fiber-filled composites, the Kelly and Tyson equation can be used to esti-... 

Table 9.2 presents the critical length evaluated by CLP curves and corresponding IFSS, calculated by the Kelly and Tyson equation, for different lignocellulosic fibers embedded in thermoset polymeric matrices. 

The average shear strength at the interface, t., whether bonded, debonded or if the surrounding matrix material is yielded, whichever occurs first, can be approximately estimated from a simple force balance equation for a constant interface shear stress (Kelly and Tyson, 1965) ... 

Drzal et al altered the above equation reflecting Weibull statistics and rearranged the Kelly and Tyson s equation, proposing the following modification to calculate the IFSS ... 

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