Material anisotropic

J. Mattsson., A.J. Niklasson and A. Eriksson, Three-Dimensional Ultrasonic Crack Detection in Anisotropic Materials, Res. Nondestr. Eval. 9 pp.59-79 (1997). 

J. Mattsson, Modelling of Scattering by Surface Breaking Cracks in Anisotropic Materials, Tech. Report 1996 7, Div. Mech., Chalmers University of Technology (1996). 

Trends in the field of economics are the centralization of the powder fabrication to enable production on a large scale and the manufacture of low quahty anisotropic materials by a much less expensive technology. An example of the latter is the introduction of alignment during pressing of the raw material mixture in the fabrication route of isotropic materials. 

Anisotropy in metals and composite materials is common as a result of manufacturing history. Anisotropic materials often display significantly different results when tested along different planes. This appHes to indentation hardness tests as well as any other test. 

In the following development we consider a plane wave of infinite lateral extent traveling in the positive Xj direction (the wave front itself lies in the Xj, Xj plane). When discussing anisotropic materials we restrict discussion to those propagation directions which produce longitudinal particle motion only i.e., if u is the particle velocity, then Uj = Uj = 0. The <100>, <110>, and <111 > direction in cubic crystals have this property, for example. The derivations presented here are heuristic with emphasis on the essential qualitative features of plastic flow. References are provided for those interested in proper quantitative features of crystal anisotropy and nonlinear thermoelasticity. 

Although much as been done, much work remains. Improved material models for anisotropic materials, brittle materials, and chemically reacting materials challenge the numerical methods to provide greater accuracy and challenge the computer manufacturers to provide more memory and speed. Phenomena with different time and length scales need to be coupled so shock waves, structural motions, electromagnetic, and thermal effects can be analyzed in a consistent manner. Smarter codes must be developed to adapt the mesh and solution techniques to optimize the accuracy without human intervention. 

The analyzer is removed and the color of the sample is observed in plane-polarized light. If the sample is colored, the stage is rotated. Colored, anisotropic materials may show pleochroism—a change in color or hue when the orientation with respect to the vibration direction of the polarizer is changed. Any pleochroism should be noted and recorded. 

Infrared ellipsometry is typically performed in the mid-infrared range of 400 to 5000 cm , but also in the near- and far-infrared. The resonances of molecular vibrations or phonons in the solid state generate typical features in the tanT and A spectra in the form of relative minima or maxima and dispersion-like structures. For the isotropic bulk calculation of optical constants - refractive index n and extinction coefficient k - is straightforward. For all other applications (thin films and anisotropic materials) iteration procedures are used. In ellipsometry only angles are measured. The results are also absolute values, obtained without the use of a standard. 

In order to describe completely the state of triaxial (as opposed to biaxial) stress in an anisotropic material, the compliance matrix will have 36 terms. The reader is referred to the more advanced composites texts listed in the Bibliography if these more complex states of stress are of interest. It is conventional to be consistent and use the terminology of the more general analysis even when one is considering the simpler plane stress situation. Hence, the compliance matrix [5] has the terms... 

The inherent anisotropy (most often only orthotropy) of composite materials leads to mechanical behavior characteristics that are quite different from those of conventional isotropic materials. The behavior of isotropic, orthotropic, and anisotropic materials under loadings of normal stress and shear stress is shown in Figure 1-4 and discussed in the following paragraphs. 

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... 

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 ... 

Identity Equation (2.97) by interpreting Equation (2.88) using Equation (2.90) as well as Equations (2.91) and (2.62). Explain tbe key logical step that enables you to use both Equations (2.90) and (2.91) for anisotropic materials and Equations (2.62) and (2.88) for orthotropic materials in this problem. That Is, in what way can we interpret a material as satistying both definitions ot a material ... 

Similar invariance concepts for anisotropic materials were also developed by Tsai and Pagano [2-7]. For anisotropy, the following definitions... 

Qi are for anisotropic materials. Qy for orthotropic materials are obtained by deleting Ug and Uy from the definitions of Qy. 

R. Byron Pipes and B. W. Cole, On the Off-Axis Strength Test for Anisotropic Materials, Journal of Composite Materials, April 1973, pp. 246-256. 

Discuss wfhether this relation is valid for anisotropic materials. That is, denwistrate whether a a angle-ply laminate of the same anisotropic laminae that are symmetric geometrically is antisymmetric or not. The transformation equations for anisotropic materials are given in Section 2.7. 

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. 

Wu [6-12] derives the stress distribution around a crack tip in an anisotropic material. He finds the intensities of the stresses a, Oy, and... 

Wave propagation in an inhomogeneous anisotropic material such as a fiber-reinforced composite material is a very complex subject. However, its study is motivated by many important applications such as the use of fiber-reinforced composites in reentry vehicle nosetips, heatshields, and other protective systems. Chou [6-56] gives an introduction to analysis of wave propagation in composite materials. Others have applied wave propagation theory to shell stress problems. 

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. 

Anisotropic material In an anisotropic material the properties vary, depending on the direction in which they are measured. There are various degrees of anisotropy, using different terms such as orthotropic or unidirectional, bidirectional, heterogeneous, and so on (Fig. 3-19). For example, cast plastics or metals tend to be reasonably isotropic. However, plastics that are extruded, injection molded, and rolled plastics and metals tend to develop an orientation in the processing flow direction (machined direction). Thus, they have different properties in the machine and transverse directions, particularly in the case of extruded or rolled materials (plastics, steels, etc.). 

RTR filament-wound pipe is, however, an anisotropic material. That is, its material properties, such as its modulus of elasticity and ultimate strength, are different in each of the principal directions of hoop and longitude. It is here where the design approaches for steel and RTR pipe part company [Fig. 4-2(c)]. This behavior is a result of the construction of filament-wound RTR pipe. 

In an anisotropic material, the properties depend on the direction in which they are tested. For example, rolled metals, which are anisotropic, tend to develop a crystal orientation in the rolling direction. Thus rolled and sheet-metal products have different mechanical properties in the two major directions. Also, extruded plastic film can have different properties in the machine and transverse directions. These materials are oriented biaxi-ally and are anisotropic. (As reviewed above under EXTRUSION, Orientation). 

---