Orthotropic lamina strength

What has been accomplished in preceding sections on stiffness relationships serves as the basis for determination of the actual stress field what remains is the definition of the allowable stress field. The first step in such a definition is the establishment of allowable stresses or strengths in the principal material directions. Such information is basic to the study of strength of an orthotropic lamina. 

That the principal stresses are not of interest in determining the strength of an orthotropic lamina is illustrated with the following example. Consider the lamina with unidirectionai fibers shown in Figure 2-16. Say that the hypotheticai strengths of the lamina in the 1-2 piane are... 

Then, obviously the maximum principal stress is lower than the largest strength. However, 02 is greater than Y, so the lamina must fail under the imposed stresses (perhaps by cracking parallel to the fibers, but not necessarily). The key observation is that strength is a function of orientation of stresses relative to the principal material coordinates of an orthotropic lamina. In contrast, for an isotropic material, strength is independent of material orientation relative to the imposed stresses (the isotropic material has no orientation). 

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. 

The strength characteristics of a composite orthotropic lamina are much more difficult to dehne than those of an isotropic material. In both cases, the engineer is interested in identifying material strength parameters which can be determined experimentally using simple tests, where the strength parameters are used to define allowable stresses for purposes of design. 

The unidirectional (orthotropic) lamina is the primary building block for developing the theory for mechanics of composite laminates. The elastic and strength... 

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. 

Several layers of orthotropic composites, e.g. reinforced with parallel systems of fibres, are stacked together in such a way that adjacent laminae are oriented in different directions and thus the strength and stiffness of the composite plate may be tailored to the specific design requirements (Figure 2.9c). 

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