Deformation Behaviour of Laminates

The previous analysis has shown that the properties of unidirectional fibre composites are highly anisotropic. To alleviate this problem, it is common to build up laminates consisting of stacks of unidirectional lamina arranged at different orientations. Clearly many permutations are possible in terms of the numbers of layers (or plies) and the relative orientation of the fibres in each 

In general it is best to aim for synunetry about the centre plane. A laminate in which the layers above the centre plane are a mirror image of those below it is described as symmetric. Thus a four stack laminate with fibres oriented at 0°, 90°, 90° and 0° is symmetric. The convention is to denote this as [0°/90°/90°/0°]t or [0°, 90j, 0°]t or [0°/90°]s. In general terms any laminate of the type [6, —0, —6, 6 i is symmetric and there may of course be any even number of layers or plies. They do not all have to be the same thickness but symmetry must be maintained. In the case of a symmetric laminate where the central ply is not repeated, this can be denoted by the use of an overbar. Thus the laminate [45/ — 45/0/90/0/ — 45/45]t can be written as [ 45, 0, 90]s. 

The in-plane stiffness behaviour of symmetric laminates may be analysed as follows. The plies in a laminate are all securely bonded together so that when the laminate is subjected to a force in the plane of the laminate, all the plies deform by the same amount. Hence, the strain is the same in every ply but because the modulus of each ply is different, the stresses are not the same. This is illustrated in Fig. 3.19. 

When external forces arc applied in the global x-y direction, they will equate to the summation of all the forces in the individual plies. Thus, for unit width 

As the strains are independent of Z they can be taken outside the integral  

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With respect to the laminates as a structural material, regardless of the type of reinforcement, there are known some behaviour characteristics during the mechanical loading of laminates. Composites with woven reinforcement demonstrate (Dauda et al. 2009) a linear relationship between stress and deformation. Whereas the reinforcement of laminates in the form braided reinforcement show a non-linear dependence is determined by an angle of orientation of the fibre bundles with respect to the axis of symmetry. The increase in flexural strength and modulus values affects the volume fraction of fibres in the composite volume, and the surface density of the strengthening. 

The impact and fracture behaviour of composites is complex. Thermosets do not undergo plastic deformation, composites are not necessarily described by linear elastic fracture mechanics (LEFM) and it is very difficult, if not impossible at the present time, to predict the initiation and progression of failure in complicated structures from the behaviour of unidirectional materials. Because of the latter much of the work on fracture has involved studies of plied or laminated specimens. 

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