Stress-strain relations transversely isotropic

If at every point of a material there is one plane in which the mechanical properties are equal in all directions, then the material is called transversely isotropic. If, for example, the 1-2 plane is the plane of isotropy, then the 1 and 2 subscripts on the stiffnesses are interchangeable. The stress-strain relations have only five independent constants ... 

The efficiency of reinforcement is related to the fiber direction in the composite and to the direction of the applied stress. The maximum strength and modulus are realized in a composite along the direction of the fiber. However, if the load is applied at 90° to the filament direction, tensile failure occurs at very low stresses, and this transverse strength is not much different than the matrix strength. To counteract this situation, one uses cross-pKed laminates having alternate layers of unidirectional libers rotated at 90°, as shown in Figure 3.47c. (A more isotropic composite results if 45° plies are also inserted.) The stress-strain behavior for several types of fiber reinforcement is compared in Figure 3.48. 

For isotropic bodies Poisson s ratio is defined as the negative ratio of transverse and longitudinal strain produced by the same stress system as above, that is uniaxial stress T[. For crystals it becomes necessary to relate the corresponding quantity to two directions. If we consider x as the transverse direction, we find... 

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