Shear ply

Fig. 6. Variation of Young s modulus (-) and shear modulus (—), with cord angle 9 for one-ply nylon—mbber system (88).

Inter-ply shear is prominently featured in cord—mbber composite laminates, and may relate to delamination-induced failures. Studies utilizing experimental, analytical, and finite element tools, with specific apphcation to tires, are significant in compliant cord—mbber composites (90—95). 

The strength of laminates is usually predicted from a combination of laminated plate theory and a failure criterion for the individual larnina. A general treatment of composite failure criteria is beyond the scope of the present discussion. Broadly, however, composite failure criteria are of two types noninteractive, such as maximum stress or maximum strain, in which the lamina is taken to fail when a critical value of stress or strain is reached parallel or transverse to the fibers in tension, compression, or shear or interactive, such as the Tsai-Hill or Tsai-Wu (1,7) type, in which failure is taken to be when some combination of stresses occurs. Generally, the ply materials do not have the same strengths in tension and compression, so that five-ply strengths must be deterrnined ... 

These values are determined by experiment. It is, however, by no means a trivial task to measure the lamina compressive and shear strengths (52,53). Also the failure of the first ply of a laminate does not necessarily coincide with the maximum load that the laminate can sustain. In many practical composite laminates first-ply failure may be accompanied by a very small reduction in the laminate stiffness. Local ply-level failures can reduce the stress-raising effects of notches and enhance fatigue performance (54). 

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. 

For cross-ply laminates, a knee in the load-deformation cun/e occurs after the mechanical and thermal interactions between layers uncouple because of failure (which might be only degradation, not necessarily fracture) of a lamina. The mechanical interactions are caused by Poisson effects and/or shear-extension coupling. The thermal interactions are caused by different coefficients of thermal expansion in different layers because of different angular orientations of the layers (even though the orthotropic materials in each lamina are the same). The interactions are disrupted if the layers in a laminate separate. 

Symmetric angle-ply laminates were described in Section 4.3.2 and found to be characterized by a full matrix of extensional stiffnesses as well as bending stiffnesses (but of course no bending-extension coupling stiffnesses because of middle-surface symmetry). The new facet of this type of laminate as opposed to specially orthotropic laminates is the appearance of the bend-twist coupling stiffnesses D. g and D2g (the shear-extension coupling stiffnesses A. g and A2g do not affect the transverse deflection w when the laminate is symmetric). The governing differential equation of equilibrium is... 

Experimental results are presented that show that high doses of electron radiation combined with thermal cycling can significantly change the mechanical and physical properties of graphite fiber-reinforced polymer-matrix composites. Polymeric materials examined have included 121 °C and 177°C cure epoxies, polyimide, amorphous thermoplastic, and semicrystalline thermoplastics. Composite panels fabricated and tested included four-ply unidirectional, four-ply [0,90, 90,0] and eight-ply quasi-isotropic [0/ 45/90]s. Test specimens with fiber orientations of [10] and [45] were cut from the unidirectional panels to determine shear properties. Mechanical and physical property tests were conducted at cold (-157°C), room (24°C) and elevated (121°C) temperatures. 

Mechanical Property Testing. Mechanical tests were performed on both unirradiated and irradiated materials at -157°C, 24°C, and 121°C. Specimens were kept dry prior to testing in an environmental chamber mounted in a tensile testing machine. Tensile test specimens of [0]4, [10]4, [45]4, and [90]4 laminates were cut from 4-ply composite panels. All specimens were straight-sided coupons. For tension and shear tests the length/width aspect ratio was 8. For the compression tests the aspect ratio was 0.25 and the unsupported length was 0.64 cm. The [0]4 laminates were used to measure the ultimate tension and compression strength, Xit the axial... 

Composite structures in service are often subjected to complex 3-D load paths. In general, a delamination will be subjected to a crack driving force with a mode I opening, a mode II forward shear and a mode III anti-plane shear, as illustrated in Fig 3.29. Because delamination is constrained to grow between individual plies, both interlaminar tension and shear stresses are commonly present at the... 

Jun, W.J, and Hong C.S. (1990). Effects of residual shear strain on the cured shape of asymmetric cross-ply thin laminates. Composites Sci. Technoi. 38, 55-67. 

Fig. 8.14. Normalized interlaminar (a) normal stress,

In particular, the techniques based on the termination of certain plies within the laminate has also shown promise. Static tensile tests of [30°/-30°/30°/90°]s carbon-epoxy laminates containing terminals of [90°] layers at the mid-plane show that premature delamination is completely suppressed with a remarkable 20% improvement in tensile strength, compared to those without a ply terminal. Cyclic fatigue on the same laminates confirms similar results in that the laminate without a ply terminal has delamination equivalent to about 40% of the laminate width after 2x10 cycles, whereas the laminates with a ply terminal exhibit no evidence of delamination even after 9x10 cycles. All these observations are in agreement with the substantially lower interlaminar normal and shear stresses for the latter laminates, as calculated from finite element analysis. A combination of the adhesive interleaf and the tapered layer end has also been explored by Llanos and Vizzini, (1992). 

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