Elasticity of composites

Smith, K. J., A. Ciferri, and J. J. Hermans Anisotropic elasticity of composite molecular networks formed from non-Gaussian chains. J. Polymer Sci., Pt. A, 2, 1025 (1964). 

Temperature coefficient, 205, 206, 335, 495, 506, 509, 511, 512 Temperature factor, 303 Temperature, effect on viscosity, 633 Tensile modulus of elasticity of composite materials, 329... 

Epq = modulus of elasticity of composite section, psi hi, ho = film coefficients, inside or outside, Btu/ft -hr/°F P = internal pressure, psig Q = heat loss through wall, Btu/ft -hr T, = temperature, outside ambient, °F T(, = temperature, outside ambient during construction, °F... 

The moduli of elasticity of composites in the fiber direction generally agree very well with values calculated from the additivity rule (Figure 35-15). But the moduli of elasticity perpendicular to the fiber direction are significantly higher than that for the behavior of elements arranged in series. 

Figure 35-15. Moduli of elasticity of composites from glass fibers and an epoxide as a function of the fiber fraction for measurements in the fiber direction ( h ) and perpendicular to the fiber direction ( 1). (After data by R. L. McCollough.)...

On Cb phosphinic the acid influences explosive durability of a polycarbonate practically a little though at her low concentration in compositions some increase of values of a breaking point is observed. Values of the maximal relative lengthening of compositions raise in comparison with initial polymer at use phosphinic acids up to 0,5 % a little. So, relative lengthening of a composition of the PC-3-t-0,5 % of phosphinic on 4,8 % is more than acid, than at an initial polycarbonate. The module of elasticity of compositions also is a little bit higher in comparison with the initial PC. 

The module of elastieity of compositions at the contents in them up to 3,0 % potassimn phosphinate remains to higher in comparison with initial polymer, but further the module of elasticity of compositions is lower, than at a polycarbonate. Apparently, it is connected to increase of polarity phosphororganie compoimds at transition from an acid to her potassium salts. Small additives potassium phosphinate raise plastic and mechanical characteristics of a polycarbonate a little. 

K. J. Smith, Jr. and R. J. Gaylord, Non-Gaussian Elasticity of Composite and Interpenetrating... 

Modulus of elasticity of composite, psi (tension) Modulus of elasticity of fiber, psi (tension)... 

The component with the lower viscosity tends to encapsulate the more viscous (or more elastic) component (207) during mixing, because this reduces the rate of energy dissipation. Thus the viscosities may be used to offset the effect of the proportions of the components to control which phase is continuous (2,209). Frequently, there is an intermediate situation where a cocontinuous or interpenetrating network of phases can be generated by careflil control of composition, microrheology, and processing conditions. Rubbery thermoplastic blends have been produced by this route (212). 

Fig. 4. The immediate effect of temperature on the modulus of elasticity of clear wood, relative to the value at 20°C. The plot is a composite of studies on the modulus as measured in hen ding, in tension parallel to grain, and in compression parallel to grain. VariabiUty in reported results is illustrated by the...

Composite Modulus of Elasticity. The modulus of elasticity of the enamel glass—steel composite system has been shown to lie between the modulus of the glass and that of the metal (29). The composite modulus can be calculated by... 

Fiber-reinforced composite materials such as boron-epoxy and graphite-epoxy are usually treated as linear elastic materials because the essentially linear elastic fibers provide the majority of the strength and stiffness. Refinement of that approximation requires consideration of some form of plasticity, viscoelasticity, or both (viscoplasticity). Very little work has been done to implement those models or idealizations of composite material behavior in structural applications. 

In Section 2.2, the stress-strain relations (generalized Hooke s law) for anisotropic and orthotropic as well as isotropic materials are discussed. These relations have two commonly accepted manners of expression compliances and stiffnesses as coefficients (elastic constants) of the stress-strain relations. The most attractive form of the stress-strain relations for orthotropic materials involves the engineering constants described in Section 2.3. The engineering constants are particularly helpful in describing composite material behavior because they are defined by the use of very obvious and simple physical measurements. Restrictions in the form of bounds are derived for the elastic constants in Section 2.4. These restrictions are useful in understanding the unusual behavior of composite materials relative to conventional isotropic materials. Attention is focused in Section 2.5 on stress-strain relations for an orthotropic material under plane stress conditions, the most common use of a composite lamina. These stress-strain relations are transformed in Section 2.6 to coordinate systems that are not aligned with the principal material... 

Hong T. Hahn and Stephen W. Tsai, Nonlinear Elastic Behavior of Unidirectional Composite Laminae. Journal of Composite Materials, January 1973, pp. 102-118. 

A strong background in elasticity is required for solution of problems in micromechanics of composite materials. Many of the available papers are quite abstract and of little direct applicability to practical analysis at this stage of development of elasticity approaches to micromechanics. Even the more sophisticated bounding approaches are a bit obscure. 

Donald F. Adams and Stephen W. Tsai, The Influence of Random Filament Packing on the Elastic Properties of Composite Materials, Joumsd of Composite Materials, July 1969, pp. 368-381. 

J. M. Whitney, Elastic Moduli of Unidirectional Composites with Anisotropic Filaments, Journal of Composite Materials, April 1967, pp. 188-193. 

The macromechanical behavior of a lamina was quantitatively described in Chapter 2. The basic three-dimensional stress-strain relations for elastic anisotropic and orthotropic materials were examined. Subsequently, those relations were specialized for the plane-stress state normally found in a lamina. The plane-stress relations were then transformed in the plane of the lamina to enable treatment of composite laminates with different laminae at various angles. The various fundamental strengths of a lamina were identified, discussed, and subsequently used in biaxial strength criteria to predict the off-axis strength of a lamina. 

Composite materials have many distinctive characteristics reiative to isotropic materials that render application of linear elastic fracture mechanics difficult. The anisotropy and heterogeneity, both from the standpoint of the fibers versus the matrix, and from the standpoint of multiple laminae of different orientations, are the principal problems. The extension to homogeneous anisotropic materials should be straightfor-wrard because none of the basic principles used in fracture mechanics is then changed. Thus, the approximation of composite materials by homogeneous anisotropic materials is often made. Then, stress-intensity factors for anisotropic materials are calculated by use of complex variable mapping techniques. 

The study of composite materials actually involves many topics, such as, for example, manufacturing processes, anisotropic elasticity, strength of anisotropic materials, and micromechanics. Truly, no one individual can claim a complete understanding of all these areas. Any practitioner will be likely to limit his attention to one or two subareas of the broad possibilities of analysis versus design, micromechanics versus macromechanics, etc. 

Spherical indentor deformability tests of composites with PE synthesized on different fillers have shown [164] that the deformation of PFCM containing high percentages of filler (and polymer concentrations of less than 10% by mass) is substantially elastic and the specimen recovers completely after release of the load. As the polymer content increased to 60% by mass considerable residual deforma-... 

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