Deformation Behaviour of a Single Ply or Lamina

The previous section illustrated how to obtain the elastic properties of a unidirectional lamina. In practice considerably more information may be required about the behavioural characteristics of a single lamina. To obtain details of the stresses and strains at various orientations in a single ply the following type of analysis is required. 

Consider the situation of a thin unidirectional lamina under a state of plane stress as shown in Fig. 3.9. The properties of the lamina are anisotropic so it will have modulus values of E and Ei in the fibre and transverse directions, respectively. The values of these parameters may be determined as illustrated above. 

The direct strains in the global X and Y directions will be given by (see Appendix C for details) 

The convention normally used is that direct stresses and strains have one suffix to indicate the direction of the stress or strain. Shear stresses and strains have two suffices. The first suffix indicates the direction of the normal to the plane on which the stress acts and the second suffix indicates the direction of the stress (or strain). Poisson s Ratio has two suffices. Thus, vi2 is the negative ratio of the strain in the 2-direction to the strain in the 1-direction for a stress applied in the 1-direction (V 2 = — il for an applied a ). v 2 is sometimes referred to as the major Poisson s Ratio and U2i is the minor Poisson s Ratio. In an isotropic material where V21 = i 2i. then the suffices are not needed and normally are not used. 

In the analysis of composites it is convenient to use matrix notation because this simplifies the computations very considerably. Thus we may write the above equations as (see Appendix E) 

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