Lamina strength shear

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). 

A key element in the experimental determination of the stiffness and strength characteristics of a lamina is the imposition of a uniform stress state in the specimen. Such loading is relatively easy for isotropic materials. However, for composite materials, the orthotropy introduces coupling between normal stresses and shear strains and between shear stresses and normal and shear strains when loaded in non-principal material coordinates for which the stress-strain relations are given in Equation (2.88). Thus, special care must be taken to ensure obtaining... 

Another test used to determine the shear modulus and shear strength of a composite material is the sandwich cross-beam test due to Shockey and described by Waddoups [2-17]. The composite lamina... 

In-Plane Shear Properties. The basic lamina in-plane shear stiffness and strength is characterized using a unidirectional hoop-wound (90°) 0.1 -m nominal internal diameter tube that is loaded in torsion. The test method has been standardized under the ASTM D5448 test method for in-plane shear properties of unidirectional fiber-resin composite cylinders. D5448 provides the specimen and hardware geometry necessary to conduct the test. The lamina in-plane shear curve is typically very nonlinear [51]. The test yields the lamina s in-plane shear strength, t12, in-plane shear strain at failure, y12, and in-plane chord shear modulus, G12. 

Therefore, moisture absorption has a larger effect on the transverse properties of a typical composite system. Despite this, the strength of a 0° composite is also affected by moisture ingress since the reloading of a broken fibre occurs through shear stress transfer Ifom the interphasal matrix. To achieve isotropy, unidirectional plies are stacked at a set of angles such as 0°, 45° and 90° to form a laminate. In this situation, moisture ingress will modify the residual stress state in the individual laminae. 

Transverse compressive strength of the lamina Shear strength of the lamina Tensile strength of fibres TensUe/compressive strength of matrix Shear strength of matrix... 

Cohesive failure of the adherend takes place when the adherend fails due to loads in excess of the adherend strength. In laminate structures the failure typically initiates from the matrix between the laminae as a result of out-of-plane loads or interlaminar shear loads. Other types of failure initiation are also possible, especially for FRP composites that do not have a layered structure. 

The Tsai-Wu failure criterion requires prior knowledge of the lamina longitudinal tension and compression strengths, the transverse tension and compression strengths and the shear strength in the 1-2 (longitudinaltranverse) plane of the lamina. 

A 5-harness satin (5-HS) weave will have its warp yarns running over four weft yarns and under one weft yarn as shown in Fig. 9.5. Other n-HS weaves used in composite materials include 8-HS, where the warp yarn passes over seven weft yarns and under one, and 12-HS where the warp yarn passes over eleven weft yarns and under one. It can easily be understood that the more yarn passes over the other yarn, the straighter and less crimped will be the yarns present in the fabric. The straighter the segments, the more the fabric composite behaves as a lamina in a laminated composite, increasing the inplane properties at the expense of out-of-plane properties and interlaminar shear strength - and of course vice versa. 

In the case of areal electrodes, as shown in Figures 5.2(a) and (c), the out-of-plane shear modes suggest, for the small characteristic ratio of thickness to the other extents of the laminae, the assumption of unidirectional electric field strength in polarization/through-thickness direction, compare with Figure 4.8(b). When only planar stress in the plane transverse to the polarization direction is regarded, then the constitutive relation an nvay reduces to Eq. (4.28). 

The fiber-bundle pull-out method [19] is similar to the single-fiber pull-out method except that instead of using a single fiber, a bundle of fibers is used. A coupon is fabricated in which a bundle of fibers or a lamina of unidirectional fibers is cast in a block of matrix. Transverse notches are cut into the coupon near the end of the fiber bundle. The coupon is loaded in tension with the load applied parallel to the fiber axes. The load versus displacement curve can be monitored and the debonding point detected. In a similar manner to the way data are reduced for the single-fiber pull-out test, the interfacial shear strength between the bundle of fibers and matrix can be calculated. 

Xi = Tensile strength in direction of fibers X[ = Compressive strength in direction of fibers Yt = Tensile strength transverse to direction of fibers Yt = Compressive strength transverse to direction of fibers S = Shear strength in plane of lamina... 

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