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Orthotropic material engineering constants

The characteristic features of a cord—mbber composite have produced the netting theory (67—70), the cord—iaextensible theory (71—80), the classical lamination theory, and the three-dimensional theory (67,81—83). From stmctural considerations, the fundamental element of cord—mbber composite is unidirectionaHy reinforced cord—mbber lamina as shown in Figure 5. From the principles of micromechanics and orthotropic elasticity laws, engineering constants of tire T cord composites in terms of constitutive material properties have been expressed (72—79,84). The most commonly used Halpin-Tsai equations (75,76) for cord—mbber single-ply lamina L, are expressed in equation 5 ... [Pg.87]

Most simple materia characterization tests are perfomned with a known load or stress. The resulting displacement or strain is then measured. The engineering constants are generally the slope of a stress-strain curve (e.g., E = o/e) or the slope of a strain-strain curve (e.g., v = -ey/ej5 for Ox = a and all other stresses are zero). Thus, the components of the compliance (Sy) matrix are determined more directly than those of the stiffness (Cy) matrix. For an orthotropic material, the compliance matrix components in terms of the engineering constants are... [Pg.64]

The preceding restrictions on engineering constants for orthotropic materials are used to examine experimental data to see if they are physically consistent within the framework of the mathematical elasticity model. For boron-epoxy composite materials, Dickerson and DiMartino [2-3] measured Poisson s ratios as high as 1.97 for the negative of the strain in the 2-direction over the strain in the 1-direction due to loading in the 1-direction (v 2)- The reported values of the Young s moduli for the two directions are E = 11.86 x 10 psi (81.77 GPa) and E2 = 1.33x10 psi (9.17 GPa). Thus,... [Pg.69]

Compare the transformed orthotropic compliances in Equation (2.88) with the anisotropic compliances in terms of engineering constants in Equation (2.91). Obviously an apparenf shear-extension coupling coefficient results when an orthotropic lamina is stressed in non-principal material coordinates. Redesignate the coordinates 1 and 2 in Equation (2.90) as X and y because, by definition, an anisotropic material has no principal material directions. Then, substitute the redesignated Sy from Equation (2.91) in Equation (2.88) along with the orthotropic compliances in Equation (2.62). Finally, the apparent engineering constants for an orthotropic iamina that is stressed in non-principal x-y coordinates are... [Pg.80]

In summary, the engineering constants for anisotropic materials and orthotropic materials loaded in non-principal material coordinates can be most effectively thought of In strictly functional terms ... [Pg.84]

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... [Pg.118]

The mechanics of materials approach to the micromechanics of material stiffnesses is discussed in Section 3.2. There, simple approximations to the engineering constants E., E2, arid orthotropic material are introduced. In Section 3.3, the elasticity approach to the micromechanics of material stiffnesses is addressed. Bounding techniques, exact solutions, the concept of contiguity, and the Halpin-Tsai approximate equations are all examined. Next, the various approaches to prediction of stiffness are compared in Section 3.4 with experimental data for both particulate composite materials and fiber-reinforced composite materials. Parallel to the study of the micromechanics of material stiffnesses is the micromechanics of material strengths which is introduced in Section 3.5. There, mechanics of materials predictions of tensile and compressive strengths are described. [Pg.126]

In dealing with engineering problems, we often desire to convert Cyij or Syu to the engineering moduli (Young s moduli, shear moduli and Poisson s ratios). The engineering moduli are easily calculated from the components of the contracted compliance matrix. The formulas are as follows (There are 9 nonzero independent elastic constants for orthotropic materials) ... [Pg.157]

The compliance matrix for an orthotropic material in terms of engineering constants is given as... [Pg.306]

Again each term on the right hand side of Elq. 2.40 represents a double summation and each coefficient of strain is an independent set of material parameters. Thus, many more than 81 parameters may be required to represent a nonlinear heterogeneous and anisotropic material. Further, for viscoelastic materials, these material parameters are time dependent. The introduction of the assumption of linearity reduces the number of parameters to 81 while homogeneity removes their spatial variation (i.e., the parameters are now constants). Symmetry of the stress and strain tensors (matrices) reduces the number of constants to 36. The existence of a strain energy potential reduces the number of constants to 21. Material symmetry reduces the number of constants further. For example, an orthotropic material, one with three planes of material symmetry, has only 9 constants and an isotropic material, one with a center of symmetry, has only two independent constants (and Eq. 2.39 reduces to Eq. 2.28). Now it is easy to see why the assumptions of linearity, homogeneity and isotropy are used for most engineering analyses. [Pg.38]

It is apparent from Equations 8.42 and 8.43 that four material elastic properties (compliance or stiffness) are needed to characterize the in-plane behavior of a linear elastic orthotropic lamina. It is convenient to define these material properties in terms of measured engineering constants (Young s moduli, El > d Ej, shear modulus Glt, and Poisson s ratios u,lt and (Xtl). The longitudinal Young s... [Pg.182]

The magnitude of the elastic moduli obtained for an anisotropic material will depend on the orientation of the coordinates used to describe the material elastic response. However, if the material elastic moduli are known for coordinates aligned with the principal material directions, then the elastic moduli for any other orientation can be determined through appropriate transformation equations. Thus, only four elastic constants are needed in order to fully characterize the in-plane maaoscopic elastic response of an orthotropic lamina. The reference coordinates in the plane of the lamina are aligned with longitudinal axis (L) parallel to the fibers, and the transverse axis (7) perpendicnlar to the fibers. The engineering orthotropic elastic moduli of the lamina defined earher are... [Pg.168]


See other pages where Orthotropic material engineering constants is mentioned: [Pg.63]    [Pg.66]    [Pg.68]    [Pg.119]    [Pg.659]    [Pg.735]    [Pg.724]    [Pg.191]    [Pg.111]    [Pg.381]   
See also in sourсe #XX -- [ Pg.63 ]




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