Non-symmetric laminates

The important point to note from this Example is that in a non-symmetrical laminate the behaviour is very complex. It can be seen that the effect of a simple uniaxial stress, or, is to produce strains and curvatures in all directions. This has relevance in a number of polymer processing situations because unbalanced cooling (for example) can result in layers which have different properties, across a moulding wall thickness. This is effectively a composite laminate structure which is likely to be non-symmetrical and complex behaviour can be expected when loading is applied. 

This is a non-symmetric laminate. The Q matrices are given in the text and the A, B and D matrices are determined from... 

The influence of the orientation of the laminae on the stiffness of the composite is illustrated in Figure 15.15b, where generic stress-strain curves for unidirectional cross-ply random laminates are shown. In the design of laminates it is necessary to define not only the orientation of the plies but also the stacking sequence, i.e., the order in which the plies are placed through the thickness. Figure 15.16 shows examples of symmetrical and non-symmetrical laminates. The most standard ply orientations are 0°,... 

Morye and Wool [82] used symmetric and non-symmetric stacking sequences with glass/flax hybrid composites and also varied the glass/flax fiber ratio, namely, 100/0, 80/20, 60/40, 40/60, and 0/10. For non-symmetric composites, flexural and impact tests were performed with the top face of the composite being either glass fibers or flax fibers. The mechanical properties of the composites were found to depend on the fiber layer arrangement in the composite, and the non-symmetrical laminates with flax at the loaded top face presented superior performance under flexure or impact. 

The previous section has illustrated a simple convenient means of analysing in-plane loading of symmetric laminates. Many laminates are of this type and so this approach is justified. However, there are also many situations where other types of loading (including bending) are applied to laminates which may be symmetric or non-symmetric. In order to deal with these situations it is necessary to adopt a more general type of analysis. 

State whether the following laminates are symmetric or non-symmetric. 

The difference in this case therefore is that we start to see some twisting of the laminate due to the non-symmetric nature of the lay-up. 

A first comparison of the three specimen types ([0°]24, [0°/90°]6s, and [0790°]i2) is shown in Fig. 4. The load-displacement values used in the analysis are plotted for all specimens tested in one laboratory (testing from the Mode-I pre-crack). Both cross-ply laminates show larger displacements for comparable delamination lengths, much more scatter and somewhat higher but comparable maximum load values compared with the unidirectional lay-up. There is no clear difference between the cross-ply laminate types, except that the symmetric lay-up yields the lowest load values and hence the largest scatter. In the data from the other laboratory, this is reversed, i.e., the non-symmetric lay-up showing the larger scatter. 

Tables 2-4 show that, for the unidirectional lay-up, averages of initiation and maximum propagation values do agree with each other and with the data presented in [4]. The R-curves are rather flat, with an increase between about 30 and 60 J/m (10-20%) over the total delamination length (Fig. 5). For the cross-ply laminates, however, this is not the case. The average initiation values for the symmetric lay-up differ by more than one standard deviation (values from [4] are not available) while for the non-symmetric lay-up, laboratory 1 and [4] agree within 15%, while laboratory 2 obtains larger average values. The averages of the maximum propagation do agree within one standard deviation and within about 20% are the same for both types of cross-ply laminates. These differences will be fiirther explored in the discussion.

According to the requirements specified in the ISO standard [1] deviation of the delamination propagation from mid-plane invalidates the test. In that sense, any data analysis of the cross-ply laminates, therefore, will yield invalid results. This point was discussed extensively in [4] where the authors also used the Finite-Element method to supplement their analysis and concluded that the corrected beam theory data reduction scheme seemed to remain applicable and that the non-symmetric cross-ply material yielded apparently valid fracture toughness data, even though these were probably affected by transverse cracking. 

Table 4.2 Number of symmetric, anti-symmetric and non-symmetric fully uncoupled laminates with seven through 21 plies...

Plates Type ill are defined as symmetrically laminated plates whose material properties are different in all directions with respect to the axis of the plate. This class of laminates includes plates in which bending-twisting coupling (non-zero D10 and D26 terms) exists. The general equation for plates Type ill under transverse loading is,... 

Stiffnesses for single-layered configurations are treated first to provide a baseline for subsequent discussion. Such stiffnesses should be recognizable in terms of concepts previously encountered by the reader in his study of plates and shells. Next, laminates that are symmetric about their middle surface are discussed and classified. Then, laminates with laminae that are antisymmetrically arranged about their middle surface are described. Finally, laminates with complete lack of middle-surface symmetry, i.e., unsymmetric laminates, are discussed. For all laminates, the question of laminae thicknesses arises. Regular laminates have equal-thickness laminae, and irregular laminates have non-equal-thickness laminae. 

For single-lap joints, all stresses as calculated above should be increased by 100% (Cm,1=2.0). For double lap joints and similar joints which may reasonably be assumed to be symmetrically loaded, only Or, as calculated above, should be increased by 20% (Cm,1=1.2). These increases are to allow for non-uniform stress distributions through the thickness of the laminate due to non-symmetry, bolt-bending and loss of lateral restraint. 

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