Stiffness and Strength

Stiffness is often a critical property of a material that determines how much a component will deform in response to force (e.g., stretching, compression, or bending). Molecular modeling has been used to predict the stiffness and strength of polymer nanocomposites with different types of nanopartides, for example, carbon 

Another way is to design a rib-wall pipe on which reinforcement ribs of a specific shape 

The next step in design is to determine the pipe deflection requirements, based on the equation shown in Fig. 4-2(f). The accepted maximum allowable pipe deflection should be no more than 5%. 

This value is the basic standard that AWWA M-II specifies for steel conduit and pipe, as do the ASTM and ASME. As is obvious, there are a number of factors that contribute to pipe deflection. These are the external loads that will be imposed on the pipe, both the dead load of the overburden as well as the live loads of such things as wheel and rail traffic. The factors affecting RTR pipe deflection can be summarized as follows  

Dead load-trench shape, overburden weight, depth of cover 

Live load-wheel load, spacing surcharge 

---

In aerospace appHcations, low density coupled with other desirable features, such as tailored thermal expansion and conductivity, high stiffness and strength, etc, ate the main drivers. Performance rather than cost is an important item. Inasmuch as continuous fiber-reinforced MMCs deUver superior performance to particle-reinforced composites, the former are ftequendy used in aerospace appHcations. In nonaerospace appHcations, cost and performance are important, ie, an optimum combination of these items is requited. It is thus understandable that particle-reinforced MMCs are increa singly finding appHcations in nonaerospace appHcations. 

Nylon-6,6 [32131 -17-2] and nylon-6 [25038-54-4] continue to be the most popular types, accounting for approximately 90% of nylon use. There are a number of different nylons commercially available Table 1 gives a summary of the properties of the more common types. In the 1990s there has been a spurt of new polyamide iatroductions designed for higher temperatures, better stiffness and strength, and/or lower moisture uptake. 

A number of high melting poiat semiaromatic nylons, iatroduced ia the 1990s, have lower moisture absorption and iacreased stiffness and strength. Apart from nylon-6 /6,T (copolymer of 6 and 6,T), the exact stmcture of these is usually proprietary and they are identified by trade names. Examples iaclude Zytel HTN (Du Pont) Amodel, referred to as polyphthalamide or PPA (Amoco) and Aden (Mitsui Petrochemical). Properties for polyphthalamide are given ia Table 2. A polyphthalamide has been defined by ASTM as "a polyamide ia which the residues of terephthaUc acid or isophthahc acid or a combination of the two comprise at least 60 molar percent of the dicarboxyhc acid portion of the repeating stmctural units ia the polymer chain" (18). 

This is more than one-half of the strength of the continuous-fibre material (eqn. 25.3). Or it is if all the fibres are aligned along the loading direction. That, of course, will not be true in a chopped-fibre composite. In a car body, for instance, the fibres are randomly oriented in the plane of the panel. Then only a fraction of them - about - are aligned so that much tensile force is transferred to them, and the contributions of the fibres to the stiffness and strength are correspondingly reduced. 

Retain a higher proportion of their room temperature stiffness and strength at elevated temperatures. 

Naturally, fibers and whiskers are of little use unless they are bonded together to take the form of a structural element that can carry loads. The binder material is usually called a matrix (not to be confused with the mathematical concept of a matrix). The purpose of the matrix is manifold support of the fibers or whiskers, protection of the fibers or whiskers, stress transfer between broken fibers or whiskers, etc. Typically, the matrix is of considerably lower density, stiffness, and strength than the fibers or whiskers. However, the combination of fibers or whiskers and a matrix can have very high strength and stiffness, yet still have low density. Matrix materials can be polymers, metals, ceramics, or carbon. The cost of each matrix escalates in that order as does the temperature resistance. 

Boron fibers exhibit the highest stiffness and strength efficiencies in Figure 1-24. When placed in a lamina as unidirectional fibers, the... 

Several experiments will now be described from which the foregoing basic stiffness and strength information can be obtained. For many, but not all, composite materials, the stress-strain behavior is linear from zero load to the ultimate or fracture load. Such linear behavior is typical for glass-epoxy composite materials and is quite reasonable for boron-epoxy and graphite-epoxy composite materials except for the shear behavior that is very nonlinear to fracture. 

A key element in the experimental determination of the stiffness and strength characteristics of a lamina is the imposition of a uniform stress state in the specimen. Such loading is relatively easy for isotropic materials. However, for composite materials, the orthotropy introduces coupling between normal stresses and shear strains and between shear stresses and normal and shear strains when loaded in non-principal material coordinates for which the stress-strain relations are given in Equation (2.88). Thus, special care must be taken to ensure obtaining... 

Now that the basic stiffnesses and strengths have been defined for the principal material coordinates, we can proceed to determine how an orthotropic lamina behaves under biaxial stress states in Section 2.9. There, we must combine the information in principal material coordinates in order to define the stiffness and strength of a lamina at arbitrary orientations under arbitrary biaxial stress states. 

Just as there must be some rationale for selecting a particular stiffness and/or strength of material for a specific structural application, there must also be a rationale for determining how best to achieve that stiffness and strength for a composite of two or more materials. That is, how can the percentages of the constituent materials be varied so as to arrive at the desired composite stiffness and strength ... 

Failure of a lamina might mean, for example, only lack of stiffness and strength perpendicular to the fibers with no degradation of lamina capability in the fiber direction. 

---