Orthotropic properties

P(l) Anisotropic, isotropic and orthotropic properties of laminates shall be as defined in 1.4. 

Lin et al. (2004) adopted the same approach but they extended the five-constant equation to a nine-constant equation, which relaxes the transversely isotropic assumption of the properties for the composite of aligned inclusions, and can be use for more general orthotropic properties. Eduljee et al. (1994) presented an orientation averaging approach capable of distinguishing between dispersed and aggregated microstructures in short-fiber composites. 

To obtain statistically reliable results from the analysis of a fracture surface by the vertical section method, a large number of sections should be examined. The parallel sections executed, for example, along rectangular coordinates may give information about possible orthotropic properties of the fracture surface. In most cases random sections oriented at different angles should be studied. 

The majority of fibres are situated approximately parallel to the horizontal plane therefore, the in-plane and out-of-plane properties are different and SIFCON exhibits clearly some orthotropic properties. 

Second, the growth process allows a variety of routes to the formation of fibers but there are no simple way s to form a dense isotropic plastic. Thus, even essentially isotropic materials will have a fibrous composite microstmcture. Weiner et al. (2000) have argued that many biological structures can be viewed as a search for isotropic properties, or at least orthotropic properties (strong in two dimensions), from fibrous materials. This would reflect the unpredictability of stresses encountered by a structure in a dynamic environment. 

Technically relevant applications are hardly concerned with complete anisotropy. Composites with a regular distribution of constituents along the principal axes are an example of a material with three orthogonal planes of symmetry. The description of such orthotropic properties requires nine independent matrix entries ... 

The rhombic crystal class as well as composites with adequate constituents and layout, for instance, possess orthotropic properties in analogy to the mechanical material properties. Therefore, only the three entries on the diagonal of the constitutive matrix are retained ... 

The adherend was assumed to behave in an orthotropic manner and no account was taken of the individual behaviour of the plies instead, homogeneous orthotropic properties were applied to the model. All mechanical properties for the composite adherends were derived from data published by the manufacturer. 

Beatty, M. W., Bruno, M. J., Iwasaki, L. R., Nickel, J. C. 2001. Strain rate dependent orthotropic properties of pristine and impulsively loaded porcine temporomandibular joint disk. /Biomed Mater Res 57(1) 25-34. 

Most of the laminates used for rigid printed circuit boards have been classified, by the National Electrical Manufacturers Association (NEMA), according to the combination of properties that determine the suitabiHty of a laminate for a particular use. Eiber reinforcements make laminate-effective properties orthotropic. 

Because the fibers generally are anisotropic, they tend to be deposited on the wire in layers under shear. There is Htde tendency for fibers to be oriented in an out-of-plane direction, except for small undulations where one fiber crosses or passes beneath another. The layered stmcture results in the different properties measured in the thickness direction as compared to those measured in the in-plane direction. The orthotropic behavior of paper is observed in most paper properties and especially in the electrical and mechanical properties. 

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 ... 

An orthotropic body has material properties that are different in three mutually perpendicular directions at a point in the body and, further, has three mutually perpendicular planes of material property symmetry. Thus, the properties depend on orientation at a point in the body. 

The values in Figures 2-11 and 2-12 are not entirely typical of all composite materials. For example, follow the hints in Exercise 2.6.7 to demonstrate that E can actually exceed both E., and E2 for some orthotropic laminae. Similarly, E, can be shown to be smaller than both E. and E2 (note that for boron-epoxy in Figure 2-12 E, is slightly smaller than E2 in the neighborhood of 6 = 60°). These results were summarized by Jones [2-6] as a simple theorem the extremum (largest and smallest) material properties do not necessarily occur in principal material coordinates. The moduli Gxy xy xyx exhibit similar peculiarities within the scope of Equation (2.97). Nothing should, therefore, be taken for granted with a new composite material its moduli as a function of 6 must be examined to truly understand its character. 

The actual invariants in invariant properties of a lamina include not only U., U4, and U5 because they are the constant terms in Equation (2.93) but functions related to U-), U4, and U5 as shown in Problem Set 2.7. The terms U2 and U3 are not invariants. The only invariants of an orthotropic lamina can be shown to be... 

The foregoing example is but one of the difficulties encountered in analysis of orthotropic materials with different properties in tension and compression. The example is included to illustrate how basic information in principal material coordinates can be transformed to other useful coordinate directions, depending on the stress field under consideration. Such transformations are simply indications that the basic information. 

For orthotropic materials, certain basic experiments can be performed to measure the properties in the principal material coordinates. The experiments, if conducted properly, generally reveal both the strength and stiffness characteristics of the material. Recall that the stiffness characteristics are... 

J. C. Ekvall, Elastic Properties of Orthotropic Monofilament Laminates, ASME Paper 61-AV-56, Aviation Conference, Los Angeles, California, 12-16 March 1961. 

Derive the summation expressions for extensional, bending-extension coupling, and bending stiffnesses for laminates with constant properties in each orthotropic lamina that is, derive Equation (4.24) from Equations (4.20) and (4.21). 

The special single-layered configurations treated in this section are isotropic, specially orthotropic, generally orthotropic, and anisotropic. The generally orthotropic configuration cannot, of course, be distinguished from an anisotropic layer from the analysis point of view, but does have only the four independent material properties of an orthotropic material. 

Because of the analytical complications involving the stiffnesses Ai6, A26, D g, and D26, a laminate is sometimes desired that does not have these stiffnesses. Laminates can be made with orthotropic layers that have principal material directions aligned with the laminate axes. If the thicknesses, locations, and material properties of the laminae are symmetric about the middle surface of the laminate, there is no coupling between bending and extension. A general example is shown in Table 4-2. Note that the material property symmetry requires equal [Q j], of the two layers that are placed at the same distance above and below the middle surface. Thus, both the orthotropic material properties, [Qjjlk. of the layers and the angle of the principal material directions to the laminate axes (i.e., the orientation of each layer) must be identical. 

A very common special case of symmetric laminates with multiple specially orthotropic layers occurs when the laminae are all of the same thickness and material properties, but have their major principal material... 

Antisymmetry of a laminate requires (1) symmetry about the middle surface of geometry (i.e., consider a pair of equal-thickness laminae, one some distance above the middle surface and the other the same distance below the middle surface), but (2i some kind of a reversal or mirror image of the material properties [Qjjlk- In fact, the orthotropic material properties [Qjj], are symmetric, but the orientations of the laminae principal material directions are not symmetric about the middle surface. Those orientations are reversed from 0° to 90° (or vice versa) or from + a to - a (a mirror image about the laminate x-axis). Because the [Qjj]k are not symmetric, bending-extension coupling exists. 

The stiffnesses of an antisymmetric laminate of anisotropic laminae do not simplify from those presented in Equations (4.22) and (4.23). However, as a consequence of antisymmetry of material properties of generally orthotropic laminae, but symmetry of their thicknesses, the shear-extension coupling stiffness A.,6,... 

Consider an angle-ply laminate composed of orthotropic laminae that are symmetrically arranged about the middle surface as shown in Figure 4-48. Because of the symmetry of both material properties and geometry, there is no coupling between bending and extension. That is, the laminate in Figure 4-48 can be subjected to and will only extend in the x-direction and contract in the y- and z-directions, but will not bend. 

Figure 6-6 Effect of Material Properties on Circumferential Stress Gq at the Edge of a Circular Hole in an Orthotropic Plate under a, (After Greszczuk [6-11])...

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