Uniaxial lamination

It is interesting to observe that as well as the expected axial and transverse strains arising from the applied axial stress, we have also a shear strain. This is because in composites we can often get coupling between the different modes of deformation. This will also be seen later where coupling between axial and flexural deformations can occur in unsymmetric laminates. Fig. 3.17 illustrates why the shear strains arise in uniaxially stressed single ply in this Example. 

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. 

Angle-ply laminates have more complicated stiffness matrices than cross-ply laminates because nontrivial coordinate transformations are involved. However, the behavior of simple angle-ply laminates (only one angle, i.e., a) will be shown to be simpler than that of cross-ply laminates because no knee results in the load-deformation diagram under uniaxial loading. Other than the preceding two differences, analysis of angle-ply laminates is conceptually the same as that of cross-ply laminates. 

Figure 5-18 Simply Supported Laminated Rectangular Plate under Uniform Uniaxial In-Plane Compression...

Figure 5-26 Buckling Loads for Anfisymmefric Cross-Ply Laminated Plates under Uniform Uniaxial Compression (After Jones [5-19])...

In the [ 45]j tensile test (ASTM D 3518,1991) shown in Fig 3.22, a uniaxial tension is applied to a ( 45°) laminate symmetric about the mid-plane to measure the strains in the longitudinal and transverse directions, and Ey. This can be accomplished by instrumenting the specimen with longitudinal and transverse element strain gauges. Therefore, the shear stress-strain relationships can be calculated from the tabulated values of and Ey, corresponding to particular values of longitudinal load, (or stress relations derived from laminated plate theory (Petit, 1969 Rosen, 1972) ... 

The [10°] off axis tension specimen shown in Fig 3.23 is another simple specimen similar in geometry to that of the [ 45 ]s tensile test. This test uses a unidirectional laminate with fibers oriented at 10° to the loading direction and the biaxial stress state (i.e. longitudinal, transverse and in-plane shear stresses on the 10° plane) occurs when it is subjected to a uniaxial tension. When this specimen fails under tension, the in-plane shear stress, which is almost uniform through the thickness, is near its critical value and gives the shear strength of the unidirectional fiber composites based on a procedure (Chamis and Sinclair, 1977) similar to the [ 45°]s tensile test. 

Effect of laminate layup and stacking sequence on stress concentration and strength of boron fiber-epoxy matrix composites containing circular holes under uniaxial tension . 

Young s modulus versus orientation for uniaxially aligned Si3N4/ BN FM (adapted from ref. [1]). The line is the predicted behavior using the brick model and laminate theory. 

In the compaction stage, two or more different powder compositions are stacked by sequential filling of the die and uniaxially pressed in an automatic press. Packing of powders and grain size are effective parameters in controlling the composition and thus the properties. After compaction, the laminates are sintered to obtain a gradual structure. 

Figure 1. Specific ultimate tensile strength vs. specific stiffness of current and developmental aerospace structural materials. Data are displayed on a log-log plot in (a), where P signifies PAN-based reinforcements Gr represents graphite fibers 0 0 and 90 0 indicate data collected parallel to and transverse to the fiber direction in uniaxial composites, respectively and Q/I represents quasi-isotropic laminates. The (f represents fiber reinforcements in MMCs. The dashed line in (b) represents the combinations of specific strength and stiffness that are double those of conventional metal alloys.

During plane-slit extrusion the melt leaving the head outlet is rapidly cooled down on cold rollers or in a water bath. Predominantly crystalline polymers are processed by plane-slit extrusion to obtain highly transparent and even thickness films, laminated or combined film materials. Special-purpose devices are needed to attain a uniaxial or biaxial film tension. 

It is important to note that the uniaxial loading of an off-axis plate generates a local (inherent) multiaxial stress state. It is therefore worth mentioning the investigations by Kawai and coworkers for the description of the off-axis fatigue behavior of UD and woven reinforced laminates [61,71,72] and their fatigue damage mechanics model [61]. The model is based on the nondimensional effective stress concept, which is the square root of the Tsai—Hill polynomial. 

Fig. 1. Temperature dependence of critical property ratios for uniaxial composite laminates and annealed stainless steel (a) ratio of thermal conductivity to Young s modulus (b) ratio of thermal conductivity to tensile yield strength (c) ratio of Young s modulus to density (d) ratio of tensile yield strength to density.

The properties of the composite laminate are strongly dependent on the orientation sequence. Successive layers of uniaxial fibers are frequently oriented in appropriate directions so that the properties of low-pressure laminates will meet particular requirements. 

Experience suggests that uniaxially reinforced laminates loaded in the filament direction (e.g., composite straps) can successfully utilize conventional, unflexi-bilized resin systems. It seems plausible that crossply laminates would benefit from a matrix capable of sustaining some strain at 4 K without cracking, particularly laminates subjected to fatigue loads. But the present state of knowledge is inadequate. 

The strength and modulus of the reinforced material falls rapidly from those predicted by the law of mixtures for unidirectional laminates, as the angle between the fibre direction and the stress is increased from zero towards 90°. We assumed above that the fibres are all parallel to the applied uniaxial stress, but if they are lying normal to the stress, the equation below applies and gives a much lower value for the composite modulus ... 

The transverse contraction of these laminates is completely different under uniaxial applied strain. The 90° laminate contracts very Uttle (Vjj 0.02), whereas the contraction of the 45° laminate is very large (Vjj 0.773). This difference in the Poisson s ratio causes additional stresses in orthotropic laminates, where the constituent plies have different ply orientations. The contraction of an angle-ply laminate, for example with 90° plies, is hindered by the small Poisson s ratio of the 90° plies. This leads to transverse stresses in other plies. Near free edges and around unloaded holes, the transverse stresses are equilibrated by interlaminar stresses. For... 

Figure 5.2 Stress-strain curves for laminates with different ply angles under uniaxial loading (CFRP T300/914c) [8]...

Unless otherwise noted, all data presented for Prepreg HiPerCompT is for 8-ply laminates, with a balanced [0-90-90-0]s stacking of uniaxial plies, and nominally 22-25% by volume of Hi-Nicalon M fibers. Data for Slurry Cast HiPerComp is for 8-ply laminates made with 0-90,8 harness satin weave cloth and a nominal volume fraction of Hi-Nicalon fiber of 33-38%. Measurement of in-plane properties were generally done in one ofthe primary fiber directions. 

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