Laminates elastic properties

The repair laminate was assumed to be reinforced with a bidirectional carbon fibre woven fabric with equal number of tows by weight in the weft and warp direction. The matrix was assumed to be epoxy. The laminate properties used for the FEA simulation were calculated using mle-of-mixtures (Daniel and Ishai, 1995), assuming a fibre volume fraction of 40%. The laminate elastic properties are given in Table 11.2. To calculate the repair thickness, the composite allowable strain (sc) was limited to 0.3%, selected as a number in between the two extremes (0.25% and 0.40%) proposed by ASME PCC-2 and also equal to the allowable strain for a class 2 repair with a 10 year lifetime. 

Fig. 3.25 Variation of elastic properties for a (+/ — 45) symmetric laminate of carbon/epoxy...

It is also important to note that although the laminae [ 45] indicates that Ex = Ey =. GN/m, this laminate is not isotropic or even quasi-isotropic. As shown in Chapter 2, in an isotropic material, the shear modulus is linked to the other elastic properties by the following equation... 

J. C. Ekvall, Elastic Properties of Orthotropic Monofilament Laminates, ASME Paper 61-AV-56, Aviation Conference, Los Angeles, California, 12-16 March 1961. 

As mentioned previously, for certain types of products, precompression at a force level higher than that of main compression may increase tablet hardness. The author has found that for materials that primarily undergo brittle fracture, application of a precompression force higher than the main compression force can result in a higher tablet hardness. However, this is typically not the case for materials with elastic properties (e.g., products prone to capping and lamination) because these products require gradual application of force to minimize elastic recovery and allow stress relaxation. 

The accuracy of the model in the lifetime prediction was verified even in this case by comparison between model estimations and experimental fatigue lives. The parameters of the calibration fatigue curves together with the elastic properties of the laminates investigated are listed in Table 7.5. In some cases, elastic and static strength properties not available in the original sources were estimated from constituent properties or taken from literature. 

Sjogren A, Krasnikov Y, Varsna J. Determination of elastic properties of impact damage in carbon fibre/epoxy laminates. Composites Part A 2001 32(9) 353—60. 

To compare the laminated sample with the monolithic control, three-point bend tests were carried out as shown in Fig. 16.16. The elastic properties of both samples were similar, with a flex modulus of 450 GPa. The bend strengths were also comparable, with 500 MPa for the monolithic and 633 MPa for the laminated sample. However, the resistance to cracking of the samples was entirely different. When a notched sample of the monolithic material was bent, the load/displace-ment curve was typical of a brittle ceramic material, with sudden cracking failure after an initial elastic deformation (Fig. 16.16(a)). The fracture toughness of the sample was calculated to be 3.6 MPa with a low fracture energy of 62 J calculated from the area under the curve. 

Note the inverted terms Ajj yield the required elastic properties of the laminate in terms of the individual ply properties Ell, 12 and Gi2. 

Elastic properties of chopped strand mat laminates vary considerably, owing to basic scatter in the fibre and matrix properties. 

The following steps may be used to determine the elastic properties of a laminate. A more detailed description is given in the Eurocomp Handbook. 

The above steps for calculating laminate stiffness and equivalent elastic properties are summarised in the following flow chart. Figure 4.11. 

These stresses and equivalent elastic properties, calculated by classical lamination theory, can then be used in the following equations to calculate the strains in the shell ... 

The elastic properties of hand lay-up laminates incorporating fabrics/woven roving are susceptible to significant batch to batch variation attributable variations in material... 

Figure 5.19(c) of the EUROCOMP Design Code shows the shear stress distribution, sn. along the so-called shear-out plane. The actual stress field depends on a number of parameters such as elastic properties of the laminate and the fastener, clearance, friction and load magnitude, and loading direction (tensile or compressive). 

Two laminates were made by resin transfer moulding (RTM). Details are given in Tables 5.12 and 5.13. The elastic properties were again determined experimentally and are given in Tables 5.15 and 5.16. 

Table 5.15 Elastic properties, strength and failure criterion parameters for RTM laminate 1.

Calculated from ultimate strength and initial tangent modulus (conservative estimation) Table 5.16 Elastic properties, strength and failure criterion parameters for RTM laminate 2. ... 

Table 2 Theoretical values of elastic properties of laminates.

Well cemented shales, under structurally sound conditions, present few problems at dam sites, though their strength limitations and elastic properties may be factors of importance in the design of concrete dams of appreciable height. They, however, have lower moduli of elasticity and lower shear strength values than concrete and, therefore, are unsatisfactory foundation materials for arch dams. Moreover, if the lamination is horizontal and well developed, then the foundations may offer little shear resistance to the horizontal forces exerted by a dam. A structure keying the dam into such a foundation is then required. 

Abstract This chapter describes the elastic qualities of advanced fibre-reinforced composites, in terms of characterization, measurement and prediction from the basic constituents, i.e. the fibre and matrix. The elastic analysis comprises applying micromechanics approaches to predict the lamina elastic properties from the basic constituents, and using classical lamination theory to predict the elastic properties of composite materials composed of several laminae stacked at different orientations. Examples are given to illustrate the theoretical analysis and give a full apprehension of its prediction capability. The last section provides an overview on identification methods for elastic proprieties based on full-field measurements. It is shown that these methodologies are very convenient for elastic characterization of anisotropic and heterogeneous materials. 

This chapter is devoted to the analysis of the elastic properties and their characterization for laminated advanced composites. It starts with a general overview of composite stiffness and then moves to lamina analysis focused on unidirectional reinforced composites. The analysis of laminated composites is addressed through the classical lamination theory (CLT). The last section describes full-field techniques coupled with inverse identification methods that can be employed to measure the elastic constants. 

The elastic properties of a [0, 90] cross-ply laminate constructed using pre-impreg-nated tapes are given by... 

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