Bending laminates

Key factors of SCC. The stress applied on a metal is nominally static or slowly increasing tensile stress. The stresses can be applied externally, but residual stresses often cause SCC failures. Internal stresses in a metal can be due to cold work or a heat treatment. In fact, all manufacturing processes create some internal stresses. Stresses introduced by cold work arise from processes such as lamination, bending, machining, rectification, drawing, drift, and riveting. Stresses introduced by thermal treatments are due to the dilation and contraction of metal or indirectly by the modification of the microstructure of the material. Welded steels contain residual stresses near the yield point. Corrosion products have been shown to be another source of stress and can cause a wedging action. 

Figure 5.10b shows ideal forming in a long-discontinuous fibre laminate (Lee et aL, 2008). As the flat laminate bends, the fibre ends move apart. This extension ability reduces wrinkling. New long-discontinuous fibre forms are available and since about 2001, these are called stretch-broken fibre or SBXF materials with the X replaced with a letter that represents a specific fibre. Carbon fibre material is called SBCF, for example. 

Fiber Cans and Tubes. The basic material used for fiber tubes and cans is a bending board. The body of a fiber can usually is of paperboard and the ends usually are of metal, paperboard, or plastic. The constmction of the body may be one of three general types sprial-wound tubes and cans, convolutely wound tubes and cans, or laminated or lap-seam cans. 

The previous section has considered the in-plane deformations of a single ply. In practice, real engineering components are likely to be subjected to this type of loading plus (or as an alternative) bending deformations. It is convenient at this stage to consider the flexural loading of a single ply because this will develop the method of solution for multi-ply laminates. 

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. 

Knowledge of the variation of stress and strain through the laminate thickness is essential to the definition of the extensional and bending stiffnesses of a laminate. The laminate is presumed to consist of per-... 

Derive the summation expressions for extensional, bending-extension coupling, and bending stiffnesses for laminates with constant properties in each orthotropic lamina that is, derive Equation (4.24) from Equations (4.20) and (4.21). 

Because of the analytical complications involving the stiffnesses Ai6, A26, D g, and D26, a laminate is sometimes desired that does not have these stiffnesses. Laminates can be made with orthotropic layers that have principal material directions aligned with the laminate axes. If the thicknesses, locations, and material properties of the laminae are symmetric about the middle surface of the laminate, there is no coupling between bending and extension. A general example is shown in Table 4-2. Note that the material property symmetry requires equal [Q j], of the two layers that are placed at the same distance above and below the middle surface. Thus, both the orthotropic material properties, [Qjjlk. of the layers and the angle of the principal material directions to the laminate axes (i.e., the orientation of each layer) must be identical. 

The aforementioned coupling that involves Aig, Ags, Dig, and D2g takes on a special form for symmetric angle-ply laminates. Those stiffnesses can be shown to be largest when N = 3 (the lowest N for which this class of laminates exists) and decrease in proportion to 1/N as N increases (see Section 4.4.4). Actually, in the expressions for the extensional and bending stiffnesses Aig and Dig,... 

Antisymmetry of a laminate requires (1) symmetry about the middle surface of geometry (i.e., consider a pair of equal-thickness laminae, one some distance above the middle surface and the other the same distance below the middle surface), but (2i some kind of a reversal or mirror image of the material properties [Qjjlk- In fact, the orthotropic material properties [Qjj], are symmetric, but the orientations of the laminae principal material directions are not symmetric about the middle surface. Those orientations are reversed from 0° to 90° (or vice versa) or from + a to - a (a mirror image about the laminate x-axis). Because the [Qjj]k are not symmetric, bending-extension coupling exists. 

Because o< the existance of bending-extension coupling, the terminology generally orthotropic and specially orthotropic have meaning only with reference to an individual layer and not to a laminate. 

The bending-extension coupling stiffnesses, Bjj, vary for different classes of antisymmetric laminates of generally orthotropic laminae, and, in fact, no general representation exists other than in the following force and moment resultants ... 

An antisymmetric cross-ply laminate consists of an even number of orthotropic laminae laid on each other with principal material directions alternating at 0° and 90° to the laminate axes as in the simple example of Figure 4-19. A more complicated example is given in Table 4-4 (where the adjacent layers do not always have the sequence 0°, then 90°, then 0°, etc.). Such laminates do not have A g, Agg, D g, and Dgg, but do have bending-extension coupling. We will show later that the coupling is such that the force and moment resultants are... 

A regular antisymmetric cross-ply laminate is delined to have laminae all of equal thickness and is common because of simplicity of fabrication. As the number of layers increases, the bending-extension coupling stiffness B.,., can be shown to approach zero. 

The bending-extension coupling stiffnesses B g and Bgg can be shown to go to zero as the number of layers in the laminate increases for a fixed laminate thickness. 

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